API Reference

Device Models
- Formulations
- Problem Templates
Decision Models
Emulation Models
Service Models
Simulation Models
Variables
Constraints
Parameters

Device Models

List of structures and methods for Device models

PowerSimulations.DeviceModel — Type

DeviceModel(
    ::Type{D},
    ::Type{B},
    feedforwards::Vector{<:AbstractAffectFeedforward}
    use_slacks::Bool,
    duals::Vector{DataType},
    services::Vector{ServiceModel}
    attributes::Dict{String, Any}
)

Establishes the model for a particular device specified by type. Uses the keyword argument feedforward to enable passing values between operation model at simulation time

Arguments

::Type{D} where D<:PSY.Device: Power System Device Type
::Type{B} where B<:AbstractDeviceFormulation: Abstract Device Formulation
feedforward::Array{<:AbstractAffectFeedforward} = Vector{AbstractAffectFeedforward}() : use to pass parameters between models
use_slacks::Bool = false : Add slacks to the device model. Implementation is model dependent and not all models feature slacks
duals::Vector{DataType} = Vector{DataType}(): use to pass constraint type to calculate the duals. The DataType needs to be a valid ConstraintType
time_series_names::Dict{Type{<:TimeSeriesParameter}, String} = get_default_time_series_names(D, B) : use to specify time series names associated to the device`
attributes::Dict{String, Any} = get_default_attributes(D, B) : use to specify attributes to the device

Example

thermal_gens = DeviceModel(ThermalStandard, ThermalBasicUnitCommitment)

source

Formulations

Refer to the Formulations Page for each Abstract Device Formulation.

Problem Templates

Refer to the Problem Templates Page for available ProblemTemplates.

Service Models

List of structures and methods for Service models

PowerSimulations.ServiceModel — Type

Establishes the model for a particular services specified by type. Uses the keyword argument use_service_name to assign the model to a service with the same name as the name in the template. Uses the keyword argument feedforward to enable passing values between operation model at simulation time

Arguments

-::Type{D}: Power System Service Type -::Type{B}: Abstract Service Formulation

Accepted Key Words

feedforward::Array{<:AbstractAffectFeedforward} : use to pass parameters between models
use_service_name::Bool : use the name as the name for the service

Example

reserves = ServiceModel(PSY.VariableReserve{PSY.ReserveUp}, RangeReserve)

source

Simulation Models

Refer to the Simulations Page to explanations on how to setup a Simulation, with Sequencing and Feedforwards.

PowerSimulations.SimulationModels — Type

SimulationModels(
    decision_models::Vector{<:DecisionModel},
    emulation_models::Union{Nothing, EmulationModel}
)

Stores the OperationProblem definitions to be used in the simulation. When creating the SimulationModels, the order in which the models are created determines the order on which the simulation is executed.

Arguments

decision_models::Vector{<:DecisionModel}: Vector of decision models.
emulation_models::Union{Nothing, EmulationModel}: Optional argument to include

an EmulationModel in the Simulation

Example

template_uc = template_unit_commitment()
template_ed = template_economic_dispatch()
my_decision_model_uc = DecisionModel(template_1, sys_uc, optimizer, name = "UC")
my_decision_model_ed = DecisionModel(template_ed, sys_ed, optimizer, name = "ED")
models = SimulationModels(
    decision_models = [
        my_decision_model_uc,
        my_decision_model_ed
    ]
)

source

PowerSimulations.SimulationSequence — Type

SimulationSequence(
    models::SimulationModels,
    feedforward::Dict{String, Vector{<:AbstractAffectFeedforward}}
    ini_cond_chronology::InitialConditionChronology
)

Construct the simulation sequence between decision and emulation models.

