Applied Soft Computing 13 (2013) 2445–2455 Contents lists available at SciVerse ScienceDirect Applied Soft Computing j ourna l ho mepage: www.elsevier.com/locate/asoc Strategic bidding using fuzzy adaptive gravitational search algorithm in a pool based electricity market J. Vijaya Kumar ∗ , D.M. Vinod Kumar, K. Edukondalu Department of Electrical Engineering, National Institute of Technology, Warangal 506004, India a r t i c l e i n f o Article history: Received 21 February 2012 Received in revised form 10 October 2012 Accepted 1 December 2012 Available online 17 December 2012 Keywords: Electricity market Bidding strategies Market clearing price (MCP) Fuzzy inference Gravitational search algorithm a b s t r a c t A novel stochastic optimization approach to solve optimal bidding strategy problem in a pool based electricity market using fuzzy adaptive gravitational search algorithm (FAGSA) is presented. Generating companies (suppliers) participate in the bidding process in order to maximize their profits in an electricity market. Each supplier will bid strategically for choosing the bidding coefficients to counter the competi- tors bidding strategy. The gravitational search algorithm (GSA) is tedious to solve the optimal bidding strategy problem because, the optimum selection of gravitational constant (G). To overcome this prob- lem, FAGSA is applied for the first time to tune the gravitational constant using fuzzy “IF/THEN” rules. The fuzzy rule-based systems are natural candidates to design gravitational constant, because they provide a way to develop decision mechanism based on specific nature of search regions, transitions between their boundaries and completely dependent on the problem. The proposed method is tested on IEEE 30-bus system and 75-bus Indian practical system and compared with GSA, particle swarm optimization (PSO) and genetic algorithm (GA). The results show that, fuzzification of the gravitational constant, improve search behavior, solution quality and reduced computational time compared against standard constant parameter algorithms. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Restructuring of the power industry mainly aims at abolishing the monopoly in the generation and trading sectors, thereby, intro- ducing competition at various levels wherever it is possible. But the sudden changes in the electricity markets have a variety of new issues such as oligopolistic nature of the market, supplier’s strategic bidding, market power misuse, price-demand elasticity and so on. Theoretically, in a perfectly competitive market, supplier should bid at their marginal production cost to maximize payoff. However, practically the electricity markets are oligopolistic nature, and power suppliers may seek to increase their profit by bidding a price higher than marginal production cost. Knowing their own costs, technical constraints and their expectation of rival and market behavior, suppliers face the problem of constructing the best optimal bid. This is known as a strategic bidding problem [1]. In general, there are three basic approaches to model the strate- gic bidding problem, viz. (i) based on the estimation of market clearing price, (ii) estimation of rival’s bidding behavior and (iii) on game theory. David [2] developed a conceptual optimal bidding ∗ Corresponding author. Tel.: +91 9290852689; fax: +91 870 2459547. E-mail addresses: jvkeee@gmail.com (J. Vijaya Kumar), vinodkumar.dm@gmail.com (D.M. Vinod Kumar). model for the first time in which a dynamic programming (DP) based approach has been used. Gross and Finlay adopted a Lagrangian relaxation-based approach for strategic bidding in England–Wales pool type electricity market [3]. Wang et al. [4] used evolutionary game approach to analyzing bidding strategies by considering elastic demand. Ebrahim and Galiana developed Nash equilibrium based bidding strategy in electricity markets [5]. David and Wen [6] proposed to develop an overall bidding strategy using two different bidding schemes for a day-ahead market using genetic algorithm (GA). The same methodology has been extended for spinning reserve market coordinated with energy market by David and Wen [7]. Chanwit et al. proposed an optimal risky bid- ding strategy for a generating company (GenCo) by self-organizing hierarchical particle swarm optimization with time-varying accel- eration coefficients (SPSO–TVAC) [8]. To construct linear bid curves in the Nord-pool market stochastic programming model has been used by Fleten et al. [9]. The opponents’ bidding behaviors are rep- resented as a discrete probability distribution function solved using Monte Carlo method by David and Wen [10]. A new approach based on fuzzy cognitive map (FCM) is introduced to model and simulate GENCO’s behavior in the electricity market with respect to profit maximization [11]. pay-as-bid (PAB) has been proposed to replace the market clearing price (MCP) in deregulated electricity mar- kets, with the expectation that it would lower market prices 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2012.12.003