components.py

# -*- coding: utf-8 -

"""This module is designed to hold components with their classes and
associated individual constraints (blocks) and groupings. Therefore this
module holds the class definition and the block directly located by each other.

This file is part of project oemof (github.com/oemof/oemof). It's copyrighted
by the contributors recorded in the version control history of the file,
available from its original location oemof/oemof/solph/components.py

SPDX-License-Identifier: GPL-3.0-or-later
"""

import numpy as np
import warnings
from pyomo.core.base.block import SimpleBlock
from pyomo.environ import (Binary, Set, NonNegativeReals, Var, Constraint,
                           Expression, BuildAction)

from oemof import network
from oemof.solph import Transformer as solph_Transformer
from oemof.solph import sequence as solph_sequence
from oemof.solph import Investment


class GenericStorage(network.Transformer):
    """
    Component `GenericStorage` to model with basic characteristics of storages.

    Parameters
    ----------
    nominal_capacity : numeric
        Absolute nominal capacity of the storage
    nominal_output_capacity_ratio : numeric
        DEPRECATED - Define the output capacity as nominal_value in the Flow
        class. In case of an investment object in the storage and the flow use
        :attr:`invest_relation_input_capacity` instead.
        OLD TEXT: Ratio between the nominal outflow of the storage and
        its capacity. For batteries this is also know as c-rate.
        Note: This ratio is used to create the Flow object for the outflow
        and set its nominal value of the storage in the constructor. If no
        investment object is defined it is also possible to set the nominal
        value of the flow directly in its constructor.
    nominal_input_capacity_ratio : numeric
        DEPRECATED - Define the input capacity as nominal_value in the Flow
        class. In case of an investment object in the storage and the flow use
        :attr:`invest_relation_output_capacity` instead.
        OLD TEXT: Ratio between the nominal inflow of the storage and
        its capacity. see: nominal_output_capacity_ratio
    invest_relation_input_capacity : numeric or None
        Ratio between the investment variable of the input Flow and the
        investment variable of the storage.

        .. math:: input\_invest =
                  capacity\_invest \cdot invest\_relation\_input\_capacity

    invest_relation_output_capacity : numeric or None
        Ratio between the investment variable of the output Flow and the
        investment variable of the storage.

        .. math:: output\_invest =
                  capacity\_invest \cdot invest\_relation\_output\_capacity

    invest_relation_input_output : numeric or None
        Ratio between the investment variable of the output Flow and the
        investment variable of the input 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 None no relation
        will be set.

        .. math:: input\_invest =
                  output\_invest \cdot invest\_relation\_input\_output

    initial_capacity : numeric
        The capacity of the storage in the first (and last) time step of
        optimization.
    capacity_loss : numeric (sequence or scalar)
        The relative loss of the storage capacity from between two consecutive
        timesteps.
    inflow_conversion_factor : numeric (sequence or scalar)
        The relative conversion factor, i.e. efficiency associated with the
        inflow of the storage.
    outflow_conversion_factor : numeric (sequence or scalar)
        see: inflow_conversion_factor
    capacity_min : numeric (sequence or scalar)
        The nominal minimum capacity of the storage as fraction of the
        nominal capacity (between 0 and 1, default: 0).
        To set different values in every time step use a sequence.
    capacity_max : numeric (sequence or scalar)
        see: capacity_min
    investment : :class:`oemof.solph.options.Investment` object
        Object indicating if a nominal_value of the flow is determined by
        the optimization problem. Note: This will refer all attributes to an
        investment variable instead of to the nominal_capacity. The
        nominal_capacity should not be set (or set to None) if an investment
        object is used.

    Note
    ----
    The following sets, variables, constraints and objective parts are created
     * :py:class:`~oemof.solph.components.GenericStorageBlock` (if no
       Investment object present)
     * :py:class:`~oemof.solph.components.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.Bus('my_bus')

    >>> my_storage = solph.components.GenericStorage(
    ...     label='storage',
    ...     nominal_capacity=1000,
    ...     inputs={my_bus: solph.Flow(nominal_value=200, variable_costs=10)},
    ...     outputs={my_bus: solph.Flow(nominal_value=200)},
    ...     capacity_loss=0.01,
    ...     initial_capacity=0,
    ...     capacity_max = 0.9,
    ...     inflow_conversion_factor=0.9,
    ...     outflow_conversion_factor=0.93)

    >>> my_investment_storage = solph.components.GenericStorage(
    ...     label='storage',
    ...     investment=solph.Investment(ep_costs=50),
    ...     inputs={my_bus: solph.Flow()},
    ...     outputs={my_bus: solph.Flow()},
    ...     capacity_loss=0.02,
    ...     initial_capacity=None,
    ...     invest_relation_input_capacity=1/6,
    ...     invest_relation_output_capacity=1/6,
    ...     inflow_conversion_factor=1,
    ...     outflow_conversion_factor=0.8)
    """

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.nominal_capacity = kwargs.get('nominal_capacity')
        self.nominal_input_capacity_ratio = kwargs.get(
            'nominal_input_capacity_ratio')
        self.nominal_output_capacity_ratio = kwargs.get(
            'nominal_output_capacity_ratio')
        self.initial_capacity = kwargs.get('initial_capacity')
        self.capacity_loss = solph_sequence(kwargs.get('capacity_loss', 0))
        self.inflow_conversion_factor = solph_sequence(
            kwargs.get('inflow_conversion_factor', 1))
        self.outflow_conversion_factor = solph_sequence(
            kwargs.get('outflow_conversion_factor', 1))
        self.capacity_max = solph_sequence(kwargs.get('capacity_max', 1))
        self.capacity_min = solph_sequence(kwargs.get('capacity_min', 0))
        self.investment = kwargs.get('investment')
        self.invest_relation_input_output = kwargs.get(
            'invest_relation_input_output')
        self.invest_relation_input_capacity = kwargs.get(
            'invest_relation_input_capacity')
        self.invest_relation_output_capacity = kwargs.get(
            'invest_relation_output_capacity')
        self._invest_group = isinstance(self.investment, Investment)

        warnings.simplefilter('always', DeprecationWarning)
        dpr_msg = ("\nDeprecated. The attributes "
                   "'nominal_input_capacity_ratio' and "
                   "'nominal_input_capacity_ratio' will be removed in "
                   "oemof >= v0.3.0.\n Please use the 'invest_relation_...' "
                   "attribute in case of the investment mode.\n Please use "
                   "the 'nominal_value' within in the Flows for the dispatch "
                   "mode.\n These measures will avoid this warning.")

