Residual Power Flow for Neural Solvers

TL;DR

This paper introduces Residual Power Flow (RPF), a new formulation based on Kirchhoff's laws, to improve neural solvers' flexibility and speed in power system operational tasks, demonstrated on the IEEE 9-bus system.

Contribution

The paper proposes RPF as a foundational residual formulation for neural power flow solvers, enhancing their flexibility and learning performance for operational tasks.

Findings

RPF improves the accuracy of neural power flow solutions.

Neural solvers with RPF are more flexible for different tasks.

The approach is effective on the IEEE 9-bus system.

Abstract

The energy transition challenges operational tasks based on simulations and optimisation. These computations need to be fast and flexible as the grid is ever-expanding, and renewables' uncertainty requires a flexible operational environment. Learned approximations, proxies or surrogates -- we refer to them as Neural Solvers -- excel in terms of evaluation speed, but are inflexible with respect to adjusting to changing tasks. Hence, neural solvers are usually applicable to highly specific tasks, which limits their usefulness in practice; a widely reusable, foundational neural solver is required. Therefore, this work proposes the Residual Power Flow (RPF) formulation. RPF formulates residual functions based on Kirchhoff's laws to quantify the infeasibility of an operating condition. The minimisation of the residuals determines the voltage solution; an additional slack variable is needed to achieve AC-feasibility. RPF forms a natural, foundational subtask of tasks subject to power flow constraints. We propose to learn RPF with neural solvers to exploit their speed. Furthermore, RPF improves learning performance compared to common power flow formulations. To solve operational tasks, we integrate the neural solver in a Predict-then-Optimise (PO) approach to combine speed and flexibility. The case study investigates the IEEE 9-bus system and three tasks (AC Optimal Power Flow (OPF), power-flow and quasi-steady state power flow) solved by PO. The results demonstrate the accuracy and flexibility of learning with RPF.