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PowerDiff.jl

A Julia package for differentiable power system analysis. Compute sensitivities of power flow solutions, optimal power flow dispatch, and locational marginal prices with respect to network parameters.

Features

  • Unified sensitivity API: calc_sensitivity(state, :operand, :parameter) returns Sensitivity{T} matrices with metadata
  • DC OPF (B-theta formulation): Susceptance-weighted Laplacian preserving network topology
  • DC power flow sensitivities: Switching and demand sensitivity for non-OPF power flow
  • AC power flow sensitivities: Voltage and current sensitivity w.r.t. power injections
  • AC OPF sensitivities: Sensitivity w.r.t. switching, demand, costs, and flow limits via implicit differentiation of KKT conditions
  • LMP computation: Locational marginal prices with energy/congestion decomposition
  • Load shedding: Sensitivity of optimal load curtailment w.r.t. demand, costs, and network constraints
  • ForwardDiff verification: All sensitivities verified against automatic differentiation

Installation

using Pkg
Pkg.add(url="https://github.com/grid-opt-alg-lab/PowerDiff.jl.git")

Quick Example

using PowerDiff, PowerModels

# Load network (make_basic_network is optional)
net = parse_file("case14.m")
dc_net = DCNetwork(net)
d = calc_demand_vector(net)

# DC OPF with sensitivity analysis
prob = DCOPFProblem(dc_net, d)
solve!(prob)

dlmp_dd = calc_sensitivity(prob, :lmp, :d)   # dLMP/dd (n x n)
dpg_dsw = calc_sensitivity(prob, :pg, :sw)   # dg/dsw (k x m)

dlmp_dd.formulation  # :dcopf
dlmp_dd.operand      # :lmp
dlmp_dd[2, 3]        # dLMP_2 / dd_3

See Getting Started for a full walkthrough.

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