solph.components._generic_storage

Complexity

Total Complexity

157

Size/Duplication

Total Lines	2369
Duplicated Lines	7.09 %

Importance

Changes

0

16 Methods

Rating	Name	Duplication	Size	Complexity
C	GenericStorage.__init__()	0	91	8
C	GenericInvestmentStorageBlock._add_storage_limit_constraints()	45	138	7
B	GenericStorageBlock._objective_expression()	14	42	8
C	GenericStorage._check_infeasible_parameter_combinations()	0	35	11
F	GenericInvestmentStorageBlock._create()	25	651	52
A	GenericStorage._check_input_for_investment()	0	6	2
A	GenericStorage._check_number_of_flows()	0	9	3
F	GenericStorageBlock._create()	70	315	23
A	GenericStorage._check_storage_for_investment()	0	4	1
A	GenericInvestmentStorageBlock.__init__()	0	2	1
F	GenericInvestmentStorageBlock._objective_expression()	14	167	22
A	GenericStorage.constraint_group()	0	5	2
C	GenericStorage._check_invest_relations()	0	46	10
A	GenericStorage._check_output_for_investment()	0	6	2
A	GenericStorageBlock.__init__()	0	2	1
A	GenericInvestmentStorageBlock._evaluate_remaining_value_difference()	0	72	4

# -*- coding: utf-8 -


"""

GenericStorage and associated individual constraints (blocks) and groupings.


SPDX-FileCopyrightText: Uwe Krien <krien@uni-bremen.de>

SPDX-FileCopyrightText: Simon Hilpert

SPDX-FileCopyrightText: Cord Kaldemeyer

SPDX-FileCopyrightText: Patrik Schönfeldt

SPDX-FileCopyrightText: FranziPl

SPDX-FileCopyrightText: jnnr

SPDX-FileCopyrightText: Stephan Günther

SPDX-FileCopyrightText: FabianTU

SPDX-FileCopyrightText: Johannes Röder

SPDX-FileCopyrightText: Ekaterina Zolotarevskaia

SPDX-FileCopyrightText: Johannes Kochems

SPDX-FileCopyrightText: Johannes Giehl

SPDX-FileCopyrightText: Raul Ciria Aylagas

SPDX-FileCopyrightText: Lennart Schürmann (Fraunhofer UMSICHT)


SPDX-License-Identifier: MIT


"""


import math

import numbers

from warnings import warn


import numpy as np

from oemof.network import Node

from oemof.tools import debugging

from oemof.tools import economics

from pyomo.core.base.block import ScalarBlock

from pyomo.environ import Binary

from pyomo.environ import BuildAction

from pyomo.environ import Constraint

from pyomo.environ import Expression

from pyomo.environ import NonNegativeReals

from pyomo.environ import Set

from pyomo.environ import Var


from oemof.solph._helpers import check_node_object_for_missing_attribute

from oemof.solph._options import Investment

from oemof.solph._plumbing import sequence

from oemof.solph._plumbing import valid_sequence



class GenericStorage(Node):

    r"""

    Component `GenericStorage` to model with basic characteristics of storages.


    The GenericStorage is designed for one input and one output.


    Parameters

    ----------

    nominal_capacity : numeric, :math:`E_{nom}` or

            :class:`oemof.solph.options.Investment` object

        Absolute nominal capacity of the storage, fixed value or

        object describing parameter of investment optimisations.

    invest_relation_input_capacity : numeric (iterable or scalar) or None, :math:`r_{cap,in}`

        Ratio between the investment variable of the input flow and the

        investment variable of the storage:

        :math:`\dot{E}_{in,invest} = E_{invest} \cdot r_{cap,in}`

    invest_relation_output_capacity : numeric (iterable or scalar) or None, :math:`r_{cap,out}`

        Ratio between the investment variable of the output flow and the

        investment variable of the storage:

        :math:`\dot{E}_{out,invest} = E_{invest} \cdot r_{cap,out}`

    invest_relation_input_output : numeric (iterable or scalar) or None, :math:`r_{in,out}`

        Ratio between the investment variable of the input flow and the

        investment variable of the output flow. This ratio used to fix the

        flow investments to each other.

        Values < 1 set the input flow lower than the output and > 1 will

        set the input flow higher than the output flow. If set to None no relation

        will be set:

        :math:`\dot{E}_{in,invest} = \dot{E}_{out,invest} \cdot r_{in,out}`

    initial_storage_level : numeric, :math:`c(-1)`

        The relative storage content in the timestep before the first

        time step of optimization (between 0 and 1).


        Note: When investment mode is used in a multi-period model,

        `initial_storage_level` is not supported.

        Storage output is forced to zero until the storage unit is invested in.

    balanced : boolean

        Couple storage level of first and last time step.

        (Total inflow and total outflow are balanced.)

    loss_rate : numeric (iterable or scalar)

        The relative loss of the storage content per hour.

    fixed_losses_relative : numeric (iterable or scalar), :math:`\gamma(t)`

        Losses per hour that are independent of the storage content but

        proportional to nominal storage capacity.


        Note: Fixed losses are not supported in investment mode.

    fixed_losses_absolute : numeric (iterable or scalar), :math:`\delta(t)`

        Losses per hour that are independent of storage content and independent

        of nominal storage capacity.


        Note: Fixed losses are not supported in investment mode.

    inflow_conversion_factor : numeric (iterable or scalar), :math:`\eta_i(t)`

        The relative conversion factor, i.e. efficiency associated with the

        inflow of the storage.

    outflow_conversion_factor : numeric (iterable or scalar), :math:`\eta_o(t)`

        see: inflow_conversion_factor

    min_storage_level : numeric (iterable or scalar), :math:`c_{min}(t)`

        The normed minimum storage content as fraction of the

        nominal storage capacity or the capacity that has been invested into

        (between 0 and 1).

        To set different values in every time step use a sequence.

    max_storage_level : numeric (iterable or scalar), :math:`c_{max}(t)`

        see: min_storage_level

    storage_costs : numeric (iterable or scalar), :math:`c_{storage}(t)`

        Cost (per energy) for having energy in the storage, starting from

        time point :math:`t_{1}`. (:math:`t_{0}` is left out to avoid counting

        it twice if balanced=True.)

    lifetime_inflow : int, :math:`n_{in}`

        Determine the lifetime of an inflow; only applicable for multi-period

        models which can invest in storage capacity and have an

        invest_relation_input_capacity defined

    lifetime_outflow : int, :math:`n_{in}`

        Determine the lifetime of an outflow; only applicable for multi-period

        models which can invest in storage capacity and have an

        invest_relation_output_capacity defined


    Notes

    -----

    The following sets, variables, constraints and objective parts are created

     * :py:class:`~oemof.solph.components._generic_storage.GenericStorageBlock`

       (if no Investment object present)

     * :py:class:`~oemof.solph.components._generic_storage.GenericInvestmentStorageBlock`

       (if Investment object present)


    Examples

    --------

    Basic usage examples of the GenericStorage with a random selection of

    attributes. See the Flow class for all Flow attributes.


    >>> from oemof import solph


    >>> my_bus = solph.buses.Bus('my_bus')


    >>> my_storage = solph.components.GenericStorage(

    ...     label='storage',

    ...     nominal_capacity=1000,

    ...     inputs={my_bus: solph.flows.Flow(nominal_capacity=200, variable_costs=10)},

    ...     outputs={my_bus: solph.flows.Flow(nominal_capacity=200)},

    ...     loss_rate=0.01,

    ...     initial_storage_level=0,

    ...     max_storage_level = 0.9,

    ...     inflow_conversion_factor=0.9,

    ...     outflow_conversion_factor=0.93)


    >>> my_investment_storage = solph.components.GenericStorage(

    ...     label='storage',

    ...     nominal_capacity=solph.Investment(ep_costs=50),

    ...     inputs={my_bus: solph.flows.Flow(nominal_capacity=solph.Investment())},

    ...     outputs={my_bus: solph.flows.Flow(nominal_capacity=solph.Investment())},

    ...     loss_rate=0.02,

    ...     initial_storage_level=None,

    ...     invest_relation_input_capacity=1/6,

    ...     invest_relation_output_capacity=1/6,

    ...     inflow_conversion_factor=1,

    ...     outflow_conversion_factor=0.8)

    """  # noqa: E501


    def __init__(

        self,

        label=None,

        inputs=None,

        outputs=None,

        parent_node=None,

        nominal_capacity=None,

        nominal_storage_capacity=None,  # Can be removed for versions >= v0.7

        initial_storage_level=None,

        invest_relation_input_output=None,

        invest_relation_input_capacity=None,

        invest_relation_output_capacity=None,

        min_storage_level=0,

        max_storage_level=1,

        balanced=True,

        loss_rate=0,

        fixed_losses_relative=0,

        fixed_losses_absolute=0,

        inflow_conversion_factor=1,

        outflow_conversion_factor=1,

        fixed_costs=0,

        storage_costs=None,

        lifetime_inflow=None,

        lifetime_outflow=None,

        custom_attributes=None,

    ):

        if inputs is None:

            inputs = {}

        if outputs is None:

            outputs = {}

        if custom_attributes is None:

            custom_attributes = {}

        super().__init__(

            label,

            inputs=inputs,

            outputs=outputs,

            parent_node=parent_node,

            custom_properties=custom_attributes,

        )

        # --- BEGIN: The following code can be removed for versions >= v0.7 ---

        if nominal_storage_capacity is not None:

            msg = (

                "For backward compatibility,"

                + " the option nominal_storage_capacity overwrites the option"

                + " nominal_capacity."

                + " Both options cannot be set at the same time."

            )

            if nominal_capacity is not None:

                raise AttributeError(msg)

            else:

                warn(msg, FutureWarning)

            nominal_capacity = nominal_storage_capacity

        # --- END ---


        self.nominal_storage_capacity = None

        self._invest_group = False

        self.invest_relation_input_output = sequence(

            invest_relation_input_output

        )

        self.invest_relation_input_capacity = sequence(

            invest_relation_input_capacity

        )

        self.invest_relation_output_capacity = sequence(

            invest_relation_output_capacity

        )

        if isinstance(nominal_capacity, numbers.Real):

            self.nominal_storage_capacity = nominal_capacity

        elif isinstance(nominal_capacity, Investment):

            self.investment = nominal_capacity

            self._invest_group = True


        self.initial_storage_level = initial_storage_level

        self.balanced = balanced

        self.loss_rate = sequence(loss_rate)

        self.fixed_losses_relative = sequence(fixed_losses_relative)

        self.fixed_losses_absolute = sequence(fixed_losses_absolute)

        self.inflow_conversion_factor = sequence(inflow_conversion_factor)

        self.outflow_conversion_factor = sequence(outflow_conversion_factor)

        self.max_storage_level = sequence(max_storage_level)

        self.min_storage_level = sequence(min_storage_level)

        self.fixed_costs = sequence(fixed_costs)

        self.storage_costs = sequence(storage_costs)

        self.lifetime_inflow = lifetime_inflow

        self.lifetime_outflow = lifetime_outflow


        # Check number of flows.

        self._check_number_of_flows()

        # Check for infeasible invest_relations

        self._check_invest_relations()

        # Check for infeasible parameter combinations

        self._check_infeasible_parameter_combinations()


    def _check_number_of_flows(self):

        """Ensure that there is only one inflow and outflow to the storage"""

        msg = "Only one {0} flow allowed in the GenericStorage {1}."

        check_node_object_for_missing_attribute(self, "inputs")

        check_node_object_for_missing_attribute(self, "outputs")

        if len(self.inputs) > 1:

            raise AttributeError(msg.format("input", self.label))

        if len(self.outputs) > 1:

            raise AttributeError(msg.format("output", self.label))


    def _check_input_for_investment(self):

        """Checks the input flow for an investment object. For sanity,

        this should be executed after _check_number_of_flows()"""

        for flow in self.inputs.values():

            is_investment = isinstance(flow.investment, Investment)

        return is_investment

The variable is_investment does not seem to be defined in case the for loop on line 269 is not entered. Are you sure this can never be the case?

    def _check_output_for_investment(self):

        """Checks the output flow for an investment object. For sanity,

        this should be executed after _check_number_of_flows()"""

        for flow in self.outputs.values():

            is_investment = isinstance(flow.investment, Investment)

        return is_investment

The variable is_investment does not seem to be defined in case the for loop on line 276 is not entered. Are you sure this can never be the case?

    def _check_storage_for_investment(self):

        """Checks the storage for an investment object (i.e. if investment

        into the capacity is possible)"""

        return hasattr(self, "investment")


    def _check_invest_relations(self):

        """Checks if the passed invest_relation keywords fit the

        passed Investment objects"""

        if self.invest_relation_input_capacity[0] is not None:

            if not self._check_input_for_investment():

                msg = (

                    "The input flow needs to have an Investment object "

                    "if `invest_relation_input_capacity` is set."

                )

                raise AttributeError(msg)

            if not self._check_storage_for_investment():

                msg = (

                    "If `invest_relation_input_capacity` is set, "

                    "`nominal_capacity` needs to be an Investment "

                    "object as well."

                )

                raise AttributeError(msg)

            self._invest_group = True

        if self.invest_relation_output_capacity[0] is not None:

            if not self._check_output_for_investment():

                msg = (

                    "The output flow needs to have an Investment object "

                    "if `invest_relation_output_capacity` is set."

                )

                raise AttributeError(msg)

            if not self._check_storage_for_investment():

                msg = (

                    "If `invest_relation_output_capacity` is set, "

                    "`nominal_capacity` needs to be an Investment "

                    "object as well."

                )

                raise AttributeError(msg)

            self._invest_group = True

        if self.invest_relation_input_output[0] is not None:

            if not self._check_input_for_investment():

                msg = (

                    "The input flow needs to have an Investment object "

                    "if `invest_relation_input_output` is set."

                )

                raise AttributeError(msg)

            if not self._check_output_for_investment():

                msg = (

                    "The output flow needs to have an Investment object "

                    "if `invest_relation_input_output` is set."

                )

                raise AttributeError(msg)


    def _check_infeasible_parameter_combinations(self):

        """Check for infeasible parameter combinations and raise error"""

        if self.initial_storage_level is not None:

            if (

                self.initial_storage_level < self.min_storage_level[0]

                or self.initial_storage_level > self.max_storage_level[0]

            ):

                e1 = (

                    "initial_storage_level must be greater or equal to "

                    "min_storage_level and smaller or equal to "

                    "max_storage_level."

                )

                raise ValueError(e1)

        """Raise errors for infeasible investment attribute combinations"""

        if (

            self.invest_relation_input_output[0] is not None

            and self.invest_relation_output_capacity[0] is not None

            and self.invest_relation_input_capacity[0] is not None

        ):

            e2 = (

                "Overdetermined. Three investment object will be coupled"

                "with three constraints. Set one invest relation to 'None'."

            )

            raise AttributeError(e2)

        if (

            hasattr(self, "investment")

            and self.fixed_losses_absolute.max() != 0

            and self.investment.existing == 0

            and self.investment.minimum.min() == 0

        ):

            e3 = (

                "With fixed_losses_absolute > 0, either investment.existing "

                "or investment.minimum has to be non-zero."

            )

            raise AttributeError(e3)


    def constraint_group(self):

        if self._invest_group is True:

            return GenericInvestmentStorageBlock

        else:

            return GenericStorageBlock



class GenericStorageBlock(ScalarBlock):

    r"""Storage without an :class:`.Investment` object.


    **The following sets are created:** (-> see basic sets at

    :class:`.Model` )


    STORAGES

        A set with all :py:class:`~.GenericStorage` objects, which do not have an

        :attr:`investment` of type :class:`.Investment`.


    STORAGES_BALANCED

        A set of  all :py:class:`~.GenericStorage` objects, with 'balanced' attribute set

        to True.


    STORAGES_WITH_INVEST_FLOW_REL

        A set with all :py:class:`~.GenericStorage` objects with two investment

        flows coupled with the 'invest_relation_input_output' attribute.


    **The following variables are created:**


    storage_content

        Storage content for every storage and timestep. The value for the

        storage content at the beginning is set by the parameter

        `initial_storage_level` or not set if `initial_storage_level` is None.

        The variable of storage s and timestep t can be accessed by:

        `om.GenericStorageBlock.storage_content[s, t]`


    intra_storage_delta

        Storage content for every storage and timestep of typical periods

        (only used in TSAM-mode). The variable of storage s and timestep t can

        be accessed by: `om.GenericStorageBlock.intra_storage_delta[s, k, t]`


    **The following constraints are created:**


    Set storage_content of last time step to one at t=0 if balanced == True

        .. math::

            E(t_{last}) = E(-1)


    Storage losses :attr:`om.Storage.losses[n, t]`

        .. math:: E_{loss}(t) = &E(t-1) \cdot

            1 - (1 - \beta(t))^{\tau(t)/(t_u)} \\

            &- \gamma(t)\cdot E_{nom} \cdot {\tau(t)/(t_u)}\\

            &- \delta(t) \cdot {\tau(t)/(t_u)}


    Storage balance :attr:`om.Storage.balance[n, t]`

        .. math:: E(t) = &E(t-1) - E_{loss}(t)\\

            &- \frac{\dot{E}_o(p, t)}{\eta_o(t)} \cdot \tau(t)\\

            &+ \dot{E}_i(p, t) \cdot \eta_i(t) \cdot \tau(t)


    Connect the invest variables of the input and the output flow.

        .. math::

          InvestmentFlowBlock.invest(source(n), n, p) + existing = \\

          (InvestmentFlowBlock.invest(n, target(n), p) + existing) \\

          * invest\_relation\_input\_output(n) \\

          \forall n \in \textrm{INVEST\_REL\_IN\_OUT} \\

          \forall p \in \textrm{PERIODS}




    =========================== ======================= =========

    symbol                      explanation             attribute

    =========================== ======================= =========

    :math:`E(t)`                energy currently stored `storage_content`

    :math:`E_{nom}`             nominal capacity of     `nominal_storage_capacity`

                                the energy storage

    :math:`c(-1)`               state before            `initial_storage_level`

                                initial time step

    :math:`c_{min}(t)`          minimum allowed storage `min_storage_level[t]`

    :math:`c_{max}(t)`          maximum allowed storage `max_storage_level[t]`

    :math:`\beta(t)`            fraction of lost energy `loss_rate[t]`

                                as share of

                                :math:`E(t)` per hour

    :math:`\gamma(t)`           fixed loss of energy    `fixed_losses_relative[t]`

                                per hour relative to

                                :math:`E_{nom}`

    :math:`\delta(t)`           absolute fixed loss     `fixed_losses_absolute[t]`

                                of energy per hour

    :math:`\dot{E}_i(t)`        energy flowing in       `inputs`

    :math:`\dot{E}_o(t)`        energy flowing out      `outputs`

    :math:`\eta_i(t)`           conversion factor       `inflow_conversion_factor[t]`

                                (i.e. efficiency)

                                when storing energy

    :math:`\eta_o(t)`           conversion factor when  `outflow_conversion_factor[t]`

                                (i.e. efficiency)

                                taking stored energy

    :math:`\tau(t)`             duration of time step

    :math:`t_u`                 time unit of losses

                                :math:`\beta(t)`,

                                :math:`\gamma(t)`

                                :math:`\delta(t)` and

                                timeincrement

                                :math:`\tau(t)`

    :math:`c_{storage}(t)`      costs of having         `storage_costs`

                                energy stored

    =========================== ======================= =========


    **The following parts of the objective function are created:**


    * :attr: `storage_costs` not 0


        .. math::

            \sum_{t \in \textrm{TIMEPOINTS} > 0} c_{storage}(t) \cdot E(t)


    * :attr:`fixed_costs` not 0


        .. math::

            \displaystyle \sum_{pp=0}^{year_{max}} E_{nom}

            \cdot c_{fixed}(pp)


    where :math:`year_{max}` denotes the last year of the optimization

      horizon, i.e. at the end of the last period.


    """  # noqa: E501


    CONSTRAINT_GROUP = True


    def __init__(self, *args, **kwargs):

        super().__init__(*args, **kwargs)


    def _create(self, group=None):

        """

        Parameters

        ----------

        group : list

            List containing storage objects.

            e.g. groups=[storage1, storage2,..]

