# -*- 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-License-Identifier: MIT
"""
from oemof.network import network
from pyomo.core.base.block import SimpleBlock
from pyomo.environ import Binary
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 import network as solph_network
from oemof.solph.options import Investment
from oemof.solph.plumbing import sequence as solph_sequence
[docs]class GenericStorage(network.Node):
r"""
Component `GenericStorage` to model with basic characteristics of storages.
The GenericStorage is designed for one input and one output.
Parameters
----------
nominal_storage_capacity : numeric, :math:`E_{nom}`
Absolute nominal capacity of the storage
invest_relation_input_capacity : numeric 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 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 or None, :math:`r_{in,out}`
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:`\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).
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 time unit.
fixed_losses_relative : numeric (iterable or scalar), :math:`\gamma(t)`
Losses independent of state of charge between two consecutive
timesteps relative to nominal storage capacity.
fixed_losses_absolute : numeric (iterable or scalar), :math:`\delta(t)`
Losses independent of state of charge and independent of
nominal storage capacity between two consecutive timesteps.
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 (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
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_storage_capacity. The
nominal_storage_capacity should not be set (or set to None) if an
investment object is used.
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.Bus('my_bus')
>>> my_storage = solph.components.GenericStorage(
... label='storage',
... nominal_storage_capacity=1000,
... inputs={my_bus: solph.Flow(nominal_value=200, variable_costs=10)},
... outputs={my_bus: solph.Flow(nominal_value=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',
... investment=solph.Investment(ep_costs=50),
... inputs={my_bus: solph.Flow()},
... outputs={my_bus: solph.Flow()},
... 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, *args, max_storage_level=1, min_storage_level=0, **kwargs
):
super().__init__(*args, **kwargs)
self.nominal_storage_capacity = kwargs.get("nominal_storage_capacity")
self.initial_storage_level = kwargs.get("initial_storage_level")
self.balanced = kwargs.get("balanced", True)
self.loss_rate = solph_sequence(kwargs.get("loss_rate", 0))
self.fixed_losses_relative = solph_sequence(
kwargs.get("fixed_losses_relative", 0)
)
self.fixed_losses_absolute = solph_sequence(
kwargs.get("fixed_losses_absolute", 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.max_storage_level = solph_sequence(max_storage_level)
self.min_storage_level = solph_sequence(min_storage_level)
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)
# Check number of flows.
self._check_number_of_flows()
# Check attributes for the investment mode.
if self._invest_group is True:
self._check_invest_attributes()
# Check for old parameter names. This is a temporary fix and should
# be removed once a general solution is found.
# TODO: https://github.com/oemof/oemof-solph/issues/560
renamed_parameters = [
("nominal_capacity", "nominal_storage_capacity"),
("initial_capacity", "initial_storage_level"),
("capacity_loss", "loss_rate"),
("capacity_min", "min_storage_level"),
("capacity_max", "max_storage_level"),
]
messages = [
"`{0}` to `{1}`".format(old_name, new_name)
for old_name, new_name in renamed_parameters
if old_name in kwargs
]
if messages:
message = (
"The following attributes have been renamed from v0.2 to v0.3:"
"\n\n {}\n\n"
"You are using the old names as parameters, thus setting "
"deprecated\n"
"attributes, which is not what you might have intended.\n"
"Use the new names, or, if you know what you're doing, set "
"these\n"
"attributes explicitly after construction instead."
)
raise AttributeError(message.format("\n ".join(messages)))
def _set_flows(self):
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 _check_invest_attributes(self):
if self.investment and self.nominal_storage_capacity is not None:
e1 = (
"If an investment object is defined the invest variable "
"replaces the nominal_storage_capacity.\n Therefore the "
"nominal_storage_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)
if (
self.investment
and sum(solph_sequence(self.fixed_losses_absolute)) != 0
and self.investment.existing == 0
and self.investment.minimum == 0
):
e3 = (
"With fixed_losses_absolute > 0, either investment.existing "
"or investment.minimum has to be non-zero."
)
raise AttributeError(e3)
self._set_flows()
def _check_number_of_flows(self):
msg = "Only one {0} flow allowed in the GenericStorage {1}."
solph_network.check_node_object_for_missing_attribute(self, "inputs")
solph_network.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))
[docs] def constraint_group(self):
if self._invest_group is True:
return GenericInvestmentStorageBlock
else:
return GenericStorageBlock
[docs]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, 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 :class:`.Storage` 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.Storage.storage_content[s, 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 balance :attr:`om.Storage.balance[n, t]`
.. math:: E(t) = &E(t-1) \cdot
(1 - \beta(t)) ^{\tau(t)/(t_u)} \\
&- \gamma(t)\cdot E_{nom} \cdot {\tau(t)/(t_u)}\\
&- \delta(t) \cdot {\tau(t)/(t_u)}\\
&- \frac{\dot{E}_o(t)}{\eta_o(t)} \cdot \tau(t)
+ \dot{E}_i(t) \cdot \eta_i(t) \cdot \tau(t)
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}
=========================== ======================= =========
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 time unit
:math:`\gamma(t)` fixed loss of energy `fixed_losses_relative[t]`
relative to
:math:`E_{nom}` per
time unit
:math:`\delta(t)` absolute fixed loss `fixed_losses_absolute[t]`
of energy per
time unit
: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)`
=========================== ======================= =========
**The following parts of the objective function are created:**
Nothing added to the objective function.
""" # 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_WITH_INVEST_FLOW_REL = Set(
initialize=[
n for n in group if n.invest_relation_input_output 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
self.storage_content = Var(
self.STORAGES, m.TIMESTEPS, bounds=_storage_content_bound_rule
)
def _storage_init_content_bound_rule(block, n):
return 0, n.nominal_storage_capacity
self.init_content = Var(
self.STORAGES,
within=NonNegativeReals,
bounds=_storage_init_content_bound_rule,
)
# set the initial storage content
for n in group:
if n.initial_storage_level is not None:
self.init_content[n] = (
n.initial_storage_level * n.nominal_storage_capacity
)
self.init_content[n].fix()
# ************* Constraints ***************************
reduced_timesteps = [x for x in m.TIMESTEPS if x > 0]
# storage balance constraint (first time step)
def _storage_balance_first_rule(block, n):
"""
Rule definition for the storage balance of every storage n for
the first timestep.
"""
expr = 0
expr += block.storage_content[n, 0]
expr += (
-block.init_content[n]
* (1 - n.loss_rate[0]) ** m.timeincrement[0]
)
expr += (
n.fixed_losses_relative[0]
* n.nominal_storage_capacity
* m.timeincrement[0]
)
expr += n.fixed_losses_absolute[0] * m.timeincrement[0]
expr += (
-m.flow[i[n], n, 0] * n.inflow_conversion_factor[0]
) * m.timeincrement[0]
expr += (
m.flow[n, o[n], 0] / n.outflow_conversion_factor[0]
) * m.timeincrement[0]
return expr == 0
self.balance_first = Constraint(
self.STORAGES, rule=_storage_balance_first_rule
)
# storage balance constraint (every time step but the first)
def _storage_balance_rule(block, n, t):
"""
Rule definition for the storage balance of every storage n and
every timestep but the first (t > 0).
"""
expr = 0
expr += block.storage_content[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]
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, reduced_timesteps, rule=_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.TIMESTEPS[-1]]
== block.init_content[n]
)
self.balanced_cstr = Constraint(
self.STORAGES_BALANCED, rule=_balanced_storage_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
[docs]class GenericInvestmentStorageBlock(SimpleBlock):
r"""
Block for all storages with :attr:`Investment` being not None.
See :class:`oemof.solph.options.Investment` for all parameters of the
Investment class.
**Variables**
All Storages are indexed by :math:`n`, which is omitted in the following
for the sake of convenience.
The following variables are created as attributes of
:attr:`om.InvestmentStorage`:
* :math:`P_i(t)`
Inflow of the storage
(created in :class:`oemof.solph.models.BaseModel`).
* :math:`P_o(t)`
Outflow of the storage
(created in :class:`oemof.solph.models.BaseModel`).
* :math:`E(t)`
Current storage content (Absolute level of stored energy).
* :math:`E_{invest}`
Invested (nominal) capacity of the storage.
* :math:`E(-1)`
Initial storage content (before timestep 0).
