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A nonlinear complementarity model for OPF problems with load tap changing transformers is created in this paper, and a modern interior point method for this model is presented as well. The proposed method includes two steps. Firstly, the OPF with the continuous variables is considering for obtaining the upper and lower bounds of the transformer taps. And then, the complementarity constraints of the transformer taps is modeled into OPF, which can be solved by the modern interior point method based on the results of the last step. Therefore, the discrete results of the LTC's taps can be calculated accurately. This method can coordinate the illogicality between the calculating time and precision effectively. Extensive numerical simulations on IEEE test systems and the simulative power system with 232 and 1047 buses have shown that this method is efficient in solving OPF problem for the discrete variables. It possesses good convergence property within a very short time. Thus it is promising for the on-line applications.