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Wind energy has been widely investigated as a promising environmental friendly and economic energy resource these years worldwide. However, high volatility and non-dispatchability make it difficult to control comparing to the traditional energy. Imbalance penalty is one of the major methods to regulate wind farm owners and enhance the benefits of renewables bid into the electricity market, so as to minimize the supply-demand mismatch and local network congestions. In this paper, we consider the optimal wind bidding strategy problem with the existence of imbalance penalty and allowed imbalance band on behalf of a wind farm owner. We provide the analytical solutions of the optimization problem for Normal and Rayleigh distributed wind power. Based on the problem and solutions, we also investigate in the related issues that can help both wind taking and supplying parties to cooperate and help build a reliable energy trading market.