Arguments

models::SimulationModels: Vector of decisions and emulation models.
feedforward = Dict{String, Vector{<:AbstractAffectFeedforward}}(): Optional dictionary to specify how information

and variables are exchanged between decision and emulation models.

ini_cond_chronology::nitialConditionChronology = InterProblemChronology(): TODO

Example

template_uc = template_unit_commitment()
template_ed = template_economic_dispatch()
my_decision_model_uc = DecisionModel(template_1, sys_uc, optimizer, name = "UC")
my_decision_model_ed = DecisionModel(template_ed, sys_ed, optimizer, name = "ED")
models = SimulationModels(
    decision_models = [
        my_decision_model_uc,
        my_decision_model_ed
    ]
)
# The following sequence set the commitment variables (`OnVariable`) for `ThermalStandard` units from UC to ED.
sequence = SimulationSequence(;
    models = models,
    feedforwards = Dict(
        "ED" => [
            SemiContinuousFeedforward(;
                component_type = ThermalStandard,
                source = OnVariable,
                affected_values = [ActivePowerVariable],
            ),
        ],
    ),
)

source

PowerSimulations.Simulation — Type

Simulation(
    sequence::SimulationSequence,
    name::String,
    steps::Int
    models::SimulationModels,
    simulation_folder::String,
    initial_time::Union{Nothing, Dates.DateTime}
)

Construct the Simulation structure to run the sequence of decision and emulation models specified.

Arguments

-sequence::SimulationSequence: Simulation sequence that specify how the decision and emulation models will be executed. -name::String: Name of the Simulation -steps::Int: Number of steps on which the sequence of models will be executed -models::SimulationModels: List of Decision and Emulation Models -simulation_folder::String: Folder on which results will be stored -initial_time::Union{Nothing, Dates.DateTime} = nothing: Initial time of which the simulation starts. If nothing it will default to the first timestamp of time series of the system.

Example

template_uc = template_unit_commitment()
template_ed = template_economic_dispatch()
my_decision_model_uc = DecisionModel(template_1, sys_uc, optimizer, name = "UC")
my_decision_model_ed = DecisionModel(template_ed, sys_ed, optimizer, name = "ED")
models = SimulationModels(
    decision_models = [
        my_decision_model_uc,
        my_decision_model_ed
    ]
)
# The following sequence set the commitment variables (`OnVariable`) for `ThermalStandard` units from UC to ED.
sequence = SimulationSequence(;
    models = models,
    feedforwards = Dict(
        "ED" => [
            SemiContinuousFeedforward(;
                component_type = ThermalStandard,
                source = OnVariable,
                affected_values = [ActivePowerVariable],
            ),
        ],
    ),
)

sim = Simulation(
    sequence = sequence,
    name = "Sim",
    steps = 5,
    models = models,
    simulation_folder = mktempdir(cleanup=true),
)

source

PowerSimulations.Simulation — Method

Simulation(directory::AbstractString, model_info::Dict)

Constructs Simulation from a serialized directory. Callers should pass any kwargs here that they passed to the original Simulation.

Arguments

directory::AbstractString: the directory returned from the call to serialize
model_info::Dict: Two-level dictionary containing model parameters that cannot be serialized. The outer dict should be keyed by the problem name. The inner dict must contain 'optimizer' and may contain 'jump_model'. These should be the same values used for the original simulation.

source

PowerSimulations.build! — Method

build!(
    sim::Simulation;
    recorders,
    console_level,
    file_level,
    serialize,
    partitions,
    index
) -> InfrastructureSystems.Simulation.SimulationBuildStatusModule.SimulationBuildStatus

Build the Simulation, problems and the related folder structure.

Arguments

sim::Simulation: simulation object
recorders::Vector{Symbol} = []: recorder names to register
serialize::Bool = true: serializes the simulation objects in the simulation
console_level = Logging.Error:
file_level = Logging.Info:

source

PowerSimulations.execute! — Method

execute!(
    sim::Simulation;
    kwargs...
) -> InfrastructureSystems.Simulation.RunStatusModule.RunStatus

Solves the simulation model for sequential Simulations.

