Power flow analysis using successive approximation and adomian decomposition methods with a new power flow formulation

The Newton-Raphson Method (NRM) is widely accepted for the power flow studies. The limitations of NRM include calculation of Jacobian matrix for each iteration, resulting in an additional calculation and an increase in computation time per iteration. Another weakness is the solution diverges when the Jacobian matrix is singular. In order to overcome these issues, this work proposes new numerical methods for the power flow studies: Successive Approximation Method (SAM) and Adomian Decomposition Method (ADM). The convergence of both methods depends on the equation formulation, contraction mapping and fixed-point theorem. Here, a new formulation of the power flow equations is introduced that satisfies the conditions for the fixed-point theorem. Both methods are coded in MATLAB platform and the NRM is also coded for as a reference method. With the standard 3-bus test system, all three methods are elaborated in detail. Later on, the methods are validated on other test systems such as 4-bus, 5-bus, 6-bus, 9-bus, 11-bus, 14-bus, 30-bus and 57-bus. Special case studies with the 14-bus system are also reported, wherein the NRM fails to provide converged solution because of singularity in Jacobian matrix. On the other hand, the SAM and ADM successfully converge in such case.