Variables

AccumulatedNewCapacity

Sets: [Year,Technology,Region] Unit: [GW]

Represents the total amount of capacity that was built in previous years and remains operational in the current year. It is defined as the sum of all past new-capacity additions within their defined operational lifetime.

AccumulatedNewStorageCapacity

Sets: [Storage,Year,Region] Unit: [PJ]

Represents the total amount of storage capacity that was built in previous years and remains operational in the current year; defined as the sum of all past new-storage-capacity additions within their defined operational lifetime.

AnnualCurtailmentCost

Sets: [Year,Fuel,Region] Unit: [M€]

The yearly expense assigned to curtailing energy. It is computed by multiplying the curtailed-energy volume in year y by its per-unit curtailment cost factor.

AnnualEmissions

Sets: [Year,Emission,Region] Unit: [Mt]

Total emissions of pollutant in a specific region for one year, defined as the sum of all technology-specific emissions. This aggregated figure is then used to enforce regional and system-wide emission limits.

AnnualFixedOperatingCost

Sets: [Year,Technology,Region] Unit: [M€]

The annual fixed operating cost for a given technology and location, calculated as the sum of fixed‐cost charges on all capacity still in service (both newly built and existing).

AnnualProductionChangeCost

Sets: [Year,Technology,Region] Unit: [M€]

The total cost over a year for adjusting a dispatchable generator’s output up or down, computed by summing all increases and decreases in output and multiplying by the per-unit production-change cost.

AnnualSectoralEmissions

Sets: [Year,Emission,Sector,Region] Unit: [Mt]

Represents the total emissions of a given pollutant from a specific sector in a particular region and year. It is calculated as the sum of all technology-level emissions assigned to that sector in that region and year, and is used to enforce the annual sectoral emission cap (if defined).

AnnualTechnologyEmission

Sets: [Year,Technology,Emission,Region] Unit: [Mt]

Defined as the total emissions of a given pollutant from a specific technology in a particular region and year.

AnnualTechnologyEmissionByMode

Sets: [Year,Technology,Emission,Mode of Operation,Region] Unit: [Mt]

Represents the annual mass of a specific pollutant emitted by a given technology when running in a particular operating mode within a region. It is computed by taking that technology’s total yearly activity in the chosen mode, multiplying by the mode’s fuel‐input ratios, and then applying the pollutant content per unit of each fuel.

AnnualTechnologyEmissionPenaltyByEmission

Sets: [Year,Technology,Emission,Region] Unit: [M€]

The penalty cost assigned to a technology for emitting a particular pollutant in a given year and location, calculated by multiplying its annual emissions of that pollutant by the applicable penalty rate.

AnnualTechnologyEmissionsPenalty

Sets: [Year,Technology,Region] Unit: [M€]

AnnualTechnologyEmissionPenaltyByEmission summed over all emissions.

AnnualTotalTradeCosts

Sets: [Year,Region] Unit: [M€]

The total yearly expense for trading fuels between regions, calculated by summing each imported fuel volume (across all routes and timeslices) multiplied by its per-unit trade cost.

AnnualVariableOperatingCost

Sets: [Year,Technology,Region] Unit: [M€]

The annual variable operating cost reflects what it costs to run a technology over the year, based on its output. Therefore, it is computed as the multiplication of technology activity with the VariableCost parameter.

CapitalInvestment

Sets: [Year,Technology,Region] Unit: [M€]

The total money spent on adding new capacity in a given year and region, calculated by multiplying the per-unit capital cost by the amount of capacity built.

CapitalInvestmentStorage

Sets: [Storage,Year,Region] Unit: [M€]

The total money spent on adding new storage capacity in a given year and region, calculated by multiplying the per-unit capital cost by the amount of capacity of the storage built.

CurtailedCapacity

Sets: [Region,Timeslice,Technology,Year] Unit: [GW]

Represents the portion of installed capacity at a given site and timeslot that remains idle even though it is technically able to operate. In other words, although that capacity could generate energy, it is held back—often because there is more supply than demand, grid limitations, or economic reasons.

CurtailedEnergy

Sets: [Year,Timeslice,Fuel,Region] Unit: [PJ]

Represents the quantity of energy in a single timeslice that was withheld even though capacity was available, calculated by converting each unit of idle capacity into its equivalent energy output.

