Note

This page is generated from inline documentation in MESSAGE/parameter_def.gms.

Parameter definition

This file contains the definition of all parameters used in MESSAGEix.

In MESSAGEix, all parameters are understood as yearly values, not as per (multi-year) period. This provides flexibility when changing the resolution of the model horizon (i.e., the set year).

General parameters of the MESSAGEix implementation

Caution

Parameters written in bold are auxiliary parameters that are either generated automatically when exporting a message_ix.Scenario to gdx or that are computed during the pre-processing stage in GAMS (see the footnotes for more individual details). These are not meant to be edited through the API when editing scenarios.

Parameter name	Index dimensions	Explanatory comments
interestrate	year	Economy-wide interest rate or social discount rate
duration_time	time	Duration of sub-annual time slices (relative to 1) [1]
duration_period (\(|y|\)) [2]	year	Duration of multi-year period (in number of years) [3]
duration_period_sum	year | year	Number of years between two periods [4]
duration_time_rel	time | time	Relative duration between sub-annual time slices [4]
df_period	year	Cumulative discount factor over period duration [4]
df_year	year	Discount factor of the last year in the period [4]

[1]

The element ‘Year’ in the set of subannual time slices time has the value of 1. This value is assigned by default when creating a new ixmp.Scenario based on the MESSAGE scheme.

[2]

The short-hand notation \(|y|\) is used for the parameters \(\text{duration_period}_y\) in the mathematical model documentation for exponents.

[3]

The values for this parameter are computed automatically when exporting a MESSAGE-scheme ixmp.Scenario to gdx. Note that in MESSAGEix, the elements of the year set are understood to be the last year in a period. See Years, periods, and time slices.

[4] (1,2,3,4)

These parameters are computed during the GAMS execution.

Parameters of the Resources section

In MESSAGEix, the volume of resources at the start of the model horizon is defined by resource_volume. The quantity of the resources that are extracted per year is dependent on two parameters. The first is bound_extraction_up, which constraints the maximum extraction of the resources (by grade) in a year. The second is resource_remaining, which is the maximum extraction of the remaining resources in a certain year, as a percentage. Extraction costs for resources are represented by resource_cost parameter.

Parameter name	Index dimensions
resource_volume	node | commodity | grade
resource_cost	node | commodity | grade | year
resource_remaining	node | commodity | grade | year
bound_extraction_up	node | commodity | level | year
commodity_stock [5]	node | commodity | level | year
historical_extraction [6]	node | commodity | grade | year

[5]

Commodity stock refers to an exogenous (initial) quantity of commodity in stock. This parameter allows (exogenous) additions to the commodity stock over the model horizon, e.g., precipitation that replenishes the water table.

[6] (1,2,3,4,5)

Historical values of new capacity and activity can be used for parametrising the vintage structure of existing capacity and implement dynamic constraints in the first model period.

Parameters of the Demand section

Parameter name	Index dimensions
demand [demand_fixed] [7]	node | commodity | level | year | time
peak_load_factor [8]	node | commodity | year

[7]

The parameter demand in a MESSAGE-scheme ixmp.Scenario is translated to the parameter demand_fixed in the MESSAGEix implementation in GAMS. The variable DEMAND is introduced as an auxiliary reporting variable; it equals demand_fixed in a MESSAGE-standalone run and reports the final demand including the price response in an iterative MESSAGE-MACRO solution.

[8] (1,2)

The parameters peak_load_factor (maximum peak load factor for reliability constraint of firm capacity) and reliability_factor (reliability of a technology (per rating)) are based on the formulation proposed by Sullivan et al., 2013 [11]. It is used in Reliability of installed capacity.

Parameters of the Technology section

Input/output mapping, costs and engineering specifications

Parameter name	Index dimensions
input [9]	node_loc | tec | year_vtg | year_act | mode | node_origin | commodity | level | time | time_origin
output [9]	node_loc | tec | year_vtg | year_act | mode | node_dest | commodity | level | time | time_dest
inv_cost [9]	node_loc | tec | year_vtg
fix_cost [9]	node_loc | tec | year_vtg | year_act
var_cost [9]	node_loc | tec | year_vtg | year_act | mode | time
levelized_cost [10]	node_loc | tec | year_vtg | time
construction_time [11]	node_loc | tec | year_vtg
technical_lifetime	node_loc | tec | year_vtg
capacity_factor [9]	node_loc | tec | year_vtg | year_act | time
operation_factor [9]	node_loc | tec | year_vtg | year_act
min_utilization_factor [9]	node_loc | tec | year_vtg | year_act
rating_bin [12]	node | tec | year_act | commodity | level | time | rating
reliability_factor [8]	node | tec | year_act | commodity | level | time | rating
flexibility_factor [13]	node_loc | tec | year_vtg | year_act | mode | commodity | level | time | rating
renewable_capacity_factor [14]	node_loc | commodity | grade | level | year
renewable_potential [14]	node | commodity | grade | level | year
emission_factor	node_loc | tec | year_vtg | year_act | mode | emission

