PowerSystems.ElectricLoad
Formulations
Electric load formulations define the optimization models that describe load units (demand) mathematical model in different operational settings, such as economic dispatch and unit commitment.
The use of reactive power variables and constraints will depend on the network model used, i.e., whether it uses (or does not use) reactive power. If the network model is purely active power-based, reactive power variables and related constraints are not created.
Table of contents
StaticPowerLoad
PowerSimulations.StaticPowerLoad
— TypeFormulation type to add a time series parameter for non-dispatchable ElectricLoad
withdrawals to power balance constraints
Variables:
No variables are created
Time Series Parameters:
Uses the max_active_power
timeseries parameter to determine the demand value at each time-step
Parameter | Default Time Series Name |
---|---|
ReactivePowerTimeSeriesParameter | max_active_power |
ActivePowerTimeSeriesParameter | max_active_power |
Expressions:
Subtracts the parameters listed above from the respective active and reactive power balance expressions created by the selected Network Formulations.
Constraints:
No constraints are created
PowerLoadInterruption
PowerSimulations.PowerLoadInterruption
— TypeFormulation type to enable (binary) load interruptions
Variables:
ActivePowerVariable
:- Bounds: [0.0, ]
- Default initial value: 0.0
- Symbol: $p^\text{ld}$
ReactivePowerVariable
:- Bounds: [0.0, ]
- Default initial value: 0.0
- Symbol: $q^\text{ld}$
OnVariable
:- Bounds: $\{0,1\}$
- Default initial value: 1
- Symbol: $u^\text{ld}$
Static Parameters:
- $P^\text{ld,max}$ =
PowerSystems.get_max_active_power(device)
- $Q^\text{ld,max}$ =
PowerSystems.get_max_reactive_power(device)
Time Series Parameters:
Parameter | Default Time Series Name |
---|---|
ReactivePowerTimeSeriesParameter | max_active_power |
ActivePowerTimeSeriesParameter | max_active_power |
Objective:
Creates an objective function term based on the FunctionData
Options where the quantity term is defined as $p^\text{ld}$.
Expressions:
- Subtract$p^\text{ld}$ and $q^\text{ld}$ terms and to the respective active and reactive power balance expressions created by the selected Network Formulations
Constraints:
\[\begin{aligned} & p_t^\text{ld} \le u_t^\text{ld} \cdot \text{ActivePowerTimeSeriesParameter}_t, \quad \forall t \in \{1,\dots, T\} \\ & q_t^\text{re} = \text{pf} \cdot p_t^\text{re}, \quad \forall t \in \{1,\dots, T\} \end{aligned}\]
on which $\text{pf} = \sin(\arctan(Q^\text{ld,max}/P^\text{ld,max}))$.
PowerLoadDispatch
PowerSimulations.PowerLoadDispatch
— TypeFormulation type to enable (continuous) load interruption dispatch
Variables:
ActivePowerVariable
:- Bounds: [0.0, ]
- Default initial value:
PowerSystems.get_active_power(device)
- Symbol: $p^\text{ld}$
ReactivePowerVariable
:- Bounds: [0.0, ]
- Default initial value:
PowerSystems.get_reactive_power(device)
- Symbol: $q^\text{ld}$
Static Parameters:
- $P^\text{ld,max}$ =
PowerSystems.get_max_active_power(device)
- $Q^\text{ld,max}$ =
PowerSystems.get_max_reactive_power(device)
Time Series Parameters:
Parameter | Default Time Series Name |
---|---|
ReactivePowerTimeSeriesParameter | max_active_power |
ActivePowerTimeSeriesParameter | max_active_power |
Objective:
Creates an objective function term based on the FunctionData
Options where the quantity term is defined as $p^\text{ld}$.
Expressions:
- Subtract$p^\text{ld}$ and $q^\text{ld}$ terms and to the respective active and reactive power balance expressions created by the selected Network Formulations
Constraints:
\[\begin{aligned} & p_t^\text{ld} \le \text{ActivePowerTimeSeriesParameter}_t, \quad \forall t \in \{1,\dots, T\}\\ & q_t^\text{ld} = \text{pf} \cdot p_t^\text{ld}, \quad \forall t \in \{1,\dots, T\}\\ \end{aligned}\]
on which $\text{pf} = \sin(\arctan(Q^\text{ld,max}/P^\text{ld,max}))$.
Valid configurations
Valid DeviceModel
s for subtypes of ElectricLoad
include the following:
Valid DeviceModel | Device Type | Formulation |
---|---|---|
DeviceModel(InterruptiblePowerLoad, PowerLoadDispatch) | InterruptiblePowerLoad | PowerLoadDispatch |
DeviceModel(ExponentialLoad, PowerLoadDispatch) | ExponentialLoad | PowerLoadDispatch |
DeviceModel(PowerLoad, PowerLoadDispatch) | PowerLoad | PowerLoadDispatch |
DeviceModel(StandardLoad, PowerLoadDispatch) | StandardLoad | PowerLoadDispatch |
DeviceModel(InterruptiblePowerLoad, PowerLoadInterruption) | InterruptiblePowerLoad | PowerLoadInterruption |
DeviceModel(ExponentialLoad, PowerLoadInterruption) | ExponentialLoad | PowerLoadInterruption |
DeviceModel(PowerLoad, PowerLoadInterruption) | PowerLoad | PowerLoadInterruption |
DeviceModel(StandardLoad, PowerLoadInterruption) | StandardLoad | PowerLoadInterruption |
DeviceModel(FixedAdmittance, StaticPowerLoad) | FixedAdmittance | StaticPowerLoad |
DeviceModel(InterruptiblePowerLoad, StaticPowerLoad) | InterruptiblePowerLoad | StaticPowerLoad |
DeviceModel(ExponentialLoad, StaticPowerLoad) | ExponentialLoad | StaticPowerLoad |
DeviceModel(PowerLoad, StaticPowerLoad) | PowerLoad | StaticPowerLoad |
DeviceModel(StandardLoad, StaticPowerLoad) | StandardLoad | StaticPowerLoad |
DeviceModel(SwitchedAdmittance, StaticPowerLoad) | SwitchedAdmittance | StaticPowerLoad |