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# -*- coding: utf-8 - |
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""" |
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GenericStorage and associated individual constraints (blocks) and groupings. |
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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: FranziPl |
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SPDX-FileCopyrightText: jnnr |
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SPDX-FileCopyrightText: Stephan Günther |
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SPDX-FileCopyrightText: FabianTU |
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SPDX-FileCopyrightText: Johannes Röder |
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SPDX-FileCopyrightText: Ekaterina Zolotarevskaia |
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SPDX-FileCopyrightText: Johannes Kochems |
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SPDX-FileCopyrightText: Johannes Giehl |
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SPDX-FileCopyrightText: Raul Ciria Aylagas |
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SPDX-FileCopyrightText: Lennart Schürmann (Fraunhofer UMSICHT) |
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SPDX-License-Identifier: MIT |
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""" |
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import math |
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import numbers |
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from warnings import warn |
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import numpy as np |
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from oemof.network import Node |
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from oemof.tools import debugging |
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from oemof.tools import economics |
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from pyomo.core.base.block import ScalarBlock |
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from pyomo.environ import Binary |
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from pyomo.environ import BuildAction |
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from pyomo.environ import Constraint |
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from pyomo.environ import Expression |
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from pyomo.environ import NonNegativeReals |
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from pyomo.environ import Set |
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from pyomo.environ import Var |
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from oemof.solph._helpers import check_node_object_for_missing_attribute |
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from oemof.solph._options import Investment |
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from oemof.solph._plumbing import sequence |
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from oemof.solph._plumbing import valid_sequence |
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class GenericStorage(Node): |
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r""" |
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Component `GenericStorage` to model with basic characteristics of storages. |
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The GenericStorage is designed for one input and one output. |
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Parameters |
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---------- |
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nominal_capacity : numeric, :math:`E_{nom}` or |
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:class:`oemof.solph.options.Investment` object |
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Absolute nominal capacity of the storage, fixed value or |
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object describing parameter of investment optimisations. |
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invest_relation_input_capacity : numeric (iterable or scalar) or None, :math:`r_{cap,in}` |
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Ratio between the investment variable of the input flow and the |
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investment variable of the storage: |
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:math:`\dot{E}_{in,invest} = E_{invest} \cdot r_{cap,in}` |
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invest_relation_output_capacity : numeric (iterable or scalar) or None, :math:`r_{cap,out}` |
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Ratio between the investment variable of the output flow and the |
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investment variable of the storage: |
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:math:`\dot{E}_{out,invest} = E_{invest} \cdot r_{cap,out}` |
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invest_relation_input_output : numeric (iterable or scalar) or None, :math:`r_{in,out}` |
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Ratio between the investment variable of the input flow and the |
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investment variable of the output flow. This ratio used to fix the |
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flow investments to each other. |
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Values < 1 set the input flow lower than the output and > 1 will |
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set the input flow higher than the output flow. If set to None no relation |
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will be set: |
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:math:`\dot{E}_{in,invest} = \dot{E}_{out,invest} \cdot r_{in,out}` |
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initial_storage_level : numeric, :math:`c(-1)` |
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The relative storage content in the timestep before the first |
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time step of optimization (between 0 and 1). |
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Note: When investment mode is used in a multi-period model, |
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`initial_storage_level` is not supported. |
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Storage output is forced to zero until the storage unit is invested in. |
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balanced : boolean |
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Couple storage level of first and last time step. |
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(Total inflow and total outflow are balanced.) |
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loss_rate : numeric (iterable or scalar) |
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The relative loss of the storage content per hour. |
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fixed_losses_relative : numeric (iterable or scalar), :math:`\gamma(t)` |
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Losses per hour that are independent of the storage content but |
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proportional to nominal storage capacity. |
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Note: Fixed losses are not supported in investment mode. |
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fixed_losses_absolute : numeric (iterable or scalar), :math:`\delta(t)` |
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Losses per hour that are independent of storage content and independent |
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of nominal storage capacity. |
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Note: Fixed losses are not supported in investment mode. |
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inflow_conversion_factor : numeric (iterable or scalar), :math:`\eta_i(t)` |
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The relative conversion factor, i.e. efficiency associated with the |
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inflow of the storage. |
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outflow_conversion_factor : numeric (iterable or scalar), :math:`\eta_o(t)` |
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see: inflow_conversion_factor |
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min_storage_level : numeric (iterable or scalar), :math:`c_{min}(t)` |
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The normed minimum storage content as fraction of the |
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nominal storage capacity or the capacity that has been invested into |
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(between 0 and 1). |
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To set different values in every time step use a sequence. |
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max_storage_level : numeric (iterable or scalar), :math:`c_{max}(t)` |
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see: min_storage_level |
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storage_costs : numeric (iterable or scalar), :math:`c_{storage}(t)` |
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Cost (per energy) for having energy in the storage, starting from |
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time point :math:`t_{1}`. (:math:`t_{0}` is left out to avoid counting |
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it twice if balanced=True.) |
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lifetime_inflow : int, :math:`n_{in}` |
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Determine the lifetime of an inflow; only applicable for multi-period |
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models which can invest in storage capacity and have an |
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invest_relation_input_capacity defined |
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lifetime_outflow : int, :math:`n_{in}` |
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Determine the lifetime of an outflow; only applicable for multi-period |
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models which can invest in storage capacity and have an |
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invest_relation_output_capacity defined |
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Notes |
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----- |
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The following sets, variables, constraints and objective parts are created |
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* :py:class:`~oemof.solph.components._generic_storage.GenericStorageBlock` |
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(if no Investment object present) |
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* :py:class:`~oemof.solph.components._generic_storage.GenericInvestmentStorageBlock` |
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(if Investment object present) |
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Examples |
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-------- |
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Basic usage examples of the GenericStorage with a random selection of |
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attributes. See the Flow class for all Flow attributes. |
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>>> from oemof import solph |
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>>> my_bus = solph.buses.Bus('my_bus') |
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>>> my_storage = solph.components.GenericStorage( |
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... label='storage', |
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... nominal_capacity=1000, |
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... inputs={my_bus: solph.flows.Flow(nominal_capacity=200, variable_costs=10)}, |
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... outputs={my_bus: solph.flows.Flow(nominal_capacity=200)}, |
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... loss_rate=0.01, |
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... initial_storage_level=0, |
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... max_storage_level = 0.9, |
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... inflow_conversion_factor=0.9, |
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... outflow_conversion_factor=0.93) |
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>>> my_investment_storage = solph.components.GenericStorage( |
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... label='storage', |
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... nominal_capacity=solph.Investment(ep_costs=50), |
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... inputs={my_bus: solph.flows.Flow(nominal_capacity=solph.Investment())}, |
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... outputs={my_bus: solph.flows.Flow(nominal_capacity=solph.Investment())}, |
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... loss_rate=0.02, |
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... initial_storage_level=None, |
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... invest_relation_input_capacity=1/6, |
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... invest_relation_output_capacity=1/6, |
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... inflow_conversion_factor=1, |
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... outflow_conversion_factor=0.8) |
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""" # noqa: E501 |
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def __init__( |
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self, |
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label=None, |
