Short answer
A C-type harmonic filter is a damped filter designed to avoid fundamental-frequency losses in its damping resistor. It has a main capacitor in series with a parallel combination: on one side the damping resistor, on the other an inductor in series with an auxiliary capacitor. The inductor and auxiliary capacitor are tuned to resonate at fundamental frequency, so at fundamental that path has near-zero impedance and the fundamental current bypasses the resistor. At harmonic frequencies the path no longer cancels, current divides into the resistor and is damped. In an illustrative case at 100 A, a plain second-order damped filter would pass about 30 A and 9 kW through a 10 Ω resistor, while the C-type passes almost none. If the auxiliary branch drifts 2 % or 5 % from resonance, resistor loss rises to about 4 W or 23 W, small but growing.
Structure
| Design | I_R | P_R |
|---|---|---|
| Plain second-order | ≈ 30 A | ≈ 9.0 kW |
| C-type, exact | ≈ 0 | ≈ 0 |
| C-type, Ca +2 % | ≈ 0.62 A | ≈ 3.8 W |
| C-type, Ca +5 % | ≈ 1.5 A | ≈ 22.5 W |
- Main capacitor C1: sets reactive output and carries all current.
- Inductor L in series with auxiliary capacitor Ca: resonant at f1.
- Resistor R in parallel with the L–Ca branch.
At f1, L–Ca impedance ≈ 0, shorting R. At harmonics, L–Ca impedance is inductive and comparable to R, so R damps the filter response.
Illustrative calculation
Illustrative example. 50 Hz; L = 10 mH; Ca chosen for resonance at 50 Hz, about 1.013 mF; R = 10 Ω; fundamental filter current 100 A. Values chosen for demonstration.
X_L = 314.16 × 0.01 ≈ 3.142 Ω
Plain second-order damped filter (R parallel to L only):
I_R ≈ 100 × 3.142 / sqrt(10^2 + 3.142^2) ≈ 30 A; P_R ≈ 9.0 kW
C-type with Ca exact: net L–Ca reactance 0; I_R ≈ 0.
C-type with Ca 2 % high: X_Ca ≈ 3.080 Ω, net ≈ 0.062 Ω; I_R ≈ 0.62 A, P_R ≈ 3.8 W.
C-type with Ca 5 % high: net ≈ 0.150 Ω; I_R ≈ 1.5 A, P_R ≈ 22.5 W.
Main versus auxiliary components
| Component | Function | Rating concern |
|---|---|---|
| Main capacitor C1 | Reactive power, full voltage | Fundamental and harmonic voltage |
| Auxiliary capacitor Ca | Fundamental resonance with L | Fundamental current, low voltage |
| Inductor L | Tuning and resonance | Current, linearity |
| Resistor R | Harmonic damping | Harmonic power, drift-induced fundamental |
The auxiliary capacitor carries the full fundamental current at a low voltage, so its kvar is small but current rating is high.
Drift and monitoring
- Ca or L drift moves the fundamental resonance; losses in R rise with the square of mistuning.
- Element failures in Ca change its capacitance; see tolerance drift in tuned harmonic filters.
- Frequency deviation of the system shifts the balance too.
- Monitor resistor current at fundamental as an indicator.
Comparison with single-tuned and plain damped filters is in single-tuned and damped filters on transformer buses. Resonance scans should model the C-type correctly; see resonance scans with frequency-dependent transformer damping.
What this article does not cover
General comparison of active and passive compensation is not repeated here.
Where this reasoning stops. Component values are illustrative; harmonic losses in R are not calculated here.
Practical takeaway
Use C-type filters where damping is needed without fundamental resistor loss, rate the auxiliary branch for full fundamental current, and monitor resistor current to detect drift of the auxiliary resonance.
Reference framework
- IEEE 1531, Guide for the application and specification of harmonic filters.