Modeling of Step Voltage Regulators in Multiphase Load Flow Solution of Distribution Systems Using Newton's Method and Augmented Nodal Analysis

The increasing complexity of distribution systems requires general, efficient, and large-scale capable methods. This paper proposes a new technique to find the tap positions of step voltage regulators in multiphase load flow solvers in a direct and efficient manner. This is achieved by applying Newton method to the system of equations obtained by using the concept of augmented matrix formulation and adding the constraint equations. This approach allows employing the regulator equations directly. The regulators are modeled by taking into account the line drop compensator circuit with its settings, i.e., the desired voltage level, bandwidth, and R' and X' settings, which represent the scaled impedance parameters of the distribution feeder between the regulator and the load center at which the voltage is controlled. The limits of the regulators such as minimum and maximum tap positions are also accounted for. The proposed technique represents a voltage regulator with transformer equations using an augmented matrix formulation. The mismatch equations are developed using the desired voltage setting in constraint equations with transformation ratio of the transformer being the unknown variable. The Jacobian matrix, which is constructed using the augmented matrix formulation, is expanded to hold the constraint equations of voltage regulators. The proposed new method is tested on a variety of test circuits including the large-scale IEEE 8500 Node Test Feeder, and the minimum number of iterations reported in the literature is achieved as presented in this paper.