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inputs=None, |
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outputs=None, |
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parent_node=None, |
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nominal_capacity=None, |
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nominal_storage_capacity=None, # Can be removed for versions >= v0.7 |
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initial_storage_level=None, |
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invest_relation_input_output=None, |
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invest_relation_input_capacity=None, |
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invest_relation_output_capacity=None, |
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min_storage_level=0, |
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max_storage_level=1, |
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balanced=True, |
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loss_rate=0, |
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fixed_losses_relative=0, |
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fixed_losses_absolute=0, |
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inflow_conversion_factor=1, |
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outflow_conversion_factor=1, |
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fixed_costs=0, |
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storage_costs=None, |
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lifetime_inflow=None, |
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lifetime_outflow=None, |
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custom_attributes=None, |
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): |
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if inputs is None: |
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inputs = {} |
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if outputs is None: |
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outputs = {} |
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if custom_attributes is None: |
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custom_attributes = {} |
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super().__init__( |
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label, |
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inputs=inputs, |
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outputs=outputs, |
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parent_node=parent_node, |
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custom_properties=custom_attributes, |
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) |
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# --- BEGIN: The following code can be removed for versions >= v0.7 --- |
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if nominal_storage_capacity is not None: |
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msg = ( |
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"For backward compatibility," |
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+ " the option nominal_storage_capacity overwrites the option" |
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+ " nominal_capacity." |
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+ " Both options cannot be set at the same time." |
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) |
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if nominal_capacity is not None: |
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raise AttributeError(msg) |
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else: |
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warn(msg, FutureWarning) |
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nominal_capacity = nominal_storage_capacity |
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# --- END --- |
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self.nominal_storage_capacity = None |
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self.investment = None |
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self._invest_group = False |
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self.invest_relation_input_output = sequence( |
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invest_relation_input_output |
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) |
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self.invest_relation_input_capacity = sequence( |
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invest_relation_input_capacity |
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) |
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self.invest_relation_output_capacity = sequence( |
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invest_relation_output_capacity |
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) |
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if isinstance(nominal_capacity, numbers.Real): |
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self.nominal_storage_capacity = nominal_capacity |
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elif isinstance(nominal_capacity, Investment): |
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self.investment = nominal_capacity |
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self._invest_group = True |
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self.initial_storage_level = initial_storage_level |
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self.balanced = balanced |
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self.loss_rate = sequence(loss_rate) |
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self.fixed_losses_relative = sequence(fixed_losses_relative) |
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self.fixed_losses_absolute = sequence(fixed_losses_absolute) |
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self.inflow_conversion_factor = sequence(inflow_conversion_factor) |
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self.outflow_conversion_factor = sequence(outflow_conversion_factor) |
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self.max_storage_level = sequence(max_storage_level) |
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self.min_storage_level = sequence(min_storage_level) |
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self.fixed_costs = sequence(fixed_costs) |
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self.storage_costs = sequence(storage_costs) |
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self.lifetime_inflow = lifetime_inflow |
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self.lifetime_outflow = lifetime_outflow |
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# Check number of flows. |
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self._check_number_of_flows() |
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# Check for infeasible invest_relations |
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self._check_invest_relations() |
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# Check for infeasible parameter combinations |
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self._check_infeasible_parameter_combinations() |
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def _check_number_of_flows(self): |
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"""Ensure that there is only one inflow and outflow to the storage""" |
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msg = "Only one {0} flow allowed in the GenericStorage {1}." |
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check_node_object_for_missing_attribute(self, "inputs") |
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check_node_object_for_missing_attribute(self, "outputs") |
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if len(self.inputs) > 1: |
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raise AttributeError(msg.format("input", self.label)) |
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if len(self.outputs) > 1: |
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raise AttributeError(msg.format("output", self.label)) |
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def _check_input_for_investment(self): |
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"""Checks the input flow for an investment object. For sanity, |
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this should be executed after _check_number_of_flows()""" |
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for flow in self.inputs.values(): |
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is_investment = isinstance(flow.investment, Investment) |
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return is_investment |
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def _check_output_for_investment(self): |
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"""Checks the output flow for an investment object. For sanity, |
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this should be executed after _check_number_of_flows()""" |
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for flow in self.outputs.values(): |
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is_investment = isinstance(flow.investment, Investment) |
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return is_investment |
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def _check_storage_for_investment(self): |
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"""Checks the storage for an investment object (i.e. if investment |
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into the capacity is possible)""" |
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return isinstance(self.investment, Investment) |
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def _check_invest_relations(self): |
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"""Checks if the passed invest_relation keywords fit the |
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passed Investment objects""" |
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if self.invest_relation_input_capacity[0] is not None: |
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if not self._check_input_for_investment(): |
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msg = ( |
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"The input flow needs to have an Investment object " |
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"if `invest_relation_input_capacity` is set." |
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) |
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raise AttributeError(msg) |
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if not self._check_storage_for_investment(): |
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msg = ( |
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298
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"If `invest_relation_input_capacity` is set, " |
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299
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"`nominal_capacity` needs to be an Investment " |
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300
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"object as well." |
|
301
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) |
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raise AttributeError(msg) |
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self._invest_group = True |
|
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if self.invest_relation_output_capacity[0] is not None: |
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if not self._check_output_for_investment(): |
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306
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msg = ( |
|
307
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"The output flow needs to have an Investment object " |
|
308
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"if `invest_relation_output_capacity` is set." |
|
309
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) |
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310
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raise AttributeError(msg) |
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311
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if not self._check_storage_for_investment(): |
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312
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msg = ( |
|
313
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"If `invest_relation_output_capacity` is set, " |
|
314
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"`nominal_capacity` needs to be an Investment " |
|
315
|
|
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"object as well." |
|
316
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|
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) |
|
317
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raise AttributeError(msg) |
|
318
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self._invest_group = True |
|
319
|
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if self.invest_relation_input_output[0] is not None: |
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320
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if not self._check_input_for_investment(): |
|
321
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msg = ( |
|
322
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"The input flow needs to have an Investment object " |
|
323
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|
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"if `invest_relation_input_output` is set." |
|
324
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) |
|
325
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raise AttributeError(msg) |
|
326
