Variables

In the following, all variables used in AnyMOD are listed. Information includes the name used throughout the model, the variables' unit, and its dimensions according to the symbols introduced in Sets and Mappings. Also, it is specified what determines the instances a variable is actually created for, in which constraints a variable appears, and the model part it is assigned to.

To increase performance, AnyMOD stores variables within DataFrames instead of using JuMPs native containers. Each variable dimension is represented by a column and integers in these columns relate to nodes within the hierarchical trees of sets (see printObject on how to export these in a readable format). An additional var column stores the corresponding variables. These variables are not JuMP variable objects, but JuMP expressions, that already include scaling factors.

All variables are defined positive. New variables beyond those listed here can freely be added to a model by using standard JuMP commands.

Dispatch of technologies

Generation and use

Quantities generated and used by technology.

To reduce model size variables are not created, if the availability is zero. Also, mode dependant variables are only created where required. For example, for a technology with mode specific generation ratios, different variables for each mode are only created for gen, but not for use.

name	gen	use
unit	GWh
dimension	$Ts_{exp}$, $Ts_{dis}$, $R_{dis}$, $C$, $Te$, ($M$)
instances	dispatch resolution of carrier expansion time-steps of technology relevant modes of technology respective availability exceeds zero
related constraints	energy balance conversion balance conversion capacity restriction energy ratio restriction variable cost equation
part	technology

Charging and discharging

Externally and internally charged and discharged quantities (see Technologies for explanation).

To reduce model size variables are not created, if the availability is zero. Also, mode dependant variables are only created where required.

name	stExt{In/Out}	stInt{In/Out}
unit	GWh
dimension	$Ts_{exp}$, $Ts_{dis}$, $R_{dis}$, $C$, $Te$, ($M$)
instances	dispatch resolution of carrier expansion time-steps of technology relevant modes of technology respective availability exceeds zero
related constraints	energy balance storage balance storage capacity restriction variable cost equation
		conversion balance
part	technology

Storage level

Quantity stored by storage system.

To reduce model size variables are not created, if the availability is zero. Also, mode dependant variables are only created where required.

name	stLvl
unit	GWh
dimension	$Ts_{exp}$, $Ts_{dis}$, $R_{dis}$, $C$, $Te$, ($M$)
instances	dispatch resolution of carrier expansion time-steps of technology relevant modes of technology availability exceeds zero
related constraints	storage balance storage capacity restriction
part	technology

Non-technology dispatch

Exchange quantities

Quantity exchanged from one region to the other. The variable is directed meaning it only denotes exchange into one direction.

Variables are only created between regions that can actually exchange energy, which depends on the definition of residual capacity.

name	exc
unit	GWh
dimension	$Ts_{dis}$, $R_{from}$, $R_{to}$, $C$
instances	dispatch resolution of carrier residual capacity between regions defined
related constraints	energy balance exchange capacity restriction variable cost equation
part	exchange

Buy and sell

Quantities bought or sold on an external market.

name	trdBuy	trdSell
unit	GWh
dimension	$Ts_{dis}$, $R_{dis}$, $C$
instances	dispatch resolution of carrier trade price defined
related constraints	energy balance trade capacity restriction trade cost equation
part	trade

Curtailment and loss-of-load

Curtailed quantities and unmet demand.

name	lss	crt
unit	GWh
dimension	$Ts_{dis}$, $R_{dis}$, $C$
instances	dispatch resolution of carrier respective costs defined
related constraints	energy balance curtailment and loss-of-load cost equation
part	balance

Capacity expansion

Expansion

Expansion of conversion, storage-input, storage-output, storage-size, and exchange capacity.

