The effect of small impedance branches on the convergence of the Newton Raphson power flow

This paper investigates the process of the Newton Raphson (N-R) method with flat voltage start when it is used for systems with small impedance branches. And find out that the divergence occurs in the cases which both ends of the small impedance branch are connected to PQ buses. Even under the cases with the divergence problem the Jacobian matrix is still nonsingular and the equations are solvable, and the results from the equations are very precise but unreasonable. So this paper draws a conclusion that it is not the numerical instability but the characteristic of the equations of the N-R method that cause the divergence. Further investigation shows that the improvement of voltage start can avoid the divergence problem. Based on the theoretical analysis, a method to prevent the N-R method from divergence by improving voltage start is presented. Experimental results validate the convergence analysis and illustrate the effectiveness of the proposed method.