* :math:`b_{invest}`
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_{exist} + E_{invest}) \cdot {\tau(t)/(t_u)}\\
&- \delta(t) \cdot {\tau(t)/(t_u)}\\
&- \frac{P_o(t)}{\eta_o(t)} \cdot \tau(t)
+ P_i(t) \cdot \eta_i(t) \cdot \tau(t)
Depending on the attribute :attr:`nonconvex`, the constraints for the
bounds of the decision variable :math:`E_{invest}` are different:\
* :attr:`nonconvex = False`
.. math::
E_{invest, min} \le E_{invest} \le E_{invest, max}
* :attr:`nonconvex = True`
.. math::
&
E_{invest, min} \cdot b_{invest} \le E_{invest}\\
&
E_{invest} \le E_{invest, max} \cdot b_{invest}\\
The following constraints are created depending on the attributes of
the :class:`.components.GenericStorage`:
* :attr:`initial_storage_level is None`
Constraint for a variable initial storage content:
.. math::
E(-1) \le E_{invest} + E_{exist}
* :attr:`initial_storage_level is not None`
An initial value for the storage content is given:
.. math::
E(-1) = (E_{invest} + E_{exist}) \cdot c(-1)
* :attr:`balanced=True`
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,invest} + P_{i,exist} =
(E_{invest} + E_{exist}) \cdot r_{cap,in}
* :attr:`invest_relation_output_capacity is not None`
Connect the invest variables of the storage and the output flow:
.. math::
P_{o,invest} + P_{o,exist} =
(E_{invest} + E_{exist}) \cdot r_{cap,out}
* :attr:`invest_relation_input_output is not None`
Connect the invest variables of the input and the output flow:
.. math::
P_{i,invest} + P_{i,exist} =
(P_{o,invest} + P_{o,exist}) \cdot r_{in,out}
* :attr:`max_storage_level`
Rule for upper bound constraint for the storage content:
.. math::
E(t) \leq E_{invest} \cdot c_{max}(t)
* :attr:`min_storage_level`
Rule for lower bound constraint for the storage content:
.. math:: E(t) \geq E_{invest} \cdot c_{min}(t)
**Objective function**
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:
* :attr:`nonconvex = False`
.. math::
E_{invest} \cdot c_{invest,var}
* :attr:`nonconvex = True`
.. math::
E_{invest} \cdot c_{invest,var}
+ c_{invest,fix} \cdot b_{invest}\\
The total value of all investment costs of all *InvestmentStorages*
can be retrieved calling
:meth:`om.GenericInvestmentStorageBlock.investment_costs.expr()`.
.. csv-table:: List of Variables
:header: "symbol", "attribute", "explanation"
:widths: 1, 1, 1
":math:`P_i(t)`", ":attr:`flow[i[n], n, t]`", "Inflow of the storage"
":math:`P_o(t)`", ":attr:`flow[n, o[n], t]`", "Outlfow of the storage"
":math:`E(t)`", ":attr:`storage_content[n, t]`", "Current storage
content (current absolute stored energy)"
":math:`E_{invest}`", ":attr:`invest[n, t]`", "Invested (nominal)
capacity of the storage"
":math:`E(-1)`", ":attr:`init_cap[n]`", "Initial storage capacity
(before timestep 0)"
":math:`b_{invest}`", ":attr:`invest_status[i, o]`", "Binary variable
for the status of investment"
":math:`P_{i,invest}`", ":attr:`InvestmentFlow.invest[i[n], n]`", "
Invested (nominal) inflow (Investmentflow)"
":math:`P_{o,invest}`", ":attr:`InvestmentFlow.invest[n, o[n]]`", "
Invested (nominal) outflow (Investmentflow)"
.. 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 outlfow 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:`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 time unit"
":math:`\gamma(t)`", "`fixed_losses_relative[t]`", "Fixed loss
of energy relative to :math:`E_{invest} + E_{exist}` per time unit"
":math:`\delta(t)`", "`fixed_losses_absolute[t]`", "Absolute
fixed loss of energy per time unit"
":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 relativ
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:`\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=None):
""" """
m = self.parent_block()
if group is None:
return None
# ########################## 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 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
]
)
# 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
]
)
# ######################### Variables ################################
self.storage_content = Var(
self.INVESTSTORAGES, m.TIMESTEPS, within=NonNegativeReals
)
def _storage_investvar_bound_rule(block, n):
"""
Rule definition to bound the invested storage capacity `invest`.