As explained here, capacity refers to capacity before efficiency!

name	expConv	expSt{In/Out/Size}	expExc
unit	GW
dimension	$Ts_{exp}$, $R_{exp}$, $Te$	$Ts_{exp}$, $R_{exp}$, $C$, $Te$	$Ts_{exp}$, $R_{from}$, $R_{to}$, $C$
instances	expansion resolution of technology		regions can exchange carrier expansion resolution of carrier
	if uses or generates carriers	each stored carrier
related constraints	definition of installed capacity expansion cost equation
part	technology		exchange

Installed capacity

Installed capacity of conversion, storage-input, storage-output, storage-size, and exchange capacity.

As explained here, capacity refers to capacity before efficiency!

name	capaConv	capaSt{In/Out/Size}	capaExc
unit	GW
dimension	$Ts_{exp}$, $R_{exp}$, $Te$	$Ts_{exp}$, $R_{exp}$, $C$, $Te$	$Ts_{exp}$, $R_{from}$, $R_{to}$, $C$
instances	superordinate dispatch resolution (usually years)
	spatial expansion resolution of technology		spatial expansion resolution of carrier regions can exchange carrier
	if uses or generates carriers	each stored carrier
related constraints	definition of installed capacity decommissioning of operated capacitiy
part	technology		exchange

Operated capacity

Operated capacity of conversion, storage-input, storage-output, storage-size, and exchange capacity.

As explained here, capacity refers to capacity before efficiency!

name	oprCapaConv	oprCapaSt{In/Out/Size}	oprCapaExc
unit	GW
dimension	$Ts_{exp}$, $R_{exp}$, $Te$	$Ts_{exp}$, $R_{exp}$, $C$, $Te$	$Ts_{exp}$, $R_{from}$, $R_{to}$, $C$
instances	superordinate dispatch resolution (usually years)
	spatial expansion resolution of technology		spatial expansion resolution of carrier regions can exchange carrier
	if uses or generates carriers	each stored carrier
related constraints	decommissioning of operated capacitiy operating cost equation
	conversion capacity restriction	storage capacity restriction	exchange capacity restriction
part	technology		exchange

Costs

The variables listed here solely serve the purpose to aggregate different kinds of costs and do not have any other function within the model. Therefore, their structure is a bit arbitrary and was chosen to facilitate reporting without adversely affecting performance.

Expansion cost

Costs of capacity expansion.

As explained here, capacity and thus also costs of capacity expansion, refer to capacity before efficiency!

name	costExp{Conv,StIn,StOut,StSize}	costExp{Exc}
unit	Mil.€
dimension	$Ts_{exp}$, $R_{exp}$, $Te$	$Ts_{exp}$, $C$
instances	expansion cost defined
related constraints	expansion cost equation
part	objective

Operating cost

Costs of operating capacity.

As explained here, capacity and thus also operating costs, refer to capacity before efficiency!

name	costOpr{Conv,StIn,StOut,StSize}	costOpr{Exc}
unit	Mil.€
dimension	$Ts_{sup}$, $R_{exp}$, $Te$	$Ts_{sup}$, $C$
instances	operating cost defined
related constraints	operating cost equation
part	objective

Variable cost

Variable costs associated with quantities dispatched. Costs incurred by emission prices are included in costVarUse.

name	costVar{Use,Gen,StIn,StOut}	costVar{Exc}
unit	Mil.€
dimension	$Ts_{sup}$, $R_{exp}$, $Te$	$Ts_{sup}$, $C$
instances	variable cost defined emission factor and emission price defined in case of use
related constraints	variable cost equation
part	objective

Trade cost

Costs and revenues from buying or selling carriers on an external market.

name	costTrdBuy	costTrdSell
unit	Mil.€
dimension	$Ts_{sup}$, $R_{exp}$, $C$
instances	trade price defined
related constraints	trade cost equation
part	objective

Curtailment and loss-of-load cost

Cost of curtailment and unmet demand.

To allow for revenues and costs from curtailment, costCrt is the only model variable that can also take negative values.

name	costCrt	costLss
unit	Mil.€
dimension	$Ts_{sup}$, $R_{exp}$, $C$
instances	respective costs defined
related constraints	curtailment and loss-of-load cost equation
part	objective