# -*- coding: utf-8 -*-
"""Creating sets, variables, constraints and parts of the objective function
for Flow objects with both Nonconvex and Investment options.
SPDX-FileCopyrightText: Uwe Krien <krien@uni-bremen.de>
SPDX-FileCopyrightText: Simon Hilpert
SPDX-FileCopyrightText: Cord Kaldemeyer
SPDX-FileCopyrightText: Patrik Schönfeldt
SPDX-FileCopyrightText: Birgit Schachler
SPDX-FileCopyrightText: jnnr
SPDX-FileCopyrightText: jmloenneberga
SPDX-FileCopyrightText: Johannes Kochems (jokochems)
SPDX-FileCopyrightText: Saeed Sayadi
SPDX-FileCopyrightText: Pierre-François Duc
SPDX-License-Identifier: MIT
"""
from pyomo.core import Binary
from pyomo.core import BuildAction
from pyomo.core import Constraint
from pyomo.core import Expression
from pyomo.core import NonNegativeReals
from pyomo.core import Set
from pyomo.core import Var
from ._non_convex_flow_block import NonConvexFlowBlock
[docs]class InvestNonConvexFlowBlock(NonConvexFlowBlock):
r"""
.. automethod:: _create_constraints
.. automethod:: _create_variables
.. automethod:: _create_sets
.. automethod:: _objective_expression
"""
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
def _create(self, group=None):
"""Creates set, variables, constraints for all flow object with
an attribute flow of type class:`.InvestNonConvexFlowBlock`.
Parameters
----------
group : list
List of oemof.solph.InvestNonConvexFlowBlock objects for which
the constraints are build.
"""
if group is None:
return None
self._create_sets(group)
self._create_variables()
self._create_constraints()
[docs] def _create_sets(self, group):
"""
Creates all sets for investment non-convex flows.
INVEST_NON_CONVEX_FLOWS
A set of flows with the attribute `nonconvex` of type
:class:`.options.NonConvex` and the attribute `invest`
of type :class:`.options.Invest`.
.. automethod:: _sets_for_non_convex_flows
"""
self.INVEST_NON_CONVEX_FLOWS = Set(
initialize=[(g[0], g[1]) for g in group]
)
self._sets_for_non_convex_flows(group)
[docs] def _create_variables(self):
r"""
Status variable (binary) `om.InvestNonConvexFlowBlock.status`:
Variable indicating if flow is >= 0 indexed by FLOWS
:math::`P_{invest}` `InvestNonConvexFlowBlock.invest`
Value of the investment variable, i.e. equivalent to the nominal
value of the flows after optimization.
:math::`status\_nominal(i,o,t)` (non-negative real number)
New paramater representing the multiplication of `P_{invest}`
(from the <class 'oemof.solph.flows.InvestmentFlow'>) and
`status(i,o,t)` (from the
<class 'oemof.solph.flows.NonConvexFlow'>)
used for the constraints on the minimum and maximum
flow constraints.
.. automethod:: _variables_for_non_convex_flows
"""
m = self.parent_block()
# Create `status` variable representing the status of the flow
# at each time step
self.status = Var(
self.INVEST_NON_CONVEX_FLOWS, m.TIMESTEPS, within=Binary
)
self._variables_for_non_convex_flows()
# Investment-related variable similar to the
# <class 'oemof.solph.flows.InvestmentFlow'> class.
def _investvar_bound_rule(block, i, o, p):
"""Rule definition for bounds of the invest variable."""
if (i, o) in self.INVEST_NON_CONVEX_FLOWS:
return 0, m.flows[i, o].investment.maximum[p]
# Create the `invest` variable for the nonconvex investment flow.
self.invest = Var(
self.INVEST_NON_CONVEX_FLOWS,
m.PERIODS,
within=NonNegativeReals,
bounds=_investvar_bound_rule,
)
# `status_nominal` is a parameter which represents the
# multiplication of a binary variable (`status`)
# and a continuous variable (`invest` or `nominal_value`)
self.status_nominal = Var(
self.INVEST_NON_CONVEX_FLOWS, m.TIMESTEPS, within=NonNegativeReals
)
[docs] def _create_constraints(self):
r"""
.. automethod:: _shared_constraints_for_non_convex_flows
.. automethod:: _minimum_invest_constraint
.. automethod:: _maximum_invest_constraint
.. automethod:: _minimum_flow_constraint
.. automethod:: _maximum_flow_constraint
.. automethod:: _linearised_investment_constraints
"""
self._shared_constraints_for_non_convex_flows()
self.minimum_investment = self._minimum_invest_constraint()
self.maximum_investment = self._maximum_invest_constraint()
self.min = self._minimum_flow_constraint()
self.max = self._maximum_flow_constraint()
self._linearised_investment_constraints()
[docs] def _linearised_investment_constraints(self):
r"""
The resulting constraint is equivalent to
.. math::
status\_nominal(i,o,t) = Y_{status}(t) \cdot P_{invest}.
However, :math:`status` and :math:`invest` are variables
(binary and continuous, respectively).
Thus, three constraints are created which combination is equivalent.
