Model adds new capacity while historical_new_capacity should be enough

[zsalimian]

Dear Sir,

I have encountered with a problem in using MESSAGE-ix equations.
I used the GAMS codes for a simple RES.
As you can see this simple model contains 4 years, in which 690 is historical year and 700 is defined to be the first year.
year_all /690,700,710,720/
year /700,710,720/
first_period(year_all) /700/
duration_time(time)=1;
duration_period(year_all)=10;
Moreover, I defined two levels, and two technologies.
level /Primary,final/
tec /wind_ppl,coal_ppl/
I considered 60-year period for lifetime of each technology.
technical_lifetime(node,'coal_ppl',year)=60;
technical_lifetime(node,'wind_ppl',year)=60;
Furthermore,the coal_ppl has historical_new_capacity(node,'coal_ppl','700')=50;
The demand for electricity is as follow:
COMMODITY_USE.fx(node,'electricity','final','700')=1;
COMMODITY_USE.fx(node, 'electricity' ,'final','710')=1.5;
COMMODITY_USE.fx(node, 'electricity' ,'final','720')=1.9;
It is expected that the model uses the following capacity to satisfy the demand historical_new_capacity(node,'coal_ppl','700') =50
However, As you see it constructs new capacities for each period, while the lifetime of capacities is 60.
It has made me confused.

Regards

Sets
node world - regions - countries - grid cells
/country/
commodity resources - electricity - water - land availability - etc.
/wind,electricity,coal/
level levels of the reference energy system or supply chain ( primary - secondary - ... - useful )
/Primary,final/
tec technologies
/wind_ppl,coal_ppl/
mode modes of operation
/standard/

• land_type types of land use
  year_all years (over entire model horizon)
  /690,700,710,720/
  year (year_all) years included in a model instance (for myopic or rolling-horizon optimization)
  /700,710,720/
  time subannual time periods (seasons - days - hours)
  /year/

;

• definition of aliases
  Alias(node,location);
  *Alias(node,node2);
  *Alias(node,node_share);
  *Alias(tec,tec2);
  *Alias(commodity,commodity2);
  *Alias(level,level2);
  *Alias(emission,emission2);
  Alias(year_all,vintage);
  Alias(year_all,year_all2);
  Alias(year_all,year_all3);
  Alias(year,year2);
  *Alias(year,year3);
  Alias(time,time2);
  *Alias(time,time3);
  Alias(time,time_act);
  Alias(time,time_od);
  *Alias(mode,mode2);
  *Alias(commodity,commodity2);

• category types and mappings
  Sets

  type_tec types of technologies
  /coal_ppl,wind_ppl/

• cat_tec(type_tec,tec) mapping of technologies to respective categories
  inv_tec(tec) technologies that have explicit investment and capacity decision variables
  /coal_ppl,wind_ppl/

renewable_tec(tec)                      technologies that use renewable energy potentials

/wind_ppl/

• addon(tec) technologies that are an add-on to other (parent) technologies
• type_addon types of add-on technologies (that can be applied mutually exclusive)
• cat_addon(type_addon,addon) mapping of add-on technologies to respective add-on technology types
• type_year types of year aggregations
  */first_model_year/
• cat_year(type_year,year_all) mapping of years to respective categories
  type_emission types of emission aggregations
  /greenhouse gases, pollutants/
• cat_emission(type_emission,emission) mapping of emissions to respective categories
• type_tec_land(type_tec) dynamic set whether emissions from land use are included in type_tec
• balance_equality(commodity,level) mapping of commodities-level where the supply-demand balance must be maintained with equality
• storage_tec and level_storage are defined at the bottom of this file.
  ;

----------------------------------------------------------------------------------------------------------------------

• assignment and computation of auxiliary parameters *
  ----------------------------------------------------------------------------------------------------------------------

• additional sets and parameters created in GAMS to make notation more concise for myopic/rolling-horizon optimization
  Sets
  first_period(year_all) flag for first period in model horizon
  /700/
  ;

Sets
node world - regions - countries - grid cells
commodity resources - electricity - water - land availability - etc.
level levels of the reference energy system or supply chain ( primary - secondary - ... - useful )
sector sectors (for integration with MACRO)
grade grades of extraction of raw materials
/1/
tec technologies
mode modes of operation
emission greenhouse gases - pollutants - etc.
land_scenario scenarios of land use (for land-use model emulator)
land_type types of land use
year_all years (over entire model horizon)
year (year_all) years included in a model instance (for myopic or rolling-horizon optimization)
time subannual time periods (seasons - days - hours)
shares share constraint relations
relation generic linear relations
lvl_spatial hierarchical levels of spatial resolution
lvl_temporal hierarchical levels of temporal resolution
rating identifies the 'quality' of the renewable energy potential (bins acc. to Sullivan)
;

