WIP: sketch of 2 variants to add commodity flow of capacity variables

message_ix/model/MESSAGE/data_load.gms

@@ -27,7 +27,8 @@ duration_period, duration_time, interestrate,
 * resources parameters
 resource_volume, resource_cost, is_bound_extraction_up, bound_extraction_up, resource_remaining,
 * technology technical-engineering parameters and economic costs
-input, output, construction_time, technical_lifetime
+input, output, construction_time, technical_lifetime,
+input_cap, output_cap, input_cap_new, output_cap_new, input_cap_ret, output_cap_ret,
 capacity_factor, operation_factor, min_utilization_factor, inv_cost, fix_cost, var_cost,
 * upper and lower bounds on new capacity investment, total installed capacity and activity (including mapping sets)
 is_bound_new_capacity_up, is_bound_new_capacity_lo, bound_new_capacity_up, bound_new_capacity_lo,

message_ix/model/MESSAGE/model_core.gms

@@ -555,6 +555,18 @@ RESOURCE_HORIZON(node,commodity,grade)$( SUM(year$map_resource(node,commodity,gr
 *         \cdot duration\_time\_rel_{h,h^A} \cdot ACT_{n^L,t,y^V,y,m,h^A} & \\
 *     - \sum_{\substack{n^L,t,m,h^A \\ y^V \leq y}} input_{n^L,t,y^V,y,m,n,c,l,h^A,h}
 *         \cdot duration\_time\_rel_{h,h^A} \cdot ACT_{n^L,t,m,y,h^A} & \\
+*     + \sum_{\substack{n^L,t}} output\_cap\_new_{n^L,t,y,n,c,l,h}
+*         \cdot CAP\_NEW_{n^L,t,y} & \\
+*     - \sum_{\substack{n^L,t}} input\_cap\_new_{n^L,t,y,n,c,l,h}
+*         \cdot CAP\_NEW_{n^L,t,y} & \\
+*     + \sum_{\substack{n^L,t \\ y^V \leq y}} output\_cap\_ret_{n^L,t,y^V,n,c,l,h}
+*         \cdot ( CAP_{n^L,t,y^V,y-1} - CAP_{n^L,t,y^V,y} ) \cdot \frac{duration\_period_y}{duration\_period_CAP_y^V} & \\
+*     - \sum_{\substack{n^L,t \\ y^V \leq y}} input\_cap\_ret_{n^L,t,y^V,n,c,l,h}
+*         \cdot ( CAP_{n^L,t,y^V,y-1} - CAP_{n^L,t,y^V,y} ) \cdot \frac{duration\_period_y}{duration\_period_CAP_y^V} & \\
+*     + \sum_{\substack{n^L,t \\ y^V \leq y}} output\_cap_{n^L,t,y^V,y,n,c,l,h}
+*         \cdot CAP_{n^L,t,y^V,y} & \\
+*     - \sum_{\substack{n^L,t \\ y^V \leq y}} input\_cap_{n^L,t,y^V,y,n,c,l,h}
+*         \cdot CAP_{n^L,t,y^V,y} & \\
 *     + \ STOCK\_CHG_{n,c,l,y,h} + \ \sum_s \Big( land\_output_{n,s,y,c,l,h} - land\_input_{n,s,y,c,l,h} \Big) \cdot & LAND_{n,s,y} \\[4pt]
 *     - \ demand\_fixed_{n,c,l,y,h}
 *     = COMMODITY\_BALANCE_{n,c,l,y,h} \quad \forall \ l \notin (L^{RES}, & L^{REN}, L^{STOR} \subseteq L)
@@ -572,6 +584,47 @@ $macro COMMODITY_BALANCE(node,commodity,level,year,time) (
 * export from node and input into technologies located at 'location' taking from 'node' and 'time2' taking from 'time'
         - input(location,tec,vintage,year,mode,node,commodity,level,time2,time)                                        \
         * duration_time_rel(time,time2) * ACT(location,tec,vintage,year,mode,time2) )                                  \
+* +++++
+* commodity input and output associated with construction of new technology capacity (during vintage period)
+  + SUM( (location,tec)$( inv_tec(tec) AND map_tec(location,tec,year) ),                                               \
+* output by all new capacity of technologies located at 'location' sending to 'node' and 'time'
+        output_cap_new(location,tec,year,node,commodity,level,time)                                                    \
+        * CAP_NEW(location,tec,year)                                                                                   \
+* input by all new capacity of technologies located at 'location' taking from 'node' and 'time'
+        - input_cap_new(location,tec,year,node,commodity,level,time)                                                   \
+        * CAP_NEW(location,tec,year) )                                                                                 \
+* commodity input and output associated with retirement of technology capacity (via differentials of capacity of successive periods)
+* for first model period (differential with historical remaining capacity)
+  + SUM( (location,tec,vintage,year2)$( inv_tec(tec) AND map_tec_lifetime(location,tec,vintage,year2)                  \
+            AND first_period(year) AND seq_period(year2,year) ),                                                       \
+* output by all new capacity of technologies located at 'location' sending to 'node' and 'time' distributed over years of periods
+        output_cap_ret(location,tec,vintage,node,commodity,level,time)                                                 \
+        * ( remaining_capacity(node,tec,vintage,year2) - CAP(location,tec,vintage,year) )                              \
+        / duration_period(year)                                                                                        \
+* input by all new capacity of technologies located at 'location' taking from 'node' and 'time' distributed over years of periods
+        - input_cap_ret(location,tec,vintage,node,commodity,level,time)                                                \
+        * ( remaining_capacity(node,tec,vintage,year2) - CAP(location,tec,vintage,year) )                              \
+        / duration_period(year) )                                                                                      \
+* for other model periods (differential with installed capacity of preceding period)
+  + SUM( (location,tec,vintage,year2)$( inv_tec(tec) AND map_tec_lifetime(location,tec,vintage,year2)                  \
+            AND NOT first_period(year) AND seq_period(year2,year) ),                                                   \
+* output by all new capacity of technologies located at 'location' sending to 'node' and 'time' distributed over years of periods
+        output_cap_ret(location,tec,vintage,node,commodity,level,time)                                                 \
+        * ( CAP(location,tec,vintage,year2) - CAP(location,tec,vintage,year) )                                         \
+        / duration_period(year)                                                                                        \
+* input by all new capacity of technologies located at 'location' taking from 'node' and 'time' distributed over years of periods
+        - input_cap_ret(location,tec,vintage,node,commodity,level,time)                                                \
+        * ( CAP(location,tec,vintage,year2) - CAP(location,tec,vintage,year) )                                         \
+        / duration_period(year) )                                                                                      \
+* commodity input and output associated with operation of capacity at any period
+  + SUM( (location,tec,vintage)$( inv_tec(tec) AND map_tec_lifetime(location,tec,vintage,year) ),                      \
+* output by all new capacity of technologies located at 'location' sending to 'node', 'year' and 'time'
+        output_cap(location,tec,vintage,year,node,commodity,level,time)                                                \
+        * CAP(location,tec,vintage,year)                                                                               \
+* input by all new capacity of technologies located at 'location' taking from 'node', 'year' and 'time'
+        - input_cap(location,tec,vintage,year,node,commodity,level,time)                                               \
+        * CAP(location,tec,vintage,year) )                                                                             \
+* +++++
 * quantity taken out from ( >0 ) or put into ( <0 ) inter-period stock (storage)
     + STOCK_CHG(node,commodity,level,year,time)$( map_stocks(node,commodity,level,year) )                              \
 * yield from land-use model emulator

