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# -*- coding: utf-8 -*- |
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""" |
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solph version of oemof.network.Edge including base constraints |
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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: Stephan Günther |
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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-License-Identifier: MIT |
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""" |
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import math |
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from warnings import warn |
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from oemof.network import network as on |
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from oemof.tools import debugging |
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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 NonNegativeIntegers |
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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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from oemof.solph._plumbing import sequence |
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class Flow(on.Edge): |
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r"""Defines a flow between two nodes. |
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Keyword arguments are used to set the attributes of this flow. Parameters |
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which are handled specially are noted below. |
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For the case where a parameter can be either a scalar or an iterable, a |
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scalar value will be converted to a sequence containing the scalar value at |
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every index. This sequence is then stored under the paramter's key. |
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Parameters |
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---------- |
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nominal_value : numeric, :math:`P_{nom}` |
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The nominal value of the flow. If this value is set the corresponding |
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optimization variable of the flow object will be bounded by this value |
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multiplied with min(lower bound)/max(upper bound). |
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max : numeric (iterable or scalar), :math:`f_{max}` |
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Normed maximum value of the flow. The flow absolute maximum will be |
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calculated by multiplying :attr:`nominal_value` with :attr:`max` |
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min : numeric (iterable or scalar), :math:`f_{min}` |
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Normed minimum value of the flow (see :attr:`max`). |
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fix : numeric (iterable or scalar), :math:`f_{fix}` |
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Normed fixed value for the flow variable. Will be multiplied with the |
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:attr:`nominal_value` to get the absolute value. |
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positive_gradient : :obj:`dict`, default: `{'ub': None}` |
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A dictionary containing the following key: |
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* `'ub'`: numeric (iterable, scalar or None), the normed *upper |
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bound* on the positive difference (`flow[t-1] < flow[t]`) of |
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two consecutive flow values. |
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negative_gradient : :obj:`dict`, default: `{'ub': None}` |
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A dictionary containing the following key: |
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* `'ub'`: numeric (iterable, scalar or None), the normed *upper |
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bound* on the negative difference (`flow[t-1] > flow[t]`) of |
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two consecutive flow values. |
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full_load_time_max : numeric, :math:`t_{full\_load,max}` |
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Upper bound on the summed flow expressed as the equivalent time that |
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the flow would have to run at full capacity to yield the same sum. The |
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value will be multiplied with the nominal_value to get the absolute |
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limit. |
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full_load_time_min : numeric, :math:`t_{full\_load,min}` |
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Lower bound on the summed flow expressed as the equivalent time that |
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the flow would have to run at full capacity to yield the same sum. The |
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value will be multiplied with the nominal_value to get the absolute |
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limit. |
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variable_costs : numeric (iterable or scalar) |
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The costs associated with one unit of the flow. If this is set the |
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costs will be added to the objective expression of the optimization |
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problem. |
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fixed : boolean |
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Boolean value indicating if a flow is fixed during the optimization |
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problem to its ex-ante set value. Used in combination with the |
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:attr:`fix`. |
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integer : boolean |
