Adjust calculation of PRICE_EMISSION

message_ix/model/MESSAGE/data_load.gms

@@ -169,7 +169,7 @@ addon_up(node,tec,year_all,mode,time,type_addon)$(
     AND map_tec_act(node,tec,year_all,mode,time)
     AND NOT addon_up(node,tec,year_all,mode,time,type_addon) ) = 1 ;
 
-* set the emission scaling parameter to 1 if only one emission is included in a category
+* set the emission scaling parameter to 1 by default
 emission_scaling(type_emission,emission)$( cat_emission(type_emission,emission)
         and not emission_scaling(type_emission,emission) ) = 1 ;
 

message_ix/model/MESSAGE/model_core.gms

@@ -131,26 +131,22 @@ Variables
 *
 * Auxiliary variables
 * ^^^^^^^^^^^^^^^^^^^
-* =========================================================================== ======================================================================================================
-* Variable                                                                    Explanatory text
-* =========================================================================== ======================================================================================================
-* :math:`\text{DEMAND}_{n,c,l,y,h} \in \mathbb{R}`                            Demand level (in equilibrium with MACRO integration)
-* :math:`\text{PRICE_COMMODITY}_{n,c,l,y,h} \in \mathbb{R}`                   Commodity price (undiscounted marginals of :ref:`commodity_balance_gt` and :ref:`commodity_balance_lt`)
-* :math:`\text{PRICE_EMISSION}_{n,\widehat{e},\widehat{t},y} \in \mathbb{R}`  Emission price (undiscounted marginals of :ref:`emission_constraint`)
-* :math:`\text{COST_NODAL_NET}_{n,y} \in \mathbb{R}`                          System costs at the node level net of energy trade revenues/cost
-* :math:`\text{GDP}_{n,y} \in \mathbb{R}`                                     Gross domestic product (GDP) in market exchange rates for MACRO reporting
-* =========================================================================== ======================================================================================================
-*
-* .. warning::
-*    Please be aware that transitioning from one period length to another for consecutive periods may result in false values of :math:`\text{PRICE_EMISSION}`. 
-*    Please see `this issue <https://github.com/iiasa/message_ix/issues/723>`_ for further information. We are currently working on a fix.
+* ======================================================================================= =======================================================================================================
+* Variable                                                                                Explanatory text
+* ======================================================================================= =======================================================================================================
+* :math:`\text{DEMAND}_{n,c,l,y,h} \in \mathbb{R}`                                        Demand level (in equilibrium with MACRO integration)
+* :math:`\text{PRICE_COMMODITY}_{n,c,l,y,h} \in \mathbb{R}`                               Commodity price (undiscounted marginals of :ref:`commodity_balance_gt` and :ref:`commodity_balance_lt`)
+* :math:`\text{PRICE_EMISSION}_{n,\widehat{e},\widehat{t},y} \in \mathbb{R}`              Emission price (undiscounted marginals of :ref:`emission_equivalence`)
+* :math:`\text{COST_NODAL_NET}_{n,y} \in \mathbb{R}`                                      System costs at the node level net of energy trade revenues/cost
+* :math:`\text{GDP}_{n,y} \in \mathbb{R}`                                                 Gross domestic product (GDP) in market exchange rates for MACRO reporting
+* ======================================================================================= =======================================================================================================
 ***
 
 Variables
 * auxiliary variables for demand, prices, costs and GDP (for reporting when MESSAGE is run with MACRO)
     DEMAND(node,commodity,level,year_all,time) demand
     PRICE_COMMODITY(node,commodity,level,year_all,time)  commodity price (derived from marginals of COMMODITY_BALANCE constraint)
-    PRICE_EMISSION(node,type_emission,type_tec,year_all) emission price (derived from marginals of EMISSION_BOUND constraint)
+    PRICE_EMISSION(node,type_emission,type_tec,year_all) emission price (derived from marginals of EMISSION_EQUIVALENCE constraint)
     COST_NODAL_NET(node,year_all)              system costs at the node level over time including effects of energy trade
     GDP(node,year_all)                         gross domestic product (GDP) in market exchange rates for MACRO reporting
 ;

message_ix/model/MESSAGE/model_solve.gms

@@ -46,18 +46,23 @@ EMISSION_CONSTRAINT.m(node,type_emission,type_tec,type_year)$(
         / SUM(year$( cat_year(type_year,year) ), duration_period(year) )
         * SUM(year$( map_first_period(type_year,year) ), duration_period(year) / df_period(year) * df_year(year) );
 