Arguments

sim::Simulation=sim: simulation object created by Simulation()

The optional keyword argument exports controls exporting of results to CSV files as the simulation runs.

Example

sim = Simulation("Test", 7, problems, "/Users/folder")
execute!(sim::Simulation; kwargs...)

source

Variables

For a list of variables for each device refer to its Formulations page.

Common Variables

PowerSimulations.ActivePowerVariable — Type

Struct to dispatch the creation of Active Power Variables

Docs abbreviation: $p$

source

PowerSimulations.ReactivePowerVariable — Type

Struct to dispatch the creation of Reactive Power Variables

Docs abbreviation: $q$

source

PowerSimulations.PieceWiseLinearCostVariable — Type

Struct to dispatch the creation of piecewise linear cost variables for objective function

Docs abbreviation: $\delta$

source

Thermal Unit Variables

PowerSimulations.OnVariable — Type

Struct to dispatch the creation of a binary commitment status variable

Docs abbreviation: $u$

source

PowerSimulations.StartVariable — Type

Struct to dispatch the creation of Binary Start Variables

Docs abbreviation: $v$

source

PowerSimulations.StopVariable — Type

Struct to dispatch the creation of Binary Stop Variables

Docs abbreviation: $w$

source

PowerSimulations.TimeDurationOn — Type

Auxiliary Variable for Thermal Generation Models to keep track of time elapsed on

source

PowerSimulations.TimeDurationOff — Type

Auxiliary Variable for Thermal Generation Models to keep track of time elapsed off

source

PowerSimulations.HotStartVariable — Type

Struct to dispatch the creation of Hot Start Variable for Thermal units with temperature considerations

Docs abbreviation: $z^\text{th}$

source

PowerSimulations.WarmStartVariable — Type

Struct to dispatch the creation of Warm Start Variable for Thermal units with temperature considerations

Docs abbreviation: $y^\text{th}$

source

PowerSimulations.ColdStartVariable — Type

Struct to dispatch the creation of Cold Start Variable for Thermal units with temperature considerations

Docs abbreviation: $x^\text{th}$

source

PowerSimulations.PowerAboveMinimumVariable — Type

Struct to dispatch the creation of Active Power Variables above minimum power for Thermal Compact formulations

Docs abbreviation: $\Delta p$

source

PowerSimulations.PowerOutput — Type

Auxiliary Variable for Thermal Generation Models that solve for power above min

source

Storage Unit Variables

PowerSimulations.ReservationVariable — Type

Struct to dispatch the creation of binary storage charge reservation variable

Docs abbreviation: $u^\text{st}$

source

Branches and Network Variables

PowerSimulations.FlowActivePowerVariable — Type

Struct to dispatch the creation of bidirectional Active Power Flow Variables

Docs abbreviation: $f$

source

PowerSimulations.FlowActivePowerSlackUpperBound — Type

Struct to dispatch the creation of active power flow upper bound slack variables. Used when there is not enough flow through the branch in the forward direction.

Docs abbreviation: $f^\text{sl,up}$

source

PowerSimulations.FlowActivePowerSlackLowerBound — Type

Struct to dispatch the creation of active power flow lower bound slack variables. Used when there is not enough flow through the branch in the reverse direction.

