Add VSC Two Terminal Loss Model

docs/src/api/PowerSimulations.md

@@ -189,6 +189,28 @@ FlowReactivePowerToFromVariable
 PhaseShifterAngle
 HVDCLosses
 HVDCFlowDirectionVariable
+HVDCActivePowerReceivedFromVariable
+HVDCActivePowerReceivedToVariable
+HVDCPiecewiseLossVariable
+HVDCPiecewiseBinaryLossVariable
+HVDCActiveDCPowerSentFromVariable
+HVDCActiveDCPowerSentToVariable
+HVDCReactivePowerSentFromVariable
+HVDCReactivePowerSentToVariable
+ConverterPowerDirection
+DCVoltageFrom
+DCVoltageTo
+SquaredDCVoltageFrom
+SquaredDCVoltageTo
+ConverterCurrent
+SquaredConverterCurrent
+ConverterPositiveCurrent
+ConverterNegativeCurrent
+ConverterCurrentDirection
+AuxBilinearConverterVariableFrom
+AuxBilinearSquaredConverterVariableFrom
+AuxBilinearConverterVariableTo
+AuxBilinearSquaredConverterVariableTo
 VoltageMagnitude
 VoltageAngle
 ```
@@ -281,6 +303,18 @@ FlowRateConstraintFromTo
 FlowRateConstraintToFrom
 HVDCPowerBalance
 NetworkFlowConstraint
+ConverterPowerCalculationConstraint
+ConverterDirectionConstraint
+ConverterCurrentBalanceConstraint
+ConverterMcCormickEnvelopes
+InterpolationVoltageConstraints
+InterpolationCurrentConstraints
+InterpolationBilinearConstraints
+CurrentAbsoluteValueConstraint
+ConverterLossesCalculationConstraint
+ConverterPowerBalanceConstraint
+ConverterACPowerCalculationConstraint
+FlowApparentPowerLimitConstraint
 RateLimitConstraint
 PhaseAngleControlLimit
 ```

src/PowerSimulations.jl

@@ -45,6 +45,10 @@ export HVDCTwoTerminalLossless
 export HVDCTwoTerminalDispatch
 export HVDCTwoTerminalUnbounded
 export PhaseAngleControl
+export HVDCTwoTerminalPiecewiseLoss
+export HVDCTwoTerminalVSCLoss
+export HVDCTwoTerminalVSCLossBilinear
+export HVDCTwoTerminalVSCLossQuadratic
 # export VoltageSourceDC
 
 ######## HVDC models ########
@@ -233,6 +237,29 @@ export LowerBoundFeedForwardSlack
 export InterfaceFlowSlackUp
 export InterfaceFlowSlackDown
 export PieceWiseLinearCostVariable
+export HVDCActivePowerReceivedFromVariable
+export HVDCActivePowerReceivedToVariable
+export HVDCPiecewiseLossVariable
+export HVDCPiecewiseBinaryLossVariable
+export HVDCActiveDCPowerSentFromVariable
+export HVDCActiveDCPowerSentToVariable
+export HVDCReactivePowerSentFromVariable
+export HVDCReactivePowerSentToVariable
+export ConverterPowerDirection
+export DCVoltageFrom
+export DCVoltageTo
+export SquaredDCVoltageFrom
+export SquaredDCVoltageTo
+export ConverterCurrent
+export SquaredConverterCurrent
+export ConverterPositiveCurrent
+export ConverterNegativeCurrent
+export ConverterCurrentDirection
+export HVDCLosses
+export AuxBilinearConverterVariableFrom
+export AuxBilinearSquaredConverterVariableFrom
+export AuxBilinearConverterVariableTo
+export AuxBilinearSquaredConverterVariableTo
 
