Variable Frequency Drives (VFDs) introduce harmonic distortions that can degrade power quality and equipment performance. Accurate harmonic filter sizing is essential to mitigate these effects and comply with industry standards.
This article explores harmonic filter sizing calculations for VFDs based on IEEE 519 and IEC standards. It covers formulas, tables, and real-world examples for precise filter design and implementation.
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- Input: VFD rated power = 100 kW, system voltage = 480 V, THD limit = 5%
- Input: Load current = 150 A, harmonic order = 5, permissible harmonic current = 10 A
- Input: System short circuit capacity = 100 MVA, VFD current = 200 A, target THD = 3%
- Input: VFD power = 75 kW, supply frequency = 60 Hz, harmonic filter tuning frequency = 360 Hz
Common Values for Harmonic Filter Sizing in VFD Applications
| Parameter | Typical Range | Units | Notes |
|---|---|---|---|
| VFD Rated Power | 1 – 2000 | kW | Common industrial VFD power ratings |
| System Voltage | 208 – 690 | Volts (V) | Typical low and medium voltage levels |
| Short Circuit Capacity (SCC) | 10 – 1000 | MVA | System fault level at point of common coupling (PCC) |
| Total Harmonic Distortion (THD) Limit | 3 – 5 | % | IEEE 519 recommended limits for voltage distortion |
| Individual Harmonic Current Limit (Ih) | 1 – 15 | % of IL | Percentage of load current per harmonic order |
| Load Current (IL) | 10 – 1000 | Amperes (A) | Current drawn by the VFD load |
| Filter Tuning Frequency | 180 – 720 | Hz | Typically 3rd, 5th, 7th harmonic frequencies |
| Filter Quality Factor (Q) | 30 – 100 | Dimensionless | Determines filter sharpness and losses |
Fundamental Formulas for Harmonic Filter Sizing
Harmonic filter sizing involves calculating the required filter components to reduce harmonic currents and voltages to acceptable levels. The following formulas are essential for designing passive harmonic filters compliant with IEEE 519 and IEC standards.
1. Total Harmonic Distortion (THD) Calculation
THD quantifies the distortion level in voltage or current waveforms.
- Ih: RMS current of the hth harmonic
- I1: RMS current of the fundamental frequency (usually 50 or 60 Hz)
2. Individual Harmonic Current Limit (IEEE 519)
IEEE 519 defines maximum allowable harmonic current limits based on the short circuit ratio (SCR).
- Isc: Short circuit current at PCC (Amps)
- IL: Maximum load current (Amps)
- Kh: Harmonic current factor for harmonic order h (from IEEE 519 tables)
3. Filter Reactance and Capacitance Calculation
To design a tuned harmonic filter, calculate the required capacitance and inductance values to target specific harmonic frequencies.
- ft: Filter tuning frequency (Hz)
- h: Harmonic order (3, 5, 7, etc.)
- f1: Fundamental frequency (50 or 60 Hz)
- C: Capacitance (Farads)
- L: Inductance (Henrys)
- XC: Capacitive reactance (Ohms)
- XL: Inductive reactance (Ohms)
4. Filter Current Rating
The filter must be rated to handle the harmonic current it will shunt.
- Ifilter: Filter current rating (Amps)
- Ih: Harmonic current to be filtered (Amps)
- Q: Filter quality factor (dimensionless, typically 30–100)
5. Short Circuit Ratio (SCR)
SCR is a key parameter for harmonic distortion assessment and filter design.
- Isc: Short circuit current at PCC (Amps)
- IL: Maximum load current (Amps)
Real-World Example 1: Sizing a 5th Harmonic Filter for a 100 kW VFD
A 100 kW VFD operates at 480 V, 60 Hz, drawing 150 A load current. The system short circuit capacity at PCC is 50 MVA. The goal is to design a 5th harmonic filter to reduce the 5th harmonic current to comply with IEEE 519 limits.
- Step 1: Calculate short circuit current (Isc) at PCC.
Given system voltage (V) = 480 V, short circuit capacity (SCC) = 50 MVA.