CurtailedEnergyAnnual

Sets: [Year,Fuel,Region] Unit: [PJ]

Represents the yearly total of energy not produced despite available capacity, obtained by summing all curtailed-energy values across every timeslice for a given fuel and region.

DemandNeedingReserveMargin

Sets: [Year,Timeslice,Region] Unit: [PJ]

Represents, for each time slice and region, the amount of demand that must be backed by generators tagged as reserve-eligible. It is calculated by summing all reserve-capable output (weighted by conversion factors, time-slice shares, and reserve tags) to ensure the required reserve margin is met.

DemandSplitByModalType

Sets: [ModalType,Timeslice,Region,Fuel,Year] Unit: [gpkm/gtkm]

Denotes the portion of a region’s specified fuel demand allocated to each transport mode and time slice. It is obtained by multiplying the annual demand for that fuel by the mode-specific share and the time-slice profile.

DiscountedAnnualCurtailmentCost

Sets: [Year,Fuel,Region] Unit: [M€]

Represents the net-present-value cost of energy curtailment in a given year for a specific fuel and region, calculated by taking the undiscounted annual curtailment cost and discounting it with the respective DiscountRate to the base year.

DiscountedAnnualProductionChangeCost

Sets: [Year,Technology,Region] Unit: [M€]

Reflects the discounted value of all ramp-up and ramp-down costs for a particular generation technology in a given region over a year, obtained by applying the technology-specific discount rate to the annual production change cost.

DiscountedAnnualTotalTradeCosts

Sets: [Year,Region] Unit: [M€]

Denotes the net-present-value of the total cost of importing fuels into a region during the year, calculated by discounting the sum of its undiscounted annual trade costs by the regional discount rate.

DiscountedCapitalInvestment

Sets: [Year,Technology,Region] Unit: [M€]

Represents the discounted total spending on new capacity additions for a given technology and region in a year, obtained by applying the technology-specific discount rate to that year’s undiscounted capital investment for each technology.

DiscountedCapitalInvestmentStorage

Sets: [Storage,Year,Region] Unit: [M€]

Captures the net-present-value of all capital spending on new storage capacity of a particular storage technology in a region and year, computed by dividing the year’s undiscounted storage investment by the region’s discount factor.

DiscountedNewTradeCapacityCosts

Sets: [Year,Fuel,Region,Region] Unit: [M€]

Represents the discounted cost of expanding cross-regional trade capacities for a given fuel pair in a particular year, obtained by applying the appropriate discount rate to that year’s undiscounted investment in new trade infrastructure.

DiscountedOperatingCost

Sets: [Year,Technology,Region] Unit: [M€]

Denotes the net-present-value of all variable and fixed operating costs for a given technology in a region over the year, calculated by discounting the sum of its undiscounted annual operating costs.

DiscountedSalvageValue

Sets: [Year,Technology,Region] Unit: [M€]

Reflects the net-present-value benefit of retiring remaining capacity for a particular technology and region in a given year, computed by applying the discount factor to that year’s undiscounted salvage value for the retired capacity.

DiscountedSalvageValueStorage

Sets: [Storage,Year,Region] Unit: [M€]

Captures the net-present-value of salvaging any remaining storage capacity of a given storage technology in a region during that year, calculated by discounting the undiscounted salvage value by the regional discount rate.

DiscountedSalvageValueTransmission

Sets: [Year,Region] Unit: [M€]

Represents the net-present-value gain from retiring transmission assets within a region in a given year, obtained by applying the appropriate discount factor to the undiscounted salvage value of those transmission lines.

DiscountedTechnologyEmissionsPenalty

Sets: [Year,Technology,Region] Unit: [M€]

Denotes the net-present-value cost of all emissions penalties incurred by a specific generation technology in a region over the year, calculated by discounting the sum of its emission-based penalties.

Export

Sets: [Year,Timeslice,Fuel,Region,Region] Unit: [PJ]

Amount of a fuel exported from one region to another in a specific timeslice in one specific year.

Import

Sets: [Year,Timeslice,Fuel,Region,Region] Unit: [PJ]

Amount of a given fuel imported into a region from another region during a specific timeslice in a specific year. The model enforces that exports from Region A to Region B exactly match imports into Region B from Region A, ensuring a balanced trade flow.

ModelPeriodCostByRegion

Sets: [Region] Unit: [M€]

Represents the cumulative net-present-value cost incurred in each region over the entire model period, calculated by summing that region’s TotalDiscountedCost across all years.

