A Feasible Reduced Space Method for Real-Time Optimal Power Flow

Pacaud, François; Maldonado, Daniel Adrian; Shin, Young Kee; Schanen, Michel; Anitescu, Mihai

doi:10.48550/arxiv.2110.02590

Cited by 1 publication

(2 citation statements)

References 22 publications

(60 reference statements)

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“…We discuss an application of the proposed method to the OPF problem in Section 4: our numerical results show that both the reduced IPM and its feasible variant are able to solve large-scale OPF instances-with up to 70,000 buses-entirely on the GPU. This result improves on the previous results reported in [21,27]. As expected, the reduced-space algorithm is competitive when the problem has fewer degrees of freedom, but it achieves respectable performance (within a factor of 3 compared with state-of-the-art methods) even on the less favorable instances.…”

Section: Contributionssupporting

confidence: 84%

“…Comparing with Table 2, we make the following observations. (i) RedLin is able to solve instances with up to 25,000 buses, which, to the best of our knowledge, is a net improvement compared with previous attempts to solve the OPF in the reduced-space [21,27]. (ii) On the largest instances, RedLin is penalized compared with LinRed, since it has to deal with the reduced Jacobian Âu .…”

Section: Benchmark Instancesmentioning

confidence: 86%

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Condensed interior-point methods: porting reduced-space approaches on GPU hardware

Pacaud¹,

Shin²,

Schanen³

et al. 2022

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The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush-Kuhn-Tucker (KKT) system at each iteration of the algorithm. When solving large-scale nonlinear problems, state-of-the art IPM solvers rely on efficient sparse linear solvers to solve the KKT system. Instead, we propose a novel reduced-space IPM algorithm that condenses the KKT system into a dense matrix whose size is proportional to the number of degrees of freedom in the problem. Depending on where the reduction occurs we derive two variants of the reduced-space method: linearize-then-reduce and reduce-then-linearize. We adapt their workflow so that the vast majority of computations are accelerated on GPUs. We provide extensive numerical results on the optimal power flow problem, comparing our GPU-accelerated reduced space IPM with Knitro and a hybrid full space IPM algorithm. By evaluating the derivatives on the GPU and solving the KKT system on the CPU, the hybrid solution is already significantly faster than the CPU-only solutions. The two reduced-space algorithms go one step further by solving the KKT system entirely on the GPU. As expected, the performance of the two reduction algorithms depends intrinsically on the number of available degrees of freedom: their performance is poor when the problem has many degrees of freedom, but the two algorithms are up to 3 times faster than Knitro as soon as the relative number of degrees of freedom becomes smaller.Mihai Anitescu dedicates this work to the 70-th birthday of Florian Potra. Florian, thank you for the great contributions to optimization in general, and interior point methods in particular, and for initiating me and many others in them.

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Section: Contributionssupporting

confidence: 84%

Section: Benchmark Instancesmentioning

confidence: 86%