The deepening of electricity reform results in increasingly frequent auctions and the surge of generators, it becomes difficult to analyze generators’ behaviors. Since it’s hard to find analytical market equilibriums, approximate equilibriums were obtained instead in previous studies by market simulations, which are strict to initial estimations and simulation results are chaotic in some cases. In this paper, a multi-unit power bidding model is proposed to reveal the bidding mechanism under clearing pricing rule by employing auction approach, for which initial estimations are non-essential. Normalized bidding price is introduced to construct generator's price-related bidding strategy. Nash equilibriums are derived depend on the marginal cost and the winning probability which are computed from bidding quantity, transmission cost and demand distribution. Furthermore, we propose a comparative analysis to explore the impact of uncertain elastic demand on the performance of the electricity market. The result indicates that, there exists market power among generators leading to social welfare decreases even under competitive conditions but elastic demand is an effective way to restrain generators’ market power. The feasibility of the models is verified by a case study. Our work provides decision support for generators and a direction for improving market efficiency.