• definition of aliases
  Alias(node,location);
  Alias(node,node2);
  Alias(node,node_share);
  Alias(tec,tec2);
  Alias(commodity,commodity2);
  Alias(level,level2);
  Alias(emission,emission2);
  Alias(year_all,vintage);
  Alias(year_all,year_all2);
  Alias(year_all,year_all3);
  Alias(year,year2);
  Alias(year,year3);
  Alias(time,time2);
  Alias(time,time3);
  Alias(time,time_act);
  Alias(time,time_od);
  Alias(mode,mode2);
  Alias(commodity,commodity2);

Sets

• historical(year_all) set of periods prior to the start of the model horizon

• model_horizon(year_all) set of periods included in the model horizon

• macro_horizon(year_all) set of periods included in the MACRO model horizon
  seq_period(year_all,year_all2) mapping of one period ('year_all') to the next ('year_all2')

• map_period(year_all,year_all2) mapping of one period ('year_all') to itself and all subsequent periods ('year_all2')

• map_first_period(type_year, year_all) mapping of a 'type_year' to the first 'year'

• first_period(year_all) flag for first period in model horizon
  last_period(year_all) flag for last period in model horizon
  /720/

• macro_initial_period(year_all) flag for period in model horizon in which to initialize model parameters in (period prior to first model period) - used in MACRO

• macro_base_period(year_all) flag for base year period in model horizon (period prior to first model period) - used in MACRO
  ;

seq_period('690','700')=yes;
*seq_period('695','710')=no;
*seq_period('690','720')=no;
seq_period('700','710')=yes;
seq_period('710','720')=yes;
*seq_period('700','720')=no;
*seq_period('710','720')=yes;
*seq_period('720','720')=no;

• category types and mappings
  Sets
  level_resource (level) subset of 'level' to mark all levels related to make hfossil resources
  /Primary/
  level_renewable(level) subset of 'level' to mark all levels related to renewable resources
  /Primary/

;

Alias(type_tec,type_tec_share);
Alias(type_tec,type_tec_total);

Sets
map_node(node,location) mapping of nodes across hierarchy levels (location is in node)
map_time(time,time2) mapping of time periods across hierarchy levels (time2 is in time)

• map_time_period and map_tec_storage are defined at the bottom of this file.

  map_resource(node,commodity,grade,year_all) mapping of resources and grades to node over time

  map_ren_grade(node,commodity,grade,year_all) mapping of renewables and grades to node over time
  map_ren_com(node,tec,commodity,year_all) mapping of technologies to renewable energy source as input
  map_rating(node,tec,commodity,level,rating,year_all) mapping of technologies to ratings bin assignment

  map_commodity(node,commodity,level,year_all,time) mapping of commodity-level to node and time
  map_stocks(node,commodity,level,year_all) mapping of commodity-level to node and time

  map_tec(node,tec,year_all) mapping of technology to node and years
  map_tec_time(node,tec,year_all,time) mapping of technology to temporal dissagregation (time)
  map_tec_mode(node,tec,year_all,mode) mapping of technology to modes
  map_tec_act(node,tec,year_all,mode,time) mapping of technology to modes AND temporal dissagregation

• map_tec_addon(tec,type_addon) mapping of types of add-on technologies to the underlying parent technology

map_spatial_hierarchy(lvl_spatial,node,node)    mapping of spatial resolution to nodes (last index is 'parent')
map_temporal_hierarchy(lvl_temporal,time,time)  mapping of temporal resolution to time (last index is 'parent')

map_shares_commodity_share(shares,node,
    node,type_tec,mode,commodity,level)   mapping for commodity share constraints (numerator)
map_shares_commodity_total(shares,node,
    node,type_tec,mode,commodity,level)   mapping for commodity share constraints (denominator)

map_land(node,land_scenario,year_all)            mapping of land-use model emulator scenarios to nodes and years
map_relation(relation,node,year_all)             mapping of generic (user-defined) relations to nodes and years

;

