Possible solutions for power-system harmonics

Standard capacitors

The presence of harmonics in the supply voltage results in abnormally high current levels through the capacitors. An allowance is made for this by designing capacitors for an r.m.s. value of current equal to 1.3 times the nominal rated current. All series elements, such as connections, fuses, switches, etc., associated with the capacitors are similarly oversized, between 1.3 to 1.5 times the nominal ratings.

Standard capacitors can be used if the percentage of non-linear loads is lower than 10% (N_LL ≤ 10%).

Capacitors with increased current rating

Capacitors with improved current capability ("heavy duty") can be used in order to increase the safety margin. The technology of these capacitors allows a higher overcurrent compared to what is strictly requested by the standards.

Another possibility is to use capacitors with increased rated current and voltage.

As the same reactive power must be generated, the capacitors must have the same capacitance.

With a rated voltage U_N (higher than the system voltage U), the rated current I_N and the rated power

Q_N will be given by the formulas:

[math]\displaystyle{ \frac{I_N}{I}=\frac{U_N}{U} }[/math] and [math]\displaystyle{ \frac{Q_N}{Q}= \left ( \frac{U_N}{U} \right )^2 }[/math]

Capacitors with improved current rating can be used if the percentage of non-linear loads is lower than 20% (N_LL ≤ 20%).

Connection of Power Factor Correction capacitors with detuned reactors

In order to attenuate the effects of harmonics (significant increase of capacitor current as well as high current and voltage distortion ), reactors should be associated to capacitors. Reactors and capacitors are configured in a series resonant circuit, tuned so that the series resonant frequency is below the lowest harmonic frequency present in the system (See Figure L31).

The use of detuned reactors thus prevents harmonic resonance problems, avoids the risk of overloading the capacitors and helps reduce voltage harmonic distortion in the network.

Fig. L31 – Simplified circuit diagram

The tuning frequency can be expressed by the relative impedance of the reactor (in %, relative to the capacitor impedance), or by the tuning order, or directly in Hz.

The most common values of relative impedance are 5.7, 7 and 14 (14% is used with high level of 3rd harmonic voltages).

Relative impedance(%)	Tuning order	Tuning frequency @50Hz (Hz)	Tuning frequency @60Hz (Hz)
5.7	4.2	210	250
7	3.8	190	230
14	2.7	135	160

Fig. L32 – Correspondance between relative impedance, tuning order and tuning frequency

In this arrangement, the presence of the reactor increases the fundamental frequency voltage (50 or 60Hz) across the capacitor.

This feature is taken into account by using capacitors which are designed with a rated voltage U_N higher than the network service voltage U_S, as shown on the following table.

Capacitor Rated Voltage UN (V)		Network Service Voltage US (V)
		50 Hz		60 Hz
		400	690	400	480	600
Relative Impedance (%)	5.7	480	830	480	575	690
	7	480	830	480	575	690
	14	480		480

Fig. L33 – Typical values of capacitor rated voltage

Summary

Practical rules are given in the following table, for selection of the suitable configuration, depending on the system parameters:

• S_SC = 3-phase short-circuit power in kVA at the busbar level
• S_n = sum of the kVA ratings of all transformers supplying (i.e. directly connected to)the busbar
• G_h = sum of the kVA ratings of all harmonic-generating devices (static converters,inverters, variable speed drives, etc.) connected to the busbar.

If the ratings of some of these devices are quoted in kW only, assume an average power factor of 0.7 to obtain the kVA ratings

General rule (for any size of transformer):
[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}G_h\le \frac{S_{sc} }{120} }[/math]	[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}\frac{S_{sc} }{120} \lt G_h\le \frac{S_{sc} }{70} }[/math]	[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}\frac{S_{sc} }{70} \lt G_h\le \frac{S_{sc} }{30} }[/math]	[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}G_h \gt \frac{S_{sc} }{30} }[/math]
Standard capacitors	Heavy Duty capacitors or capacitors with voltage rating increased by 10%	Heavy Duty capacitors or capacitors with voltage rating increased by 20% + detuned reactor	Harmonic filtering necessary See chapter Power harmonics management
Simplified rule (if transformer rating ≤ 2MVA):
[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}G_h \le 0.1 \times S_n }[/math]	[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}0.1 \times S_n \lt G_h \le 0.2 \times S_n }[/math]	[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}0.2 \times S_n \lt G_h \le 0.5 \times S_n }[/math]	[math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}G_h \gt 0.5 \times S_n }[/math]
Standard capacitors	Heavy Duty capacitors or capacitors with voltage rating increased by 10%	Heavy Duty capacitors or capacitors with voltage rating increased by 20% + detuned reactor	Harmonic filtering necessary See chapter Power harmonics management

Fig. L34 – Simplified rules