Digital Determination of Output Voltage Harmonics in a Single-Phase Voltage Controller
Digital Determination of Output Voltage Harmonics in a Single-Phase Voltage Controller
In this Demonstration, the output voltage of a single-phase AC-AC voltage controller is measured at a sampling frequency of times the fundamental frequency ( is an integer exponent). The number of measurement samples taken within one cycle of the fundamental frequency gives a vector of measured values, which is then used to calculate the discrete Fourier transform (DFT) of the voltage waveform.
n-1
2
n
n
2
For instance, implies that a voltage is measured at a sampling frequency equal to ×50=32×50=1600Hz, which means that =64 measurement samples are taken within one fundamental frequency cycle ( in this case). The highest harmonic component to be detected in this case would be ×50Hz=1600Hz, that is, the voltage harmonic; this frequency, the highest to be detected and represented by the DFT algorithm, is called the Nyquist frequency. In this particular example, however, due to the symmetry of the waveform, the result will always go up to the previous odd harmonic, that is, the harmonic (or ) for this example.
n=6
50Hz
6-1
2
6
2
0.020s
50Hz
6-1
2
nd
32
st
31
1550Hz