Comprehensive distribution power flow: modeling, formulation, solution algorithms and analysis

The objective of this work was to develop a formulation and an efficient solution algorithm for the distribution power flow problem which takes into account the detailed and extensive modeling necessary for use in the distribution automation environment of a real world electric power distribution system. The formulations for the three classes of existing algorithms for radial systems were generalized and were extended to handle the comprehensive modeling already presented in the context of more traditional but less efficient methods, such as Newton-Raphson and Implicit $Z\sb{bus}$ Gauss. The modeling includes unbalanced three-phase, two-phase, and single-phase branches, constant power, constant current, and constant impedance loads connected in wye or delta formations, cogenerators, shunt capacitors, line charging capacitance, switches, and three-phase transformers of various connection types. The three classes of algorithms explored are: network reduction methods, backward/forward sweep methods, and fast decoupled methods. Within each of the three classes, new algorithms were developed and existing methods were extended to include the comprehensive modeling of the general formulation. Proofs of convergence for the backward/forward sweep and fast decoupled methods are also provided. In addition to the radial algorithms, the compensation method used to handle weakly meshed systems was generalized to encompass three-phase networks with loops, multiple sources, and three-phase PV buses. This compensation method can be applied in conjunction with any of the radial power flow solvers. Termination of the radial solver, at each iteration, is based on an adaptive criterion. A generalized correction step for the compensation method was also developed. All of the proposed methods were evaluated and compared on various test systems based on data from real distribution systems. The test systems range in size from 63 buses to over 1000 buses. The most efficient algorithm in each class was shown to require significantly less computation than both the Newton-Raphson and the Implicit $Z\sb{bus}$ Gauss methods, with the backward/forward sweep and fast decoupled methods typically showing an improvement of more than a factor of three.