Under the environmental crisis of global warming, more efforts are put in application of low carbon energy, especially low-carbon electricity. Development of wind generation is one potential solution to provide low-carbon electricity source. This paper researches operation of wind generation in a de-regulated power market. It develops bidding models under two schemes for variable wind generation to analyze the competition among generation companies (GENCOs) considering transmission constraints. The proposed method employs the supply function equilibrium (SFE) for modeling the bidding strategy of GENCOs. The bidding process is solved as a bi-level optimization problem. In the upper level, the profit of an individual GENCO is maximized; while in the lower level, the market clearing process of the independent system operator (ISO) is modeled to minimize the production cost. An intelligent search based on genetic algorithm and Monte Carlo simulation (MCS) is applied to obtain the solution. The PJM five-bus system and the IEEE 118-bus system are used for numerical studies. The results show when wind GENCOs play as strategic bidders to set the price, they can make significant profit uplifts as opposed to playing as a price taker, because the profit gain will outweigh the cost to cover wind uncertainty and reliability issues. However, this may result in an increase in total production cost and the profit of other units, which means consumers need to pay more. Thus, it is necessary to update the existing market architecture and structure considering these pros and cons in order to maintain a healthy competitive market.