| 1 |  |  | # -*- coding: utf-8 -*- | 
            
                                                                                                            
                            
            
                                    
            
            
                | 2 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 3 |  |  | """Creating sets, variables, constraints and parts of the objective function | 
            
                                                                                                            
                            
            
                                    
            
            
                | 4 |  |  | for Flow objects with nonconvex but without investment options. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 5 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 6 |  |  | SPDX-FileCopyrightText: Uwe Krien <[email protected]> | 
            
                                                                                                            
                            
            
                                    
            
            
                | 7 |  |  | SPDX-FileCopyrightText: Simon Hilpert | 
            
                                                                                                            
                            
            
                                    
            
            
                | 8 |  |  | SPDX-FileCopyrightText: Cord Kaldemeyer | 
            
                                                                                                            
                            
            
                                    
            
            
                | 9 |  |  | SPDX-FileCopyrightText: Patrik Schönfeldt | 
            
                                                                                                            
                            
            
                                    
            
            
                | 10 |  |  | SPDX-FileCopyrightText: Birgit Schachler | 
            
                                                                                                            
                            
            
                                    
            
            
                | 11 |  |  | SPDX-FileCopyrightText: jnnr | 
            
                                                                                                            
                            
            
                                    
            
            
                | 12 |  |  | SPDX-FileCopyrightText: jmloenneberga | 
            
                                                                                                            
                            
            
                                    
            
            
                | 13 |  |  | SPDX-FileCopyrightText: Johannes Kochems | 
            
                                                                                                            
                            
            
                                    
            
            
                | 14 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 15 |  |  | SPDX-License-Identifier: MIT | 
            
                                                                                                            
                            
            
                                    
            
            
                | 16 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 17 |  |  | """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 18 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 19 |  |  | from pyomo.core import Binary | 
            
                                                                                                            
                            
            
                                    
            
            
                | 20 |  |  | from pyomo.core import BuildAction | 
            
                                                                                                            
                            
            
                                    
            
            
                | 21 |  |  | from pyomo.core import Constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 22 |  |  | from pyomo.core import Expression | 
            
                                                                                                            
                            
            
                                    
            
            
                | 23 |  |  | from pyomo.core import NonNegativeReals | 
            
                                                                                                            
                            
            
                                    
            
            
                | 24 |  |  | from pyomo.core import Set | 
            
                                                                                                            
                            
            
                                    
            
            
                | 25 |  |  | from pyomo.core import Var | 
            
                                                                                                            
                            
            
                                    
            
            
                | 26 |  |  | from pyomo.core.base.block import ScalarBlock | 
            
                                                                                                            
                            
            
                                    
            
            
                | 27 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 28 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 29 |  |  | class NonConvexFlowBlock(ScalarBlock): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 30 |  |  |     r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 31 |  |  |     .. automethod:: _create_constraints | 
            
                                                                                                            
                            
            
                                    
            
            
                | 32 |  |  |     .. automethod:: _create_variables | 
            
                                                                                                            
                            
            
                                    
            
            
                | 33 |  |  |     .. automethod:: _create_sets | 
            
                                                                                                            
                            
            
                                    
            
            
                | 34 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 35 |  |  |     .. automethod:: _objective_expression | 
            
                                                                                                            
                            
            
                                    
            
            
                | 36 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 37 |  |  |     Parameters are defined in :class:`Flow`. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 38 |  |  |     """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 39 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 40 |  |  |     def __init__(self, *args, **kwargs): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 41 |  |  |         super().__init__(*args, **kwargs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 42 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 43 |  |  |     def _create(self, group=None): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 44 |  |  |         """Creates set, variables, constraints for all flow object with | 
            
                                                                                                            
                            
            
                                    
            
            
                | 45 |  |  |         an attribute flow of type class:`.NonConvexFlowBlock`. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 46 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 47 |  |  |         Parameters | 
            
                                                                                                            
                            
            
                                    
            
            
                | 48 |  |  |         ---------- | 
            
                                                                                                            
                            
            
                                    
            
            
                | 49 |  |  |         group : list | 
            
                                                                                                            
                            
            
                                    
            
            
                | 50 |  |  |             List of oemof.solph.NonConvexFlowBlock objects for which | 
            
                                                                                                            
                            
            
                                    
            
            
                | 51 |  |  |             the constraints are build. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 52 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 53 |  |  |         if group is None: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 54 |  |  |             return None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 55 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 56 |  |  |         self._create_sets(group) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 57 |  |  |         self._create_variables() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 58 |  |  |         self._create_constraints() | 
            
                                                                                                            
                                                                
            
                                    
            
            
                | 59 |  |  |  | 
            
                                                                        
                            
            
                                    
            
            
                | 60 |  |  |     def _create_sets(self, group): | 
            
                                                                        
                            
            
                                    
            
            
                | 61 |  |  |         r""" | 
            
                                                                        
                            
            
                                    
            
            
                | 62 |  |  |         **The following sets are created:** (-> see basic sets at | 
            
                                                                        
                            
            
                                    
            
            
                | 63 |  |  |         :class:`.Model` ) | 
            
                                                                        
                            
            
                                    
            
            
                | 64 |  |  |  | 
            
                                                                        
                            
            
                                    
            
            
                | 65 |  |  |         NONCONVEX_FLOWS | 
            
                                                                        
                            
            
                                    
            
            
                | 66 |  |  |             A set of flows with the attribute `nonconvex` of type | 
            
                                                                        
                            