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if not self._check_output_for_investment(): |
|
327
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|
msg = ( |
|
328
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|
"The output flow needs to have an Investment object " |
|
329
|
|
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"if `invest_relation_input_output` is set." |
|
330
|
|
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) |
|
331
|
|
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raise AttributeError(msg) |
|
332
|
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|
333
|
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def _check_infeasible_parameter_combinations(self): |
|
334
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|
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"""Check for infeasible parameter combinations and raise error""" |
|
335
|
|
|
if self.initial_storage_level is not None: |
|
336
|
|
|
if ( |
|
337
|
|
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self.initial_storage_level < self.min_storage_level[0] |
|
338
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or self.initial_storage_level > self.max_storage_level[0] |
|
339
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|
): |
|
340
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|
|
e1 = ( |
|
341
|
|
|
"initial_storage_level must be greater or equal to " |
|
342
|
|
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"min_storage_level and smaller or equal to " |
|
343
|
|
|
"max_storage_level." |
|
344
|
|
|
) |
|
345
|
|
|
raise ValueError(e1) |
|
346
|
|
|
"""Raise errors for infeasible investment attribute combinations""" |
|
347
|
|
|
if ( |
|
348
|
|
|
self.invest_relation_input_output[0] is not None |
|
349
|
|
|
and self.invest_relation_output_capacity[0] is not None |
|
350
|
|
|
and self.invest_relation_input_capacity[0] is not None |
|
351
|
|
|
): |
|
352
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|
|
e2 = ( |
|
353
|
|
|
"Overdetermined. Three investment object will be coupled" |
|
354
|
|
|
"with three constraints. Set one invest relation to 'None'." |
|
355
|
|
|
) |
|
356
|
|
|
raise AttributeError(e2) |
|
357
|
|
|
if ( |
|
358
|
|
|
self.investment |
|
359
|
|
|
and self.fixed_losses_absolute.max() != 0 |
|
360
|
|
|
and self.investment.existing == 0 |
|
361
|
|
|
and self.investment.minimum.min() == 0 |
|
362
|
|
|
): |
|
363
|
|
|
e3 = ( |
|
364
|
|
|
"With fixed_losses_absolute > 0, either investment.existing " |
|
365
|
|
|
"or investment.minimum has to be non-zero." |
|
366
|
|
|
) |
|
367
|
|
|
raise AttributeError(e3) |
|
368
|
|
|
|
|
369
|
|
|
def constraint_group(self): |
|
370
|
|
|
if self._invest_group is True: |
|
371
|
|
|
return GenericInvestmentStorageBlock |
|
372
|
|
|
else: |
|
373
|
|
|
return GenericStorageBlock |
|
374
|
|
|
|
|
375
|
|
|
|
|
376
|
|
|
class GenericStorageBlock(ScalarBlock): |
|
377
|
|
|
r"""Storage without an :class:`.Investment` object. |
|
378
|
|
|
|
|
379
|
|
|
**The following sets are created:** (-> see basic sets at |
|
380
|
|
|
:class:`.Model` ) |
|
381
|
|
|
|
|
382
|
|
|
STORAGES |
|
383
|
|
|
A set with all :py:class:`~.GenericStorage` objects, which do not have an |
|
384
|
|
|
:attr:`investment` of type :class:`.Investment`. |
|
385
|
|
|
|
|
386
|
|
|
STORAGES_BALANCED |
|
387
|
|
|
A set of all :py:class:`~.GenericStorage` objects, with 'balanced' attribute set |
|
388
|
|
|
to True. |
|
389
|
|
|
|
|
390
|
|
|
STORAGES_WITH_INVEST_FLOW_REL |
|
391
|
|
|
A set with all :py:class:`~.GenericStorage` objects with two investment |
|
392
|
|
|
flows coupled with the 'invest_relation_input_output' attribute. |
|
393
|
|
|
|
|
394
|
|
|
**The following variables are created:** |
|
395
|
|
|
|
|
396
|
|
|
storage_content |
|
397
|
|
|
Storage content for every storage and timestep. The value for the |
|
398
|
|
|
storage content at the beginning is set by the parameter |
|
399
|
|
|
`initial_storage_level` or not set if `initial_storage_level` is None. |
|
400
|
|
|
The variable of storage s and timestep t can be accessed by: |
|
401
|
|
|
`om.GenericStorageBlock.storage_content[s, t]` |
|
402
|
|
|
|
|
403
|
|
|
intra_storage_delta |
|
404
|
|
|
Storage content for every storage and timestep of typical periods |
|
405
|
|
|
(only used in TSAM-mode). The variable of storage s and timestep t can |
|
406
|
|
|
be accessed by: `om.GenericStorageBlock.intra_storage_delta[s, k, t]` |
|
407
|
|
|
|
|
408
|
|
|
**The following constraints are created:** |
|
409
|
|
|
|
|
410
|
|
|
Set storage_content of last time step to one at t=0 if balanced == True |
|
411
|
|
|
.. math:: |
|
412
|
|
|
E(t_{last}) = E(-1) |
|
413
|
|
|
|
|
414
|
|
|
Storage losses :attr:`om.Storage.losses[n, t]` |
|
415
|
|
|
.. math:: E_{loss}(t) = &E(t-1) \cdot |
|
416
|
|
|
1 - (1 - \beta(t))^{\tau(t)/(t_u)} \\ |
|
417
|
|
|
&- \gamma(t)\cdot E_{nom} \cdot {\tau(t)/(t_u)}\\ |
|
418
|
|
|
&- \delta(t) \cdot {\tau(t)/(t_u)} |
|
419
|
|
|
|
|
420
|
|
|
Storage balance :attr:`om.Storage.balance[n, t]` |
|
421
|
|
|
.. math:: E(t) = &E(t-1) - E_{loss}(t)\\ |
|
422
|
|
|
&- \frac{\dot{E}_o(p, t)}{\eta_o(t)} \cdot \tau(t)\\ |
|
423
|
|
|
&+ \dot{E}_i(p, t) \cdot \eta_i(t) \cdot \tau(t) |
|
424
|
|
|
|
|
425
|
|
|
Connect the invest variables of the input and the output flow. |
|
426
|
|
|
.. math:: |
|
427
|
|
|
InvestmentFlowBlock.invest(source(n), n, p) + existing = \\ |
|
428
|
|
|
(InvestmentFlowBlock.invest(n, target(n), p) + existing) \\ |
|
429
|
|
|
* invest\_relation\_input\_output(n) \\ |
|
430
|
|
|
\forall n \in \textrm{INVEST\_REL\_IN\_OUT} \\ |
|
431
|
|
|
\forall p \in \textrm{PERIODS} |
|
432
|
|
|
|
|
433
|
|
|
|
|
434
|
|
|
|
|
435
|
|
|
=========================== ======================= ========= |
|
436
|
|
|
symbol explanation attribute |
|
437
|
|
|
=========================== ======================= ========= |
|
438
|
|
|
:math:`E(t)` energy currently stored `storage_content` |
|
439
|
|
|
:math:`E_{nom}` nominal capacity of `nominal_storage_capacity` |
|
440
|
|
|
the energy storage |
|
441
|
|
|
:math:`c(-1)` state before `initial_storage_level` |
|
442
|
|
|
initial time step |
|
443
|
|
|
:math:`c_{min}(t)` minimum allowed storage `min_storage_level[t]` |
|
444
|
|
|
:math:`c_{max}(t)` maximum allowed storage `max_storage_level[t]` |
|
445
|
|
|
:math:`\beta(t)` fraction of lost energy `loss_rate[t]` |
|
446
|
|
|
as share of |
|
447
|
|
|
:math:`E(t)` per hour |
|
448
|
|
|
:math:`\gamma(t)` fixed loss of energy `fixed_losses_relative[t]` |
|
449
|
|
|
per hour relative to |
|
450
|
|
|
:math:`E_{nom}` |
|
451
|
|
|
:math:`\delta(t)` absolute fixed loss `fixed_losses_absolute[t]` |
|
452
|
|
|
of energy per hour |
|
453
|
|
|
:math:`\dot{E}_i(t)` energy flowing in `inputs` |
|
454
|
|
|
:math:`\dot{E}_o(t)` energy flowing out `outputs` |
|
455
|
|
|
:math:`\eta_i(t)` conversion factor `inflow_conversion_factor[t]` |
|
456
|
|
|
(i.e. efficiency) |
|
457
|
|
|
when storing energy |
|
458
|
|
|
:math:`\eta_o(t)` conversion factor when `outflow_conversion_factor[t]` |
|
459
|
|
|
(i.e. efficiency) |
|
460
|
|
|
taking stored energy |
|
461
|
|
|
:math:`\tau(t)` duration of time step |
|
462
|
|
|
:math:`t_u` time unit of losses |
|
463
|
|
|
:math:`\beta(t)`, |
|
464
|
|
|
:math:`\gamma(t)` |
|
465
|
|
|
:math:`\delta(t)` and |
|
466
|
|
|
timeincrement |
|
467
|
|
|
:math:`\tau(t)` |
|
468
|
|
|
:math:`c_{storage}(t)` costs of having `storage_costs` |
|
469
|
|
|
energy stored |
|
470
|
|
|
=========================== ======================= ========= |
|
471
|
|
|
|
|
472
|
|
|
**The following parts of the objective function are created:** |
|
473
|
|
|
|
|
474
|
|
|
* :attr: `storage_costs` not 0 |
|
475
|
|
|
|
|
476
|
|
|
.. math:: |
|
477
|
|
|
\sum_{t \in \textrm{TIMEPOINTS} > 0} c_{storage}(t) \cdot E(t) |
|
478
|
|
|
|
|
479
|
|
|
* :attr:`fixed_costs` not 0 |
|
480
|
|
|
|
|
481
|
|
|
.. math:: |
|
482
|
|
|
\displaystyle \sum_{pp=0}^{year_{max}} E_{nom} |
|
483
|
|
|
\cdot c_{fixed}(pp) |
|
484
|
|
|
|
|
485
|
|
|
where :math:`year_{max}` denotes the last year of the optimization |
|
486
|
|
|
horizon, i.e. at the end of the last period. |
|
487
|
|
|
|
|
488
|
|
|
""" # noqa: E501 |
|
489
|
|
|
|
|
490
|
|
|
CONSTRAINT_GROUP = True |
|
491
|
|
|
|
|
492
|
|
|
def __init__(self, *args, **kwargs): |
|
493
|
|
|
super().__init__(*args, **kwargs) |
|
494
|
|
|
|
|
495
|
|
|
def _create(self, group=None): |
|
496
|
|
|
""" |
|
497
|
|
|
Parameters |
|
498
|
|
|
---------- |
|
499
|
|
|
group : list |
|
500
|
|
|
List containing storage objects. |
|
501
|
|
|
e.g. groups=[storage1, storage2,..] |
|
502
|
|
|
""" |
|
503
|
|
|
m = self.parent_block() |
|
504
|
|
|
|
|
505
|
|
|
if group is None: |
|
506
|
|
|
return None |
|
507
|
|
|
|
|
508
|
|
|
i = {n: [i for i in n.inputs][0] for n in group} |
|
509
|
|
|
o = {n: [o for o in n.outputs][0] for n in group} |
|
510
|
|
|
|
|
511
|
|
|
# ************* SETS ********************************* |
|
512
|
|
|
|
|
513
|
|
|
self.STORAGES = Set(initialize=[n for n in group]) |
|
514
|
|
|
|
|
515
|
|
|
self.STORAGES_BALANCED = Set( |
|
516
|
|
|
initialize=[n for n in group if n.balanced is True] |
|
517
|
|
|
) |
|
518
|
|
|
|
|
519
|
|
|
self.STORAGES_INITITAL_LEVEL = Set( |
|
520
|
|
|
initialize=[ |
|
521
|
|
|
n for n in group if n.initial_storage_level is not None |
|
522
|
|
|
] |
|
523
|
|
|
) |
|
524
|
|
|
|
|
525
|
|
|
self.STORAGES_WITH_INVEST_FLOW_REL = Set( |
|
526
|
|
|
initialize=[ |
|
527
|
|
|
n |
|
528
|
|
|
for n in group |
|
529
|
|
|
if n.invest_relation_input_output[0] is not None |
|
530
|
|
|
] |
|
531
|
|
|
) |
|
532
|
|
|
|
|
533
|
|
|
# ************* VARIABLES ***************************** |
|
534
|
|
|
|
|
535
|
|
|
def _storage_content_bound_rule(block, n, t): |
|
536
|
|
|
""" |
|
537
|
|
|
Rule definition for bounds of storage_content variable of |
|
538
|
|
|
storage n in timestep t. |
|
539
|
|
|
""" |
|
540
|
|
|
bounds = ( |
|
541
|
|
|
n.nominal_storage_capacity * n.min_storage_level[t], |
|
542
|
|
|
n.nominal_storage_capacity * n.max_storage_level[t], |
|
543
|
|
|
) |
|
544
|
|
|
return bounds |
|
545
|
|
|
|
|
546
|
|
|
if not m.TSAM_MODE: |
|
547
|
|
|
self.storage_content = Var( |
|
548
|
|
|
self.STORAGES, m.TIMEPOINTS, bounds=_storage_content_bound_rule |
|
549
|
|
|
) |
|
550
|
|
|
|
|
551
|
|
|
self.storage_losses = Var(self.STORAGES, m.TIMESTEPS) |
|
552
|
|
|
|
|
553
|
|
|
# set the initial storage content |
|
554
|
|
|
# ToDo: More elegant code possible? |
|
555
|
|
|
for n in group: |
|
556
|
|
|
if n.initial_storage_level is not None: |
|
557
|
|
|
self.storage_content[n, 0] = ( |
|
558
|
|
|
n.initial_storage_level * n.nominal_storage_capacity |
|
559
|
|
|
) |
|
560
|
|
|
self.storage_content[n, 0].fix() |
|
561
|
|
|
else: |
|
562
|
|
|
# called "inter" in https://doi.org/10.1016/j.apenergy.2018.01.023 |
|
563
|
|
|
self.inter_storage_content = Var( |
|
564
|
|
|
self.STORAGES, m.CLUSTERS_OFFSET, within=NonNegativeReals |
|
565
|
|
|
) |
|
566
|
|
|
# called "intra" in https://doi.org/10.1016/j.apenergy.2018.01.023 |
|
567
|
|
|
self.intra_storage_delta = Var( |
|
568
|
|
|
self.STORAGES, m.TIMEINDEX_TYPICAL_CLUSTER_OFFSET |
|
569
|
|
|
) |
|
570
|
|
|
# set the initial intra storage content |
|
571
|
|
|
# first timestep in intra storage is always zero |
|
572
|
|
|
for n in group: |
|
573
|
|
|
for p, k in m.TYPICAL_CLUSTERS: |
|
574
|
|
|
self.intra_storage_delta[n, p, k, 0] = 0 |
|
575
|
|
|
self.intra_storage_delta[n, p, k, 0].fix() |
|
576
|
|
|
if n.initial_storage_level is not None: |
|
577
|
|
|
self.inter_storage_content[n, 0] = ( |
|
578
|
|
|
n.initial_storage_level * n.nominal_storage_capacity |
|
579
|
|
|
) |
|
580
|
|
|
self.inter_storage_content[n, 0].fix() |
|
581
|
|
|
# ************* Constraints *************************** |
|
582
|
|
|
|
|
583
|
|
View Code Duplication |
def _storage_inter_minimum_level_rule(block): |
|
|
|
|
|
|
584
|
|
|
# See FINE implementation at |
|
585
|
|
|
# https://github.com/FZJ-IEK3-VSA/FINE/blob/ |
|
586
|
|
|
# 57ec32561fb95e746c505760bd0d61c97d2fd2fb/FINE/storage.py#L1329 |
|
587
|
|
|
for n in self.STORAGES: |
|
588
|
|
|
for p, i, g in m.TIMEINDEX_CLUSTER: |
|
589
|
|
|
t = m.get_timestep_from_tsam_timestep(p, i, g) |
|
590
|
|
|
lhs = n.nominal_storage_capacity * n.min_storage_level[t] |
|
591
|
|
|
k = m.es.tsa_parameters[p]["order"][i] |
|
592
|
|
|
tk = m.get_timestep_from_tsam_timestep(p, k, g) |
|
593
|
|
|
inter_i = ( |
|
594
|
|
|
sum( |
|
595
|
|
|
len(m.es.tsa_parameters[ip]["order"]) |
|
596
|
|
|
for ip in range(p) |
|
597
|
|
|
) |
|
598
|
|
|
+ i |
|
599
|
|
|
) |
|
600
|
|
|
rhs = ( |
|
601
|
|
|
self.inter_storage_content[n, inter_i] |
|
602
|
|
|
* (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk]) |
|
603
|
|
|
+ self.intra_storage_delta[n, p, k, g] |
|
604
|
|
|
) |
|
605
|
|
|
self.storage_inter_minimum_level.add( |
|
606
|
|
|
(n, p, i, g), lhs <= rhs |
|
607
|
|
|
) |
|
608
|
|
|
|
|
609
|
|
|
if m.TSAM_MODE: |
|
610
|
|
|
self.storage_inter_minimum_level = Constraint( |
|
611
|
|
|
self.STORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True |
|
612
|
|
|
) |
|
613
|
|
|
|
|
614
|
|
|
self.storage_inter_minimum_level_build = BuildAction( |
|
615
|
|
|
rule=_storage_inter_minimum_level_rule |
|
616
|
|
|
) |
|
617
|
|
|
|
|
618
|
|
View Code Duplication |
def _storage_inter_maximum_level_rule(block): |
|
|
|
|
|
|
619
|
|
|
for n in self.STORAGES: |
|
620
|
|
|
for p, i, g in m.TIMEINDEX_CLUSTER: |
|
621
|
|
|
t = m.get_timestep_from_tsam_timestep(p, i, g) |
|
622
|
|
|
k = m.es.tsa_parameters[p]["order"][i] |
|
623
|
|
|
tk = m.get_timestep_from_tsam_timestep(p, k, g) |
|
624
|
|
|
inter_i = ( |
|
625
|
|
|
sum( |
|
626
|
|
|
len(m.es.tsa_parameters[ip]["order"]) |
|
627
|
|
|
for ip in range(p) |
|
628
|
|
|
) |
|
629
|
|
|
+ i |
|
630
|
|
|
) |
|
631
|
|
|
lhs = ( |
|
632
|
|
|
self.inter_storage_content[n, inter_i] |
|
633
|
|
|
* (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk]) |
|
634
|
|
|
+ self.intra_storage_delta[n, p, k, g] |
|
635
|
|
