solph.flows._investment_flow_block.InvestmentFlowBlock._create_constraints()

Complexity

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32

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Total Lines	478
Code Lines	164

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Ratio	0 %

Importance

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0

# -*- coding: utf-8 -*-
    def _create_constraints(self):
        r"""Creates all constraints for standard flows.

        Depending on the attributes of the *InvestmentFlowBlock*
        and *SimpleFlowBlock*, different constraints are created.
        The following constraints are created
        for all *InvestmentFlowBlock* objects:\

            Total capacity / energy

            .. math::
                &
                if \quad p=0:\\
                &
                P_{total}(p) = P_{invest}(p) + P_{exist}(p) \\
                &\\
                &
                else:\\
                &
                P_{total}(p) = P_{total}(p-1) + P_{invest}(p) - P_{old}(p) \\
                &\\
                &
                \forall p \in \textrm{PERIODS}

            Upper bound for the flow value

            .. math::
                &
                P(p, t) \le ( P_{total}(p) ) \cdot f_{max}(t) \\
                &
                \forall p, t \in \textrm{TIMEINDEX}

        For a multi-period model, the old capacity is defined as follows:

            .. math::
                &
                P_{old}(p) = P_{old,exo}(p) + P_{old,end}(p)\\
                &\\
                &
                if \quad p=0:\\
                &
                P_{old,end}(p) = 0\\
                &\\
                &
                else \quad if \quad l \leq year(p):\\
                &
                P_{old,end}(p) = P_{invest}(p_{comm})\\
                &\\
                &
                else:\\
                &
                P_{old,end}(p) = 0\\
                &\\
                &
                if \quad p=0:\\
                &
                P_{old,exo}(p) = 0\\
                &\\
                &
                else \quad if \quad l - a \leq year(p):\\
                &
                P_{old,exo}(p) = P_{exist} (*)\\
                &\\
                &
                else:\\
                &
                P_{old,exo}(p) = 0\\
                &\\
                &
                \forall p \in \textrm{PERIODS}

            where:

            * (*) is only performed for the first period the condition
              is True. A decommissioning flag is then set to True
              to prevent having falsely added old capacity in future periods.
            * :math:`year(p)` is the year corresponding to period p
            * :math:`p_{comm}` is the commissioning period of the flow
              (which is determined by the model itself)

        Depending on the attribute :attr:`nonconvex`, the constraints for the
        bounds of the decision variable :math:`P_{invest}(p)` are different:\

            * :attr:`nonconvex = False`

            .. math::
                &
                P_{invest, min}(p) \le P_{invest}(p) \le P_{invest, max}(p) \\
                &
                \forall p \in \textrm{PERIODS}

            * :attr:`nonconvex = True`

            .. math::
                &
                P_{invest, min}(p) \cdot Y_{invest}(p) \le P_{invest}(p)\\
                &
                P_{invest}(p) \le P_{invest, max}(p) \cdot Y_{invest}(p)\\
                &\\
                &
                \forall p \in \textrm{PERIODS}

        For all *InvestmentFlowBlock* objects
        (independent of the attribute :attr:`nonconvex`),
        the following additional constraints are created, if the appropriate
        attribute of the *SimpleFlowBlock*
        (see :class:`oemof.solph.flows._simple_flow_block.SimpleFlowBlock`)
        is set:

            * :attr:`fix` is not None

                Actual value constraint for investments with fixed flow values

            .. math::
                &
                P(p, t) = P_{total}(p) \cdot f_{fix}(t) \\
                &\\
                &
                \forall p, t \in \textrm{TIMEINDEX}

            * :attr:`min != 0`

                Lower bound for the flow values

            .. math::
                &
                P(p, t) \geq P_{total}(p) \cdot f_{min}(t) \\
                &\\
                &
                \forall p, t \in \textrm{TIMEINDEX}

            * :attr:`full_load_time_max is not None`

                Upper bound for the sum of all flow values
                (e.g. maximum full load hours)

