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A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback

Heng Liang, Yujin Huang, Changhong Zhao

TL;DR

The paper tackles real-time OPF for networks with large DER penetration and limited communications by developing a data-driven, local-feedback controller that tracks time-varying OPF solutions. It linearizes the branch-flow model to enable local updates of controllable injections using gradients of the local cost plus learnable policies u_{蠒,i} driven by local voltage measurements, and it projects onto local feasibility sets to maintain safety. A probabilistic reformulation via chance constraints is introduced, with a stochastic primal-dual learning algorithm (and a gradient-free variant) to train the DNN-based policy without requiring pre-solved OPF data, yielding an 系-universal parametrization and an explicit tracking bound that depends on problem dynamics and approximation quality. Empirical results on the IEEE 37-bus feeder show improved tracking accuracy, reduced objective gaps, and lower voltage violations, while offering computational speedups over centralized benchmarks, indicating practical potential for fast, scalable, locally-implemented real-time OPF.

Abstract

The increasing penetration of distributed energy resources (DERs) adds variability as well as fast control capabilities to power networks. Dispatching the DERs based on local information to provide real-time optimal network operation is the desideratum. In this paper, we propose a data-driven real-time algorithm that uses only the local measurements to solve time-varying AC optimal power flow (OPF). Specifically, we design a learnable function that takes the local feedback as input in the algorithm. The learnable function, under certain conditions, will result in a unique stationary point of the algorithm, which in turn transfers the OPF problems to be optimized over the parameters of the function. We then develop a stochastic primal-dual update to solve the variant of the OPF problems based on a deep neural network (DNN) parametrization of the learnable function, which is referred to as the training stage. We also design a gradient-free alternative to bypass the cumbersome gradient calculation of the nonlinear power flow model. The OPF solution-tracking error bound is established in the sense of universal approximation of DNN. Numerical results on the IEEE 37-bus test feeder show that the proposed method can track the time-varying OPF solutions with higher accuracy and faster computation compared to benchmark methods.

A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback

TL;DR

The paper tackles real-time OPF for networks with large DER penetration and limited communications by developing a data-driven, local-feedback controller that tracks time-varying OPF solutions. It linearizes the branch-flow model to enable local updates of controllable injections using gradients of the local cost plus learnable policies u_{蠒,i} driven by local voltage measurements, and it projects onto local feasibility sets to maintain safety. A probabilistic reformulation via chance constraints is introduced, with a stochastic primal-dual learning algorithm (and a gradient-free variant) to train the DNN-based policy without requiring pre-solved OPF data, yielding an 系-universal parametrization and an explicit tracking bound that depends on problem dynamics and approximation quality. Empirical results on the IEEE 37-bus feeder show improved tracking accuracy, reduced objective gaps, and lower voltage violations, while offering computational speedups over centralized benchmarks, indicating practical potential for fast, scalable, locally-implemented real-time OPF.

Abstract

The increasing penetration of distributed energy resources (DERs) adds variability as well as fast control capabilities to power networks. Dispatching the DERs based on local information to provide real-time optimal network operation is the desideratum. In this paper, we propose a data-driven real-time algorithm that uses only the local measurements to solve time-varying AC optimal power flow (OPF). Specifically, we design a learnable function that takes the local feedback as input in the algorithm. The learnable function, under certain conditions, will result in a unique stationary point of the algorithm, which in turn transfers the OPF problems to be optimized over the parameters of the function. We then develop a stochastic primal-dual update to solve the variant of the OPF problems based on a deep neural network (DNN) parametrization of the learnable function, which is referred to as the training stage. We also design a gradient-free alternative to bypass the cumbersome gradient calculation of the nonlinear power flow model. The OPF solution-tracking error bound is established in the sense of universal approximation of DNN. Numerical results on the IEEE 37-bus test feeder show that the proposed method can track the time-varying OPF solutions with higher accuracy and faster computation compared to benchmark methods.

Paper Structure

This paper contains 14 sections, 3 theorems, 49 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model and Problem Formulation
  3. A Data-Driven Real-Time OPF Algorithm
  4. Learning Parametrization
  5. Reformulation via Chance Constraints
  6. Primal-Dual Learning
  7. DNN Parametrization and Tracking Performance
  8. Gradient-Free Learning with Nonlinear Model
  9. Numerical Results
  10. Gradient-Based Learning
  11. Gradient-Free Learning
  12. Conclusion
  13. Proof of Theorem \ref{['thm::1']}
  14. Proof of Theorem \ref{['thm::2']}

Key Result

Theorem 1

Let Assumption ass::1 hold. Suppose the function $u_{\varphi_i}:=[u_{\varphi_{p,i}},u_{\varphi_{q,i}}]^{\top}$ satisfies the following conditions, for all $i\in \mathcal{N}$: C1). The function $u_{\varphi_i}(v_i,d_i)$ is separable with respective to variables $v_i$ and $d_i$, i.e., $u_{\varphi_i}(v_ Moreover, if $\alpha<\frac{2m}{\xi^2}$ and function $u_{\vartheta_i}$ satisfies: C3).$u_{\vartheta_

Figures (7)

  • Figure 1: Illustration of OPF problem transformations for learning.
  • Figure 2: Framework of training and testing (operation) stages.
  • Figure 3: Architecture of the proposed neural network.
  • Figure 4: The voltage profiles: (a) without control; (b) the primal-dual controller anese2018optimal; (c) the proposed data-driven controller (trained with $\beta=0.1$).
  • Figure 5: OPF objectives and the absolute gaps between the real-time operations $\boldsymbol{x}^t$ and optimal solutions $\boldsymbol{x}^{*,t}$: (a) the primal-dual controller anese2018optimal; (b) the proposed data-driven controller (trained with $\beta=0.1$).
  • ...and 2 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • Definition 1
  • Theorem 2