 # Auxiliary variables
 export TimeDurationOn
@@ -270,8 +297,19 @@ export FlowReactivePowerFromToConstraint
 export FlowReactivePowerToFromConstraint
 export FrequencyResponseConstraint
 export HVDCPowerBalance
-export HVDCLosses
 export HVDCFlowDirectionVariable
+export ConverterACPowerCalculationConstraint
+export ConverterCurrentBalanceConstraint
+export ConverterLossesCalculationConstraint
+export FlowApparentPowerLimitConstraint
+export ConverterPowerBalanceConstraint
+export ConverterPowerCalculationConstraint
+export ConverterDirectionConstraint
+export ConverterMcCormickEnvelopes
+export InterpolationVoltageConstraints
+export InterpolationCurrentConstraints
+export InterpolationBilinearConstraints
+export CurrentAbsoluteValueConstraint
 export InputActivePowerVariableLimitsConstraint
 export NetworkFlowConstraint
 export NodalBalanceActiveConstraint
@@ -325,6 +363,8 @@ export RawACE
 export ProductionCostExpression
 export ActivePowerRangeExpressionLB
 export ActivePowerRangeExpressionUB
+export ReceivedHVDCActivePowerFromExpression
+export ReceivedHVDCActivePowerToExpression
 
 #################################################################################
 # Imports

src/core/constraints.jl

@@ -336,6 +336,7 @@ struct InterfaceFlowLimit <: ConstraintType end
 struct HVDCFlowCalculationConstraint <: ConstraintType end
 
 abstract type PowerVariableLimitsConstraint <: ConstraintType end
+
 """
 Struct to create the constraint to limit active power input expressions.
 For more information check [Device Formulations](@ref formulation_intro).
@@ -401,3 +402,189 @@ struct LineFlowBoundConstraint <: ConstraintType end
 
 abstract type EventConstraint <: ConstraintType end
 struct OutageConstraint <: EventConstraint end
+
+################ HVDC VSC McCormick Model ##################
+
+"""
+Struct to create the constraints that set the losses through a lossy Interconnecting Power Converter.
+
+The specified constraint is formulated as:
+```math
+\\begin{align*}
+& i_c^{dc} = \\sum_{j \\in \\mathcal{B}^{DC}} \\frac{1}{r_{i,j}} (v_i - v_j), \\quad \\forall t \\in \\{1,\\dots, T\\} 
+\\end{align*}
+```
+"""
+struct ConverterCurrentBalanceConstraint <: ConstraintType end
+
+"""
+Struct to create the constraints that compute the converter DC power based on current and voltage.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& p_c = 0.5 \\cdot (γ^{sq} - v^{sq} - i^{sq}), \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& γ_c = v_c + i_c, \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+\\end{align*}
+```
+"""
+struct ConverterPowerCalculationConstraint <: ConstraintType end
+
+"""
+Struct to create the constraints that decide the operation direction of the converter.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& I_c^{min} (1 - κ_c) \\le i_c \\le κ_c * I_c^{max},  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& P_c^{min} (1 - κ_c) \\le p_c \\le κ_c * P_c^{max}, \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+\\end{align*}
+```
+"""
+struct ConverterDirectionConstraint <: ConstraintType end
+
+"""
+Struct to create the McCormick envelopes constraints that decide the bounds on the DC active power.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& p_c \\ge V^{min} i_c + v_c I^{min} - I^{min}V^{min},  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& p_c \\ge V^{max} i_c + v_c I^{max} - I^{max}V^{max},  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& p_c \\le V^{max} i_c + v_c I^{min} - I^{min}V^{max},  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& p_c \\le V^{min} i_c + v_c I^{max} - I^{max}V^{min},  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+\\end{align*}
+```
+"""
+struct ConverterMcCormickEnvelopes <: ConstraintType end
+
+"""
+Struct to create the Quadratic PWL interpolation constraints that decide square value of the voltage.
+In this case x = voltage and y = squared_voltage.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& x = x_0 + \\sum_{k=1}^K (x_{k} - x_{k-1}) \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& y = y_0 + \\sum_{k=1}^K (x_{k} - x_{k-1}) \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& z_k \\le \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\}, \\forall k \\in \\{1,\\dots, K-1\\} \\\\
+& z_k \\ge \\delta_{k+1},  \\quad \\forall t \\in \\{1,\\dots, T\\}, \\forall k \\in \\{1,\\dots, K-1\\} \\\\
+\\end{align*}
+```
+"""
+struct InterpolationVoltageConstraints <: ConstraintType end
+
+"""
+Struct to create the Quadratic PWL interpolation constraints that decide square value of the current.
+In this case x = current and y = squared_current.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& x = x_0 + \\sum_{k=1}^K (x_{k} - x_{k-1}) \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& y = y_0 + \\sum_{k=1}^K (x_{k} - x_{k-1}) \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& z_k \\le \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\}, \\forall k \\in \\{1,\\dots, K-1\\} \\\\
+& z_k \\ge \\delta_{k+1},  \\quad \\forall t \\in \\{1,\\dots, T\\}, \\forall k \\in \\{1,\\dots, K-1\\} \\\\
+\\end{align*}
+```
+"""
+struct InterpolationCurrentConstraints <: ConstraintType end
+
+"""
+Struct to create the Quadratic PWL interpolation constraints that decide square value of the bilinear variable γ.
+In this case x = γ and y = squared_γ.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& x = x_0 + \\sum_{k=1}^K (x_{k} - x_{k-1}) \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& y = y_0 + \\sum_{k=1}^K (x_{k} - x_{k-1}) \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\} \\\\
+& z_k \\le \\delta_k,  \\quad \\forall t \\in \\{1,\\dots, T\\}, \\forall k \\in \\{1,\\dots, K-1\\} \\\\
+& z_k \\ge \\delta_{k+1},  \\quad \\forall t \\in \\{1,\\dots, T\\}, \\forall k \\in \\{1,\\dots, K-1\\} \\\\
+\\end{align*}
+```
+"""
+struct InterpolationBilinearConstraints <: ConstraintType end
+
+"""
+Struct to create the constraints that set the absolute value for the current to use in losses through a lossy Interconnecting Power Converter.
+
+The specified constraint is formulated as:
+```math
+\\begin{align*}
+& i_c^{dc} = i_c^+ - i_c^-, \\quad \\forall t \\in \\{1,\\dots, T\\}  \\\\
+& i_c^+ \\le I_{max} \\cdot \\nu_c,  \\quad \\forall t \\in \\{1,\\dots, T\\}  \\\\
+& i_c^+ \\le I_{max} \\cdot (1 - \\nu_c),  \\quad \\forall t \\in \\{1,\\dots, T\\}  
+\\end{align*}
+```
+"""
+struct CurrentAbsoluteValueConstraint <: ConstraintType end
+
+"""
+Struct to create the constraints that set the losses for the converter to use in losses through a lossy Interconnecting Power Converter.
+
+The specified constraint for the bilinear model is formulated as:
+```math
+\\begin{align*}
+& p_c^{loss} = a_c + b_c |i_c| + c_c i_c^2,  \\quad \\forall t \\in \\{1,\\dots, T\\}  
+\\end{align*}
+```
+
+For the quadratic model is formulated as:
+```math
+\\begin{align*}
+& p_c^{loss} = a_c + b_c |p_c^{from}| + c_c (p_c^{from})^2,  \\quad \\forall t \\in \\{1,\\dots, T\\}  
+\\end{align*}
+```
+"""
+struct ConverterLossesCalculationConstraint <: ConstraintType end
+
+################ HVDC VSC AC Bilinear Model ##################
+
+"""
+Struct to create the constraints that compute the converter DC power based on current and voltage.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& p_c = v_c \\cdot i_c, \\quad \\forall t \\in \\{1,\\dots, T\\} 
+\\end{align*}
+```
+"""
+struct ConverterACPowerCalculationConstraint <: ConstraintType end
+
+"""
+Struct to create the constraints that decide the operation direction of the converter.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& p_c * i_c \\ge 0.0,  \\quad \\forall t \\in \\{1,\\dots, T\\}
+\\end{align*}
+```
+"""
+struct ConverterACDirectionConstraint <: ConstraintType end
+
+"""
+Struct to create the constraints that decide the flow apparent power limits to the VSC Line.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& p_c^2 + q_c^2 \\le rating^2,  \\quad \\forall t \\in \\{1,\\dots, T\\}
+\\end{align*}
+```
+"""
+struct FlowApparentPowerLimitConstraint <: ConstraintType end
+
+"""
+Struct to create the constraints that balance the DC Power to the VSC Line.
+
+The specified constraints are formulated as:
+```math
+\\begin{align*}
+& p_c^{from} = - p_c^{to} - p_c^{loss}, \\quad \\forall t \\in \\{1,\\dots, T\\}
+\\end{align*}
+```
+"""
+struct ConverterPowerBalanceConstraint <: ConstraintType end

src/core/definitions.jl

@@ -37,7 +37,11 @@ const JuMPFloatMatrix = DenseAxisArray{Float64, 2}
 const JuMPFloatArray = DenseAxisArray{Float64}
 const JuMPVariableArray = DenseAxisArray{JuMP.VariableRef}
 
