Single-phase transformer with generalized magnetic circuit


This case is the beginning of the simulation of electrical machines as the objective is to generalize the magnetic circuit representation. The transformer has been represented as coupled inductors with their leakage inductances and mutual inductances. The coupled equations that result are expressed in the matrix form and are solved after transforming them through elementary row operations. This method can be used for more complex machines later as will be shown by subsequent simulation cases.

The transformer has been considered to be a 1:2 transformer. The primary of the transformer is fed by an single-phase inverter. The secondary of the transformer consists of an LC filter that interfaces to a resistive load. This will be a typical application in many power electronic circuits - for example a shunt compensator connected to a distribution system through a step-up transformer. Below is the output of the inverter. The output is a typical PWM switched waveform.

Result 1

The secondary voltage is plotted in the waveform below with the primary voltage. It shows the step up ratio of 2. However, the secondary voltage is seen to be sinusoidal because of the effect of the LC filter.

Result 2

The figure below shows the primary and secondary currents of the transformer which also shows the ratio of 2. In this case the primary current is twice the secondary current.

Result 3

The voltage at the load is very similar to the voltage at the secondary. The load current is however smooth as the voltage has been filtered at the load terminal. load voltage is scaled down by a factor of 20.

Result 4

To show how the transformer deals with a purely switched voltage with no load at the output, the waveform below shows the secondary voltage to be a stepped up voltage of the primary voltage. The secondary voltage has a spike at every instant of inverter switching due to the leakage inductance that has been modeled with the transformer.

Result 5

This simulation has started the series of simulations on electrical machines. The main effort in the simulation was to be able to represent a magnetic circuit in a generalized form and solve them as matrix equation. Moreover, it needs to be understood that the transformer is essentially a current driven model - the primary and the secondary windings are current sources modeled as voltages behind resistances. For that purpose, the resistance has been chosen to be large to avoid potential glitches in the current due to non-ideal voltages on the primary or the secondary as in this case where the primary voltage is the output of a single-phase inverter.