• additional sets created in GAMS to make notation more concise
  Sets
  map_tec_lifetime(node,tec,vintage,year_all) mapping of technologies to periods within technical lifetime
  ;

map_resource(node,commodity,grade,year_all)=yes;
*map_resource(node,'oil',grade,year_all)=yes;
*map_resource(node,'wind',grade,year_all)=yes;
*map_resource(node,commodity,grade,year_all)=yes;
map_tec_act(node,tec,year_all,mode,time)=yes;
map_tec_lifetime(node,tec,vintage,year_all)=yes;

*map_tec_lifetime(node,tec,'700','710')=no;
map_tec_time(node,tec,year_all,time)=yes;
map_tec(node,tec,year_all)=yes;
map_ren_com(node,'wind_ppl','wind',year_all)=yes;
map_ren_grade(node,'wind','1',year_all)=yes;
map_time(time,time2)=yes;

Parameters

• general parameters
  interestrate(year_all) interest rate (to compute discount factor)
  duration_time(time) duration of one time slice (relative to 1)
  duration_period(year_all) duration of one multi-year period (in years)
  duration_period_sum(year_all,year_all2) number of years between two periods ('year_all' must precede 'year_all2')
  df_period(year_all) cumulative discount factor over period duration
  df_year(year_all) discount factor of the last year in the period
  ;

Parameters

• general parameters
• interestrate(year_all) interest rate (to compute discount factor)
• duration_time(time) duration of one time slice (relative to 1)
• duration_period(year_all) duration of one multi-year period (in years)
• duration_period_sum(year_all,year_all2) number of years between two periods ('year_all' must precede 'year_all2')
  duration_time_rel(time,time2) relative duration of subannual time period ('time2' relative to parent 'time')
• df_period(year_all) cumulative discount factor over period duration
• df_year(year_all) discount factor of the last year in the period
  ;

Parameters

• technology input-output mapping and costs parameters
  var_cost(node,tec,vintage,year_all,mode,time) variable costs of operation (per unit of capacity maintained)
  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)

• engineering parameters
  construction_time(node,tec,vintage) duration of construction of new capacity (in years)
  technical_lifetime(node,tec,vintage) maximum technical lifetime (from year of construction)
  capacity_factor(node,tec,vintage,year_all,time) capacity factor by subannual time slice
  operation_factor(node,tec,vintage,year_all) yearly total operation factor

;

Parameters
construction_time_factor(node,tec,year_all) scaling factor to account for construction time of new capacity
remaining_capacity(node,tec,year_all,year_all) scaling factor to account for remaining capacity in period
end_of_horizon_factor(node,tec,year_all) multiplier for value of investment at end of model horizon
beyond_horizon_lifetime(node,tec,year_all) remaining technical lifetime at the end of model horizon
beyond_horizon_factor(node,tec,year_all) discount factor of remaining lifetime beyond model horizon
;

Parameters

fixed_new_capacity(node,tec,year_all)               fixed new-built capacity
fixed_capacity(node,tec,vintage,year_all)           fixed maintained capacity
fixed_activity(node,tec,vintage,year_all,mode,time) fixed activity level
input(node,tec,vintage,year_all,mode,node,commodity,level,time,time)  relative share of input per unit of activity

;

Parameters
*from Python
coal_fraction
demand_per_year
historic_demand
historic_generation
grid_efficiency
;

Parameter

elapsed_years(year_all)    elapsed years since the start of the model horizon (not including 'year_all' period)
remaining_years(year_all)  remaining years until the end of the model horizon (including last period)

;

Parameters
initial_new_capacity_up(node,tec,year_all) dynamic upper bound on new capacity (fixed initial term)
initial_activity_up(node,tec,year_all,time) dynamic upper bound on activity (fixed initial term)
initial_new_capacity_lo(node,tec,year_all) dynamic lower bound on new capacity (fixed initial term)
initial_activity_lo(node,tec,year_all,time) dynamic lower bound on activity (fixed initial term)
growth_new_capacity_up(node,tec,year_all) dynamic upper bound on new capacity (growth rate)
growth_activity_up(node,tec,year_all,time) dynamic upper bound on activity (growth rate)
growth_new_capacity_lo(node,tec,year_all) dynamic lower bound on new capacity (growth rate)
growth_activity_lo(node,tec,year_all,time) dynamic lower bound on activity (growth rate)
soft_new_capacity_lo(node,tec,year_all) soft relaxation of dynamic lower bound on new capacity (growth rate)
soft_new_capacity_up(node,tec,year_all) soft relaxation of dynamic upper bound on new capacity (growth rate)
soft_activity_up(node,tec,year_all,time) soft relaxation of dynamic upper bound on activity (growth rate)
soft_activity_lo(node,tec,year_all,time) soft relaxation of dynamic lower bound on activity (growth rate)
;