        # DEPRECATED. Set nominal_value of in/out Flows using
        # nominal_input_capacity_ratio / nominal_input_capacity_ratio
        if self._invest_group is False and (
                self.nominal_input_capacity_ratio is not None or
                self.nominal_output_capacity_ratio is not None):
            self._set_flows(dpr_msg)

        # Check attributes for the investment mode.
        if self._invest_group is True:
            self._check_invest_attributes(dpr_msg)

    def _check_invest_attributes(self, dpr_msg):
        if self.nominal_input_capacity_ratio is not None:
            warnings.warn(dpr_msg, DeprecationWarning)
            self.invest_relation_input_capacity = (
                self.nominal_input_capacity_ratio)
        if self.nominal_output_capacity_ratio is not None:
            warnings.warn(dpr_msg, DeprecationWarning)
            self.invest_relation_output_capacity = (
                self.nominal_output_capacity_ratio)
        if self.investment and self.nominal_capacity is not None:
            e1 = ("If an investment object is defined the invest variable "
                  "replaces the nominal_capacity.\n Therefore the "
                  "nominal_capacity should be 'None'.\n")
            raise AttributeError(e1)
        if (self.invest_relation_input_output is not None and
                self.invest_relation_output_capacity is not None and
                self.invest_relation_input_capacity is not None):
            e2 = ("Overdetermined. Three investment object will be coupled"
                  "with three constraints. Set one invest relation to 'None'.")
            raise AttributeError(e2)
        for flow in self.inputs.values():
            if (self.invest_relation_input_capacity is not None and
                    not isinstance(flow.investment, Investment)):
                flow.investment = Investment()
        for flow in self.outputs.values():
            if (self.invest_relation_output_capacity is not None and
                    not isinstance(flow.investment, Investment)):
                flow.investment = Investment()

    def _set_flows(self, dpr_msg):
        """ Sets correct attributes of input / output flows based on the
        storage object attributes. This method is called in the constructor by
        default. It may be called in sub-classed components at the
        end of the constructor to ensure correct setting of attributes.
        """
        warnings.warn(dpr_msg, DeprecationWarning)
        for flow in self.inputs.values():
            if (self.nominal_input_capacity_ratio is not None and
                    not isinstance(flow.investment, Investment)):
                flow.nominal_value = (self.nominal_input_capacity_ratio *
                                      self.nominal_capacity)
        for flow in self.outputs.values():
            if (self.nominal_output_capacity_ratio is not None and
                    not isinstance(flow.investment, Investment)):
                flow.nominal_value = (self.nominal_output_capacity_ratio *
                                      self.nominal_capacity)

    def constraint_group(self):
        if self._invest_group is True:
            return GenericInvestmentStorageBlock
        else:
            return GenericStorageBlock


class GenericStorageBlock(SimpleBlock):
    r"""Storage without an :class:`.Investment` object.

    **The following sets are created:** (-> see basic sets at
    :class:`.Model` )

    STORAGES
        A set with all :class:`.Storage` objects
        (and no attr:`investement` of type :class:`.Investment`)

    STORAGES_WITH_INVEST_FLOW_REL
        A set with all :class:`.Storage` objects with two investment flows
        coupled with the 'invest_relation_input_output' attribute.

    **The following variables are created:**

    capacity
        Capacity (level) for every storage and timestep. The value for the
        capacity at the beginning is set by the parameter `initial_capacity` or
        not set if `initial_capacity` is None.
        The variable of storage s and timestep t can be accessed by:
        `om.Storage.capacity[s, t]`

    **The following constraints are created:**

    Storage balance :attr:`om.Storage.balance[n, t]`
        .. math:: capacity(n, t) = &capacity(n, previous(t)) \cdot
            (1 - capacity\_loss_n(t))) \\
            &- \frac{flow(n, o, t)}{\eta(n, o, t)} \cdot \tau
            + flow(i, n, t) \cdot \eta(i, n, t) \cdot \tau

    Connect the invest variables of the input and the output flow.
        .. math::
          InvestmentFlow.invest(source(n), n) + existing = \\
          (InvestmentFlow.invest(n, target(n)) + existing) * \\
          invest\_relation\_input\_output(n) \\
          \forall n \in \textrm{INVEST\_REL\_IN\_OUT}

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

    Nothing added to the objective function.

    """

    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}

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

        self.STORAGES_WITH_INVEST_FLOW_REL = Set(initialize=[
            n for n in group if n.invest_relation_input_output is not None])

        def _storage_capacity_bound_rule(block, n, t):
            """Rule definition for bounds of capacity variable of storage n
            in timestep t
            """
            bounds = (n.nominal_capacity * n.capacity_min[t],
                      n.nominal_capacity * n.capacity_max[t])
            return bounds
        self.capacity = Var(self.STORAGES, m.TIMESTEPS,
                            bounds=_storage_capacity_bound_rule)

        # set the initial capacity of the storage
        for n in group:
            if n.initial_capacity is not None:
                self.capacity[n, m.TIMESTEPS[-1]] = (n.initial_capacity *
                                                     n.nominal_capacity)
                self.capacity[n, m.TIMESTEPS[-1]].fix()

        # storage balance constraint
        def _storage_balance_rule(block, n, t):
            """Rule definition for the storage balance of every storage n and
            timestep t
            """
            expr = 0
            expr += block.capacity[n, t]
            expr += - block.capacity[n, m.previous_timesteps[t]] * (
                1 - n.capacity_loss[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
        self.balance = Constraint(self.STORAGES, m.TIMESTEPS,
                                  rule=_storage_balance_rule)

        def _power_coupled(block, n):
            """Rule definition for constraint to connect the input power
            and output power
            """
            expr = ((m.InvestmentFlow.invest[n, o[n]] +
                     m.flows[n, o[n]].investment.existing) *
                    n.invest_relation_input_output ==
                    (m.InvestmentFlow.invest[i[n], n] +
                     m.flows[i[n], n].investment.existing))
            return expr
        self.power_coupled = Constraint(
                self.STORAGES_WITH_INVEST_FLOW_REL, rule=_power_coupled)

    def _objective_expression(self):
        r"""Objective expression for storages with no investment.
        Note: This adds nothing as variable costs are already
        added in the Block :class:`Flow`.
        """
        if not hasattr(self, 'STORAGES'):
            return 0

        return 0


class GenericInvestmentStorageBlock(SimpleBlock):
    r"""Storage with an :class:`.Investment` object.

    **The following sets are created:** (-> see basic sets at
    :class:`.Model` )

    INVESTSTORAGES
        A set with all storages containing an Investment object.
    INVEST_REL_CAP_IN
        A set with all storages containing an Investment object with coupled 
        investment of input power and storage capacity
    INVEST_REL_CAP_OUT
        A set with all storages containing an Investment object with coupled 
        investment of output power and storage capacity
    INVEST_REL_IN_OUT
        A set with all storages containing an Investment object with coupled
        investment of input and output power
    INITIAL_CAPACITY
        A subset of the set INVESTSTORAGES where elements of the set have an
        initial_capacity attribute.
    MIN_INVESTSTORAGES
        A subset of INVESTSTORAGES where elements of the set have an
        capacity_min attribute greater than zero for at least one time step.

    **The following variables are created:**

    capacity :attr:`om.InvestmentStorage.capacity[n, t]`
        Level of the storage (indexed by STORAGES and TIMESTEPS)

    invest :attr:`om.InvestmentStorage.invest[n, t]`
        Nominal capacity of the storage (indexed by STORAGES)


    **The following constraints are build:**

    Storage balance
      .. math::
        capacity(n, t) =  &capacity(n, t\_previous(t)) \cdot
        (1 - capacity\_loss(n)) \\
        &- (flow(n, target(n), t)) / (outflow\_conversion\_factor(n) \cdot
        \tau) \\
        &+ flow(source(n), n, t) \cdot inflow\_conversion\_factor(n) \cdot \
        \tau \textrm{,} \\
        &\forall n \in \textrm{INVESTSTORAGES} \textrm{,} \\
        &\forall t \in \textrm{TIMESTEPS}.

    Initial capacity of :class:`.network.Storage`
        .. math::
          capacity(n, t_{last}) = invest(n) \cdot
          initial\_capacity(n), \\
          \forall n \in \textrm{INITIAL\_CAPACITY,} \\
          \forall t \in \textrm{TIMESTEPS}.

    Connect the invest variables of the storage and the input flow.
        .. math:: InvestmentFlow.invest(source(n), n) + existing =
          (invest(n) + existing) * invest\_relation\_input\_capacity(n) \\
          \forall n \in \textrm{INVEST\_REL\_CAP\_IN}

    Connect the invest variables of the storage and the output flow.
        .. math:: InvestmentFlow.invest(n, target(n)) + existing =
          (invest(n) + existing) * invest\_relation\_output_capacity(n) \\
          \forall n \in \textrm{INVEST\_REL\_CAP\_OUT}

    Connect the invest variables of the input and the output flow.
        .. math:: InvestmentFlow.invest(source(n), n) + existing ==
          (InvestmentFlow.invest(n, target(n)) + existing) *
          invest\_relation\_input_output(n) \\
          \forall n \in \textrm{INVEST\_REL\_IN\_OUT}

    Maximal capacity :attr:`om.InvestmentStorage.max_capacity[n, t]`
        .. math:: capacity(n, t) \leq invest(n) \cdot capacity\_min(n, t), \\
            \forall n \in \textrm{MAX\_INVESTSTORAGES,} \\
            \forall t \in \textrm{TIMESTEPS}.

    Minimal capacity :attr:`om.InvestmentStorage.min_capacity[n, t]`
        .. math:: capacity(n, t) \geq invest(n) \cdot capacity\_min(n, t),
            \\
            \forall n \in \textrm{MIN\_INVESTSTORAGES,} \\
            \forall t \in \textrm{TIMESTEPS}.


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

    Equivalent periodical costs (investment costs):
        .. math::
            \\sum_n invest(n) \cdot ep\_costs(n)

    The expression can be accessed by
    :attr:`om.InvestStorages.investment_costs` and their value after
    optimization by :meth:`om.InvestStorages.investment_costs()` .