[9] (1,2,3,4,5,6,7,8)

Fixed and variable cost parameters and technical specifications are indexed over both the year of construction (vintage) and the year of operation (actual). This allows to represent changing technology characteristics depending on the age of the plant.

[10]

The parameter levelized_cost is computed in the GAMS pre-processing under the assumption of full capacity utilization until the end of the technical lifetime. As these are calculated in the preprocessing, the reported levelized_cost in the output GDX-file exclude fuel costs.

[11]

The construction time only has an effect on the investment costs; in MESSAGEix, each unit of new-built capacity is available instantaneously at the beginning of the model period.

[12]

Maximum share of technology in commodity use per rating. The upper bound of a contribution by any technology to the constraints on system reliability (Reliability of installed capacity) and flexibility (Equation SYSTEM_FLEXIBILITY_CONSTRAINT) can depend on the share of the technology output in the total commodity use at a specific level.

[13]

Contribution of technologies towards operation flexibility constraint. It is used in Equation SYSTEM_FLEXIBILITY_CONSTRAINT.

[14] (1,2)

renewable_capacity_factor refers to the quality of renewable potential by grade and renewable_potential refers to the size of the renewable potential per grade.

Bounds on capacity and activity

The following parameters specify upper and lower bounds on new capacity, total installed capacity, and activity. The bounds on activity are implemented as the aggregate over all vintages in a specific period (Equation ACTIVITY_BOUND_UP and Equation ACTIVITY_BOUND_LO).

Parameter name	Index names
bound_new_capacity_up	node_loc | tec | year_vtg
bound_new_capacity_lo	node_loc | tec | year_vtg
bound_total_capacity_up	node_loc | tec | year_act
bound_total_capacity_lo	node_loc | tec | year_act
bound_activity_up	node_loc | tec | year_act | mode | time
bound_activity_lo	node_loc | tec | year_act | mode | time

Dynamic constraints on new capacity and activity

These parameters are used in the dynamic constraint equations to limit the growth (or decline) of activity or of new capacity in each period, relative to the preceding period. The soft_ parameters control ‘soft’ relaxation of these dynamic constraints, using the method of Keppo and Strubegger (2010) [5].

The growth_ and soft_ parameters are expressed as relative annual change and are unitless. Because these are annual values, are compounded in the constraint equations by duration_period (\(|y|\)) to obtain the relative inter-period change.

Example: a value of 0.05 for growth_activity_up sets an upper bound of \(1 + 0.05 = 105\%\) activity in one year relative to activity in the preceding year. In a period with duration \(|y| = 5 \text{ years}\), the activity in the representative year is bounded at \((1.05)^5 = 128\%\) of the activity in the representative year of the preceding period.

Because these parameters do not have a mode (\(m\)) dimension, they cannot be used to constraint the activity/new capacity of single modes of technologies; only the total across all modes.

Parameter name	Index names
initial_new_capacity_up	node_loc | tec | year_vtg
growth_new_capacity_up	node_loc | tec | year_vtg
soft_new_capacity_up	node_loc | tec | year_vtg
initial_new_capacity_lo	node_loc | tec | year_vtg
growth_new_capacity_lo	node_loc | tec | year_vtg
soft_new_capacity_lo	node_loc | tec | year_vtg
initial_activity_up	node_loc | tec | year_act | time
growth_activity_up	node_loc | tec | year_act | time
soft_activity_up	node_loc | tec | year_act | time
initial_activity_lo	node_loc | tec | year_act | time
growth_activity_lo	node_loc | tec | year_act | time
soft_activity_lo	node_loc | tec | year_act | time

Parameters for the add-on technologies

The implementation of MESSAGEix includes the functionality to introduce “add-on technologies” that are specifically linked to parent technologies. This feature can be used to model mitigation options (scrubber, cooling). Upper and lower bounds of add-on technologies are defined relative to the parent: addon_up and addon_lo, respectively.

