Page 277 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 265

Harmonic currents are also known to cause overheating in rotating machinery,
particularly synchronous generators. This applies to both solid-rotor synchronous
generators and salient-pole synchronous generators feeding unbalanced networks.
Harmonic currents produce an electromagnetic force that causes currents to flow in
the rotor adding to the heating. Positive sequence harmonics, e.g. 7th, 13th, rotate in
the same direction as the fundamental frequency and induce harmonic orders 6th,
8th, 12th, 14th, in the rotor. Negative sequence harmonics, e.g. 5th, 11th, rotate
against the direction of the rotor and produce harmonic orders 4th, 6th, 10th, 12th,
and so on, in the rotor. The resulting pulsating magnetic fields caused by the
opposing rotating pairs, e.g. 6th and 12th, may require a derating of the machine.
To illustrate the point, the derating of a synchronous generator operating near a six-
pulse rectifier, can be quite considerable, depending on the particular machine
design. On the other hand, derating for balanced 12-pulse rectifier operation is, on
average, minimal (Miller, 1982).
Induction motors are much less affected by harmonics than are synchronous
generators. However, excessive harmonic currents can lead to overheating, particu-
larly in cases when they are connected to systems where capacitors in resonance with
the system are aggravating one or more harmonics.
2
Harmonic currents carried by transformers will increase the load loss, I R,bya
factor greater than the mere increase in RMS current. The increase depends on the
2
proportion of I R loss proportional to frequency squared (eddy current loss), and the
amount proportional to the first power of frequency (stray load loss). The same rule-
of-thumb holds for current limiting and tuning reactors. Precise information about
the amount and order of each significant harmonic is mandatory in reactor design
practise.

7.3 Resonance in electric power systems

Banks of capacitors are very often added to power systems to provide reactive power
compensation, with voltage support and power factor correction being two popular
applications. An issue of great importance to bear in mind is that the capacitor bank
and the inductance of the system will be in parallel resonance in one or more
frequency points, and that harmonics injected into the system at coincident frequen-
cies will be amplified.
The small system shown in Figure 7.1 is used to illustrate the principle of harmonic
current flow and resonance. To simplify the explanation, it is assumed that the
harmonic source generates constant harmonic currents. The one-line diagram of
Figure 7.1(a) may be represented on a per-phase basis by the equivalent circuit in
Figure 7.1(b).
The n-th harmonic current divides between the capacitor and the supply according
to the equation
I n ˆ I sn ‡ I fn (7:1)
The impedance of the capacitor branch at any frequency is given by

Z f ˆ Z fc ‡ Z fl (7:2)