Successive Zooming Optimization and its Application to Voltage Stability Problem

Abstract

Optimization became a major concern in various fields of research. There are several soft computing techniques e.g. Particle Swarm Optimization, Ant Colony Optimization etc. They differ from each other, the way particles move in search space and few other minor differences. In most of these techniques first we create several particles and find the best among them. Then the other particles move towards the best particles and we check their status. This process continues for several iterations and we find optimal value. But this social movement process requires much programming efforts, especially when the number of control variables is large. In case it is a power system problem, where load flow is required, first we create the random values for the control variables, using these variables as input we conduct power flow and then we find the local solution for the objective. After that, all the particles which we created move toward the best particle or crazy particle and we repeat the process until it converges. For movement of all these particles we need to apply velocity and position update formula to all the particles and followed by conduct of load flow repeatedly. If case the selected system is very large and we have many control variables, the movement of particles become a lengthy process and requires great computer programming effort. Hence to avoid this programming effort we propose a novel optimization technique where the created particles are not supposed to move. In spite of dragging all the particles towards the best particle, we create new particles near the best particles. This is something like zooming the small area near the best particle and then finding new potential particles. This zooming and finding new particles step continues until convergence. Based on its zooming the small area steps this technique is named as Successive Zooming Optimization or simply Zooming Optimization (Z.O.). This technique gives approximately same result as those by existing techniques. This technique is very useful for beginners because the programming effort required is comparatively less. This technique is applied to voltage stability problem. A 26- bus system of an electric utility company and IEEE standard-14 bus systems are considered for analysis. Results obtained for 14-bus test system were compared with an analytical method, ‘Davidson-Fletcher-Powel-Method.