Docs abbreviation: $f^\text{sl,lo}$

source

PowerSimulations.FlowActivePowerFromToVariable — Type

Struct to dispatch the creation of unidirectional Active Power Flow Variables

Docs abbreviation: $f^\text{from-to}$

source

PowerSimulations.FlowActivePowerToFromVariable — Type

Struct to dispatch the creation of unidirectional Active Power Flow Variables

Docs abbreviation: $f^\text{to-from}$

source

PowerSimulations.FlowReactivePowerFromToVariable — Type

Struct to dispatch the creation of unidirectional Reactive Power Flow Variables

Docs abbreviation: $f^\text{q,from-to}$

source

PowerSimulations.FlowReactivePowerToFromVariable — Type

Struct to dispatch the creation of unidirectional Reactive Power Flow Variables

Docs abbreviation: $f^\text{q,to-from}$

source

PowerSimulations.PhaseShifterAngle — Type

Struct to dispatch the creation of Phase Shifters Variables

Docs abbreviation: $\theta^\text{shift}$

source

PowerSimulations.HVDCLosses — Type

Struct to dispatch the creation of HVDC Losses Auxiliary Variables

Docs abbreviation: $\ell$

source

PowerSimulations.HVDCFlowDirectionVariable — Type

Struct to dispatch the creation of HVDC Flow Direction Auxiliary Variables

Docs abbreviation: $u^\text{dir}$

source

PowerSimulations.VoltageMagnitude — Type

Struct to dispatch the creation of Voltage Magnitude Variables for AC formulations

Docs abbreviation: $v$

source

PowerSimulations.VoltageAngle — Type

Struct to dispatch the creation of Voltage Angle Variables for AC/DC formulations

Docs abbreviation: $\theta$

source

Services Variables

PowerSimulations.ActivePowerReserveVariable — Type

Struct to dispatch the creation of Active Power Reserve Variables

Docs abbreviation: $r$

source

PowerSimulations.ServiceRequirementVariable — Type

Struct to dispatch the creation of Service Requirement Variables

Docs abbreviation: $\text{req}$

source

PowerSimulations.SystemBalanceSlackUp — Type

Struct to dispatch the creation of System-wide slack up variables. Used when there is not enough generation.

Docs abbreviation: $p^\text{sl,up}$

source

PowerSimulations.SystemBalanceSlackDown — Type

Struct to dispatch the creation of System-wide slack down variables. Used when there is not enough load curtailment.

Docs abbreviation: $p^\text{sl,dn}$

source

PowerSimulations.ReserveRequirementSlack — Type

Struct to dispatch the creation of Reserve requirement slack variables. Used when there is not reserves in the system to satisfy the requirement.

Docs abbreviation: $r^\text{sl}$

source

PowerSimulations.InterfaceFlowSlackUp — Type

Struct to dispatch the creation of Interface Flow Slack Up variables

Docs abbreviation: $f^\text{sl,up}$

source

PowerSimulations.InterfaceFlowSlackDown — Type

Struct to dispatch the creation of Interface Flow Slack Down variables

Docs abbreviation: $f^\text{sl,dn}$

source

Feedforward Variables

PowerSimulations.UpperBoundFeedForwardSlack — Type

Struct to dispatch the creation of Slack variables for UpperBoundFeedforward

Docs abbreviation: $p^\text{ff,ubsl}$

source

PowerSimulations.LowerBoundFeedForwardSlack — Type

Struct to dispatch the creation of Slack variables for LowerBoundFeedforward

Docs abbreviation: $p^\text{ff,lbsl}$

source

Constraints

Common Constraints

PowerSimulations.PieceWiseLinearCostConstraint — Type

Struct to create the PieceWiseLinearCostConstraint associated with a specified variable.

See Piecewise linear cost functions for more information.

source

Network Constraints

PowerSimulations.CopperPlateBalanceConstraint — Type

Struct to create the constraint to balance power in the copperplate model. For more information check Network Formulations.

The specified constraint is generally formulated as:

\[\sum_{c \in \text{components}} p_t^c = 0, \quad \forall t \in \{1, \dots, T\}\]

source

PowerSimulations.NodalBalanceActiveConstraint — Type

Struct to create the constraint to balance active power in nodal formulation. For more information check Network Formulations.

The specified constraint depends on the network model chosen.

source

PowerSimulations.NodalBalanceReactiveConstraint — Type

Struct to create the constraint to balance reactive power in nodal formulation. For more information check Network Formulations.

The specified constraint depends on the network model chosen.

source

Power Variable Limit Constraints

PowerSimulations.ActivePowerVariableLimitsConstraint — Type

Struct to create the constraint to limit active power expressions. For more information check Device Formulations.

