## 8111 Harmonic Analysis

Let us consider the switching interval number 3, where 2p/3< t<p. The switches that are on during this period are Si, S2, and S3. The inverter configuration in this interval is shown in Figure 8.6. The line-to-line square-wave voltage can be written in terms of the fundamental and harmonic components using Fourier series analysis as follows:   FIGURE 8.7 Dominant harmonic components in inverter output voltages.

Note that the harmonics present are the 6n±1 (n is an integer) components, and that the triple harmonics are absent. The harmonic phase voltages that are 30° phase shifted from the line voltages are

Vm = ^ v^ jsiii (00i)+|siii (5«oi) + ^ sin (7«w)+- -. j

The dominant harmonic components are shown in Figure 8.7.

Harmonics do not contribute to the output power, but they increase power losses, which degrades the efficiency and increases the thermal loading of the machine. Harmonic losses do not vary significantly with the load. The interactions of fundamental air gap mmfs with harmonic air gap mmfs produce torque pulsations, which may be significant at low speeds.

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