            
                                    
            
            
                | 67 |  |  |             :class:`.options.NonConvex`. | 
            
                                                                        
                            
            
                                    
            
            
                | 68 |  |  |  | 
            
                                                                        
                            
            
                                    
            
            
                | 69 |  |  |  | 
            
                                                                        
                            
            
                                    
            
            
                | 70 |  |  |         .. automethod:: _sets_for_non_convex_flows | 
            
                                                                        
                            
            
                                    
            
            
                | 71 |  |  |         """ | 
            
                                                                        
                            
            
                                    
            
            
                | 72 |  |  |         self.NONCONVEX_FLOWS = Set(initialize=[(g[0], g[1]) for g in group]) | 
            
                                                                        
                            
            
                                    
            
            
                | 73 |  |  |  | 
            
                                                                        
                            
            
                                    
            
            
                | 74 |  |  |         self._sets_for_non_convex_flows(group) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 75 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 76 |  |  |     def _create_variables(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 77 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 78 |  |  |         :math:`Y_{status}` (binary) `om.NonConvexFlowBlock.status`: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 79 |  |  |             Variable indicating if flow is >= 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 80 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 81 |  |  |         :math:`P_{max,status}` Status_nominal (continuous) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 82 |  |  |             Variable indicating if flow is >= 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 83 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 84 |  |  |         .. automethod:: _variables_for_non_convex_flows | 
            
                                                                                                            
                            
            
                                    
            
            
                | 85 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 86 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 87 |  |  |         self.status = Var(self.NONCONVEX_FLOWS, m.TIMESTEPS, within=Binary) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 88 |  |  |         for o, i in self.NONCONVEX_FLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 89 |  |  |             if m.flows[o, i].nonconvex.initial_status is not None: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 90 |  |  |                 for t in range( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 91 |  |  |                     0, m.flows[o, i].nonconvex.first_flexible_timestep | 
            
                                                                                                            
                            
            
                                    
            
            
                | 92 |  |  |                 ): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 93 |  |  |                     self.status[o, i, t] = m.flows[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 94 |  |  |                         o, i | 
            
                                                                                                            
                            
            
                                    
            
            
                | 95 |  |  |                     ].nonconvex.initial_status | 
            
                                                                                                            
                            
            
                                    
            
            
                | 96 |  |  |                     self.status[o, i, t].fix() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 97 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 98 |  |  |         # `status_nominal` is a parameter which represents the | 
            
                                                                                                            
                            
            
                                    
            
            
                | 99 |  |  |         # multiplication of a binary variable (`status`) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 100 |  |  |         # and a continuous variable (`invest` or `nominal_value`) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 101 |  |  |         self.status_nominal = Var( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 102 |  |  |             self.NONCONVEX_FLOWS, m.TIMESTEPS, within=NonNegativeReals | 
            
                                                                                                            
                            
            
                                    
            
            
                | 103 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 104 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 105 |  |  |         self._variables_for_non_convex_flows() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 106 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 107 |  |  |     def _create_constraints(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 108 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 109 |  |  |         The following constraints are created: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 110 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 111 |  |  |         .. automethod:: _status_nominal_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 112 |  |  |         .. automethod:: _minimum_flow_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 113 |  |  |         .. automethod:: _maximum_flow_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 114 |  |  |         .. automethod:: _shared_constraints_for_non_convex_flows | 
            
                                                                                                            
                            
            
                                    
            
            
                | 115 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 116 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 117 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 118 |  |  |         self.status_nominal_constraint = self._status_nominal_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 119 |  |  |         self.min = self._minimum_flow_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 120 |  |  |         self.max = self._maximum_flow_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 121 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 122 |  |  |         self._shared_constraints_for_non_convex_flows() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 123 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 124 |  |  |     def _objective_expression(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 125 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 126 |  |  |         The following terms are to the cost function: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 127 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 128 |  |  |         .. automethod:: _startup_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 129 |  |  |         .. automethod:: _shutdown_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 130 |  |  |         .. automethod:: _activity_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 131 |  |  |         .. automethod:: _inactivity_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 132 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 133 |  |  |         if not hasattr(self, "NONCONVEX_FLOWS"): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 134 |  |  |             return 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 135 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 136 |  |  |         startup_costs = self._startup_costs() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 137 |  |  |         shutdown_costs = self._shutdown_costs() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 138 |  |  |         activity_costs = self._activity_costs() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 139 |  |  |         inactivity_costs = self._inactivity_costs() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 140 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 141 |  |  |         self.activity_costs = Expression(expr=activity_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 142 |  |  |         self.inactivity_costs = Expression(expr=inactivity_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 143 |  |  |         self.startup_costs = Expression(expr=startup_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 144 |  |  |         self.shutdown_costs = Expression(expr=shutdown_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 145 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 146 |  |  |         self.costs = Expression( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 147 |  |  |             expr=( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 148 |  |  |                 startup_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 149 |  |  |                 + shutdown_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 150 |  |  |                 + activity_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 151 |  |  |                 + inactivity_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 152 |  |  |             ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 153 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 154 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 155 |  |  |         return self.costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 156 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 157 |  |  |     def _sets_for_non_convex_flows(self, group): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 158 |  |  |         r"""Creates all sets for non-convex flows. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 159 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 160 |  |  |         MIN_FLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 161 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute `min` | 
            
                                                                                                            
                            
            
                                    
