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) with Sensitivity{T} return type
• DC OPF: B-theta formulation with analytical KKT sensitivities for demand, switching, cost, flow limits, and susceptances
• DC power flow: Switching and demand sensitivities via matrix perturbation theory
• AC power flow: Voltage and current sensitivities w.r.t. power injections
• AC OPF: Full sensitivity analysis (switching, demand, costs, flow limits) via implicit differentiation of KKT conditions
• LMP analysis: Locational marginal prices with energy/congestion decomposition
• Load shedding: Sensitivity of optimal load curtailment to network parameters

Installation

Requires Julia 1.9 or later.

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

Quick Start

using PowerDiff, PowerModels

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

# Solve DC OPF and compute sensitivities
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[2, 3]        # dLMP_2 / dd_3

See the Getting Started guide for DC/AC power flow and OPF walkthroughs.

Documentation

• Getting Started — DC PF, DC OPF, AC PF, AC OPF walkthroughs
• Sensitivity API — Operand/parameter tables, valid combinations, indexing
• Mathematical Background — B-theta formulation, KKT implicit differentiation
• Advanced Topics — Type hierarchy, caching, solver configuration
• API Reference — Full docstring reference

Dependencies

• PowerModels.jl — Power system modeling
• JuMP.jl — Optimization modeling
• Ipopt.jl — Default solver for DC and AC OPF
• ForwardDiff.jl — Automatic differentiation

License

Apache License 2.0