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The state space averaging method, switch cycle average method and switching function method for modeling of static var generator (SVG) main circuit are reviewed. The commonness among the three methods is found and the power model of SVG is carried out by the instantaneous reactive power theory and the main circuit model of SVG. Based this power model, the bivariate PI control strategy is introduced to control SVG. In order to shorten the response time of SVG, the nonlinear inverse system PI control strategy is proposed by using the inverse function of the power model. The simulation results by PSCAD illustrate the accuracy of the model and the validity of the control strategy.