|
) |
|
636
|
|
|
rhs = n.nominal_storage_capacity * n.max_storage_level[t] |
|
637
|
|
|
self.storage_inter_maximum_level.add( |
|
638
|
|
|
(n, p, i, g), lhs <= rhs |
|
639
|
|
|
) |
|
640
|
|
|
|
|
641
|
|
|
if m.TSAM_MODE: |
|
642
|
|
|
self.storage_inter_maximum_level = Constraint( |
|
643
|
|
|
self.STORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True |
|
644
|
|
|
) |
|
645
|
|
|
|
|
646
|
|
|
self.storage_inter_maximum_level_build = BuildAction( |
|
647
|
|
|
rule=_storage_inter_maximum_level_rule |
|
648
|
|
|
) |
|
649
|
|
|
|
|
650
|
|
|
def _storage_losses_rule(block, n, t): |
|
651
|
|
|
expr = block.storage_content[n, t] * ( |
|
652
|
|
|
1 - (1 - n.loss_rate[t]) ** m.timeincrement[t] |
|
653
|
|
|
) |
|
654
|
|
|
expr += ( |
|
655
|
|
|
n.fixed_losses_relative[t] |
|
656
|
|
|
* n.nominal_storage_capacity |
|
657
|
|
|
* m.timeincrement[t] |
|
658
|
|
|
) |
|
659
|
|
|
expr += n.fixed_losses_absolute[t] * m.timeincrement[t] |
|
660
|
|
|
|
|
661
|
|
|
return expr == block.storage_losses[n, t] |
|
662
|
|
|
|
|
663
|
|
|
if not m.TSAM_MODE: |
|
664
|
|
|
self.losses = Constraint( |
|
665
|
|
|
self.STORAGES, m.TIMESTEPS, rule=_storage_losses_rule |
|
666
|
|
|
) |
|
667
|
|
|
|
|
668
|
|
|
def _storage_balance_rule(block, n, t): |
|
669
|
|
|
""" |
|
670
|
|
|
Rule definition for the storage balance of every storage n and |
|
671
|
|
|
every timestep. |
|
672
|
|
|
""" |
|
673
|
|
|
expr = block.storage_content[n, t] |
|
674
|
|
|
expr -= block.storage_losses[n, t] |
|
675
|
|
|
expr += ( |
|
676
|
|
|
m.flow[i[n], n, t] * n.inflow_conversion_factor[t] |
|
|
|
|
|
|
677
|
|
|
) * m.timeincrement[t] |
|
678
|
|
|
expr -= ( |
|
679
|
|
|
m.flow[n, o[n], t] / n.outflow_conversion_factor[t] |
|
|
|
|
|
|
680
|
|
|
) * m.timeincrement[t] |
|
681
|
|
|
return expr == block.storage_content[n, t + 1] |
|
682
|
|
|
|
|
683
|
|
View Code Duplication |
def _intra_storage_balance_rule(block, n, p, k, g): |
|
|
|
|
|
|
684
|
|
|
""" |
|
685
|
|
|
Rule definition for the storage balance of every storage n and |
|
686
|
|
|
every timestep. |
|
687
|
|
|
""" |
|
688
|
|
|
t = m.get_timestep_from_tsam_timestep(p, k, g) |
|
689
|
|
|
expr = 0 |
|
690
|
|
|
expr += block.intra_storage_delta[n, p, k, g + 1] |
|
691
|
|
|
expr += ( |
|
692
|
|
|
-block.intra_storage_delta[n, p, k, g] |
|
693
|
|
|
* (1 - n.loss_rate[t]) ** m.timeincrement[t] |
|
694
|
|
|
) |
|
695
|
|
|
expr += ( |
|
696
|
|
|
n.fixed_losses_relative[t] |
|
697
|
|
|
* n.nominal_storage_capacity |
|
698
|
|
|
* m.timeincrement[t] |
|
699
|
|
|
) |
|
700
|
|
|
expr += n.fixed_losses_absolute[t] * m.timeincrement[t] |
|
701
|
|
|
expr += ( |
|
702
|
|
|
-m.flow[i[n], n, t] * n.inflow_conversion_factor[t] |
|
|
|
|
|
|
703
|
|
|
) * m.timeincrement[t] |
|
704
|
|
|
expr += ( |
|
705
|
|
|
m.flow[n, o[n], t] / n.outflow_conversion_factor[t] |
|
|
|
|
|
|
706
|
|
|
) * m.timeincrement[t] |
|
707
|
|
|
return expr == 0 |
|
708
|
|
|
|
|
709
|
|
|
if not m.TSAM_MODE: |
|
710
|
|
|
self.balance = Constraint( |
|
711
|
|
|
self.STORAGES, m.TIMESTEPS, rule=_storage_balance_rule |
|
712
|
|
|
) |
|
713
|
|
|
else: |
|
714
|
|
|
self.intra_balance = Constraint( |
|
715
|
|
|
self.STORAGES, |
|
716
|
|
|
m.TIMEINDEX_TYPICAL_CLUSTER, |
|
717
|
|
|
rule=_intra_storage_balance_rule, |
|
718
|
|
|
) |
|
719
|
|
|
|
|
720
|
|
|
def _inter_storage_balance_rule(block, n, i): |
|
721
|
|
|
""" |
|
722
|
|
|
Rule definition for the storage balance of every storage n and |
|
723
|
|
|
every timestep. |
|
724
|
|
|
""" |
|
725
|
|
|
ii = 0 |
|
726
|
|
|
for p in m.PERIODS: |
|
727
|
|
|
ii += len(m.es.tsa_parameters[p]["order"]) |
|
728
|
|
|
if ii > i: |
|
729
|
|
|
ii -= len(m.es.tsa_parameters[p]["order"]) |
|
730
|
|
|
ii = i - ii |
|
731
|
|
|
break |
|
732
|
|
|
|
|
733
|
|
|
k = m.es.tsa_parameters[p]["order"][ii] |
|
|
|
|
|
|
734
|
|
|
|
|
735
|
|
|
# Calculate inter losses over whole typical period |
|
736
|
|
|
t0 = m.get_timestep_from_tsam_timestep(p, k, 0) |
|
737
|
|
|
losses = math.prod( |
|
738
|
|
|
( |
|
739
|
|
|
(1 - n.loss_rate[t0 + s]) |
|
740
|
|
|
** m.es.tsa_parameters[p]["segments"][(k, s)] |
|
741
|
|
|
if "segments" in m.es.tsa_parameters[p] |
|
742
|
|
|
else 1 - n.loss_rate[t0 + s] |
|
743
|
|
|
) |
|
744
|
|
|
for s in range(m.es.tsa_parameters[p]["timesteps"]) |
|
745
|
|
|
) |
|
746
|
|
|
|
|
747
|
|
|
expr = 0 |
|
748
|
|
|
expr += block.inter_storage_content[n, i + 1] |
|
749
|
|
|
expr += -block.inter_storage_content[n, i] * losses |
|
750
|
|
|
expr += -self.intra_storage_delta[ |
|
751
|
|
|
n, p, k, m.es.tsa_parameters[p]["timesteps"] |
|
752
|
|
|
] |
|
753
|
|
|
return expr == 0 |
|
754
|
|
|
|
|
755
|
|
|
if m.TSAM_MODE: |
|
756
|
|
|
self.inter_balance = Constraint( |
|
757
|
|
|
self.STORAGES, |
|
758
|
|
|
m.CLUSTERS, |
|
759
|
|
|
rule=_inter_storage_balance_rule, |
|
760
|
|
|
) |
|
761
|
|
|
|
|
762
|
|
|
def _balanced_storage_rule(block, n): |
|
763
|
|
|
""" |
|
764
|
|
|
Storage content of last time step == initial storage content |
|
765
|
|
|
if balanced. |
|
766
|
|
|
""" |
|
767
|
|
|
return ( |
|
768
|
|
|
block.storage_content[n, m.TIMEPOINTS.at(-1)] |
|
769
|
|
|
== block.storage_content[n, m.TIMEPOINTS.at(1)] |
|
770
|
|
|
) |
|
771
|
|
|
|
|
772
|
|
|
def _balanced_inter_storage_rule(block, n): |
|
773
|
|
|
""" |
|
774
|
|
|
Storage content of last time step == initial storage content |
|
775
|
|
|
if balanced. |
|
776
|
|
|
""" |
|
777
|
|
|
return ( |
|
778
|
|
|
block.inter_storage_content[n, m.CLUSTERS_OFFSET.at(-1)] |
|
779
|
|
|
== block.inter_storage_content[n, m.CLUSTERS_OFFSET.at(1)] |
|
780
|
|
|
) |
|
781
|
|
|
|
|
782
|
|
|
if not m.TSAM_MODE: |
|
783
|
|
|
self.balanced_cstr = Constraint( |
|
784
|
|
|
self.STORAGES_BALANCED, rule=_balanced_storage_rule |
|
785
|
|
|
) |
|
786
|
|
|
else: |
|
787
|
|
|
self.balanced_cstr = Constraint( |
|
788
|
|
|
self.STORAGES_BALANCED, rule=_balanced_inter_storage_rule |
|
789
|
|
|
) |
|
790
|
|
|
|
|
791
|
|
|
def _power_coupled(_): |
|
792
|
|
|
""" |
|
793
|
|
|
Rule definition for constraint to connect the input power |
|
794
|
|
|
and output power |
|
795
|
|
|
""" |
|
796
|
|
|
for n in self.STORAGES_WITH_INVEST_FLOW_REL: |
|
797
|
|
|
for p in m.PERIODS: |
|
798
|
|
|
expr = ( |
|
799
|
|
|
m.InvestmentFlowBlock.total[n, o[n], p] |
|
|
|
|
|
|
800
|
|
|
) * n.invest_relation_input_output[p] == ( |
|
801
|
|
|
m.InvestmentFlowBlock.total[i[n], n, p] |
|
|
|
|
|
|
802
|
|
|
) |
|
803
|
|
|
self.power_coupled.add((n, p), expr) |
|
804
|
|
|
|
|
805
|
|
|
self.power_coupled = Constraint( |
|
806
|
|
|
self.STORAGES_WITH_INVEST_FLOW_REL, m.PERIODS, noruleinit=True |
|
807
|
|
|
) |
|
808
|
|
|
|
|
809
|
|
|
self.power_coupled_build = BuildAction(rule=_power_coupled) |
|
810
|
|
|
|
|
811
|
|
|
def _objective_expression(self): |
|
812
|
|
|
r""" |
|
813
|
|
|
Objective expression for storages with no investment. |
|
814
|
|
|
|
|
815
|
|
|
* Fixed costs (will not have an impact on the actual optimisation). |
|
816
|
|
|
* Variable costs for storage content. |
|
817
|
|
|
""" |
|
818
|
|
|
m = self.parent_block() |
|
819
|
|
|
|
|
820
|
|
|
fixed_costs = 0 |
|
821
|
|
|
|
|
822
|
|
|
for n in self.STORAGES: |
|
823
|
|
|
if valid_sequence(n.fixed_costs, len(m.PERIODS)): |
|
824
|
|
|
fixed_costs += sum( |
|
825
|
|
|
n.nominal_storage_capacity * n.fixed_costs[pp] |
|
826
|
|
|
for pp in range(m.es.end_year_of_optimization) |
|
827
|
|
|
) |
|
828
|
|
|
self.fixed_costs = Expression(expr=fixed_costs) |
|
829
|
|
|
|
|
830
|
|
|
storage_costs = 0 |
|
831
|
|
|
|
|
832
|
|
|
for n in self.STORAGES: |
|
833
|
|
View Code Duplication |
if valid_sequence(n.storage_costs, len(m.TIMESTEPS)): |
|
|
|
|
|
|
834
|
|
|
# We actually want to iterate over all TIMEPOINTS except the |
|
835
|
|
|
# 0th. As integers are used for the index, this is equicalent |
|
836
|
|
|
# to iterating over the TIMESTEPS with one offset. |
|
837
|
|
|
if not m.TSAM_MODE: |
|
838
|
|
|
for t in m.TIMESTEPS: |
|
839
|
|
|
storage_costs += ( |
|
840
|
|
|
self.storage_content[n, t + 1] * n.storage_costs[t] |
|
841
|
|
|
) |
|
842
|
|
|
else: |
|
843
|
|
|
for t in m.TIMESTEPS_ORIGINAL: |
|
844
|
|
|
storage_costs += ( |
|
845
|
|
|
self.storage_content[n, t + 1] |
|
846
|
|
|
* n.storage_costs[t + 1] |
|
847
|
|
|
) |
|
848
|
|
|
|
|
849
|
|
|
self.storage_costs = Expression(expr=storage_costs) |
|
850
|
|
|
self.costs = Expression(expr=storage_costs + fixed_costs) |
|
851
|
|
|
|
|
852
|
|
|
return self.costs |
|
853
|
|
|
|
|
854
|
|
|
|
|
855
|
|
|
class GenericInvestmentStorageBlock(ScalarBlock): |
|
856
|
|
|
r""" |
|
857
|
|
|
Block for all storages with :attr:`Investment` being not None. |
|
858
|
|
|
See :class:`.Investment` for all parameters of the |
|
859
|
|
|
Investment class. |
|
860
|
|
|
|
|
861
|
|
|
**Variables** |
|
862
|
|
|
|
|
863
|
|
|
All Storages are indexed by :math:`n` (denoting the respective storage |
|
864
|
|
|
unit), which is omitted in the following for the sake of convenience. |
|
865
|
|
|
The following variables are created as attributes of |
|
866
|
|
|
:attr:`om.GenericInvestmentStorageBlock`: |
|
867
|
|
|
|
|
868
|
|
|
* :math:`P_i(p, t)` |
|
869
|
|
|
|
|
870
|
|
|
Inflow of the storage |
|
871
|
|
|
(created in :class:`oemof.solph.models.Model`). |
|
872
|
|
|
|
|
873
|
|
|
* :math:`P_o(p, t)` |
|
874
|
|
|
|
|
875
|
|
|
Outflow of the storage |
|
876
|
|
|
(created in :class:`oemof.solph.models.Model`). |
|
877
|
|
|
|
|
878
|
|
|
* :math:`E(t)` |
|
879
|
|
|
|
|
880
|
|
|
Current storage content (Absolute level of stored energy). |
|
881
|
|
|
|
|
882
|
|
|
* :math:`E_{invest}(p)` |
|
883
|
|
|
|
|
884
|
|
|
Invested (nominal) capacity of the storage in period p. |
|
885
|
|
|
|
|
886
|
|
|
* :math:`E_{total}(p)` |
|
887
|
|
|
|
|
888
|
|
|
Total installed (nominal) capacity of the storage in period p. |
|
889
|
|
|
|
|
890
|
|
|
* :math:`E_{old}(p)` |
|
891
|
|
|
|
|
892
|
|
|
Old (nominal) capacity of the storage to be decommissioned in period p. |
|
893
|
|
|
|
|
894
|
|
|
* :math:`E_{old,exo}(p)` |
|
895
|
|
|
|
|
896
|
|
|
Exogenous old (nominal) capacity of the storage to be decommissioned |
|
897
|
|
|
in period p; existing capacity reaching its lifetime. |
|
898
|
|
|
|
|
899
|
|
|
* :math:`E_{old,endo}(p)` |
|
900
|
|
|
|
|
901
|
|
|
Endogenous old (nominal) capacity of the storage to be decommissioned |
|
902
|
|
|
in period p; endgenous investments reaching their lifetime. |
|
903
|
|
|
|
|
904
|
|
|
* :math:`E(-1)` |
|
905
|
|
|
|
|
906
|
|
|
Initial storage content (before timestep 0). |
|
907
|
|
|
Not applicable for a multi-period model. |
|
908
|
|
|
|
|
909
|
|
|
* :math:`b_{invest}(p)` |
|
910
|
|
|
|
|
911
|
|
|
Binary variable for the status of the investment, if |
|
912
|
|
|
:attr:`nonconvex` is `True`. |
|
913
|
|
|
|
|
914
|
|
|
**Constraints** |
|
915
|
|
|
|
|
916
|
|
|
The following constraints are created for all investment storages: |
|
917
|
|
|
|
|
918
|
|
|
Storage balance (Same as for :class:`.GenericStorageBlock`) |
|
919
|
|
|
|
|
920
|
|
|
.. math:: E(t) = &E(t-1) \cdot |
|
921
|
|
|
(1 - \beta(t)) ^{\tau(t)/(t_u)} \\ |
|
922
|
|
|
&- \gamma(t)\cdot (E_{total}(p)) \cdot {\tau(t)/(t_u)}\\ |
|
923
|
|
|
&- \delta(t) \cdot {\tau(t)/(t_u)}\\ |
|
924
|
|
|
&- \frac{\dot{E}_o(p, t))}{\eta_o(t)} \cdot \tau(t) |
|
925
|
|
|
+ \dot{E}_i(p, t) \cdot \eta_i(t) \cdot \tau(t) |
|
926
|
|
|
|
|
927
|
|
|
Total storage capacity (p > 0 for multi-period model only) |
|
928
|
|
|
|
|
929
|
|
|
.. math:: |
|
930
|
|
|
& |
|
931
|
|
|
if \quad p=0:\\ |
|
932
|
|
|
& |
|
933
|
|
|
E_{total}(p) = E_{exist} + E_{invest}(p)\\ |
|
934
|
|
|
&\\ |
|
935
|
|
|
& |
|
936
|
|
|
else:\\ |
|
937
|
|
|
& |
|
938
|
|
|
E_{total}(p) = E_{total}(p-1) + E_{invest}(p) - E_{old}(p)\\ |
|
939
|
|
|
&\\ |
|
940
|
|
|
& |
|
941
|
|
|
\forall p \in \textrm{PERIODS} |
|
942
|
|
|
|
|
943
|
|
|
Old storage capacity (p > 0 for multi-period model only) |
|
944
|
|
|
|
|
945
|
|
|
.. math:: |
|
946
|
|
|
& |
|
947
|
|
|
E_{old}(p) = E_{old,exo}(p) + E_{old,end}(p)\\ |
|
948
|
|
|
&\\ |
|
949
|
|
|
& |
|
950
|
|
|
if \quad p=0:\\ |
|
951
|
|
|
& |
|
952
|
|
|
E_{old,end}(p) = 0\\ |
|
953
|
|
|
&\\ |
|
954
|
|
|
& |
|
955
|
|
|
else \quad if \quad l \leq year(p):\\ |
|
956
|
|
|
& |
|
957
|
|
|
E_{old,end}(p) = E_{invest}(p_{comm})\\ |
|
958
|
|
|
&\\ |
|
959
|
|
|
& |
|
960
|
|
|
else:\\ |
|
961
|
|
|
& |
|
962
|
|
|
E_{old,end}(p)\\ |
|
963
|
|
|
&\\ |
|
964
|
|
|
& |
|
965
|
|
|
if \quad p=0:\\ |
|
966
|
|
|
& |
|
967
|
|
|
E_{old,exo}(p) = 0\\ |
|
968
|
|
|
&\\ |
|
969
|
|
|
& |
|
970
|
|
|
else \quad if \quad l - a \leq year(p):\\ |
|
971
|
|
|
& |
|
972
|
|
|
E_{old,exo}(p) = E_{exist} (*)\\ |
|
973
|
|
|
&\\ |
|
974
|
|
|
& |
|
975
|
|
|
else:\\ |
|
976
|
|
|
& |
|
977
|
|
|
E_{old,exo}(p) = 0\\ |
|
978
|
|
|
&\\ |
|
979
|
|
|
& |
|
980
|
|
|
\forall p \in \textrm{PERIODS} |
|
981
|
|
|
|
|
982
|
|
|
where: |
|
983
|
|
|
|
|
984
|
|
|
* (*) is only performed for the first period the condition is True. |
|
985
|
|
|
A decommissioning flag is then set to True to prevent having falsely |
|
986
|
|
|
added old capacity in future periods. |
|
987
|
|
|
* :math:`year(p)` is the year corresponding to period p |
|
988
|
|
|
* :math:`p_{comm}` is the commissioning period of the storage |
|
989
|
|
|
|
|
990
|
|
|
Depending on the attribute :attr:`nonconvex`, the constraints for the |
|
991
|
|
|
bounds of the decision variable :math:`E_{invest}(p)` are different:\ |
|
992
|
|
|
|
|
993
|
|
|
* :attr:`nonconvex = False` |
|
994
|
|
|
|
|
995
|
|
|
.. math:: |
|
996
|
|
|
& |
|
997
|
|
|
E_{invest, min}(p) \le E_{invest}(p) \le E_{invest, max}(p) \\ |
|
998
|
|
|
& |
|
999
|
|
|
\forall p \in \textrm{PERIODS} |
|
1000
|
|
|
|
|
1001
|
|
|
* :attr:`nonconvex = True` |
|
1002
|
|
|
|
|
1003
|
|
|
.. math:: |
|
1004
|
|
|
& |
|
1005
|
|
|
E_{invest, min}(p) \cdot b_{invest}(p) \le E_{invest}(p)\\ |
|
1006
|
|
|
& |
|
1007
|
|
|
E_{invest}(p) \le E_{invest, max}(p) \cdot b_{invest}(p)\\ |
|
1008
|
|
|
& |
|
1009
|
|
|
\forall p \in \textrm{PERIODS} |
|
1010
|
|
|
|
|
1011
|
|
|
