Manifolds in Power Systems Optimization

TL;DR

This paper demonstrates how manifold optimization offers a robust, efficient, and accessible approach for solving complex power flow problems in electrical power systems, outperforming traditional methods in accuracy and computational time.

Contribution

It introduces manifold optimization to power systems, showcasing its advantages and providing practical applications and tutorials for power flow analysis in electrical networks.

Findings

MO achieves high accuracy in power flow optimization.

MO offers competitive computational times compared to traditional methods.

Tools like Manopt simplify implementation of MO in power systems.

Abstract

Manifold optimization (MO) is a powerful mathematical framework that can be applied to solving complex optimization problems with objective functions (OFs) and constraints on complex geometric structures, which is particularly useful in advanced power systems. We explore the application of MO techniques, which offer a robust framework for solving complex, non-convex optimization problems in electrical power distribution systems (EPDS) and electrical power transmission systems (EPTS), particularly for power flow analysis. This paper introduces the principles of MO and demonstrates its advantages over conventional methods by applying it to power flow optimization. For EPDS, a cost function derived from a backward-forward sweep (BFS) algorithm is optimized using the Manopt toolbox, yielding high accuracy and competitive computational times on 14-bus, 33-bus, and 69-bus systems when compared to established solvers. Similarly, for EPTS, MO applied via Manopt to 3-bus and 4-bus systems effectively solves power flow equations, matching traditional methods such as Newton-Raphson in performance. The study highlights that tools such as Manopt can mitigate implementation complexities, positioning MO as an efficient and accessible tool for power system analysis and potentially broader planning applications. The paper provides a comprehensive tutorial on MO, detailing its theoretical foundations, practical methodologies, and specific applications in power systems, particularly in power flow optimization.