Harmonic Filter Calculator Formula
Understand the math behind the harmonic filter calculator. Each variable explained with a worked example.
Formulas Used
Tuning Frequency
tuning_frequency = tuning_freqCapacitance
capacitance_uf = c_farads * 1e6Inductance
inductance_mh = l_henrys * 1000Xc at Fundamental
xc_at_fund = xc_fundXl at Fundamental
xl_at_fund = xl_fundVariables
| Variable | Description | Default |
|---|---|---|
fundamental_hz | Fundamental Frequency(Hz) | 60 |
harmonic_order | Harmonic to Filter | 5 |
filter_kvar | Filter Reactive Power(kVAR) | 50 |
system_voltage | System Voltage (L-L)(V) | 480 |
tuning_freq | Derived value= fundamental_hz * harmonic_order | calculated |
omega_fund | Derived value= 2 * pi * fundamental_hz | calculated |
omega_tune | Derived value= 2 * pi * tuning_freq | calculated |
xc_fund | Derived value= pow(system_voltage, 2) / (filter_kvar * 1000) | calculated |
c_farads | Derived value= 1 / (omega_fund * xc_fund) | calculated |
xl_fund | Derived value= xc_fund / pow(harmonic_order, 2) | calculated |
l_henrys | Derived value= xl_fund / omega_fund | calculated |
How It Works
Single-Tuned Harmonic Filter Design
A series LC filter tuned to a specific harmonic frequency provides a low-impedance path that diverts harmonic current away from the system.
Design Steps
1. Capacitive reactance at fundamental: Xc = V^2 / kVAR 2. Inductive reactance at fundamental: Xl = Xc / n^2 3. Capacitance: C = 1 / (omega x Xc) 4. Inductance: L = Xl / omega
Where n is the harmonic order and omega = 2 x pi x f_fundamental.
Filters are typically tuned slightly below the target harmonic (e.g., 4.7th instead of 5th) to avoid resonance with system impedance.
Worked Example
5th harmonic filter, 50 kVAR, 480 V, 60 Hz system.
- 01Tuning frequency: 60 x 5 = 300 Hz
- 02Xc at 60 Hz: 480^2 / 50000 = 4.608 ohms
- 03Xl at 60 Hz: 4.608 / 25 = 0.184 ohms
- 04C = 1 / (377 x 4.608) = 575.7 microfarads
- 05L = 0.184 / 377 = 0.49 mH
Frequently Asked Questions
Why tune below the exact harmonic?
Component tolerances and temperature variations can shift the tuning point. Detuning slightly low prevents dangerous parallel resonance.
How many harmonics need filters?
The 5th and 7th are typically the largest for 6-pulse drives. The 11th and 13th may also need filtering for 12-pulse systems.
Can one filter handle multiple harmonics?
A single-tuned filter targets one harmonic. For multiple harmonics, use multiple filter branches or a broadband (high-pass) filter.
Ready to run the numbers?
Open Harmonic Filter Calculator