Hybrid Optimization Strategies for Global Optimality in Non-Convex Programming Using SQP and IPMs: Avoiding the Maratos Effect in PMU Placement – A Case Study

Abstract

This study investigates the optimum configuration of Phasor Measurement Units (PMUs) for strategic placement within power transmission networks, utilizing nonlinear programming to obtain complete power network observability and maximize the coverage of observed buses throughout the grid. To address this complex engineering problem, we first solve a 0-1 integer linear programming model. We then apply solution methods based on sequential quadratic programming and interior-point approaches in solving equivalent nonlinear programming models, incorporating a necessary and sufficient stopping criterion to ensure global optimality while avoiding the Maratos effect. Our approach avoids these infeasibility issues by leveraging a piecewise convex feasible region, permitting the optimizer solver to simultaneously satisfy both feasibility and optimality without the need for a penalty function to perform in the iterative process. This leads to the successful rejection of the Maratos effect, a crucial key factor in ensuring the accuracy and effectiveness of the optimization process without destroying the super-linear convergence close to optimality. Representative numerical results are presented, along with a discussion of optimality conditions essential for achieving the best solution. The minimization problem is solved in MATLAB in a two-stage process. Initially, an objective function with a single product is minimized to determine the number of PMUs required for wide-area monitoring, control, and state estimation. A second product is subsequently added to the objective function to maximize the observability of network buses. The optimal PMU placement set solutions are produced to give all network buses observed directly or indirectly. In order to find out globally optimal solutions, IEEE power networks are performed with the mathematical algorithms in MATLAB.