Parameters
historical_new_capacity(node,tec,year_all) historical new capacity
historical_activity(node,tec,year_all,mode,time) historical activity
;

Parameters
act_to_cap
;

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
  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)
  levelized_cost(node,tec,year_all,time) levelized costs (per unit of new capacity)

• engineering parameters
  construction_time(node,tec,vintage) duration of construction of new capacity (in years)
  technical_lifetime(node,tec,vintage) maximum technical lifetime (from year of construction)
  capacity_factor(node,tec,vintage,year_all,time) capacity factor by subannual time slice
  operation_factor(node,tec,vintage,year_all) yearly total operation factor
  min_utilization_factor(node,tec,vintage,year_all) yearly minimum utilization factor
  rating_bin(node,tec,year_all,commodity,level,time,rating) maximum share of technology in commodity use per rating
  reliability_factor(node,tec,year_all,commodity,level,time,rating) reliability of a technology (per rating)
  flexibility_factor(node,tec,vintage,year_all,mode,commodity,level,time,rating) contribution of technologies towards operation flexibility constraint
  renewable_capacity_factor(node,commodity,grade,level,year_all) quality of renewable potential grade (>= 1)
  renewable_potential(node,commodity,grade,level,year_all) size of renewable potential per grade
  emission_factor(node,tec,year_all,year_all,mode,emission) emission intensity of activity
  ;

Parameter

• resource and commodity parameters
  resource_volume(node,commodity,grade) volume of resources in-situ at start of the model horizon
  resource_cost(node,commodity,grade,year_all) extraction costs for resource
  resource_remaining(node,commodity,grade,year_all) maximum extraction relative to remaining resources (by year)
  bound_extraction_up(node,commodity,grade,year_all) upper bound on extraction of resources by grade
  commodity_stock(node,commodity,level,year_all) exogenous (initial) quantity of commodity in stock
  historical_extraction(node,commodity,grade,year_all) historical extraction
  ;
  Parameter
  duration_period_sum(year_all,year_all2) number of years between two periods ('year_all' must precede 'year_all2')
  duration_time_rel(time,time2) relative duration of subannual time period ('time2' relative to parent 'time')
  elapsed_years(year_all) elapsed years since the start of the model horizon (not including 'year_all' period)
  remaining_years(year_all) remaining years until the end of the model horizon (including last period)
  year_order(year_all) order for members of set 'year_all'
  ;

Parameter

bound_new_capacity_up(node,inv_tec,year)

;
bound_new_capacity_up(node,inv_tec,year)=100;

• define order of set 'year_all' (to use as equivalent of ORD operator on the dynamic set year (subset of 'year_all') )
  year_order(year_all) = ORD(year_all) ;
  resource_remaining(node,commodity,grade,year_all)=150;
  resource_cost(node,commodity,grade,year_all)=0.01;
  interestrate(year)=0;
  *first_period(year_all)=700;
  duration_time(time)=1;
  inv_cost(node,'coal_ppl',year_all)=100;
  *inv_cost(node,'thermal_ppl',year_all)=500;
  inv_cost(node,'wind_ppl',year_all)=200;

fix_cost(node,'coal_ppl',vintage,year)=30;
*fix_cost(node,'thermal_ppl',vintage,year)=30;
fix_cost(node,'wind_ppl',vintage,year)=30;

var_cost(node,'coal_ppl',vintage,year_all,mode,time)=30;
*var_cost(node,'thermal_ppl',vintage,year_all,mode,time)=30;
var_cost(node,'wind_ppl',vintage,year_all,mode,time)=0;

duration_period(year_all)=10;

• auxiliary parameters for duration between periods (years) - not including the final period 'year_all2'
  duration_period_sum(year_all,year_all2) =
  SUM(year_all3$( ORD(year_all) <= ORD(year_all3) AND ORD(year_all3) < ORD(year_all2) ) , duration_period(year_all3) ) ;
  input(node,tec,vintage,year_all,mode,node,commodity,level,time,time)=1;
  display duration_period_sum;
  input(node,'coal_ppl',vintage,year_all,mode,node,'coal',level,time,time)=1;

