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.
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 |
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 U_{N} (V) | Network Service Voltage U_{S }(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 |
Summary
Practical rules are suggested in Fig. L34, 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{ G_h\le \frac{S_{sc} }{120} }[/math] | [math]\displaystyle{ \frac{S_{sc} }{120} \lt G_h\le \frac{S_{sc} }{70} }[/math] | [math]\displaystyle{ \frac{S_{sc} }{70} \lt G_h\le \frac{S_{sc} }{30} }[/math] | [math]\displaystyle{ 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{ G_h \le 0.1 \times S_n }[/math] | [math]\displaystyle{ 0.1 \times S_n \lt G_h \le 0.2 \times S_n }[/math] | [math]\displaystyle{ 0.2 \times S_n \lt G_h \le 0.5 \times S_n }[/math] | [math]\displaystyle{ 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 |