Note

No default addon_conversion factor (conversion factor between add-on and parent technology activity) is set. This is to avoid default conversion factors of 1 being set for technologies with multiple modes, of which only a single mode should be linked to the add-on technology.

Parameter name	Index names
addon_conversion	node | tec | year_vtg | year_act | mode | time | type_addon
addon_up	node | tec | year_act | mode | time | type_addon
addon_lo	node | tec | year_act | mode | time | type_addon

Parameters for representing storage solutions

The MESSAGEix formulation includes “storage” solutions to model sub-annual, inter-temporal storage of commodities in each period. This feature can be used to model electricity storage (pumped hydro, batteries, compressed air energy storage, etc.), thermal energy storage, demand side management, and in general any technology for storing commodities (gas, hydrogen, water, etc.) over sub-annual timesteps. The user defines the chronological order of sub-annual time slices by assigning a number to them in parameter time_order. This order is used by storage equations to shift the stored commodity in a correct timeline, e.g., from Jan through to Dec, and not vice versa. The last sub-annual time slice is linked to the first one to close the loop of the year. Parameter storage_initial is to set an initial amount for the content of storage in any desirable time slice (optionally). This initial value is a cost-free stored media that storage can discharge in the same or following time slices. storage_self_discharge represents the self-discharge (loss) of storage as % of the level of stored media in each time slice. This allows to model time-related losses in storage separately, in addition to charging and discharging losses.

Parameter name	Index names
storage_initial	node | tec | level | commodity | year_act | time
storage_self_discharge	node | tec | level | commodity | year_act | time
time_order	lvl_temporal | time

Cost parameters for ‘soft’ relaxations of dynamic constraints

The implementation of MESSAGEix includes the functionality for ‘soft’ relaxations of dynamic constraints on new-built capacity and activity (see Keppo and Strubegger, 2010 [5]). Refer to the section Dynamic constraints on new capacity and activity. Absolute cost and levelized cost multipliers are used for the relaxation of upper and lower bounds.

Parameter name	Index names
abs_cost_new_capacity_soft_up	node_loc | tec | year_vtg
abs_cost_new_capacity_soft_lo	node_loc | tec | year_vtg
level_cost_new_capacity_soft_up	node_loc | tec | year_vtg
level_cost_new_capacity_soft_lo	node_loc | tec | year_vtg
abs_cost_activity_soft_up	node_loc | tec | year_act | time
abs_cost_activity_soft_lo	node_loc | tec | year_act | time
level_cost_activity_soft_up	node_loc | tec | year_act | time
level_cost_activity_soft_lo	node_loc | tec | year_act | time

Historical capacity and activity values

To model the transition of an energy system, the initial energy system with its energy mix needs to be defined first. The historical activity and the historical new capacity do this. These parameters have to be defined in order to limit the capacity in the first model period.

Historical data on new capacity and activity levels are therefore included in MESSAGEix for correct accounting of the vintage portfolio and a seamless implementation of dynamic constraints from historical years to model periods.

Parameter name	Index names
historical_new_capacity [6]	node_loc | tec | year_vtg
historical_activity [6]	node_loc | tec | year_act | mode | time

The activity in the historic period can be defined with

\[\begin{split}\sum_{m} \text{ACT}_{n,t,y^V,y,m,h} \leq \text{duration_time}_{h} \cdot \text{capacity_factor}_{n,t,y^V,y,h} \\ \cdot \text{CAP}_{n,t,y^V,y} \quad t \ \in \ T^{\text{INV}}\end{split}\]

and the historical new capacity with

\[\text{CAP_NEW}_{n,t,y^V} = \frac{\text{CAP}_{n,t,y^V,y}}{\text{duration_period}_{y}}\]

Both equations are equally valid for model periods. However, to calculate historical_new_capacity and historical_activity all parameters must describe the historic period.

The duration_period of the first period (historic period) is set to the value that appears most frequently in the model. If, for example, the majority of periods in the model consists of 10 years, the duration_period of the first period is likewise 10 years.

Auxiliary investment cost parameters and multipliers

Auxiliary investment cost parameters include the remaining technical lifetime at the end of model horizon (beyond_horizon_lifetime) in addition to the different scaling factors and multipliers as listed below. These factors account for remaining capacity (remaining_capacity) or construction time of new capacity (construction_time_factor), the value of investment at the end of model horizon (end_of_horizon_factor) or the discount factor of remaining lifetime beyond model horizon (beyond_horizon_factor).

