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among electric generation companies is a major goal of restructuring in the electricity industry. In electricity market, a huge volume of commodities will be traded through competitive bidding. The choice between uniform and pay-as-bid pricing for electricity auction has been one of most important issues in deregulated electricity market. This paper proposes a constrained Bertrand model for analyzing the electricity auction market of price competition model. The issue of the two pricing rules of uniform and pay-as-bid is studied from the viewpoint of consumer's benefit. This paper also shows that transmission congestion depends on the pricing mechanism. Pay-as-bid pricing gives less possibility of transmission congestion by price competition, and less burden to consumers in the simulation results.