Merge pull request #997 from oemof/feature/remaining-value

Compare differences in remaining value vs. actual value

docs/usage.rst

@@ -1270,6 +1270,11 @@ Besides the `invest` variable, new variables are introduced as well. These are:
       has not yet been tested.
     * For now, both, the `timeindex` as well as the `timeincrement` of an energy system have to be defined since they
       have to be of the same length for a multi-period model.
+    * You can choose whether or not to re-evaluate assets at the end of the optimization horizon. If you set attribute
+      `use_remaining_value` of the energy system to True (defaults to False), this leads to the model evaluating the
+      different in value at the end of the optimization horizon vs. at the time the investment was made. The difference
+      in value is added to or subtracted from the respective investment costs increment, assuming assets are to be
+      liquidated / re-evaluated at the end of the optimization horizon.
     * Also please be aware, that periods correspond to years by default. You could also choose
       monthly periods, but you would need to be very careful in parameterizing your energy system and your model and also,
       this would mean monthly discounting (if applicable) as well as specifying your plants lifetimes in months.

docs/whatsnew/v0-5-2.rst

@@ -4,9 +4,14 @@ v0.5.2 (????)
 API changes
 ###########
 
+* New bool attribute `use_remaining_value` of `oemof.solph.EnergySystem`
+
 New features
 ############
 
+* Allow for evaluating differences in the remaining vs. the original value
+  for multi-period investments.
+
 Documentation
 #############
 

src/oemof/solph/_energy_system.py

@@ -62,6 +62,10 @@ class EnergySystem(es.EnergySystem):
         For a standard model, periods are not (to be) declared, i.e. None.
         A list with one entry is derived, i.e. [0].
 
+    use_remaining_value : bool
+        If True, compare the remaining value of an investment to the
+        original value (only applicable for multi-period models)
+
     kwargs
     """
 
@@ -71,6 +75,7 @@ def __init__(
         timeincrement=None,
         infer_last_interval=None,
         periods=None,
+        use_remaining_value=False,
         **kwargs,
     ):
         # Doing imports at runtime is generally frowned upon, but should work
@@ -160,7 +165,8 @@ def __init__(
             timeindex=timeindex, timeincrement=timeincrement, **kwargs
         )
 
-        if periods is not None:
+        self.periods = periods
+        if self.periods is not None:
             msg = (
                 "CAUTION! You specified the 'periods' attribute for your "
                 "energy system.\n This will lead to creating "
@@ -171,11 +177,10 @@ def __init__(
                 "please report them."
             )
             warnings.warn(msg, debugging.SuspiciousUsageWarning)
-        self.periods = periods
-        if self.periods is not None:
             self._extract_periods_years()
             self._extract_periods_matrix()
             self._extract_end_year_of_optimization()
+            self.use_remaining_value = use_remaining_value
 
     def _extract_periods_years(self):
         """Map years in optimization to respective period based on time indices

src/oemof/solph/components/_generic_storage.py

@@ -902,6 +902,21 @@ class GenericInvestmentStorageBlock(ScalarBlock):
                 &
                 \forall p \in \textrm{PERIODS}
 
+        In case, the remaining lifetime of a storage is greater than 0 and
+        attribute `use_remaining_value` of the energy system is True,
+        the difference in value for the investment period compared to the
+        last period of the optimization horizon is accounted for
+        as an adder to the investment costs:
+
+            .. math::
+                &
+                E_{invest}(p) \cdot (A(c_{invest,var}(p), l_{r}, ir) -
+                A(c_{invest,var}(|P|), l_{r}, ir)\\
+                & \cdot \frac {1}{ANF(l_{r}, ir)} \cdot DF^{-|P|}\\
+                &\\
+                &
+                \forall p \in \textrm{PERIODS}
+
         * :attr:`nonconvex = True`
 
             .. math::
@@ -913,6 +928,24 @@ class GenericInvestmentStorageBlock(ScalarBlock):
                 &
                 \forall p \in \textrm{PERIODS}
 
+        In case, the remaining lifetime of a storage is greater than 0 and
+        attribute `use_remaining_value` of the energy system is True,
+        the difference in value for the investment period compared to the
+        last period of the optimization horizon is accounted for
+        as an adder to the investment costs:
+
+            .. math::
+                &
+                (E_{invest}(p) \cdot (A(c_{invest,var}(p), l_{r}, ir) -
+                A(c_{invest,var}(|P|), l_{r}, ir)\\
+                & \cdot \frac {1}{ANF(l_{r}, ir)} \cdot DF^{-|P|}\\
+                &
+                +  (c_{invest,fix}(p) - c_{invest,fix}(|P|))
+                \cdot b_{invest}(p)) \cdot DF^{-p}\\
+                &\\
+                &
+                \forall p \in \textrm{PERIODS}
+
         * :attr:`fixed_costs` not None for investments
 
