MPA-DNN: Projection-Aware Unsupervised Learning for Multi-period DC-OPF

TL;DR

The paper tackles fast, feasible multi-period DC-OPF under inter-temporal constraints by introducing MPA-DNN, a projection-aware neural network trained in an unsupervised manner. A differentiable projection layer enforces hard feasibility over the entire horizon by solving a constrained QP that minimizes $\tfrac{1}{2}\|\mathbf{x}-\mathbf{z}\|_2^2$ subject to multi-period constraints, enabling end-to-end gradient flow through KKT-based backpropagation. The approach yields near-optimal generation costs while strictly satisfying ramp and energy storage dynamics, demonstrated on the IEEE 39-bus system with an ESS, and shows superior generalization under load variations compared to supervised baselines. This framework eliminates the need for labeled optimization solutions and provides a practical pathway for real-time, constraint-aware DL surrogates in power system operations.

Abstract

Ensuring both feasibility and efficiency in optimal power flow (OPF) operations has become increasingly important in modern power systems with high penetrations of renewable energy and energy storage. While deep neural networks (DNNs) have emerged as promising fast surrogates for OPF solvers, they often fail to satisfy critical operational constraints, especially those involving inter-temporal coupling, such as generator ramping limits and energy storage operations. To deal with these issues, we propose a Multi-Period Projection-Aware Deep Neural Network (MPA-DNN) that incorporates a projection layer for multi-period dispatch into the network. By doing so, our model enforces physical feasibility through the projection, enabling end-to-end learning of constraint-compliant dispatch trajectories without relying on labeled data. Experimental results demonstrate that the proposed method achieves near-optimal performance while strictly satisfying all constraints in varying load conditions.

Figures (2)

• Figure 1: MPA-DNN architecture with a differentiable projection layer and gradient flow through the KKT system. The input is a 24-hour load profile vector, which is mapped to a raw generation vector $\mathbf{z}$ via a deep neural network. The differentiable projection layer solves a constrained QP to obtain a feasible dispatch $\widetilde{\mathbf{x}}$ by projecting $\mathbf{z}$ onto the feasible set $\mathcal{F}$ over the entire time horizon. The loss function is computed using $\widetilde{\mathbf{x}}$. The network parameters are updated through the projection layer by the backpropagation.
• Figure 2: Ramping comparison for Generator 1 over a 24-hour horizon under load scale of 1.050. The figure shows that MPA-DNN and the solver produce feasible trajectories within the ramping limits, while SPA-DNN violates ramping constraints during hour 15–16.