The following constraints are created depending on the attributes of |
|
1012
|
|
|
the :class:`.GenericStorage`: |
|
1013
|
|
|
|
|
1014
|
|
|
* :attr:`initial_storage_level is None`; |
|
1015
|
|
|
not applicable for multi-period model |
|
1016
|
|
|
|
|
1017
|
|
|
Constraint for a variable initial storage content: |
|
1018
|
|
|
|
|
1019
|
|
|
.. math:: |
|
1020
|
|
|
E(-1) \le E_{exist} + E_{invest}(0) |
|
1021
|
|
|
|
|
1022
|
|
|
* :attr:`initial_storage_level is not None`; |
|
1023
|
|
|
not applicable for multi-period model |
|
1024
|
|
|
|
|
1025
|
|
|
An initial value for the storage content is given: |
|
1026
|
|
|
|
|
1027
|
|
|
.. math:: |
|
1028
|
|
|
E(-1) = (E_{invest}(0) + E_{exist}) \cdot c(-1) |
|
1029
|
|
|
|
|
1030
|
|
|
* :attr:`balanced=True`; |
|
1031
|
|
|
not applicable for multi-period model |
|
1032
|
|
|
|
|
1033
|
|
|
The energy content of storage of the first and the last timestep |
|
1034
|
|
|
are set equal: |
|
1035
|
|
|
|
|
1036
|
|
|
.. math:: |
|
1037
|
|
|
E(-1) = E(t_{last}) |
|
1038
|
|
|
|
|
1039
|
|
|
* :attr:`invest_relation_input_capacity is not None` |
|
1040
|
|
|
|
|
1041
|
|
|
Connect the invest variables of the storage and the input flow: |
|
1042
|
|
|
|
|
1043
|
|
|
.. math:: |
|
1044
|
|
|
& |
|
1045
|
|
|
P_{i,total}(p) = |
|
1046
|
|
|
E_{total}(p) \cdot r_{cap,in} \\ |
|
1047
|
|
|
& |
|
1048
|
|
|
\forall p \in \textrm{PERIODS} |
|
1049
|
|
|
|
|
1050
|
|
|
* :attr:`invest_relation_output_capacity is not None` |
|
1051
|
|
|
|
|
1052
|
|
|
Connect the invest variables of the storage and the output flow: |
|
1053
|
|
|
|
|
1054
|
|
|
.. math:: |
|
1055
|
|
|
& |
|
1056
|
|
|
P_{o,total}(p) = |
|
1057
|
|
|
E_{total}(p) \cdot r_{cap,out}\\ |
|
1058
|
|
|
& |
|
1059
|
|
|
\forall p \in \textrm{PERIODS} |
|
1060
|
|
|
|
|
1061
|
|
|
* :attr:`invest_relation_input_output is not None` |
|
1062
|
|
|
|
|
1063
|
|
|
Connect the invest variables of the input and the output flow: |
|
1064
|
|
|
|
|
1065
|
|
|
.. math:: |
|
1066
|
|
|
& |
|
1067
|
|
|
P_{i,total}(p) = |
|
1068
|
|
|
P_{o,total}(p) \cdot r_{in,out}\\ |
|
1069
|
|
|
& |
|
1070
|
|
|
\forall p \in \textrm{PERIODS} |
|
1071
|
|
|
|
|
1072
|
|
|
* :attr:`max_storage_level` |
|
1073
|
|
|
|
|
1074
|
|
|
Rule for upper bound constraint for the storage content: |
|
1075
|
|
|
|
|
1076
|
|
|
.. math:: |
|
1077
|
|
|
& |
|
1078
|
|
|
E(t) \leq E_{total}(p) \cdot c_{max}(t)\\ |
|
1079
|
|
|
& |
|
1080
|
|
|
\forall p, t \in \textrm{TIMEINDEX} |
|
1081
|
|
|
|
|
1082
|
|
|
* :attr:`min_storage_level` |
|
1083
|
|
|
|
|
1084
|
|
|
Rule for lower bound constraint for the storage content: |
|
1085
|
|
|
|
|
1086
|
|
|
.. math:: |
|
1087
|
|
|
& |
|
1088
|
|
|
E(t) \geq E_{total}(p) \cdot c_{min}(t)\\ |
|
1089
|
|
|
& |
|
1090
|
|
|
\forall p, t \in \textrm{TIMEINDEX} |
|
1091
|
|
|
|
|
1092
|
|
|
|
|
1093
|
|
|
**Objective function** |
|
1094
|
|
|
|
|
1095
|
|
|
Objective terms for a standard model and a multi-period model differ |
|
1096
|
|
|
quite strongly. Besides, the part of the objective function added by the |
|
1097
|
|
|
investment storages also depends on whether a convex or nonconvex |
|
1098
|
|
|
investment option is selected. The following parts of the objective |
|
1099
|
|
|
function are created: |
|
1100
|
|
|
|
|
1101
|
|
|
*Standard model* |
|
1102
|
|
|
|
|
1103
|
|
|
* :attr:`nonconvex = False` |
|
1104
|
|
|
|
|
1105
|
|
|
.. math:: |
|
1106
|
|
|
E_{invest}(0) \cdot c_{invest,var}(0) |
|
1107
|
|
|
|
|
1108
|
|
|
* :attr:`nonconvex = True` |
|
1109
|
|
|
|
|
1110
|
|
|
.. math:: |
|
1111
|
|
|
E_{invest}(0) \cdot c_{invest,var}(0) |
|
1112
|
|
|
+ c_{invest,fix}(0) \cdot b_{invest}(0)\\ |
|
1113
|
|
|
|
|
1114
|
|
|
Where 0 denotes the 0th (investment) period since |
|
1115
|
|
|
in a standard model, there is only this one period. |
|
1116
|
|
|
|
|
1117
|
|
|
*Multi-period model* |
|
1118
|
|
|
|
|
1119
|
|
|
* :attr:`nonconvex = False` |
|
1120
|
|
|
|
|
1121
|
|
|
.. math:: |
|
1122
|
|
|
& |
|
1123
|
|
|
E_{invest}(p) \cdot A(c_{invest,var}(p), l, ir) |
|
1124
|
|
|
\cdot \frac {1}{ANF(d, ir)} \cdot DF^{-p}\\ |
|
1125
|
|
|
& |
|
1126
|
|
|
\forall p \in \textrm{PERIODS} |
|
1127
|
|
|
|
|
1128
|
|
|
In case, the remaining lifetime of a storage is greater than 0 and |
|
1129
|
|
|
attribute `use_remaining_value` of the energy system is True, |
|
1130
|
|
|
the difference in value for the investment period compared to the |
|
1131
|
|
|
last period of the optimization horizon is accounted for |
|
1132
|
|
|
as an adder to the investment costs: |
|
1133
|
|
|
|
|
1134
|
|
|
.. math:: |
|
1135
|
|
|
& |
|
1136
|
|
|
E_{invest}(p) \cdot (A(c_{invest,var}(p), l_{r}, ir) - |
|
1137
|
|
|
A(c_{invest,var}(|P|), l_{r}, ir)\\ |
|
1138
|
|
|
& \cdot \frac {1}{ANF(l_{r}, ir)} \cdot DF^{-|P|}\\ |
|
1139
|
|
|
&\\ |
|
1140
|
|
|
& |
|
1141
|
|
|
\forall p \in \textrm{PERIODS} |
|
1142
|
|
|
|
|
1143
|
|
|
* :attr:`nonconvex = True` |
|
1144
|
|
|
|
|
1145
|
|
|
.. math:: |
|
1146
|
|
|
& |
|
1147
|
|
|
(E_{invest}(p) \cdot A(c_{invest,var}(p), l, ir) |
|
1148
|
|
|
\cdot \frac {1}{ANF(d, ir)}\\ |
|
1149
|
|
|
& |
|
1150
|
|
|
+ c_{invest,fix}(p) \cdot b_{invest}(p)) \cdot DF^{-p} \\ |
|
1151
|
|
|
& |
|
1152
|
|
|
\forall p \in \textrm{PERIODS} |
|
1153
|
|
|
|
|
1154
|
|
|
In case, the remaining lifetime of a storage is greater than 0 and |
|
1155
|
|
|
attribute `use_remaining_value` of the energy system is True, |
|
1156
|
|
|
the difference in value for the investment period compared to the |
|
1157
|
|
|
last period of the optimization horizon is accounted for |
|
1158
|
|
|
as an adder to the investment costs: |
|
1159
|
|
|
|
|
1160
|
|
|
.. math:: |
|
1161
|
|
|
& |
|
1162
|
|
|
(E_{invest}(p) \cdot (A(c_{invest,var}(p), l_{r}, ir) - |
|
1163
|
|
|
A(c_{invest,var}(|P|), l_{r}, ir)\\ |
|
1164
|
|
|
& \cdot \frac {1}{ANF(l_{r}, ir)} \cdot DF^{-|P|}\\ |
|
1165
|
|
|
& |
|
1166
|
|
|
+ (c_{invest,fix}(p) - c_{invest,fix}(|P|)) |
|
1167
|
|
|
\cdot b_{invest}(p)) \cdot DF^{-p}\\ |
|
1168
|
|
|
&\\ |
|
1169
|
|
|
& |
|
1170
|
|
|
\forall p \in \textrm{PERIODS} |
|
1171
|
|
|
|
|
1172
|
|
|
* :attr:`fixed_costs` not None for investments |
|
1173
|
|
|
|
|
1174
|
|
|
.. math:: |
|
1175
|
|
|
& |
|
1176
|
|
|
\sum_{pp=year(p)}^{limit_{end}} |
|
1177
|
|
|
E_{invest}(p) \cdot c_{fixed}(pp) \cdot DF^{-pp}) |
|
1178
|
|
|
\cdot DF^{-p}\\ |
|
1179
|
|
|
& |
|
1180
|
|
|
\forall p \in \textrm{PERIODS} |
|
1181
|
|
|
|
|
1182
|
|
|
* :attr:`fixed_costs` not None for existing capacity |
|
1183
|
|
|
|
|
1184
|
|
|
.. math:: |
|
1185
|
|
|
\sum_{pp=0}^{limit_{exo}} E_{exist} \cdot c_{fixed}(pp) |
|
1186
|
|
|
\cdot DF^{-pp} |
|
1187
|
|
|
|
|
1188
|
|
|
where: |
|
1189
|
|
|
|
|
1190
|
|
|
* :math:`A(c_{invest,var}(p), l, ir)` A is the annuity for |
|
1191
|
|
|
investment expenses :math:`c_{invest,var}(p)`, lifetime :math:`l` |
|
1192
|
|
|
and interest rate :math:`ir`. |
|
1193
|
|
|
* :math:`l_{r}` is the remaining lifetime at the end of the |
|
1194
|
|
|
optimization horizon (in case it is greater than 0 and |
|
1195
|
|
|
smaller than the actual lifetime). |
|
1196
|
|
|
* :math:`ANF(d, ir)` is the annuity factor for duration :math:`d` |
|
1197
|
|
|
and interest rate :math:`ir`. |
|
1198
|
|
|
* :math:`d=min\{year_{max} - year(p), l\}` defines the |
|
1199
|
|
|
number of years within the optimization horizon that investment |
|
1200
|
|
|
annuities are accounted for. |
|
1201
|
|
|
* :math:`year(p)` denotes the start year of period :math:`p`. |
|
1202
|
|
|
* :math:`year_{max}` denotes the last year of the optimization |
|
1203
|
|
|
horizon, i.e. at the end of the last period. |
|
1204
|
|
|
* :math:`limit_{end}=min\{year_{max}, year(p) + l\}` is used as an |
|
1205
|
|
|
upper bound to ensure fixed costs for endogenous investments |
|
1206
|
|
|
to occur within the optimization horizon. |
|
1207
|
|
|
* :math:`limit_{exo}=min\{year_{max}, l - a\}` is used as an |
|
1208
|
|
|
upper bound to ensure fixed costs for existing capacities to occur |
|
1209
|
|
|
within the optimization horizon. :math:`a` is the initial age |
|
1210
|
|
|
of an asset. |
|
1211
|
|
|
* :math:`DF=(1+dr)` is the discount factor. |
|
1212
|
|
|
|
|
1213
|
|
|
The annuity / annuity factor hereby is: |
|
1214
|
|
|
|
|
1215
|
|
|
.. math:: |
|
1216
|
|
|
& |
|
1217
|
|
|
A(c_{invest,var}(p), l, ir) = c_{invest,var}(p) \cdot |
|
1218
|
|
|
\frac {(1+ir)^l \cdot ir} {(1+ir)^l - 1}\\ |
|
1219
|
|
|
&\\ |
|
1220
|
|
|
& |
|
1221
|
|
|
ANF(d, ir)=\frac {(1+ir)^d \cdot ir} {(1+ir)^d - 1} |
|
1222
|
|
|
|
|
1223
|
|
|
They are retrieved, using oemof.tools.economics annuity function. The |
|
1224
|
|
|
interest rate :math:`ir` for the annuity is defined as weighted |
|
1225
|
|
|
average costs of capital (wacc) and assumed constant over time. |
|
1226
|
|
|
|
|
1227
|
|
|
The overall summed cost expressions for all *InvestmentFlowBlock* objects |
|
1228
|
|
|
can be accessed by |
|
1229
|
|
|
|
|
1230
|
|
|
* :attr:`om.GenericInvestmentStorageBlock.investment_costs`, |
|
1231
|
|
|
* :attr:`om.GenericInvestmentStorageBlock.fixed_costs` and |
|
1232
|
|
|
* :attr:`om.GenericInvestmentStorageBlock.costs`. |
|
1233
|
|
|
|
|
1234
|
|
|
Their values after optimization can be retrieved by |
|
1235
|
|
|
|
|
1236
|
|
|
* :meth:`om.GenericInvestmentStorageBlock.investment_costs`, |
|
1237
|
|
|
* :attr:`om.GenericInvestmentStorageBlock.period_investment_costs` |
|
1238
|
|
|
(yielding a dict keyed by periods); note: this is not a Pyomo expression, |
|
1239
|
|
|
but calculated, |
|
1240
|
|
|
* :meth:`om.GenericInvestmentStorageBlock.fixed_costs` and |
|
1241
|
|
|
* :meth:`om.GenericInvestmentStorageBlock.costs`. |
|
1242
|
|
|
|
|
1243
|
|
|
.. csv-table:: List of Variables |
|
1244
|
|
|
:header: "symbol", "attribute", "explanation" |
|
1245
|
|
|
:widths: 1, 1, 1 |
|
1246
|
|
|
|
|
1247
|
|
|
":math:`P_i(p, t)`", ":attr:`flow[i[n], n, p, t]`", "Inflow |
|
1248
|
|
|
of the storage" |
|
1249
|
|
|
":math:`P_o(p, t)`", ":attr:`flow[n, o[n], p, t]`", "Outflow |
|
1250
|
|
|
of the storage" |
|
1251
|
|
|
":math:`E(t)`", ":attr:`storage_content[n, t]`", "Current storage |
|
1252
|
|
|
content (current absolute stored energy)" |
|
1253
|
|
|
":math:`E_{loss}(t)`", ":attr:`storage_losses[n, t]`", "Current storage |
|
1254
|
|
|
losses (absolute losses per time step)" |
|
1255
|
|
|
":math:`E_{invest}(p)`", ":attr:`invest[n, p]`", "Invested (nominal) |
|
1256
|
|
|
capacity of the storage" |
|
1257
|
|
|
":math:`E_{old}(p)`", ":attr:`old[n, p]`", " |
|
1258
|
|
|
| Old (nominal) capacity of the storage |
|
1259
|
|
|
| to be decommissioned in period p" |
|
1260
|
|
|
":math:`E_{old,exo}(p)`", ":attr:`old_exo[n, p]`", " |
|
1261
|
|
|
| Old (nominal) capacity of the storage |
|
1262
|
|
|
| to be decommissioned in period p |
|
1263
|
|
|
| which was exogenously given by :math:`E_{exist}`" |
|
1264
|
|
|
":math:`E_{old,end}(p)`", ":attr:`old_end[n, p]`", " |
|
1265
|
|
|
| Old (nominal) capacity of the storage |
|
1266
|
|
|
| to be decommissioned in period p |
|
1267
|
|
|
| which was endogenously determined by :math:`E_{invest}(p_{comm})` |
|
1268
|
|
|
| where :math:`p_{comm}` is the commissioning period" |
|
1269
|
|
|
":math:`E(-1)`", ":attr:`init_cap[n]`", "Initial storage capacity |
|
1270
|
|
|
(before timestep 0)" |
|
1271
|
|
|
":math:`b_{invest}(p)`", ":attr:`invest_status[i, o, p]`", "Binary |
|
1272
|
|
|
variable for the status of investment" |
|
1273
|
|
|
":math:`P_{i,invest}(p)`", " |
|
1274
|
|
|
:attr:`InvestmentFlowBlock.invest[i[n], n, p]`", " |
|
1275
|
|
|
Invested (nominal) inflow (InvestmentFlowBlock)" |
|
1276
|
|
|
":math:`P_{o,invest}`", " |
|
1277
|
|
|
:attr:`InvestmentFlowBlock.invest[n, o[n]]`", " |
|
1278
|
|
|
Invested (nominal) outflow (InvestmentFlowBlock)" |
|
1279
|
|
|
|
|
1280
|
|
|
.. csv-table:: List of Parameters |
|
1281
|
|
|
:header: "symbol", "attribute", "explanation" |
|
1282
|
|
|
:widths: 1, 1, 1 |
|
1283
|
|
|
|
|
1284
|
|
|
":math:`E_{exist}`", "`flows[i, o].investment.existing`", " |
|
1285
|
|
|
Existing storage capacity" |
|
1286
|
|
|
":math:`E_{invest,min}`", "`flows[i, o].investment.minimum`", " |
|
1287
|
|
|
Minimum investment value" |
|
1288
|
|
|
":math:`E_{invest,max}`", "`flows[i, o].investment.maximum`", " |
|
1289
|
|
|
Maximum investment value" |
|
1290
|
|
|
":math:`P_{i,exist}`", "`flows[i[n], n].investment.existing` |
|
1291
|
|
|
", "Existing inflow capacity" |
|
1292
|
|
|
":math:`P_{o,exist}`", "`flows[n, o[n]].investment.existing` |
|
1293
|
|
|
", "Existing outflow capacity" |
|
1294
|
|
|
":math:`c_{invest,var}`", "`flows[i, o].investment.ep_costs` |
|
1295
|
|
|
", "Variable investment costs" |
|
1296
|
|
|
":math:`c_{invest,fix}`", "`flows[i, o].investment.offset`", " |
|
1297
|
|
|
Fix investment costs" |
|
1298
|
|
|
":math:`c_{fixed}`", "`flows[i, o].investment.fixed_costs`", " |
|
1299
|
|
|
Fixed costs; only allowed in multi-period model" |
|
1300
|
|
|
":math:`r_{cap,in}`", ":attr:`invest_relation_input_capacity`", " |
|
1301
|
|
|
Relation of storage capacity and nominal inflow" |
|
1302
|
|
|
":math:`r_{cap,out}`", ":attr:`invest_relation_output_capacity`", " |
|
1303
|
|
|
Relation of storage capacity and nominal outflow" |
|
1304
|
|
|
":math:`r_{in,out}`", ":attr:`invest_relation_input_output`", " |
|
1305
|
|
|
Relation of nominal in- and outflow" |
|
1306
|
|
|
":math:`\beta(t)`", "`loss_rate[t]`", "Fraction of lost energy |
|
1307
|
|
|
as share of :math:`E(t)` per hour" |
|
1308
|
|
|
":math:`\gamma(t)`", "`fixed_losses_relative[t]`", "Fixed loss |
|
1309
|
|
|
of energy relative to :math:`E_{invest} + E_{exist}` per hour" |
|
1310
|
|
|
":math:`\delta(t)`", "`fixed_losses_absolute[t]`", "Absolute |
|
1311
|
|
|
fixed loss of energy per hour" |
|
1312
|
|
|
":math:`\eta_i(t)`", "`inflow_conversion_factor[t]`", " |
|
1313
|
|
|
Conversion factor (i.e. efficiency) when storing energy" |
|
1314
|
|
|
":math:`\eta_o(t)`", "`outflow_conversion_factor[t]`", " |
|
1315
|
|
|
Conversion factor when (i.e. efficiency) taking stored energy" |
|
1316
|
|
|
