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# -*- coding: utf-8 -*- |
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"""Creating sets, variables, constraints and parts of the objective function |
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for Flow objects with nonconvex but without investment options. |
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SPDX-FileCopyrightText: Uwe Krien <[email protected]> |
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SPDX-FileCopyrightText: Simon Hilpert |
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SPDX-FileCopyrightText: Cord Kaldemeyer |
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SPDX-FileCopyrightText: Patrik Schönfeldt |
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SPDX-FileCopyrightText: Birgit Schachler |
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SPDX-FileCopyrightText: jnnr |
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SPDX-FileCopyrightText: jmloenneberga |
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SPDX-FileCopyrightText: Johannes Kochems |
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SPDX-License-Identifier: MIT |
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""" |
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from pyomo.core import Binary |
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from pyomo.core import BuildAction |
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from pyomo.core import Constraint |
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from pyomo.core import Expression |
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from pyomo.core import NonNegativeReals |
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from pyomo.core import Set |
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from pyomo.core import Var |
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from pyomo.core.base.block import ScalarBlock |
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class NonConvexFlowBlock(ScalarBlock): |
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r""" |
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.. automethod:: _create_constraints |
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.. automethod:: _create_variables |
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.. automethod:: _create_sets |
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.. automethod:: _objective_expression |
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Parameters are defined in :class:`Flow`. |
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""" |
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def __init__(self, *args, **kwargs): |
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super().__init__(*args, **kwargs) |
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def _create(self, group=None): |
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"""Creates set, variables, constraints for all flow object with |
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an attribute flow of type class:`.NonConvexFlowBlock`. |
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Parameters |
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---------- |
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group : list |
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List of oemof.solph.NonConvexFlowBlock objects for which |
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the constraints are build. |
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""" |
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if group is None: |
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return None |
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self._create_sets(group) |
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self._create_variables() |
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self._create_constraints() |
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def _create_sets(self, group): |
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r""" |
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**The following sets are created:** (-> see basic sets at |
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:class:`.Model` ) |
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NONCONVEX_FLOWS |
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A set of flows with the attribute `nonconvex` of type |
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:class:`.options.NonConvex`. |
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.. automethod:: _sets_for_non_convex_flows |
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""" |
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self.NONCONVEX_FLOWS = Set(initialize=[(g[0], g[1]) for g in group]) |
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self._sets_for_non_convex_flows(group) |
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def _create_variables(self): |
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r""" |
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:math:`Y_{status}` (binary) `om.NonConvexFlowBlock.status`: |
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Variable indicating if flow is >= 0 |
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:math:`P_{max,status}` Status_nominal (continuous) |
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Variable indicating if flow is >= 0 |
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.. automethod:: _variables_for_non_convex_flows |
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""" |
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m = self.parent_block() |
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self.status = Var(self.NONCONVEX_FLOWS, m.TIMESTEPS, within=Binary) |
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for o, i in self.NONCONVEX_FLOWS: |
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if m.flows[o, i].nonconvex.initial_status is not None: |
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for t in range( |
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0, m.flows[o, i].nonconvex.first_flexible_timestep |
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): |
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self.status[o, i, t] = m.flows[ |
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o, i |
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].nonconvex.initial_status |
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self.status[o, i, t].fix() |
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# `status_nominal` is a parameter which represents the |
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# multiplication of a binary variable (`status`) |
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# and a continuous variable (`invest` or `nominal_value`) |
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self.status_nominal = Var( |
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self.NONCONVEX_FLOWS, m.TIMESTEPS, within=NonNegativeReals |
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) |
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self._variables_for_non_convex_flows() |
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def _create_constraints(self): |
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""" |
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The following constraints are created: |
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.. automethod:: _status_nominal_constraint |
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.. automethod:: _minimum_flow_constraint |
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.. automethod:: _maximum_flow_constraint |
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.. automethod:: _shared_constraints_for_non_convex_flows |
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""" |
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self.status_nominal_constraint = self._status_nominal_constraint() |
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self.min = self._minimum_flow_constraint() |
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self.max = self._maximum_flow_constraint() |
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self._shared_constraints_for_non_convex_flows() |
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def _objective_expression(self): |
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r""" |
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The following terms are to the cost function: |
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.. automethod:: _startup_costs |
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.. automethod:: _shutdown_costs |
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.. automethod:: _activity_costs |
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.. automethod:: _inactivity_costs |
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""" |
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if not hasattr(self, "NONCONVEX_FLOWS"): |
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return 0 |
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startup_costs = self._startup_costs() |
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shutdown_costs = self._shutdown_costs() |
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activity_costs = self._activity_costs() |
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inactivity_costs = self._inactivity_costs() |
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self.activity_costs = Expression(expr=activity_costs) |
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self.inactivity_costs = Expression(expr=inactivity_costs) |
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self.startup_costs = Expression(expr=startup_costs) |
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self.shutdown_costs = Expression(expr=shutdown_costs) |
