[Paper Review] DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks

Liang Heng, Changhong Zhao|arXiv (Cornell University)|Sep 22, 2023

Optimal Power Flow Distribution4 citations

TL;DR

DeepOPF-U proposes a unified deep neural network that solves AC optimal power flow (OPF) across multiple and expanding power networks using elastic input/output layers to handle varying numbers of buses, lines, loads, and distributed energy resources (DERs). It achieves near-optimal solutions with up to 4,880× speedup over traditional solvers, maintaining high constraint satisfaction and generalizability without retraining.

ABSTRACT

The traditional machine learning models to solve optimal power flow (OPF) are mostly trained for a given power network and lack generalizability to today's power networks with varying topologies and growing plug-and-play distributed energy resources (DERs). In this paper, we propose DeepOPF-U, which uses one unified deep neural network (DNN) to solve alternating-current (AC) OPF problems in different power networks, including a set of power networks that is successively expanding. Specifically, we design elastic input and output layers for the vectors of given loads and OPF solutions with varying lengths in different networks. The proposed method, using a single unified DNN, can deal with different and growing numbers of buses, lines, loads, and DERs. Simulations of IEEE 57/118/300-bus test systems and a network growing from 73 to 118 buses verify the improved performance of DeepOPF-U compared to existing DNN-based solution methods.

Motivation & Objective

• Address the lack of generalizability in existing DNN-based OPF models that require retraining for each new network topology.
• Enable a single deep neural network to solve AC OPF problems across multiple power networks with different topologies and sizes.
• Support plug-and-play integration of new buses, lines, loads, and DERs in expanding networks without retraining.
• Maintain high solution quality and computational efficiency across diverse and evolving power system configurations.

Proposed method

• Design elastic input and output layers with plug-and-play neurons to dynamically handle load and solution vectors of varying lengths across different networks.
• Introduce an incremental training process to sequentially update the unified DNN weights for new or expanded networks without full retraining.
• Use a single unified DNN to learn the load-to-solution mapping across multiple networks, including those expanding from 73 to 118 buses.
• Encode network topology and admittance data into the input representation to preserve structural information.
• Train the unified DNN on data from multiple networks simultaneously, enabling generalization across topological variations.
• Apply a loss function that minimizes the gap between predicted and true OPF objective values while enforcing constraint satisfaction.

Experimental results

Research questions

• RQ1 Can a single deep neural network generalize across multiple power networks with different topologies and sizes?
• RQ2 How well can a unified DNN maintain solution quality when handling networks with varying numbers of buses, lines, loads, and DERs?
• RQ3 To what extent can the unified DNN adapt to network expansion without retraining?
• RQ4 How does the performance of the unified DNN compare to existing DNN-based OPF methods in terms of accuracy, constraint satisfaction, and speedup?
• RQ5 What is the trade-off between model generalizability and computational efficiency in multi-network AC OPF solving?

Key findings

• DeepOPF-U achieves an average speed-up of ×4880 over the MIPS solver on the IEEE 2,000-bus system, significantly outperforming DACOPF (×184) and EACOPF (×373).
• The method maintains near-perfect constraint satisfaction: 100% for voltage magnitude and branch flow limits, and over 99.7% for active/reactive power generation limits.
• The objective value gap between DeepOPF-U predictions and MIPS solutions is only 0.23%, indicating high solution accuracy.
• DeepOPF-U uses 44% less storage than DeepOPF-V, which requires a separate DNN per feeder, demonstrating superior scalability.
• In expanding networks from 73 to 118 buses, DeepOPF-U successfully tracks time-varying OPF solutions with minimal deviation from ground-truth values.
• The unified DNN achieves 99.67% average load satisfaction for active power and 99.63% for reactive power, showing robustness in load handling.