# -*- 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: MIT
"""
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
[docs]class GenericStorage(network.Transformer):
"""
Component `GenericStorage` to model with basic characteristics of storages.
Parameters
----------
nominal_storage_capacity : numeric
Absolute nominal capacity of the storage
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_storage_level : numeric
The content of the storage in the first time step of optimization.
balanced : boolian
Couple storage level of first and last time step.
(Total inflow and total outflow are balanced.)
loss_rate : 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
min_storage_level : numeric (sequence or scalar)
The minimum storaged energy of the storage 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 (sequence or scalar)
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.
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_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)
"""
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.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 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/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)
self._set_flows()
[docs] def constraint_group(self):
if self._invest_group is True:
return GenericInvestmentStorageBlock
else:
return GenericStorageBlock
# Todo: accessed by
[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 :class:`.Storage` 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:**
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:**
Set last time step to the initial capacity if :attr:`balanced == True`
.. math::
E(t_{last}) = &E(-1)
Storage balance :attr:`om.Storage.balance[n, t]`
.. math:: E(t) = &E(t-1) \cdot
(1 - \delta(t))) \\
&- \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 :py:obj:`capacity`
:math:`E_{nom}` nominal capacity of :py:obj:`nominal_storage_capacity`
the energy storage
:math:`c(-1)` state before :py:obj:`initial_storage_level`
initial time step
:math:`c_{min}(t)` minimum allowed storage :py:obj:`min_storage_level[t]`
:math:`c_{max}(t)` maximum allowed storage :py:obj:`max_storage_level[t]`
:math:`\delta(t)` fraction of lost energy :py:obj:`loss_rate[t]`
(e.g. leakage) per time
:math:`\dot{E}_i(t)` energy flowing in :py:obj:`inputs`
:math:`\dot{E}_o(t)` energy flowing out :py:obj:`outputs`
:math:`\eta_i(t)` conversion factor :py:obj:`inflow_conversion_factor[t]`
(i.e. efficiency)
when storing energy
:math:`\eta_o(t)` conversion factor when :py:obj:`outflow_conversion_factor[t]`
(i.e. efficiency)
taking stored energy
:math:`\tau(t)` length of the time step
=========================== ======================= =========
**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}
# ************* 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_capacity_bound_rule(block, n, t):
"""Rule definition for bounds of capacity 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.capacity = Var(self.STORAGES, m.TIMESTEPS,
bounds=_storage_capacity_bound_rule)
def _storage_init_capacity_bound_rule(block, n):
return 0, n.nominal_storage_capacity
self.init_cap = Var(self.STORAGES, within=NonNegativeReals,
bounds=_storage_init_capacity_bound_rule)
# set the initial capacity of the storage
for n in group:
if n.initial_storage_level is not None:
self.init_cap[n] = (n.initial_storage_level *
n.nominal_storage_capacity)
self.init_cap[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.capacity[n, 0]
expr += - block.init_cap[n] * (
1 - n.loss_rate[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.capacity[n, t]
expr += - block.capacity[n, t-1] * (
1 - n.loss_rate[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):
"""capacity of last time step == initial capacity if balanced"""
return block.capacity[n, m.TIMESTEPS[-1]] == block.init_cap[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"""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_STORAGE_LEVEL
A subset of the set INVESTSTORAGES where elements of the set have an
initial_storage_level attribute.
MIN_INVESTSTORAGES
A subset of INVESTSTORAGES where elements of the set have an
min_storage_level 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
Same as for :class:`.GenericStorageBlock`.
Initial capacity of :class:`.network.Storage`
.. math::
E(n, -1) = invest(n) \cdot c(n, -1), \\
\forall n \in \textrm{INITIAL\_STORAGE\_LEVEL}.
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:: E(n, t) \leq invest(n) \cdot c_{min}(n, t), \\
\forall n \in \textrm{MAX\_INVESTSTORAGES,} \\
\forall t \in \textrm{TIMESTEPS}.
Minimal capacity :attr:`om.InvestmentStorage.min_capacity[n, t]`
.. math:: E(n, t) \geq invest(n) \cdot c_{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()` .
The symbols are the same as in:class:`.GenericStorageBlock`.
