Power systems optimization: Manifold approach

• Manifold optimization (MO) is applied to power flow analysis in distribution and transmission systems. • A new cost function for EPDS is derived from the Backward/Forward Sweep (BFS) algorithm. • The open-source Manopt toolbox is used for solving power flow problems. • The MO-based approach achieves high accuracy and e!ciency, validated against commercial solvers. • MO is presented as an accessible and powerful alternative to traditional methods. Solving the power flow problem efficiently and reliably remains a central challenge in power systems engineering. Many optimization models used for strategic planning and asset allocation in electrical networks may inherit the non-convexity of the traditional power flow model set of constraints, making them harder to solve with conventional methods. Additionally, the classical discretization techniques typically employed can reduce the accuracy of the results. This paper introduces Manifold optimization (MO) as a novel and powerful approach for this task. Our contribution is a practical methodology that reformulates the power flow problem using a cost function derived from a backward-forward sweep (BFS) method, which is then solved using the open-source Manopt toolbox. This approach avoids the complexities of both non-convex solvers and intricate manifold geometries. We demonstrate the method’s effectiveness on standard electrical power distribution systems (EPDS) (33-bus, 69-bus) and electrical power transmission systems (EPTS) (3-bus, 4-bus) test systems. Key findings show that our MO-based approach achieves solution accuracy that exactly matches benchmark nonlinear solvers such as Knitro while offering competitive computational times and the significant advantage of being a free, open-source alternative to expensive commercial software. Furthermore, although the BFS formulation is used here as the basis for the cost function, it still preserves the flexibility required for strategic planning and asset allocation problems, similarly to traditional mathematical optimization models. Therefore, study positions MO as an accessible, robust, and highly accurate tool for power system analysis, with clear potential for broader planning and operational applications.