            .. math::
                \sum_{p, t} P(p, t) \cdot \tau(t) \leq P_{total}(p)
                \cdot t_{full\_load, min}

            * :attr:`full_load_time_min is not None`

                Lower bound for the sum of all flow values
                (e.g. minimum full load hours)

            .. math::
                \sum_{p, t} P(t) \cdot \tau(t) \geq P_{total}
                \cdot t_{full\_load, min}

            * :attr:`overall_maximum` is not None
              (for multi-period model only)

                Overall maximum of total installed capacity / energy for flow

            .. math::
                &
                P_{total}(p) \leq P_{overall,max} \\
                &\\
                &
                \forall p \in \textrm{PERIODS}

            * :attr:`overall_minimum` is not None
              (for multi-period model only)

                Overall minimum of total installed capacity / energy for flow;
                applicable only in last period

            .. math::
                P_{total}(p_{last}) \geq P_{overall,min}
        """
        m = self.parent_block()

        self.minimum_rule = self._minimum_investment_constraint()
        self.maximum_rule = self._maximum_investment_constraint()

        # Handle unit lifetimes
        def _total_capacity_rule(block):
            """Rule definition for determining total installed
            capacity (taking decommissioning into account)
            """
            for i, o in self.INVESTFLOWS:
                for p in m.PERIODS:
                    if p == 0:
                        expr = (
                            self.total[i, o, p]
                            == self.invest[i, o, p]
                            + m.flows[i, o].investment.existing
                        )
                        self.total_rule.add((i, o, p), expr)
                    # applicable for multi-period model only
                    else:
                        expr = (
                            self.total[i, o, p]
                            == self.invest[i, o, p]
                            + self.total[i, o, p - 1]
                            - self.old[i, o, p]
                        )
                        self.total_rule.add((i, o, p), expr)

        self.total_rule = Constraint(
            self.INVESTFLOWS, m.PERIODS, noruleinit=True
        )
        self.total_rule_build = BuildAction(rule=_total_capacity_rule)

        if m.es.periods is not None:

            def _old_capacity_rule_end(block):
                """Rule definition for determining old endogenously installed
                capacity to be decommissioned due to reaching its lifetime.
                Investment and decommissioning periods are linked within
                the constraint. The respective decommissioning period is
                determined for every investment period based on the components
                lifetime and a matrix describing its age of each endogenous
                investment. Decommissioning can only occur at the beginning of
                each period.

                Note
                ----
                For further information on the implementation check
                PR#957 https://github.com/oemof/oemof-solph/pull/957
                """
                for i, o in self.INVESTFLOWS:
                    lifetime = m.flows[i, o].investment.lifetime
                    if lifetime is None:
                        msg = (
                            "You have to specify a lifetime "
                            "for a Flow with an associated "
                            "investment object in "
                            f"a multi-period model! Value for {(i, o)} "
                            "is missing."
                        )
                        raise ValueError(msg)

                    # get the period matrix describing the temporal distance
                    # between all period combinations.
                    periods_matrix = m.es.periods_matrix

                    # get the index of the minimum value in each row greater
                    # equal than the lifetime. This value equals the
                    # decommissioning period if not zero. The index of this
                    # value represents the investment period. If np.where
                    # condition is not met in any row, min value will be zero
                    decomm_periods = np.argmin(
                        np.where(
                            (periods_matrix >= lifetime),
                            periods_matrix,
                            np.inf,
                        ),
                        axis=1,
                    )

                    # no decommissioning in first period
                    expr = self.old_end[i, o, 0] == 0
                    self.old_rule_end.add((i, o, 0), expr)

                    # all periods not in decomm_periods have no decommissioning
                    # zero is excluded
                    for p in m.PERIODS:
                        if p not in decomm_periods and p != 0:
                            expr = self.old_end[i, o, p] == 0
                            self.old_rule_end.add((i, o, p), expr)