        """

        m = self.parent_block()


        if group is None:

            return None


        i = {n: [i for i in n.inputs][0] for n in group}

        o = {n: [o for o in n.outputs][0] for n in group}


        #  ************* SETS *********************************


        self.STORAGES = Set(initialize=[n for n in group])


        self.STORAGES_BALANCED = Set(

            initialize=[n for n in group if n.balanced is True]

        )


        self.STORAGES_INITITAL_LEVEL = Set(

            initialize=[

                n for n in group if n.initial_storage_level is not None

            ]

        )


        self.STORAGES_WITH_INVEST_FLOW_REL = Set(

            initialize=[

                n

                for n in group

                if n.invest_relation_input_output[0] is not None

            ]

        )


        #  ************* VARIABLES *****************************


        def _storage_content_bound_rule(block, n, t):

            """

            Rule definition for bounds of storage_content variable of

            storage n in timestep t.

            """

            bounds = (

                n.nominal_storage_capacity * n.min_storage_level[t],

                n.nominal_storage_capacity * n.max_storage_level[t],

            )

            return bounds


        if not m.TSAM_MODE:

            self.storage_content = Var(

                self.STORAGES, m.TIMEPOINTS, bounds=_storage_content_bound_rule

            )


            self.storage_losses = Var(self.STORAGES, m.TIMESTEPS)


            # set the initial storage content

            # ToDo: More elegant code possible?

            for n in group:

                if n.initial_storage_level is not None:

                    self.storage_content[n, 0] = (

                        n.initial_storage_level * n.nominal_storage_capacity

                    )

                    self.storage_content[n, 0].fix()

        else:

            # called "inter" in https://doi.org/10.1016/j.apenergy.2018.01.023

            self.inter_storage_content = Var(

                self.STORAGES, m.CLUSTERS_OFFSET, within=NonNegativeReals

            )

            # called "intra" in https://doi.org/10.1016/j.apenergy.2018.01.023

            self.intra_storage_delta = Var(

                self.STORAGES, m.TIMEINDEX_TYPICAL_CLUSTER_OFFSET

            )

            # set the initial intra storage content

            # first timestep in intra storage is always zero

            for n in group:

                for p, k in m.TYPICAL_CLUSTERS:

                    self.intra_storage_delta[n, p, k, 0] = 0

                    self.intra_storage_delta[n, p, k, 0].fix()

                if n.initial_storage_level is not None:

                    self.inter_storage_content[n, 0] = (

                        n.initial_storage_level * n.nominal_storage_capacity

                    )

                    self.inter_storage_content[n, 0].fix()

        #  ************* Constraints ***************************


        def _storage_inter_minimum_level_rule(block):

This code seems to be duplicated in your project.

            # See FINE implementation at

            # https://github.com/FZJ-IEK3-VSA/FINE/blob/

            # 57ec32561fb95e746c505760bd0d61c97d2fd2fb/FINE/storage.py#L1329

            for n in self.STORAGES:

                for p, i, g in m.TIMEINDEX_CLUSTER:

                    t = m.get_timestep_from_tsam_timestep(p, i, g)

                    lhs = n.nominal_storage_capacity * n.min_storage_level[t]

                    k = m.es.tsa_parameters[p]["order"][i]

                    tk = m.get_timestep_from_tsam_timestep(p, k, g)

                    inter_i = (

                        sum(

                            len(m.es.tsa_parameters[ip]["order"])

                            for ip in range(p)

                        )

                        + i

                    )

                    rhs = (

                        self.inter_storage_content[n, inter_i]

                        * (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk])

                        + self.intra_storage_delta[n, p, k, g]

                    )

                    self.storage_inter_minimum_level.add(

                        (n, p, i, g), lhs <= rhs

                    )


        if m.TSAM_MODE:

            self.storage_inter_minimum_level = Constraint(

                self.STORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True

            )


            self.storage_inter_minimum_level_build = BuildAction(

                rule=_storage_inter_minimum_level_rule

            )


        def _storage_inter_maximum_level_rule(block):

This code seems to be duplicated in your project.

            for n in self.STORAGES:

                for p, i, g in m.TIMEINDEX_CLUSTER:

                    t = m.get_timestep_from_tsam_timestep(p, i, g)

                    k = m.es.tsa_parameters[p]["order"][i]

                    tk = m.get_timestep_from_tsam_timestep(p, k, g)

                    inter_i = (

                        sum(

                            len(m.es.tsa_parameters[ip]["order"])

                            for ip in range(p)

                        )

                        + i

                    )

                    lhs = (

                        self.inter_storage_content[n, inter_i]

                        * (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk])

                        + self.intra_storage_delta[n, p, k, g]

                    )

                    rhs = n.nominal_storage_capacity * n.max_storage_level[t]

                    self.storage_inter_maximum_level.add(

                        (n, p, i, g), lhs <= rhs

                    )


        if m.TSAM_MODE:

            self.storage_inter_maximum_level = Constraint(

                self.STORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True

            )


            self.storage_inter_maximum_level_build = BuildAction(

                rule=_storage_inter_maximum_level_rule

            )


        def _storage_losses_rule(block, n, t):

            expr = block.storage_content[n, t] * (

                1 - (1 - n.loss_rate[t]) ** m.timeincrement[t]

            )

            expr += (

                n.fixed_losses_relative[t]

                * n.nominal_storage_capacity

                * m.timeincrement[t]

            )

            expr += n.fixed_losses_absolute[t] * m.timeincrement[t]


            return expr == block.storage_losses[n, t]


        if not m.TSAM_MODE:

            self.losses = Constraint(

                self.STORAGES, m.TIMESTEPS, rule=_storage_losses_rule

            )


        def _storage_balance_rule(block, n, t):

            """

            Rule definition for the storage balance of every storage n and

            every timestep.

            """

            expr = block.storage_content[n, t]

            expr -= block.storage_losses[n, t]

            expr += (

                m.flow[i[n], n, t] * n.inflow_conversion_factor[t]

The variable i does not seem to be defined for all execution paths.

            ) * m.timeincrement[t]

            expr -= (

                m.flow[n, o[n], t] / n.outflow_conversion_factor[t]

The variable o does not seem to be defined for all execution paths.

            ) * m.timeincrement[t]

            return expr == block.storage_content[n, t + 1]


        def _intra_storage_balance_rule(block, n, p, k, g):

This code seems to be duplicated in your project.

            """

            Rule definition for the storage balance of every storage n and

            every timestep.

            """

            t = m.get_timestep_from_tsam_timestep(p, k, g)

            expr = 0

            expr += block.intra_storage_delta[n, p, k, g + 1]

            expr += (

                -block.intra_storage_delta[n, p, k, g]

                * (1 - n.loss_rate[t]) ** m.timeincrement[t]

            )

            expr += (

                n.fixed_losses_relative[t]

                * n.nominal_storage_capacity

                * m.timeincrement[t]

            )

            expr += n.fixed_losses_absolute[t] * m.timeincrement[t]

            expr += (

                -m.flow[i[n], n, t] * n.inflow_conversion_factor[t]

The variable i does not seem to be defined for all execution paths.

            ) * m.timeincrement[t]

            expr += (

                m.flow[n, o[n], t] / n.outflow_conversion_factor[t]

The variable o does not seem to be defined for all execution paths.

            ) * m.timeincrement[t]

            return expr == 0


        if not m.TSAM_MODE:

            self.balance = Constraint(

                self.STORAGES, m.TIMESTEPS, rule=_storage_balance_rule

            )

        else:

            self.intra_balance = Constraint(

                self.STORAGES,

                m.TIMEINDEX_TYPICAL_CLUSTER,

                rule=_intra_storage_balance_rule,

            )


        def _inter_storage_balance_rule(block, n, i):

            """

            Rule definition for the storage balance of every storage n and

            every timestep.

            """

            ii = 0

            for p in m.PERIODS:

                ii += len(m.es.tsa_parameters[p]["order"])

                if ii > i:

                    ii -= len(m.es.tsa_parameters[p]["order"])

                    ii = i - ii

                    break


            k = m.es.tsa_parameters[p]["order"][ii]

The variable p does not seem to be defined in case the for loop on line 725 is not entered. Are you sure this can never be the case?

            # Calculate inter losses over whole typical period

            t0 = m.get_timestep_from_tsam_timestep(p, k, 0)

            losses = math.prod(

                (

                    (1 - n.loss_rate[t0 + s])

                    ** m.es.tsa_parameters[p]["segments"][(k, s)]

                    if "segments" in m.es.tsa_parameters[p]

                    else 1 - n.loss_rate[t0 + s]

                )

                for s in range(m.es.tsa_parameters[p]["timesteps"])

            )


            expr = 0

            expr += block.inter_storage_content[n, i + 1]

            expr += -block.inter_storage_content[n, i] * losses

            expr += -self.intra_storage_delta[

                n, p, k, m.es.tsa_parameters[p]["timesteps"]

            ]

            return expr == 0


        if m.TSAM_MODE:

            self.inter_balance = Constraint(

                self.STORAGES,

                m.CLUSTERS,

                rule=_inter_storage_balance_rule,

            )


        def _balanced_storage_rule(block, n):

            """

            Storage content of last time step == initial storage content

            if balanced.

            """

            return (

                block.storage_content[n, m.TIMEPOINTS.at(-1)]

                == block.storage_content[n, m.TIMEPOINTS.at(1)]

            )


        def _balanced_inter_storage_rule(block, n):

            """

            Storage content of last time step == initial storage content

            if balanced.

            """

            return (

                block.inter_storage_content[n, m.CLUSTERS_OFFSET.at(-1)]

                == block.inter_storage_content[n, m.CLUSTERS_OFFSET.at(1)]

            )


        if not m.TSAM_MODE:

            self.balanced_cstr = Constraint(

                self.STORAGES_BALANCED, rule=_balanced_storage_rule

            )

        else:

            self.balanced_cstr = Constraint(

                self.STORAGES_BALANCED, rule=_balanced_inter_storage_rule

            )


        def _power_coupled(_):

            """

            Rule definition for constraint to connect the input power

            and output power

            """

            for n in self.STORAGES_WITH_INVEST_FLOW_REL:

                for p in m.PERIODS:

                    expr = (

                        m.InvestmentFlowBlock.total[n, o[n], p]

The variable o does not seem to be defined for all execution paths.

                    ) * n.invest_relation_input_output[p] == (

                        m.InvestmentFlowBlock.total[i[n], n, p]

The variable i does not seem to be defined for all execution paths.

                    )

                    self.power_coupled.add((n, p), expr)


        self.power_coupled = Constraint(

            self.STORAGES_WITH_INVEST_FLOW_REL, m.PERIODS, noruleinit=True

        )


        self.power_coupled_build = BuildAction(rule=_power_coupled)


    def _objective_expression(self):

        r"""

        Objective expression for storages with no investment.


