# Simulation tools

A model is developped to solve three-phase four-wire radial
distribution networks. The network topology is presented in fig. 1.The
model is solved with a hybrid method. This implies that a part of the
network is implemented in the frequency domain and the other part is
simulated in the time domain. The line elements and the linear loads
are simulated in the frequency domain, the nonlinear loads in the time
domain (e.g. by using Plecs, a Matlab toolbox). The output data of this
part (e.g.\ the currents) can be transformed to the frequency domain by
performing a fast fourier transform (FFT) on the steady state current
of the nonlinear load. For all calculations the first 40 harmonics are
considered.

The model is solved with the iterative forward-backward method. This method consists of two steps, the backward and the forward sweep respectively. In the backward sweep, the voltage is calculated in every node, starting from the source and taking into consideration the voltage drop in every line section. In the first step, the voltage spectrum of the HV-bus, which is considered to be constant, is used in every node. Then the harmonic current drawn by every load is calculated. In the forward sweep, the harmonic current through every branch is calculated. This iterative method continues until convergence is achieved.

To obtain a more accurate model of a distribution network a transformer model has been developped. This model calculates the magnetizing current in every backward sweep.