ModelPeriodEmissions

Sets: [Region,Emission] Unit: [Mt]

Represents the cumulative emissions of a pollutant in a specific region over the entire model horizon, including exogenous emissions. It is used to enforce emission limits over the entire model period.

NetTrade

Sets: [Year,Timeslice,Fuel,Region] Unit: [PJ]

Net trade measures, for each region, fuel, year, and time slice, which shows the difference between exports (adjusted upward to account for trade losses) and imports into that region.

NetTradeAnnual

Sets: [Year,Fuel,Region] Unit: [PJ]

Represents the yearly net volume of a specific fuel traded by a region , calculated as the sum of net trade across all time slices. A positive value indicates the region, across the year, exports more energy than it imports (net exporter), while a negative value means it receives more energy than it exports (net importer).

NewCapacity

Sets: [Year,Technology,Region] Unit: [GW]

Represents the amount of new generation capacity added in a given year and region, measured in Gigawatts (for most technologies).

NewStorageCapacity

Sets: [Storage,Year,Region] Unit: [PJ]

Represents the amount of new storage capacity added in a given year and region, measured in energy units (usually Petaojoules).

NewTradeCapacity

Sets: [Year,Fuel,Region,Region] Unit: [GW/PJ]

Represents the additional inter-regional transport capacity installed in a given year for the trade of a specific fuel between two regions. Electricity transmission is given in GW, gas pipelines are given in PJ/year.

NewTradeCapacityCosts

Sets: [Year,Fuel,Region,Region] Unit: [M€]

Represents the annual cost of building additional trade capacity for a fuel between two regions, calculated as the new capacity amount multiplied by the per-unit growth cost and the distance of that trade route.

OperatingCost

Sets: [Year,Technology,Region] Unit: [M€]

Represents the total annual expense to run a technology at a location, computed by summing its fixed and variable operating costs.

Production

Sets: [Year,Timeslice,Fuel,Region] Unit: [PJ]

Represents the energy output of a given fuel in a particular region during a specific timeslice, calculated by summing the production of that fuel of all technologies.

ProductionAnnual

Sets: [Year,Fuel,Region] Unit: [PJ]

Denotes the total yearly energy output of a given fuel in a region, obtained by summing all production values for that fuel for all technologies across the entire year.

ProductionByTechnology

Sets: [Year,Timeslice,Technology,Fuel,Region] Unit: [PJ]

Amount of fuel produced by a single technology in a region during one timeslice.

ProductionByTechnologyAnnual

Sets: [Year,Technology,Fuel,Region] Unit: [PJ]

Gives the annual total energy of a particular fuel produced by a single technology in a region, calculated as the sum of technology outputs for that fuel for all timeslices in the year.

ProductionDownChangeInTimeslice

Sets: [Year,Timeslice,Fuel,Technology,Region] Unit: [PJ]

Measures the decrease in energy production of a given fuel by a specific technology from the previous timeslice to the current one, capturing downward ramping.

ProductionSplitByModalType

Sets: [ModalType,Timeslice,Region,Fuel,Year] Unit: [%]

Indicates the percentage share of a fuel’s production in a region and timeslice that is allocated to a particular transport mode, determined by tagging each technology-mode pair and dividing its fuel output by the total fuel production in that slice.

ProductionUpChangeInTimeslice

Sets: [Year,Timeslice,Fuel,Technology,Region] Unit: [PJ]

Measures the increase in energy production of a given fuel by a specific technology from the previous timeslice to the current one, capturing upward ramping.

RateOfActivity

Sets: [Year,Timeslice,Technology,Mode of Operation,Region] Unit: [GW]

Represents the actual power output of a given technology running in a specific mode and region during a single timeslice. The sum of all mode-specific RateOfActivity values for that technology equals its total available capacity (after applying availability, minus any reserved or curtailed capacity).

RateOfProduction

Sets: [Year,Timeslice,Fuel,Region] Unit: [GW]

Denotes the instantaneous generation rate of a particular fuel in a region during one timeslice, calculated by adding up each technology’s combined mode-specific production rates for that fuel.

RateOfProductionByTechnology

Sets: [Year,Timeslice,Technology,Fuel,Region] Unit: [GW]

Specifies the instantaneous production rate (usually in GW) of a particular fuel by one technology in a region during a timeslice, obtained by summing that technology’s mode-specific production rates for the fuel.

RateOfProductionByTechnologyByMode

Sets: [Year,Timeslice,Technology,Mode of Operation,Fuel,Region] Unit: [GW]

Gives the instantaneous production rate (usually in GW) of a particular fuel by a specific technology operating in one mode of operation and region during a timeslice.

RateOfTotalActivity

Sets: [Year,Timeslice,Technology,Region] Unit: [GW]

Represents the total capacity (usually in GW) of a technology that operates in a region during a timeslice, summed across all its operating modes.

RateOfUse

Sets: [Year,Timeslice,Fuel,Region] Unit: [GW]

Denotes the instantaneous fuel consumption rate for a given fuel in a region and timeslice, obtained by summing all technologies’ mode-specific usage rates for that fuel.

RateOfUseByTechnology

Sets: [Year,Timeslice,Technology,Fuel,Region] Unit: [GW]

Specifies the instantaneous consumption rate of a particular fuel by one technology in a region during a timeslice, calculated by summing that technology’s mode-specific usage rates for the fuel (including time‐dependent efficiencies).

RateOfUseByTechnologyByMode

Sets: [Year,Timeslice,Technology,Mode of Operation,Fuel,Region] Unit: [GW]

Gives the instantaneous consumption rate of a specific fuel by a technology running in a certain mode and region during a timeslice.

RETargetMin

Sets: [Year,Region] Unit: [PJ]

RETotalDemandOfTargetFuelAnnual

Sets: [Year,Region,Fuel] Unit: [PJ]

SalvageValue

Sets: [Year,Technology,Region] Unit: [M€]

Represents the remaining undepreciated value of newly built capacity at the end of the model horizon, for each technology and region. For any unit of capacity added in year y, if its operational lifetime extends beyond the final model year, that leftover portion is considered a “salvage” asset with some resale or secondary-use value. Two depreciation methods determine how much of the original capital cost survives at the horizon:

  • DepreciationMethod 1: Annuitized:

When a technology’s discount rate is positive, the asset’s full operational life extends past the last model year, and the DepreciationMethod 1 is chosen, the model computes salvage as follows:

\[{\small SalvageValue_{y,t,r} = \; CapitalCost_{r,t,y}\;\cdot\; NewCapacity_{y,t,r} \;\left(\, 1 \;-\; \frac{ \bigl(1 + DiscountRate_{r,t}\bigr)^{\,\bigl(\max(\mathcal{Y}) - y + 1\bigr)} \;-\; 1 }{ \bigl(1 + DiscountRate_{r,t}\bigr)^{\,\bigl(OperationalLife_t\bigr)} \;-\; 1 } \right) }\]

  • DepreciationMethod 2: Straight-Line:

If a technology’s discount rate is zero (so Method 1 would divide by zero), or DepreciationMethod 2 is chosen, the salvage calculation falls back to straight-line depreciation:

\[{\small SalvageValue_{y,t,r} = \; CapitalCost_{r,t,y}\;\cdot\; NewCapacity_{y,t,r} \;\left(\, 1 \;-\; \frac{ \bigl(\max(\mathcal{Y}) - y + 1\bigr) }{ \bigl(OperationalLife_{t}\bigr) } \right) }\]

SalvageValueStorage

Sets: [Storage,Year,Region] Unit: [M€]

Represents the remaining undepreciated value of storage capacity at the end of the model horizon, analogous to how SalvageValue captures undepreciated value for generation technologies.

StorageLevelTSStart

Sets: [Storage,Year,Timeslice,Region] Unit: [PJ]

Represents the state of charge at the beginning of each timeslice for a given storage asset in a region. For any timeslice beyond the first, it equals the previous timeslice’s start level plus the net charging minus discharging, all scaled by the timeslice fraction. For the first timeslice, it is initialized from the year-start level. It is also constrained not to exceed the sum of available storage capacity.

StorageLevelYearFinish

Sets: [Storage,Year,Region] Unit: [PJ]

The state of charge at the end of each year for a given storage asset and region, which by construction equals the level at the start of the same year (ensuring a cyclical, year-to-year accounting of stored energy).

StorageLevelYearStart

Sets: [Storage,Year,Region] Unit: [PJ]

The state of charge at the beginning of each year for a storage asset and region, which must lie between storage-specific upper and lower bounds based on the total storage capacity.

StorageLowerLimit

Sets: [Storage,Year,Region] Unit: [PJ]

Defines the minimum allowable storage level for each asset, year, and region, set as a fixed fraction of total available storage capacity to ensure a required minimum reserve of stored energy.