*farz minkone kole sal dar madare
operation_factor(node,tec,vintage,year_all)=1;

capacity_factor(node,'coal_ppl',year,year,time2)=1;
*capacity_factor(node,'thermal_ppl',year,year,time2)=1;
capacity_factor(node,'wind_ppl',year,year,time2)=0.36;

technical_lifetime(node,'coal_ppl',year)=60;
*technical_lifetime(node,'thermal_ppl',year)=10;
technical_lifetime(node,'wind_ppl',year)=60;

coal_fraction = 0.5;
demand_per_year = 1;

*1., 1.5, 1.9

historic_demand = 0.85 * demand_per_year;
grid_efficiency = 0.9;
historic_generation = historic_demand / grid_efficiency;
*///zarfiat jadidi ke az ghabl fix mikonin ta sale khasi be madar biad
*///baraye tarife zarfiate mojood karbord dare

historical_new_capacity(node,'coal_ppl','700')=50;
*historical_new_capacity(node,'coal_ppl',year_all)=0$(ord(year_all)>699);
*historical_new_capacity(node,'thermal_ppl',year_all)=0;
historical_new_capacity(node,'wind_ppl',year_all)=0;
*min_utilization_factor(node,inv_tec,vintage,year)=0.5;
renewable_potential(node,commodity,grade,level,year_all)=100;

df_year(year_all) = 1 ;

df_period(year_all) =
df_year(year_all) * (

• multiply the per-year discount factor by the geometric series of over the duration of the period
  ( ( 1 - POWER( 1 / ( 1 + interestrate(year_all) ), duration_period(year_all) ) )
  / ( 1 - 1 / ( 1 + interestrate(year_all) ) ) )$( interestrate(year_all) )
• if interest rate = 0, multiply by the number of years in that period
  + ( duration_period(year_all) )$( interestrate(year_all) eq 0 ) )
  ;

remaining_capacity(node,'coal_ppl',vintage,year_all)= 1;
*remaining_capacity(node,'coal_ppl','700','710')= 0;
*remaining_capacity(node,'coal_ppl','700','705')= 0.5;
*remaining_capacity(node,'coal_ppl','710','720')= 1;

*remaining_capacity(node,'coal_ppl',vintage,'710')= 1;
*remaining_capacity(node,'coal_ppl',vintage,'700')= 1;
*remaining_capacity(node,'coal_ppl',vintage,'700')= 1;
*remaining_capacity(node,'coal_ppl',vintage,'720')= 1;
*remaining_capacity(node,'coal_ppl',vintage,'700')= 1;
*remaining_capacity(node,'coal_ppl',vintage,'700')= 1;

remaining_capacity(node,tec,vintage,year_all)$( map_tec_lifetime(node,tec,vintage,year_all)
AND ( technical_lifetime(node,tec,vintage) - duration_period_sum(vintage,year_all) < duration_period(year_all) )
AND ( technical_lifetime(node,tec,vintage) - duration_period_sum(vintage,year_all) > 0 ) )
= ( technical_lifetime(node,tec,vintage) - duration_period_sum(vintage,year_all) ) / duration_period(year_all) ;

display remaining_capacity,technical_lifetime,duration_period_sum;

• compute auxiliary parameters for relative duration of subannual time periods
  duration_time_rel(time,time2)$( map_time(time,time2) )
  = duration_time(time2) / duration_time(time) ;

renewable_capacity_factor(node,commodity,grade,level_renewable,year)=1;

construction_time(node,inv_tec,year)=1;

• set default construction_time_factor to 1
  construction_time_factor(node,inv_tec,year)$( map_tec(node,inv_tec,year) )
  = 1;

• compute the construction_time_factor
  construction_time_factor(node,inv_tec,year)$( map_tec(node,inv_tec,year) AND construction_time(node,inv_tec,year) )
  =
  ( 1 + interestrate(year) ) ** construction_time(node,inv_tec,year) ;

display construction_time_factor;

• compute the cumulative discount factor of the technical lifetime remaining beyond the model horizon

---

• auxiliary parameter for duration until the end of the model horizon - including the last period
  remaining_years(year_all) = SUM(year_all2$( ORD(year_all) <= ORD(year_all2) ) , duration_period(year_all2) ) ;

• compute the scaling investment parameters for all periods in the model horizon
  *year(year_all)$( model_horizon(year_all) ) = yes ;

• compute the technical lifetime remaining beyond the overall model horizon
  beyond_horizon_lifetime(node,inv_tec,vintage)$( map_tec(node,inv_tec,vintage) )
  =
  technical_lifetime(node,inv_tec,vintage) - remaining_years(vintage) ;
  beyond_horizon_lifetime(node,inv_tec,vintage)$( beyond_horizon_lifetime(node,inv_tec,vintage) < 0 ) = 0 ;

beyond_horizon_factor(node,inv_tec,vintage)$( beyond_horizon_lifetime(node,inv_tec,vintage) )
= sum(last_period,

• compute the discount factor of the very last year (not period) in the model horizon
  df_year(last_period) * POWER( 1 / ( 1 + interestrate(last_period) ), duration_period(last_period) ) * (

• multiply this by the geometric series of remaining technical lifetime if interestrate of last model period > 0
  (
  ( 1 - POWER( 1 / ( 1 + interestrate(last_period) ), beyond_horizon_lifetime(node,inv_tec,vintage) ) )
  / ( 1 - 1 / ( 1 + interestrate(last_period) ) )
  )$( interestrate(last_period) )

• if interest rate = 0, multiply by remaining technical lifetime
  + ( beyond_horizon_lifetime(node,inv_tec,vintage) )$( interestrate(last_period) eq 0 )
  )
  ) ;

• deterine the parameter end_of_horizon_factor used for scaling investment costs to account for

• technical lifetime beyond the model horizon
  end_of_horizon_factor(node,inv_tec,vintage)$( map_tec(node,inv_tec,vintage) )
  =
  sum(year_all$( map_tec_lifetime(node,inv_tec,vintage,year_all) )
  , df_period(year_all) )
  / ( sum(year_all$( map_tec_lifetime(node,inv_tec,vintage,year_all) )
  ,
  df_period(year_all) )
  + beyond_horizon_factor(node,inv_tec,vintage) ) ;

resource_volume(node,'coal',grade)=1000;
*resource_volume(node,'oil',grade)=1000;

display historical_new_capacity,duration_time_rel,input,beyond_horizon_factor,end_of_horizon_factor,construction_time_factor;

Variables

COST_NODAL(node, year_all)                   system costs at the node level over time

• auxiliary variables for finrm-capacity formulation
  COMMODITY_USE(node,commodity,level,year_all) total amount of a commodity & level that was used or consumed
  ;

Variables
OBJ objective value of the optimisation problem
;

Positive Variables

• resource production/extraction variable
  EXT(node,commodity,grade,year_all) extraction of fossil resources
  CAP_NEW(node,tec,year_all) new capacity by year
  CAP(node,tec,vintage,year_all) total installed capacity by year

• use of renewable resources
  REN(node, tec, commodity, grade, year_all, time) activity of renewables specified per renewables grade

  ACT(node,tec,vintage,year_all,mode,time) activity of technology by mode-year-timeperiod
  ;

• CAP.fx(node,inv_tec,vintage,first_period)=remaining_capacity(node,inv_tec,vintage,first_period) duration_period(vintage) * historical_new_capacity(node,inv_tec,vintage);
  COMMODITY_USE.fx(node,'electricity','final','700')=demand_per_year;
  COMMODITY_USE.fx(node,'electricity','final','710')=demand_per_year1.5;
  COMMODITY_USE.fx(node,'electricity','final','720')=demand_per_year*1.9;

Equations
OBJECTIVE objective value of the optimisation problem
COST_ACCOUNTING_NODAL cost accounting at node level over time
EXTRACTION_EQUIVALENCE auxiliary equation to simplify the resource extraction formulation
CAPACITY_MAINTENANCE_HIST constraint for capacity maintenance historical installation (built before start of model horizon)
OPERATION_CONSTRAINT constraint on maximum yearly operation (scheduled down-time for maintenance)
CAPACITY_CONSTRAINT capacity constraint for technology (by sub-annual time slice)
COMMODITY_USE_LEVEL aggregate use of commodity by level as defined by total input into technologies
CAPACITY_MAINTENANCE_NEW constraint for capacity maintenance of new capacity built in the current period (vintage == year)
RENEWABLES_POTENTIAL_CONSTRAINT constraint on renewable resource potential
RENEWABLES_CAPACITY_REQUIREMENT lower bound on required overcapacity when using lower grade potentials
RENEWABLES_EQUIVALENCE equation to define the renewables extraction
RESOURCE_HORIZON
RESOURCE_CONSTRAINT
CAPACITY_MAINTENANCE

• MIN_UTILIZATION_CONSTRAINT
• NEW_CAPACITY_BOUND_UP
• NEW_CAPACITY_CONSTRAINT_UP
  ;

