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load, the usual remedy is to move the high impedance parallel resonant frequency to a

value that does not correspond to any of the system’s harmonic frequencies by connecting

a reactor L in series with the capacitor bank, as shown in Figure 7.4.

Lsc

Vn

In

I

C

L

Fig. 7.4 Simple circuit with damping inductor L

The value of L, usually many times bigger than Lsc, is chosen to create a series resonant

condition with C to present a path of low impedance to the problem harmonic. The above

arrangement has the added advantage of reducing the sensitivity of the calculation to the

value of Lsc, which is rarely known with any degree of accuracy in practice and can vary to

a large extent with different load conditions.

S7: Supply Harmonics

123 EEE8044: Fundamentals

Exercise 7.3

A small industrial user was fed from a 500 kVA, 11 kV/433 V transformer with a leakage

impedance of 4.75% and negligible resistance. He had a 400 kVA 6-pulse rectifier load

and site measurements showed excessive levels of harmonic distortion. The user had a

95 kVA power factor correction capacitor bank and the harmonic measurements were

carried out with and without this unit, at full load.

A significant increase in distortion levels was detected with the PF correction capacitor

bank in the circuit. Transformer and capacitor values indicated resonance at about 500 Hz.

The difference between measured levels of harmonics with and without the PFC unit was

greatest at the 11th harmonic.

Calculate the resonant frequency and the THD with and without the power factor

correction unit.

Hints:

The ac current waveform will contain harmonics of the order (6k ± 1), where k = 1, 2, 3,

etc.

The rms value of the nth current harmonic In is given by

n

0.78 Id

.

Remember to set up a spreadsheet to do your calculations.

Turn to the end of the booklet for answers to the problems

S7: Supply Harmonics

124 EEE8044: Fundamentals

7.6 Methods of Harmonic Elimination

No modern power system can be totally free from harmonics, but it is possible to control

the level of voltage distortion by a number of means. These are described in the following

sections.

Of course, increasing the capacity of the system, by installing bigger transformers, will

reduce the harmonic problem significantly because of the smaller supply impedances and

the resulting reduction in THD. This solution, however, is not usually feasible, largely due

to the cost involved.

In a way, the most surprising thing about harmonics and harmonic distortion is that they do

not cause more problems than they do. Even today with the large increase in the percentage

of the total electrical load controlled by power electronics equipment, few customers

experience problems with harmonics, despite the significant levels of THD present on the

network. However, when problems do occur, they are serious problems and measures must

be taken to reduce the impact of the harmonic problem. These include the use of deltaconnected

transformers, the installation of passive LC filters, using higher pulse number

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