Risk of resonance due to power-system harmonics
Considering the simplified circuit represented on Figure L29 (no PFC capacitors connected):
The voltage distortion V_{h} at the busbar level results from two different factors:
- connection of non-linear loads generating harmonic currents I_{h},
- voltage distortion U_{h} present on the supply network due to non-linear loads outside of the considered circuit (incoming harmonic voltage).
A significant indicator of harmonic importance is the percentage of non-linear loads N_{LL}, calculated by the formula:
[math]\displaystyle{ N_{LL(\%)}= \frac {\text{Power of non-linear loads}}{\text{Power of supply transformer}} }[/math]
The connection of PFC capacitors (without reactors) results in the amplification of harmonic currents at the busbar level, and an increase of the voltage distortion.
Capacitors are linear reactive devices, and consequently do not generate harmonics. The installation of capacitors in a power system (in which the impedances are predominantly inductive) can, however, result in total or partial resonance occurring at one of the harmonic frequencies.
Because of harmonics, the current I_{C} circulating through the PFC capacitors is higher compared to the situation where only the fundamental current I_{1} is present.
If the natural frequency of the capacitor bank/ power-system reactance combination is close to a particular harmonic, then partial resonance will occur, with amplified values of voltage and current at the harmonic frequency concerned. In this particular case, the elevated current will cause overheating of the capacitor, with degradation of the dielectric, which may result in its eventual failure.
The order h_{0 } of the natural resonant frequency between the system inductance and the capacitor bank is given by:
[math]\displaystyle{ h_0= \sqrt{\frac {S_{sc} }{Q} } }[/math]
Where:
S_{sc} = the level of system short-circuit power (kVA) at the point of connection of the capacitor
Q = capacitor bank rating in kvar
h_{0} = the order of the natural frequency f_{0}, i.e. f_{0}/50 for a 50 Hz system, or f_{0}/60 for a 60 Hz system.
For example:
Transformer power rating : | S = 630kVA |
Short-circuit voltage : | U_{sc} = 6% |
Short-circuit power at the busbar level : | S_{sc} ~ 10 MVA |
Reactive power of the capacitor bank : | Q = 350 kvar |
Then:
[math]\displaystyle{ h_0= \sqrt{\frac {S_{sc} }{Q} } = \sqrt{\frac {10.10^3}{350} } = 5.5 }[/math]
The natural frequency of the capacitor/system-inductance combination is close to the 5th harmonic frequency of the system.
For a 50Hz system, the natural frequency f_{0 } is then equal to f_{0 } = 50 x h_{0 } = 50 x 5.5 = 275 Hz