Optimal static state estimation using improved particle swarm optimization and gravitational search algorithm Sourav Mallick ⇑ , S.P. Ghoshal, P. Acharjee, S.S. Thakur Department of Electrical Engineering, National Institute of Technology, Durgapur 713 209, India article info Article history: Received 5 November 2012 Received in revised form 4 March 2013 Accepted 29 March 2013 Available online 29 April 2013 Keywords: Static state estimation Improved particle swarm optimization Gravitational search algorithm Ill-conditioned system abstract In this paper, two novel evolutionary search techniques based on Improved Particle Swarm Optimization (IPSO) algorithm and Gravitational Search Algorithm (GSA), have been proposed to solve the static State Estimation (SE) problem as an optimization problem. The proposed methods are tested on five IEEE stan- dard test systems along with two ill-conditioned test systems under different simulated conditions and the results are compared with the same of standard Weighted Least Square State Estimation (WLS-SE) technique, Particle Swarm Optimization (PSO) based SE and Hybrid Particle Swarm Optimization Gravi- tational Search Algorithm (PSOGSA) based SE technique. The optimization performance and the statistical error analysis show the superiority of the proposed GSA based SE technique over the other two techniques. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Power industry is expanding rapidly in most of the countries over the world. The deregulation of power market with transmis- sion open access has been successfully implemented in some coun- tries. This deregulation of the electric power industry has introduced new possibilities for market participants in an efficient and secure environment. It is well understood that an electric power system can be operated in efficient, economic and secure manner, if it’s states are known at present time [1]. Schweppe et al. formulated the SE problem as Weighted Least Square (WLS) problem [2–4]. The drawback of WLS technique is that it requires the proper and a limited range of values for the weighting factors to obtain a solution. Thereafter, the volume of work on SE has grown enormously and the use of SE has become so widespread that a new power system Energy Control Center (ECC) without it would be an oddity. Of course, SE has become a mature and field proven work horse but various aspects of SE such as the solution algorithm [5–16], detection and identification of bad data [17–21], topological error detection [22–24], observabil- ity analysis [25–28] continue to be investigated so as to enrich the SE software used in ECCs. A state estimator assigns the values of power system states, i.e. the voltage magnitudes and phase angles at all buses of the system based on the redundant power system measurements using a se- lected statistical criterion that minimizes or maximizes an objec- tive function. As the system size increases, the search space of the classical optimization technique increases exponentially. Therefore, the use of meta-heuristic techniques to obtain the exact solution is evident. Particle Swarm Optimization (PSO) and Gravi- tational Search Algorithm (GSA) are among the popular meta-heu- ristic techniques. Based on the social behavior of birds’ flocking or fish schooling, PSO was developed by Eberhart and Kennedy in 1995 [29,30]. Compared to many other evolutionary techniques, it is computationally inexpensive in terms of memory requirement and CPU times [31–34]. PSO has the fast converging feature and better global searching ability at the beginning of the run. But, it has local searching problem near the end of the run. While solving problem with exponential complexity, sometimes it suffers from local optima at the end of execution of a program [34]. In order to overcome this trapping in local optima, many improvisations are adopted by the researchers [35–40]. One such improvisation is the introduction of craziness [35–37] to PSO particles. In order to achieve faster convergence rate and better success ra- tio than the swarm optimization, researchers are searching new algorithms throughout the world. GSA proposed by Rashedi et al. in 2009 [41], is such a new optimization algorithm based on Newto- nian physics. GSA is constructed approximately on law of gravity and the notion of mass interactions. Various researchers have ap- plied GSA to solve various problems in different fields [42–47]. In this paper, Improved Particle Swarm Optimization (IPSO) and GSA based state estimation techniques have been proposed to solve SE problem as an optimization problem and to improve the error performance analysis based on statistical indices of SE. IPSO and GSA based techniques are tested for SE of IEEE 5-bus, IEEE 14-bus, IEEE 30-bus, IEEE 57-bus, IEEE 118-bus, ill-conditioned 11-bus and ill-conditioned 13-bus test systems under different 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.03.035 ⇑ Corresponding author. Tel.: +91 9434205918. E-mail address: sourav.nitdgp2009@gmail.com (S. Mallick). Electrical Power and Energy Systems 52 (2013) 254–265 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes