The Newton method is a simple implementation of the Newton-Raphson method that uses the Y-Bus matrix as reference for reproducing the effects of the Jacobian matrix when calculating the circuit model voltages. However, in this version of the Newton algorithm the Y-Bus matrix remains unchanged, offering a different implementation from the original method.


In this method, the injection currents are adjusted to reduce the voltage mismatch obtained after operating:



Where Iinj is the input, Ysystem is the Y-BUs admittance matrix and V is the partial voltage for the present iteration. At each iteration the voltage is added until the voltage mismatch is below the convergence tolerance as follows:



The implementation of this algorithm is depicted below:


Figure 2. Newton method implementation in OpenDSS


The current injections are associated to each PCE mode defined when describing the circuit.