":math:`c(-1)`", "`initial_storage_level`", "Initial relative |
|
1317
|
|
|
storage content (before timestep 0)" |
|
1318
|
|
|
":math:`c_{max}`", "`flows[i, o].max[t]`", "Normed maximum |
|
1319
|
|
|
value of storage content" |
|
1320
|
|
|
":math:`c_{min}`", "`flows[i, o].min[t]`", "Normed minimum |
|
1321
|
|
|
value of storage content" |
|
1322
|
|
|
":math:`l`", "`flows[i, o].investment.lifetime`", " |
|
1323
|
|
|
Lifetime for investments in storage capacity" |
|
1324
|
|
|
":math:`a`", "`flows[i, o].investment.age`", " |
|
1325
|
|
|
Initial age of existing capacity / energy" |
|
1326
|
|
|
":math:`\tau(t)`", "", "Duration of time step" |
|
1327
|
|
|
":math:`t_u`", "", "Time unit of losses :math:`\beta(t)`, |
|
1328
|
|
|
:math:`\gamma(t)`, :math:`\delta(t)` and timeincrement :math:`\tau(t)`" |
|
1329
|
|
|
|
|
1330
|
|
|
""" |
|
1331
|
|
|
|
|
1332
|
|
|
CONSTRAINT_GROUP = True |
|
1333
|
|
|
|
|
1334
|
|
|
def __init__(self, *args, **kwargs): |
|
1335
|
|
|
super().__init__(*args, **kwargs) |
|
1336
|
|
|
|
|
1337
|
|
|
def _create(self, group): |
|
1338
|
|
|
"""Create a storage block for investment modeling""" |
|
1339
|
|
|
m = self.parent_block() |
|
1340
|
|
|
|
|
1341
|
|
|
# ########################## CHECKS ################################### |
|
1342
|
|
|
if m.es.periods is not None: |
|
1343
|
|
|
for n in group: |
|
1344
|
|
|
error_fixed_absolute_losses = ( |
|
1345
|
|
|
"For a multi-period investment model, fixed absolute" |
|
1346
|
|
|
" losses are not supported. Please remove parameter." |
|
1347
|
|
|
) |
|
1348
|
|
|
if n.fixed_losses_absolute[0] != 0: |
|
1349
|
|
|
raise ValueError(error_fixed_absolute_losses) |
|
1350
|
|
|
error_initial_storage_level = ( |
|
1351
|
|
|
"For a multi-period model, initial_storage_level is" |
|
1352
|
|
|
" not supported.\nIt needs to be removed since it" |
|
1353
|
|
|
" has no effect.\nstorage_content will be zero," |
|
1354
|
|
|
" until there is some usable storage capacity installed." |
|
1355
|
|
|
) |
|
1356
|
|
|
if n.initial_storage_level is not None: |
|
1357
|
|
|
raise ValueError(error_initial_storage_level) |
|
1358
|
|
|
|
|
1359
|
|
|
# ########################## SETS ##################################### |
|
1360
|
|
|
|
|
1361
|
|
|
self.INVESTSTORAGES = Set(initialize=[n for n in group]) |
|
1362
|
|
|
|
|
1363
|
|
|
self.CONVEX_INVESTSTORAGES = Set( |
|
1364
|
|
|
initialize=[n for n in group if n.investment.nonconvex is False] |
|
1365
|
|
|
) |
|
1366
|
|
|
|
|
1367
|
|
|
self.NON_CONVEX_INVESTSTORAGES = Set( |
|
1368
|
|
|
initialize=[n for n in group if n.investment.nonconvex is True] |
|
1369
|
|
|
) |
|
1370
|
|
|
|
|
1371
|
|
|
self.INVESTSTORAGES_BALANCED = Set( |
|
1372
|
|
|
initialize=[n for n in group if n.balanced is True] |
|
1373
|
|
|
) |
|
1374
|
|
|
|
|
1375
|
|
|
self.INVESTSTORAGES_NO_INIT_CONTENT = Set( |
|
1376
|
|
|
initialize=[n for n in group if n.initial_storage_level is None] |
|
1377
|
|
|
) |
|
1378
|
|
|
|
|
1379
|
|
|
self.INVESTSTORAGES_INIT_CONTENT = Set( |
|
1380
|
|
|
initialize=[ |
|
1381
|
|
|
n for n in group if n.initial_storage_level is not None |
|
1382
|
|
|
] |
|
1383
|
|
|
) |
|
1384
|
|
|
|
|
1385
|
|
|
self.INVEST_REL_CAP_IN = Set( |
|
1386
|
|
|
initialize=[ |
|
1387
|
|
|
n |
|
1388
|
|
|
for n in group |
|
1389
|
|
|
if n.invest_relation_input_capacity[0] is not None |
|
1390
|
|
|
] |
|
1391
|
|
|
) |
|
1392
|
|
|
|
|
1393
|
|
|
self.INVEST_REL_CAP_OUT = Set( |
|
1394
|
|
|
initialize=[ |
|
1395
|
|
|
n |
|
1396
|
|
|
for n in group |
|
1397
|
|
|
if n.invest_relation_output_capacity[0] is not None |
|
1398
|
|
|
] |
|
1399
|
|
|
) |
|
1400
|
|
|
|
|
1401
|
|
|
self.INVEST_REL_IN_OUT = Set( |
|
1402
|
|
|
initialize=[ |
|
1403
|
|
|
n |
|
1404
|
|
|
for n in group |
|
1405
|
|
|
if n.invest_relation_input_output[0] is not None |
|
1406
|
|
|
] |
|
1407
|
|
|
) |
|
1408
|
|
|
|
|
1409
|
|
|
# The storage content is a non-negative variable, therefore it makes no |
|
1410
|
|
|
# sense to create an additional constraint if the lower bound is zero |
|
1411
|
|
|
# for all time steps. |
|
1412
|
|
|
self.MIN_INVESTSTORAGES = Set( |
|
1413
|
|
|
initialize=[ |
|
1414
|
|
|
n |
|
1415
|
|
|
for n in group |
|
1416
|
|
|
if sum([n.min_storage_level[t] for t in m.TIMESTEPS]) > 0 |
|
1417
|
|
|
] |
|
1418
|
|
|
) |
|
1419
|
|
|
|
|
1420
|
|
|
self.OVERALL_MAXIMUM_INVESTSTORAGES = Set( |
|
1421
|
|
|
initialize=[ |
|
1422
|
|
|
n for n in group if n.investment.overall_maximum is not None |
|
1423
|
|
|
] |
|
1424
|
|
|
) |
|
1425
|
|
|
|
|
1426
|
|
|
self.OVERALL_MINIMUM_INVESTSTORAGES = Set( |
|
1427
|
|
|
initialize=[ |
|
1428
|
|
|
n for n in group if n.investment.overall_minimum is not None |
|
1429
|
|
|
] |
|
1430
|
|
|
) |
|
1431
|
|
|
|
|
1432
|
|
|
self.EXISTING_INVESTSTORAGES = Set( |
|
1433
|
|
|
initialize=[n for n in group if n.investment.existing is not None] |
|
1434
|
|
|
) |
|
1435
|
|
|
|
|
1436
|
|
|
# ######################### Variables ################################ |
|
1437
|
|
|
if not m.TSAM_MODE: |
|
1438
|
|
|
self.storage_content = Var( |
|
1439
|
|
|
self.INVESTSTORAGES, m.TIMEPOINTS, within=NonNegativeReals |
|
1440
|
|
|
) |
|
1441
|
|
|
else: |
|
1442
|
|
|
self.inter_storage_content = Var( |
|
1443
|
|
|
self.INVESTSTORAGES, m.CLUSTERS_OFFSET, within=NonNegativeReals |
|
1444
|
|
|
) |
|
1445
|
|
|
self.intra_storage_delta = Var( |
|
1446
|
|
|
self.INVESTSTORAGES, m.TIMEINDEX_TYPICAL_CLUSTER_OFFSET |
|
1447
|
|
|
) |
|
1448
|
|
|
# set the initial intra storage content |
|
1449
|
|
|
# first timestep in intra storage is always zero |
|
1450
|
|
|
for n in group: |
|
1451
|
|
|
for p, k in m.TYPICAL_CLUSTERS: |
|
1452
|
|
|
self.intra_storage_delta[n, p, k, 0] = 0 |
|
1453
|
|
|
self.intra_storage_delta[n, p, k, 0].fix() |
|
1454
|
|
|
|
|
1455
|
|
|
def _storage_investvar_bound_rule(_, n, p): |
|
1456
|
|
|
""" |
|
1457
|
|
|
Rule definition to bound the invested storage capacity `invest`. |
|
1458
|
|
|
""" |
|
1459
|
|
|
if n in self.CONVEX_INVESTSTORAGES: |
|
1460
|
|
|
return n.investment.minimum[p], n.investment.maximum[p] |
|
1461
|
|
|
else: # n in self.NON_CONVEX_INVESTSTORAGES |
|
1462
|
|
|
return 0, n.investment.maximum[p] |
|
1463
|
|
|
|
|
1464
|
|
|
self.invest = Var( |
|
1465
|
|
|
self.INVESTSTORAGES, |
|
1466
|
|
|
m.PERIODS, |
|
1467
|
|
|
within=NonNegativeReals, |
|
1468
|
|
|
bounds=_storage_investvar_bound_rule, |
|
1469
|
|
|
) |
|
1470
|
|
|
|
|
1471
|
|
|
# Total capacity |
|
1472
|
|
|
self.total = Var( |
|
1473
|
|
|
self.INVESTSTORAGES, |
|
1474
|
|
|
m.PERIODS, |
|
1475
|
|
|
within=NonNegativeReals, |
|
1476
|
|
|
initialize=0, |
|
1477
|
|
|
) |
|
1478
|
|
|
|
|
1479
|
|
|
if m.es.periods is not None: |
|
1480
|
|
|
# Old capacity to be decommissioned (due to lifetime) |
|
1481
|
|
|
self.old = Var( |
|
1482
|
|
|
self.INVESTSTORAGES, m.PERIODS, within=NonNegativeReals |
|
1483
|
|
|
) |
|
1484
|
|
|
|
|
1485
|
|
|
# Old endogenous capacity to be decommissioned (due to lifetime) |
|
1486
|
|
|
self.old_end = Var( |
|
1487
|
|
|
self.INVESTSTORAGES, m.PERIODS, within=NonNegativeReals |
|
1488
|
|
|
) |
|
1489
|
|
|
|
|
1490
|
|
|
# Old exogenous capacity to be decommissioned (due to lifetime) |
|
1491
|
|
|
self.old_exo = Var( |
|
1492
|
|
|
self.INVESTSTORAGES, m.PERIODS, within=NonNegativeReals |
|
1493
|
|
|
) |
|
1494
|
|
|
|
|
1495
|
|
|
# create status variable for a non-convex investment storage |
|
1496
|
|
|
self.invest_status = Var( |
|
1497
|
|
|
self.NON_CONVEX_INVESTSTORAGES, m.PERIODS, within=Binary |
|
1498
|
|
|
) |
|
1499
|
|
|
|
|
1500
|
|
|
# ######################### CONSTRAINTS ############################### |
|
1501
|
|
|
i = {n: [i for i in n.inputs][0] for n in group} |
|
1502
|
|
|
o = {n: [o for o in n.outputs][0] for n in group} |
|
1503
|
|
|
|
|
1504
|
|
|
# Handle unit lifetimes |
|
1505
|
|
|
def _total_storage_capacity_rule(block): |
|
1506
|
|
|
"""Rule definition for determining total installed |
|
1507
|
|
|
capacity (taking decommissioning into account) |
|
1508
|
|
|
""" |
|
1509
|
|
|
for n in self.INVESTSTORAGES: |
|
1510
|
|
|
for p in m.PERIODS: |
|
1511
|
|
|
if p == 0: |
|
1512
|
|
|
expr = ( |
|
1513
|
|
|
self.total[n, p] |
|
1514
|
|
|
== self.invest[n, p] + n.investment.existing |
|
1515
|
|
|
) |
|
1516
|
|
|
self.total_storage_rule.add((n, p), expr) |
|
1517
|
|
|
else: |
|
1518
|
|
|
expr = ( |
|
1519
|
|
|
self.total[n, p] |
|
1520
|
|
|
== self.invest[n, p] |
|
1521
|
|
|
+ self.total[n, p - 1] |
|
1522
|
|
|
- self.old[n, p] |
|
1523
|
|
|
) |
|
1524
|
|
|
self.total_storage_rule.add((n, p), expr) |
|
1525
|
|
|
|
|
1526
|
|
|
self.total_storage_rule = Constraint( |
|
1527
|
|
|
self.INVESTSTORAGES, m.PERIODS, noruleinit=True |
|
1528
|
|
|
) |
|
1529
|
|
|
|
|
1530
|
|
|
self.total_storage_rule_build = BuildAction( |
|
1531
|
|
|
rule=_total_storage_capacity_rule |
|
1532
|
|
|
) |
|
1533
|
|
|
|
|
1534
|
|
|
# multi-period storage implementation for time intervals |
|
1535
|
|
|
if m.es.periods is not None: |
|
1536
|
|
|
|
|
1537
|
|
|
def _old_storage_capacity_rule_end(block): |
|
1538
|
|
|
"""Rule definition for determining old endogenously installed |
|
1539
|
|
|
capacity to be decommissioned due to reaching its lifetime. |
|
1540
|
|
|
Investment and decommissioning periods are linked within |
|
1541
|
|
|
the constraint. The respective decommissioning period is |
|
1542
|
|
|
determined for every investment period based on the components |
|
1543
|
|
|
lifetime and a matrix describing its age of each endogenous |
|
1544
|
|
|
investment. Decommissioning can only occur at the beginning of |
|
1545
|
|
|
each period. |
|
1546
|
|
|
|
|
1547
|
|
|
Note |
|
1548
|
|
|
---- |
|
1549
|
|
|
For further information on the implementation check |
|
1550
|
|
|
PR#957 https://github.com/oemof/oemof-solph/pull/957 |
|
1551
|
|
|
""" |
|
1552
|
|
|
for n in self.INVESTSTORAGES: |
|
1553
|
|
|
lifetime = n.investment.lifetime |
|
1554
|
|
|
if lifetime is None: |
|
1555
|
|
|
msg = ( |
|
1556
|
|
|
"You have to specify a lifetime " |
|
1557
|
|
|
"for a Flow going into or out of " |
|
1558
|
|
|
"a GenericStorage unit " |
|
1559
|
|
|
"in a multi-period model!" |
|
1560
|
|
|
f" Value for {n} is missing." |
|
1561
|
|
|
) |
|
1562
|
|
|
raise ValueError(msg) |
|
1563
|
|
|
# get the period matrix describing the temporal distance |
|
1564
|
|
|
# between all period combinations. |
|
1565
|
|
|
periods_matrix = m.es.periods_matrix |
|
1566
|
|
|
|
|
1567
|
|
|
# get the index of the minimum value in each row greater |
|
1568
|
|
|
# equal than the lifetime. This value equals the |
|
1569
|
|
|
# decommissioning period if not zero. The index of this |
|
1570
|
|
|
# value represents the investment period. If np.where |
|
1571
|
|
|
# condition is not met in any row, min value will be zero |
|
1572
|
|
|
decomm_periods = np.argmin( |
|
1573
|
|
|
np.where( |
|
1574
|
|
|
(periods_matrix >= lifetime), |
|
1575
|
|
|
periods_matrix, |
|
1576
|
|
|
np.inf, |
|
1577
|
|
|
), |
|
1578
|
|
|
axis=1, |
|
1579
|
|
|
) |
|
1580
|
|
|
|
|
1581
|
|
|
# no decommissioning in first period |
|
1582
|
|
|
expr = self.old_end[n, 0] == 0 |
|
1583
|
|
|
self.old_rule_end.add((n, 0), expr) |
|
1584
|
|
|
|
|
1585
|
|
|
# all periods not in decomm_periods have no decommissioning |
|
1586
|
|
|
# zero is excluded |
|
1587
|
|
|
for p in m.PERIODS: |
|
1588
|
|
|
if p not in decomm_periods and p != 0: |
|
1589
|
|
|
expr = self.old_end[n, p] == 0 |
|
1590
|
|
|
self.old_rule_end.add((n, p), expr) |
|
1591
|
|
|
|
|
1592
|
|
|
# multiple invests can be decommissioned in the same period |
|
1593
|
|
|
# but only sequential ones, thus a bookkeeping is |
|
1594
|
|
|
# introduced andconstraints are added to equation one |
|
1595
|
|
|
# iteration later. |
|
1596
|
|
|
last_decomm_p = np.nan |
|
1597
|
|
|
# loop over invest periods (values are decomm_periods) |
|
1598
|
|
|
for invest_p, decomm_p in enumerate(decomm_periods): |
|
1599
|
|
|
# Add constraint of iteration before |
|
1600
|
|
|
# (skipped in first iteration by last_decomm_p = nan) |
|
1601
|
|
|
if (decomm_p != last_decomm_p) and ( |
|
1602
|
|
|
last_decomm_p is not np.nan |
|
1603
|
|
|
): |
|
1604
|
|
|
expr = self.old_end[n, last_decomm_p] == expr |
|
1605
|
|
|
self.old_rule_end.add((n, last_decomm_p), expr) |
|
1606
|
|
|
|
|
1607
|
|
|
# no decommissioning if decomm_p is zero |
|
1608
|
|
|
if decomm_p == 0: |
|
1609
|
|
|
# overwrite decomm_p with zero to avoid |
|
1610
|
|
|
# chaining invest periods in next iteration |
|
1611
|
|
|
last_decomm_p = 0 |
|
1612
|
|
|
|
|
1613
|
|
|
# if decomm_p is the same as the last one chain invest |
|
1614
|
|
|
# period |
|
1615
|
|
|
elif decomm_p == last_decomm_p: |
|
1616
|
|
|
expr += self.invest[n, invest_p] |
|
1617
|
|
|
# overwrite decomm_p |
|
1618
|
|
|
last_decomm_p = decomm_p |
|
1619
|
|
|
|
|
1620
|
|
|
# if decomm_p is not zero, not the same as the last one |
|
1621
|
|
|
# and it's not the first period |
|
1622
|
|
|
else: |
|
1623
|
|
|
expr = self.invest[n, invest_p] |
|
1624
|
|
|
# overwrite decomm_p |
|
1625
|
|
|
last_decomm_p = decomm_p |
|
1626
|
|
|
|
|
1627
|
|
|
# Add constraint of very last iteration |
|
1628
|
|
|
if last_decomm_p != 0: |
|
1629
|
|
|
expr = self.old_end[n, last_decomm_p] == expr |
|
1630
|
|
|
self.old_rule_end.add((n, last_decomm_p), expr) |
|
1631
|
|
|
|
|
1632
|
|
|
self.old_rule_end = Constraint( |
|
1633
|
|
|
self.INVESTSTORAGES, m.PERIODS, noruleinit=True |
|
1634
|
|
|
) |
|
1635
|
|
|
|
|
1636
|
|
|
self.old_rule_end_build = BuildAction( |
|
1637
|
|
|
rule=_old_storage_capacity_rule_end |
|
1638
|
|
|
) |
|
1639
|
|
|
|
|
1640
|
|
|
def _old_storage_capacity_rule_exo(block): |
|
1641
|
|
|
"""Rule definition for determining old exogenously given |
|
1642
|
|
|
capacity to be decommissioned due to reaching its lifetime |
|
1643
|
|
|
""" |
|
1644
|
|
|
for n in self.INVESTSTORAGES: |
|
1645
|
|
|
age = n.investment.age |
|
1646
|
|
|
lifetime = n.investment.lifetime |
|
1647
|
|
|
is_decommissioned = False |
|
1648
|
|
|
for p in m.PERIODS: |
|
1649
|
|
|