            
            
                | 162 |  |  |             being not None in the first timestep. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 163 |  |  |         ACTIVITYCOSTFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 164 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 165 |  |  |             `activity_costs` being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 166 |  |  |         INACTIVITYCOSTFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 167 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 168 |  |  |             `inactivity_costs` being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 169 |  |  |         STARTUPFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 170 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 171 |  |  |             `maximum_startups` or `startup_costs` | 
            
                                                                                                            
                            
            
                                    
            
            
                | 172 |  |  |             being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 173 |  |  |         MAXSTARTUPFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 174 |  |  |             A subset of set STARTUPFLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 175 |  |  |             `maximum_startups` being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 176 |  |  |         SHUTDOWNFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 177 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 178 |  |  |             `maximum_shutdowns` or `shutdown_costs` | 
            
                                                                                                            
                            
            
                                    
            
            
                | 179 |  |  |             being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 180 |  |  |         MAXSHUTDOWNFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 181 |  |  |             A subset of set SHUTDOWNFLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 182 |  |  |             `maximum_shutdowns` being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 183 |  |  |         MINUPTIMEFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 184 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 185 |  |  |             `minimum_uptime` being > 0. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 186 |  |  |         MINDOWNTIMEFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 187 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 188 |  |  |             `minimum_downtime` being > 0. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 189 |  |  |         POSITIVE_GRADIENT_FLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 190 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 191 |  |  |             `positive_gradient` being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 192 |  |  |         NEGATIVE_GRADIENT_FLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 193 |  |  |             A subset of set NONCONVEX_FLOWS with the attribute | 
            
                                                                                                            
                            
            
                                    
            
            
                | 194 |  |  |             `negative_gradient` being not None. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 195 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 196 |  |  |         self.MIN_FLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 197 |  |  |             initialize=[(g[0], g[1]) for g in group if g[2].min[0] is not None] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 198 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 199 |  |  |         self.STARTUPFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 200 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 201 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 202 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 203 |  |  |                 if g[2].nonconvex.startup_costs[0] is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 204 |  |  |                 or g[2].nonconvex.maximum_startups is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 205 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 206 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 207 |  |  |         self.MAXSTARTUPFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 208 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 209 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 210 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 211 |  |  |                 if g[2].nonconvex.maximum_startups is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 212 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 213 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 214 |  |  |         self.SHUTDOWNFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 215 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 216 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 217 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 218 |  |  |                 if g[2].nonconvex.shutdown_costs[0] is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 219 |  |  |                 or g[2].nonconvex.maximum_shutdowns is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 220 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 221 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 222 |  |  |         self.MAXSHUTDOWNFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 223 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 224 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 225 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 226 |  |  |                 if g[2].nonconvex.maximum_shutdowns is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 227 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 228 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 229 |  |  |         self.MINUPTIMEFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 230 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 231 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 232 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 233 |  |  |                 if g[2].nonconvex.minimum_uptime.max() > 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 234 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 235 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 236 |  |  |         self.MINDOWNTIMEFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 237 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 238 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 239 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 240 |  |  |                 if g[2].nonconvex.minimum_downtime.max() > 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 241 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 242 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 243 |  |  |         self.NEGATIVE_GRADIENT_FLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 244 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 245 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 246 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 247 |  |  |                 if g[2].nonconvex.negative_gradient_limit[0] is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 248 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 249 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 250 |  |  |         self.POSITIVE_GRADIENT_FLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 251 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 252 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 253 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 254 |  |  |                 if g[2].nonconvex.positive_gradient_limit[0] is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 255 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 256 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 257 |  |  |         self.ACTIVITYCOSTFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 258 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 259 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 260 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 261 |  |  |                 if g[2].nonconvex.activity_costs[0] is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 262 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 263 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 264 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 265 |  |  |         self.INACTIVITYCOSTFLOWS = Set( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 266 |  |  |             initialize=[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 267 |  |  |                 (g[0], g[1]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 268 |  |  |                 for g in group | 
            
                                                                                                            
                            
            
                                    
            
            
                | 269 |  |  |                 if g[2].nonconvex.inactivity_costs[0] is not None | 
            
                                                                                                            
                            
            
                                    
            
            
                | 270 |  |  |             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 271 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 272 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 273 |  |  |     def _variables_for_non_convex_flows(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 274 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 275 |  |  |         :math:`Y_{startup}` (binary) `NonConvexFlowBlock.startup`: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 276 |  |  |             Variable indicating startup of flow (component) indexed by | 
            
                                                                                                            
                            
            
                                    
            
            
                | 277 |  |  |             STARTUPFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 278 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 279 |  |  |         :math:`Y_{shutdown}` (binary) `NonConvexFlowBlock.shutdown`: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 280 |  |  |             Variable indicating shutdown of flow (component) indexed by | 
            
                                                                                                            
                            
            
                                    
            
            
                | 281 |  |  |             SHUTDOWNFLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 282 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 283 |  |  |         :math:`\dot{P}_{up}` (continuous) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 284 |  |  |             `NonConvexFlowBlock.positive_gradient`: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 285 |  |  |             Variable indicating the positive gradient, i.e. the load increase | 
            
                                                                                                            
                            
            
                                    
            
            
                | 286 |  |  |             between two consecutive timesteps, indexed by | 
            
                                                                                                            
                            
            
                                    
