The AC Optimal Power Flow problem (AC-OPF) is one of the most foundational optimization problems that arises in the design and operations of power networks. Mathematically the AC-OPF is a large-scale, sparse, non-convex nonlinear continuous optimization problem. In practice AC-OPF is most often solved to local optimality conditions using interior point methods. This project proposes AC-OPF as proxy-application for testing the viability of different nonlinear optimization frameworks, as performant solutions to AC-OPF has proven to be a necessary (but not always sufficient) condition for solving a wide range of industrial network optimization tasks.
- Communicate the technical requirements for solving real-world continuous non-convex mathematical optimization problems.
- Highlight scalability requirements for the problem sizes that occur in practice.
- Provide a consistent implementation for solving AC-OPF in different NLP modeling frameworks.
- All decision variables are continuous
- The objective function may be non-convex
- The constraints include a system of equality and inequality functions, which can be non-convex (the equality constraints usually cannot be expressed explicitly as a manifold)
- The constraints can take the form of polynomial and transcendental functions (e.g.
x^2*y^3,sin(x)*cos(y)) - Derivative computations should be handled by the modeling layer (e.g., via Automatic Differentiation). The user lacks the time or expertise to hard-code Jacobian and Hessian oracles.
At present this project is focused on comparing NLP modeling layers that are available in the Julia programming langue. However, other modeling layers may be considered in the future.
This work is not intended for comparing different nonlinear optimization algorithms, which are often independent of the NLP modeling layer. Consequently, the Ipopt solver is used as a standard NLP algorithm whenever it is accessible from the modeling layer.
This work adopts the mathematical model and data format that is used in the IEEE PES benchmark library for AC-OPF, PGLib-OPF. The Julia package PowerModels is used for parsing the problem data files and making standard data transformations.
In this formulation the equations encode the following properties: (1) minimization of generator fuel costs; (2) a voltage phase reference angle; (3) power balance (i.e. energy conservation); (4,5) Ohm's Law for the flow power; (6) power flow limits; and (7) angle difference limits.
AC-OPF is naturally modeled as continuous nonlinear optimization problem over complex data and variables. However, the implementations in this repository use the projection into real numbers to support the broadest possible set of optimization modeling frameworks.
In this formulation the complex voltage terms expand into the following expressions, |Vᵢ|^2 = (vᵢ)^2, ∠Vᵢ = θᵢ, Vᵢ * conj(Vⱼ) = vᵢ*vⱼ*cos(θᵢ-θⱼ) + im*vᵢ*vⱼ*sin(θᵢ-θⱼ), which is the source of the transcendental functions in the implementations.
Each of these files is designed to be stand-alone and can be tested with minimal package dependencies. Consequently, there is some code replication between implementations.
jump.jl: implementation using JuMPnlpmodels.jl: implementation using ADNLPModelsnonconvex.jl: implementation using Nonconvexoptim.jl: implementation using Optimoptimization.jl: implementation using Optimization
data/*: small example datasetstest/*: basic tests for the primary AC-OPF implementationsdebug/*: scripts for debugging NLP modeling layersvariants/*: additional variants of the AC-OPF problem
This code is provided under a BSD license as part of the Grid Optimization Competition Solvers project, C19076.