Application of Newton-Raphson method in three-phase unbalanced power flow

Renewable energy sources are in the forefront of new energy in power systems. They are predominantly connected to distribution systems at lower voltage levels. Distribution systems have three phases and are largely unbalanced in their line parameters and loads. A large percentage of these systems suffer from severe imbalance in their phases. In the past, two methods of analysis were commonly used. The first is the 'ladder iterative technique' that consider unbalanced systems. However, this method does not possess information about the distribution system. The second method uses the 'Newton Raphson Technique' with 2N equations. It is superior since it computes a Jacobian that holds information about the distribution system. However, predominant implementations of Newton Raphson method assume that the system is balanced and they suffer from poor convergence properties. In order to overcome these difficulties, this research furthers a recent development of single phase 3N equation model of distribution systems by enlarging it to model three phase distribution systems. The Jacobian models each of the three phases using a set of 3N equations. Modeling of network components and formulation of three phase power flow equations are presented. The important characteristics of the Jacobin matrix are also presented. The method is developed and coded. It is tested on standard IEEE distribution systems with 4, 13,34,37, and 123 nodes. The results are compared with published IEEE data.