OBJECTIVE..
OBJ =E= SUM( (node,year), df_period(year) * COST_NODAL(node,year) ) ;

COST_ACCOUNTING_NODAL(node, year)..
COST_NODAL(node, year) =E=

• resource extraction costs
  SUM((commodity,grade)$( map_resource(node,commodity,grade,year) )
  ,
  resource_cost(node,commodity,grade,year) * EXT(node,commodity,grade,year) )
  • SUM((tec)$( map_tec(node,tec,year) )
    ,
    ( inv_cost(node,tec,year) * construction_time_factor(node,tec,year)
    * end_of_horizon_factor(node,tec,year) * CAP_NEW(node,tec,year)
    + SUM(vintage$( map_tec_lifetime(node,tec,vintage,year) )
    ,
    fix_cost(node,tec,vintage,year) * CAP(node,tec,vintage,year) ) )$( inv_tec(tec) )
    + SUM((vintage,mode,time)$( map_tec_lifetime(node,tec,vintage,year) AND map_tec_act(node,tec,year,mode,time) )
    ,
    var_cost(node,tec,vintage,year,mode,time) * ACT(node,tec,vintage,year,mode,time) )
    )
    ;

*///tec az sum dovom hazf shode
EXTRACTION_EQUIVALENCE(node,'coal',year)..
SUM(grade$( map_resource(node,'coal',grade,year) ),EXT(node,'coal',grade,year) )
=E= SUM((location,vintage,mode,level_resource,time_act,time_od)$( map_tec_act(node,'coal_ppl',year,mode,time_act) AND map_tec_lifetime(node,'coal_ppl',vintage,year) ),
input(location,'coal_ppl',vintage,year,mode,node,'coal',level_resource,time_act,time_od)
* ACT(location,'coal_ppl',vintage,year,mode,time_act) ) ;

---

RESOURCE_CONSTRAINT(node,commodity,grade,year)$( map_resource(node,commodity,grade,year)
AND resource_remaining(node,commodity,grade,year) )..

• extraction per year
  EXT(node,commodity,grade,year) =L=
• remaining resources multiplied by remaining-resources-factor
  resource_remaining(node,commodity,grade,year)
  • ( resource_volume(node,commodity,grade)
    • SUM(year2$( year_order(year2) < year_order(year) ),
      duration_period(year2) * EXT(node,commodity,grade,year2) ) ) ;

---

CAPACITY_MAINTENANCE_HIST(node,inv_tec,vintage,first_period)..
CAP(node,inv_tec,vintage,first_period)
=L= remaining_capacity(node,inv_tec,vintage,first_period) *
duration_period(vintage) * historical_new_capacity(node,inv_tec,vintage) ;

**
CAPACITY_MAINTENANCE(node,inv_tec,vintage,year)$( map_tec_lifetime(node,inv_tec,vintage,year)
AND NOT first_period(year) AND year_order(vintage) < year_order(year))..
CAP(node,inv_tec,vintage,year)
=L= remaining_capacity(node,inv_tec,vintage,year) *
( SUM(year2$( seq_period(year2,year) ),
CAP(node,inv_tec,vintage,year2) ) ) ;

******///////////////////
CAPACITY_MAINTENANCE_NEW(node,inv_tec,vintage,vintage)$( map_tec_lifetime(node,inv_tec,vintage,vintage) )..
CAP(node,inv_tec,vintage,vintage)
=E= remaining_capacity(node,inv_tec,vintage,vintage)
* duration_period(vintage) * CAP_NEW(node,inv_tec,vintage) ;
;

---

---

RESOURCE_HORIZON(node,commodity,grade)$( SUM(year$map_resource(node,commodity,grade,year), 1 ) )..
SUM(year, duration_period(year) * EXT(node,commodity,grade,year) ) =L= resource_volume(node,commodity,grade) ;

---

RENEWABLES_EQUIVALENCE(node,renewable_tec,commodity,year,time)$(
map_tec(node,renewable_tec,year) AND map_ren_com(node,renewable_tec,commodity,year)
)..
SUM(grade$( map_ren_grade(node,'wind',grade,year) )
, REN(node,renewable_tec,commodity,grade,year,time) )
=E= SUM((location,vintage,mode,level_renewable,time_act)$(map_tec_act(node,renewable_tec,year,mode,time) AND map_tec_lifetime(node,renewable_tec,vintage,year) )
,
input(location,renewable_tec,vintage,year,mode,node,commodity,level_renewable,time_act,time)
* ACT(location,renewable_tec,vintage,year,mode,time) ) ;