    """

    CONSTRAINT_GROUP = True

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

    def _create(self, group=None):
        """
        """
        m = self.parent_block()
        if group is None:
            return None

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

        self.INVESTSTORAGES = Set(initialize=[n for n in group])
        self.INVEST_REL_CAP_IN = Set(initialize=[
            n for n in group if n.invest_relation_input_capacity is not None])
    
        self.INVEST_REL_CAP_OUT = Set(initialize=[
            n for n in group if n.invest_relation_output_capacity is not None])
    
        self.INVEST_REL_IN_OUT = Set(initialize=[
            n for n in group if n.invest_relation_input_output is not None])

        self.INITIAL_CAPACITY = Set(initialize=[
            n for n in group if n.initial_capacity is not None])

        # The capacity is set as 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.capacity_min[t] for t in m.TIMESTEPS]) > 0])

        # ######################### Variables  ################################
        self.capacity = Var(self.INVESTSTORAGES, m.TIMESTEPS,
                            within=NonNegativeReals)

        def _storage_investvar_bound_rule(block, n):
            """Rule definition to bound the invested storage capacity `invest`.
            """
            return n.investment.minimum, n.investment.maximum
        self.invest = Var(self.INVESTSTORAGES, within=NonNegativeReals,
                          bounds=_storage_investvar_bound_rule)

        # ######################### 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}

        def _storage_balance_rule(block, n, t):
            """Rule definition for the storage energy balance.
            """
            expr = 0
            expr += block.capacity[n, t]
            expr += - block.capacity[n, m.previous_timesteps[t]] * (
                1 - n.capacity_loss[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
        self.balance = Constraint(self.INVESTSTORAGES, m.TIMESTEPS,
                                  rule=_storage_balance_rule)

        def _initial_capacity_invest_rule(block, n):
            """Rule definition for constraint to connect initial storage
            capacity with capacity of last timesteps.
            """
            expr = (self.capacity[n, m.TIMESTEPS[-1]] ==
                    (n.investment.existing + self.invest[n]) *
                    n.initial_capacity)
            return expr
        self.initial_capacity = Constraint(
            self.INITIAL_CAPACITY, rule=_initial_capacity_invest_rule)
        
        def _power_coupled(block, n):
            """Rule definition for constraint to connect the input power
            and output power
            """
            expr = ((m.InvestmentFlow.invest[n, o[n]] +
                     m.flows[n, o[n]].investment.existing) *
                    n.invest_relation_input_output ==
                    (m.InvestmentFlow.invest[i[n], n] +
                     m.flows[i[n], n].investment.existing))
            return expr
        self.power_coupled = Constraint(
                self.INVEST_REL_IN_OUT, rule=_power_coupled)

        def _storage_capacity_inflow_invest_rule(block, n):
            """Rule definition of constraint connecting the inflow
            `InvestmentFlow.invest of storage with invested capacity `invest`
            by nominal_capacity__inflow_ratio
            """
            expr = ((m.InvestmentFlow.invest[i[n], n] +
                     m.flows[i[n], n].investment.existing) ==
                    (n.investment.existing + self.invest[n]) *
                    n.invest_relation_input_capacity)
            return expr
        self.storage_capacity_inflow = Constraint(
            self.INVEST_REL_CAP_IN, rule=_storage_capacity_inflow_invest_rule)

        def _storage_capacity_outflow_invest_rule(block, n):
            """Rule definition of constraint connecting outflow
            `InvestmentFlow.invest` of storage and invested capacity `invest`
            by nominal_capacity__outflow_ratio
            """
            expr = ((m.InvestmentFlow.invest[n, o[n]] +
                     m.flows[n, o[n]].investment.existing) ==
                    (n.investment.existing + self.invest[n]) *
                    n.invest_relation_output_capacity)
            return expr
        self.storage_capacity_outflow = Constraint(
            self.INVEST_REL_CAP_OUT,
            rule=_storage_capacity_outflow_invest_rule)

        def _max_capacity_invest_rule(block, n, t):
            """Rule definition for upper bound constraint for the storage cap.
            """
            expr = (self.capacity[n, t] <=
                    (n.investment.existing + self.invest[n]) *
                    n.capacity_max[t])
            return expr
        self.max_capacity = Constraint(
            self.INVESTSTORAGES, m.TIMESTEPS, rule=_max_capacity_invest_rule)

        def _min_capacity_invest_rule(block, n, t):
            """Rule definition of lower bound constraint for the storage cap.
            """
            expr = (self.capacity[n, t] >=
                    (n.investment.existing + self.invest[n]) *
                    n.capacity_min[t])
            return expr
        # Set the lower bound of the storage capacity if the attribute exists
        self.min_capacity = Constraint(
            self.MIN_INVESTSTORAGES, m.TIMESTEPS,
            rule=_min_capacity_invest_rule)

    def _objective_expression(self):
        """Objective expression with fixed and investement costs."""
        if not hasattr(self, 'INVESTSTORAGES'):
            return 0

        investment_costs = 0

        for n in self.INVESTSTORAGES:
            if n.investment.ep_costs is not None:
                investment_costs += self.invest[n] * n.investment.ep_costs
            else:
                raise ValueError("Missing value for investment costs!")

        self.investment_costs = Expression(expr=investment_costs)

        return investment_costs


class GenericCHP(network.Transformer):
    r"""
    Component `GenericCHP` to model combined heat and power plants.

    Can be used to model (combined cycle) extraction or back-pressure turbines
    and used a mixed-integer linear formulation. Thus, it induces more
    computational effort than the `ExtractionTurbineCHP` for the
    benefit of higher accuracy.

    The full set of equations is described in:
    Mollenhauer, E., Christidis, A. & Tsatsaronis, G.
    Evaluation of an energy- and exergy-based generic modeling
    approach of combined heat and power plants
    Int J Energy Environ Eng (2016) 7: 167.
    https://doi.org/10.1007/s40095-016-0204-6

    For a general understanding of (MI)LP CHP representation, see:
    Fabricio I. Salgado, P.
    Short - Term Operation Planning on Cogeneration Systems: A Survey
    Electric Power Systems Research (2007)
    Electric Power Systems Research
    Volume 78, Issue 5, May 2008, Pages 835-848
    https://doi.org/10.1016/j.epsr.2007.06.001

    Note
    ----
    An adaption for the flow parameter `H_L_FG_share_max` has been made to
    set the flue gas losses at maximum heat extraction `H_L_FG_max` as share of
    the fuel flow `H_F` e.g. for combined cycle extraction turbines.
    The flow parameter `H_L_FG_share_min` can be used to set the flue gas
    losses at minimum heat extraction `H_L_FG_min` as share of
    the fuel flow `H_F` e.g. for motoric CHPs.
    The boolean component parameter `back_pressure` can be set to model
    back-pressure characteristics.

    Also have a look at the examples on how to use it.

    Parameters
    ----------
    fuel_input : dict
        Dictionary with key-value-pair of `oemof.Bus` and `oemof.Flow` object
        for the fuel input.
    electrical_output : dict
        Dictionary with key-value-pair of `oemof.Bus` and `oemof.Flow` object
        for the electrical output. Related parameters like `P_max_woDH` are
        passed as attributes of the `oemof.Flow` object.
    heat_output : dict
        Dictionary with key-value-pair of `oemof.Bus` and `oemof.Flow` object
        for the heat output. Related parameters like `Q_CW_min` are passed as
        attributes of the `oemof.Flow` object.
    Beta : list of numerical values
        Beta values in same dimension as all other parameters (length of
        optimization period).
    back_pressure : boolean
        Flag to use back-pressure characteristics. Set to `True` and
        `Q_CW_min` to zero for back-pressure turbines. See paper above for more
        information.

    Note
    ----
    The following sets, variables, constraints and objective parts are created
     * :py:class:`~oemof.solph.components.GenericCHPBlock`

    Examples
    --------
    >>> from oemof import solph
    >>> bel = solph.Bus(label='electricityBus')
    >>> bth = solph.Bus(label='heatBus')
    >>> bgas = solph.Bus(label='commodityBus')
    >>> ccet = solph.components.GenericCHP(
    ...    label='combined_cycle_extraction_turbine',
    ...    fuel_input={bgas: solph.Flow(
    ...        H_L_FG_share_max=[0.183])},
    ...    electrical_output={bel: solph.Flow(
    ...        P_max_woDH=[155.946],
    ...        P_min_woDH=[68.787],
    ...        Eta_el_max_woDH=[0.525],
    ...        Eta_el_min_woDH=[0.444])},
    ...    heat_output={bth: solph.Flow(
    ...        Q_CW_min=[10.552])},
    ...    Beta=[0.122], back_pressure=False)
    >>> type(ccet)
    <class 'oemof.solph.components.GenericCHP'>
    """

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

        self.fuel_input = kwargs.get('fuel_input')
        self.electrical_output = kwargs.get('electrical_output')
        self.heat_output = kwargs.get('heat_output')
        self.Beta = solph_sequence(kwargs.get('Beta'))
        self.back_pressure = kwargs.get('back_pressure')
        self._alphas = None

        # map specific flows to standard API
        fuel_bus = list(self.fuel_input.keys())[0]
        fuel_flow = list(self.fuel_input.values())[0]
        fuel_bus.outputs.update({self: fuel_flow})

        self.outputs.update(kwargs.get('electrical_output'))
        self.outputs.update(kwargs.get('heat_output'))

    def _calculate_alphas(self):
        """
        Calculate alpha coefficients.

        A system of linear equations is created from passed capacities and
        efficiencies and solved to calculate both coefficients.
        """
        alphas = [[], []]

        eb = list(self.electrical_output.keys())[0]

        attrs = [self.electrical_output[eb].P_min_woDH,
                 self.electrical_output[eb].Eta_el_min_woDH,
                 self.electrical_output[eb].P_max_woDH,
                 self.electrical_output[eb].Eta_el_max_woDH]

        length = [len(a) for a in attrs if not isinstance(a, (int, float))]
        max_length = max(length)

        if all(len(a) == max_length for a in attrs):
            if max_length == 0:
                max_length += 1  # increment dimension for scalars from 0 to 1
            for i in range(0, max_length):
                A = np.array([[1, self.electrical_output[eb].P_min_woDH[i]],
                              [1, self.electrical_output[eb].P_max_woDH[i]]])
                b = np.array([self.electrical_output[eb].P_min_woDH[i] /
                              self.electrical_output[eb].Eta_el_min_woDH[i],
                              self.electrical_output[eb].P_max_woDH[i] /
                              self.electrical_output[eb].Eta_el_max_woDH[i]])
                x = np.linalg.solve(A, b)
                alphas[0].append(x[0])
                alphas[1].append(x[1])
        else:
            error_message = ('Attributes to calculate alphas ' +
                             'must be of same dimension.')
            raise ValueError(error_message)

        self._alphas = alphas

    @property
    def alphas(self):
        """Compute or return the _alphas attribute."""
        if self._alphas is None:
            self._calculate_alphas()
        return self._alphas

    def constraint_group(self):
        return GenericCHPBlock


class GenericCHPBlock(SimpleBlock):
    r"""Block for the relation of nodes with type class:`.GenericCHP`.

    TODO: Add test

    **The following constraints are created:**

    .. _GenericCHP-equations:

    .. math::
        &
        (1)\qquad \dot{H}_F(t) = fuel\ input \\
        &
        (2)\qquad \dot{Q}(t) = heat\ output \\
        &
        (3)\qquad P_{el}(t) = power\ output\\
        &
        (4)\qquad \dot{H}_F(t) = \alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot P_{el,woDH}(t)\\
        &
        (5)\qquad \dot{H}_F(t) = \alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot ( P_{el}(t) + \beta \cdot \dot{Q}(t) )\\
        &
        (6)\qquad \dot{H}_F(t) \leq Y(t) \cdot \frac{P_{el, max, woDH}(t)}{\eta_{el,max,woDH}(t)}\\
        &
        (7)\qquad \dot{H}_F(t) \geq Y(t) \cdot \frac{P_{el, min, woDH}(t)}{\eta_{el,min,woDH}(t)}\\
        &
        (8)\qquad \dot{H}_{L,FG,max}(t) = \dot{H}_F(t) \cdot \dot{H}_{L,FG,sharemax}(t)\\
        &
        (9)\qquad \dot{H}_{L,FG,min}(t) = \dot{H}_F(t) \cdot \dot{H}_{L,FG,sharemin}(t)\\
        &
        (10)\qquad P_{el}(t) + \dot{Q}(t) + \dot{H}_{L,FG,max}(t) + \dot{Q}_{CW, min}(t) \cdot Y(t) = / \leq \dot{H}_F(t)\\
        &
        (11)\qquad P_{el}(t) + \dot{Q}(t) + \dot{H}_{L,FG,min}(t) + \dot{Q}_{CW, min}(t) \cdot Y(t) \geq \dot{H}_F(t)\\[10pt]
        &
        \forall t \in \textrm{TIMESTEPS}, \\
        &
        \forall n \in \textrm{VARIABLE\_FRACTION\_TRANSFORMERS}.


