An Efficient Primal-Dual Interior-Point Algorithm for Volt/VAR Optimization in Rectangular Voltage Coordinates

Abstract

Security and reliability of electrical power supply has become indispensable to modern society, and the system operator is challenged to manage the increasingly complex modern power system in a manner that ensures the expected reliability and security of system operation. In this context, Volt/VAR optimization (VVO) plays a key role in the efficient delivery of power through the transmission system, contributing significantly to the security, reliability, quality and economy of system operation. This article presents the design and implementation of an efficient primal-dual interior-point algorithm for the solution of the VVO problem. The primal-dual interior-point method combines efficient constraint handling by means of logarithmic barrier functions, Lagrangian theory of optimization, and the Newton method to constitute one of the most efficient deterministic algorithms for large-scale nonlinear optimization. The developed algorithm also incorporates the efficient Newton-Raphson load flow computation, which ensures that the solution is feasible with respect to the power flow balance equations at each iteration of the VVO algorithm. Both the VVO and Newton-Raphson load flow problems are formulated in the rectangular coordinates of system voltages. This is a departure from most researchers, who make use of the polar formulation, and adds considerably to the efficiency of the developed algorithm. The efficiency and effectiveness of the developed algorithm has been demonstrated by means of case studies performed on the 6-bus and IEEE 14-bus, 30-bus and 118-bus test systems, which have been selected to analyse the computational efficiency and scalability of the algorithm as it is applied to systems of various sizes. The extensive analyses that have been conducted reveal the developed primal-dual interior-point algorithm's effectiveness and efficiency, particularly in being able to successfully solve the VVO problem for systems of widely varying sizes without disproportionate increase in computational cost or deterioration in the quality of the results. The developed algorithm exhibits characteristics of fast convergence, high efficiency, and scalability to large-scale problems.INDEX TERMS Volt/VAR optimization, reactive power/voltage control, primal-dual interior-point method, optimal power flow, Newton's method, Newton-Raphson load flow, Lagrange multiplier method, rectangular voltage coordinates

Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

“…This is especially advantageous for the PDIPM algorithm, which is solved using the Newton method. Further details are provided in the companion article [20]. The comparative performance analysis of the two algorithms presented in this article reveals key insights into the important performance characteristics of the two approaches to optimization (i.e., heuristic vs. classical approaches) and may serve as a useful aid in the development and design of advanced optimization methods that combine their synergistic properties to devise more efficient algorithm.…”

“…The main focus of this article is to present a comparative analysis of the particle swarm optimization (PSO) algorithm and the primal-dual interior-point method (PDIPM), both applied to the solution of the Volt/VAR optimization problem. A detailed design and implementation of the PSO-based VVO algorithm is presented in this article, whereas the detailed design and implementation of the PDIPM-based VVO algorithm has been presented by the authors in [20]. After presenting the design and implementation of the PSO-VVO algorithm as well as the detailed analysis of four case studies (the same set of case studies considered in [20]), the article then presents the comparative performance analysis of the two algorithms.…”

“…A detailed design and implementation of the PSO-based VVO algorithm is presented in this article, whereas the detailed design and implementation of the PDIPM-based VVO algorithm has been presented by the authors in [20]. After presenting the design and implementation of the PSO-VVO algorithm as well as the detailed analysis of four case studies (the same set of case studies considered in [20]), the article then presents the comparative performance analysis of the two algorithms. The Volt/VAR optimization problem is formulated in the rectangular voltage coordinates and incorporates the Newton-Raphson load flow computation, also formulated in rectangular coordinates, as presented in [20].…”

“…After presenting the design and implementation of the PSO-VVO algorithm as well as the detailed analysis of four case studies (the same set of case studies considered in [20]), the article then presents the comparative performance analysis of the two algorithms. The Volt/VAR optimization problem is formulated in the rectangular voltage coordinates and incorporates the Newton-Raphson load flow computation, also formulated in rectangular coordinates, as presented in [20]. The reason for the choice of the rectangular coordinate formulation over the polar formulation is the relative computational advantage of the former.…”

“…• Detailed development and implementation of the PSO-based Volt/VAR optimization algorithm, showing how the generic PSO algorithm is adapted for application to the VVO problem formulated in rectangular coordinates; • Incorporation of the Newton-Raphson load flow computation (also formulated in rectangular coordinates) into the PSO-VVO algorithm, which gives the algorithm the desirable characteristic of being feasible with respect to the active and reactive power flow constraints at every iteration of the PSO-VVO algorithm. The detailed implementation of the Newton-Raphson load flow computation has been presented by the authors in [20];…”