relation_storage added as an option (relation_equality removed)

message_ix/core.py

@@ -34,6 +34,14 @@ def init_storage(scen, *args, **kwargs):
     # Initiating a parameter to specify the order of sub-annual time steps
     scen.init_par('time_seq', idx_sets=['time'])
 
+    # Initiating a parameter for relating the content f storage in two
+    # different time steps (in even in two periods) together
+    scen.init_par('relation_storage',
+                  idx_sets=['node', 'technology', 'level', 'year', 'year',
+                            'time', 'time'],
+                  idx_names=['node', 'technology', 'level', 'year_first',
+                             'year_last', 'time_first', 'time_last'])
+
     # Initiating two parameters for specifying lower and upper bounds of
     # storage reservoir, and storage losses all as % of installed capacity
     # (values should be between 0 and 1)

message_ix/model/MESSAGE/data_load.gms

@@ -18,7 +18,7 @@ $LOAD inv_tec, renewable_tec
 $LOAD shares
 $LOAD addon, type_addon, cat_addon, map_tec_addon
 * Added for storage
-$LOAD storage_tec, level_storage, map_tec_storage
+$LOAD storage_tec, level_storage, map_tec_storage, relation_storage
 $GDXIN
 
 Execute_load '%in%'

message_ix/model/MESSAGE/model_core.gms

@@ -309,7 +309,7 @@ Equations
 * Added for storage
     STORAGE_CHANGE                  change in the content of storage
     STORAGE_BALANCE                 storage commodity (content) balance
-    STORAGE_EQUALITY                equality in the content of storage in two different time steps (like first and last timesteps)
+    STORAGE_REL                     relation between the content of storage in two different time steps (time_first * value = time_last)
     STORAGE_BOUND_LO                lower bound of the content of storage
     STORAGE_BOUND_UP                upper bound of the content of storage
 ;
@@ -1992,15 +1992,14 @@ STORAGE_BALANCE(node,storage_tec,level,year,time2)$ ( storage_loss(node,storage_
     (1 - storage_loss(node,storage_tec,level,year,time) ) ) ;
 
 ***
-* Equation STORAGE_EQUALITY
+* Equation STORAGE_RELATION
 * """""""""""""""""""""""""""""""
 *   .. math::
 *      STORAGE_{n,t,l,y,h} \eq ... (math notation to be added)
 ***
 * We can add a test to check if the storage bounds defined by the user in first and last time period doesn't violate this equation
-STORAGE_EQUALITY(node,storage_tec,level_storage,year,time)$(SUM(commodity, storage_loss(node,storage_tec,commodity,level_storage,year,time) ) AND
-    SUM((time2,year2), map_time_first_last(year,year2,time,time2) ) )..
-       STORAGE(node,storage_tec,level_storage,year,time) =E= SUM( (time2,year2)$map_time_first_last(year,year2,time,time2), STORAGE(node,storage_tec,level_storage,year,time2) );
+STORAGE_REL(node,storage_tec,level_storage,year,year2,time,time2)$(relation_storage(node,storage_tec,level_storage,year,year2,time,time2) )..
+       STORAGE(node,storage_tec,level_storage,year,time) =L= relation_storage(node,storage_tec,level_storage,year,year2,time,time2) * STORAGE(node,storage_tec,level_storage,year2,time2);
 
 ***
 * Equation STORAGE_BOUND_UP

message_ix/model/MESSAGE/parameter_def.gms

@@ -707,5 +707,6 @@ Parameters
     bound_storage_lo(node,tec,level,year_all,time)                      lower bound of storage content (percentage of capacity)
     bound_storage_up(node,tec,level,year_all,time)                      upper bound of storage content (percentage of capacity)
     storage_loss(node,tec,level,year_all,time)                          storage loss per timestep (percentage of capacity)
+    relation_storage(node,tec,level,year_all,year_all,time,time)        relation between the content of storage in two time steps (and two periods) (a value between -1 and +1)
     time_seq(time)                                                      sequence of subannual timesteps
 ;

message_ix/model/includes/period_parameter_assignment.gms

@@ -15,7 +15,6 @@ Sets
     macro_base_period(year_all)      flag for base year period in model horizon (period prior to first model period) - used in MACRO
 * Added for storage
     map_time_period(year_all,year_all2,time,time2)           mapping of one sub-annual timestep (time) to the next (time2)
-    map_time_first_last(year_all,year_all2,time,time2)       mapping of the first and last sub-annual timesteps in one period
 
 ;
 
@@ -50,11 +49,6 @@ map_period(year_all,year_all2)$( ORD(year_all) <= ORD(year_all2) ) = yes ;
 map_time_period(year_all,year_all2,time,time2)$( ORD(year_all) = ORD(year_all2) AND time_seq(time) AND
     (time_seq(time) + 1 = time_seq(time2) ) ) = yes;
 
-* mapping of first and last time steps in a period
-map_time_first_last(year_all,year_all2,time,time2)$( ( ORD(year_all) = ORD(year_all2)) AND
-    (time_seq(time) = smin(time3$time_seq(time3),time_seq(time3) ) AND
-    time_seq(time2) = smax(time3$time_seq(time3),time_seq(time3) ) ) ) = yes;
-
 * dynamic sets (singleton) with first and last periods in model horizon of MESSAGEix (for easier reference)
 first_period(year_all) = no ;
 first_period(year_all)$( cat_year("firstmodelyear",year_all) ) = yes ;

tests/test_storage.py

@@ -80,6 +80,14 @@ def add_storage_data(scen, time_order):
     for h in time_order.keys():
         scen.add_par('time_seq', h, time_order[h], '-')
 
+    # Adding a relation between storage content of two time steps (optional)
+    yr_first = yr_last = scen.set('year').tolist()[0]
+    time_first = 'a'
+    time_last = 'd'
+    scen.add_par('relation_storage', ['node', 'dam', 'storage',
+                                      yr_first, yr_last,
+                                      time_first, time_last], 1.25, '%')
+
     # Adding minimum and maximum bound, and losses for storage (percentage)
     for year, h in product(set(scen.set('year')), time_order.keys()):
         storage_spec = ['node', 'dam', 'storage', year, h]