# Harmonics

A knowledge of the harmonic components of voltage and current in a power system is necessary because of the possibility of resonance and also the enhanced interference with communication circuits. The direct-voltage output of a converter has a waveform containing a harmonic content, which results in current and voltage harmonics along the line. These are normally reduced by a smoothing inductor. The

**Figure 9.24 **Variation of seventh harmonic current with delay angle a and commutation angle (Reproduced with permission from the International Journal of Electrical Engineering Education)

currents produced by the converter currents on the a.c. side contain harmonics. The current waveform in the a.c. system produced by a delta-star transformer bridge converter is shown in Figures 9.14 and 9.17. As given in equation (9.8), the order of the harmonics produced is 6n ± 1, where n is the number of valves.

Figure 9.24 shows the variation of the seventh harmonic component with both commutation (overlap) angle (g) and delay angle (a). Generally, the harmonics reduce with decreasing in g this being more pronounced at higher harmonics. Changes in *a* for a given g value do not cause large decreases in the harmonic components, the largest change being for values between 0 and 10°. For normal operation, *a* is less than 10° and g is perhaps of the order of 20°; hence the harmonics are small. During a severe fault, as discussed before, a may reach nearly 90^{°}, g is small, and the harmonics produced are large.

The harmonic voltages and currents produced in the a.c. system by the converter current waveform may be determined by representing the system components by their reactances at the particular harmonic frequency. Most of the system components have resonance frequencies between the fifth and eleventh harmonics.

It is usual to provide filters (L-C shunt resonance circuits) tuned to the harmonic frequencies. A typical installation is shown in detail in Figure 9.25. At the fundamental frequency the filters are capacitive and help to meet the reactive-power requirements of the converters.

**Figure 9.25 **Single-line diagram of the main circuit of an h.v.d.c. scheme showing filter banks and shunt compensation. (Reproduced with permission from IEEE)

# Variable Compensators

Rapid control of the reactive power compensation is achieved using TCR (thyristor- controlled reactor), MSR/MSC (mechanically switched reactor or capacitor) and TSC (thyristor-switched capacitor). Their selection depends upon the application and speed of response required for stability and overvoltage control.