MATLAB Examples

# Three-Phase Saturable Transformer

This example shows the transformer saturation phenomenon.

G. Sybille (Hydro-Quebec)

## Description

A three-phase transformer is energized on a 500 kV network. The transformer rated 450 MVA, 500 kV/230 kV/60 kV consists of three windings connected in Y/Y/Delta.

The power system is simulated by an equivalent circuit consisting of an inductive source (short-circuit power of 3000 MVA) and a parallel RC load. The capacitor reactive power has been selected in order to produce a resonance at 240 Hz (4th harmonic).

The transformer saturation characteristics is approximated by a single slope Xsat of 0.32 pu, corresponding to an air core reactance Xac = 0.40 pu (Xac = Xsat+Xh = 0.32+0.08 = 0.40 pu.) seen from the primary. Three residual fluxes ( -0.8 - 0.4 0.4 pu) are specified for phases A B and C.

The Multimeter and Scope2 blocks are used to monitor extra signals without using measurement blocks. The six signals obtained at the output of the Multimeter are the three currents in the circuit breaker and the three fluxes inside the core of the saturable transformer. The flux on phase A is also obtained by integrating the phase A voltage at the unloaded output of winding two. The voltage and flux are converted to p.u. with gain blocks using proper scaling. The Fourier block measures the 4th harmonic content of the phase A primary voltage.

In order to allow further signal processing, signals displayed on Scope1 are sampled at 1/60/333 s (333 samples/ cycle) and stored in a variable named 'psbtransfosat_str' (structure with time).

## Simulation

Start the simulation and observe voltage, current and flux waveforms on Scope1 and Scope2.

Observe the transformer inrush currents and overvoltage after breaker closing. Because of the 0.8 pu residual flux on phase A and breaker closing at an instant causing maximum flux offset, the flux exceeds 2 pu on phase A. Compare the flux in phase A measured by the multimeter (yellow trace on 2nd input of Scope2) and the flux obtained by integration of the secondary voltage (first trace of Scope2).

Voltage Va contains a high level of 4th harmonic (displayed on 3rd trace of Scope1) due to the 4th harmonic content of current injected into the network resonating at that particular frequency (max. of 0.23 pu at t = 0.32 s). When simulation is completed, open the Powergui and select 'FFT Analysis' to display the 0 - 1000 Hz frequency spectrum of signals saved in the 'psbtransfosat_str' structure. The FFT will be performed on a 2-cycle window starting at 0.32 s (instant of highest 4th harmonic). Select input labeled 'Va (pu)' and click on Display to obtain the Va voltage spectrum. Note that distortion is caused mainly by harmonic orders 2 to 6 (highest content = 23% of 4th harmonic as obtained from the Fourier block).