            
            
                | 287 |  |  |             POSITIVE_GRADIENT_FLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 288 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 289 |  |  |         :math:`\dot{P}_{down}` (continuous) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 290 |  |  |             `NonConvexFlowBlock.negative_gradient`: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 291 |  |  |             Variable indicating the negative gradient, i.e. the load decrease | 
            
                                                                                                            
                            
            
                                    
            
            
                | 292 |  |  |             between two consecutive timesteps, indexed by | 
            
                                                                                                            
                            
            
                                    
            
            
                | 293 |  |  |             NEGATIVE_GRADIENT_FLOWS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 294 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 295 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 296 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 297 |  |  |         if self.STARTUPFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 298 |  |  |             self.startup = Var(self.STARTUPFLOWS, m.TIMESTEPS, within=Binary) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 299 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 300 |  |  |         if self.SHUTDOWNFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 301 |  |  |             self.shutdown = Var(self.SHUTDOWNFLOWS, m.TIMESTEPS, within=Binary) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 302 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 303 |  |  |         if self.POSITIVE_GRADIENT_FLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 304 |  |  |             self.positive_gradient = Var( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 305 |  |  |                 self.POSITIVE_GRADIENT_FLOWS, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 306 |  |  |                 m.TIMESTEPS, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 307 |  |  |                 within=NonNegativeReals, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 308 |  |  |             ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 309 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 310 |  |  |         if self.NEGATIVE_GRADIENT_FLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 311 |  |  |             self.negative_gradient = Var( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 312 |  |  |                 self.NEGATIVE_GRADIENT_FLOWS, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 313 |  |  |                 m.TIMESTEPS, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 314 |  |  |                 within=NonNegativeReals, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 315 |  |  |             ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 316 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 317 |  |  |     def _startup_costs(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 318 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 319 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 320 |  |  |             \sum_{i, o \in STARTUPFLOWS} \sum_t  Y_{startup}(t) \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 321 |  |  |             \cdot c_{startup} | 
            
                                                                                                            
                            
            
                                    
            
            
                | 322 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 323 |  |  |         startup_costs = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 324 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 325 |  |  |         if self.STARTUPFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 326 |  |  |             m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 327 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 328 |  |  |             for i, o in self.STARTUPFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 329 |  |  |                 if m.flows[i, o].nonconvex.startup_costs[0] is not None: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 330 |  |  |                     startup_costs += sum( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 331 |  |  |                         self.startup[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 332 |  |  |                         * m.flows[i, o].nonconvex.startup_costs[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 333 |  |  |                         for t in m.TIMESTEPS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 334 |  |  |                     ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 335 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 336 |  |  |             self.startup_costs = Expression(expr=startup_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 337 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 338 |  |  |         return startup_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 339 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 340 |  |  |     def _shutdown_costs(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 341 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 342 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 343 |  |  |             \sum_{SHUTDOWNFLOWS} \sum_t Y_{shutdown}(t) \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 344 |  |  |             \cdot c_{shutdown} | 
            
                                                                                                            
                            
            
                                    
            
            
                | 345 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 346 |  |  |         shutdown_costs = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 347 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 348 |  |  |         if self.SHUTDOWNFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 349 |  |  |             m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 350 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 351 |  |  |             for i, o in self.SHUTDOWNFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 352 |  |  |                 if m.flows[i, o].nonconvex.shutdown_costs[0] is not None: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 353 |  |  |                     shutdown_costs += sum( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 354 |  |  |                         self.shutdown[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 355 |  |  |                         * m.flows[i, o].nonconvex.shutdown_costs[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 356 |  |  |                         for t in m.TIMESTEPS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 357 |  |  |                     ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 358 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 359 |  |  |             self.shutdown_costs = Expression(expr=shutdown_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 360 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 361 |  |  |         return shutdown_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 362 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 363 |  |  |     def _activity_costs(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 364 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 365 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 366 |  |  |             \sum_{ACTIVITYCOSTFLOWS} \sum_t Y_{status}(t) \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 367 |  |  |             \cdot c_{activity} | 
            
                                                                                                            
                            
            
                                    
            
            
                | 368 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 369 |  |  |         activity_costs = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 370 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 371 |  |  |         if self.ACTIVITYCOSTFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 372 |  |  |             m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 373 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 374 |  |  |             for i, o in self.ACTIVITYCOSTFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 375 |  |  |                 if m.flows[i, o].nonconvex.activity_costs[0] is not None: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 376 |  |  |                     activity_costs += sum( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 377 |  |  |                         self.status[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 378 |  |  |                         * m.flows[i, o].nonconvex.activity_costs[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 379 |  |  |                         for t in m.TIMESTEPS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 380 |  |  |                     ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 381 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 382 |  |  |             self.activity_costs = Expression(expr=activity_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 383 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 384 |  |  |         return activity_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 385 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 386 |  |  |     def _inactivity_costs(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 387 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 388 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 389 |  |  |             \sum_{INACTIVITYCOSTFLOWS} \sum_t (1 - Y_{status}(t)) \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 390 |  |  |             \cdot c_{inactivity} | 
            
                                                                                                            
                            
            
                                    
            
            
                | 391 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 392 |  |  |         inactivity_costs = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 393 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 394 |  |  |         if self.INACTIVITYCOSTFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 395 |  |  |             m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 396 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 397 |  |  |             for i, o in self.INACTIVITYCOSTFLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 398 |  |  |                 if m.flows[i, o].nonconvex.inactivity_costs[0] is not None: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 399 |  |  |                     inactivity_costs += sum( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 400 |  |  |                         (1 - self.status[i, o, t]) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 401 |  |  |                         * m.flows[i, o].nonconvex.inactivity_costs[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 402 |  |  |                         for t in m.TIMESTEPS | 
            
