Capacitor Bank Resonance with 6-Pulse VFD Loads on an 11 kV Bus
An 11 kV industrial bus supplies two 800 kW 6-pulse VFDs and a 2 MVA capacitor bank connected in two 1 MVA steps. The 11 kV source fault level is 50 MVA. Since the VFDs were commissioned, capacitor fuses have blown on step switching, capacitor currents measure about 1.6 times rated, and the 5th-harmonic voltage distortion at the bus reaches 12% with the bank in service, falling to 4% when it is switched out. The plant needs about 1.5 MVAr to avoid a power-factor penalty. Capacitor units are rated 11 kV, 50 Hz, and the relay is a simple overcurrent plus unbalance scheme. The utility requires no voltage distortion above 5% and no resonance below the 5th harmonic. A 7% series reactor is available from stores, but the plant engineer proposes a 5.67% reactor instead.
1. Calculate the parallel resonance order and explain why the 5th harmonic is excited. Decide whether the 2 MVA bank is acceptable as installed.
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Take the equivalent phase values: Xc = V²/Q = 11²/2 = 60.5 Ω. Source reactance Xs = 11²/50 = 2.42 Ω. Parallel resonance h = √(Xc/Xs) = √(60.5/2.42) = √25 = 5.0. A 6-pulse VFD produces 5th, 7th, 11th and 13th harmonics, with the 5th normally largest. That harmonic coincides with the resonance, so the bank amplifies 5th voltage and current. The measured 12% distortion with the bank in, and 4% with it out, is consistent; the 1.6 pu capacitor current is also consistent with resonance. The bank is not acceptable as installed, even though it supplies the required 1.5 MVAr. Adding more capacitance would move the resonance lower and could make the problem worse. The correct fix is to detune the bank below the 5th, not to increase the bank size.
2. Evaluate the 7% and 5.67% reactor options. Determine the capacitor voltage duty and state what rating the units require.
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With a series reactor of percentage p, the series resonance is h = √(100/p). A 7% reactor gives 3.78; 5.67% gives 4.20. Both are below the 5th, but 5.67% is too close: with the bank Q and the existing 5th voltage, it can still amplify the 5th, and reactor/capacitor harmonic current will be higher. Select 7%, giving about 25% margin below the 5th. Check capacitor voltage: Vc = V × Xc/(Xc − XL) = 11 × 60.5/(60.5 − 4.235) = 11.83 kV. The existing 11 kV units are therefore under-rated; use at least 12 kV, preferably 13.2 kV heavy-duty units. The reactor must be rated for fundamental plus harmonic current. The bank output at 11 kV will be about 2.15 MVAr, so step size and overvoltage protection need review. Verify with a harmonic study using the actual VFD spectrum and source impedance, including the case with one 1 MVA step out.
3. Recommend protection and switching changes for the detuned bank and explain why the 5.67% reactor from stores should or should not be used.
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Replace the simple overcurrent with a dedicated capacitor relay with unbalance or neutral-voltage protection, overvoltage, and harmonic overcurrent. Set overcurrent above the detuned bank inrush and above expected 5th/7th current. Use a reactor-rated switching device and avoid restrikes; vacuum switching is acceptable but check reactor insulation and capacitor discharge resistors. Add a 5th-harmonic filter if the 7% reactor still leaves distortion above 5%. Do not use the 5.67% reactor merely because it is in stores: the small saving is not worth the reduced margin below the 5th, and the existing 11 kV capacitor units are already under-rated for the reactor voltage rise. Commission with harmonic measurements at the bus and at the capacitor, and confirm the resonance has moved to about 3.8 with the bank in service.