Network Formulations

Type Hierarchy

We begin with the top of the hierarchy, where we can distinguish between conic and non-conic power flow models.

PowerModels.AbstractConicModels = Union{PowerModels.AbstractConicModel, PowerModels.AbstractBFConicModel}
PowerModels.AbstractConicModel <: PowerModels.AbstractPowerModel
PowerModels.AbstractBFModel <: PowerModels.AbstractPowerModel
PowerModels.AbstractBFQPModel <: PowerModels.AbstractBFModel
PowerModels.AbstractBFConicModel <: PowerModels.AbstractBFModel

We begin with the top of the hierarchy, where we can distinguish between AC and DC power flow models.

PowerModels.AbstractACPModel <: PowerModels.AbstractPowerModel
PowerModels.AbstractDCPModel <: PowerModels.AbstractPowerModel
PowerModelsDistribution.AbstractNLPUBFModel <: PowerModels.AbstractBFQPModel
PowerModelsDistribution.AbstractConicUBFModel <: PowerModels.AbstractBFConicModel
PowerModelsDistribution.AbstractLPUBFModel <: PowerModelsDistribution.AbstractNLPUBFModel

From there, different Models are possible:

#Bus injection models:
PowerModels.AbstractACPModel <: PowerModels.AbstractPowerModel
PowerModels.AbstractDCPModel <: PowerModels.AbstractPowerModel

#Branch flow models:
PowerModelsDistribution.SDPUBFModel <: PowerModelsDistribution.AbstractConicUBFModel
PowerModelsDistribution.SOCNLPUBFModel <: PowerModelsDistribution.AbstractNLPUBFModel
PowerModelsDistribution.SOCConicUBFModel <: PowerModelsDistribution.AbstractConicUBFModel

PowerModelsDistribution.LPLinUBFModel <: PowerModels.AbstractBFModel
PowerModelsDistribution.LPUBFFullModel <: PowerModelsDistribution.AbstractLPUBFModel
PowerModelsDistribution.LPUBFDiagModel <: PowerModelsDistribution.AbstractLPUBFModel

Power Models

Each of these Models can be used as the type parameter for a PowerModel:

mutable struct PowerModels.ACPPowerModel <: PowerModels.AbstractACPModel PowerModels.@pm_fields end
mutable struct PowerModels.DCPPowerModel <: PowerModels.AbstractDCPModel PowerModels.@pm_fields end

mutable struct PowerModels.SOCWRPowerModel <: PowerModels.SOCWRModel PowerModels.@pm_fields end

mutable struct PowerModelsDistribution.SDPUBFPowerModel <: PowerModelsDistribution.SDPUBFModel PowerModels.@pm_fields end
mutable struct PowerModelsDistribution.SOCNLPUBFPowerModel <: PowerModelsDistribution.SOCNLPUBFModel PowerModels.@pm_fields end
mutable struct PowerModelsDistribution.SOCConicUBFPowerModel <: PowerModelsDistribution.SOCConicUBFModel PowerModels.@pm_fields end

mutable struct PowerModelsDistribution.LPUBFFullPowerModel <: PowerModelsDistribution.LPUBFFullModel PowerModels.@pm_fields end
mutable struct PowerModelsDistribution.LPUBFDiagPowerModel <: PowerModelsDistribution.LPUBFDiagModel PowerModels.@pm_fields end
mutable struct PowerModelsDistribution.LPLinUBFPowerModel <: PowerModelsDistribution.LPLinUBFModel PowerModels.@pm_fields end

Union Types

To support both conic and quadratically-constrained formulation variants for the unbalanced branch flow model, the union type AbstractUBFModels is defined. These formulations extend AbstractBFModel and are therefore also AbstractWModels (as defined in PowerModels proper).

AbstractUBFModels = Union{AbstractNLPUBFModel, AbstractConicUBFModel}

Optimization problem classes

• NLP (nonconvex): ACPPowerModel
• SDP: SDPUBFPowerModel
• SOC(-representable): SOCWRPowerModel, SOCNLPUBFPowerModel, SOCConicUBFPowerModel
• Linear: LPUBFFullPowerModel, LPUBFDiagPowerModel, LPLinUBFPowerModel, DCPPowerModel

Matrix equations versus scalar equations

JuMP supports vectorized syntax, but not for nonlinear constraints. Therefore, certain formulations must be implemented in a scalar fashion. Other formulations can be written as matrix (in)equalities. The current implementations are categorized as follows:

• Scalar: ACPPowerModel, DCPPowerModel, LPLinUBFPowerModel, SOCWRPowerModel
• Matrix: SDPUBFPowerModel, SOCNLPUBFPowerModel, SOCConicUBFPowerModel, LPUBFFullPowerModel, LPUBFDiagPowerModel