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SUMMARY This paper investigates bidding strategy problems of generation companies in electricity markets. A new bidding model is set up, and a solution approach is presented. Compared with existing models, the model proposed in this paper has some different characteristics. First, the model adopts a bilevel optimization framework where the upper-level optimization is to maximize the profit of generation companies, and the aim of the lower-level optimization is the maximal social welfare and the security of the operation system considered by the Independent System Operator. This model combines practical situations faced by market agents in real-life operations and the requirement of both the system security and the social welfare. Second, the popular risk measure, called conditional value at risk, is used in the bidding model, which can quantify the market risk and describe the competitive mechanism effectively. For solving the complicated bilevel optimization model, a hybrid particle swarm optimization algorithm is presented. Numerical examples are used to validate the model and the algorithm. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]