Continuation power flow with the nonlinear predictor of the Lagrange's polynomial interpolation formula

In this paper, a new continuation power flow method is presented with the nonlinear approximate predictor. The proposed method makes use of the Lagrange's polynomial interpolation formula as the predictor of the predictor-corrector method. The conventional continuation power flow method plays a key role to draw the P-V curve for static voltage instability analysis. The conventional continuation power flow method has a drawback that it is inclined to be time-consuming in large power systems. It is not easy to take the large step-size because of the error between the predicted and the actual solution. This paper presents two strategies to improve the conventional method. One is to evaluate the predicted solution with the nonlinear approximate predictor of the Lagrange's polynomial interpolation formula. The other is to use the rule-based step-size control to speed up the computational time. The proposed method is successfully applied in the 118-node and 235-node system.