                                                                                                            
                            
            
                                    
            
            
                | 403 |  |  |                     ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 404 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 405 |  |  |             self.inactivity_costs = Expression(expr=inactivity_costs) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 406 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 407 |  |  |         return inactivity_costs | 
            
                                                                                                            
                            
            
                                    
            
            
                | 408 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 409 |  |  |     def _min_downtime_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 410 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 411 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 412 |  |  |             (Y_{status}(t-1) - Y_{status}(t)) \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 413 |  |  |             \cdot t_{down,minimum} \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 414 |  |  |             \leq t_{down,minimum} \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 415 |  |  |             - \sum_{n=0}^{t_{down,minimum}-1} Y_{status}(t+n) \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 416 |  |  |             \forall t \in \textrm{TIMESTEPS} | \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 417 |  |  |             t \neq \{0..t_{down,minimum}\} \cup \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 418 |  |  |             \{t\_max-t_{down,minimum}..t\_max\} , \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 419 |  |  |             \forall (i,o) \in \textrm{MINDOWNTIMEFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 420 |  |  |             \\ \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 421 |  |  |             Y_{status}(t) = Y_{status,0} \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 422 |  |  |             \forall t \in \textrm{TIMESTEPS} | \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 423 |  |  |             t = \{0..t_{down,minimum}\} \cup \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 424 |  |  |             \{t\_max-t_{down,minimum}..t\_max\} , \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 425 |  |  |             \forall (i,o) \in \textrm{MINDOWNTIMEFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 426 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 427 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 428 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 429 |  |  |         def min_downtime_rule(_, i, o, t): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 430 |  |  |             """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 431 |  |  |             Rule definition for min-downtime constraints of non-convex flows. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 432 |  |  |             """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 433 |  |  |             if ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 434 |  |  |                 m.flows[i, o].nonconvex.first_flexible_timestep | 
            
                                                                                                            
                            
            
                                    
            
            
                | 435 |  |  |                 < t | 
            
                                                                                                            
                            
            
                                    
            
            
                | 436 |  |  |                 < m.TIMESTEPS.at(-1) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 437 |  |  |             ): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 438 |  |  |                 # We have a 2D matrix of constraints, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 439 |  |  |                 # so testing is easier then just calling the rule for valid t. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 440 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 441 |  |  |                 expr = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 442 |  |  |                 expr += ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 443 |  |  |                     self.status[i, o, t - 1] - self.status[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 444 |  |  |                 ) * m.flows[i, o].nonconvex.minimum_downtime[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 445 |  |  |                 expr += -m.flows[i, o].nonconvex.minimum_downtime[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 446 |  |  |                 expr += sum( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 447 |  |  |                     self.status[i, o, d] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 448 |  |  |                     for d in range( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 449 |  |  |                         t, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 450 |  |  |                         min( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 451 |  |  |                             t + m.flows[i, o].nonconvex.minimum_downtime[t], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 452 |  |  |                             len(m.TIMESTEPS), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 453 |  |  |                         ), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 454 |  |  |                     ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 455 |  |  |                 ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 456 |  |  |                 return expr <= 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 457 |  |  |             else: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 458 |  |  |                 return Constraint.Skip | 
            
                                                                                                            
                            
            
                                    
            
            
                | 459 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 460 |  |  |         return Constraint( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 461 |  |  |             self.MINDOWNTIMEFLOWS, m.TIMESTEPS, rule=min_downtime_rule | 
            
                                                                                                            
                            
            
                                    
            
            
                | 462 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 463 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 464 |  |  |     def _min_uptime_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 465 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 466 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 467 |  |  |             (Y_{status}(t)-Y_{status}(t-1)) \cdot t_{up,minimum} \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 468 |  |  |             \leq \sum_{n=0}^{t_{up,minimum}-1} Y_{status}(t+n) \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 469 |  |  |             \forall t \in \textrm{TIMESTEPS} | \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 470 |  |  |             t \neq \{0..t_{up,minimum}\} \cup \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 471 |  |  |             \{t\_max-t_{up,minimum}..t\_max\} , \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 472 |  |  |             \forall (i,o) \in \textrm{MINUPTIMEFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 473 |  |  |             \\ \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 474 |  |  |             Y_{status}(t) = Y_{status,0} \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 475 |  |  |             \forall t \in \textrm{TIMESTEPS} | \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 476 |  |  |             t = \{0..t_{up,minimum}\} \cup \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 477 |  |  |             \{t\_max-t_{up,minimum}..t\_max\} , \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 478 |  |  |             \forall (i,o) \in \textrm{MINUPTIMEFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 479 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 480 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 481 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 482 |  |  |         def _min_uptime_rule(_, i, o, t): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 483 |  |  |             """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 484 |  |  |             Rule definition for min-uptime constraints of non-convex flows. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 485 |  |  |             """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 486 |  |  |             if ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 487 |  |  |                 m.flows[i, o].nonconvex.first_flexible_timestep | 
            
                                                                                                            
                            
            
                                    
            
            
                | 488 |  |  |                 < t | 
            
                                                                                                            
                            
            
                                    