message_ix/model/MESSAGE/parameter_def.gms

@@ -180,6 +180,24 @@ Parameter
 *    * - output [#tecvintage]_
 *      - ``node_loc`` | ``tec`` | ``year_vtg`` | ``year_act`` | ``mode`` |
 *        ``node_dest`` | ``commodity`` | ``level`` | ``time`` | ``time_dest``
+*    * - input_cap [#tecvintage]_
+*      - ``node_loc`` | ``tec`` | ``year_vtg`` | ``year_act`` |
+*        ``node_origin`` | ``commodity`` | ``level`` | ``time_origin``
+*    * - output_cap [#tecvintage]_
+*      - ``node_loc`` | ``tec`` | ``year_vtg`` | ``year_act`` |
+*        ``node_dest`` | ``commodity`` | ``level`` | ``time_dest``
+*    * - input_cap_new [#tecvintage]_
+*      - ``node_loc`` | ``tec`` | ``year_vtg`` |
+*        ``node_origin`` | ``commodity`` | ``level`` | ``time_origin``
+*    * - output_cap_new [#tecvintage]_
+*      - ``node_loc`` | ``tec`` | ``year_vtg`` |
+*        ``node_dest`` | ``commodity`` | ``level`` | ``time_dest``
+*    * - input_cap_ret [#tecvintage]_
+*      - ``node_loc`` | ``tec`` | ``year_vtg`` |
+*        ``node_origin`` | ``commodity`` | ``level`` | ``time_origin``
+*    * - output_cap_ret [#tecvintage]_
+*      - ``node_loc`` | ``tec`` | ``year_vtg`` |
+*        ``node_dest`` | ``commodity`` | ``level`` | ``time_dest``
 *    * - inv_cost [#tecvintage]_
 *      - ``node_loc`` | ``tec`` | ``year_vtg``
 *    * - fix_cost [#tecvintage]_
@@ -235,6 +253,17 @@ Parameters
 * technology input-output mapping and costs parameters
     input(node,tec,vintage,year_all,mode,node,commodity,level,time,time)  relative share of input per unit of activity
     output(node,tec,vintage,year_all,mode,node,commodity,level,time,time) relative share of output per unit of activity
+* +++++
+* commodity input and output associated with construction of capacity
+    input_cap_new(node,tec,vintage,node,commodity,level,time)  relative share of input per unit of new capacity built
+    output_cap_new(node,tec,vintage,node,commodity,level,time) relative share of output per unit of new capacity built
+* commodity input and output associated with retirement of capacity
+    input_cap_ret(node,tec,vintage,node,commodity,level,time)  relative share of input per unit of capacity retired
+    output_cap_ret(node,tec,vintage,node,commodity,level,time) relative share of output per unit of capacity retired
+* commodity input and output associated with operation of capacity at any period
+    input_cap(node,tec,vintage,year_all,node,commodity,level,time)  relative share of input per unit of capacity
+    output_cap(node,tec,vintage,year_all,node,commodity,level,time) relative share of output per unit of capacity
+* +++++
     inv_cost(node,tec,year_all)                         investment costs (per unit of new capacity)
     fix_cost(node,tec,vintage,year_all)                 fixed costs per year (per unit of capacity maintained)
     var_cost(node,tec,vintage,year_all,mode,time)       variable costs of operation (per unit of capacity maintained)

message_ix/models.py

@@ -199,6 +199,9 @@ def item(ix_type, expr):
     "initial_new_capacity_lo": item("par", "nl t yv"),
     "initial_new_capacity_up": item("par", "nl t yv"),
     "input": item("par", "nl t yv ya m no c l h ho"),
+    "input_cap": item("par", "nl t yv ya no c l ho"),
+    "input_cap_new": item("par", "nl t yv no c l ho"),
+    "input_cap_ret": item("par", "nl t yv no c l ho"),
     "interestrate": dict(ix_type="par", idx_sets=["year"]),
     "inv_cost": item("par", "nl t yv"),
     "land_cost": item("par", "n land_scenario y"),
@@ -213,6 +216,9 @@ def item(ix_type, expr):
     "min_utilization_factor": item("par", "nl t yv ya"),
     "operation_factor": item("par", "nl t yv ya"),
     "output": item("par", "nl t yv ya m nd c l h hd"),
+    "output_cap": item("par", "nl t yv ya nd c l hd"),
+    "output_cap_new": item("par", "nl t yv nd c l hd"),
+    "output_cap_ret": item("par", "nl t yv nd c l hd"),
     "peak_load_factor": item("par", "n c l y h"),
     "rating_bin": item("par", "n t ya c l h r"),
     "ref_activity": item("par", "nl t ya m h"),