Parameter name	Index names
construction_time_factor	node | tec | year
remaining_capacity	node | tec | year
end_of_horizon_factor	node | tec | year
beyond_horizon_lifetime	node | tec | year
beyond_horizon_factor	node | tec | year

Parameters of the Emission section

The implementation of MESSAGEix includes a flexible and versatile accounting of emissions across different categories and species, with the option to define upper bounds and taxes on various (aggregates of) emissions and pollutants, (sets of) technologies, and (sets of) years.

Parameter name	Index dimensions
historical_emission [6]	node | emission | type_tec | year
emission_scaling [15]	type_emission | emission
bound_emission	node | type_emission | type_tec | type_year
tax_emission	node | type_emission | type_tec | type_year

[15]

The parameter emission_scaling is the scaling factor to harmonize bounds or taxes across types of emissions. It allows to efficiently aggregate different emissions/pollutants and set bounds or taxes on various categories.

Parameters of the Land-Use model emulator section

The implementation of MESSAGEix includes a land-use model emulator, which draws on exogenous land-use scenarios (provided by another model) to derive supply of commodities (e.g., biomass) and emissions from agriculture and forestry. The parameters listed below refer to the assigned land scenario.

Parameter name	Index dimensions
historical_land [6]	node | land_scenario | year
land_cost	node | land_scenario | year
land_input	node | land_scenario | year | commodity | level | time
land_output	node | land_scenario | year | commodity | level | time
land_use	node | land_scenario | year | land_type
land_emission	node | land_scenario | year | emission
initial_land_scen_up	node | land_scenario | year
growth_land_scen_up	node | land_scenario | year
initial_land_scen_lo	node | land_scenario | year
growth_land_scen_lo	node | land_scenario | year
initial_land_up	node | year | land_type
dynamic_land_up	node | land_scenario | year | land_type
growth_land_up	node | year | land_type
initial_land_lo	node | year | land_type
dynamic_land_lo	node | land_scenario | year | land_type
growth_land_lo	node | year | land_type

Parameters of the Share Constraints section

Share constraints define the share of a given commodity/mode to be active on a certain level. For the mathematical formulation, refer to Constraints on shares of technologies and commodities.

Parameter name	Index dimensions
share_commodity_up	shares | node_share | year_act | time
share_commodity_lo	shares | node | year_act | time
share_mode_up	shares | node_loc | technology | mode | year_act | time
share_mode_lo	shares | node_loc | technology | mode | year_act | time

Parameters of the Relations section

Generic linear relations are implemented in MESSAGEix. This feature is intended for development and testing only - all new features should be implemented as specific new mathematical formulations and associated sets & parameters. For the formulation of the relations, refer to Section of generic relations (linear constraints).

Parameter name	Index dimensions
relation_upper	relation | node_rel | year_rel
relation_lower	relation | node_rel | year_rel
relation_cost	relation | node_rel | year_rel
relation_new_capacity	relation | node_rel | year_rel | tec
relation_total_capacity	relation | node_rel | year_rel | tec
relation_activity	relation | node_rel | year_rel | node_loc | tec | year_act | mode

Fixed variable values

The following parameters allow to set variable values to a specific value. The value is usually taken from a solution of another model instance (e.g., scenarios where a shock sets in later to mimic imperfect foresight).

The fixed values do not override any upper or lower bounds that may be defined, so fixing variables to values outside of that range will yield an infeasible model.

Parameter name	Index dimensions
fixed_extraction	node | commodity | grade | year
fixed_stock	node | commodity | level | year
fixed_new_capacity	node | technology | year_vtg
fixed_capacity	node | technology | year_vtg | year_act
fixed_activity	node | technology | year_vtg | year_act | mode | time
fixed_land	node | land_scenario | year

Note that the variable \(\text{STOCK_CHG}\) is determined implicitly by the \(\text{STOCK}\) variable and therefore does not need to be explicitly fixed.

Auxiliary reporting parameters

The following parameters are used for reporting (post-processing) solved models. They assign monetary value to the net total system costs from trading and emission taxes (total_cost). Morevoer, they also assign a value to the total trade of commodities (the difference between the revenues from exports and the costs of imports, trade_cost) and to the costs from importing (import_cost) and the revenues from exporting (export_cost) in each node and year.

Parameter name	Index dimensions
total_cost	node | year
trade_cost	node | year
import_cost	node | commodity | year
export_cost	node | commodity | year