Power quality and networks
Capacitor bank voltage rise and parallel resonance
- where
- steady-state voltage rise (%)
- capacitor bank rating (Mvar)
- short-circuit level at the bank (MVA)
- parallel resonance harmonic order
- resonant frequency (Hz)
- system frequency (Hz)
Explain this equation
Estimates the voltage step when a capacitor bank is switched in and the harmonic order at which the bank resonates with the source inductance. Use both when siting a pf-correction or reactive-compensation bank.
Ssc represents the source reactance: a stiff network has high Ssc and low reactance. Qc represents the bank’s capacitive admittance. The ratio of the two sets both the voltage rise and the resonant point.
The reactive current from the bank flowing through the source reactance raises the voltage by Qc/Ssc in per unit. Parallel resonance happens where the source reactance, which rises with frequency, equals the capacitive reactance, which falls with it; that crossover is at h = √(Ssc/Qc).
Sense check: 350 kvar on a 10 MVA busbar gives a 3.5 % rise and resonance near the 5th harmonic (h ≈ 5.3). Quadrupling the bank halves h.
Watch out: a resonance near 5, 7, 11 or 13 will amplify the harmonic currents of drives and rectifiers. Check at both minimum and maximum fault level.
Estimates the voltage step when a shunt capacitor bank is switched in, and the harmonic order at which the bank resonates in parallel with the source inductance.
Enter your values to see the result.
Good to know
Use the minimum and maximum credible fault levels at the bank: the resonant order moves as the network changes. A bank with series detuning reactors (tuning order h = 1/√p for a reactor of p per unit: a 7 % reactor tunes to about 3.8 × f0, a 5.67 % reactor to 4.2 × f0) is inductive above its tuning frequency, so it cannot form a parallel resonance with the source at the 5th or higher harmonics; this simple formula does not apply to detuned banks. The voltage-step figure is the quantity compared with ENA P28 step-change limits.
Common mistake
Using the upstream grid fault level instead of the fault level at the capacitor bus. Downstream of a transformer, the transformer impedance dominates and lowers Ssc, so the resonance falls towards the 5th or 7th harmonic.
Limits
Assumes the source is purely inductive and the bank is the only capacitance; cable capacitance, loads (which add damping) and other banks are ignored. Use a frequency scan for design.
Sources
- Schneider Electric, Electrical Installation Guide – Risk of resonance due to power-system harmonics
- IEEE 1036-2020 Guide for the application of shunt power capacitors
- IEC 60871-1:2014 Shunt capacitors for a.c. power systems having a rated voltage above 1000 V – Part 1: General
- ENA Engineering Recommendation P28 Issue 2 (2019): Voltage fluctuations and the connection of disturbing equipment to transmission and distribution networks in the UK
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.