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Set True to bound the flow values to integers. |
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Notes |
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----- |
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See :py:class:`~oemof.solph.flows._flow.FlowBlock` for the variables, |
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constraints and objective parts, that are created for a FLow object. |
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Examples |
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-------- |
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Creating a fixed flow object: |
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>>> f = Flow(nominal_value=2, fix=[10, 4, 4], variable_costs=5) |
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>>> f.variable_costs[2] |
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5 |
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>>> f.fix[2] |
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4 |
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Creating a flow object with time-depended lower and upper bounds: |
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>>> f1 = Flow(min=[0.2, 0.3], max=0.99, nominal_value=100) |
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>>> f1.max[1] |
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0.99 |
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""" |
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def __init__(self, **kwargs): |
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# TODO: Check if we can inherit from pyomo.core.base.var _VarData |
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# then we need to create the var object with |
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# pyomo.core.base.IndexedVarWithDomain before any FlowBlock is created. |
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# E.g. create the variable in the energy system and populate with |
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# information afterwards when creating objects. |
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# --- BEGIN: The following code can be removed for versions >= v0.6 --- |
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msg = ( |
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"\nThe parameter 'summed_{0}' ist deprecated and will be removed " |
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"in version v0.6.\nRename the parameter to 'full_load_time_{0}', " |
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"to avoid this warning and future problems. " |
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) |
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if "summed_max" in kwargs: |
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warn(msg.format("max"), FutureWarning) |
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kwargs["full_load_time_max"] = kwargs["summed_max"] |
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if "summed_min" in kwargs: |
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warn(msg.format("min"), FutureWarning) |
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kwargs["full_load_time_min"] = kwargs["summed_min"] |
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# --- END --- |
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super().__init__() |
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scalars = [ |
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"nominal_value", |
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"full_load_time_max", |
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"full_load_time_min", |
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"investment", |
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"nonconvex", |
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"integer", |
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] |
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sequences = ["fix", "variable_costs", "min", "max"] |
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dictionaries = ["positive_gradient", "negative_gradient"] |
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defaults = { |
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"variable_costs": 0, |
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"positive_gradient": {"ub": None}, |
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"negative_gradient": {"ub": None}, |
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} |
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need_nominal_value = [ |
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"fix", |
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"full_load_time_max", |
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"full_load_time_min", |
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"max", |
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"min", |
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# --- BEGIN: To be removed for versions >= v0.6 --- |
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"summed_max", |
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"summed_min", |
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# --- END --- |
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] |
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keys = [k for k in kwargs if k != "label"] |
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if "fixed_costs" in keys: |
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raise AttributeError( |
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"The `fixed_costs` attribute has been removed" " with v0.2!" |
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) |
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if "actual_value" in keys: |
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raise AttributeError( |
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"The `actual_value` attribute has been renamed" |
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" to `fix` with v0.4. The attribute `fixed` is" |
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" set to True automatically when passing `fix`." |
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) |
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if "fixed" in keys: |
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msg = ( |
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"The `fixed` attribute is deprecated.\nIf you have defined " |
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"the `fix` attribute the flow variable will be fixed.\n" |
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"The `fixed` attribute does not change anything." |
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) |
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warn(msg, debugging.SuspiciousUsageWarning) |
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# It is not allowed to define min or max if fix is defined. |
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if kwargs.get("fix") is not None and ( |
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kwargs.get("min") is not None or kwargs.get("max") is not None |
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): |
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raise AttributeError( |
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"It is not allowed to define `min`/`max` if `fix` is defined." |
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) |
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# Set default value for min and max |
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if kwargs.get("min") is None: |
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if "bidirectional" in keys: |
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defaults["min"] = -1 |
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else: |
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defaults["min"] = 0 |
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if kwargs.get("max") is None: |
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defaults["max"] = 1 |
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# Check gradient dictionaries for non-valid keys |
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for gradient_dict in ["negative_gradient", "positive_gradient"]: |
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if gradient_dict in kwargs: |
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if list(kwargs[gradient_dict].keys()) != list( |
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defaults[gradient_dict].keys() |
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): |
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msg = ( |
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"Only the key 'ub' is allowed for the '{0}' attribute" |
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) |
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raise AttributeError(msg.format(gradient_dict)) |
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for attribute in set(scalars + sequences + dictionaries + keys): |
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value = kwargs.get(attribute, defaults.get(attribute)) |
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View Code Duplication |
if attribute in dictionaries: |
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setattr( |
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self, |
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attribute, |
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{"ub": sequence(value["ub"])}, |
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) |
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else: |
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setattr( |
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self, |
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attribute, |
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sequence(value) if attribute in sequences else value, |
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) |
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# Checking for impossible attribute combinations |
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if self.investment and self.nominal_value is not None: |
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raise ValueError( |
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"Using the investment object the nominal_value" |
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" has to be set to None." |
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) |
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if self.investment and self.nonconvex: |
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raise ValueError( |
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"Investment flows cannot be combined with " |
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+ "nonconvex flows!" |
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) |
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infinite_error_msg = ( |
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"{} must be a finite value. Passing an infinite " |
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"value is not allowed." |
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) |
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if not self.investment: |
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if self.nominal_value is None: |
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for attr in need_nominal_value: |
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if kwargs.get(attr) is not None: |
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raise AttributeError( |
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"If {} is set in a flow (except InvestmentFlow), " |
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"nominal_value must be set as well.\n" |
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"Otherwise, it won't have any effect.".format(attr) |
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) |
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elif not math.isfinite(self.nominal_value): |
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raise ValueError(infinite_error_msg.format("nominal_value")) |
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if not math.isfinite(self.max[0]): |
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raise ValueError(infinite_error_msg.format("max")) |
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# Checking for impossible gradient combinations |
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View Code Duplication |
if self.nonconvex: |
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if self.nonconvex.positive_gradient["ub"][0] is not None and ( |
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self.positive_gradient["ub"][0] is not None |