        * Fixed costs (will not have an impact on the actual optimisation).

        * Variable costs for storage content.

        """

        m = self.parent_block()


        fixed_costs = 0


        for n in self.STORAGES:

            if valid_sequence(n.fixed_costs, len(m.PERIODS)):

                fixed_costs += sum(

                    n.nominal_storage_capacity * n.fixed_costs[pp]

                    for pp in range(m.es.end_year_of_optimization)

                )

        self.fixed_costs = Expression(expr=fixed_costs)


        storage_costs = 0


        for n in self.STORAGES:

            if valid_sequence(n.storage_costs, len(m.TIMESTEPS)):

This code seems to be duplicated in your project.

                # We actually want to iterate over all TIMEPOINTS except the

                # 0th. As integers are used for the index, this is equicalent

                # to iterating over the TIMESTEPS with one offset.

                if not m.TSAM_MODE:

                    for t in m.TIMESTEPS:

                        storage_costs += (

                            self.storage_content[n, t + 1] * n.storage_costs[t]

                        )

                else:

                    for t in m.TIMESTEPS_ORIGINAL:

                        storage_costs += (

                            self.storage_content[n, t + 1]

                            * n.storage_costs[t + 1]

                        )


        self.storage_costs = Expression(expr=storage_costs)

        self.costs = Expression(expr=storage_costs + fixed_costs)


        return self.costs



class GenericInvestmentStorageBlock(ScalarBlock):

    r"""

    Block for all storages with :attr:`Investment` being not None.

    See :class:`.Investment` for all parameters of the

    Investment class.


    **Variables**


    All Storages are indexed by :math:`n` (denoting the respective storage

    unit), which is omitted in the following for the sake of convenience.

    The following variables are created as attributes of

    :attr:`om.GenericInvestmentStorageBlock`:


    * :math:`P_i(p, t)`


        Inflow of the storage

        (created in :class:`oemof.solph.models.Model`).


    * :math:`P_o(p, t)`


        Outflow of the storage

        (created in :class:`oemof.solph.models.Model`).


    * :math:`E(t)`


        Current storage content (Absolute level of stored energy).


    * :math:`E_{invest}(p)`


        Invested (nominal) capacity of the storage in period p.


    * :math:`E_{total}(p)`


        Total installed (nominal) capacity of the storage in period p.


    * :math:`E_{old}(p)`


        Old (nominal) capacity of the storage to be decommissioned in period p.


    * :math:`E_{old,exo}(p)`


        Exogenous old (nominal) capacity of the storage to be decommissioned

        in period p; existing capacity reaching its lifetime.


    * :math:`E_{old,endo}(p)`


        Endogenous old (nominal) capacity of the storage to be decommissioned

        in period p; endgenous investments reaching their lifetime.


    * :math:`E(-1)`


        Initial storage content (before timestep 0).

        Not applicable for a multi-period model.


    * :math:`b_{invest}(p)`


        Binary variable for the status of the investment, if

        :attr:`nonconvex` is `True`.


    **Constraints**


    The following constraints are created for all investment storages:


        Storage balance (Same as for :class:`.GenericStorageBlock`)


        .. math:: E(t) = &E(t-1) \cdot

            (1 - \beta(t)) ^{\tau(t)/(t_u)} \\

            &- \gamma(t)\cdot (E_{total}(p)) \cdot {\tau(t)/(t_u)}\\

            &- \delta(t) \cdot {\tau(t)/(t_u)}\\

            &- \frac{\dot{E}_o(p, t))}{\eta_o(t)} \cdot \tau(t)

            + \dot{E}_i(p, t) \cdot \eta_i(t) \cdot \tau(t)


        Total storage capacity (p > 0 for multi-period model only)


        .. math::

            &

            if \quad p=0:\\

            &

            E_{total}(p) = E_{exist} + E_{invest}(p)\\

            &\\

            &

            else:\\

            &

            E_{total}(p) = E_{total}(p-1) + E_{invest}(p) - E_{old}(p)\\

            &\\

            &

            \forall p \in \textrm{PERIODS}


        Old storage capacity (p > 0 for multi-period model only)


        .. math::

            &

            E_{old}(p) = E_{old,exo}(p) + E_{old,end}(p)\\

            &\\

            &

            if \quad p=0:\\

            &

            E_{old,end}(p) = 0\\

            &\\

            &

            else \quad if \quad l \leq year(p):\\

            &

            E_{old,end}(p) = E_{invest}(p_{comm})\\

            &\\

            &

            else:\\

            &

            E_{old,end}(p)\\

            &\\

            &

            if \quad p=0:\\

            &

            E_{old,exo}(p) = 0\\

            &\\

            &

            else \quad if \quad l - a \leq year(p):\\

            &

            E_{old,exo}(p) = E_{exist} (*)\\

            &\\

            &

            else:\\

            &

            E_{old,exo}(p) = 0\\

            &\\

            &

            \forall p \in \textrm{PERIODS}


        where:


        * (*) is only performed for the first period the condition is True.

          A decommissioning flag is then set to True to prevent having falsely

          added old capacity in future periods.

        * :math:`year(p)` is the year corresponding to period p

        * :math:`p_{comm}` is the commissioning period of the storage


    Depending on the attribute :attr:`nonconvex`, the constraints for the

    bounds of the decision variable :math:`E_{invest}(p)` are different:\


        * :attr:`nonconvex = False`


        .. math::

            &

            E_{invest, min}(p) \le E_{invest}(p) \le E_{invest, max}(p) \\

            &

            \forall p \in \textrm{PERIODS}


        * :attr:`nonconvex = True`


        .. math::

            &

            E_{invest, min}(p) \cdot b_{invest}(p) \le E_{invest}(p)\\

            &

            E_{invest}(p) \le E_{invest, max}(p) \cdot b_{invest}(p)\\

            &

            \forall p \in \textrm{PERIODS}


    The following constraints are created depending on the attributes of

    the :class:`.GenericStorage`:


        * :attr:`initial_storage_level is None`;

          not applicable for multi-period model


            Constraint for a variable initial storage content:


        .. math::

               E(-1) \le E_{exist} + E_{invest}(0)


        * :attr:`initial_storage_level is not None`;

          not applicable for multi-period model


            An initial value for the storage content is given:


        .. math::

               E(-1) = (E_{invest}(0) + E_{exist}) \cdot c(-1)


        * :attr:`balanced=True`;

          not applicable for multi-period model


            The energy content of storage of the first and the last timestep

            are set equal:


        .. math::

            E(-1) = E(t_{last})


        * :attr:`invest_relation_input_capacity is not None`


            Connect the invest variables of the storage and the input flow:


        .. math::

            &

            P_{i,total}(p) =

            E_{total}(p) \cdot r_{cap,in} \\

            &

            \forall p \in \textrm{PERIODS}


        * :attr:`invest_relation_output_capacity is not None`


            Connect the invest variables of the storage and the output flow:


        .. math::

            &

            P_{o,total}(p) =

            E_{total}(p) \cdot r_{cap,out}\\

            &

            \forall p \in \textrm{PERIODS}


        * :attr:`invest_relation_input_output is not None`


            Connect the invest variables of the input and the output flow:


        .. math::

            &

            P_{i,total}(p) =

            P_{o,total}(p) \cdot r_{in,out}\\

            &

            \forall p \in \textrm{PERIODS}


        * :attr:`max_storage_level`


            Rule for upper bound constraint for the storage content:


        .. math::

            &

            E(t) \leq E_{total}(p) \cdot c_{max}(t)\\

            &

            \forall p, t \in \textrm{TIMEINDEX}


        * :attr:`min_storage_level`


            Rule for lower bound constraint for the storage content:


        .. math::

            &

            E(t) \geq E_{total}(p) \cdot c_{min}(t)\\

            &

            \forall p, t \in \textrm{TIMEINDEX}



    **Objective function**


    Objective terms for a standard model and a multi-period model differ

    quite strongly. Besides, the part of the objective function added by the

    investment storages also depends on whether a convex or nonconvex

    investment option is selected. The following parts of the objective

    function are created:


    *Standard model*


        * :attr:`nonconvex = False`


            .. math::

                E_{invest}(0) \cdot c_{invest,var}(0)


        * :attr:`nonconvex = True`


            .. math::

                E_{invest}(0) \cdot c_{invest,var}(0)

                + c_{invest,fix}(0) \cdot b_{invest}(0)\\


    Where 0 denotes the 0th (investment) period since

    in a standard model, there is only this one period.


    *Multi-period model*


        * :attr:`nonconvex = False`


            .. math::

                &

                E_{invest}(p) \cdot A(c_{invest,var}(p), l, ir)

                \cdot \frac {1}{ANF(d, ir)} \cdot DF^{-p}\\

                &

                \forall p \in \textrm{PERIODS}


        In case, the remaining lifetime of a storage is greater than 0 and

        attribute `use_remaining_value` of the energy system is True,

        the difference in value for the investment period compared to the

        last period of the optimization horizon is accounted for

        as an adder to the investment costs:


            .. math::

                &

                E_{invest}(p) \cdot (A(c_{invest,var}(p), l_{r}, ir) -

                A(c_{invest,var}(|P|), l_{r}, ir)\\

                & \cdot \frac {1}{ANF(l_{r}, ir)} \cdot DF^{-|P|}\\

                &\\

                &

                \forall p \in \textrm{PERIODS}


        * :attr:`nonconvex = True`


            .. math::

                &

                (E_{invest}(p) \cdot A(c_{invest,var}(p), l, ir)

                \cdot \frac {1}{ANF(d, ir)}\\

                &

                +  c_{invest,fix}(p) \cdot b_{invest}(p)) \cdot DF^{-p} \\

                &

                \forall p \in \textrm{PERIODS}


        In case, the remaining lifetime of a storage is greater than 0 and

        attribute `use_remaining_value` of the energy system is True,

        the difference in value for the investment period compared to the

        last period of the optimization horizon is accounted for

        as an adder to the investment costs:


            .. math::

                &

                (E_{invest}(p) \cdot (A(c_{invest,var}(p), l_{r}, ir) -

                A(c_{invest,var}(|P|), l_{r}, ir)\\

                & \cdot \frac {1}{ANF(l_{r}, ir)} \cdot DF^{-|P|}\\

                &

                +  (c_{invest,fix}(p) - c_{invest,fix}(|P|))

                \cdot b_{invest}(p)) \cdot DF^{-p}\\

                &\\

                &

                \forall p \in \textrm{PERIODS}


        * :attr:`fixed_costs` not None for investments


            .. math::

                &

                \sum_{pp=year(p)}^{limit_{end}}

                E_{invest}(p) \cdot c_{fixed}(pp) \cdot DF^{-pp})

                \cdot DF^{-p}\\

                &

                \forall p \in \textrm{PERIODS}


        * :attr:`fixed_costs` not None for existing capacity


            .. math::

                \sum_{pp=0}^{limit_{exo}} E_{exist} \cdot c_{fixed}(pp)

                \cdot DF^{-pp}


    where:


    * :math:`A(c_{invest,var}(p), l, ir)` A is the annuity for

      investment expenses :math:`c_{invest,var}(p)`, lifetime :math:`l`

      and interest rate :math:`ir`.

