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A GPU-Accelerated Distributed Algorithm for Optimal Power Flow in Distribution Systems

Minseok Ryu, Geunyeong Byeon, Kibaek Kim

TL;DR

This work tackles the challenge of scalable, distributed, multi-phase OPF for distribution networks with dynamic topology. It introduces a solver-free, GPU-accelerated ADMM based on component-wise decomposition, isolating bound constraints to enable closed-form, matrix-operations on GPUs and row-reduction to guarantee full row rank where needed. Numerical results on IEEE tests from 13 to 8500 buses demonstrate substantial speedups over CPU-based approaches and strong scalability, especially for large networks. The approach reduces per-iteration time by orders of magnitude and holds promise for real-time or near real-time distribution system optimization, with future directions including convex relaxations and privacy-preserving techniques.

Abstract

We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable adaptable decomposition, we advocate a componentwise decomposition strategy. However, this approach can lead to a prolonged computation time mainly due to the excessive iterations required for achieving consensus among a large number of fine-grained components. To overcome this, we introduce a technique that segregates equality constraints from inequality constraints, enabling GPU parallelism to reduce per-iteration time by orders of magnitude, thereby significantly accelerating the overall computation. Numerical experiments on IEEE test systems ranging from 13 to 8500 buses demonstrate the superior scalability of the proposed approach compared to its CPU-based counterparts.

A GPU-Accelerated Distributed Algorithm for Optimal Power Flow in Distribution Systems

TL;DR

This work tackles the challenge of scalable, distributed, multi-phase OPF for distribution networks with dynamic topology. It introduces a solver-free, GPU-accelerated ADMM based on component-wise decomposition, isolating bound constraints to enable closed-form, matrix-operations on GPUs and row-reduction to guarantee full row rank where needed. Numerical results on IEEE tests from 13 to 8500 buses demonstrate substantial speedups over CPU-based approaches and strong scalability, especially for large networks. The approach reduces per-iteration time by orders of magnitude and holds promise for real-time or near real-time distribution system optimization, with future directions including convex relaxations and privacy-preserving techniques.

Abstract

We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable adaptable decomposition, we advocate a componentwise decomposition strategy. However, this approach can lead to a prolonged computation time mainly due to the excessive iterations required for achieving consensus among a large number of fine-grained components. To overcome this, we introduce a technique that segregates equality constraints from inequality constraints, enabling GPU parallelism to reduce per-iteration time by orders of magnitude, thereby significantly accelerating the overall computation. Numerical experiments on IEEE test systems ranging from 13 to 8500 buses demonstrate the superior scalability of the proposed approach compared to its CPU-based counterparts.
Paper Structure (29 sections, 31 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 29 sections, 31 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work and contributions
  3. Paper structure
  4. Mathematical Formulations
  5. Centralized multi-phase OPF model
  6. Operational bound constraints
  7. Power balance equations
  8. Voltage dependent load model
  9. Linearized power flow equations
  10. Multi-phase OPF model
  11. Distributed multi-phase OPF model
  12. A GPU-accelerated distributed algorithm
  13. Reformulations
  14. Closed-form solution expressions
  15. Termination criterion
  16. ...and 14 more sections

Figures (4)

  • Figure 1: (a) Average wall-clock time consumed for the local update. (b) Average computation time for solving the subproblems. (c) Average communication time. Note that the results from the first, second, and third rows are associated with the IEEE 13, 123, and 8500 instances, respectively.
  • Figure 2: Primal (left) and dual (right) residuals at each iteration of Algorithm \ref{['alg:admm']} when a CPU and a GPU, respectively, is used for solving the IEEE 13 instance.
  • Figure 3: Average time for conducting global, local, and dual updates per iteration and their summation (referred as total) when multiple CPUs (top), GPUs (middle), and threads in a GPU (bottom), respectively. Both multiple CPUs and GPUs computations are done in parallel.
  • Figure 4: Comparison of total time: a GPU versus 16 CPUs. Note that the y-axis is log-scaled.