"""
if n in self.CONVEX_INVESTSTORAGES:
return n.investment.minimum, n.investment.maximum
elif n in self.NON_CONVEX_INVESTSTORAGES:
return 0, n.investment.maximum
self.invest = Var(
self.INVESTSTORAGES,
within=NonNegativeReals,
bounds=_storage_investvar_bound_rule,
)
self.init_content = Var(self.INVESTSTORAGES, within=NonNegativeReals)
# create status variable for a non-convex investment storage
self.invest_status = Var(self.NON_CONVEX_INVESTSTORAGES, 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}
reduced_timesteps = [x for x in m.TIMESTEPS if x > 0]
def _inv_storage_init_content_max_rule(block, n):
"""Constraint for a variable initial storage capacity."""
return (
block.init_content[n]
<= n.investment.existing + block.invest[n]
)
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."""
return block.init_content[n] == n.initial_storage_level * (
n.investment.existing + block.invest[n]
)
self.init_content_fix = Constraint(
self.INVESTSTORAGES_INIT_CONTENT,
rule=_inv_storage_init_content_fix_rule,
)
def _storage_balance_first_rule(block, n):
"""
Rule definition for the storage balance of every storage n for the
first time step.
"""
expr = 0
expr += block.storage_content[n, 0]
expr += (
-block.init_content[n]
* (1 - n.loss_rate[0]) ** m.timeincrement[0]
)
expr += (
n.fixed_losses_relative[0]
* (n.investment.existing + self.invest[n])
* m.timeincrement[0]
)
expr += n.fixed_losses_absolute[0] * m.timeincrement[0]
expr += (
-m.flow[i[n], n, 0] * n.inflow_conversion_factor[0]
) * m.timeincrement[0]
expr += (
m.flow[n, o[n], 0] / n.outflow_conversion_factor[0]
) * m.timeincrement[0]
return expr == 0
self.balance_first = Constraint(
self.INVESTSTORAGES, rule=_storage_balance_first_rule
)
def _storage_balance_rule(block, n, t):
"""
Rule definition for the storage balance of every storage n for the
every time step but the first.
"""
expr = 0
expr += block.storage_content[n, t]
expr += (
-block.storage_content[n, t - 1]
* (1 - n.loss_rate[t]) ** m.timeincrement[t]
)
expr += (
n.fixed_losses_relative[t]
* (n.investment.existing + self.invest[n])
* 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
self.balance = Constraint(
self.INVESTSTORAGES, reduced_timesteps, rule=_storage_balance_rule
)
def _balanced_storage_rule(block, n):
return (
block.storage_content[n, m.TIMESTEPS[-1]]
== block.init_content[n]
)
self.balanced_cstr = Constraint(
self.INVESTSTORAGES_BALANCED, rule=_balanced_storage_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_storage_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_storage_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_storage_content_invest_rule(block, n, t):
"""
Rule definition for upper bound constraint for the
storage content.
"""
expr = (
self.storage_content[n, t]
<= (n.investment.existing + self.invest[n])
* n.max_storage_level[t]
)
return expr
self.max_storage_content = Constraint(
self.INVESTSTORAGES,
m.TIMESTEPS,
rule=_max_storage_content_invest_rule,
)
def _min_storage_content_invest_rule(block, n, t):
"""
Rule definition of lower bound constraint for the
storage content.
"""
expr = (
self.storage_content[n, t]
>= (n.investment.existing + self.invest[n])
* n.min_storage_level[t]
)
return expr
# Set the lower bound of the storage content if the attribute exists
self.min_storage_content = Constraint(
self.MIN_INVESTSTORAGES,
m.TIMESTEPS,
rule=_min_storage_content_invest_rule,
)
def maximum_invest_limit(block, n):
"""
Constraint for the maximal investment in non convex investment
storage.
"""
return (
n.investment.maximum * self.invest_status[n] - self.invest[n]
) >= 0
self.limit_max = Constraint(
self.NON_CONVEX_INVESTSTORAGES, rule=maximum_invest_limit
)
def smallest_invest(block, n):
"""
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] - (n.investment.minimum * self.invest_status[n])
>= 0
)
self.limit_min = Constraint(
self.NON_CONVEX_INVESTSTORAGES, rule=smallest_invest
)
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.CONVEX_INVESTSTORAGES:
investment_costs += self.invest[n] * n.investment.ep_costs
for n in self.NON_CONVEX_INVESTSTORAGES:
investment_costs += (
self.invest[n] * n.investment.ep_costs
+ self.invest_status[n] * n.investment.offset
)
self.investment_costs = Expression(expr=investment_costs)
return investment_costs