Optimal Power Flow

acOptimalPowerFlow(system::PowerSystem, optimizer;
    iteration, tolerance, bridge, interval, name,
    magnitude, angle, active, reactive, actwise, reactwise, verbose)

The function sets up the optimization model for solving the AC optimal power flow problem.

Arguments

The function requires the PowerSystem type to establish the framework. Next, the optimizer argument is also required to create and solve the optimization problem. Specifically, JuliaGrid constructs the AC optimal power flow using the JuMP package and provides support for commonly employed solvers. For more detailed information, please consult the JuMP documentation.

Keywords

Users can configure the following parameters:

• iteration: Specifies the maximum number of iterations.
• tolerance: Specifies the allowed deviation from the optimal solution.
• bridge: Manage the bridging mechanism (default: false).
• interval: Uses interval form for two-sided constraints (default: true).
• name: Manage the creation of string names (default: true).
• verbose: Controls the output display, ranging from silent mode (0) to detailed output (3).

Additionally, users can modify the variable names used for printing and writing by setting the keywords for the variables magnitude, angle, active, and reactive, as well as the helper variables actwise and reactwise. For instance, users can choose magnitude = "V" and angle = "θ" to display equations in a more readable format.

Updates

If the AC model has not been created, the function automatically initiates an update within the ac field of the PowerSystem type.

Returns

The function returns an instance of the AcOptimalPowerFlow type.

Example

system = powerSystem("case14.h5")
acModel!(system)

analysis = acOptimalPowerFlow(system, Ipopt.Optimizer; iteration = 50, verbose = 1)

solve!(analysis::AcOptimalPowerFlow)

The function solves the AC optimal power flow model, computing the active and reactive power outputs of the generators, as well as the bus voltage magnitudes and angles.

Updates

The calculated active and reactive powers, as well as voltage magnitudes and angles, are stored in the power.generator and voltage fields of the AcOptimalPowerFlow type.

Example

system = powerSystem("case14.h5")
acModel!(system)

analysis = acOptimalPowerFlow(system, Ipopt.Optimizer)
solve!(analysis)

setInitialPoint!(analysis::AcOptimalPowerFlow)

The function sets the initial point of the AC optimal power flow to the values from the PowerSystem type.

Updates

The function modifies the voltage and generator fields of the AcOptimalPowerFlow type.

Example

system = powerSystem("case14.h5")
acModel!(system)

analysis = acOptimalPowerFlow(system, Ipopt.Optimizer)
powerFlow!(analysis)

updateBus!(analysis; label = 14, reactive = 0.13, magnitude = 1.2, angle = -0.17)

setInitialPoint!(analysis)
powerFlow!(analysis)

setInitialPoint!(target::AcOptimalPowerFlow, source::Analysis)

The function initializes the AC optimal power flow based on results from the Analysis type, whether from an AC or DC analysis.

The function assigns the active and reactive power outputs of the generators, along with the bus voltage magnitudes and angles in the target argument, using data from the source argument. This allows users to initialize primal values as needed. Additionally, if source is of type AcOptimalPowerFlow, the function also assigns initial dual values in the target argument based on data from source.

If source comes from a DC analysis, only the active power outputs of the generators and bus voltage angles are assigned in the target argument, while the reactive power outputs of the generators and bus voltage magnitudes remain unchanged. Additionally, if source is of type DcOptimalPowerFlow, the corresponding dual variable values are also assigned in the target argument.

Updates

This function may modify the voltage, generator, and method.dual fields of the AcOptimalPowerFlow type.

Example

Use the AC power flow results to initialize the AC optimal power flow:

system = powerSystem("case14.h5")
acModel!(system)

source = newtonRaphson(system)
powerFlow!(source)

target = acOptimalPowerFlow(system, Ipopt.Optimizer)

setInitialPoint!(target, source)
powerFlow!(target)

powerFlow!(analysis::AcOptimalPowerFlow; iteration, tolerance, power, current, verbose)

The function serves as a wrapper for solving AC optimal power flow and includes the functions:

• solve!,
• power!,
• current!.

It computes the active and reactive power outputs of the generators, as well as the bus voltage magnitudes and angles, with an option to compute the powers and currents related to buses and branches.

Keywords

Users can use the following keywords:

• iteration: Specifies the maximum number of iterations.
• tolerance: Specifies the allowed deviation from the optimal solution.
• power: Enables the computation of powers (default: false).
• current: Enables the computation of currents (default: false).
• verbose: Controls the output display, ranging from the default silent mode (0) to detailed output (3).

Example

system = powerSystem("case14.h5")
acModel!(system)

analysis = acOptimalPowerFlow(system, Ipopt.Optimizer)
powerFlow!(analysis; power = true, verbose = 1)

dcOptimalPowerFlow(system::PowerSystem, optimizer;
    iteration, tolerance, bridge, interval, name, angle, active, actwise, verbose)

The function sets up the optimization model for solving the DC optimal power flow problem.

Arguments

The function requires the PowerSystem type to establish the framework. Next, the optimizer argument is also required to create and solve the optimization problem. Specifically, JuliaGrid constructs the DC optimal power flow using the JuMP package and provides support for commonly employed solvers. For more detailed information, please consult the JuMP documentation.

Keywords

Users can configure the following parameters:

• iteration: Specifies the maximum number of iterations.
• tolerance: Specifies the allowed deviation from the optimal solution.
• bridge: Controls the bridging mechanism (default: false).
• interval: Uses interval form for two-sided expression constraints (default: true).
• name: Enables or disables the creation of string names (default: true).
• verbose: Controls the output display, ranging from the default silent mode (0) to detailed output (3).

Additionally, users can modify the variable names used for printing and writing by setting the keywords for the voltage variables angle and active, as well as the helper variable actwise. For example, users may set angle = "θ", active = "P", and actwise = "H" to display equations in a more readable format.

Updates

If the DC model has not been created, the function automatically initiates an update within the dc field of the PowerSystem type.

Returns

The function returns an instance of the DcOptimalPowerFlow type.

Example

system = powerSystem("case14.h5")
dcModel!(system)

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)

solve!(analysis::DcOptimalPowerFlow)

The function solves the DC optimal power flow model, computing the active power outputs of the generators, as well as the bus voltage angles.

Updates

The calculated active powers, as well as voltage angles, are stored in the power.generator and voltage fields of the DcOptimalPowerFlow type.

Example

system = powerSystem("case14.h5")
dcModel!(system)

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)
solve!(analysis)

setInitialPoint!(analysis::DcOptimalPowerFlow)

The function sets the initial point of the DC optimal power flow to the values from the PowerSystem type.

Updates

The function modifies the voltage and generator fields of the DcOptimalPowerFlow type.

Example

system = powerSystem("case14.h5")
dcModel!(system)

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)
powerFlow!(analysis)

updateBus!(analysis; label = 14, active = 0.1, angle = -0.17)

setInitialPoint!(analysis)
powerFlow!(analysis)

setInitialPoint!(target::DcOptimalPowerFlow, source::Analysis)

The function initializes the DC optimal power flow based on results from the Analysis type, whether from an AC or DC analysis.

The function assigns the active power outputs of the generators, along with the bus voltage angles in the target argument, using data from the source argument. This allows users to initialize primal values as needed. Additionally, if source is of type AcOptimalPowerFlow or DcOptimalPowerFlow, the function also assigns initial dual values in the target argument based on data from source.

Updates

This function may modify the voltage, generator, and method.dual fields of the DcOptimalPowerFlow type.

Example

Use the DC power flow results to initialize the DC optimal power flow:

system = powerSystem("case14.h5")
dcModel!(system)

source = dcPowerFlow(system)
solve!(source)

target = dcOptimalPowerFlow(system, Ipopt.Optimizer)

setInitialPoint!(target, source)
solve!(target)

powerFlow!(analysis::DcOptimalPowerFlow; iteration, tolerance, power, verbose)

The function serves as a wrapper for solving DC optimal power flow and includes the functions:

• solve!,
• power!.

It computes the active power outputs of the generators, as well as the bus voltage angles, with an option to compute the powers related to buses and branches.

Keywords

Users can use the following keywords:

• iteration: Specifies the maximum number of iterations.
• tolerance: Specifies the allowed deviation from the optimal solution.
• power: Enables the computation of powers (default: false).
• verbose: Controls the output display, ranging from the default silent mode (0) to detailed output (3).

Example

system = powerSystem("case14.h5")
dcModel!(system)

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)
powerFlow!(analysis; power = true, verbose = 1)

@addVariable(analysis::OptimalPowerFlow, expr, primal, lower, upper, args..., kwargs...)

This macro wraps the JuMP @variable macro, adding an optimization variable defined by expr to the model. In addition to creating the JuMP variable, it also registers the variable within the JuliaGrid framework and optionally sets initial values for both primal and dual variables.

The positional arguments args and keyword arguments kwargs are consistent with those accepted by the @variable macro in JuMP.

Additionally, the following keyword arguments can be used:

• primal: Sets the initial primal value.
• lower: If a lower bound is defined, sets the initial dual value.
• upper: If an upper bound is defined, sets the initial dual value.

Example

system = powerSystem("case14.h5")

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)

@addVariable(analysis, 0.0 <= x <= 0.2, primal = 0.1, lower = 10.0, upper = 0.0)
@addVariable(analysis, y[i = 1:2] <= 0.2, primal = [0.1, 0.2], upper = [0.0; -2.5])

@addConstraint(analysis::OptimalPowerFlow, expr, dual, args..., kwargs...)

