# Feasible Path Identification in Optimal Power Flow with Sequential Convex Restriction

## TL;DR

This paper introduces a convex optimization-based algorithm to find feasible paths in nonconvex AC optimal power flow problems, enabling reliable transitions between operating points and improving solutions efficiently.

## Contribution

It proposes a novel sequential convex restriction method to compute feasible paths in nonconvex OPF problems, addressing the challenge of disconnected feasible spaces.

## Key findings

- Algorithm successfully finds feasible paths in various test cases.
- Converges to high-quality solutions in few iterations.
- Enables reliable transition between operating points.

## Abstract

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is not always clear that there exists a feasible path to reach the desired operating point. Transitioning between operating points while avoiding constraint violations can be challenging since the feasible space of the OPF problem is nonconvex and potentially disconnected. To address this problem, we propose an algorithm that computes a provably feasible path from an initial operating point to a desired operating point. Given an initial feasible point, the algorithm solves a sequence of convex quadratically constrained optimization problems over conservative convex inner approximations of the OPF feasible space. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to improve the operating point locally. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations.