PowerSystems.RenewableGen Formulations

Renewable generation formulations define the optimization models that describe renewable units mathematical model in different operational settings, such as economic dispatch and unit commitment.

Table of contents

1. RenewableFullDispatch
2. RenewableConstantPowerFactor
3. Valid configurations

RenewableFullDispatch

Variables:

• ActivePowerVariable:

  • Bounds: [0.0, ]
  • Symbol: $p^\text{re}$

• ReactivePowerVariable:

  • Bounds: [0.0, ]
  • Symbol: $q^\text{re}$

Static Parameters:

• $P^\text{re,min}$ = PowerSystems.get_active_power_limits(device).min
• $Q^\text{re,min}$ = PowerSystems.get_reactive_power_limits(device).min
• $Q^\text{re,max}$ = PowerSystems.get_reactive_power_limits(device).max

Time Series Parameters:

Uses the max_active_power timeseries parameter to limit the available active power at each time-step.

Objective:

Adds two terms to the objective function based on the FunctionData Options:

• $+ C^\text{re,var} \cdot p_t^\text{re}$ from the variable field of RenewableGenerationCost (the VOM cost of dispatching the unit).
• $- C^\text{re,curt} \cdot p_t^\text{re}$ from the curtailment_cost field of RenewableGenerationCost (an incentive to dispatch up to $\text{ActivePowerTimeSeriesParameter}_t$; defaults to $0$).

The net contribution is $(C^\text{re,var} - C^\text{re,curt}) \cdot p_t^\text{re}$: when $C^\text{re,curt} > C^\text{re,var}$ the cost coefficient is negative, creating a marginal incentive to dispatch up to the time-series limit; when $C^\text{re,curt} < C^\text{re,var}$ the incentive favors curtailment, though system constraints (load balance, reserves) may still require some dispatch. CurtailmentCostExpression reports the per-device dollar value of curtailed energy $C^\text{re,curt} \cdot (p^\text{re,max}_t - p_t^\text{re})$ and is not propagated to ProductionCostExpression.

Expressions:

Adds $p^\text{re}$ and $q^\text{re}$ terms to the respective active and reactive power balance expressions created by the selected Network Formulations.

Constraints:

\[\begin{aligned} & P^\text{re,min} \le p_t^\text{re} \le \text{ActivePowerTimeSeriesParameter}_t, \quad \forall t \in \{1,\dots, T\} \\ & Q^\text{re,min} \le q_t^\text{re} \le Q^\text{re,max}, \quad \forall t \in \{1,\dots, T\} \end{aligned}\]

RenewableConstantPowerFactor

Variables:

• ActivePowerVariable:

  • Bounds: [0.0, ]
  • Default initial value: PowerSystems.get_active_power(device)
  • Symbol: $p^\text{re}$

• ReactivePowerVariable:

  • Bounds: [0.0, ]
  • Default initial value: PowerSystems.get_reactive_power(device)
  • Symbol: $q^\text{re}$

Static Parameters:

• $P^\text{re,min}$ = PowerSystems.get_active_power_limits(device).min
• $Q^\text{re,min}$ = PowerSystems.get_reactive_power_limits(device).min
• $Q^\text{re,max}$ = PowerSystems.get_reactive_power_limits(device).max
• $\text{pf}$ = PowerSystems.get_power_factor(device)

Time Series Parameters:

Objective:

Adds two terms to the objective function based on the FunctionData Options:

• $+ C^\text{re,var} \cdot p_t^\text{re}$ from the variable field of RenewableGenerationCost (the VOM cost of dispatching the unit).
• $- C^\text{re,curt} \cdot p_t^\text{re}$ from the curtailment_cost field of RenewableGenerationCost (an incentive to dispatch up to $\text{ActivePowerTimeSeriesParameter}_t$; defaults to $0$).

The net contribution is $(C^\text{re,var} - C^\text{re,curt}) \cdot p_t^\text{re}$: when $C^\text{re,curt} > C^\text{re,var}$ the cost coefficient is negative, creating a marginal incentive to dispatch up to the time-series limit; when $C^\text{re,curt} < C^\text{re,var}$ the incentive favors curtailment, though system constraints (load balance, reserves) may still require some dispatch. CurtailmentCostExpression reports the per-device dollar value of curtailed energy $C^\text{re,curt} \cdot (p^\text{re,max}_t - p_t^\text{re})$ and is not propagated to ProductionCostExpression.

Expressions:

Adds $p^\text{re}$ and $q^\text{re}$ terms to the respective active and reactive power balance expressions created by the selected Network Formulations

Constraints:

\[\begin{aligned} & P^\text{re,min} \le p_t^\text{re} \le \text{ActivePowerTimeSeriesParameter}_t, \quad \forall t \in \{1,\dots, T\} \\ & q_t^\text{re} = \text{pf} \cdot p_t^\text{re}, \quad \forall t \in \{1,\dots, T\} \end{aligned}\]

Valid configurations

Valid DeviceModels for subtypes of RenewableGen include the following: