Power factor correction (PFC) capacitor banks are essential in industrial facilities to avoid utility low power factor penalties. However, in modern facilities dominated by non-linear loads (Variable Frequency Drives, rectifiers, UPS systems, induction heaters), connecting un-detuned capacitors often triggers catastrophic parallel resonance, resulting in blown fuses and bulging or exploding capacitor cans.
1. The Mechanism of Harmonic Resonance
Capacitive reactance decreases as frequency increases ($X_C = 1 / 2pi f C$), while inductive reactance increases ($X_L = 2pi f L$). At a specific harmonic frequency, the inductive impedance of the supply transformer and the capacitive impedance of the capacitor bank become equal, creating a parallel resonant circuit.
When this resonant frequency coincides with a harmonic generated by on-site non-linear loads (typically the 5th harmonic at 250Hz or 7th harmonic at 350Hz), the harmonic current is amplified by 5 to 20 times, severely destroying both the capacitors and the transformer.
2. Sizing the Reactance Ratio ($p = X_L / X_C$)
By connecting an iron-core detuned reactor (AIKey CKSG series) in series with the capacitor bank, the resonant frequency of the combination is intentionally shifted below the lowest prevailing harmonic in the system.
| Reactance Ratio ($p$) | Series Resonant Frequency (50Hz) | Primary Suppression Target | System Condition |
|---|---|---|---|
| 7% (or 6%) | 189 Hz (7%) / 204 Hz (6%) | 5th (250Hz), 7th (350Hz), 11th (550Hz) | Standard commercial buildings, manufacturing plants with 3-phase VFD drives |
| 14% (or 12.5%) | 134 Hz (14%) / 141 Hz (12.5%) | 3rd (150Hz), 5th, 7th harmonics | Heavy single-phase loads, computer data centers, fluorescent lighting, arc furnaces |
3. Capacitor Overvoltage: Sizing Capacitor Voltage Rating
When a reactor is placed in series with a capacitor, it creates a voltage rise across the capacitor terminals according to the formula:
U_c = U_n / (1 – p)
For a standard 400V grid with a 7% reactor ($p = 0.07$), the voltage across the capacitor becomes $400 / 0.93 = 430text{V}$. Therefore, standard 400V capacitors will rapidly fail; capacitors rated for at least 450V or 480V must be selected. For a 14% reactor, 525V capacitors are mandatory.
4. Core Linearity Requirements (≥ 1.8x In)
A detuned reactor must remain strictly linear under harmonic current peaks. If the magnetic core saturates under peak current, its inductance drops precipitously, returning the bank into an un-detuned state that causes destructive resonance. AIKey CKSG reactors utilize multi-gap iron cores bonded with Class H epoxy resin, maintaining linearity up to 1.8 to 2.0 times rated current.