                    # multiple invests can be decommissioned in the same period
                    # but only sequential ones, thus a bookkeeping is
                    # introduced and constraints are added to equation one
                    # iteration later.
                    last_decomm_p = np.nan
                    # loop over invest periods (values are decomm_periods)
                    for invest_p, decomm_p in enumerate(decomm_periods):
                        # Add constraint of iteration before
                        # (skipped in first iteration by last_decomm_p = nan)
                        if (decomm_p != last_decomm_p) and (
                            last_decomm_p is not np.nan
                        ):
                            expr = self.old_end[i, o, last_decomm_p] == expr
                            self.old_rule_end.add((i, o, last_decomm_p), expr)

                        # no decommissioning if decomm_p is zero
                        if decomm_p == 0:
                            # overwrite decomm_p with zero to avoid
                            # chaining invest periods in next iteration
                            last_decomm_p = 0

                        # if decomm_p is the same as the last one chain invest
                        # period
                        elif decomm_p == last_decomm_p:
                            expr += self.invest[i, o, invest_p]
                            # overwrite decomm_p
                            last_decomm_p = decomm_p

                        # if decomm_p is not zero, not the same as the last one
                        # and it's not the first period
                        else:
                            expr = self.invest[i, o, invest_p]
                            # overwrite decomm_p
                            last_decomm_p = decomm_p

                    # Add constraint of very last iteration
                    if last_decomm_p != 0:
                        expr = self.old_end[i, o, last_decomm_p] == expr
                        self.old_rule_end.add((i, o, last_decomm_p), expr)

            self.old_rule_end = Constraint(
                self.INVESTFLOWS, m.PERIODS, noruleinit=True
            )
            self.old_rule_end_build = BuildAction(rule=_old_capacity_rule_end)

            def _old_capacity_rule_exo(block):
                """Rule definition for determining old exogenously given
                capacity to be decommissioned due to reaching its lifetime
                """
                for i, o in self.INVESTFLOWS:
                    age = m.flows[i, o].investment.age
                    lifetime = m.flows[i, o].investment.lifetime
                    is_decommissioned = False
                    for p in m.PERIODS:
                        # No shutdown in first period
                        if p == 0:
                            expr = self.old_exo[i, o, p] == 0
                            self.old_rule_exo.add((i, o, p), expr)
                        elif lifetime - age <= m.es.periods_years[p]:
                            # Track decommissioning status
                            if not is_decommissioned:
                                expr = (
                                    self.old_exo[i, o, p]
                                    == m.flows[i, o].investment.existing
                                )
                                is_decommissioned = True
                            else:
                                expr = self.old_exo[i, o, p] == 0
                            self.old_rule_exo.add((i, o, p), expr)
                        else:
                            expr = self.old_exo[i, o, p] == 0
                            self.old_rule_exo.add((i, o, p), expr)

            self.old_rule_exo = Constraint(
                self.INVESTFLOWS, m.PERIODS, noruleinit=True
            )
            self.old_rule_exo_build = BuildAction(rule=_old_capacity_rule_exo)

            def _old_capacity_rule(block):
                """Rule definition for determining (overall) old capacity
                to be decommissioned due to reaching its lifetime
                """
                for i, o in self.INVESTFLOWS:
                    for p in m.PERIODS:
                        expr = (
                            self.old[i, o, p]
                            == self.old_end[i, o, p] + self.old_exo[i, o, p]
                        )
                        self.old_rule.add((i, o, p), expr)

            self.old_rule = Constraint(
                self.INVESTFLOWS, m.PERIODS, noruleinit=True
            )
            self.old_rule_build = BuildAction(rule=_old_capacity_rule)

        def _investflow_fixed_rule(block):
            """Rule definition of constraint to fix flow variable
            of investment flow to (normed) actual value
            """
            for i, o in self.FIXED_INVESTFLOWS:
                for p, t in m.TIMEINDEX:
                    expr = (
                        m.flow[i, o, t]
                        == self.total[i, o, p] * m.flows[i, o].fix[t]
                    )
                    self.fixed.add((i, o, p, t), expr)

