Convergence Analysis On The Newton Power Flow In Rectangular Form

Essentially, Power flow is the solution of multiple nonlinear equations, so numerical iteration must be used. The convergence of iteration is an important indicator to the algorithms. So study on the convergence of power flow is very significant.With the rapid development of the power industry, there are more and more ill conditions in the power system, which may cause the divergence of power flow. To solve the problem, many studies have been taken on, and many valuable algorithms have been presented. With their own advantage, the effects of their practical applications vary. The Newton-Raphson Power flow gets the most widely use. Also, from the practical point, dealing with ill-conditioned power flow problems by improved conventional Newton-Raphson method is more meaningful.Power systems with small impedance branches are a common ill condition, which may lead to the divergence of the power flow. Considering the small impedance branch model and investigating the process of the Newton-Raphson method in rectangular form, it's found out that the divergence of the N-R Power flow in rectangular form with flat start occurs only when both ends of the small impedance branch are connected to PQ buses; otherwise the power flow converges without problem. The Newton-Raphson method in rectangular form along leads to the problem. Case study validates the conclusion.Based on the analyses, an improved Newton power flow in rectangular form for systems with small impedance branches by constructing the Jacobin matrix is presented. Analysis and case study on the systems with small impedance in the three conditions validated that the proposed method converges in condition which normal Newton power flow in rectangular form diverges, and has no negative effect on the convergence of power flow under the other two cases that normal Newton power flow in rectangular form converges.