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or self.negative_gradient["ub"][0] is not None |
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): |
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raise ValueError( |
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"You specified a positive gradient in your nonconvex " |
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"option. This cannot be combined with a positive or a " |
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"negative gradient for a standard flow!" |
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) |
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View Code Duplication |
if self.nonconvex: |
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if self.nonconvex.negative_gradient["ub"][0] is not None and ( |
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self.positive_gradient["ub"][0] is not None |
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or self.negative_gradient["ub"][0] is not None |
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): |
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raise ValueError( |
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"You specified a negative gradient in your nonconvex " |
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"option. This cannot be combined with a positive or a " |
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"negative gradient for a standard flow!" |
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) |
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class FlowBlock(ScalarBlock): |
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r"""Flow block with definitions for standard flows. |
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See :class:`~oemof.solph.flows._flow.Flow` class for all parameters of the *Flow*. |
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**Variables** |
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All *Flow* objects are indexed by a starting and ending node |
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:math:`(i, o)`, which is omitted in the following for the sake of |
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convenience. The creation of some variables depend on the values of |
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*Flow* attributes. The following variables are created: |
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* :math:`P(t)` |
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Actual flow value (created in :class:`~oemof.solph._models.Model`). |
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The variable is bound to: :math:`f_{min}(t) \cdot P_{nom} \ge P(t) \le f_{max}(t) \cdot P_{nom}`. |
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If `Flow.fix` is not None the variable is bound to |
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:math:`P(t) = f_{fix}`. |
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* :math:`ve_n` (`Flow.negative_gradient` is not `None`) |
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Difference of a flow in consecutive timesteps if flow is reduced. The |
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variable is bound to: :math:`0 \ge ve_n \ge ve_n^{max}`. |
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* :math:`ve_p` (`Flow.positive_gradient` is not `None`) |
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Difference of a flow in consecutive timesteps if flow is increased. The |
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variable is bound to: :math:`0 \ge ve_p \ge ve_p^{max}`. |
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The following variable is build for Flows with the attribute |
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`integer_flows` being not None. |
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* :math:`i`(`Flow.integer` is `True`) |
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All flow values are integers. Variable is bound to non-negative |
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integers. |
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**Constraints** |
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The following constraints are created, if the appropriate attribute of the |
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*Flow* (see :class:`oemof.solph.network.Flow`) object is set: |
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* `Flow.full_load_time_max` is not `None` (full_load_time_max_constr): |
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.. math:: |
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\sum_t P(t) \cdot \tau \leq F_{max} \cdot P_{nom} |
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325
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* `Flow.full_load_time_min` is not `None` (full_load_time_min_constr): |
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.. math:: |
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327
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\sum_t P(t) \cdot \tau \geq F_{min} \cdot P_{nom} |
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* `Flow.negative_gradient` is not `None` (negative_gradient_constr): |
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.. math:: |
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P(t-1) - P(t) \geq ve_n(t) |
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334
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* `Flow.positive_gradient` is not `None` (positive_gradient_constr): |
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.. math:: |
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336
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P(t) - P(t-1) \geq ve_p(t) |
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338
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* `Flow.integer` is `True` |
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.. math:: |
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340
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P(t) = i(t) |
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342
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**Objective function** |
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344
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Depending on the attributes of the `Flow` object the following parts of |
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345
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the objective function are created: |
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347
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* `Flow.variable_costs` is not `None`: |
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.. math:: |
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349
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\sum_{(i,o)} \sum_t P(t) \cdot c_{var}(i, o, t) |
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351
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.. csv-table:: List of Variables |
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:header: "symbol", "attribute", "explanation" |
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:widths: 1, 1, 1 |
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355
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":math:`P(t)`", ":command:`flow[i, o][t]`", "Actual flow value" |
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356
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":math:`ve_n`", ":command:`negative_gradient[n, o, t]`", "Negative gradient of the flow" |
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357
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":math:`ve_p`", ":command:`positive_gradient[n, o, t]`", "Positive gradient of the flow" |
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":math:`i`", ":command:`integer_flow[i, o, t]`","Integer flow" |
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359
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360
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361
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.. csv-table:: List of Parameters |
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362
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:header: "symbol", "attribute", "explanation" |
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363
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:widths: 1, 1, 1 |
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364
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365
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":math:`P_{nom}`", ":command:`flows[i, o].nominal_value`","Nominal value of the flow" |
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366
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":math:`F_{max}`",":command:`flow[i, o].full_load_time_max`", "Maximal full |
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367
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load time" |
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368
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":math:`F_{min}`",":command:`flow[i, o].full_load_time_min`", "Minimal full |
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369
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load time" |
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370
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":math:`c_{var}`", ":command:`variable\_costs[t]`", "Variable cost of the flow" |
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371
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":math:`f_{max}`", ":command:`flows[i, o].max[t]`", "Normed maximum value of the flow, the absolute maximum is :math:`f_{max} \cdot P_{nom}`" |
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372
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":math:`f_{min}`", ":command:`flows[i, o].min[t]`", "Normed minimum value of the flow, the absolute minimum is :math:`f_{min} \cdot P_{nom}`" |
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373
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|
":math:`f_{fix}`", ":command:`flows[i, o].min[t]`", "Normed fixed value of the flow, the absolute fixed value is :math:`f_{fix} \cdot P_{nom}`" |
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374
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|
":math:`ve_n^{max}`",":command:`flows[i, o].negative_gradient`","Normed maximal negative gradient of the flow, the absolute maximum gradient is :math:`ve_n^{max} \cdot P_{nom}`" |
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375
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|
":math:`ve_p^{max}`",":command:`flows[i, o].positive_gradient`","Normed maximal positive gradient of the flow, the absolute maximum gradient is :math:`ve_n^{max} \cdot P_{nom}`" |
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376
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377
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Note |
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378
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|
---- |
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379
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|
|
See the :class:`~oemof.solph.flows._flow.Flow` class for the definition of |
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380
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|
|
all parameters from the "List of Parameters above. |
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381
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|
382
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|
|
""" # noqa: E501 |
|
383
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|
384
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|
|
def __init__(self, *args, **kwargs): |
|
385
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|
|
super().__init__(*args, **kwargs) |
|
386
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|
387
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|
def _create(self, group=None): |
|
388
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|
r"""Creates sets, variables and constraints for all standard flows. |
|
389
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|
|
|
|
390
|
|
|
Parameters |
|
391
|
|
|
---------- |
|
392
|
|
|
group : list |
|
393
|
|
|
List containing tuples containing flow (f) objects and the |
|
394
|
|
|
associated source (s) and target (t) |
|
395
|
|
|
of flow e.g. groups=[(s1, t1, f1), (s2, t2, f2),..] |
|
396
|
|
|
""" |
|
397
|
|
|
if group is None: |
|
398
|
|
|
return None |
|
399
|
|
|
|
|
400
|
|
|
m = self.parent_block() |
|
401
|
|
|
|
|
402
|
|
|
# ########################## SETS ################################# |
|
403
|
|
|
# set for all flows with an global limit on the flow over time |
|
404
|
|
|
self.FULL_LOAD_TIME_MAX_FLOWS = Set( |
