Continuous Analogy Of Newton’s Method For Power Flow And Optimal Power Flow

Power flow (PF) and optimal power flow (OPF) are the widely used tools in network planning and power system dispatch. In the deregulated environments, more and more interconnected large power systems are operating in stressed conditions because of the great complexity of the structure of network and the rapid increase on the load. As a result, the convergence trouble for PF and OPF problems is becoming worse. This paper introduces the continuous analogy of Newton’s method for ill conditioned power flow cases, and presents a primal-dual interior point method (PDIPM) based on the continuous analogy of Newton’s method for OPF problems to overcome the convergence difficulty.By introducing a novel model for power flow, the PF problem is formulated as a set of autonomous ordinary differential equations (ODE). The new model is easy to derive, and it has simple structure. It allows unifying the standard Newton’s method and most robust techniques in a unique framework. Several numerical methods can be used to integrate ODE. A general framework of applying numerical integration techniques for solving ill conditioned power flow cases is formed. Furthermore, this model is a fresh idea of power flow solution indeed. The efficiency and practicability of the new approache are verified by simulation results of UCTE system and three actual domestic power systems with nodes up to8076.Besides, on the basis of PDIPM, this paper presents a new framework of PDIPM based on the continuous analogy of Newton’s method. It overcomes the convergence difficulty of OPF problems for the large scale AC/DC systems when using PDIPM. Based on the continuous analogy of Newton’s method, the nonlinear KKT equations in the PDIPM are transformed to a set of ODE. Therefore, many numerical integration methods can be used to calculate the ODE. Furthermore, a different direction is obtained through a numerical integration method, whose convergence is better than that through the Newton’s method. The new proposed method is easy to update the OPF software based on PDIPM due to little modification. Simulations are carried out to evaluate the performance of the proposed algorithm on five actual large scale systems, the largest one of which has11585lines. The algorithm shows long step length, good convergence and strong robustness especially for large scale AC/DC systems with stressed conditions.