Allocation of VAr support using LP and NLP based optimal power flows

Characteristics of linear programming (LP) and nonlinear programming (NLP)-based optimal power flows (OPFs) are discussed, which allocate (auctions) reactive power support among competing generators in a deregulated environment. LP-based AC OPF algorithms are frequently used in practice to optimise the operation and reinforcement of power systems owing to their reliability. The alternative methods are NLP-based OPF algorithms, which have developed rapidly in this past decade motivated by the performance of interior-point algorithms. While LP algorithms offer reliable performance, the latter offer computation speed and accuracy for achieving the solution. An LP-based direct reactive OPF and a NLP-based direct reactive OPF using an interior-point algorithm, which concurrently solve load flow and optimisation problems, are developed and analysed. The issue of performance arises from the difficulties associated with the convergence of a direct LP OPF and the need for a technique to enforce the convergence of such an OPF. As the LP OPF may not converge spontaneously to the optimal point, questions arise as to whether such approaches are appropriate for facilitating the provision of VAr support in a competitive environment. Although the overall reactive requirement calculated by the OPF may be reasonably accurate, a generator's individual commitment may vary considerably. In contrast, the NLP OPF shows different characteristics: it converges spontaneously and the solutions are accurate. A comparison between those two streams of algorithms is presented. Extensive case studies are carried out over the IEEE-118 bus system to illustrate the impact of different starting points on the solutions for both LP and NLP algorithms.