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Exploiting Convexity of Neural Networks in Dynamic Operating Envelope Optimization for Distributed Energy Resources

Hongyi Li, Liming Liu, Yunyi Li, Zhaoyu Wang

TL;DR

This work tackles the non-convexity of power-flow equations in dynamic operating envelope (DOE) optimization for distributed energy resources by leveraging input convex neural networks (ICNNs). By embedding constraint-aware ICNNs, the non-convex power-flow constraints are replaced with convex, linearizable surrogates, and a tight linear relaxation is proven to produce equivalent solutions. The approach includes a constraint retrenchment strategy to reduce problem dimensionality and computation, enabling fast DOE calculations on large radial networks. Case studies on the IEEE 123-node and EPRI Ckt5 feeders demonstrate improved accuracy and substantial speedups over benchmark methods, highlighting potential for real-time DER coordination. The results indicate that ICNN-based DOE optimization can robustly maintain network limits while expanding DER participation in local energy markets and demand response programs.

Abstract

The increasing penetration of distributed energy resources (DERs) brings opportunities and challenges to the operation of distribution systems. To ensure network integrity, dynamic operating envelopes (DOEs) are issued by utilities to DERs as their time-varying export/import power limits. Due to the non-convex nature of power flow equations, the optimization of DOEs faces a dilemma of solution accuracy and computation efficiency. To bridge this gap, in this paper, we facilitate DOE optimization by exploiting the convexity of input convex neural networks (ICNNs). A DOE optimization model is first presented, comprehensively considering multiple operational constraints. We propose a constraint embedding method that allows us to replace the non-convex power flow constraints with trained ICNN models and convexify the problem. To further speed up DOE optimization, we propose a linear relaxation of the ICNN-based DOE optimization problem, for which the tightness is theoretically proven. The effectiveness of the proposed method is validated with numerical case studies. Results show that the proposed ICNN-based method outperforms other benchmark methods in optimizing DOEs in terms of both solution quality and solution time.

Exploiting Convexity of Neural Networks in Dynamic Operating Envelope Optimization for Distributed Energy Resources

TL;DR

This work tackles the non-convexity of power-flow equations in dynamic operating envelope (DOE) optimization for distributed energy resources by leveraging input convex neural networks (ICNNs). By embedding constraint-aware ICNNs, the non-convex power-flow constraints are replaced with convex, linearizable surrogates, and a tight linear relaxation is proven to produce equivalent solutions. The approach includes a constraint retrenchment strategy to reduce problem dimensionality and computation, enabling fast DOE calculations on large radial networks. Case studies on the IEEE 123-node and EPRI Ckt5 feeders demonstrate improved accuracy and substantial speedups over benchmark methods, highlighting potential for real-time DER coordination. The results indicate that ICNN-based DOE optimization can robustly maintain network limits while expanding DER participation in local energy markets and demand response programs.

Abstract

The increasing penetration of distributed energy resources (DERs) brings opportunities and challenges to the operation of distribution systems. To ensure network integrity, dynamic operating envelopes (DOEs) are issued by utilities to DERs as their time-varying export/import power limits. Due to the non-convex nature of power flow equations, the optimization of DOEs faces a dilemma of solution accuracy and computation efficiency. To bridge this gap, in this paper, we facilitate DOE optimization by exploiting the convexity of input convex neural networks (ICNNs). A DOE optimization model is first presented, comprehensively considering multiple operational constraints. We propose a constraint embedding method that allows us to replace the non-convex power flow constraints with trained ICNN models and convexify the problem. To further speed up DOE optimization, we propose a linear relaxation of the ICNN-based DOE optimization problem, for which the tightness is theoretically proven. The effectiveness of the proposed method is validated with numerical case studies. Results show that the proposed ICNN-based method outperforms other benchmark methods in optimizing DOEs in terms of both solution quality and solution time.

Paper Structure

This paper contains 20 sections, 1 theorem, 22 equations, 13 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Dynamic Operating Envelopes for Distributed Energy Resources
  3. Dynamic Operating Envelope Calculation Framework
  4. DOE Optimization Problem
  5. Input Convex Neural Network for DOE Optimization Problem
  6. Preliminaries of Input Convex Neural Networks
  7. Mathematic Model of ICNN
  8. Exact Inference of ICNN
  9. Learning Power Flow Constraints with ICNN
  10. Constraint Retrenchment Strategy
  11. Case Study
  12. Experiment Setup
  13. Test systems
  14. Benchmarks:
  15. Accuracy of ICNN
  16. ...and 5 more sections

Key Result

Theorem 1

Given definitions (y definition), (lim definition) and constraint (non-negative), optimizing the ICNN-based DOE optimization problem (MIP DOE) is equivalent to optimizing the following LP problem:

Figures (13)

  • Figure 1: DOE optimization framework for DERs in the distribution system.
  • Figure 2: Illustration of ICNN.
  • Figure 3: Proposed constraint embedding method that encodes constraint parameters in violation-regularization layers.
  • Figure 4: Illustration of a radial distribution system.
  • Figure 5: Modified IEEE 123-bus test feeder.
  • ...and 8 more figures

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • proof
  • Remark 4
  • Remark 5