An Efficient Learning-Based Solver for Two-Stage DC Optimal Power Flow with Feasibility Guarantees

TL;DR

This paper tackles uncertainty in two-stage DCOPF by learning a feasible, fast policy using two neural networks: one for the first stage and one for the recourse cost. Feasibility is guaranteed by a gauge map that maps neural outputs to the DCOPF constraint set, enabling end-to-end, unsupervised training that minimizes the actual two-stage cost. The approach achieves orders-of-magnitude speedups over traditional solvers while maintaining near-benchmark quality on IEEE 118-bus and 2000-bus systems, and outperforms affine policies and simple scenario-reduction baselines. The method is scalable and leverages scenario-based forecasting within a principled, constraint-aware learning framework, with potential extensions to AC OPF in future work.

Abstract

In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains computationally challenging to solve due to the large number of scenarios needed to accurately represent the uncertainties. To mitigate the computational issues, many techniques have been proposed to approximate the second-stage decisions so they can be dealt more efficiently. The challenge of finding good policies to approximate the second-stage decisions is that these solutions need to be feasible, which has been difficult to achieve with existing policies. To address these challenges, this paper proposes a learning method to solve the two-stage problem in a more efficient and optimal way. A technique called the gauge map is incorporated into the learning architecture design to guarantee the learned solutions' feasibility to the network constraints. Namely, we can design policies that are feed forward functions and only output feasible solutions. Simulation results on standard IEEE systems show that, compared to iterative solvers and the widely used affine policy, our proposed method not only learns solutions of good quality but also accelerates the computation by orders of magnitude.

Figures (4)

• Figure 1: The architecture used for training in the proposed algorithm. When making decisions in real time, we only need the network $\phi^{0}$ to predict the first-stage decisions from the given load forecast.
• Figure 2: In the RLD problem, non-negative orthant constraints can be enforced using ReLU activation in the last neural layer. For the reserve scheduling problem, the Tanh activation is used at the last neural layer and then the hypercubic output is passed through the transformation layers in \ref{['phi0-mapping']} to obtain a feasible solution.
• Figure 3: An illustrative example of the gauge map from $\mathbb{B}_{\infty}$ to a polyhedral C-set $\mathcal{Q}$. The $1$, $\frac{3}{4}$, $\frac{1}{2}$ and $\frac{1}{5}$ level curves of each set are plotted in blue. For each point in $\mathbb{B}_{\infty}$, it is transformed to its image (marked using the same color) in $\mathcal{Q}$ with the same level curve.
• Figure 4: The hypercubic output from the neural layers is transformed to a feasible solution for $\bm{\theta}$ by the gauge map. Then the value of the objective function can be easily computed.

Theorems & Definitions (8)

• Definition 1: C-set Blanchini07
• Theorem 4.1
• Definition 2: Gauge function Blanchini07
• Proposition 1
• Definition 3: gauge mapTabas2021ComputationallyES
• Theorem 4.2
• Theorem 4.3
• proof