# 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 | ||

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 | ||

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 | ||

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 | ||

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 | ||

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 | ||

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 | |||

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 | |||

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 | 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 | |||

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 | ||

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 | ||

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 | ||

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 | ||

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 | ||

part | objective |