[Paper Review] DeepOPF: Deep Neural Network for DC Optimal Power Flow

Xiang Pan, Tianyu Zhao+1 more|arXiv (Cornell University)|May 11, 2019

Optimal Power Flow Distribution35 references4 citations

TL;DR

DeepOPF proposes a deep neural network (DNN) framework to solve DC optimal power flow (DC-OPF) problems by learning the high-dimensional mapping between load inputs and optimal dispatch decisions. It achieves feasible solutions with negligible optimality loss while accelerating computation by two orders of magnitude compared to conventional solvers, leveraging problem structure and uniform sampling to reduce overfitting and model complexity.

ABSTRACT

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving direct current optimal power flow (DC-OPF) problems. DeepOPF is inspired by the observation that solving DC-OPF for a given power network is equivalent to characterizing a high-dimensional mapping between the load inputs and the dispatch and transmission decisions. We construct and train a DNN model to learn such mapping, then we apply it to obtain optimized operating decisions upon arbitrary load inputs. We adopt uniform sampling to address the over-fitting problem common in generic DNN approaches. We leverage on a useful structure in DC-OPF to significantly reduce the mapping dimension, subsequently cutting down the size of our DNN model and the amount of training data/time needed. We also design a post-processing procedure to ensure the feasibility of the obtained solution. Simulation results of IEEE test cases show that DeepOPF always generates feasible solutions with negligible optimality loss, while speeding up the computing time by two orders of magnitude as compared to conventional approaches implemented in a state-of-the-art solver.

Motivation & Objective

• To develop a deep learning-based approach for solving DC-OPF problems efficiently and scalably.
• To exploit the structural properties of DC-OPF to reduce the dimensionality of the mapping, thereby shrinking model size and training cost.
• To ensure solution feasibility through a post-processing procedure, overcoming a common challenge in DNN-based optimization.
• To achieve high computational speedup without sacrificing solution quality, enabling real-time deployment in power system operations.
• To demonstrate the feasibility and accuracy of DNNs in replacing traditional convex solvers for repeated DC-OPF instances.

Proposed method

• The method formulates DC-OPF as a high-dimensional regression problem mapping load profiles to optimal generator outputs and line flows.
• A deep feedforward neural network is trained to learn this mapping using uniform sampling to mitigate overfitting.
• The architecture integrates structural constraints of DC-OPF to reduce the effective mapping dimension, decreasing model complexity and data requirements.
• A pre-processing step normalizes load inputs to improve training stability and convergence.
• A post-processing procedure adjusts the DNN output to enforce physical and operational constraints, ensuring feasibility.
• The loss function is designed to prioritize accurate prediction of high-impact variables (e.g., large generators), minimizing total cost deviation.

Experimental results

Research questions

• RQ1 Can a deep neural network effectively approximate the solution mapping of DC-OPF for a given power network?
• RQ2 How can structural properties of DC-OPF be exploited to reduce the dimensionality of the learning task and improve model efficiency?
• RQ3 Can uniform sampling effectively prevent overfitting in DNN-based DC-OPF solutions?
• RQ4 To what extent can a DNN-based approach maintain solution feasibility and optimality compared to conventional solvers?
• RQ5 How does model depth affect prediction accuracy and computational efficiency in the context of DC-OPF?

Key findings

• DeepOPF consistently generates feasible solutions across all IEEE test cases, with no infeasibility observed in simulations.
• The method achieves optimality loss of less than 0.4% on average, with the best-case deviation at only +83$/hr (0.2%) on the IEEE 118-bus system.
• Computing time is reduced by two orders of magnitude—down to 0.17 milliseconds per solution—compared to state-of-the-art convex solvers.
• The training time per epoch is negligible (e.g., 19.0 seconds for the 300-bus case), making amortized training cost acceptable over repeated use.
• Deeper networks (e.g., three hidden layers) yield better accuracy than shallow ones, with a 50% reduction in cost deviation compared to single-layer models.
• Prediction errors are acceptably small across all generators, with minimal impact on total cost, especially for low-output units.