Resonance

The idea

Capacitor banks are installed for good reasons: they supply reactive power locally and prop up the voltage. But a capacitor next to an inductive network is never just a capacitor — together they make a resonant pair, like a mass on a spring.

Seen from the bus, the two sit in parallel. At most frequencies one or the other dominates and the combined impedance stays low. But at the frequency where their reactances are equal, they form a parallel resonance: current circulates between the capacitor and the inductance, and to anything injecting current at that frequency, the bus looks like an enormous impedance.

Voltage distortion is injected current × bus impedance. So the question is never whether there is a resonance — with a capacitor bank installed, there always is one — but where it sits. The resonant order follows a usefully simple rule: h ≈ √(fault level ÷ bank size). Bigger banks tune the resonance lower, down toward the 7th and 5th — exactly where six-pulse drives inject.

Try it

Resize the bank and walk the peak across the injection orders.

Why it matters

• This is how mild networks go bad overnight. Nothing changed but a new capacitor bank — and the 7th-harmonic voltage triples. The injected currents were always there; the bank moved the amplifier onto them.
• The frequency scan needs no load data at all. The resonance is a property of the network itself. A scan tells you where the peaks sit before a single harmonic source is modeled — the cheapest useful harmonic result there is.
• The fix is tuning, not removal. A detuning reactor in series with the bank shifts the resonance to a safe frequency (and the bank still does its reactive-power job). But a filter that fixes one order can create a new resonance at another — always re-run the scan after the fix.

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