-const TwoTerminalHVDCTypes = Union{PSY.TwoTerminalHVDCLine, PSY.TwoTerminalVSCDCLine}
+const TwoTerminalHVDCTypes = Union{
+    PSY.TwoTerminalHVDCLine,
+    PSY.TwoTerminalVSCDCLine,
+    PSY.TwoTerminalVSCLine,
+}
 # Settings constants
 const UNSET_HORIZON = Dates.Millisecond(0)
 const UNSET_RESOLUTION = Dates.Millisecond(0)
@@ -61,6 +65,7 @@ const OBJECTIVE_FUNCTION_NEGATIVE = -1.0
 const INITIALIZATION_PROBLEM_HORIZON_COUNT = 3
 # The DEFAULT_RESERVE_COST value is used to avoid degeneracy of the solutions, reserve cost isn't provided.
 const DEFAULT_RESERVE_COST = 1.0
+const DEFAULT_INTERPOLATION_LENGTH = 4
 const KiB = 1024
 const MiB = KiB * KiB
 const GiB = MiB * KiB

src/core/expressions.jl

@@ -12,6 +12,8 @@ struct ActivePowerRangeExpressionLB <: RangeConstraintLBExpressions end
 struct ActivePowerRangeExpressionUB <: RangeConstraintUBExpressions end
 struct ComponentReserveUpBalanceExpression <: ExpressionType end
 struct ComponentReserveDownBalanceExpression <: ExpressionType end
+struct ReceivedHVDCActivePowerFromExpression <: ExpressionType end
+struct ReceivedHVDCActivePowerToExpression <: ExpressionType end
 struct InterfaceTotalFlow <: ExpressionType end
 struct PTDFBranchFlow <: ExpressionType end
 
@@ -20,5 +22,7 @@ should_write_resulting_value(::Type{InterfaceTotalFlow}) = true
 should_write_resulting_value(::Type{RawACE}) = true
 should_write_resulting_value(::Type{ActivePowerBalance}) = true
 should_write_resulting_value(::Type{ReactivePowerBalance}) = true
+should_write_resulting_value(::Type{ReceivedHVDCActivePowerFromExpression}) = true
+should_write_resulting_value(::Type{ReceivedHVDCActivePowerToExpression}) = true
 
 convert_result_to_natural_units(::Type{InterfaceTotalFlow}) = true

src/core/formulations.jl

@@ -135,9 +135,21 @@ Branch type to represent lossy power flow on DC lines
 """
 struct HVDCTwoTerminalDispatch <: AbstractTwoTerminalDCLineFormulation end
 """
-Branch type to represent piecewise lossy power flow on two terminal DC lines
+Branch type to represent piecewise lossy power flow (with respect to power) on two terminal DC lines
 """
 struct HVDCTwoTerminalPiecewiseLoss <: AbstractTwoTerminalDCLineFormulation end
+"""
+Branch type to represent physical lossy model on two terminal DC lines using interpolation methods for quadratic losses
+"""
+struct HVDCTwoTerminalVSCLoss <: AbstractTwoTerminalDCLineFormulation end
+"""
+Branch type to represent physical lossy model using a bilinear model. Only usable with AC Network Models.
+"""
+struct HVDCTwoTerminalVSCLossBilinear <: AbstractTwoTerminalDCLineFormulation end
+"""
+Branch type to represent physical lossy model using a quadratic loss model with respect to power. Only usable with AC Network Models.
+"""
+struct HVDCTwoTerminalVSCLossQuadratic <: AbstractTwoTerminalDCLineFormulation end
 
 # Not Implemented
 # struct VoltageSourceDC <: AbstractTwoTerminalDCLineFormulation end