            
            
                | 489 |  |  |                 < m.TIMESTEPS.at(-1) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 490 |  |  |             ): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 491 |  |  |                 # We have a 2D matrix of constraints, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 492 |  |  |                 # so testing is easier then just calling the rule for valid t. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 493 |  |  |                 expr = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 494 |  |  |                 expr += ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 495 |  |  |                     self.status[i, o, t] - self.status[i, o, t - 1] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 496 |  |  |                 ) * m.flows[i, o].nonconvex.minimum_uptime[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 497 |  |  |                 expr += -sum( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 498 |  |  |                     self.status[i, o, u] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 499 |  |  |                     for u in range( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 500 |  |  |                         t, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 501 |  |  |                         min( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 502 |  |  |                             t + m.flows[i, o].nonconvex.minimum_uptime[t], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 503 |  |  |                             len(m.TIMESTEPS), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 504 |  |  |                         ), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 505 |  |  |                     ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 506 |  |  |                 ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 507 |  |  |                 return expr <= 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 508 |  |  |             else: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 509 |  |  |                 return Constraint.Skip | 
            
                                                                                                            
                            
            
                                    
            
            
                | 510 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 511 |  |  |         return Constraint( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 512 |  |  |             self.MINUPTIMEFLOWS, m.TIMESTEPS, rule=_min_uptime_rule | 
            
                                                                                                            
                            
            
                                    
            
            
                | 513 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 514 |  |  |  | 
            
                                                                                                            
                            
            
                                                                    
                                                                                                        
            
            
                | 515 |  | View Code Duplication |     def _shutdown_constraint(self): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                                                                            
                            
            
                                    
            
            
                | 516 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 517 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 518 |  |  |             Y_{shutdown}(t) \geq Y_{status}(t-1) - Y_{status}(t) \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 519 |  |  |             \forall t \in \textrm{TIMESTEPS}, \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 520 |  |  |             \forall \textrm{SHUTDOWNFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 521 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 522 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 523 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 524 |  |  |         def _shutdown_rule(_, i, o, t): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 525 |  |  |             """Rule definition for shutdown constraints of non-convex flows.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 526 |  |  |             if t > m.TIMESTEPS.at(1): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 527 |  |  |                 expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 528 |  |  |                     self.shutdown[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 529 |  |  |                     >= self.status[i, o, t - 1] - self.status[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 530 |  |  |                 ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 531 |  |  |             else: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 532 |  |  |                 expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 533 |  |  |                     self.shutdown[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 534 |  |  |                     >= m.flows[i, o].nonconvex.initial_status | 
            
                                                                                                            
                            
            
                                    
            
            
                | 535 |  |  |                     - self.status[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 536 |  |  |                 ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 537 |  |  |             return expr | 
            
                                                                                                            
                            
            
                                    
            
            
                | 538 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 539 |  |  |         return Constraint(self.SHUTDOWNFLOWS, m.TIMESTEPS, rule=_shutdown_rule) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 540 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 541 |  |  |     def _startup_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 542 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 543 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 544 |  |  |             Y_{startup}(t) \geq Y_{status}(t) - Y_{status}(t-1) \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 545 |  |  |             \forall t \in \textrm{TIMESTEPS}, \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 546 |  |  |             \forall \textrm{STARTUPFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 547 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 548 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 549 |  |  |  | 
            
                                                                                                            
                            
            
                                                                    
                                                                                                        
            
            
                | 550 |  | View Code Duplication |         def _startup_rule(_, i, o, t): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                                                                            
                            
            
                                    
            
            
                | 551 |  |  |             """Rule definition for startup constraint of nonconvex flows.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 552 |  |  |             if t > m.TIMESTEPS.at(1): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 553 |  |  |                 expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 554 |  |  |                     self.startup[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 555 |  |  |                     >= self.status[i, o, t] - self.status[i, o, t - 1] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 556 |  |  |                 ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 557 |  |  |             else: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 558 |  |  |                 expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 559 |  |  |                     self.startup[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 560 |  |  |                     >= self.status[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 561 |  |  |                     - m.flows[i, o].nonconvex.initial_status | 
            
                                                                                                            
                            
            
                                    
            
            
                | 562 |  |  |                 ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 563 |  |  |             return expr | 
            
                                                                                                            
                            
            
                                    
            
            
                | 564 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 565 |  |  |         return Constraint(self.STARTUPFLOWS, m.TIMESTEPS, rule=_startup_rule) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 566 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 567 |  |  |     def _max_startup_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 568 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 569 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 570 |  |  |             \sum_{t \in \textrm{TIMESTEPS}} Y_{startup}(t) \leq \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 571 |  |  |                 N_{start}(i,o)\\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 572 |  |  |             \forall (i,o) \in \textrm{MAXSTARTUPFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 573 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 574 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 575 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 576 |  |  |         def _max_startup_rule(_, i, o): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 577 |  |  |             """Rule definition for maximum number of start-ups.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 578 |  |  |             lhs = sum(self.startup[i, o, t] for t in m.TIMESTEPS) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 579 |  |  |             return lhs <= m.flows[i, o].nonconvex.maximum_startups | 
            
                                                                                                            
                            
            
                                    
            
            
                | 580 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 581 |  |  |         return Constraint(self.MAXSTARTUPFLOWS, rule=_max_startup_rule) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 582 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 583 |  |  |     def _max_shutdown_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 584 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 585 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 586 |  |  |             \sum_{t \in \textrm{TIMESTEPS}} Y_{startup}(t) \leq \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 587 |  |  |                 N_{shutdown}(i,o)\\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 588 |  |  |             \forall (i,o) \in \textrm{MAXSHUTDOWNFLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 589 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 590 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 591 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 592 |  |  |         def _max_shutdown_rule(_, i, o): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 593 |  |  |             """Rule definition for maximum number of start-ups.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 594 |  |  |             lhs = sum(self.shutdown[i, o, t] for t in m.TIMESTEPS) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 595 |  |  |             return lhs <= m.flows[i, o].nonconvex.maximum_shutdowns | 
            
                                                                                                            
                            
            
                                    
            
            
                | 596 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 597 |  |  |         return Constraint(self.MAXSHUTDOWNFLOWS, rule=_max_shutdown_rule) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 598 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 599 |  |  |     def _maximum_flow_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 600 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 601 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 602 |  |  |             P(t) \leq max(i, o, t) \cdot P_{nom} \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 603 |  |  |                 \cdot status(t), \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 604 |  |  |             \forall t \in \textrm{TIMESTEPS}, \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 605 |  |  |             \forall (i, o) \in \textrm{NONCONVEX_FLOWS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 606 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 607 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 608 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 609 |  |  |         def _maximum_flow_rule(_, i, o, t): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 610 |  |  |             """Rule definition for MILP maximum flow constraints.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 611 |  |  |             expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 612 |  |  |                 self.status_nominal[i, o, t] * m.flows[i, o].max[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 613 |  |  |                 >= m.flow[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 614 |  |  |             ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 615 |  |  |             return expr | 
            
                                                                                                            
                            
            
                                    
            
            
                | 616 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 617 |  |  |         return Constraint(self.MIN_FLOWS, m.TIMESTEPS, rule=_maximum_flow_rule) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 618 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 619 |  |  |     def _minimum_flow_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 620 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 621 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 622 |  |  |             P(t) \geq min(i, o, t) \cdot P_{nom} \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 623 |  |  |                 \cdot Y_{status}(t), \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 624 |  |  |             \forall (i, o) \in \textrm{NONCONVEX_FLOWS}, \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 625 |  |  |             \forall t \in \textrm{TIMESTEPS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 626 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 627 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 628 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 629 |  |  |         def _minimum_flow_rule(_, i, o, t): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 630 |  |  |             """Rule definition for MILP minimum flow constraints.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 631 |  |  |             expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 632 |  |  |                 self.status_nominal[i, o, t] * m.flows[i, o].min[t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 633 |  |  |                 <= m.flow[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 634 |  |  |             ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 635 |  |  |             return expr | 
            
                                                                                                            
                            
            
                                    
            
            
                | 636 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 637 |  |  |         return Constraint(self.MIN_FLOWS, m.TIMESTEPS, rule=_minimum_flow_rule) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 638 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 639 |  |  |     def _status_nominal_constraint(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 640 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 641 |  |  |         .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 642 |  |  |             P_{max,status}(t) =  Y_{status}(t) \cdot P_{nom}, \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 643 |  |  |             \forall t \in \textrm{TIMESTEPS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 644 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 645 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 646 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 647 |  |  |         def _status_nominal_rule(_, i, o, t): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 648 |  |  |             """Rule definition for status_nominal""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 649 |  |  |             expr = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 650 |  |  |                 self.status_nominal[i, o, t] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 651 |  |  |                 == self.status[i, o, t] * m.flows[i, o].nominal_value | 
            
                                                                                                            
                            
            
                                    
            
            
                | 652 |  |  |             ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 653 |  |  |             return expr | 
            
                                                                                                            
                            
            
                                    
            
            
                | 654 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 655 |  |  |         return Constraint( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 656 |  |  |             self.NONCONVEX_FLOWS, m.TIMESTEPS, rule=_status_nominal_rule | 
            
                                                                                                            
                            
            
                                    
            
            
                | 657 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 658 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 659 |  |  |     def _shared_constraints_for_non_convex_flows(self): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 660 |  |  |         r""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 661 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 662 |  |  |         .. automethod:: _startup_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 663 |  |  |         .. automethod:: _max_startup_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 664 |  |  |         .. automethod:: _shutdown_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 665 |  |  |         .. automethod:: _max_shutdown_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 666 |  |  |         .. automethod:: _min_uptime_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 667 |  |  |         .. automethod:: _min_downtime_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 668 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 669 |  |  |         positive_gradient_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 670 |  |  |             .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 671 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 672 |  |  |                 P(t) \cdot Y_{status}(t) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 673 |  |  |                 - P(t-1) \cdot Y_{status}(t-1)  \leq \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 674 |  |  |                 \dot{P}_{up}(t), \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 675 |  |  |                 \forall t \in \textrm{TIMESTEPS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 676 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 677 |  |  |         negative_gradient_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 678 |  |  |             .. math:: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 679 |  |  |                 P(t-1) \cdot Y_{status}(t-1) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 680 |  |  |                 - P(t) \cdot Y_{status}(t) \leq \ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 681 |  |  |                 \dot{P}_{down}(t), \\ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 682 |  |  |                 \forall t \in \textrm{TIMESTEPS}. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 683 |  |  |         """ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 684 |  |  |         m = self.parent_block() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 685 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 686 |  |  |         self.startup_constr = self._startup_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 687 |  |  |         self.max_startup_constr = self._max_startup_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 688 |  |  |         self.shutdown_constr = self._shutdown_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 689 |  |  |         self.max_shutdown_constr = self._max_shutdown_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 690 |  |  |         self.min_uptime_constr = self._min_uptime_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 691 |  |  |         self.min_downtime_constr = self._min_downtime_constraint() | 
            
                                                                                                            
                            
            
                                    
            
            
                | 692 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 693 |  |  |         def _positive_gradient_flow_constraint(_): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 694 |  |  |             r"""Rule definition for positive gradient constraint.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 695 |  |  |             for i, o in self.POSITIVE_GRADIENT_FLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 696 |  |  |                 for index in range(1, len(m.TIMEINDEX) + 1): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 697 |  |  |                     if m.TIMEINDEX[index][1] > 0: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 698 |  |  |                         lhs = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 699 |  |  |                             m.flow[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 700 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 701 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 702 |  |  |                                 m.TIMESTEPS[index], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 703 |  |  |                             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 704 |  |  |                             * self.status[i, o, m.TIMESTEPS[index]] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 705 |  |  |                             - m.flow[i, o, m.TIMESTEPS[index - 1]] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 706 |  |  |                             * self.status[i, o, m.TIMESTEPS[index - 1]] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 707 |  |  |                         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 708 |  |  |                         rhs = self.positive_gradient[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 709 |  |  |                             i, o, m.TIMEINDEX[index][1] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 710 |  |  |                         ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 711 |  |  |                         self.positive_gradient_constr.add( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 712 |  |  |                             ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 713 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 714 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 715 |  |  |                                 m.TIMESTEPS[index], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 716 |  |  |                             ), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 717 |  |  |                             lhs <= rhs, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 718 |  |  |                         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 719 |  |  |                     else: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 720 |  |  |                         lhs = self.positive_gradient[i, o, 0] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 721 |  |  |                         rhs = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 722 |  |  |                         self.positive_gradient_constr.add( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 723 |  |  |                             ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 724 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 725 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 726 |  |  |                                 m.TIMESTEPS[index], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 727 |  |  |                             ), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 728 |  |  |                             lhs == rhs, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 729 |  |  |                         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 730 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 731 |  |  |         self.positive_gradient_constr = Constraint( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 732 |  |  |             self.POSITIVE_GRADIENT_FLOWS, m.TIMESTEPS, noruleinit=True | 
            
                                                                                                            
                            
            
                                    
            
            
                | 733 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 734 |  |  |         self.positive_gradient_build = BuildAction( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 735 |  |  |             rule=_positive_gradient_flow_constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 736 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 737 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 738 |  |  |         def _negative_gradient_flow_constraint(_): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 739 |  |  |             r"""Rule definition for negative gradient constraint.""" | 
            
                                                                                                            
                            
            
                                    
            
            
                | 740 |  |  |             for i, o in self.NEGATIVE_GRADIENT_FLOWS: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 741 |  |  |                 for index in range(1, len(m.TIMESTEPS) + 1): | 
            
                                                                                                            
                            
            
                                    
            
            
                | 742 |  |  |                     if m.TIMESTEPS[index] > 0: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 743 |  |  |                         lhs = ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 744 |  |  |                             m.flow[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 745 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 746 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 747 |  |  |                                 m.TIMESTEPS[index - 1], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 748 |  |  |                             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 749 |  |  |                             * self.status[i, o, m.TIMESTEPS[index - 1]] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 750 |  |  |                             - m.flow[ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 751 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 752 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 753 |  |  |                                 m.TIMESTEPS[index], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 754 |  |  |                             ] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 755 |  |  |                             * self.status[i, o, m.TIMESTEPS[index]] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 756 |  |  |                         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 757 |  |  |                         rhs = self.negative_gradient[i, o, m.TIMESTEPS[index]] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 758 |  |  |                         self.negative_gradient_constr.add( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 759 |  |  |                             ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 760 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 761 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 762 |  |  |                                 m.TIMESTEPS[index], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 763 |  |  |                             ), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 764 |  |  |                             lhs <= rhs, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 765 |  |  |                         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 766 |  |  |                     else: | 
            
                                                                                                            
                            
            
                                    
            
            
                | 767 |  |  |                         lhs = self.negative_gradient[i, o, 0] | 
            
                                                                                                            
                            
            
                                    
            
            
                | 768 |  |  |                         rhs = 0 | 
            
                                                                                                            
                            
            
                                    
            
            
                | 769 |  |  |                         self.negative_gradient_constr.add( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 770 |  |  |                             ( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 771 |  |  |                                 i, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 772 |  |  |                                 o, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 773 |  |  |                                 m.TIMESTEPS[index], | 
            
                                                                                                            
                            
            
                                    
            
            
                | 774 |  |  |                             ), | 
            
                                                                                                            
                            
            
                                    
            
            
                | 775 |  |  |                             lhs == rhs, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 776 |  |  |                         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 777 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 778 |  |  |         self.negative_gradient_constr = Constraint( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 779 |  |  |             self.NEGATIVE_GRADIENT_FLOWS, m.TIMESTEPS, noruleinit=True | 
            
                                                                                                            
                            
            
                                    
            
            
                | 780 |  |  |         ) | 
            
                                                                                                            
                            
            
                                    
            
            
                | 781 |  |  |         self.negative_gradient_build = BuildAction( | 
            
                                                                                                            
                            
            
                                    
            
            
                | 782 |  |  |             rule=_negative_gradient_flow_constraint | 
            
                                                                                                            
                                                                
            
                                    
            
            
                | 783 |  |  |         ) | 
            
                                                        
            
                                    
            
            
                | 784 |  |  |  |