The specified constraint depends on the UpperBound and LowerBound expressions, but in its most basic formulation is of the form:

\[P^\text{min} \le p_t \le P^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.ReactivePowerVariableLimitsConstraint — Type

Struct to create the constraint to limit reactive power expressions. For more information check Device Formulations.

The specified constraint depends on the UpperBound and LowerBound expressions, but in its most basic formulation is of the form:

\[Q^\text{min} \le q_t \le Q^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.ActivePowerVariableTimeSeriesLimitsConstraint — Type

Struct to create the constraint to limit active power expressions by a time series parameter. For more information check Device Formulations.

The specified constraint depends on the UpperBound expressions, but in its most basic formulation is of the form:

\[p_t \le \text{ActivePowerTimeSeriesParameter}_t, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.InputActivePowerVariableLimitsConstraint — Type

Struct to create the constraint to limit active power input expressions. For more information check Device Formulations.

The specified constraint depends on the UpperBound and LowerBound expressions, but in its most basic formulation is of the form:

\[P^\text{min} \le p_t^\text{in} \le P^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.OutputActivePowerVariableLimitsConstraint — Type

Struct to create the constraint to limit active power output expressions. For more information check Device Formulations.

The specified constraint depends on the UpperBound and LowerBound expressions, but in its most basic formulation is of the form:

\[P^\text{min} \le p_t^\text{out} \le P^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

Services Constraints

PowerSimulations.RequirementConstraint — Type

Struct to create the constraint for satisfying active power reserve requirements. For more information check Service Formulations.

The constraint is as follows:

\[\sum_{d\in\mathcal{D}_s} r_{d,t} + r_t^\text{sl} \ge \text{Req},\quad \forall t\in \{1,\dots, T\} \quad \text{(for a ConstantReserve)} \\ \sum_{d\in\mathcal{D}_s} r_{d,t} + r_t^\text{sl} \ge \text{RequirementTimeSeriesParameter}_{t},\quad \forall t\in \{1,\dots, T\} \quad \text{(for a VariableReserve)}\]

source

PowerSimulations.ParticipationFractionConstraint — Type

Struct to create the constraint to participation assignments limits in the active power reserves. For more information check Service Formulations.

The constraint is as follows:

\[r_{d,t} \le \text{Req} \cdot \text{PF} ,\quad \forall d\in \mathcal{D}_s, \forall t\in \{1,\dots, T\} \quad \text{(for a ConstantReserve)} \\ r_{d,t} \le \text{RequirementTimeSeriesParameter}_{t} \cdot \text{PF}\quad \forall d\in \mathcal{D}_s, \forall t\in \{1,\dots, T\}, \quad \text{(for a VariableReserve)}\]

source

PowerSimulations.ReservePowerConstraint — Type

Struct to create the constraint for ensuring that NonSpinning Reserve can be delivered from turn-off thermal units.

For more information check Service Formulations for NonSpinningReserve.

The constraint is as follows:

\[r_{d,t} \le (1 - u_{d,t}^\text{th}) \cdot R^\text{limit}_d, \quad \forall d \in \mathcal{D}_s, \forall t \in \{1,\dots, T\}\]

source

Thermal Unit Constraints

PowerSimulations.ActiveRangeICConstraint — Type

Struct to create the constraint for starting up ThermalMultiStart units. For more information check ThermalGen Formulations for ThermalMultiStartUnitCommitment.

The specified constraint is formulated as:

\[\max\{P^\text{th,max} - P^\text{th,shdown}, 0\} \cdot w_1^\text{th} \le u^\text{th,init} (P^\text{th,max} - P^\text{th,min}) - P^\text{th,init}\]

source

PowerSimulations.CommitmentConstraint — Type

Struct to create the commitment constraint between the on, start, and stop variables. For more information check ThermalGen Formulations.