    * :math:`l_{r}` is the remaining lifetime at the end of the

      optimization horizon (in case it is greater than 0 and

      smaller than the actual lifetime).

    * :math:`ANF(d, ir)` is the annuity factor for duration :math:`d`

      and interest rate :math:`ir`.

    * :math:`d=min\{year_{max} - year(p), l\}` defines the

      number of years within the optimization horizon that investment

      annuities are accounted for.

    * :math:`year(p)` denotes the start year of period :math:`p`.

    * :math:`year_{max}` denotes the last year of the optimization

      horizon, i.e. at the end of the last period.

    * :math:`limit_{end}=min\{year_{max}, year(p) + l\}` is used as an

      upper bound to ensure fixed costs for endogenous investments

      to occur within the optimization horizon.

    * :math:`limit_{exo}=min\{year_{max}, l - a\}` is used as an

      upper bound to ensure fixed costs for existing capacities to occur

      within the optimization horizon. :math:`a` is the initial age

      of an asset.

    * :math:`DF=(1+dr)` is the discount factor.


    The annuity / annuity factor hereby is:


        .. math::

            &

            A(c_{invest,var}(p), l, ir) = c_{invest,var}(p) \cdot

                \frac {(1+ir)^l \cdot ir} {(1+ir)^l - 1}\\

            &\\

            &

            ANF(d, ir)=\frac {(1+ir)^d \cdot ir} {(1+ir)^d - 1}


    They are retrieved, using oemof.tools.economics annuity function. The

    interest rate :math:`ir` for the annuity is defined as weighted

    average costs of capital (wacc) and assumed constant over time.


    The overall summed cost expressions for all *InvestmentFlowBlock* objects

    can be accessed by


    * :attr:`om.GenericInvestmentStorageBlock.investment_costs`,

    * :attr:`om.GenericInvestmentStorageBlock.fixed_costs` and

    * :attr:`om.GenericInvestmentStorageBlock.costs`.


    Their values  after optimization can be retrieved by


    * :meth:`om.GenericInvestmentStorageBlock.investment_costs`,

    * :attr:`om.GenericInvestmentStorageBlock.period_investment_costs`

      (yielding a dict keyed by periods); note: this is not a Pyomo expression,

      but calculated,

    * :meth:`om.GenericInvestmentStorageBlock.fixed_costs` and

    * :meth:`om.GenericInvestmentStorageBlock.costs`.


    .. csv-table:: List of Variables

        :header: "symbol", "attribute", "explanation"

        :widths: 1, 1, 1


        ":math:`P_i(p, t)`", ":attr:`flow[i[n], n, p, t]`", "Inflow

        of the storage"

        ":math:`P_o(p, t)`", ":attr:`flow[n, o[n], p, t]`", "Outflow

        of the storage"

        ":math:`E(t)`", ":attr:`storage_content[n, t]`", "Current storage

        content (current absolute stored energy)"

        ":math:`E_{loss}(t)`", ":attr:`storage_losses[n, t]`", "Current storage

        losses (absolute losses per time step)"

        ":math:`E_{invest}(p)`", ":attr:`invest[n, p]`", "Invested (nominal)

        capacity of the storage"

        ":math:`E_{old}(p)`", ":attr:`old[n, p]`", "

        | Old (nominal) capacity of the storage

        | to be decommissioned in period p"

        ":math:`E_{old,exo}(p)`", ":attr:`old_exo[n, p]`", "

        | Old (nominal) capacity of the storage

        | to be decommissioned in period p

        | which was exogenously given by :math:`E_{exist}`"

        ":math:`E_{old,end}(p)`", ":attr:`old_end[n, p]`", "

        | Old (nominal) capacity of the storage

        | to be decommissioned in period p

        | which was endogenously determined by :math:`E_{invest}(p_{comm})`

        | where :math:`p_{comm}` is the commissioning period"

        ":math:`E(-1)`", ":attr:`init_cap[n]`", "Initial storage capacity

        (before timestep 0)"

        ":math:`b_{invest}(p)`", ":attr:`invest_status[i, o, p]`", "Binary

        variable for the status of investment"

        ":math:`P_{i,invest}(p)`", "

        :attr:`InvestmentFlowBlock.invest[i[n], n, p]`", "

        Invested (nominal) inflow (InvestmentFlowBlock)"

        ":math:`P_{o,invest}`", "

        :attr:`InvestmentFlowBlock.invest[n, o[n]]`", "

        Invested (nominal) outflow (InvestmentFlowBlock)"


    .. csv-table:: List of Parameters

        :header: "symbol", "attribute", "explanation"

        :widths: 1, 1, 1


        ":math:`E_{exist}`", "`flows[i, o].investment.existing`", "

        Existing storage capacity"

        ":math:`E_{invest,min}`", "`flows[i, o].investment.minimum`", "

        Minimum investment value"

        ":math:`E_{invest,max}`", "`flows[i, o].investment.maximum`", "

        Maximum investment value"

        ":math:`P_{i,exist}`", "`flows[i[n], n].investment.existing`

        ", "Existing inflow capacity"

        ":math:`P_{o,exist}`", "`flows[n, o[n]].investment.existing`

        ", "Existing outflow capacity"

        ":math:`c_{invest,var}`", "`flows[i, o].investment.ep_costs`

        ", "Variable investment costs"

        ":math:`c_{invest,fix}`", "`flows[i, o].investment.offset`", "

        Fix investment costs"

        ":math:`c_{fixed}`", "`flows[i, o].investment.fixed_costs`", "

        Fixed costs; only allowed in multi-period model"

        ":math:`r_{cap,in}`", ":attr:`invest_relation_input_capacity`", "

        Relation of storage capacity and nominal inflow"

        ":math:`r_{cap,out}`", ":attr:`invest_relation_output_capacity`", "

        Relation of storage capacity and nominal outflow"

        ":math:`r_{in,out}`", ":attr:`invest_relation_input_output`", "

        Relation of nominal in- and outflow"

        ":math:`\beta(t)`", "`loss_rate[t]`", "Fraction of lost energy

        as share of :math:`E(t)` per hour"

        ":math:`\gamma(t)`", "`fixed_losses_relative[t]`", "Fixed loss

        of energy relative to :math:`E_{invest} + E_{exist}` per hour"

        ":math:`\delta(t)`", "`fixed_losses_absolute[t]`", "Absolute

        fixed loss of energy per hour"

        ":math:`\eta_i(t)`", "`inflow_conversion_factor[t]`", "

        Conversion factor (i.e. efficiency) when storing energy"

        ":math:`\eta_o(t)`", "`outflow_conversion_factor[t]`", "

        Conversion factor when (i.e. efficiency) taking stored energy"

        ":math:`c(-1)`", "`initial_storage_level`", "Initial relative

        storage content (before timestep 0)"

        ":math:`c_{max}`", "`flows[i, o].max[t]`", "Normed maximum

        value of storage content"

        ":math:`c_{min}`", "`flows[i, o].min[t]`", "Normed minimum

        value of storage content"

        ":math:`l`", "`flows[i, o].investment.lifetime`", "

        Lifetime for investments in storage capacity"

        ":math:`a`", "`flows[i, o].investment.age`", "

        Initial age of existing capacity / energy"

        ":math:`\tau(t)`", "", "Duration of time step"

        ":math:`t_u`", "", "Time unit of losses :math:`\beta(t)`,

        :math:`\gamma(t)`, :math:`\delta(t)` and timeincrement :math:`\tau(t)`"


    """


    CONSTRAINT_GROUP = True


    def __init__(self, *args, **kwargs):

        super().__init__(*args, **kwargs)


    def _create(self, group):

        """Create a storage block for investment modeling"""

        m = self.parent_block()


        # ########################## CHECKS ###################################

        if m.es.periods is not None:

            for n in group:

                error_fixed_absolute_losses = (

                    "For a multi-period investment model, fixed absolute"

                    " losses are not supported. Please remove parameter."

                )

                if n.fixed_losses_absolute[0] != 0:

                    raise ValueError(error_fixed_absolute_losses)

                error_initial_storage_level = (

                    "For a multi-period model, initial_storage_level is"

                    " not supported.\nIt needs to be removed since it"

                    " has no effect.\nstorage_content will be zero,"

                    " until there is some usable storage capacity installed."