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self.costs = Expression( |
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expr=( |
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startup_costs |
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+ shutdown_costs |
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+ activity_costs |
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+ inactivity_costs |
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) |
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) |
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return self.costs |
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def _sets_for_non_convex_flows(self, group): |
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r"""Creates all sets for non-convex flows. |
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MIN_FLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute `min` |
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being not None in the first timestep. |
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ACTIVITYCOSTFLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`activity_costs` being not None. |
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INACTIVITYCOSTFLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`inactivity_costs` being not None. |
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STARTUPFLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`maximum_startups` or `startup_costs` |
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being not None. |
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MAXSTARTUPFLOWS |
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A subset of set STARTUPFLOWS with the attribute |
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`maximum_startups` being not None. |
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SHUTDOWNFLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`maximum_shutdowns` or `shutdown_costs` |
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being not None. |
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MAXSHUTDOWNFLOWS |
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A subset of set SHUTDOWNFLOWS with the attribute |
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`maximum_shutdowns` being not None. |
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MINUPTIMEFLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`minimum_uptime` being > 0. |
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MINDOWNTIMEFLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`minimum_downtime` being > 0. |
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POSITIVE_GRADIENT_FLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`positive_gradient` being not None. |
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NEGATIVE_GRADIENT_FLOWS |
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A subset of set NONCONVEX_FLOWS with the attribute |
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`negative_gradient` being not None. |
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""" |
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self.MIN_FLOWS = Set( |
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initialize=[(g[0], g[1]) for g in group if g[2].min[0] is not None] |
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) |
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self.STARTUPFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.startup_costs[0] is not None |
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or g[2].nonconvex.maximum_startups is not None |
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] |
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) |
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self.MAXSTARTUPFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.maximum_startups is not None |
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] |
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) |
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self.SHUTDOWNFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.shutdown_costs[0] is not None |
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or g[2].nonconvex.maximum_shutdowns is not None |
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] |
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) |
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self.MAXSHUTDOWNFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.maximum_shutdowns is not None |
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] |
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) |
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self.MINUPTIMEFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.minimum_uptime.max() > 0 |
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] |
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) |
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self.MINDOWNTIMEFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.minimum_downtime.max() > 0 |
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] |
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) |
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self.NEGATIVE_GRADIENT_FLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.negative_gradient_limit[0] is not None |
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] |
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) |
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self.POSITIVE_GRADIENT_FLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.positive_gradient_limit[0] is not None |
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] |
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) |
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self.ACTIVITYCOSTFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.activity_costs[0] is not None |
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] |
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) |
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self.INACTIVITYCOSTFLOWS = Set( |
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initialize=[ |
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(g[0], g[1]) |
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for g in group |
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if g[2].nonconvex.inactivity_costs[0] is not None |
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] |
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) |
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def _variables_for_non_convex_flows(self): |
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r""" |
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:math:`Y_{startup}` (binary) `NonConvexFlowBlock.startup`: |
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Variable indicating startup of flow (component) indexed by |
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STARTUPFLOWS |
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:math:`Y_{shutdown}` (binary) `NonConvexFlowBlock.shutdown`: |
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Variable indicating shutdown of flow (component) indexed by |
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SHUTDOWNFLOWS |
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:math:`\dot{P}_{up}` (continuous) |
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`NonConvexFlowBlock.positive_gradient`: |
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Variable indicating the positive gradient, i.e. the load increase |
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between two consecutive timesteps, indexed by |
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POSITIVE_GRADIENT_FLOWS |
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:math:`\dot{P}_{down}` (continuous) |
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`NonConvexFlowBlock.negative_gradient`: |
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Variable indicating the negative gradient, i.e. the load decrease |
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between two consecutive timesteps, indexed by |
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NEGATIVE_GRADIENT_FLOWS |
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""" |
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m = self.parent_block() |
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if self.STARTUPFLOWS: |
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self.startup = Var(self.STARTUPFLOWS, m.TIMESTEPS, within=Binary) |
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if self.SHUTDOWNFLOWS: |
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self.shutdown = Var(self.SHUTDOWNFLOWS, m.TIMESTEPS, within=Binary) |
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if self.POSITIVE_GRADIENT_FLOWS: |
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self.positive_gradient = Var( |
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self.POSITIVE_GRADIENT_FLOWS, |
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m.TIMESTEPS, |
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within=NonNegativeReals, |
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) |
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if self.NEGATIVE_GRADIENT_FLOWS: |
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self.negative_gradient = Var( |
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self.NEGATIVE_GRADIENT_FLOWS, |
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m.TIMESTEPS, |
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within=NonNegativeReals, |
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) |
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def _startup_costs(self): |
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r""" |
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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
|
|
|
|