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264 Harmonic studies of power compensating plant

be addressed differently because measurements may not be economic or the network
may not exist. In such cases, digital simulations based on mathematical modelling
provide a viable alternative to actual measurements (Dommel, 1969). Research
efforts worldwide have produced accurate and reliable models for predicting power
systems harmonic distortion. Time and frequency domain solutions have been used
for such a purpose. Owing to its popularity, most frequency domain techniques use
Fourier's transform (Semlyen et al., 1988) but alternative transforms such as Hartley
(Acha et al., 1997), Walsh (Rico and Acha, 1998) and Wavelets can also be used for
alternative harmonic solutions.
The thrust of this chapter is to present harmonic models of power plant compensa-
tion equipment, but it is useful to set the scene by first examining some of the adverse
effects caused by the existence of harmonics and the potential harmonic magnifica-
tion problems which may be introduced by a bank of capacitors, together with the
beneficial effects brought about by the use of tuning reactors.
Models of TCR, SVC and TCSC are presented in Sections 7.4, 7.5 and 7.6,
respectively. These models use Fourier's transform and are used to solve harmonic
distortion problems in power systems containing electronic compensation. They
come in the form of harmonic admittance and impedance matrices, respectively. In
the absence of harmonics build up due to, for instance, resonance conditions, these
plant components may be considered linear, time-variant. The harmonic admittance
and impedance models are derived by `linearizing' the TCR equations, in a manner
that resembles the linearization exercise associated with, say, the non-linear equa-
tions of magnetic iron cores (Semlyen and Rajakovic, 1989).
It should be noted that linear, time-invariant components generate no harmonic
distortion whereas non-linear and linear, time-variant components do generate
harmonic distortion. Examples of linear, time-invariant components are banks of
capacitors, thyristor-switched capacitors, air-core inductors, transmission lines and
cables. Examples of non-linear components are, saturated transformers and rotating
machinery, salient pole synchronous generators feeding unbalanced systems, electric
arc furnaces, fluorescent lamps, microwave ovens, computing equipment and line
commutated AC±DC converters (Acha and Madrigal, 2001). Time-variant compon-
ents are, for instance, SVCs and TCSCs operating under medium to low harmonic
voltage distortion, VSC-based equipment with PWM control, e.g. STATCOM,
DVR, UPFC and HVDC light.

7.2 Effect of harmonics on electrical equipment

In industrial installations, the first evidence of excessive harmonic levels is blown
capacitor fuses or failed capacitors in capacitor banks. Current standards cover the
characteristics of shunt power capacitors (IEEE IAS/PES, 1993). It is well known
that continuous operation with excessive harmonic current leads to increased voltage
stress and excessive temperature rises, resulting in a much reduced power plant
equipment's useful life. For instance, a 10% increase in voltage stress will result in
7% increase in temperature, reducing the life expectancy to 30% (Miller, 1982). More
severe capacitor failure may be initiated by dielectric corona, which depends on both
intensity and duration of excessive peak voltages.