Harmonic Parallel-Resonance Order
Why a bigger PF cap bank can land on the 5th harmonic, the check pf-correction never makes: the power-factor capacitors and the source inductance form a parallel LC circuit whose resonant order is h = sqrt(MVA_sc / MVAR_cap). If it lands on a harmonic the nonlinear loads produce (5/7/11/13th), the resonance AMPLIFIES it into destructive overvoltage and current. A 200 MVA bus with a 1.2 MVAR bank resonates at the 12.9th -- near the 13th, so the flag fires; double the bank to 2.4 MVAR and it walks DOWN to the 9.1th, because a bigger bank lowers the order toward the strong low harmonics. Ignores load damping; a detuning reactor or harmonic study is the fix. A screening aid; a harmonic study governs.
Formula and source
h_resonant = sqrt(MVA_sc / MVAR_cap); flag if h_resonant is within 0.5 of the 5th, 7th, 11th, or 13th harmonic.
Parallel-resonance order of a power-factor capacitor bank (IEEE 519 / IEEE 1531 harmonic filter and resonance guidance), first-principles, by name; a harmonic study governs.
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