The specified constraints are formulated as:

\[u_1^\text{th} = u^\text{th,init} + v_1^\text{th} - w_1^\text{th} \\ u_t^\text{th} = u_{t-1}^\text{th} + v_t^\text{th} - w_t^\text{th}, \quad \forall t \in \{2,\dots,T\} \\ v_t^\text{th} + w_t^\text{th} \le 1, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.DurationConstraint — Type

Struct to create the duration constraint for commitment formulations, i.e. min-up and min-down.

For more information check ThermalGen Formulations.

source

PowerSimulations.RampConstraint — Type

Struct to create the RampConstraint associated with a specified thermal device or reserve service.

For thermal units, see more information in Thermal Formulations. The constraint is as follows:

\[-R^\text{th,dn} \le p_t^\text{th} - p_{t-1}^\text{th} \le R^\text{th,up}, \quad \forall t\in \{1, \dots, T\}\]

For Ramp Reserve, see more information in Service Formulations. The constraint is as follows:

\[r_{d,t} \le R^\text{th,up} \cdot \text{TF}\quad \forall d\in \mathcal{D}_s, \forall t\in \{1,\dots, T\}, \quad \text{(for ReserveUp)} \\ r_{d,t} \le R^\text{th,dn} \cdot \text{TF}\quad \forall d\in \mathcal{D}_s, \forall t\in \{1,\dots, T\}, \quad \text{(for ReserveDown)}\]

source

PowerSimulations.StartupInitialConditionConstraint — Type

Struct to create the start-up initial condition constraints for ThermalMultiStart.

For more information check ThermalGen Formulations for ThermalMultiStartUnitCommitment.

source

PowerSimulations.StartupTimeLimitTemperatureConstraint — Type

Struct to create the start-up time limit constraints for ThermalMultiStart.

For more information check ThermalGen Formulations for ThermalMultiStartUnitCommitment.

source

Renewable Unit Constraints

PowerSimulations.EqualityConstraint — Type

Struct to create the constraint that sets the reactive power to the power factor in the RenewableConstantPowerFactor formulation for renewable units.

For more information check RenewableGen Formulations.

The specified constraint is formulated as:

\[q_t^\text{re} = \text{pf} \cdot p_t^\text{re}, \quad \forall t \in \{1,\dots, T\}\]

source

Branches Constraints

PowerSimulations.FlowLimitConstraint — Type

Struct to create the constraint that set the flow limits through a PhaseShiftingTransformer.

For more information check Branch Formulations.

The specified constraint is formulated as:

\[-R^\text{max} \le f_t \le R^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.FlowRateConstraint — Type

Struct to create the constraint that set the flow limits through an HVDC two-terminal branch.

For more information check Branch Formulations.

The specified constraint is formulated as:

\[R^\text{min} \le f_t \le R^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

PowerSimulations.FlowRateConstraintFromTo — Type

Struct to create the constraint that set the flow from-to limits through an HVDC two-terminal branch.

For more information check Branch Formulations.

The specified constraint is formulated as:

\[R^\text{from,min} \le f_t^\text{from-to} \le R^\text{from,max}, \forall t \in \{1,\dots, T\}\]

source

PowerSimulations.FlowRateConstraintToFrom — Type

Struct to create the constraint that set the flow to-from limits through an HVDC two-terminal branch.

For more information check Branch Formulations.

The specified constraint is formulated as:

\[R^\text{to,min} \le f_t^\text{to-from} \le R^\text{to,max},\quad \forall t \in \{1,\dots, T\}\]

source

PowerSimulations.HVDCLossesAbsoluteValue — Type

Struct to create the constraints that set the losses through a lossy HVDC two-terminal line.

For more information check Branch Formulations.

