Implementation of Broyden’s Method to Compute the Three-Phase Power Flow in Electrical Distribution Networks with Asymmetric Loading

This paper deals with the solution to the power flow equations in three-phase asymmetric networks by applying Broyden’s method in the complex domain. These equations are obtained using the nodal voltage technique and the admittance representation of the network. The power flow formulation considers multiple asymmetric constant power loads with both star and delta connections. Broyden’s method is generally formulated for a set of nonlinear equations. In this work, F(x) = 0 is achieved by utilizing an adaptive matrix A
i
, which is initially estimated and updated in each iteration using a recursive Broyden’s formula. Numerical results in the three IEEE rest systems (8-, 25-, and 37-bus) with star and load connections demonstrate that Broyden’s method reaches the exact numerical values of the grid power losses for star and load connections. This is compared with multiple algorithms that solve the power flow problem, as is the case of the Newton-Raphson, backward/forward, and triangular algorithms. A demonstration is provided to show the adaptability of the numerical method in addressing the power flow problem in three-phase unbalanced networks efficiently. Our demonstration establishes the equivalence between the backward/forward power flow approach and Broyden’s formulation.