Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Efficient Probabilistic Optimal Power Flow Assessment Using an Adaptive Stochastic Spectral Embedding Surrogate Model

Xiaoting Wang, Jingyu Liu, Xiaozhe Wang

TL;DR

The paper tackles the challenge of efficiently solving probabilistic AC-OPF under uncertainty from renewable energy and varying loads. It introduces Adaptive Stochastic Spectral Embedding (ASSE), a surrogate that adaptively partitions the uncertain input space and builds PCE-based residual expansions on each subdomain, guided by Sobol' indices and least-angle regression for coefficients. In a 9-bus test case, ASSE closely matches Monte Carlo results and outperforms sparse PCE in capturing non-Gaussian and localized responses, often using a low PCE order and achieving substantial computational savings. The approach offers a scalable, interpretable tool for probabilistic security assessment and planning in power systems with high penetrations of renewable energy.

Abstract

This paper presents an adaptive stochastic spectral embedding (ASSE) method to solve the probabilistic AC optimal power flow (AC-OPF), a critical aspect of power system operation. The proposed method can efficiently and accurately estimate the probabilistic characteristics of AC-OPF solutions. An adaptive domain partition strategy and expansion coefficient calculation algorithm are integrated to enhance its performance. Numerical studies on a 9-bus system demonstrate that the proposed ASSE method offers accurate and fast evaluations compared to the Monte Carlo simulations. A comparison with a sparse polynomial chaos expansion method, an existing surrogate model, further demonstrates its efficacy in accurately assessing the responses with strongly local behaviors.

Efficient Probabilistic Optimal Power Flow Assessment Using an Adaptive Stochastic Spectral Embedding Surrogate Model

TL;DR

The paper tackles the challenge of efficiently solving probabilistic AC-OPF under uncertainty from renewable energy and varying loads. It introduces Adaptive Stochastic Spectral Embedding (ASSE), a surrogate that adaptively partitions the uncertain input space and builds PCE-based residual expansions on each subdomain, guided by Sobol' indices and least-angle regression for coefficients. In a 9-bus test case, ASSE closely matches Monte Carlo results and outperforms sparse PCE in capturing non-Gaussian and localized responses, often using a low PCE order and achieving substantial computational savings. The approach offers a scalable, interpretable tool for probabilistic security assessment and planning in power systems with high penetrations of renewable energy.

Abstract

This paper presents an adaptive stochastic spectral embedding (ASSE) method to solve the probabilistic AC optimal power flow (AC-OPF), a critical aspect of power system operation. The proposed method can efficiently and accurately estimate the probabilistic characteristics of AC-OPF solutions. An adaptive domain partition strategy and expansion coefficient calculation algorithm are integrated to enhance its performance. Numerical studies on a 9-bus system demonstrate that the proposed ASSE method offers accurate and fast evaluations compared to the Monte Carlo simulations. A comparison with a sparse polynomial chaos expansion method, an existing surrogate model, further demonstrates its efficacy in accurately assessing the responses with strongly local behaviors.
Paper Structure (11 sections, 11 equations, 5 figures, 3 tables)

This paper contains 11 sections, 11 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Probabilistic AC-OPF
  3. Probabilistic AC-OPF
  4. Adaptive Stochastic Spectral Embedding
  5. The SSE Representation
  6. The PCE-based Residuals Expansion
  7. Adaptive Sequential Partition
  8. The Adaptive Sparse Procedure for Calculating $c_l$
  9. ASSE-based Probabilistic AC-OPF
  10. Simulation Studies
  11. Conclusions

Figures (5)

  • Figure 1: The CDFs of $P_{G_1}$ by the ASSE, SPCE, and MC simulations.
  • Figure 2: The CDFs of $P_{G_2}$ by the ASSE, SPCE, and MC simulations.
  • Figure 3: The CDFs of $Q_{G_1}$ by the ASSE, SPCE, and MC simulations.
  • Figure 4: The CDFs of $Q_{G_2}$ by the ASSE, SPCE, and MC simulations.
  • Figure 5: Validation errors $e_{\mathrm{Val}}$ of different training sample sizes $N_{\mathrm{ED}}$ for $P_{G_1}$ and $Q_{G_2}$ by the ASSE, and SPCE method. Left: $P_{G_1}$, Right: $Q_{G_2}$.