The specified constraints are formulated as:

\[\begin{align*} & f_t^\text{to-from} - f_t^\text{from-to} \le \ell_t,\quad \forall t \in \{1,\dots, T\} \\ & f_t^\text{from-to} - f_t^\text{to-from} \le \ell_t,\quad \forall t \in \{1,\dots, T\} \end{align*}\]

source

PowerSimulations.HVDCPowerBalance — Type

Struct to create the constraints that set the power balance across a lossy HVDC two-terminal line.

For more information check Branch Formulations.

The specified constraints are formulated as:

\[\begin{align*} & f_t^\text{to-from} - f_t^\text{from-to} \le L_1 \cdot f_t^\text{to-from} - L_0,\quad \forall t \in \{1,\dots, T\} \\ & f_t^\text{from-to} - f_t^\text{to-from} \ge L_1 \cdot f_t^\text{from-to} + L_0,\quad \forall t \in \{1,\dots, T\} \\ & f_t^\text{from-to} - f_t^\text{to-from} \ge - M^\text{big} (1 - u^\text{dir}_t),\quad \forall t \in \{1,\dots, T\} \\ & f_t^\text{to-from} - f_t^\text{from-to} \ge - M^\text{big} u^\text{dir}_t,\quad \forall t \in \{1,\dots, T\} \\ \end{align*}\]

source

PowerSimulations.NetworkFlowConstraint — Type

Struct to create the constraint the AC branch flows depending on the network model. For more information check Branch Formulations.

The specified constraint depends on the network model chosen. The most common application is the StaticBranch in a PTDF Network Model:

\[f_t = \sum_{i=1}^N \text{PTDF}_{i,b} \cdot \text{Bal}_{i,t}, \quad \forall t \in \{1,\dots, T\}\]

source

PowerSimulations.RateLimitConstraint — Type

Struct to create the constraint that set the AC flow limits through branches.

For more information check Branch Formulations.

The specified constraint is formulated as:

\[\begin{align*} & f_t - f_t^\text{sl,up} \le R^\text{max},\quad \forall t \in \{1,\dots, T\} \\ & f_t + f_t^\text{sl,lo} \ge -R^\text{max},\quad \forall t \in \{1,\dots, T\} \end{align*}\]

source

PowerSimulations.PhaseAngleControlLimit — Type

Struct to create the constraint that set the angle limits through a PhaseShiftingTransformer.

For more information check Branch Formulations.

The specified constraint is formulated as:

\[\Theta^\text{min} \le \theta^\text{shift}_t \le \Theta^\text{max}, \quad \forall t \in \{1,\dots,T\}\]

source

Feedforward Constraints

PowerSimulations.FeedforwardSemiContinuousConstraint — Type

Struct to create the constraint for semicontinuous feedforward limits.

For more information check Feedforward Formulations.

The specified constraint is formulated as:

\[\begin{align*} & \text{ActivePowerRangeExpressionUB}_t := p_t^\text{th} - \text{on}_t^\text{th}P^\text{th,max} \le 0, \quad \forall t\in \{1, \dots, T\} \\ & \text{ActivePowerRangeExpressionLB}_t := p_t^\text{th} - \text{on}_t^\text{th}P^\text{th,min} \ge 0, \quad \forall t\in \{1, \dots, T\} \end{align*}\]

source

PowerSimulations.FeedforwardUpperBoundConstraint — Type

Struct to create the constraint for upper bound feedforward limits.

For more information check Feedforward Formulations.

The specified constraint is formulated as:

\[\begin{align*} & \text{AffectedVariable}_t - p_t^\text{ff,ubsl} \le \text{SourceVariableParameter}_t, \quad \forall t \in \{1,\dots, T\} \end{align*}\]

source

PowerSimulations.FeedforwardLowerBoundConstraint — Type

Struct to create the constraint for lower bound feedforward limits.

For more information check Feedforward Formulations.

The specified constraint is formulated as:

\[\begin{align*} & \text{AffectedVariable}_t + p_t^\text{ff,lbsl} \ge \text{SourceVariableParameter}_t, \quad \forall t \in \{1,\dots, T\} \end{align*}\]

source