Interpolation algorithm plays an important role in the fixed step integration method, it can accurately get the action time of the switch. 2S-DIRK method has L-stability and 2-order accuracy, but the linear interpolation method based on 2S-DIRK will reduce the calculation accuracy to 1-order, which cannot be used in large power grid simulation. In this paper, based on Runge Kutta formula, a special 2-order interpolation algorithm was proposed. This algorithm does not satisfy the value of the middle point but can ensure that the accuracy of the interpolation process is not less than 2-order. The L-stability and the 2 order of accuracy in 2S-DRIK method are guaranteed. Finally, a combined example of LCC-HVDC system and IEEE9 system is used to verify that the proposed method can maintain the 2-order of accuracy in the whole calculation process.