                )

                if n.initial_storage_level is not None:

                    raise ValueError(error_initial_storage_level)


        # ########################## SETS #####################################


        self.INVESTSTORAGES = Set(initialize=[n for n in group])


        self.CONVEX_INVESTSTORAGES = Set(

            initialize=[n for n in group if n.investment.nonconvex is False]

        )


        self.NON_CONVEX_INVESTSTORAGES = Set(

            initialize=[n for n in group if n.investment.nonconvex is True]

        )


        self.INVESTSTORAGES_BALANCED = Set(

            initialize=[n for n in group if n.balanced is True]

        )


        self.INVESTSTORAGES_NO_INIT_CONTENT = Set(

            initialize=[n for n in group if n.initial_storage_level is None]

        )


        self.INVESTSTORAGES_INIT_CONTENT = Set(

            initialize=[

                n for n in group if n.initial_storage_level is not None

            ]

        )


        self.INVEST_REL_CAP_IN = Set(

            initialize=[

                n

                for n in group

                if n.invest_relation_input_capacity[0] is not None

            ]

        )


        self.INVEST_REL_CAP_OUT = Set(

            initialize=[

                n

                for n in group

                if n.invest_relation_output_capacity[0] is not None

            ]

        )


        self.INVEST_REL_IN_OUT = Set(

            initialize=[

                n

                for n in group

                if n.invest_relation_input_output[0] is not None

            ]

        )


        # The storage content is a non-negative variable, therefore it makes no

        # sense to create an additional constraint if the lower bound is zero

        # for all time steps.

        self.MIN_INVESTSTORAGES = Set(

            initialize=[

                n

                for n in group

                if sum([n.min_storage_level[t] for t in m.TIMESTEPS]) > 0

            ]

        )


        self.OVERALL_MAXIMUM_INVESTSTORAGES = Set(

            initialize=[

                n for n in group if n.investment.overall_maximum is not None

            ]

        )


        self.OVERALL_MINIMUM_INVESTSTORAGES = Set(

            initialize=[

                n for n in group if n.investment.overall_minimum is not None

            ]

        )


        self.EXISTING_INVESTSTORAGES = Set(

            initialize=[n for n in group if n.investment.existing is not None]

        )


        # ######################### Variables  ################################

        if not m.TSAM_MODE:

            self.storage_content = Var(

                self.INVESTSTORAGES, m.TIMEPOINTS, within=NonNegativeReals

            )

        else:

            self.inter_storage_content = Var(

                self.INVESTSTORAGES, m.CLUSTERS_OFFSET, within=NonNegativeReals

            )

            self.intra_storage_delta = Var(

                self.INVESTSTORAGES, m.TIMEINDEX_TYPICAL_CLUSTER_OFFSET

            )

            # set the initial intra storage content

            # first timestep in intra storage is always zero

            for n in group:

                for p, k in m.TYPICAL_CLUSTERS:

                    self.intra_storage_delta[n, p, k, 0] = 0

                    self.intra_storage_delta[n, p, k, 0].fix()


        def _storage_investvar_bound_rule(_, n, p):

            """

            Rule definition to bound the invested storage capacity `invest`.

            """

            if n in self.CONVEX_INVESTSTORAGES:

                return n.investment.minimum[p], n.investment.maximum[p]

            else:  # n in self.NON_CONVEX_INVESTSTORAGES

                return 0, n.investment.maximum[p]


        self.invest = Var(

            self.INVESTSTORAGES,

            m.PERIODS,

            within=NonNegativeReals,

            bounds=_storage_investvar_bound_rule,

        )


        # Total capacity

        self.total = Var(

            self.INVESTSTORAGES,

            m.PERIODS,

            within=NonNegativeReals,

            initialize=0,

        )


        if m.es.periods is not None:

            # Old capacity to be decommissioned (due to lifetime)

            self.old = Var(

                self.INVESTSTORAGES, m.PERIODS, within=NonNegativeReals

            )


            # Old endogenous capacity to be decommissioned (due to lifetime)

            self.old_end = Var(

                self.INVESTSTORAGES, m.PERIODS, within=NonNegativeReals

            )


            # Old exogenous capacity to be decommissioned (due to lifetime)

            self.old_exo = Var(

                self.INVESTSTORAGES, m.PERIODS, within=NonNegativeReals

            )


        # create status variable for a non-convex investment storage

        self.invest_status = Var(

            self.NON_CONVEX_INVESTSTORAGES, m.PERIODS, within=Binary

        )


        # ######################### CONSTRAINTS ###############################

        i = {n: [i for i in n.inputs][0] for n in group}

        o = {n: [o for o in n.outputs][0] for n in group}


        # Handle unit lifetimes

        def _total_storage_capacity_rule(block):

            """Rule definition for determining total installed

            capacity (taking decommissioning into account)

            """

            for n in self.INVESTSTORAGES:

                for p in m.PERIODS:

                    if p == 0:

                        expr = (

                            self.total[n, p]

                            == self.invest[n, p] + n.investment.existing

                        )

                        self.total_storage_rule.add((n, p), expr)

                    else:

                        expr = (

                            self.total[n, p]

                            == self.invest[n, p]

                            + self.total[n, p - 1]

                            - self.old[n, p]

                        )

                        self.total_storage_rule.add((n, p), expr)


        self.total_storage_rule = Constraint(

            self.INVESTSTORAGES, m.PERIODS, noruleinit=True

        )


        self.total_storage_rule_build = BuildAction(

            rule=_total_storage_capacity_rule

        )


        # multi-period storage implementation for time intervals

        if m.es.periods is not None:


            def _old_storage_capacity_rule_end(block):

                """Rule definition for determining old endogenously installed

                capacity to be decommissioned due to reaching its lifetime.

                Investment and decommissioning periods are linked within

                the constraint. The respective decommissioning period is

                determined for every investment period based on the components

                lifetime and a matrix describing its age of each endogenous

                investment. Decommissioning can only occur at the beginning of

                each period.


                Note

                ----

                For further information on the implementation check

                PR#957 https://github.com/oemof/oemof-solph/pull/957

                """

                for n in self.INVESTSTORAGES:

                    lifetime = n.investment.lifetime

                    if lifetime is None:

                        msg = (

                            "You have to specify a lifetime "

                            "for a Flow going into or out of "

                            "a GenericStorage unit "

                            "in a multi-period model!"

                            f" Value for {n} is missing."

                        )

                        raise ValueError(msg)

                    # get the period matrix describing the temporal distance

                    # between all period combinations.

                    periods_matrix = m.es.periods_matrix


                    # get the index of the minimum value in each row greater

                    # equal than the lifetime. This value equals the

                    # decommissioning period if not zero. The index of this

                    # value represents the investment period. If np.where

                    # condition is not met in any row, min value will be zero

                    decomm_periods = np.argmin(

                        np.where(

                            (periods_matrix >= lifetime),

                            periods_matrix,

                            np.inf,

                        ),

                        axis=1,

                    )


                    # no decommissioning in first period

                    expr = self.old_end[n, 0] == 0

                    self.old_rule_end.add((n, 0), expr)


                    # all periods not in decomm_periods have no decommissioning

                    # zero is excluded

                    for p in m.PERIODS:

                        if p not in decomm_periods and p != 0:

                            expr = self.old_end[n, p] == 0

                            self.old_rule_end.add((n, p), expr)


                    # multiple invests can be decommissioned in the same period

                    # but only sequential ones, thus a bookkeeping is

                    # introduced andconstraints are added to equation one

                    # iteration later.

                    last_decomm_p = np.nan

                    # loop over invest periods (values are decomm_periods)

                    for invest_p, decomm_p in enumerate(decomm_periods):

                        # Add constraint of iteration before

                        # (skipped in first iteration by last_decomm_p = nan)

                        if (decomm_p != last_decomm_p) and (

                            last_decomm_p is not np.nan

                        ):

                            expr = self.old_end[n, last_decomm_p] == expr

                            self.old_rule_end.add((n, last_decomm_p), expr)


                        # no decommissioning if decomm_p is zero

                        if decomm_p == 0:

                            # overwrite decomm_p with zero to avoid

                            # chaining invest periods in next iteration

                            last_decomm_p = 0


                        # if decomm_p is the same as the last one chain invest

                        # period

                        elif decomm_p == last_decomm_p:

                            expr += self.invest[n, invest_p]

                            # overwrite decomm_p

                            last_decomm_p = decomm_p


                        # if decomm_p is not zero, not the same as the last one

                        # and it's not the first period

                        else:

                            expr = self.invest[n, invest_p]

                            # overwrite decomm_p

                            last_decomm_p = decomm_p


                    # Add constraint of very last iteration

                    if last_decomm_p != 0:

                        expr = self.old_end[n, last_decomm_p] == expr

                        self.old_rule_end.add((n, last_decomm_p), expr)


            self.old_rule_end = Constraint(

                self.INVESTSTORAGES, m.PERIODS, noruleinit=True

            )


            self.old_rule_end_build = BuildAction(

                rule=_old_storage_capacity_rule_end

            )


            def _old_storage_capacity_rule_exo(block):

                """Rule definition for determining old exogenously given

                capacity to be decommissioned due to reaching its lifetime

                """

                for n in self.INVESTSTORAGES:

                    age = n.investment.age

                    lifetime = n.investment.lifetime

                    is_decommissioned = False

                    for p in m.PERIODS:

                        # No shutdown in first period

                        if p == 0:

                            expr = self.old_exo[n, p] == 0

                            self.old_rule_exo.add((n, p), expr)

                        elif lifetime - age <= m.es.periods_years[p]:

                            # Track decommissioning status

                            if not is_decommissioned:

                                expr = (

                                    self.old_exo[n, p] == n.investment.existing

                                )

                                is_decommissioned = True

                            else:

                                expr = self.old_exo[n, p] == 0

                            self.old_rule_exo.add((n, p), expr)

                        else:

                            expr = self.old_exo[n, p] == 0

                            self.old_rule_exo.add((n, p), expr)


            self.old_rule_exo = Constraint(

                self.INVESTSTORAGES, m.PERIODS, noruleinit=True

            )


            self.old_rule_exo_build = BuildAction(

                rule=_old_storage_capacity_rule_exo

            )


            def _old_storage_capacity_rule(block):

                """Rule definition for determining (overall) old capacity

                to be decommissioned due to reaching its lifetime

                """

                for n in self.INVESTSTORAGES:

                    for p in m.PERIODS:

                        expr = (

                            self.old[n, p]

                            == self.old_end[n, p] + self.old_exo[n, p]

                        )

                        self.old_rule.add((n, p), expr)


            self.old_rule = Constraint(

                self.INVESTSTORAGES, m.PERIODS, noruleinit=True

            )


            self.old_rule_build = BuildAction(rule=_old_storage_capacity_rule)


            def _initially_empty_rule(_):

                """Ensure storage to be empty initially"""

                for n in self.INVESTSTORAGES:

                    expr = self.storage_content[n, 0] == 0

                    self.initially_empty.add((n, 0), expr)


            if not m.TSAM_MODE:

                # inter and intra initial storage contents are handled above

                self.initially_empty = Constraint(

                    self.INVESTSTORAGES, m.TIMESTEPS, noruleinit=True

                )


                self.initially_empty_build = BuildAction(

                    rule=_initially_empty_rule

                )


        # Standard storage implementation for discrete time points

        else:


            def _inv_storage_init_content_max_rule(block, n):

                """Constraint for a variable initial storage capacity."""

                if not m.TSAM_MODE:

                    lhs = block.storage_content[n, 0]

                else:

                    lhs = block.intra_storage_delta[n, 0, 0, 0]

                return lhs <= n.investment.existing + block.invest[n, 0]


            self.init_content_limit = Constraint(

                self.INVESTSTORAGES_NO_INIT_CONTENT,

                rule=_inv_storage_init_content_max_rule,

            )


            def _inv_storage_init_content_fix_rule(block, n):

                """Constraint for a fixed initial storage capacity."""

                if not m.TSAM_MODE:

                    lhs = block.storage_content[n, 0]

                else:

                    lhs = block.intra_storage_delta[n, 0, 0, 0]

                return lhs == n.initial_storage_level * (

                    n.investment.existing + block.invest[n, 0]

                )


            self.init_content_fix = Constraint(

                self.INVESTSTORAGES_INIT_CONTENT,

                rule=_inv_storage_init_content_fix_rule,

            )


        def _storage_balance_rule(block, n, p, t):

            """

            Rule definition for the storage balance of every storage n and

            every timestep.

            """

            expr = 0

            expr += block.storage_content[n, t + 1]

            expr += (

                -block.storage_content[n, t]

                * (1 - n.loss_rate[t]) ** m.timeincrement[t]

            )

            expr += (

                n.fixed_losses_relative[t]

                * self.total[n, p]

                * m.timeincrement[t]

            )

            expr += n.fixed_losses_absolute[t] * m.timeincrement[t]

            expr += (

                -m.flow[i[n], n, t] * n.inflow_conversion_factor[t]

            ) * m.timeincrement[t]

            expr += (

                m.flow[n, o[n], t] / n.outflow_conversion_factor[t]

            ) * m.timeincrement[t]

            return expr == 0


        def _intra_storage_balance_rule(block, n, p, k, g):

This code seems to be duplicated in your project.

            """

            Rule definition for the storage balance of every storage n and

            every timestep.

            """

            t = m.get_timestep_from_tsam_timestep(p, k, g)

            expr = 0

            expr += block.intra_storage_delta[n, p, k, g + 1]

            expr += (

                -block.intra_storage_delta[n, p, k, g]

                * (1 - n.loss_rate[t]) ** m.timeincrement[t]

            )

            expr += (

                n.fixed_losses_relative[t]

                * self.total[n, p]

                * m.timeincrement[t]

            )

            expr += n.fixed_losses_absolute[t] * m.timeincrement[t]

            expr += (

                -m.flow[i[n], n, t] * n.inflow_conversion_factor[t]

            ) * m.timeincrement[t]

            expr += (

                m.flow[n, o[n], t] / n.outflow_conversion_factor[t]

            ) * m.timeincrement[t]

            return expr == 0


        if not m.TSAM_MODE:

            self.balance = Constraint(

                self.INVESTSTORAGES,

                m.TIMEINDEX,

                rule=_storage_balance_rule,

            )

        else:

            self.intra_balance = Constraint(

                self.INVESTSTORAGES,

                m.TIMEINDEX_TYPICAL_CLUSTER,

                rule=_intra_storage_balance_rule,

            )


        def _inter_storage_balance_rule(block, n, i):

            """

            Rule definition for the storage balance of every storage n and

            every timestep.

            """

            ii = 0

            for p in m.PERIODS:

                ii += len(m.es.tsa_parameters[p]["order"])

                if ii > i:

                    ii -= len(m.es.tsa_parameters[p]["order"])

                    ii = i - ii

                    break


            k = m.es.tsa_parameters[p]["order"][ii]

The variable p does not seem to be defined in case the for loop on line 1809 is not entered. Are you sure this can never be the case?

            t = m.get_timestep_from_tsam_timestep(

                p, k, m.es.tsa_parameters[p]["timesteps"] - 1

            )

            expr = 0

            expr += block.inter_storage_content[n, i + 1]

            expr += -block.inter_storage_content[n, i] * (

                1 - n.loss_rate[t]

            ) ** (m.timeincrement[t] * m.es.tsa_parameters[p]["timesteps"])

            expr += -self.intra_storage_delta[

                n, p, k, m.es.tsa_parameters[p]["timesteps"]

            ]

            return expr == 0


        if m.TSAM_MODE:

            self.inter_balance = Constraint(

                self.INVESTSTORAGES,

                m.CLUSTERS,

                rule=_inter_storage_balance_rule,

            )


        if m.es.periods is None and not m.TSAM_MODE:


            def _balanced_storage_rule(block, n):

                return (

                    block.storage_content[n, m.TIMEPOINTS.at(-1)]

                    == block.storage_content[n, m.TIMEPOINTS.at(1)]

                )


            self.balanced_cstr = Constraint(

                self.INVESTSTORAGES_BALANCED, rule=_balanced_storage_rule

            )


        def _power_coupled(block):

            """

            Rule definition for constraint to connect the input power

            and output power

            """

            for n in self.INVEST_REL_IN_OUT:

                for p in m.PERIODS:

                    expr = (

                        m.InvestmentFlowBlock.total[n, o[n], p]

                    ) * n.invest_relation_input_output[p] == (

                        m.InvestmentFlowBlock.total[i[n], n, p]

                    )

                    self.power_coupled.add((n, p), expr)


        self.power_coupled = Constraint(

            self.INVEST_REL_IN_OUT, m.PERIODS, noruleinit=True

        )


        self.power_coupled_build = BuildAction(rule=_power_coupled)


        def _storage_capacity_inflow_invest_rule(block):

            """

            Rule definition of constraint connecting the inflow

            `InvestmentFlowBlock.invest of storage with invested capacity

            `invest` by nominal_storage_capacity__inflow_ratio

            """

            for n in self.INVEST_REL_CAP_IN:

                for p in m.PERIODS:

                    expr = (

                        m.InvestmentFlowBlock.total[i[n], n, p]

                        == self.total[n, p]

                        * n.invest_relation_input_capacity[p]

                    )

                    self.storage_capacity_inflow.add((n, p), expr)


        self.storage_capacity_inflow = Constraint(

            self.INVEST_REL_CAP_IN, m.PERIODS, noruleinit=True

        )


        self.storage_capacity_inflow_build = BuildAction(

            rule=_storage_capacity_inflow_invest_rule

        )


        def _storage_capacity_outflow_invest_rule(block):

            """

            Rule definition of constraint connecting outflow

            `InvestmentFlowBlock.invest` of storage and invested capacity

            `invest` by nominal_storage_capacity__outflow_ratio

            """

            for n in self.INVEST_REL_CAP_OUT:

                for p in m.PERIODS:

                    expr = (

                        m.InvestmentFlowBlock.total[n, o[n], p]

                        == self.total[n, p]

                        * n.invest_relation_output_capacity[p]

                    )

                    self.storage_capacity_outflow.add((n, p), expr)


        self.storage_capacity_outflow = Constraint(

            self.INVEST_REL_CAP_OUT, m.PERIODS, noruleinit=True

        )


        self.storage_capacity_outflow_build = BuildAction(

            rule=_storage_capacity_outflow_invest_rule

        )


        self._add_storage_limit_constraints()


        def maximum_invest_limit(block, n, p):

            """

            Constraint for the maximal investment in non convex investment

            storage.

            """

            return (

                n.investment.maximum[p] * self.invest_status[n, p]

                - self.invest[n, p]

            ) >= 0


        self.limit_max = Constraint(

            self.NON_CONVEX_INVESTSTORAGES,

            m.PERIODS,

            rule=maximum_invest_limit,

        )


        def smallest_invest(block, n, p):

            """

            Constraint for the minimal investment in non convex investment

            storage if the invest is greater than 0. So the invest variable

            can be either 0 or greater than the minimum.

            """

            return (

                self.invest[n, p]

                - n.investment.minimum[p] * self.invest_status[n, p]

                >= 0

            )


        self.limit_min = Constraint(

            self.NON_CONVEX_INVESTSTORAGES, m.PERIODS, rule=smallest_invest

        )


        if m.es.periods is not None:


            def _overall_storage_maximum_investflow_rule(block):

                """Rule definition for maximum overall investment

                in investment case.

                """

                for n in self.OVERALL_MAXIMUM_INVESTSTORAGES:

                    for p in m.PERIODS:

                        expr = self.total[n, p] <= n.investment.overall_maximum

                        self.overall_storage_maximum.add((n, p), expr)


            self.overall_storage_maximum = Constraint(

                self.OVERALL_MAXIMUM_INVESTSTORAGES, m.PERIODS, noruleinit=True

            )


            self.overall_maximum_build = BuildAction(

                rule=_overall_storage_maximum_investflow_rule

            )


            def _overall_minimum_investflow_rule(block):

                """Rule definition for minimum overall investment

                in investment case.


                Note: This is only applicable for the last period

                """

                for n in self.OVERALL_MINIMUM_INVESTSTORAGES:

                    expr = (

                        n.investment.overall_minimum

                        <= self.total[n, m.PERIODS[-1]]

                    )

                    self.overall_minimum.add(n, expr)


            self.overall_minimum = Constraint(

                self.OVERALL_MINIMUM_INVESTSTORAGES, noruleinit=True

            )


            self.overall_minimum_build = BuildAction(

                rule=_overall_minimum_investflow_rule

            )


    def _add_storage_limit_constraints(self):

        m = self.parent_block()

        if not m.TSAM_MODE:

            if m.es.periods is None:


                def _max_storage_content_invest_rule(_, n, t):

                    """

                    Rule definition for upper bound constraint for the

                    storage content.

                    """

                    expr = (

                        self.storage_content[n, t]

                        <= self.total[n, 0] * n.max_storage_level[t]

                    )

                    return expr


                self.max_storage_content = Constraint(

                    self.INVESTSTORAGES,

                    m.TIMEPOINTS,

                    rule=_max_storage_content_invest_rule,

                )


                def _min_storage_content_invest_rule(_, n, t):

                    """

                    Rule definition of lower bound constraint for the

                    storage content.

                    """

                    expr = (

                        self.storage_content[n, t]

                        >= self.total[n, 0] * n.min_storage_level[t]

                    )

                    return expr


                self.min_storage_content = Constraint(

                    self.MIN_INVESTSTORAGES,

                    m.TIMEPOINTS,

                    rule=_min_storage_content_invest_rule,

                )

            else:


                def _max_storage_content_invest_rule(_, n, p, t):

                    """

                    Rule definition for upper bound constraint for the

                    storage content.

                    """

                    expr = (

                        self.storage_content[n, t]

                        <= self.total[n, p] * n.max_storage_level[t]

                    )

                    return expr


                self.max_storage_content = Constraint(

                    self.INVESTSTORAGES,

                    m.TIMEINDEX,

                    rule=_max_storage_content_invest_rule,

                )


                def _min_storage_content_invest_rule(_, n, p, t):

                    """

                    Rule definition of lower bound constraint for the

                    storage content.

                    """

                    expr = (

                        self.storage_content[n, t]

                        >= self.total[n, p] * n.min_storage_level[t]

                    )

                    return expr


                self.min_storage_content = Constraint(

                    self.MIN_INVESTSTORAGES,

                    m.TIMEINDEX,

                    rule=_min_storage_content_invest_rule,

                )

        else:


            def _storage_inter_maximum_level_rule(block):

This code seems to be duplicated in your project.

                for n in self.INVESTSTORAGES:

                    for p, i, g in m.TIMEINDEX_CLUSTER:

                        t = m.get_timestep_from_tsam_timestep(p, i, g)

                        k = m.es.tsa_parameters[p]["order"][i]

                        tk = m.get_timestep_from_tsam_timestep(p, k, g)

                        inter_i = (

                            sum(

                                len(m.es.tsa_parameters[ip]["order"])

                                for ip in range(p)

                            )

                            + i

                        )

                        lhs = (

                            self.inter_storage_content[n, inter_i]

                            * (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk])

                            + self.intra_storage_delta[n, p, k, g]

                        )

                        rhs = self.total[n, p] * n.max_storage_level[t]

                        self.storage_inter_maximum_level.add(

                            (n, p, i, g), lhs <= rhs

                        )


            self.storage_inter_maximum_level = Constraint(

                self.INVESTSTORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True

            )


            self.storage_inter_maximum_level_build = BuildAction(

                rule=_storage_inter_maximum_level_rule

            )


            def _storage_inter_minimum_level_rule(block):

This code seems to be duplicated in your project.

                # See FINE implementation at

                # https://github.com/FZJ-IEK3-VSA/FINE/blob/

                # 57ec32561fb95e746c505760bd0d61c97d2fd2fb/FINE/storage.py#L1329

                for n in self.INVESTSTORAGES:

                    for p, i, g in m.TIMEINDEX_CLUSTER:

                        t = m.get_timestep_from_tsam_timestep(p, i, g)

                        lhs = self.total[n, p] * n.min_storage_level[t]

                        k = m.es.tsa_parameters[p]["order"][i]

                        tk = m.get_timestep_from_tsam_timestep(p, k, g)

                        inter_i = (

                            sum(

                                len(m.es.tsa_parameters[ip]["order"])

                                for ip in range(p)

                            )

                            + i

                        )

                        rhs = (

                            self.inter_storage_content[n, inter_i]

                            * (1 - n.loss_rate[t]) ** (g * m.timeincrement[tk])

                            + self.intra_storage_delta[n, p, k, g]

                        )

                        self.storage_inter_minimum_level.add(

                            (n, p, i, g), lhs <= rhs

                        )


            self.storage_inter_minimum_level = Constraint(

                self.INVESTSTORAGES, m.TIMEINDEX_CLUSTER, noruleinit=True

            )


            self.storage_inter_minimum_level_build = BuildAction(

                rule=_storage_inter_minimum_level_rule

            )


    def _objective_expression(self):

        """Objective expression with fixed and investment costs."""

        m = self.parent_block()


        investment_costs = 0

        storage_costs = 0

        period_investment_costs = {p: 0 for p in m.PERIODS}

        fixed_costs = 0


        if m.es.periods is None:

            for n in self.CONVEX_INVESTSTORAGES:

                for p in m.PERIODS:

                    investment_costs += (

                        self.invest[n, p] * n.investment.ep_costs[p]

                    )

            for n in self.NON_CONVEX_INVESTSTORAGES:

                for p in m.PERIODS:

                    investment_costs += (

                        self.invest[n, p] * n.investment.ep_costs[p]

                        + self.invest_status[n, p] * n.investment.offset[p]

                    )


        else:

            msg = (

                "You did not specify an interest rate.\n"

                "It will be set equal to the discount_rate of {} "

                "of the model as a default.\nThis corresponds to a "

                "social planner point of view and does not reflect "

                "microeconomic interest requirements."

            )

            for n in self.CONVEX_INVESTSTORAGES:

                lifetime = n.investment.lifetime

                interest = 0

                if interest == 0:

                    warn(

                        msg.format(m.discount_rate),

                        debugging.SuspiciousUsageWarning,

                    )

                    interest = m.discount_rate

                for p in m.PERIODS:

                    annuity = economics.annuity(

                        capex=n.investment.ep_costs[p],

                        n=lifetime,

                        wacc=interest,

                    )

                    duration = min(

                        m.es.end_year_of_optimization - m.es.periods_years[p],

                        lifetime,

                    )

                    present_value_factor = 1 / economics.annuity(

                        capex=1, n=duration, wacc=interest

                    )

                    investment_costs_increment = (

                        self.invest[n, p] * annuity * present_value_factor

                    )

                    remaining_value_difference = (

                        self._evaluate_remaining_value_difference(

                            m,

                            p,

                            n,

                            m.es.end_year_of_optimization,

                            lifetime,

                            interest,

                        )

                    )

                    investment_costs += (

                        investment_costs_increment + remaining_value_difference

                    )

                    period_investment_costs[p] += investment_costs_increment


            for n in self.NON_CONVEX_INVESTSTORAGES:

                lifetime = n.investment.lifetime

                interest = 0

                if interest == 0:

                    warn(

                        msg.format(m.discount_rate),

                        debugging.SuspiciousUsageWarning,

                    )

                    interest = m.discount_rate

                for p in m.PERIODS:

                    annuity = economics.annuity(

                        capex=n.investment.ep_costs[p],

                        n=lifetime,

                        wacc=interest,

                    )

                    duration = min(

                        m.es.end_year_of_optimization - m.es.periods_years[p],

                        lifetime,

                    )

                    present_value_factor = 1 / economics.annuity(

                        capex=1, n=duration, wacc=interest

                    )

                    investment_costs_increment = (

                        self.invest[n, p] * annuity * present_value_factor

                        + self.invest_status[n, p] * n.investment.offset[p]

                    )

                    remaining_value_difference = (

                        self._evaluate_remaining_value_difference(

                            m,

                            p,

                            n,

                            m.es.end_year_of_optimization,

                            lifetime,

                            interest,

                            nonconvex=True,

                        )

                    )

                    investment_costs += (

                        investment_costs_increment + remaining_value_difference

                    )

                    period_investment_costs[p] += investment_costs_increment


            for n in self.INVESTSTORAGES:

                if valid_sequence(n.investment.fixed_costs, len(m.PERIODS)):

                    lifetime = n.investment.lifetime

                    for p in m.PERIODS:

                        range_limit = min(

                            m.es.end_year_of_optimization,

                            m.es.periods_years[p] + lifetime,

                        )

                        fixed_costs += sum(

                            self.invest[n, p] * n.investment.fixed_costs[pp]

                            for pp in range(

                                m.es.periods_years[p],

                                range_limit,

                            )

                        )


            for n in self.EXISTING_INVESTSTORAGES:

                if valid_sequence(n.investment.fixed_costs, len(m.PERIODS)):

                    lifetime = n.investment.lifetime

                    age = n.investment.age

                    range_limit = min(

                        m.es.end_year_of_optimization, lifetime - age

                    )

                    fixed_costs += sum(

                        n.investment.existing * n.investment.fixed_costs[pp]

                        for pp in range(range_limit)

                    )


        for n in self.INVESTSTORAGES:

            if valid_sequence(n.storage_costs, len(m.TIMESTEPS)):

This code seems to be duplicated in your project.

                # We actually want to iterate over all TIMEPOINTS except the

                # 0th. As integers are used for the index, this is equicalent

                # to iterating over the TIMESTEPS with one offset.

                if not m.TSAM_MODE:

                    for t in m.TIMESTEPS:

                        storage_costs += (

                            self.storage_content[n, t + 1] * n.storage_costs[t]

                        )

                else:

                    for t in m.TIMESTEPS_ORIGINAL:

                        storage_costs += (

                            self.storage_content[n, t + 1]

                            * n.storage_costs[t + 1]

                        )


        self.storage_costs = Expression(expr=storage_costs)


        self.investment_costs = Expression(expr=investment_costs)

        self.period_investment_costs = period_investment_costs

        self.fixed_costs = Expression(expr=fixed_costs)

        self.costs = Expression(

            expr=investment_costs + fixed_costs + storage_costs

        )


        return self.costs


    def _evaluate_remaining_value_difference(

        self,

        m,

        p,

        n,

        end_year_of_optimization,

        lifetime,

        interest,

        nonconvex=False,

    ):

        """Evaluate and return the remaining value difference of an investment


        The remaining value difference in the net present values if the asset

        was to be liquidated at the end of the optimization horizon and the

        net present value using the original investment expenses.


        Parameters

        ----------

        m : oemof.solph.models.Model

            Optimization model


        p : int

            Period in which investment occurs


        n : oemof.solph.components.GenericStorage

            storage unit


        end_year_of_optimization : int

            Last year of the optimization horizon


        lifetime : int

            lifetime of investment considered


        interest : float

            Demanded interest rate for investment


        nonconvex : bool

            Indicating whether considered flow is nonconvex.

        """

        if m.es.use_remaining_value:

            if end_year_of_optimization - m.es.periods_years[p] < lifetime:

                remaining_lifetime = lifetime - (

                    end_year_of_optimization - m.es.periods_years[p]

                )

                remaining_annuity = economics.annuity(

                    capex=n.investment.ep_costs[-1],

                    n=remaining_lifetime,

                    wacc=interest,

                )

                original_annuity = economics.annuity(

                    capex=n.investment.ep_costs[p],

                    n=remaining_lifetime,

                    wacc=interest,

                )

                present_value_factor_remaining = 1 / economics.annuity(

                    capex=1, n=remaining_lifetime, wacc=interest

                )

                convex_investment_costs = (

                    self.invest[n, p]

                    * (remaining_annuity - original_annuity)

                    * present_value_factor_remaining

                )

                if nonconvex:

                    return convex_investment_costs + self.invest_status[

                        n, p

                    ] * (n.investment.offset[-1] - n.investment.offset[p])

                else:

                    return convex_investment_costs

            else:

                return 0

        else:

            return 0