This macro wraps the JuMP @constraint macro, adding an constraint defined by expr to the model. In addition to creating the JuMP constraint, it also registers the constraint within the JuliaGrid framework and optionally sets initial dual value.

The positional arguments args and keyword arguments kwargs are consistent with those accepted by the @constraint macro in JuMP.

Additionally, the keyword dual can be used to set the initial dual value.

Example

system = powerSystem("case14.h5")

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)

@addVariable(analysis, 0.0 <= x[i = 1:2] <= 0.2)
@addConstraint(analysis, x[1] + 2 * x[2] <= 1.2, dual = 0.1)

addDual!(analysis::OptimalPowerFlow, field::Symbol, subfield::Symbol;
    label, index, subindex, dual, lower, upper)

Assigns an initial dual value to a specific constraint in the optimal power flow model.

For DC optimal power flow, only field is required to identify the constraint. For AC optimal power flow, both field and subfield must be provided to target the specific constraint type.

Arguments

• field: Specifies the primary constraint category.
• subfield: Specifies the constraint subtype within the selected field.

Initial dual values are assigned according to the selected constraint:

• :slack: Slack angle constraint.
• :capability: Generator capability constraints:
  • :active: Active power.
  • :reactive: Reactive power.
  • :lower: PQ capability curve.
  • :upper: PQ capability curve.
• :balance: Power balance constraints:
  • :active: Active power balance.
  • :reactive: Reactive power balance.
• :voltage: Voltage constraints:
  • :magnitude: Voltage magnitude.
  • :angle: Angle difference.
• :flow: Branch power flow constraints:
  • :from: From-bus end.
  • :to: To-bus end.
• :piecewise: Piecewise linear cost constraints:
  • :active: Active power.
  • :reactive: Reactive power.
• :variable: Constraint on external user-defined variable.
• :constraint: External user-defined constraint.

Keywords

The following keyword arguments can be used:

• label: Identifies the constraint by the label of a bus, branch, or generator.
• index: Identifies the constraint by numerical index.
• subindex: Specify a subconstraint index for :piecewise constraints only.
• dual: Sets the dual value for equality or interval constraints.
• lower: Sets the dual value associated with the lower bound.
• upper: Sets the dual value associated with the upper bound.

Examples

AC optimal power flow:

system = powerSystem("case14.h5")

analysis = acOptimalPowerFlow(system, Ipopt.Optimizer)

addDual!(analysis, :balance, :active; index = 2, dual = 258.23)
addDual!(analysis, :voltage, :magnitude; index = 2, lower = 0.0, upper = 587.23)

DC optimal power flow:

system = powerSystem("case14.h5")

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)

addDual!(analysis, :balance; index = 2, dual = 258.23)
addDual!(analysis, :capability; index = 2, lower = 0.0, upper = 587.23)

remove!(analysis::OptimalPowerFlow, field::Symbol, subfield::Symbol; label, index)

Removes a specific constraint from the optimal power flow model.

For DC optimal power flow, only field is required to identify the constraint. For AC optimal power flow, both field and subfield must be provided to target the specific constraint type.

Arguments

• field: Specifies the primary constraint category.
• subfield: Specifies the constraint subtype within the selected field.

The constraint to be removed can correspond to one of the following:

• :slack: Slack angle constraint.
• :capability: Generator capability constraints:
  • :active: Active power.
  • :reactive: Reactive power.
  • :lower: PQ capability curve.
  • :upper: PQ capability curve.
• :balance: Power balance constraints:
  • :active: Active power balance.
  • :reactive: Reactive power balance.
• :voltage: Voltage constraints:
  • :magnitude: Voltage magnitude.
  • :angle: Angle difference.
• :flow: Branch power flow constraints:
  • :from: From-bus end.
  • :to: To-bus end.
• :piecewise: Piecewise linear cost constraints:
  • :active: Active power.
  • :reactive: Reactive power.
• :variable: Constraint on external user-defined variable.
• :constraint: External user-defined constraint.

Keywords

The following keyword arguments can be used:

• label: Identifies the constraint by the label of a bus, branch, or generator.
• index: Identifies the constraint by numerical index.

Examples

AC optimal power flow:

system = powerSystem("case14.h5")

analysis = acOptimalPowerFlow(system, Ipopt.Optimizer)

remove!(analysis, :balance, :active; index = 2)
remove!(analysis, :voltage, :magnitude; index = 2)

DC optimal power flow:

system = powerSystem("case14.h5")

analysis = dcOptimalPowerFlow(system, Ipopt.Optimizer)

remove!(analysis, :balance; index = 2)
remove!(analysis, :capability; index = 2)