This example shows the harmonic analysis of PWM waveforms using the Powergui/FFT tool.
The system consists of two independent circuits illustrating single-phase PWM voltage-sourced converters (VSC).
1. Half-bridge converter
2. Full-bridge converter
The converters are built with the IGBT/Diode block which is the basic building block of all VSCs. The IGBT/Diode block is a simplified model of an IGBT (or GTO or MOSFET)/Diode pair where the forward voltages of the forced-commutated device and diode are ignored. You may replace these blocks by individual IGBT and diode blocks for a more detailed representation. VSCs are controlled in open loop with the PWM Generator block. The two circuits use the same DC voltage (Vdc = 400V), carrier frequency (1080 Hz) and modulation index (m = 0.8).
In order to allow further signal processing, signals displayed on the two Scope blocks (sampled at simulation sampling rate of 3240 samples/cycle) are stored in two variables named sps1phPWM1_str and sps1phPWM2_str (structures with time).
Run the simulation and observe the following two waveforms on the two Scope blocks: Current into the load (trace 1), Voltage generated by the PWM inverter (trace 2).
Once the simulation is completed, open the Powergui and select FFT Analysis to display the 0 - 5000 Hz frequency spectrum of signals saved in the three sps1phPWMx_str structures. The FFT will be performed on a 2-cycle window starting at t = 0.1 - 2/60 (last 2 cycles of recording). For each circuit, select Input labeled 'V inverter' . Click on Display and observe the frequency spectrum of last 2 cycles.
The fundamental component of V inverter is displayed above the spectrum window. Compare the magnitude of the fundamental component of the inverter voltage with the theoretical values given in the circuit. Compare also the harmonic contents in the inverter voltage.
The half-bridge inverter generates a bipolar voltage (-200V or +200V) . Harmonics occur around the carrier frequency (1080 Hz +- k*60 Hz), with a maximum of 103% at 1080 Hz.
The full-bridge inverter generates a monopolar voltage varying between 0 and+400V for one half cycle and then between 0 and -400V for the next half cycle. For the same DC voltage and modulation index, the fundamental component magnitude is twice the value obtained with the half-bridge. Harmonics generated by the full-bridge are lower and they appear at double of the carrier frequency (maximum of 40% at 2*1080+-60 Hz) As a result, the current obtained with the full-bridge is smoother.
If you now perform a FFT on the signal I load you will notice that the THD of load current is 7.3% for the half-bridge inverter as compared to only 2% for the full-bridge inverter.