# No shutdown in first period |
|
1650
|
|
|
if p == 0: |
|
1651
|
|
|
expr = self.old_exo[n, p] == 0 |
|
1652
|
|
|
self.old_rule_exo.add((n, p), expr) |
|
1653
|
|
|
elif lifetime - age <= m.es.periods_years[p]: |
|
1654
|
|
|
# Track decommissioning status |
|
1655
|
|
|
if not is_decommissioned: |
|
1656
|
|
|
expr = ( |
|
1657
|
|
|
self.old_exo[n, p] == n.investment.existing |
|
1658
|
|
|
) |
|
1659
|
|
|
is_decommissioned = True |
|
1660
|
|
|
else: |
|
1661
|
|
|
expr = self.old_exo[n, p] == 0 |
|
1662
|
|
|
self.old_rule_exo.add((n, p), expr) |
|
1663
|
|
|
else: |
|
1664
|
|
|
expr = self.old_exo[n, p] == 0 |
|
1665
|
|
|
self.old_rule_exo.add((n, p), expr) |
|
1666
|
|
|
|
|
1667
|
|
|
self.old_rule_exo = Constraint( |
|
1668
|
|
|
self.INVESTSTORAGES, m.PERIODS, noruleinit=True |
|
1669
|
|
|
) |
|
1670
|
|
|
|
|
1671
|
|
|
self.old_rule_exo_build = BuildAction( |
|
1672
|
|
|
rule=_old_storage_capacity_rule_exo |
|
1673
|
|
|
) |
|
1674
|
|
|
|
|
1675
|
|
|
def _old_storage_capacity_rule(block): |
|
1676
|
|
|
"""Rule definition for determining (overall) old capacity |
|
1677
|
|
|
to be decommissioned due to reaching its lifetime |
|
1678
|
|
|
""" |
|
1679
|
|
|
for n in self.INVESTSTORAGES: |
|
1680
|
|
|
for p in m.PERIODS: |
|
1681
|
|
|
expr = ( |
|
1682
|
|
|
self.old[n, p] |
|
1683
|
|
|
== self.old_end[n, p] + self.old_exo[n, p] |
|
1684
|
|
|
) |
|
1685
|
|
|
self.old_rule.add((n, p), expr) |
|
1686
|
|
|
|
|
1687
|
|
|
self.old_rule = Constraint( |
|
1688
|
|
|
self.INVESTSTORAGES, m.PERIODS, noruleinit=True |
|
1689
|
|
|
) |
|
1690
|
|
|
|
|
1691
|
|
|
self.old_rule_build = BuildAction(rule=_old_storage_capacity_rule) |
|
1692
|
|
|
|
|
1693
|
|
|
def _initially_empty_rule(_): |
|
1694
|
|
|
"""Ensure storage to be empty initially""" |
|
1695
|
|
|
for n in self.INVESTSTORAGES: |
|
1696
|
|
|
expr = self.storage_content[n, 0] == 0 |
|
1697
|
|
|
self.initially_empty.add((n, 0), expr) |
|
1698
|
|
|
|
|
1699
|
|
|
if not m.TSAM_MODE: |
|
1700
|
|
|
# inter and intra initial storage contents are handled above |
|
1701
|
|
|
self.initially_empty = Constraint( |
|
1702
|
|
|
self.INVESTSTORAGES, m.TIMESTEPS, noruleinit=True |
|
1703
|
|
|
) |
|
1704
|
|
|
|
|
1705
|
|
|
self.initially_empty_build = BuildAction( |
|
1706
|
|
|
rule=_initially_empty_rule |
|
1707
|
|
|
) |
|
1708
|
|
|
|
|
1709
|
|
|
# Standard storage implementation for discrete time points |
|
1710
|
|
|
else: |
|
1711
|
|
|
|
|
1712
|
|
|
def _inv_storage_init_content_max_rule(block, n): |
|
1713
|
|
|
"""Constraint for a variable initial storage capacity.""" |
|
1714
|
|
|
if not m.TSAM_MODE: |
|
1715
|
|
|
lhs = block.storage_content[n, 0] |
|
1716
|
|
|
else: |
|
1717
|
|
|
lhs = block.intra_storage_delta[n, 0, 0, 0] |
|
1718
|
|
|
return lhs <= n.investment.existing + block.invest[n, 0] |
|
1719
|
|
|
|
|
1720
|
|
|
self.init_content_limit = Constraint( |
|
1721
|
|
|
self.INVESTSTORAGES_NO_INIT_CONTENT, |
|
1722
|
|
|
rule=_inv_storage_init_content_max_rule, |
|
1723
|
|
|
) |
|
1724
|
|
|
|
|
1725
|
|
|
def _inv_storage_init_content_fix_rule(block, n): |
|
1726
|
|
|
"""Constraint for a fixed initial storage capacity.""" |
|
1727
|
|
|
if not m.TSAM_MODE: |
|
1728
|
|
|
lhs = block.storage_content[n, 0] |
|
1729
|
|
|
else: |
|
1730
|
|
|
lhs = block.intra_storage_delta[n, 0, 0, 0] |
|
1731
|
|
|
return lhs == n.initial_storage_level * ( |
|
1732
|
|
|
n.investment.existing + block.invest[n, 0] |
|
1733
|
|
|
) |
|
1734
|
|
|
|
|
1735
|
|
|
self.init_content_fix = Constraint( |
|
1736
|
|
|
self.INVESTSTORAGES_INIT_CONTENT, |
|
1737
|
|
|
rule=_inv_storage_init_content_fix_rule, |
|
1738
|
|
|
) |
|
1739
|
|
|
|
|
1740
|
|
|
def _storage_balance_rule(block, n, p, t): |
|
1741
|
|
|
""" |
|
1742
|
|
|
Rule definition for the storage balance of every storage n and |
|
1743
|
|
|
every timestep. |
|
1744
|
|
|
""" |
|
1745
|
|
|
expr = 0 |
|
1746
|
|
|
expr += block.storage_content[n, t + 1] |
|
1747
|
|
|
expr += ( |
|
1748
|
|
|
-block.storage_content[n, t] |
|
1749
|
|
|
* (1 - n.loss_rate[t]) ** m.timeincrement[t] |
|
1750
|
|
|
) |
|
1751
|
|
|
expr += ( |
|
1752
|
|
|
n.fixed_losses_relative[t] |
|
1753
|
|
|
* self.total[n, p] |
|
1754
|
|
|
* m.timeincrement[t] |
|
1755
|
|
|
) |
|
1756
|
|
|
expr += n.fixed_losses_absolute[t] * m.timeincrement[t] |
|
1757
|
|
|
expr += ( |
|
1758
|
|
|
-m.flow[i[n], n, t] * n.inflow_conversion_factor[t] |
|
1759
|
|
|
) * m.timeincrement[t] |
|
1760
|
|
|
expr += ( |
|
1761
|
|
|
m.flow[n, o[n], t] / n.outflow_conversion_factor[t] |
|
1762
|
|
|
) * m.timeincrement[t] |
|
1763
|
|
|
return expr == 0 |
|
1764
|
|
|
|
|
1765
|
|
View Code Duplication |
def _intra_storage_balance_rule(block, n, p, k, g): |
|
|
|
|
|
|
1766
|
|
|
""" |
|
1767
|
|
|
Rule definition for the storage balance of every storage n and |
|
1768
|
|
|
every timestep. |
|
1769
|
|
|
""" |
|
1770
|
|
|
t = m.get_timestep_from_tsam_timestep(p, k, g) |
|
1771
|
|
|
expr = 0 |
|
1772
|
|
|
expr += block.intra_storage_delta[n, p, k, g + 1] |
|
1773
|
|
|
expr += ( |
|
1774
|
|
|
-block.intra_storage_delta[n, p, k, g] |
|
1775
|
|
|
* (1 - n.loss_rate[t]) ** m.timeincrement[t] |
|
1776
|
|
|
) |
|
1777
|
|
|
expr += ( |
|
1778
|
|
|
n.fixed_losses_relative[t] |
|
1779
|
|
|
* self.total[n, p] |
|
1780
|
|
|
* m.timeincrement[t] |
|
1781
|
|
|
) |
|
1782
|
|
|
expr += n.fixed_losses_absolute[t] * m.timeincrement[t] |
|
1783
|
|
|
expr += ( |
|
1784
|
|
|
-m.flow[i[n], n, t] * n.inflow_conversion_factor[t] |
|
1785
|
|
|
) * m.timeincrement[t] |
|
1786
|
|
|
expr += ( |
|
1787
|
|
|
m.flow[n, o[n], t] / n.outflow_conversion_factor[t] |
|
1788
|
|
|
) * m.timeincrement[t] |
|
1789
|
|
|
return expr == 0 |
|
1790
|
|
|
|
|
1791
|
|
|
if not m.TSAM_MODE: |
|
1792
|
|
|
self.balance = Constraint( |
|
1793
|
|
|
self.INVESTSTORAGES, |
|
1794
|
|
|
m.TIMEINDEX, |
|
1795
|
|
|
rule=_storage_balance_rule, |
|
1796
|
|
|
) |
|
1797
|
|
|
else: |
|
1798
|
|
|
self.intra_balance = Constraint( |
|
1799
|
|
|
self.INVESTSTORAGES, |
|
1800
|
|
|
m.TIMEINDEX_TYPICAL_CLUSTER, |
|
1801
|
|
|
rule=_intra_storage_balance_rule, |
|
1802
|
|
|
) |
|
1803
|
|
|
|
|
1804
|
|
|
def _inter_storage_balance_rule(block, n, i): |
|
1805
|
|
|
""" |
|
1806
|
|
|
Rule definition for the storage balance of every storage n and |
|
1807
|
|
|
every timestep. |
|
1808
|
|
|
""" |
|
1809
|
|
|
ii = 0 |
|
1810
|
|
|
for p in m.PERIODS: |
|
1811
|
|
|
ii += len(m.es.tsa_parameters[p]["order"]) |
|
1812
|
|
|
if ii > i: |
|
1813
|
|
|
ii -= len(m.es.tsa_parameters[p]["order"]) |
|
1814
|
|
|
ii = i - ii |
|
1815
|
|
|
break |
|
1816
|
|
|
|
|
1817
|
|
|
k = m.es.tsa_parameters[p]["order"][ii] |
|
|
|
|
|
|
1818
|
|
|
t = m.get_timestep_from_tsam_timestep( |
|
1819
|
|
|
p, k, m.es.tsa_parameters[p]["timesteps"] - 1 |
|
1820
|
|
|
) |
|
1821
|
|
|
expr = 0 |
|
1822
|
|
|
expr += block.inter_storage_content[n, i + 1] |
|
1823
|
|
|
expr += -block.inter_storage_content[n, i] * ( |
|
1824
|
|
|
1 - n.loss_rate[t] |
|
1825
|
|
|
) ** (m.timeincrement[t] * m.es.tsa_parameters[p]["timesteps"]) |
|
1826
|
|
|
expr += -self.intra_storage_delta[ |
|
1827
|
|
|
n, p, k, m.es.tsa_parameters[p]["timesteps"] |
|
1828
|
|
|
] |
|
1829
|
|
|
return expr == 0 |
|
1830
|
|
|
|
|
1831
|
|
|
if m.TSAM_MODE: |
|
1832
|
|
|
self.inter_balance = Constraint( |
|
1833
|
|
|
self.INVESTSTORAGES, |
|
1834
|
|
|
m.CLUSTERS, |
|
1835
|
|
|
rule=_inter_storage_balance_rule, |
|
1836
|
|
|
) |
|
1837
|
|
|
|
|
1838
|
|
|
if m.es.periods is None and not m.TSAM_MODE: |
|
1839
|
|
|
|
|
1840
|
|
|
def _balanced_storage_rule(block, n): |
|
1841
|
|
|
return ( |
|
1842
|
|
|
block.storage_content[n, m.TIMEPOINTS.at(-1)] |
|
1843
|
|
|
== block.storage_content[n, m.TIMEPOINTS.at(1)] |
|
1844
|
|
|
) |
|
1845
|
|
|
|
|
1846
|
|
|
self.balanced_cstr = Constraint( |
|
1847
|
|
|
self.INVESTSTORAGES_BALANCED, rule=_balanced_storage_rule |
|
1848
|
|
|
) |
|
1849
|
|
|
|
|
1850
|
|
|
def _power_coupled(block): |
|
1851
|
|
|
""" |
|
1852
|
|
|
Rule definition for constraint to connect the input power |
|
1853
|
|
|
and output power |
|
1854
|
|
|
""" |
|
1855
|
|
|
for n in self.INVEST_REL_IN_OUT: |
|
1856
|
|
|
for p in m.PERIODS: |
|
1857
|
|
|
expr = ( |
|
1858
|
|
|
m.InvestmentFlowBlock.total[n, o[n], p] |
|
1859
|
|
|
) * n.invest_relation_input_output[p] == ( |
|
1860
|
|
|
m.InvestmentFlowBlock.total[i[n], n, p] |
|
1861
|
|
|
) |
|
1862
|
|
|
self.power_coupled.add((n, p), expr) |
|
1863
|
|
|
|
|
1864
|
|
|
self.power_coupled = Constraint( |
|
1865
|
|
|
self.INVEST_REL_IN_OUT, m.PERIODS, noruleinit=True |
|
1866
|
|
|
) |
|
1867
|
|
|
|
|
1868
|
|
|
self.power_coupled_build = BuildAction(rule=_power_coupled) |
|
1869
|
|
|
|
|
1870
|
|
|
def _storage_capacity_inflow_invest_rule(block): |
|
1871
|
|
|
""" |
|
1872
|
|
|
Rule definition of constraint connecting the inflow |
|
1873
|
|
|
`InvestmentFlowBlock.invest of storage with invested capacity |
|
1874
|
|
|
`invest` by nominal_storage_capacity__inflow_ratio |
|
1875
|
|
|
""" |
|
1876
|
|
|
for n in self.INVEST_REL_CAP_IN: |
|
1877
|
|
|
for p in m.PERIODS: |
|
1878
|
|
|
expr = ( |
|
1879
|
|
|
m.InvestmentFlowBlock.total[i[n], n, p] |
|
1880
|
|
|
== self.total[n, p] |
|
1881
|
|
|
* n.invest_relation_input_capacity[p] |
|
1882
|
|
|
) |
|
1883
|
|
|
self.storage_capacity_inflow.add((n, p), expr) |
|
1884
|
|
|
|
|
1885
|
|
|
self.storage_capacity_inflow = Constraint( |
|
1886
|
|
|
self.INVEST_REL_CAP_IN, m.PERIODS, noruleinit=True |
|
1887
|
|
|
) |
|
1888
|
|
|
|
|
1889
|
|
|
self.storage_capacity_inflow_build = BuildAction( |
|
1890
|
|
|
rule=_storage_capacity_inflow_invest_rule |
|
1891
|
|
|
) |
|
1892
|
|
|
|
|
1893
|
|
|
def _storage_capacity_outflow_invest_rule(block): |
|
1894
|
|
|
""" |
|
1895
|
|
|
Rule definition of constraint connecting outflow |
|
1896
|
|
|
`InvestmentFlowBlock.invest` of storage and invested capacity |
|
1897
|
|
|
`invest` by nominal_storage_capacity__outflow_ratio |
|
1898
|
|
|
""" |
|
1899
|
|
|
for n in self.INVEST_REL_CAP_OUT: |
|
1900
|
|
|
for p in m.PERIODS: |
|
1901
|
|
|
expr = ( |
|
1902
|
|
|
m.InvestmentFlowBlock.total[n, o[n], p] |
|
1903
|
|
|
== self.total[n, p] |
|
1904
|
|
|
* n.invest_relation_output_capacity[p] |
|
1905
|
|
|
) |
|
1906
|
|
|
self.storage_capacity_outflow.add((n, p), expr) |
|
1907
|
|
|
|
|
1908
|
|
|
self.storage_capacity_outflow = Constraint( |
|
1909
|
|
|
self.INVEST_REL_CAP_OUT, m.PERIODS, noruleinit=True |
|
1910
|
|
|
) |
|
1911
|
|
|
|
|
1912
|
|
|
self.storage_capacity_outflow_build = BuildAction( |
|
1913
|
|
|
rule=_storage_capacity_outflow_invest_rule |
|
1914
|
|
|
) |
|
1915
|
|
|
|
|
1916
|
|
|
self._add_storage_limit_constraints() |
|
1917
|
|
|
|
|
1918
|
|
|
def maximum_invest_limit(block, n, p): |
|
1919
|
|
|
""" |
|
1920
|
|
|
Constraint for the maximal investment in non convex investment |
|
1921
|
|
|
storage. |
|
1922
|
|
|
""" |
|
1923
|
|
|
return ( |
|
1924
|
|
|
n.investment.maximum[p] * self.invest_status[n, p] |
|
1925
|
|
|
- self.invest[n, p] |
|
1926
|
|
|
) >= 0 |
|
1927
|
|
|
|
|
1928
|
|
|
self.limit_max = Constraint( |
|
1929
|
|
|
self.NON_CONVEX_INVESTSTORAGES, |
|
1930
|
|
|
m.PERIODS, |
|
1931
|
|
|
rule=maximum_invest_limit, |
|
1932
|
|
|
) |
|
1933
|
|
|
|
|
1934
|
|
|
def smallest_invest(block, n, p): |
|
1935
|
|
|
""" |
|
1936
|
|
|
Constraint for the minimal investment in non convex investment |
|
1937
|
|
|
storage if the invest is greater than 0. So the invest variable |
|
1938
|
|
|
can be either 0 or greater than the minimum. |
|
1939
|
|
|
""" |
|
1940
|
|
|
return ( |
|
1941
|
|
|
self.invest[n, p] |
|
1942
|
|
|
- n.investment.minimum[p] * self.invest_status[n, p] |
|
1943
|
|
|
>= 0 |
|
1944
|
|
|
) |
|
1945
|
|
|
|
|
1946
|
|
|
self.limit_min = Constraint( |
|
1947
|
|
|
self.NON_CONVEX_INVESTSTORAGES, m.PERIODS, rule=smallest_invest |
|
1948
|
|
|
) |
|
1949
|
|
|
|
|
1950
|
|
|
if m.es.periods is not None: |
|
1951
|
|
|
|
|
1952
|
|
|
def _overall_storage_maximum_investflow_rule(block): |
|
1953
|
|
|
"""Rule definition for maximum overall investment |
|
1954
|
|
|
in investment case. |
|
1955
|
|
|
""" |
|
1956
|
|
|
for n in self.OVERALL_MAXIMUM_INVESTSTORAGES: |
|
1957
|
|
|
for p in m.PERIODS: |
|
1958
|
|
|
expr = self.total[n, p] <= n.investment.overall_maximum |
|
1959
|
|
|
self.overall_storage_maximum.add((n, p), expr) |
|
1960
|
|
|
|
|
1961
|
|
|
self.overall_storage_maximum = Constraint( |
|
1962
|
|
|
self.OVERALL_MAXIMUM_INVESTSTORAGES, m.PERIODS, noruleinit=True |
|
1963
|
|
|
) |
|
1964
|
|
|
|
|
1965
|
|
|
self.overall_maximum_build = BuildAction( |
|
1966
|
|
|
rule=_overall_storage_maximum_investflow_rule |
|
1967
|
|
|
) |
|
1968
|
|
|
|
|
1969
|
|
|
def _overall_minimum_investflow_rule(block): |
|
1970
|
|
|
"""Rule definition for minimum overall investment |
|
1971
|
|
|
in investment case. |
|
1972
|
|
|
|
|
1973
|
|
|
Note: This is only applicable for the last period |
|
1974
|
|
|
""" |
|
1975
|
|
|
for n in self.OVERALL_MINIMUM_INVESTSTORAGES: |
|
1976
|
|
|
expr = ( |
|
1977
|
|
|
n.investment.overall_minimum |
|
1978
|
|
|
<= self.total[n, m.PERIODS[-1]] |
|
1979
|
|
|
) |
|
1980
|
|
|
self.overall_minimum.add(n, expr) |
|
1981
|
|
|
|
|
1982
|
|
|
self.overall_minimum = Constraint( |
|
1983
|
|
|
self.OVERALL_MINIMUM_INVESTSTORAGES, noruleinit=True |
|
1984
|
|
|
) |
|
1985
|
|
|
|
|
1986
|
|
|
self.overall_minimum_build = BuildAction( |
|
1987
|
|
|
rule=_overall_minimum_investflow_rule |
|
1988
|
|
|
) |
|
1989
|
|
|
|
|
1990
|
|
|
def _add_storage_limit_constraints(self): |
|
1991
|
|
|
m = self.parent_block() |
|
1992
|
|
|
if not m.TSAM_MODE: |
|
1993
|
|
|
if m.es.periods is None: |
|
1994
|
|
|
|
|
1995
|
|
|
def _max_storage_content_invest_rule(_, n, t): |
|
1996
|
|
|
""" |
|
1997
|
|
|
Rule definition for upper bound constraint for the |
|
1998
|
|
|
storage content. |
|
1999
|
|
|
""" |
|
2000
|
|
|
expr = ( |
|
2001
|
|
|
self.storage_content[n, t] |
|
2002
|
|
|
<= self.total[n, 0] * n.max_storage_level[t] |
|
2003
|
|
|
) |
|
2004
|
|
|
return expr |
|
2005
|
|
|
|
|
2006
|
|
|