-
-* assign auxiliary variables DEMAND, PRICE_COMMODITY and PRICE_EMISSION for integration with MACRO and reporting
+* assign auxiliary variable DEMAND for integration with MACRO
     DEMAND.l(node,commodity,level,year,time) = demand_fixed(node,commodity,level,year,time) ;
+
+* assign auxiliary variables PRICE_COMMODITY and PRICE_EMISSION for reporting
     PRICE_COMMODITY.l(node,commodity,level,year,time) =
         ( COMMODITY_BALANCE_GT.m(node,commodity,level,year,time) + COMMODITY_BALANCE_LT.m(node,commodity,level,year,time) )
             / df_period(year) ;
-    PRICE_EMISSION.l(node,type_emission,type_tec,year)$( SUM(type_year$( cat_year(type_year,year) ), 1 ) ) =
-        SMAX(type_year$( cat_year(type_year,year) ),
-               - EMISSION_CONSTRAINT.m(node,type_emission,type_tec,type_year) )
-            / df_year(year) ;
+
+* calculate PRICE_EMISSION based on the marginals of EMISSION_EQUIVALENCE
+    PRICE_EMISSION.l(node,type_emission,type_tec,year)$( SUM(emission$( cat_emission(type_emission,emission) ),
+         EMISSION_EQUIVALENCE.m(node,emission,type_tec,year) ) ) =
+        SMAX(emission$( cat_emission(type_emission,emission) ),
+               EMISSION_EQUIVALENCE.m(node,emission,type_tec,year) / emission_scaling(type_emission,emission) )
+            / df_period(year);
     PRICE_EMISSION.l(node,type_emission,type_tec,year)$(
-        PRICE_EMISSION.l(node,type_emission,type_tec,year) = - inf ) = 0 ;
+        ( PRICE_EMISSION.l(node,type_emission,type_tec,year) = eps ) or
+        ( PRICE_EMISSION.l(node,type_emission,type_tec,year) = -inf ) ) = 0 ;
 
 %AUX_BOUNDS% AUX_ACT_BOUND_LO(node,tec,year_all,year_all2,mode,time)$( ACT.l(node,tec,year_all,year_all2,mode,time) < 0 AND
 %AUX_BOUNDS%    ACT.l(node,tec,year_all,year_all2,mode,time) = -%AUX_BOUND_VALUE% ) = yes ;

message_ix/models.py

@@ -4,7 +4,7 @@
 from dataclasses import InitVar, dataclass, field
 from functools import partial
 from pathlib import Path
-from typing import Mapping, MutableMapping, Optional, Tuple
+from typing import MutableMapping, Optional, Tuple
 from warnings import warn
 
 import ixmp.model.gams
@@ -175,7 +175,7 @@ class GAMSModel(ixmp.model.gams.GAMSModel):
 
     #: Mapping from model item (equation, parameter, set, or variable) names to
     #: :class:`.Item` describing the item.
-    items: Mapping[str, Item]
+    items: MutableMapping[str, Item]
 
     def __init__(self, name=None, **model_options):
         # Update the default options with any user-provided options
@@ -557,7 +557,7 @@ def initialize(cls, scenario):
 var(
     "PRICE_EMISSION",
     "n type_emission type_tec y",
-    "Emission price (derived from marginals of EMISSION_BOUND constraint)",
+    "Emission price (derived from marginals of EMISSION_EQUIVALENCE constraint)",
 )
 var(
     "REL",
@@ -768,7 +768,7 @@ def initialize(cls, scenario):
 )
 equ(
     "EMISSION_EQUIVALENCE",
-    "",
+    "n e type_tec y",
     "Auxiliary equation to simplify the notation of emissions",
 )
 equ("EXTRACTION_BOUND_UP", "", "Upper bound on extraction (by grade)")