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

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.