Formulations
Modeling formulations are created by dispatching on abstract subtypes of PowerSimulations.AbstractDeviceFormulation
FixedOutput
PowerSimulations.FixedOutput — TypeFormulation type to augment the power balance constraint expression with a time series parameter
Variables:
No variables are created for DeviceModel(<:DeviceType, FixedOutput)
Static Parameters:
- ThermalGen:
- $P^\text{th,max}$ =
PowerSystems.get_max_active_power(device) - $Q^\text{th,max}$ =
PowerSystems.get_max_reactive_power(device)
- $P^\text{th,max}$ =
- Storage:
- $P^\text{st,max}$ =
PowerSystems.get_max_active_power(device) - $Q^\text{st,max}$ =
PowerSystems.get_max_reactive_power(device)
- $P^\text{st,max}$ =
Time Series Parameters:
| Device Type | Parameter | Default Time Series Name |
|---|---|---|
| RenewableGen | ReactivePowerTimeSeriesParameter | max_active_power |
| RenewableGen | ActivePowerTimeSeriesParameter | max_active_power |
| HydroGen | ReactivePowerTimeSeriesParameter | max_active_power |
| HydroGen | ActivePowerTimeSeriesParameter | max_active_power |
| ElectricLoad | ReactivePowerTimeSeriesParameter | max_active_power |
| ElectricLoad | ActivePowerTimeSeriesParameter | max_active_power |
Objective:
No objective terms are created for DeviceModel(<:DeviceType, FixedOutput)
Expressions:
Adds the active and reactive parameters listed for specific device types above to the respective active and reactive power balance expressions created by the selected Network Formulations.
Constraints:
No constraints are created for DeviceModel(<:DeviceType, FixedOutput)
FunctionData Options
PowerSimulations can represent variable costs using a variety of different methods depending on the data available in each device. The following describes the objective function terms that are populated for each variable cost option.
LinearFunctionData
variable_cost = LinearFunctionData(c): creates a fixed marginal cost term in the objective function
\[\begin{aligned} & \text{min} \sum_{t} c * G_t \end{aligned}\]
QuadraticFunctionData and PolynomialFunctionData
variable_cost::QuadraticFunctionData and variable_cost::PolynomialFunctionData: create a polynomial cost term in the objective function
\[\begin{aligned} & \text{min} \sum_{t} \sum_{n} C_n * G_t^n \end{aligned}\]
where
- For
QuadraticFunctionData:- $C_0$ =
get_constant_term(variable_cost) - $C_1$ =
get_proportional_term(variable_cost) - $C_2$ =
get_quadratic_term(variable_cost)
- $C_0$ =
- For
PolynomialFunctionData:- $C_n$ =
get_coefficients(variable_cost)[n]
- $C_n$ =
`andPiecewiseLinearSlopeData`
variable_cost::PiecewiseLinearData and variable_cost::PiecewiseLinearSlopeData: create a piecewise linear cost term in the objective function
\[\begin{aligned} & \text{min} \sum_{t} f(G_t) \end{aligned}\]
where
- For
variable_cost::PiecewiseLinearData, $f(x)$ is the piecewise linear function obtained by connecting the(x, y)pointsget_points(variable_cost)in order. - For
variable_cost = PiecewiseLinearSlopeData([x0, x1, x2, ...], y0, [s0, s1, s2, ...]), $f(x)$ is the piecewise linear function obtained by starting at(x0, y0), drawing a segment at slopes0tox=x1, drawing a segment at slopes1tox=x2, etc.
StorageCost
Adds an objective function cost term according to:
\[\begin{aligned} & \text{min} \sum_{t} \quad [E^{surplus}_t * C^{penalty} - E^{shortage}_t * C^{value}] \end{aligned}\]
Impact of different cost configurations:
The following table describes all possible configurations of the StorageCost with the target constraint in hydro or storage device models. Cases 1(a) & 2(a) will not impact the model's operations, and the target constraint will be rendered useless. In most cases that have no energy target and a non-zero value for $C^{value}$, if this cost is too high ($C^{value} >> 0$) or too low ($C^{value} <<0$) can result in either the model holding on to stored energy till the end of the model not storing any energy in the device. This is caused by the fact that when the energy target is zero, we have $E_t = - E^{shortage}_t$, and $- E^{shortage}_t * C^{value}$ in the objective function is replaced by $E_t * C^{value}$, thus resulting in $C^{value}$ to be seen as the cost of stored energy.
| Case | Energy Target | Energy Shortage Cost | Energy Value / Energy Surplus cost | Effect |
|---|---|---|---|---|
| Case 1(a) | $\hat{E}=0$ | $C^{penalty}=0$ | $C^{value}=0$ | no change |
| Case 1(b) | $\hat{E}=0$ | $C^{penalty}=0$ | $C^{value}<0$ | penalty for storing energy |
| Case 1(c) | $\hat{E}=0$ | $C^{penalty}>0$ | $C^{value}=0$ | no penalties or incentives applied |
| Case 1(d) | $\hat{E}=0$ | $C^{penalty}=0$ | $C^{value}>0$ | incentive for storing energy |
| Case 1(e) | $\hat{E}=0$ | $C^{penalty}>0$ | $C^{value}<0$ | penalty for storing energy |
| Case 1(f) | $\hat{E}=0$ | $C^{penalty}>0$ | $C^{value}>0$ | incentive for storing energy |
| Case 2(a) | $\hat{E}>0$ | $C^{penalty}=0$ | $C^{value}=0$ | no change |
| Case 2(b) | $\hat{E}>0$ | $C^{penalty}=0$ | $C^{value}<0$ | penalty on energy storage in excess of target |
| Case 2(c) | $\hat{E}>0$ | $C^{penalty}>0$ | $C^{value}=0$ | penalty on energy storage short of target |
| Case 2(d) | $\hat{E}>0$ | $C^{penalty}=0$ | $C^{value}>0$ | incentive on excess energy |
| Case 2(e) | $\hat{E}>0$ | $C^{penalty}>0$ | $C^{value}<0$ | penalty on both excess/shortage of energy |
| Case 2(f) | $\hat{E}>0$ | $C^{penalty}>0$ | $C^{value}>0$ | penalty for shortage, incentive for excess energy |