    Where :math:`= / \leq` depends on the CHP being backpressure or not. Constraint (11) is set only if
    :math:`\dot{H}_{L,FG,min}` is given, e.g. for a motoric CHP. The coefficients :math:`\alpha_0` and :math:`\alpha_1`
    can be determined given the efficiencies maximal/minimal load:

    .. math::
        &
        \eta_{el,max,woDH} = \frac{P_{el,max,woDH}(t)}{\alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot P_{el,max,woDH}(t)}\\
        &
        \eta_{el,min,woDH} = \frac{P_{el,min,woDH}(t)}{\alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot P_{el,min,woDH}(t)}\\

    =============================== ======================== =========
    math. symbol                    explanation              attribute
    =============================== ======================== =========
    :math:`\dot{H}_{F}`             input of enthalpy        :py:obj:`H_F[n,t]`
                                    through fuel input
    :math:`P_{el}`                  provided                 :py:obj:`P[n,t]`
                                    electric power
    :math:`P_{el,woDH}`             electric power without   :py:obj:`P_woDH[n,t]`
                                    district heating
    :math:`P_{el,min,woDH}`         min. electric power      :py:obj:`P_min_woDH[t]`
                                    without district heating
    :math:`P_{el,max,woDH}`         max. electric power      :py:obj:`P_max_woDH[t]`
                                    without district heating
    :math:`\dot{Q}`                 provided heat            :py:obj:`Q[n,t]`

    :math:`\dot{Q}_{CW, min}`       minimal therm. condenser :py:obj:`Q_CW_min[t]`
                                    load to cooling water
    :math:`\dot{H}_{L,FG,min}`      flue gas enthalpy loss   :py:obj:`H_L_FG_min[n, t]`
                                    at min heat extraction
    :math:`\dot{H}_{L,FG,max}`      flue gas enthalpy loss   :py:obj:`H_L_FG_max[n, t]`
                                    at max heat extraction
    :math:`\dot{H}_{L,FG,sharemin}` share of flue gas loss   :py:obj:`H_L_FG_share_min[t]`
                                    at min heat extraction
    :math:`\dot{H}_{L,FG,sharemax}` share of flue gas loss   :py:obj:`H_L_FG_share_max[t]`
                                    at max heat extraction
    :math:`Y`                       status variable          :py:obj:`Y[n,t]`
                                    on/off
    :math:`\alpha_0`                coefficient              :py:obj:`n.alphas[0][t]`
                                    describing efficiency
    :math:`\alpha_1`                coefficient              :py:obj:`n.alphas[1][t]`
                                    describing efficiency
    :math:`\beta`                   power loss index         :py:obj:`Beta[t]`

    :math:`\eta_{el,min,woDH}`      el. eff. at min. fuel    :py:obj:`Eta_el_min_woDH[t]`
                                    flow w/o distr. heating
    :math:`\eta_{el,max,woDH}`      el. eff. at max. fuel    :py:obj:`Eta_el_max_woDH[t]`
                                    flow w/o distr. heating

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


    """
    CONSTRAINT_GROUP = True

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

    def _create(self, group=None):
        """
        Create constraints for GenericCHPBlock.

        Parameters
        ----------
        group : list
            List containing `GenericCHP` objects.
            e.g. groups=[ghcp1, gchp2,..]
        """
        m = self.parent_block()

        if group is None:
            return None

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

        # variables
        self.H_F = Var(self.GENERICCHPS, m.TIMESTEPS, within=NonNegativeReals)
        self.H_L_FG_max = Var(self.GENERICCHPS, m.TIMESTEPS,
                              within=NonNegativeReals)
        self.H_L_FG_min = Var(self.GENERICCHPS, m.TIMESTEPS,
                              within=NonNegativeReals)
        self.P_woDH = Var(self.GENERICCHPS, m.TIMESTEPS,
                          within=NonNegativeReals)
        self.P = Var(self.GENERICCHPS, m.TIMESTEPS, within=NonNegativeReals)
        self.Q = Var(self.GENERICCHPS, m.TIMESTEPS, within=NonNegativeReals)
        self.Y = Var(self.GENERICCHPS, m.TIMESTEPS, within=Binary)

        # constraint rules
        def _H_flow_rule(block, n, t):
            """Link fuel consumption to component inflow."""
            expr = 0
            expr += self.H_F[n, t]
            expr += - m.flow[list(n.fuel_input.keys())[0], n, t]
            return expr == 0
        self.H_flow = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                 rule=_H_flow_rule)

        def _Q_flow_rule(block, n, t):
            """Link heat flow to component outflow."""
            expr = 0
            expr += self.Q[n, t]
            expr += - m.flow[n, list(n.heat_output.keys())[0], t]
            return expr == 0
        self.Q_flow = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                 rule=_Q_flow_rule)

        def _P_flow_rule(block, n, t):
            """Link power flow to component outflow."""
            expr = 0
            expr += self.P[n, t]
            expr += - m.flow[n, list(n.electrical_output.keys())[0], t]
            return expr == 0
        self.P_flow = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                 rule=_P_flow_rule)

        def _H_F_1_rule(block, n, t):
            """Set P_woDH depending on H_F."""
            expr = 0
            expr += - self.H_F[n, t]
            expr += n.alphas[0][t] * self.Y[n, t]
            expr += n.alphas[1][t] * self.P_woDH[n, t]
            return expr == 0
        self.H_F_1 = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                rule=_H_F_1_rule)

        def _H_F_2_rule(block, n, t):
            """Determine relation between H_F, P and Q."""
            expr = 0
            expr += - self.H_F[n, t]
            expr += n.alphas[0][t] * self.Y[n, t]
            expr += n.alphas[1][t] * (self.P[n, t] + n.Beta[t] * self.Q[n, t])
            return expr == 0
        self.H_F_2 = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                rule=_H_F_2_rule)

        def _H_F_3_rule(block, n, t):
            """Set upper value of operating range via H_F."""
            expr = 0
            expr += self.H_F[n, t]
            expr += - self.Y[n, t] * \
                (list(n.electrical_output.values())[0].P_max_woDH[t] /
                 list(n.electrical_output.values())[0].Eta_el_max_woDH[t])
            return expr <= 0
        self.H_F_3 = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                rule=_H_F_3_rule)

        def _H_F_4_rule(block, n, t):
            """Set lower value of operating range via H_F."""
            expr = 0
            expr += self.H_F[n, t]
            expr += - self.Y[n, t] * \
                (list(n.electrical_output.values())[0].P_min_woDH[t] /
                 list(n.electrical_output.values())[0].Eta_el_min_woDH[t])
            return expr >= 0
        self.H_F_4 = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                rule=_H_F_4_rule)

        def _H_L_FG_max_rule(block, n, t):
            """Set max. flue gas loss as share fuel flow share."""
            expr = 0
            expr += - self.H_L_FG_max[n, t]
            expr += self.H_F[n, t] * \
                list(n.fuel_input.values())[0].H_L_FG_share_max[t]
            return expr == 0
        self.H_L_FG_max_def = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                         rule=_H_L_FG_max_rule)

        def _Q_max_res_rule(block, n, t):
            """Set maximum Q depending on fuel and electrical flow."""
            expr = 0
            expr += self.P[n, t] + self.Q[n, t] + self.H_L_FG_max[n, t]
            expr += list(n.heat_output.values())[0].Q_CW_min[t] * self.Y[n, t]
            expr += - self.H_F[n, t]
            # back-pressure characteristics or one-segment model
            if n.back_pressure is True:
                return expr == 0
            else:
                return expr <= 0
        self.Q_max_res = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                    rule=_Q_max_res_rule)

        def _H_L_FG_min_rule(block, n, t):
            """Set min. flue gas loss as fuel flow share."""
            # minimum flue gas losses e.g. for motoric CHPs
            if getattr(list(n.fuel_input.values())[0],
                       'H_L_FG_share_min', None):
                expr = 0
                expr += - self.H_L_FG_min[n, t]
                expr += self.H_F[n, t] * \
                    list(n.fuel_input.values())[0].H_L_FG_share_min[t]
                return expr == 0
            else:
                return Constraint.Skip
        self.H_L_FG_min_def = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                         rule=_H_L_FG_min_rule)

        def _Q_min_res_rule(block, n, t):
            """Set minimum Q depending on fuel and eletrical flow."""
            # minimum restriction for heat flows e.g. for motoric CHPs
            if getattr(list(n.fuel_input.values())[0],
                       'H_L_FG_share_min', None):
                expr = 0
                expr += self.P[n, t] + self.Q[n, t] + self.H_L_FG_min[n, t]
                expr += list(n.heat_output.values())[0].Q_CW_min[t] \
                    * self.Y[n, t]
                expr += - self.H_F[n, t]
                return expr >= 0
            else:
                return Constraint.Skip
        self.Q_min_res = Constraint(self.GENERICCHPS, m.TIMESTEPS,
                                    rule=_Q_min_res_rule)

    def _objective_expression(self):
        r"""Objective expression for generic CHPs with no investment.

        Note: This adds nothing as variable costs are already
        added in the Block :class:`Flow`.
        """
        if not hasattr(self, 'GENERICCHPS'):
            return 0

        return 0


class ExtractionTurbineCHP(solph_Transformer):
    r"""
    A CHP with an extraction turbine in a linear model. For more options see
    the :class:`~oemof.solph.components.GenericCHP` class.

    One main output flow has to be defined and is tapped by the remaining flow.
    The conversion factors have to be defined for the maximum tapped flow (
    full CHP mode) and for no tapped flow (full condensing mode). Even though
    it is possible to limit the variability of the tapped flow, so that the
    full condensing mode will never be reached.

    Parameters
    ----------
    conversion_factors : dict
        Dictionary containing conversion factors for conversion of inflow
        to specified outflow. Keys are output bus objects.
        The dictionary values can either be a scalar or a sequence with length
        of time horizon for simulation.
    conversion_factor_full_condensation : dict
        The efficiency of the main flow if there is no tapped flow. Only one
        key is allowed. Use one of the keys of the conversion factors. The key
        indicates the main flow. The other output flow is the tapped flow.

    Note
    ----
    The following sets, variables, constraints and objective parts are created
     * :py:class:`~oemof.solph.components.ExtractionTurbineCHPBlock`

    Examples
    --------
    >>> from oemof import solph
    >>> bel = solph.Bus(label='electricityBus')
    >>> bth = solph.Bus(label='heatBus')
    >>> bgas = solph.Bus(label='commodityBus')
    >>> et_chp = solph.components.ExtractionTurbineCHP(
    ...    label='variable_chp_gas',
    ...    inputs={bgas: solph.Flow(nominal_value=10e10)},
    ...    outputs={bel: solph.Flow(), bth: solph.Flow()},
    ...    conversion_factors={bel: 0.3, bth: 0.5},
    ...    conversion_factor_full_condensation={bel: 0.5})
    """

    def __init__(self, conversion_factor_full_condensation, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.conversion_factor_full_condensation = {
            k: solph_sequence(v) for k, v in
            conversion_factor_full_condensation.items()}

    def constraint_group(self):
        return ExtractionTurbineCHPBlock


class ExtractionTurbineCHPBlock(SimpleBlock):
    r"""Block for the linear relation of nodes with type
    :class:`~oemof.solph.components.ExtractionTurbineCHP`

    **The following sets are created:** (-> see basic sets at
    :class:`.Model` )

    VARIABLE_FRACTION_TRANSFORMERS
        A set with all
        :class:`~oemof.solph.components.ExtractionTurbineCHP` objects.

    **The following two constraints are created:**

    .. _ETCHP-equations:

        .. math::
            &
            \dot H_{Fuel} =
            \frac{P_{el} + \dot Q_{th} \cdot \beta}
                 {\eta_{el,woExtr}} \\
            &
            P_{el} \geq \dot Q_{th} \cdot
            \frac{\eta_{el,maxExtr}}
                 {\eta_{th,maxExtr}}

    where :math:`\beta` is defined as:
    
         .. math::
            \beta = \frac{\eta_{el,woExtr} - \eta_{el,maxExtr}}{\eta_{th,maxExtr}}

    where the first equation is the result of the relation between the input
    flow and the two output flows, the second equation stems from how the two
    output flows relate to each other, and the symbols used are defined as
    follows:
    

    ========================= ======================== =========
    symbol                    explanation              attribute
    ========================= ======================== =========
    :math:`\dot H_{Fuel}`     fuel input flow          :py:obj:`flow(inflow, n, t)` is the *flow* from :py:obj:`inflow`
                                                       node to the node :math:`n` at timestep :math:`t`
    :math:`P_{el}`            electric power           :py:obj:`flow(n, main_output, t)` is the *flow* from the  
                                                       node :math:`n` to the :py:obj:`main_output` node at timestep :math:`t`
    :math:`\dot Q_{th}`       thermal output           :py:obj:`flow(n, tapped_output, t)` is the *flow* from the 
                                                       node :math:`n` to the :py:obj:`tapped_output` node at timestep :math:`t`
    :math:`\beta`             power loss index         :py:obj:`main_flow_loss_index` at node :math:`n` at timestep :math:`t`
                                                       as defined above
    :math:`\eta_{el,woExtr}`  electric efficiency      :py:obj:`conversion_factor_full_condensation` at node :math:`n` 
                              without heat extraction  at timestep :math:`t`
    :math:`\eta_{el,maxExtr}` electric efficiency      :py:obj:`conversion_factors` for the :py:obj:`main_output` at
                              with max heat extraction node :math:`n` at timestep :math:`t`
    :math:`\eta_{th,maxExtr}` thermal efficiency with  :py:obj:`conversion_factors` for the :py:obj:`tapped_output` 
                              maximal heat extraction  at node :math:`n` at timestep :math:`t`
    ========================= ======================== =========		


    """

    CONSTRAINT_GROUP = True

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

    def _create(self, group=None):
        """ Creates the linear constraint for the
        :class:`oemof.solph.Transformer` block.

        Parameters
        ----------
        group : list
            List of :class:`oemof.solph.ExtractionTurbineCHP` (trsf) objects
            for which the linear relation of inputs and outputs is created
            e.g. group = [trsf1, trsf2, trsf3, ...]. Note that the relation
            is created for all existing relations of the inputs and all outputs
            of the transformer. The components inside the list need to hold
            all needed attributes.
        """
        if group is None:
            return None

        m = self.parent_block()

        for n in group:
            n.inflow = list(n.inputs)[0]
            n.main_flow = (
                [k for k, v in n.conversion_factor_full_condensation.items()]
                [0])
            n.main_output = [o for o in n.outputs if n.main_flow == o][0]
            n.tapped_output = [o for o in n.outputs if n.main_flow != o][0]
            n.conversion_factor_full_condensation_sq = (
                n.conversion_factor_full_condensation[n.main_output])
            n.flow_relation_index = [
                n.conversion_factors[n.main_output][t] /
                n.conversion_factors[n.tapped_output][t]
                for t in m.TIMESTEPS]
            n.main_flow_loss_index = [
                (n.conversion_factor_full_condensation_sq[t] -
                 n.conversion_factors[n.main_output][t]) /
                n.conversion_factors[n.tapped_output][t]
                for t in m.TIMESTEPS]

        def _input_output_relation_rule(block):
            """Connection between input, main output and tapped output.
            """
            for t in m.TIMESTEPS:
                for g in group:
                    lhs = m.flow[g.inflow, g, t]
                    rhs = (
                        (m.flow[g, g.main_output, t] +
                         m.flow[g, g.tapped_output, t] *
                         g.main_flow_loss_index[t]) /
                        g.conversion_factor_full_condensation_sq[t]
                        )
                    block.input_output_relation.add((g, t), (lhs == rhs))
        self.input_output_relation = Constraint(group, m.TIMESTEPS,
                                                noruleinit=True)
        self.input_output_relation_build = BuildAction(
            rule=_input_output_relation_rule)

        def _out_flow_relation_rule(block):
            """Relation between main and tapped output in full chp mode.
            """
            for t in m.TIMESTEPS:
                for g in group:
                    lhs = m.flow[g, g.main_output, t]
                    rhs = (m.flow[g, g.tapped_output, t] *
                           g.flow_relation_index[t])
                    block.out_flow_relation.add((g, t), (lhs >= rhs))
        self.out_flow_relation = Constraint(group, m.TIMESTEPS,
                                            noruleinit=True)
        self.out_flow_relation_build = BuildAction(
                rule=_out_flow_relation_rule)