A Convex Neural Network Solver for DCOPF with Generalization Guarantees

Abstract

The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of scenarios, which can be computationally challenging. As an alternative to iterative solvers, neural networks are often trained and used to solve DCOPF. These approaches can offer orders of magnitude reduction in computational time, but they cannot guarantee generalization, and small training error does not imply small testing errors. In this work, we propose a novel algorithm for solving DCOPF that guarantees the generalization performance. First, by utilizing the convexity of DCOPF problem, we train an input convex neural network. Second, we construct the training loss based on KKT optimality conditions. By combining these two techniques, the trained model has provable generalization properties, where small training error implies small testing errors. In experiments, our algorithm improves the optimality ratio of the solutions by a factor of five in comparison to end-to-end models.

Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

“…This echoes the critical challenge of ensuring the DNN solutions feasibility. Some efforts have been put to improve DNN feasibility, e.g., considering solution generalization [47] or appealing to post-processing schemes [5]. While the projection based post-processing step can retrieve a feasible solution in the face of infeasibility, the scheme turns to be computationally expensive and inefficient.…”

“…However, such a calibration region is not the minimal one while forms the outer bound of it. Denote the calibration rate on (45)- (47) as (x, y, z), it is easy to see that any combination such that 7x + 9y = 6 and z = 8/9 − y is the minimal supporting one.…”

Data-Driven Demand-Side Flexibility Quantification: Prediction and Approximation of Flexibility Envelopes

“…Although the original optimization problem can be solved reasonably fast with commercial iterative solvers, it nonetheless entails high computational burdens and limits the response speed. If additional scenarios of weather forecasts and occupants interaction are considered to account for uncertainties, the computational burden will be exacerbated [8]. Additionally, the original flexibility envelope consists of a notable number of data points, and periodical reporting of envelopes from multiple buildings represents a significant communication load.…”

“…In the energy domain, ML has found applications in efficient power system security assessments [9], approximation of optimization-based control policies in buildings [10] and model-free methods enhancing scalability [11]. Preliminary works use ML techniques to approximate solutions to generic large-scale mixed-integer programs [12], obtain optimal power flow solutions with gen- eralization guarantee [8] and speed up optimization processes by classifying active/non-active constraints [13]. Motivated by works with a similar rationale, we apply popular ML techniques to reduce computational efforts due to repeated optimization.…”

“…Motivated by works with a similar rationale, we apply popular ML techniques to reduce computational efforts due to repeated optimization. ML models, once trained, have lower computational cost than iterative solvers, as only function evaluations are needed [8].…”