StorageUpperLimit

Sets: [Storage,Year,Region] Unit: [PJ]

Defines the maximum allowable storage level for each asset, year, and region expressed as a fraction of total available storage capacity so that storage holdings cannot exceed physical capacity.

TotalActivityInReserveMargin

Sets: [Region,Year,Timeslice] Unit: [GW]

Represents, for each region and timeslice, the total energy-equivalent output from all generators that qualify as reserve-eligible. It is calculated by summing each technology’s timeslice-level generation only for those technologies and fuels tagged to provide reserves, thereby measuring the amount of capacity available to meet the reserve margin requirements.

TotalActivityPerYear

Sets: [Region,Timeslice,Technology,Year] Unit: [PJ]

Represents the total potential energy a technology could generate in a region during a specific timeslice and year.

TotalAnnualTechnologyActivityByMode

Sets: [Year,Technology,Mode of Operation,Region] Unit: [PJ]

Denotes the actual annual energy output of a given technology in a particular operating mode and region, obtained by summing its activity over all timeslices in the year.

TotalCapacityAnnual

Sets: [Year,Technology,Region] Unit: [GW]

Denotes the total available capacity of a given technology in a region during a year, calculated as the sum of its residual capacity and the accumulated new capacity still within its operational life.

TotalDiscountedCost

Sets: [Year,Region] Unit: [M€]

Represents the overall net-present-value expenditure for a region in a specific year, obtained by summing:

TotalDiscountedCostByTechnology

Sets: [Year,Technology,Region] Unit: [M€]

Represents the net-present-value cost of operating and investing in a specific technology and region during a given year. It is calculated as the sum of:

minus DiscountedSalvageValue (residual value recovered at horizon).

TotalDiscountedStorageCost

Sets: [Storage,Year,Region] Unit: [M€]

Denotes the net-present-value cost of adding and operating storage capacity in a region during a given year. It equals the DiscountedCapitalInvestmentStorage minus the DiscountedSalvageValue of that storage at the end of the model horizon.

TotalREProductionAnnual

Sets: [Year,Region,Fuel] Unit: [PJ]

Represents the total annual energy output (in PJ) from all renewable technologies producing a given fuel in a region and year. It is used to enforce both minimum renewable production targets and year-to-year growth paths based on specified demand ratios.

TotalTechnologyAnnualActivity

Sets: [Year,Technology,Region] Unit: [PJ]

Represents the total annual energy output of a given technology in a region and year, calculated by summing its annual production across all fuels.

TotalTechnologyModelPeriodActivity

Sets: [Technology,Region] Unit: [PJ]

Represents the sum of a technology’s annual output over the entire model horizon. Therefore, it represents the total energy generation of a technology across all years.

TotalTradeCapacity

Sets: [Year,Fuel,Region,Region] Unit: [GW/PJ]

Represents the total available transport capacity for a specific fuel between two regions in a given year. It equals the preset trade capacity plus any newly added and commissioned trade capacity that comes online that year.

TotalTradeCosts

Sets: [Year,Timeslice,Region] Unit: [M€]

Use

Sets: [Year,Timeslice,Fuel,Region] Unit: [PJ]

Represents the total energy consumption of a given fuel in a region during a specific timeslice.

UseAnnual

Sets: [Year,Fuel,Region] Unit: [PJ]

Represents the total annual energy consumption of a given fuel in a region.

UseByTechnology

Sets: [Year,Timeslice,Technology,Fuel,Region] Unit: [PJ]

Represents the energy content of a fuel consumed by a technology per region and timeslice.

UseByTechnologyAnnual

Sets: [Year,Technology,Fuel,Region] Unit: [PJ]

Represents the total yearly energy of a fuel consumed by a technology in a specific region, calculated by summing the timeslice-level fuel use (in PJ) across all timeslices.

VariableOperatingCost

Sets: [Year,Timeslice,Technology,Region] Unit: [M€]

WeightedAnnualEmissions

Sets: [Year,Emission,Region] Unit: [Mt]

For each region and pollutant, weighted emissions for year y are defined so that they lie halfway between that year’s actual emissions and the next year’s, except in the final year where they simply equal that year’s emissions. This approach ensures that when the model integrates (sums) emissions over the multi-year intervals, it properly approximates the area under as a linear interpolation between those two years.

The following graphs illustrates the two different approaches:

../_images/weighted_emissions.drawio.svg