RENEWABLES_CAPACITY_REQUIREMENT(node,inv_tec,commodity,year)$(SUM( (vintage,mode,time,grade,level_renewable),
map_tec_lifetime(node,inv_tec,vintage,year) AND map_tec_act(node,inv_tec,year,mode,time) AND map_ren_com(node,inv_tec,commodity,year)
AND
renewable_capacity_factor(node,commodity,grade,level_renewable,year) > 0 ))..
SUM( (vintage,time)$map_ren_com(node,inv_tec,commodity,year)
,
CAP(node,inv_tec,vintage,year)
* operation_factor(node,inv_tec,vintage,year)
* capacity_factor(node,inv_tec,vintage,year,time) )
=G= SUM((grade,time,level_renewable)$(renewable_capacity_factor(node,commodity,grade,level_renewable,year) > 0),
REN(node,inv_tec,commodity,grade,year,time)
/ renewable_capacity_factor(node,commodity,grade,level_renewable,year)) ;

---

RENEWABLES_POTENTIAL_CONSTRAINT(node,commodity,grade,year)$( map_ren_grade(node,commodity,grade,year))
..
SUM((renewable_tec,time)$( map_ren_com(node,renewable_tec,commodity,year) )
,
REN(node,renewable_tec,commodity,grade,year,time) )
=L= SUM(level_renewable, renewable_potential(node,commodity,grade,level_renewable,year) ) ;

OPERATION_CONSTRAINT(node,inv_tec,vintage,year)$( map_tec_lifetime(node,inv_tec,vintage,year) AND operation_factor(node,inv_tec,vintage,year) < 1 )..
SUM((mode,time)$( map_tec_act(node,inv_tec,year,mode,time) )
, ACT(node,inv_tec,vintage,year,mode,time) ) =L=
operation_factor(node,inv_tec,vintage,year) * capacity_factor(node,inv_tec,vintage,year,'year')
* CAP(node,inv_tec,vintage,year) ;

CAPACITY_CONSTRAINT(node,inv_tec,vintage,year,time)$( map_tec_time(node,inv_tec,year,time) AND map_tec_lifetime(node,inv_tec,vintage,year) )..
SUM(mode$( map_tec_act(node,inv_tec,year,mode,time) )
, ACT(node,inv_tec,vintage,year,mode,time) )
=L= duration_time(time) * capacity_factor(node,inv_tec,vintage,year,time) * CAP(node,inv_tec,vintage,year) ;

---

COMMODITY_USE_LEVEL(node,'electricity','final',year,time)
flexibility_factor(node,tec,vintage,year,mode,commodity,level,time,rating) ) )
..
COMMODITY_USE(node,'electricity','final',year)
=E=
SUM( (location,tec,vintage,mode,time2)$( map_tec_act(location,tec,year,mode,time2) AND map_tec_lifetime(location,tec,vintage,year) )
,
input(location,tec,vintage,year,mode,node,'electricity','final',time2,time)
* duration_time_rel(time,time2)
* ACT(location,tec,vintage,year,mode,time2) ) ;

option limrow=100000;
Model MESSAGE_LP / all / ;
Solve MESSAGE_LP using lp minimizing OBJ ;

[behnam-zakeri]

Thanks @zsalimian for posting your question. From what you have shared, I see that you have combined several GAMS files of MESSAGEix, from loading data and mapping files to the core formulation and post-processing, into one single file. Furthermore, you have specified your input data hard-coded in GAMS and have changed some parts of the GAMS code to fit your purpose. In principle, we encourage the users for flexible use of the code, and modify it as they wish. However, we do not have enough capacity to read new codes developed by different users and comment on that.
So, if you believe a part of MESSAGEix GAMS formulation is not working as intended in the documentation, please replicate the issue using a simple example using the original code. For example, for this case you showed, please use the original code of MESSAGEix and specify your input data in an interface convenient to you (preferably jupyter notebook), then check the model input and output, e.g., by looking into GDX files, and see if the behavior is what you expect or not. You may be able to do this by making some changes to the Westeros baseline scenario. I hope this helps you find a way to resolve your question.

[glatterf42]

I'm marking this as an answer since it does not look like this question is actively pursued from the team and no further input has been given. If this topic is still relevant, please open another discussion/issue.