self.max_storage_content = Constraint( |
|
2007
|
|
|
self.INVESTSTORAGES, |
|
2008
|
|
|
m.TIMEPOINTS, |
|
2009
|
|
|
rule=_max_storage_content_invest_rule, |
|
2010
|
|
|
) |
|
2011
|
|
|
|
|
2012
|
|
|
def _min_storage_content_invest_rule(_, n, t): |
|
2013
|
|
|
""" |
|
2014
|
|
|
Rule definition of lower bound constraint for the |
|
2015
|
|
|
storage content. |
|
2016
|
|
|
""" |
|
2017
|
|
|
expr = ( |
|
2018
|
|
|
self.storage_content[n, t] |
|
2019
|
|
|
>= self.total[n, 0] * n.min_storage_level[t] |
|
2020
|
|
|
) |
|
2021
|
|
|
return expr |
|
2022
|
|
|
|
|
2023
|
|
|
self.min_storage_content = Constraint( |
|
2024
|
|
|
self.MIN_INVESTSTORAGES, |
|
2025
|
|
|
m.TIMEPOINTS, |
|
2026
|
|
|
rule=_min_storage_content_invest_rule, |
|
2027
|
|
|
) |
|
2028
|
|
|
else: |
|
2029
|
|
|
|
|
2030
|
|
|
def _max_storage_content_invest_rule(_, n, p, t): |
|
2031
|
|
|
""" |
|
2032
|
|
|
Rule definition for upper bound constraint for the |
|
2033
|
|
|
storage content. |
|
2034
|
|
|
""" |
|
2035
|
|
|
expr = ( |
|
2036
|
|
|
self.storage_content[n, t] |
|
2037
|
|
|
<= self.total[n, p] * n.max_storage_level[t] |
|
2038
|
|
|
) |
|
2039
|
|
|
return expr |
|
2040
|
|
|
|
|
2041
|
|
|
self.max_storage_content = Constraint( |
|
2042
|
|
|
self.INVESTSTORAGES, |
|
2043
|
|
|
m.TIMEINDEX, |
|
2044
|
|
|
rule=_max_storage_content_invest_rule, |
|
2045
|
|
|
) |
|
2046
|
|
|
|
|
2047
|
|
|
def _min_storage_content_invest_rule(_, n, p, t): |
|
2048
|
|
|
""" |
|
2049
|
|
|
Rule definition of lower bound constraint for the |
|
2050
|
|
|
storage content. |
|
2051
|
|
|
""" |
|
2052
|
|
|
expr = ( |
|
2053
|
|
|
self.storage_content[n, t] |
|
2054
|
|
|
>= self.total[n, p] * n.min_storage_level[t] |
|
2055
|
|
|
) |
|
2056
|
|
|
return expr |
|
2057
|
|
|
|
|
2058
|
|
|
self.min_storage_content = Constraint( |
|
2059
|
|
|
self.MIN_INVESTSTORAGES, |
|
2060
|
|
|
m.TIMEINDEX, |
|
2061
|
|
|
rule=_min_storage_content_invest_rule, |
|
2062
|
|
|
) |
|
2063
|
|
|
else: |
|
2064
|
|
|
|
|
2065
|
|
View Code Duplication |
def _storage_inter_maximum_level_rule(block): |
|
|
|
|
|
|
2066
|
|
|
for n in self.INVESTSTORAGES: |
|
2067
|
|
|
for p, i, g in m.TIMEINDEX_CLUSTER: |
|
2068
|
|
|
t = m.get_timestep_from_tsam_timestep(p, i, g) |
|
2069
|
|
|
k = m.es.tsa_parameters[p]["order"][i] |
|
2070
|
|
|
tk = m.get_timestep_from_tsam_timestep(p, k, g) |
|
2071
|
|
|
inter_i = ( |
|
2072
|
|
|
sum( |
|
2073
|
|
|
len(m.es.tsa_parameters[ip]["order"]) |
|
2074
|
|
|
for ip in range(p) |
|
2075
|
|
|
) |
|
2076
|
|
|
+ i |
|
2077
|
|
|
) |
|
2078
|
|
|
lhs = ( |
|
2079
|
|
|
self.inter_storage_content[n, inter_i] |
|
2080
|
|
|
* (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk]) |
|
2081
|
|
|
+ self.intra_storage_delta[n, p, k, g] |
|
2082
|
|
|
) |
|
2083
|
|
|
rhs = self.total[n, p] * n.max_storage_level[t] |
|
2084
|
|
|
self.storage_inter_maximum_level.add( |
|
2085
|
|
|
(n, p, i, g), lhs <= rhs |
|
2086
|
|
|
) |
|
2087
|
|
|
|
|
2088
|
|
|
self.storage_inter_maximum_level = Constraint( |
|
2089
|
|
|
self.INVESTSTORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True |
|
2090
|
|
|
) |
|
2091
|
|
|
|
|
2092
|
|
|
self.storage_inter_maximum_level_build = BuildAction( |
|
2093
|
|
|
rule=_storage_inter_maximum_level_rule |
|
2094
|
|
|
) |
|
2095
|
|
|
|
|
2096
|
|
View Code Duplication |
def _storage_inter_minimum_level_rule(block): |
|
|
|
|
|
|
2097
|
|
|
# See FINE implementation at |
|
2098
|
|
|
# https://github.com/FZJ-IEK3-VSA/FINE/blob/ |
|
2099
|
|
|
# 57ec32561fb95e746c505760bd0d61c97d2fd2fb/FINE/storage.py#L1329 |
|
2100
|
|
|
for n in self.INVESTSTORAGES: |
|
2101
|
|
|
for p, i, g in m.TIMEINDEX_CLUSTER: |
|
2102
|
|
|
t = m.get_timestep_from_tsam_timestep(p, i, g) |
|
2103
|
|
|
lhs = self.total[n, p] * n.min_storage_level[t] |
|
2104
|
|
|
k = m.es.tsa_parameters[p]["order"][i] |
|
2105
|
|
|
tk = m.get_timestep_from_tsam_timestep(p, k, g) |
|
2106
|
|
|
inter_i = ( |
|
2107
|
|
|
sum( |
|
2108
|
|
|
len(m.es.tsa_parameters[ip]["order"]) |
|
2109
|
|
|
for ip in range(p) |
|
2110
|
|
|
) |
|
2111
|
|
|
+ i |
|
2112
|
|
|
) |
|
2113
|
|
|
rhs = ( |
|
2114
|
|
|
self.inter_storage_content[n, inter_i] |
|
2115
|
|
|
* (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk]) |
|
2116
|
|
|
+ self.intra_storage_delta[n, p, k, g] |
|
2117
|
|
|
) |
|
2118
|
|
|
self.storage_inter_minimum_level.add( |
|
2119
|
|
|
(n, p, i, g), lhs <= rhs |
|
2120
|
|
|
) |
|
2121
|
|
|
|
|
2122
|
|
|
self.storage_inter_minimum_level = Constraint( |
|
2123
|
|
|
self.INVESTSTORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True |
|
2124
|
|
|
) |
|
2125
|
|
|
|
|
2126
|
|
|
self.storage_inter_minimum_level_build = BuildAction( |
|
2127
|
|
|
rule=_storage_inter_minimum_level_rule |
|
2128
|
|
|
) |
|
2129
|
|
|
|
|
2130
|
|
|
def _objective_expression(self): |
|
2131
|
|
|
"""Objective expression with fixed and investment costs.""" |
|
2132
|
|
|
m = self.parent_block() |
|
2133
|
|
|
|
|
2134
|
|
|
investment_costs = 0 |
|
2135
|
|
|
storage_costs = 0 |
|
2136
|
|
|
period_investment_costs = {p: 0 for p in m.PERIODS} |
|
2137
|
|
|
fixed_costs = 0 |
|
2138
|
|
|
|
|
2139
|
|
|
if m.es.periods is None: |
|
2140
|
|
|
for n in self.CONVEX_INVESTSTORAGES: |
|
2141
|
|
|
for p in m.PERIODS: |
|
2142
|
|
|
investment_costs += ( |
|
2143
|
|
|
self.invest[n, p] * n.investment.ep_costs[p] |
|
2144
|
|
|
) |
|
2145
|
|
|
for n in self.NON_CONVEX_INVESTSTORAGES: |
|
2146
|
|
|
for p in m.PERIODS: |
|
2147
|
|
|
investment_costs += ( |
|
2148
|
|
|
self.invest[n, p] * n.investment.ep_costs[p] |
|
2149
|
|
|
+ self.invest_status[n, p] * n.investment.offset[p] |
|
2150
|
|
|
) |
|
2151
|
|
|
|
|
2152
|
|
|
else: |
|
2153
|
|
|
msg = ( |
|
2154
|
|
|
"You did not specify an interest rate.\n" |
|
2155
|
|
|
"It will be set equal to the discount_rate of {} " |
|
2156
|
|
|
"of the model as a default.\nThis corresponds to a " |
|
2157
|
|
|
"social planner point of view and does not reflect " |
|
2158
|
|
|
"microeconomic interest requirements." |
|
2159
|
|
|
) |
|
2160
|
|
|
for n in self.CONVEX_INVESTSTORAGES: |
|
2161
|
|
|
lifetime = n.investment.lifetime |
|
2162
|
|
|
interest = 0 |
|
2163
|
|
|
if interest == 0: |
|
2164
|
|
|
warn( |
|
2165
|
|
|
msg.format(m.discount_rate), |
|
2166
|
|
|
debugging.SuspiciousUsageWarning, |
|
2167
|
|
|
) |
|
2168
|
|
|
interest = m.discount_rate |
|
2169
|
|
|
for p in m.PERIODS: |
|
2170
|
|
|
annuity = economics.annuity( |
|
2171
|
|
|
capex=n.investment.ep_costs[p], |
|
2172
|
|
|
n=lifetime, |
|
2173
|
|
|
wacc=interest, |
|
2174
|
|
|
) |
|
2175
|
|
|
duration = min( |
|
2176
|
|
|
m.es.end_year_of_optimization - m.es.periods_years[p], |
|
2177
|
|
|
lifetime, |
|
2178
|
|
|
) |
|
2179
|
|
|
present_value_factor = 1 / economics.annuity( |
|
2180
|
|
|
capex=1, n=duration, wacc=interest |
|
2181
|
|
|
) |
|
2182
|
|
|
investment_costs_increment = ( |
|
2183
|
|
|
self.invest[n, p] * annuity * present_value_factor |
|
2184
|
|
|
) |
|
2185
|
|
|
remaining_value_difference = ( |
|
2186
|
|
|
self._evaluate_remaining_value_difference( |
|
2187
|
|
|
m, |
|
2188
|
|
|
p, |
|
2189
|
|
|
n, |
|
2190
|
|
|
m.es.end_year_of_optimization, |
|
2191
|
|
|
lifetime, |
|
2192
|
|
|
interest, |
|
2193
|
|
|
) |
|
2194
|
|
|
) |
|
2195
|
|
|
investment_costs += ( |
|
2196
|
|
|
investment_costs_increment + remaining_value_difference |
|
2197
|
|
|
) |
|
2198
|
|
|
period_investment_costs[p] += investment_costs_increment |
|
2199
|
|
|
|
|
2200
|
|
|
for n in self.NON_CONVEX_INVESTSTORAGES: |
|
2201
|
|
|
lifetime = n.investment.lifetime |
|
2202
|
|
|
interest = 0 |
|
2203
|
|
|
if interest == 0: |
|
2204
|
|
|
warn( |
|
2205
|
|
|
msg.format(m.discount_rate), |
|
2206
|
|
|
debugging.SuspiciousUsageWarning, |
|
2207
|
|
|
) |
|
2208
|
|
|
interest = m.discount_rate |
|
2209
|
|
|
for p in m.PERIODS: |
|
2210
|
|
|
annuity = economics.annuity( |
|
2211
|
|
|
capex=n.investment.ep_costs[p], |
|
2212
|
|
|
n=lifetime, |
|
2213
|
|
|
wacc=interest, |
|
2214
|
|
|
) |
|
2215
|
|
|
duration = min( |
|
2216
|
|
|
m.es.end_year_of_optimization - m.es.periods_years[p], |
|
2217
|
|
|
lifetime, |
|
2218
|
|
|
) |
|
2219
|
|
|
present_value_factor = 1 / economics.annuity( |
|
2220
|
|
|
capex=1, n=duration, wacc=interest |
|
2221
|
|
|
) |
|
2222
|
|
|
investment_costs_increment = ( |
|
2223
|
|
|
self.invest[n, p] * annuity * present_value_factor |
|
2224
|
|
|
+ self.invest_status[n, p] * n.investment.offset[p] |
|
2225
|
|
|
) |
|
2226
|
|
|
remaining_value_difference = ( |
|
2227
|
|
|
self._evaluate_remaining_value_difference( |
|
2228
|
|
|
m, |
|
2229
|
|
|
p, |
|
2230
|
|
|
n, |
|
2231
|
|
|
m.es.end_year_of_optimization, |
|
2232
|
|
|
lifetime, |
|
2233
|
|
|
interest, |
|
2234
|
|
|
nonconvex=True, |
|
2235
|
|
|
) |
|
2236
|
|
|
) |
|
2237
|
|
|
investment_costs += ( |
|
2238
|
|
|
investment_costs_increment + remaining_value_difference |
|
2239
|
|
|
) |
|
2240
|
|
|
period_investment_costs[p] += investment_costs_increment |
|
2241
|
|
|
|
|
2242
|
|
|
for n in self.INVESTSTORAGES: |
|
2243
|
|
|
if valid_sequence(n.investment.fixed_costs, len(m.PERIODS)): |
|
2244
|
|
|
lifetime = n.investment.lifetime |
|
2245
|
|
|
for p in m.PERIODS: |
|
2246
|
|
|
range_limit = min( |
|
2247
|
|
|
m.es.end_year_of_optimization, |
|
2248
|
|
|
m.es.periods_years[p] + lifetime, |
|
2249
|
|
|
) |
|
2250
|
|
|
fixed_costs += sum( |
|
2251
|
|
|
self.invest[n, p] * n.investment.fixed_costs[pp] |
|
2252
|
|
|
for pp in range( |
|
2253
|
|
|
m.es.periods_years[p], |
|
2254
|
|
|
range_limit, |
|
2255
|
|
|
) |
|
2256
|
|
|
) |
|
2257
|
|
|
|
|
2258
|
|
|
for n in self.EXISTING_INVESTSTORAGES: |
|
2259
|
|
|
if valid_sequence(n.investment.fixed_costs, len(m.PERIODS)): |
|
2260
|
|
|
lifetime = n.investment.lifetime |
|
2261
|
|
|
age = n.investment.age |
|
2262
|
|
|
range_limit = min( |
|
2263
|
|
|
m.es.end_year_of_optimization, lifetime - age |
|
2264
|
|
|
) |
|
2265
|
|
|
fixed_costs += sum( |
|
2266
|
|
|
n.investment.existing * n.investment.fixed_costs[pp] |
|
2267
|
|
|
for pp in range(range_limit) |
|
2268
|
|
|
) |
|
2269
|
|
|
|
|
2270
|
|
|
for n in self.INVESTSTORAGES: |
|
2271
|
|
View Code Duplication |
if valid_sequence(n.storage_costs, len(m.TIMESTEPS)): |
|
|
|
|
|
|
2272
|
|
|
# We actually want to iterate over all TIMEPOINTS except the |
|
2273
|
|
|
# 0th. As integers are used for the index, this is equicalent |
|
2274
|
|
|
# to iterating over the TIMESTEPS with one offset. |
|
2275
|
|
|
if not m.TSAM_MODE: |
|
2276
|
|
|
for t in m.TIMESTEPS: |
|
2277
|
|
|
storage_costs += ( |
|
2278
|
|
|
self.storage_content[n, t + 1] * n.storage_costs[t] |
|
2279
|
|
|
) |
|
2280
|
|
|
else: |
|
2281
|
|
|
for t in m.TIMESTEPS_ORIGINAL: |
|
2282
|
|
|
storage_costs += ( |
|
2283
|
|
|
self.storage_content[n, t + 1] |
|
2284
|
|
|
* n.storage_costs[t + 1] |
|
2285
|
|
|
) |
|
2286
|
|
|
|
|
2287
|
|
|
self.storage_costs = Expression(expr=storage_costs) |
|
2288
|
|
|
|
|
2289
|
|
|
self.investment_costs = Expression(expr=investment_costs) |
|
2290
|
|
|
self.period_investment_costs = period_investment_costs |
|
2291
|
|
|
self.fixed_costs = Expression(expr=fixed_costs) |
|
2292
|
|
|
self.costs = Expression( |
|
2293
|
|
|
expr=investment_costs + fixed_costs + storage_costs |
|
2294
|
|
|
) |
|
2295
|
|
|
|
|
2296
|
|
|
return self.costs |
|
2297
|
|
|
|
|
2298
|
|
|
def _evaluate_remaining_value_difference( |
|
2299
|
|
|
self, |
|
2300
|
|
|
m, |
|
2301
|
|
|
p, |
|
2302
|
|
|
n, |
|
2303
|
|
|
end_year_of_optimization, |
|
2304
|
|
|
lifetime, |
|
2305
|
|
|
interest, |
|
2306
|
|
|
nonconvex=False, |
|
2307
|
|
|
): |
|
2308
|
|
|
"""Evaluate and return the remaining value difference of an investment |
|
2309
|
|
|
|
|
2310
|
|
|
The remaining value difference in the net present values if the asset |
|
2311
|
|
|
was to be liquidated at the end of the optimization horizon and the |
|
2312
|
|
|
net present value using the original investment expenses. |
|
2313
|
|
|
|
|
2314
|
|
|
Parameters |
|
2315
|
|
|
---------- |
|
2316
|
|
|
m : oemof.solph.models.Model |
|
2317
|
|
|
Optimization model |
|
2318
|
|
|
|
|
2319
|
|
|
p : int |
|
2320
|
|
|
Period in which investment occurs |
|
2321
|
|
|
|
|
2322
|
|
|
n : oemof.solph.components.GenericStorage |
|
2323
|
|
|
storage unit |
|
2324
|
|
|
|
|
2325
|
|
|
end_year_of_optimization : int |
|
2326
|
|
|
Last year of the optimization horizon |
|
2327
|
|
|
|
|
2328
|
|
|
lifetime : int |
|
2329
|
|
|
lifetime of investment considered |
|
2330
|
|
|
|
|
2331
|
|
|
interest : float |
|
2332
|
|
|
Demanded interest rate for investment |
|
2333
|
|
|
|
|
2334
|
|
|
nonconvex : bool |
|
2335
|
|
|
Indicating whether considered flow is nonconvex. |
|
2336
|
|
|
""" |
|
2337
|
|
|
if m.es.use_remaining_value: |
|
2338
|
|
|
if end_year_of_optimization - m.es.periods_years[p] < lifetime: |
|
2339
|
|
|
remaining_lifetime = lifetime - ( |
|
2340
|
|
|
end_year_of_optimization - m.es.periods_years[p] |
|
2341
|
|
|
) |
|
2342
|
|
|
remaining_annuity = economics.annuity( |
|
2343
|
|
|
capex=n.investment.ep_costs[-1], |
|
2344
|
|
|
n=remaining_lifetime, |
|
2345
|
|
|
wacc=interest, |
|
2346
|
|
|
) |
|
2347
|
|
|
original_annuity = economics.annuity( |
|
2348
|
|
|
capex=n.investment.ep_costs[p], |
|
2349
|
|
|
n=remaining_lifetime, |
|
2350
|
|
|
wacc=interest, |
|
2351
|
|
|
) |
|
2352
|
|
|
present_value_factor_remaining = 1 / economics.annuity( |
|
2353
|
|
|
capex=1, n=remaining_lifetime, wacc=interest |
|
2354
|
|
|
) |
|
2355
|
|
|
convex_investment_costs = ( |
|
2356
|
|
|
self.invest[n, p] |
|
2357
|
|
|
* (remaining_annuity - original_annuity) |
|
2358
|
|
|
* present_value_factor_remaining |
|
2359
|
|
|
) |
|
2360
|
|
|
if nonconvex: |
|
2361
|
|
|
return convex_investment_costs + self.invest_status[ |
|
2362
|
|
|
n, p |
|
2363
|
|
|
] * (n.investment.offset[-1] - n.investment.offset[p]) |
|
2364
|
|
|
else: |
|
2365
|
|
|
return convex_investment_costs |
|
2366
|
|
|
else: |
|
2367
|
|
|
return 0 |
|
2368
|
|
|
else: |
|
2369
|
|
|
return 0 |
|
2370
|
|
|
|