        self.fixed = Constraint(
            self.FIXED_INVESTFLOWS, m.TIMEINDEX, noruleinit=True
        )
        self.fixed_build = BuildAction(rule=_investflow_fixed_rule)

        def _max_investflow_rule(block):
            """Rule definition of constraint setting an upper bound of flow
            variable in investment case.
            """
            for i, o in self.NON_FIXED_INVESTFLOWS:
                for p, t in m.TIMEINDEX:
                    expr = (
                        m.flow[i, o, t]
                        <= self.total[i, o, p] * m.flows[i, o].max[t]
                    )
                    self.max.add((i, o, p, t), expr)

        self.max = Constraint(
            self.NON_FIXED_INVESTFLOWS, m.TIMEINDEX, noruleinit=True
        )
        self.max_build = BuildAction(rule=_max_investflow_rule)

        def _min_investflow_rule(block):
            """Rule definition of constraint setting a lower bound on flow
            variable in investment case.
            """
            for i, o in self.MIN_INVESTFLOWS:
                for p, t in m.TIMEINDEX:
                    expr = (
                        m.flow[i, o, t]
                        >= self.total[i, o, p] * m.flows[i, o].min[t]
                    )
                    self.min.add((i, o, p, t), expr)

        self.min = Constraint(
            self.MIN_INVESTFLOWS, m.TIMEINDEX, noruleinit=True
        )
        self.min_build = BuildAction(rule=_min_investflow_rule)

        def _full_load_time_max_investflow_rule(_, i, o):
            """Rule definition for build action of max. sum flow constraint
            in investment case.
            """
            expr = sum(
                m.flow[i, o, t] * m.timeincrement[t] for t in m.TIMESTEPS
            ) <= (
                m.flows[i, o].full_load_time_max
                * sum(self.total[i, o, p] for p in m.PERIODS)
            )
            return expr

        self.full_load_time_max = Constraint(
            self.FULL_LOAD_TIME_MAX_INVESTFLOWS,
            rule=_full_load_time_max_investflow_rule,
        )

        def _full_load_time_min_investflow_rule(_, i, o):
            """Rule definition for build action of min. sum flow constraint
            in investment case.
            """
            expr = sum(
                m.flow[i, o, t] * m.timeincrement[t] for t in m.TIMESTEPS
            ) >= (
                sum(self.total[i, o, p] for p in m.PERIODS)
                * m.flows[i, o].full_load_time_min
            )
            return expr

        self.full_load_time_min = Constraint(
            self.FULL_LOAD_TIME_MIN_INVESTFLOWS,
            rule=_full_load_time_min_investflow_rule,
        )

        if m.es.periods is not None:

            def _overall_maximum_investflow_rule(block):
                """Rule definition for maximum overall investment
                in investment case.
                """
                for i, o in self.OVERALL_MAXIMUM_INVESTFLOWS:
                    for p in m.PERIODS:
                        expr = (
                            self.total[i, o, p]
                            <= m.flows[i, o].investment.overall_maximum
                        )
                        self.overall_maximum.add((i, o, p), expr)

            self.overall_maximum = Constraint(
                self.OVERALL_MAXIMUM_INVESTFLOWS, m.PERIODS, noruleinit=True
            )
            self.overall_maximum_build = BuildAction(
                rule=_overall_maximum_investflow_rule
            )

            def _overall_minimum_investflow_rule(block, i, o):
                """Rule definition for minimum overall investment
                in investment case.

                Note: This is only applicable for the last period
                """
                expr = (
                    m.flows[i, o].investment.overall_minimum
                    <= self.total[i, o, m.PERIODS[-1]]
                )
                return expr

            self.overall_minimum = Constraint(
                self.OVERALL_MINIMUM_INVESTFLOWS,
                rule=_overall_minimum_investflow_rule,
            )