.. automethod:: _linearised_investment_constraint_1
.. automethod:: _linearised_investment_constraint_2
.. automethod:: _linearised_investment_constraint_3
The following cases may occur:
* Case :math:`status = 0`
.. math::
(1) \Rightarrow status\_nominal = 0,\\
(2) \Rightarrow \text{ trivially fulfilled},\\
(3) \Rightarrow \text{ trivially fulfilled}.
* Case :math:`status = 1`
.. math::
(1) \Rightarrow \text{ trivially fulfilled},\\
(2) \Rightarrow status\_nominal \leq P_{invest},\\
(3) \Rightarrow status\_nominal \geq P_{invest}.
So, in total :math:`status\_nominal = P_{invest}`,
which is the desired result.
"""
self.invest_nc_one = self._linearised_investment_constraint_1()
self.invest_nc_two = self._linearised_investment_constraint_2()
self.invest_nc_three = self._linearised_investment_constraint_3()
[docs] def _linearised_investment_constraint_1(self):
r"""
.. math::
status\_nominal(i,o,t)
\leq Y_{status}(t) \cdot P_{invest, max}\quad (1)
"""
m = self.parent_block()
def _linearization_rule_invest_non_convex_one(_, i, o, p, t):
expr = (
self.status[i, o, t] * m.flows[i, o].investment.maximum[p]
>= self.status_nominal[i, o, t]
)
return expr
return Constraint(
self.MIN_FLOWS,
m.TIMEINDEX,
rule=_linearization_rule_invest_non_convex_one,
)
[docs] def _linearised_investment_constraint_2(self):
r"""
.. math::
status\_nominal(i,o,t) \leq P_{invest}\quad (2)
"""
m = self.parent_block()
def _linearization_rule_invest_non_convex_two(_, i, o, p, t):
expr = self.invest[i, o, p] >= self.status_nominal[i, o, t]
return expr
return Constraint(
self.MIN_FLOWS,
m.TIMEINDEX,
rule=_linearization_rule_invest_non_convex_two,
)
[docs] def _linearised_investment_constraint_3(self):
r"""
.. math::
status\_nominal(i,o,t) \geq
P_{invest} - (1 - Y_{status}(t)) \cdot P_{invest, max}\quad (3)
"""
m = self.parent_block()
def _linearization_rule_invest_non_convex_three(_, i, o, p, t):
expr = (
self.invest[i, o, p]
- (1 - self.status[i, o, t])
* m.flows[i, o].investment.maximum[p]
<= self.status_nominal[i, o, t]
)
return expr
return Constraint(
self.MIN_FLOWS,
m.TIMEINDEX,
rule=_linearization_rule_invest_non_convex_three,
)
[docs] def _objective_expression(self):
r"""Objective expression for nonconvex investment flows.
If `nonconvex.startup_costs` is set by the user:
.. math::
\sum_{i, o \in STARTUPFLOWS} \sum_t startup(i, o, t) \
\cdot c_{startup}
If `nonconvex.shutdown_costs` is set by the user:
.. math::
\sum_{i, o \in SHUTDOWNFLOWS} \sum_t shutdown(i, o, t) \
\cdot c_{shutdown}
.. math::
P_{invest} \cdot c_{invest,var}
"""
if not hasattr(self, "INVEST_NON_CONVEX_FLOWS"):
return 0
m = self.parent_block()
startup_costs = self._startup_costs()
shutdown_costs = self._shutdown_costs()
activity_costs = self._activity_costs()
inactivity_costs = self._inactivity_costs()
investment_costs = 0
for i, o in self.INVEST_NON_CONVEX_FLOWS:
for p in m.PERIODS:
investment_costs += (
self.invest[i, o, p] * m.flows[i, o].investment.ep_costs[p]
+ m.flows[i, o].investment.offset[p]
)
self.investment_costs = Expression(expr=investment_costs)
return (
startup_costs
+ shutdown_costs
+ activity_costs
+ inactivity_costs
+ investment_costs
)
[docs] def _minimum_invest_constraint(self):
r"""
.. math::
P_{invest, min} \le P_{invest}
"""
m = self.parent_block()
def _min_invest_rule(_):
"""Rule definition for applying a minimum investment"""
for i, o in self.INVEST_NON_CONVEX_FLOWS:
for p in m.PERIODS:
expr = (
m.flows[i, o].investment.minimum[p]
<= self.invest[i, o, p]
)
self.minimum_investment.add((i, o, p), expr)
self.minimum_investment = Constraint(
self.INVEST_NON_CONVEX_FLOWS, m.PERIODS, noruleinit=True
)
self.minimum_rule_build = BuildAction(rule=_min_invest_rule)
return self.minimum_investment
[docs] def _maximum_invest_constraint(self):
r"""
.. math::
P_{invest} \le P_{invest, max}
"""
m = self.parent_block()
def _max_invest_rule(_):
"""Rule definition for applying a minimum investment"""
for i, o in self.INVEST_NON_CONVEX_FLOWS:
for p in m.PERIODS:
expr = (
self.invest[i, o, p]
<= m.flows[i, o].investment.maximum[p]
)
self.maximum_investment.add((i, o, p), expr)
self.maximum_investment = Constraint(
self.INVEST_NON_CONVEX_FLOWS, m.PERIODS, noruleinit=True
)
self.maximum_rule_build = BuildAction(rule=_max_invest_rule)
return self.maximum_investment