"""
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.INVESTSTORAGES_BALANCED = Set(initialize=[
n for n in group if n.balanced is True])
self.INVESTSTORAGES_NO_INIT_CAP = Set(initialize=[
n for n in group if n.initial_storage_level is None])
self.INVESTSTORAGES_INIT_CAP = 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 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.min_storage_level[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)
self.init_cap = Var(self.INVESTSTORAGES, within=NonNegativeReals)
def _inv_storage_init_cap_max_rule(block, n):
return block.init_cap[n] <= n.investment.existing + block.invest[n]
self.init_cap_limit = Constraint(self.INVESTSTORAGES_NO_INIT_CAP,
rule=_inv_storage_init_cap_max_rule)
def _inv_storage_init_cap_fix_rule(block, n):
return block.init_cap[n] == n.initial_storage_level * (
n.investment.existing + block.invest[n])
self.init_cap_fix = Constraint(self.INVESTSTORAGES_INIT_CAP,
rule=_inv_storage_init_cap_fix_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}
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 and
timestep t
"""
expr = 0
expr += block.capacity[n, 0]
expr += - block.init_cap[n] * (
1 - n.loss_rate[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)
# 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
timestep t
"""
expr = 0
expr += block.capacity[n, t]
expr += - block.capacity[n, t - 1] * (
1 - n.loss_rate[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.capacity[n, m.TIMESTEPS[-1]] == block.init_cap[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_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.max_storage_level[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.min_storage_level[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
[docs]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
[docs] def constraint_group(self):
return GenericCHPBlock
[docs]class GenericCHPBlock(SimpleBlock):
r"""
Block for the relation of the :math:`n` nodes with
type class:`.GenericCHP`.
**The following constraints are created:**
.. _GenericCHP-equations1-10:
.. 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)\\
where :math:`= / \leq` depends on the CHP being back pressure or not.
The coefficients :math:`\alpha_0` and :math:`\alpha_1`
can be determined given the efficiencies maximal/minimal load:
.. math::
&
\eta_{el,max,woDH}(t) = \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}(t) = \frac{P_{el,min,woDH}(t)}{\alpha_0(t)
\cdot Y(t) + \alpha_1(t) \cdot P_{el,min,woDH}(t)}\\
**For the attribute** :math:`\dot{H}_{L,FG,min}` **being not None**,
e.g. for a motoric CHP, **the following is created:**
**Constraint:**
.. _GenericCHP-equations11:
.. math::
&
(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]
The symbols used are defined as follows (with Variables (V) and Parameters (P)):
=============================== =============================== ==== =======================
math. symbol attribute type explanation
=============================== =============================== ==== =======================
:math:`\dot{H}_{F}` :py:obj:`H_F[n,t]` V input of enthalpy
through fuel input
:math:`P_{el}` :py:obj:`P[n,t]` V provided
electric power
:math:`P_{el,woDH}` :py:obj:`P_woDH[n,t]` V electric power without
district heating
:math:`P_{el,min,woDH}` :py:obj:`P_min_woDH[n,t]` P min. electric power
without district heating
:math:`P_{el,max,woDH}` :py:obj:`P_max_woDH[n,t]` P max. electric power
without district heating
:math:`\dot{Q}` :py:obj:`Q[n,t]` V provided heat
:math:`\dot{Q}_{CW, min}` :py:obj:`Q_CW_min[n,t]` P minimal therm. condenser
load to cooling water
:math:`\dot{H}_{L,FG,min}` :py:obj:`H_L_FG_min[n,t]` V flue gas enthalpy loss
at min heat extraction
:math:`\dot{H}_{L,FG,max}` :py:obj:`H_L_FG_max[n,t]` V flue gas enthalpy loss
at max heat extraction
:math:`\dot{H}_{L,FG,sharemin}` :py:obj:`H_L_FG_share_min[n,t]` P share of flue gas loss
at min heat extraction
:math:`\dot{H}_{L,FG,sharemax}` :py:obj:`H_L_FG_share_max[n,t]` P share of flue gas loss
at max heat extraction
:math:`Y` :py:obj:`Y[n,t]` V status variable
on/off
:math:`\alpha_0` :py:obj:`n.alphas[0][n,t]` P coefficient
describing efficiency
:math:`\alpha_1` :py:obj:`n.alphas[1][n,t]` P coefficient
describing efficiency
:math:`\beta` :py:obj:`Beta[n,t]` P power loss index
:math:`\eta_{el,min,woDH}` :py:obj:`Eta_el_min_woDH[n,t]` P el. eff. at min. fuel
flow w/o distr. heating
:math:`\eta_{el,max,woDH}` :py:obj:`Eta_el_max_woDH[n,t]` P el. eff. at max. fuel
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