|
405
|
|
|
initialize=[ |
|
406
|
|
|
(g[0], g[1]) |
|
407
|
|
|
for g in group |
|
408
|
|
|
if g[2].full_load_time_max is not None |
|
409
|
|
|
and g[2].nominal_value is not None |
|
410
|
|
|
] |
|
411
|
|
|
) |
|
412
|
|
|
|
|
413
|
|
|
self.FULL_LOAD_TIME_MIN_FLOWS = Set( |
|
414
|
|
|
initialize=[ |
|
415
|
|
|
(g[0], g[1]) |
|
416
|
|
|
for g in group |
|
417
|
|
|
if g[2].full_load_time_min is not None |
|
418
|
|
|
and g[2].nominal_value is not None |
|
419
|
|
|
] |
|
420
|
|
|
) |
|
421
|
|
|
|
|
422
|
|
|
self.NEGATIVE_GRADIENT_FLOWS = Set( |
|
423
|
|
|
initialize=[ |
|
424
|
|
|
(g[0], g[1]) |
|
425
|
|
|
for g in group |
|
426
|
|
|
if g[2].negative_gradient["ub"][0] is not None |
|
427
|
|
|
] |
|
428
|
|
|
) |
|
429
|
|
|
|
|
430
|
|
|
self.POSITIVE_GRADIENT_FLOWS = Set( |
|
431
|
|
|
initialize=[ |
|
432
|
|
|
(g[0], g[1]) |
|
433
|
|
|
for g in group |
|
434
|
|
|
if g[2].positive_gradient["ub"][0] is not None |
|
435
|
|
|
] |
|
436
|
|
|
) |
|
437
|
|
|
|
|
438
|
|
|
self.INTEGER_FLOWS = Set( |
|
439
|
|
|
initialize=[(g[0], g[1]) for g in group if g[2].integer] |
|
440
|
|
|
) |
|
441
|
|
|
# ######################### Variables ################################ |
|
442
|
|
|
|
|
443
|
|
|
self.positive_gradient = Var(self.POSITIVE_GRADIENT_FLOWS, m.TIMESTEPS) |
|
444
|
|
|
|
|
445
|
|
|
self.negative_gradient = Var(self.NEGATIVE_GRADIENT_FLOWS, m.TIMESTEPS) |
|
446
|
|
|
|
|
447
|
|
|
self.integer_flow = Var( |
|
448
|
|
|
self.INTEGER_FLOWS, m.TIMESTEPS, within=NonNegativeIntegers |
|
449
|
|
|
) |
|
450
|
|
|
# set upper bound of gradient variable |
|
451
|
|
|
for i, o, f in group: |
|
452
|
|
|
if m.flows[i, o].positive_gradient["ub"][0] is not None: |
|
453
|
|
|
for t in m.TIMESTEPS: |
|
454
|
|
|
self.positive_gradient[i, o, t].setub( |
|
455
|
|
|
f.positive_gradient["ub"][t] * f.nominal_value |
|
456
|
|
|
) |
|
457
|
|
|
if m.flows[i, o].negative_gradient["ub"][0] is not None: |
|
458
|
|
|
for t in m.TIMESTEPS: |
|
459
|
|
|
self.negative_gradient[i, o, t].setub( |
|
460
|
|
|
f.negative_gradient["ub"][t] * f.nominal_value |
|
461
|
|
|
) |
|
462
|
|
|
|
|
463
|
|
|
# ######################### CONSTRAINTS ############################### |
|
464
|
|
|
|
|
465
|
|
|
def _flow_full_load_time_max_rule(model): |
|
466
|
|
|
"""Rule definition for build action of max. sum flow constraint.""" |
|
467
|
|
|
for inp, out in self.FULL_LOAD_TIME_MAX_FLOWS: |
|
468
|
|
|
lhs = sum( |
|
469
|
|
|
m.flow[inp, out, ts] * m.timeincrement[ts] |
|
|
|
|
|
|
470
|
|
|
for ts in m.TIMESTEPS |
|
471
|
|
|
) |
|
472
|
|
|
rhs = ( |
|
473
|
|
|
m.flows[inp, out].full_load_time_max |
|
474
|
|
|
* m.flows[inp, out].nominal_value |
|
475
|
|
|
) |
|
476
|
|
|
self.full_load_time_max_constr.add((inp, out), lhs <= rhs) |
|
477
|
|
|
|
|
478
|
|
|
self.full_load_time_max_constr = Constraint( |
|
479
|
|
|
self.FULL_LOAD_TIME_MAX_FLOWS, noruleinit=True |
|
480
|
|
|
) |
|
481
|
|
|
self.full_load_time_max_build = BuildAction( |
|
482
|
|
|
rule=_flow_full_load_time_max_rule |
|
483
|
|
|
) |
|
484
|
|
|
|
|
485
|
|
|
def _flow_full_load_time_min_rule(model): |
|
486
|
|
|
"""Rule definition for build action of min. sum flow constraint.""" |
|
487
|
|
|
for inp, out in self.FULL_LOAD_TIME_MIN_FLOWS: |
|
488
|
|
|
lhs = sum( |
|
489
|
|
|
m.flow[inp, out, ts] * m.timeincrement[ts] |
|
|
|
|
|
|
490
|
|
|
for ts in m.TIMESTEPS |
|
491
|
|
|
) |
|
492
|
|
|
rhs = ( |
|
493
|
|
|
m.flows[inp, out].full_load_time_min |
|
494
|
|
|
* m.flows[inp, out].nominal_value |
|
495
|
|
|
) |
|
496
|
|
|
self.full_load_time_min_constr.add((inp, out), lhs >= rhs) |
|
497
|
|
|
|
|
498
|
|
|
self.full_load_time_min_constr = Constraint( |
|
499
|
|
|
self.FULL_LOAD_TIME_MIN_FLOWS, noruleinit=True |
|
500
|
|
|
) |
|
501
|
|
|
self.full_load_time_min_build = BuildAction( |
|
502
|
|
|
rule=_flow_full_load_time_min_rule |
|
503
|
|
|
) |
|
504
|
|
|
|
|
505
|
|
|
def _positive_gradient_flow_rule(model): |
|
506
|
|
|
"""Rule definition for positive gradient constraint.""" |
|
507
|
|
|
for inp, out in self.POSITIVE_GRADIENT_FLOWS: |
|
508
|
|
|
for ts in m.TIMESTEPS: |
|
|
|
|
|
|
509
|
|
|
if ts > 0: |
|
510
|
|
|
lhs = m.flow[inp, out, ts] - m.flow[inp, out, ts - 1] |
|
511
|
|
|
rhs = self.positive_gradient[inp, out, ts] |
|
512
|
|
|
self.positive_gradient_constr.add( |
|
513
|
|
|
(inp, out, ts), lhs <= rhs |
|
514
|
|
|
) |
|
515
|
|
|
|
|
516
|
|
|
self.positive_gradient_constr = Constraint( |
|
517
|
|
|
self.POSITIVE_GRADIENT_FLOWS, m.TIMESTEPS, noruleinit=True |
|
518
|
|
|
) |
|
519
|
|
|
self.positive_gradient_build = BuildAction( |
|
520
|
|
|
rule=_positive_gradient_flow_rule |
|
521
|
|
|
) |
|
522
|
|
|
|
|
523
|
|
|
def _negative_gradient_flow_rule(model): |
|
524
|
|
|
"""Rule definition for negative gradient constraint.""" |
|
525
|
|
|
for inp, out in self.NEGATIVE_GRADIENT_FLOWS: |
|
526
|
|
|
for ts in m.TIMESTEPS: |
|
|
|
|
|
|
527
|
|
|
if ts > 0: |
|
528
|
|
|
lhs = m.flow[inp, out, ts - 1] - m.flow[inp, out, ts] |
|
529
|
|
|
rhs = self.negative_gradient[inp, out, ts] |
|
530
|
|
|
self.negative_gradient_constr.add( |
|
531
|
|
|
(inp, out, ts), lhs <= rhs |
|
532
|
|
|
) |
|
533
|
|
|
|
|
534
|
|
|
self.negative_gradient_constr = Constraint( |
|
535
|
|
|
self.NEGATIVE_GRADIENT_FLOWS, m.TIMESTEPS, noruleinit=True |
|
536
|
|
|
) |
|
537
|
|
|
self.negative_gradient_build = BuildAction( |
|
538
|
|
|
rule=_negative_gradient_flow_rule |
|
539
|
|
|
) |
|
540
|
|
|
|
|
541
|
|
|
def _integer_flow_rule(block, ii, oi, ti): |
|
542
|
|
|
"""Force flow variable to NonNegativeInteger values.""" |
|
543
|
|
|
return self.integer_flow[ii, oi, ti] == m.flow[ii, oi, ti] |
|
|
|
|
|
|
544
|
|
|
|
|
545
|
|
|
self.integer_flow_constr = Constraint( |
|
546
|
|
|
self.INTEGER_FLOWS, m.TIMESTEPS, rule=_integer_flow_rule |
|
547
|
|
|
) |
|
548
|
|
|
|
|
549
|
|
|
def _objective_expression(self): |
|
550
|
|
|
r"""Objective expression for all standard flows with fixed costs |
|
551
|
|
|
and variable costs. |
|
552
|
|
|
""" |
|
553
|
|
|
m = self.parent_block() |
|
554
|
|
|
|
|
555
|
|
|
variable_costs = 0 |
|
556
|
|
|
|
|
557
|
|
|
for i, o in m.FLOWS: |
|
558
|
|
|
if m.flows[i, o].variable_costs[0] is not None: |
|
559
|
|
|
for t in m.TIMESTEPS: |
|
560
|
|
|
variable_costs += ( |
|
561
|
|
|
m.flow[i, o, t] |
|
562
|
|
|
* m.objective_weighting[t] |
|
563
|
|
|
* m.flows[i, o].variable_costs[t] |
|
564
|
|
|
) |
|
565
|
|
|
|
|
566
|
|
|
return variable_costs |
|
567
|
|
|
|