Reduced-space optimization, for optimal power flow.
Author exanauts
15 Stars
Updated Last
4 Months Ago
Started In
October 2020



Argos.jl extends the power-system modeler ExaPF.jl and the interior-point solver MadNLP.jl to solve optimal power flow (OPF) problems entirely in Julia.

The package is structured as follows:

  • in src/Evaluators/, various optimization evaluators implement the different callbacks (objective, gradient, Hessian) required in the optimization algorithms.
  • in src/Algorithms/, an Augmented Lagrangian algorithm is implemented, targeting primarily the resolution of large-scale OPF problems on GPU architectures.
  • in src/Wrappers/, a wrapper for MathOptInterface and a wrapper for NLPModels.jl are implemented.


One can install Argos with the default package manager:

add Argos

To check that everything is working as expected, please run

test Argos

By default, this command tests all the Evaluators implemented in Argos on the CPU and, if available, on a CUDA GPU.


The function run_opf is the entry point to Argos. It takes as input a path to a MATPOWER file and solves the associated OPF with MadNLP:

# Solve in the full-space
ips = Argos.run_opf("data/case9.m", Argos.FullSpace())

The second argument specifies the formulation used inside MadNLP to solve the OPF problem. FullSpace() implements the classical full-space formulation, (as implemented inside MATPOWER or PowerModels.jl). Alternatively, one may want to solve the OPF using the reduced-space formulation of Dommel and Tinney:

# Solve in the reduced-space
ips = Argos.run_opf("data/case9.m", Argos.DommelTinney())

How to use Argos' evaluators?

Argos implements two evaluators to solve the OPF problem: the FullSpaceEvaluator implements the classical OPF formulation in the full-space, whereas ReducedSpaceEvaluator implements the reduced-space formulation of Dommel & Tinney.

Using an evaluator

Instantiating a new evaluator from a MATPOWER file simply amounts to

# Reduced-space evaluator
nlp = Argos.ReducedSpaceEvaluator("case57.m")
# Full-space evaluator
flp = Argos.FullSpaceEvaluator("case57.m")

An initial optimization variable can be computed as

u = Argos.initial(nlp)

The variable u is the control that will be used throughout the optimization. Once a new point u obtained, one can refresh all the structures inside nlp with:

Argos.update!(nlp, u)

Once the structures are refreshed, the other callbacks can be evaluated as well:

Argos.objective(nlp, u) # objective
Argos.gradient(nlp, u)  # reduced gradient
Argos.jacobian(nlp, u)  # reduced Jacobian
Argos.hessian(nlp, u)   # reduced Hessian

MOI wrapper

Argos implements a wrapper to MathOptInterface to solve the optimal power flow problem with any nonlinear optimization solver compatible with MathOptInterface:

nlp = Argos.ReducedSpaceEvaluator("case57.m")
optimizer = Ipopt.Optimizer() # MOI optimizer
# Update tolerance to be above tolerance of Newton-Raphson subsolver
MOI.set(optimizer, MOI.RawOptimizerAttribute("tol"), 1e-5)
# Solve reduced space problem
solution = Argos.optimize!(optimizer, nlp)

NLPModels wrapper

Alternatively, one can use NLPModels.jl to wrap any evaluators implemented in Argos. This amounts simply to:

nlp = Argos.FullSpaceEvaluator("case57.m")
# Wrap in NLPModels
model = Argos.OPFModel(nlp)

x0 = NLPModels.get_x0(model)
obj = NLPModels.obj(model, x0)

Once the evaluator is wrapped inside NLPModels.jl, we can leverage any solver implemented in JuliaSmoothOptimizers to solve the OPF problem.

How to deport the solution of the OPF on the GPU?

ExaPF.jl is using KernelAbstractions to implement all its core operations. Hence, deporting the computation on GPU accelerators is straightforward. Argos.jl inherits this behavior and all evaluators can be instantiated on GPU accelerators, simply as

using CUDAKernels # Load CUDA backend for KernelAbstractions
using ArgosCUDA
nlp = Argos.ReducedSpaceEvaluator("case57.m"; device=CUDADevice())

When doing so, all kernels are instantiated on the GPU to avoid memory transfer between the host and the device. The sparse linear algebra operations are handled by cuSPARSE, and the sparse factorizations are performed using cusolverRF via the Julia wrapper CUSOLVERRF.jl. This package is loaded via the included ArgosCUDA.jl package in /lib. When deporting the computation on the GPU, the reduced Hessian can be evaluated in parallel.

Batch evaluation of the reduced Hessian

Instead of computing the reduced Hessian one Hessian-vector product after one Hessian-vector product, the Hessian-vector products can be evaluated in batch. To activate the batch evaluation for the reduced Hessian, please specify the number of Hessian-vector products to perform in one batch as

nlp = Argos.ReducedSpaceEvaluator("case57.m"; device=CUDADevice(), nbatch_hessian=8)

Note that on large instances, the batch computation can be demanding in terms of GPU's memory.

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