- Step 2: Calculate short circuit ratio (SCR).
- Step 3: Determine IEEE 519 harmonic current limit factor (K5) for 5th harmonic.
For SCR > 50, K5 ≈ 4% (from IEEE 519 tables).
- Step 4: Calculate maximum allowable 5th harmonic current (I5,limit).
- Step 5: Estimate actual 5th harmonic current without filter (assumed 15% of load current).
- Step 6: Calculate required filter current rating.
Assuming filter quality factor Q = 50, the filter must shunt the difference between actual and allowable harmonic current.
- Step 7: Calculate filter capacitance (C) for 5th harmonic (300 Hz).
Fundamental frequency f1 = 60 Hz, harmonic order h = 5, tuning frequency ft = 300 Hz.
Assuming filter voltage rating V = 480 V line-to-line, and reactive power Qc = 50 kVAR (typical for 100 kW VFD), calculate capacitance:
- Step 8: Calculate inductance (L) for tuning.
This filter will effectively reduce the 5th harmonic current to meet IEEE 519 limits.
Real-World Example 2: Multi-Harmonic Filter Design for a 200 kW VFD System
A 200 kW VFD system at 400 V, 50 Hz, draws 350 A load current. The short circuit capacity at PCC is 100 MVA. The goal is to design a multi-tuned harmonic filter targeting 3rd, 5th, and 7th harmonics to comply with IEC 61000-3-12 standards.
- Step 1: Calculate short circuit current (Isc).
- Step 2: Calculate SCR.
- Step 3: Determine harmonic current limits per IEC 61000-3-12.
IEC limits are similar to IEEE 519 but slightly more stringent for some harmonics. Assume limits:
| Harmonic Order (h) | Max Harmonic Current (%) |
|---|---|
| 3 | 2.0% |
| 5 | 3.5% |
| 7 | 3.0% |
- Step 4: Calculate allowable harmonic currents.
| Harmonic Order (h) | Allowable Current (A) |
|---|---|
| 3 | 0.02 × 350 = 7 A |
| 5 | 0.035 × 350 = 12.25 A |
| 7 | 0.03 × 350 = 10.5 A |
- Step 5: Estimate actual harmonic currents without filters (assumed 10%, 15%, 12% respectively).
| Harmonic Order (h) | Actual Current (A) |
|---|---|
| 3 | 0.10 × 350 = 35 A |
| 5 | 0.15 × 350 = 52.5 A |
| 7 | 0.12 × 350 = 42 A |
- Step 6: Calculate filter current ratings for each harmonic (Q = 50).
| Harmonic Order (h) | Filter Current (A) |
|---|---|
| 3 | (35 – 7) / 50 = 0.56 |
| 5 | (52.5 – 12.25) / 50 = 0.81 |
| 7 | (42 – 10.5) / 50 = 0.63 |
- Step 7: Calculate capacitance and inductance for each tuned filter.
| Harmonic Order (h) | Tuning Frequency (Hz) | Capacitance (μF) | Inductance (mH) |
|---|---|---|---|
| 3 | 150 | 5.8 | 10.3 |
| 5 | 250 | 3.5 | 7.1 |
| 7 | 350 | 2.5 | 5.0 |
These values are calculated based on reactive power compensation and tuning frequency formulas, ensuring effective harmonic mitigation.
Additional Technical Considerations for Harmonic Filter Sizing
- Filter Quality Factor (Q): Higher Q values yield sharper tuning but increase losses and risk of resonance.
- System Impedance: Accurate knowledge of system impedance at PCC is critical for filter design.
- Multiple VFDs: Harmonic interactions from multiple drives require coordinated filter design.
- Thermal Ratings: Filters must be rated for thermal stresses due to harmonic currents.
- Standards Compliance: Always verify filter design against latest IEEE 519-2014 and IEC 61000-3-12 standards.
- Filter Types: Single-tuned, double-tuned, and high-pass filters have different applications and performance.
For further reading, consult the official IEEE 519-2014 standard document available at IEEE Standards Association and IEC 61000-3-12 at IEC Webstore.