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Uncertainty-Aware Capacity Expansion for Real-World DER Deployment via End-to-End Network Integration

Yiyuan Pan, Yiheng Xie, Steven Low

TL;DR

This work addresses capacity expansion for DER deployment in real distribution grids by integrating a three-phase unbalanced distribution model with a robust two-stage optimization and an end-to-end predictive training loop. It introduces an affine-policy–based single-stage reformulation to handle box uncertainty and couples an LSTM predictor with differentiable optimization under conformal prediction to guarantee coverage. The approach is validated on real Southern California grid data, showing improved task performance and robust, uncertainty-aware DER siting and dispatch decisions. The results provide a tractable, adaptive planning tool for practical deployment in distribution networks facing stochastic prices and loads.

Abstract

The deployment of distributed energy resource (DER) devices plays a critical role in distribution grids, offering multiple value streams, including decarbonization, provision of ancillary services, non-wire alternatives, and enhanced grid flexibility. However, existing research on capacity expansion suffers from two major limitations that undermine the realistic accuracy of the proposed models: (i) the lack of modeling of three-phase unbalanced AC distribution networks, and (ii) the absence of explicit treatment of model uncertainty. To address these challenges, we develop a two-stage robust optimization model that incorporates a 3-phase unbalanced power flow model for solving the capacity expansion problem. Furthermore, we integrate a predictive neural network with the optimization model in an end-to-end training framework to handle uncertain variables with provable guarantees. Finally, we validate the proposed framework using real-world power grid data collected from our partner distribution system operators. The experimental results demonstrate that our hybrid framework, which combines the strengths of optimization models and neural networks, provides tractable decision-making support for DER deployments in real-world scenarios.

Uncertainty-Aware Capacity Expansion for Real-World DER Deployment via End-to-End Network Integration

TL;DR

This work addresses capacity expansion for DER deployment in real distribution grids by integrating a three-phase unbalanced distribution model with a robust two-stage optimization and an end-to-end predictive training loop. It introduces an affine-policy–based single-stage reformulation to handle box uncertainty and couples an LSTM predictor with differentiable optimization under conformal prediction to guarantee coverage. The approach is validated on real Southern California grid data, showing improved task performance and robust, uncertainty-aware DER siting and dispatch decisions. The results provide a tractable, adaptive planning tool for practical deployment in distribution networks facing stochastic prices and loads.

Abstract

The deployment of distributed energy resource (DER) devices plays a critical role in distribution grids, offering multiple value streams, including decarbonization, provision of ancillary services, non-wire alternatives, and enhanced grid flexibility. However, existing research on capacity expansion suffers from two major limitations that undermine the realistic accuracy of the proposed models: (i) the lack of modeling of three-phase unbalanced AC distribution networks, and (ii) the absence of explicit treatment of model uncertainty. To address these challenges, we develop a two-stage robust optimization model that incorporates a 3-phase unbalanced power flow model for solving the capacity expansion problem. Furthermore, we integrate a predictive neural network with the optimization model in an end-to-end training framework to handle uncertain variables with provable guarantees. Finally, we validate the proposed framework using real-world power grid data collected from our partner distribution system operators. The experimental results demonstrate that our hybrid framework, which combines the strengths of optimization models and neural networks, provides tractable decision-making support for DER deployments in real-world scenarios.

Paper Structure

This paper contains 22 sections, 3 theorems, 35 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Related Works
  4. Methodology
  5. Capacity Expansion Optimization Problem
  6. Problem Overview
  7. Objective Function
  8. OPF Constraints
  9. Non-invertible Admittance Matrices
  10. Single-stage Reformulation
  11. Electricity Price Uncertainty
  12. Load Demand Uncertainty
  13. Hybrid Traning Framework
  14. Network Module
  15. Optimization as a Differentiable Module
  16. ...and 7 more sections

Key Result

Proposition 1

For a box uncertainty set $\mathcal{U}=\{h\in[0,1]^m$$|\sum\nolimits_{i=1}^m h_i\le k\}$, we have $\hat{\mathcal{U}}=\beta\cdot\text{conv}(\mathbf{e}_1,...,\frac{k}{m}\mathbf{e})$ as its dominant set, where $\beta=\text{min}(k,\frac{m}{k})$.

Figures (3)

  • Figure 1: Hybrid training framework for capacity expansion.
  • Figure 2: Simplified regional grid topology.
  • Figure 3: Predictive efficacy at varying confidence $\alpha$.

Theorems & Definitions (7)

  • Definition 1
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Definition 2
  • Proposition 3