             .. math::
@@ -929,12 +962,14 @@ class GenericInvestmentStorageBlock(ScalarBlock):
                 \sum_{pp=0}^{limit_{exo}} E_{exist} \cdot c_{fixed}(pp)
                 \cdot DF^{-pp}
 
-
     whereby:
 
     * :math:`A(c_{invest,var}(p), l, ir)` A is the annuity for
       investment expenses :math:`c_{invest,var}(p)`, lifetime :math:`l`
       and interest rate :math:`ir`.
+    * :math:`l_{r}` is the remaining lifetime at the end of the
+      optimization horizon (in case it is greater than 0 and
+      smaller than the actual lifetime).
     * :math:`ANF(d, ir)` is the annuity factor for duration :math:`d`
       and interest rate :math:`ir`.
     * :math:`d=min\{year_{max} - year(p), l\}` defines the
@@ -1765,7 +1800,19 @@ def _objective_expression(self):
                     investment_costs_increment = (
                         self.invest[n, p] * annuity * present_value_factor
                     ) * (1 + m.discount_rate) ** (-m.es.periods_years[p])
-                    investment_costs += investment_costs_increment
+                    remaining_value_difference = (
+                        self._evaluate_remaining_value_difference(
+                            m,
+                            p,
+                            n,
+                            m.es.end_year_of_optimization,
+                            lifetime,
+                            interest,
+                        )
+                    )
+                    investment_costs += (
+                        investment_costs_increment + remaining_value_difference
+                    )
                     period_investment_costs[p] += investment_costs_increment
 
             for n in self.NON_CONVEX_INVESTSTORAGES:
@@ -1794,7 +1841,20 @@ def _objective_expression(self):
                         self.invest[n, p] * annuity * present_value_factor
                         + self.invest_status[n, p] * n.investment.offset[p]
                     ) * (1 + m.discount_rate) ** (-m.es.periods_years[p])
-                    investment_costs += investment_costs_increment
+                    remaining_value_difference = (
+                        self._evaluate_remaining_value_difference(
+                            m,
+                            p,
+                            n,
+                            m.es.end_year_of_optimization,
+                            lifetime,
+                            interest,
+                            nonconvex=True,
+                        )
+                    )
+                    investment_costs += (
+                        investment_costs_increment + remaining_value_difference
+                    )
                     period_investment_costs[p] += investment_costs_increment
 
             for n in self.INVESTSTORAGES:
@@ -1835,3 +1895,79 @@ def _objective_expression(self):
         self.costs = Expression(expr=investment_costs + fixed_costs)
 
         return self.costs
+
+    def _evaluate_remaining_value_difference(
+        self,
+        m,
+        p,
+        n,
+        end_year_of_optimization,
+        lifetime,
+        interest,
+        nonconvex=False,
+    ):
+        """Evaluate and return the remaining value difference of an investment
+
+        The remaining value difference in the net present values if the asset
+        was to be liquidated at the end of the optimization horizon and the
+        net present value using the original investment expenses.
+
+        Parameters
+        ----------
+        m : oemof.solph.models.Model
+            Optimization model
+
+        p : int
+            Period in which investment occurs
+
+        n : oemof.solph.components.GenericStorage
+            storage unit
+
+        end_year_of_optimization : int
+            Last year of the optimization horizon
+
+        lifetime : int
+            lifetime of investment considered
+
+        interest : float
+            Demanded interest rate for investment
+
+        nonconvex : bool
+            Indicating whether considered flow is nonconvex.
+        """
+        if m.es.use_remaining_value:
+            if end_year_of_optimization - m.es.periods_years[p] < lifetime:
+                remaining_lifetime = lifetime - (
+                    end_year_of_optimization - m.es.periods_years[p]
+                )
+                remaining_annuity = economics.annuity(
+                    capex=n.investment.ep_costs[-1],
+                    n=remaining_lifetime,
+                    wacc=interest,
+                )
+                original_annuity = economics.annuity(
+                    capex=n.investment.ep_costs[p],
+                    n=remaining_lifetime,
+                    wacc=interest,
+                )
+                present_value_factor_remaining = 1 / economics.annuity(
+                    capex=1, n=remaining_lifetime, wacc=interest
+                )
+                if nonconvex:
+                    return (
+                        self.invest[n, p]
+                        * (remaining_annuity - original_annuity)
+                        * present_value_factor_remaining
+                        + self.invest_status[n, p]
+                        * (n.investment.offset[-1] - n.investment.offset[p])
+                    ) * (1 + m.discount_rate) ** (-end_year_of_optimization)
+                else:
+                    return (
+                        self.invest[n, p]
+                        * (remaining_annuity - original_annuity)
+                        * present_value_factor_remaining
+                    ) * (1 + m.discount_rate) ** (-end_year_of_optimization)
+            else:
+                return 0
+        else:
+            return 0