Phase Difference Between Fundamental & Harmonics
Interactive demonstration of how harmonic magnitude and phase affect the resulting electrical waveform
1. Simulation Controls
5th Harmonic
20% of fundamental
0°
0% harmonic reduction
2. Waveform Visualization
Harmonic is in phase with its reference position.
3. What Is Being Added?
v(t) = V₁ sin(ωt) + Vₕ sin(nωt + φ)
Fundamental
The fundamental is the normal power-frequency waveform, for example 50 Hz in many power systems.
The fundamental is the normal power-frequency waveform, for example 50 Hz in many power systems.
Harmonic
The harmonic has a frequency that is an integer multiple of the fundamental. For example, the 5th harmonic of 50 Hz is 250 Hz.
The harmonic has a frequency that is an integer multiple of the fundamental. For example, the 5th harmonic of 50 Hz is 250 Hz.
Phase Difference
The phase angle φ determines where the harmonic waveform begins relative to its reference position.
The phase angle φ determines where the harmonic waveform begins relative to its reference position.
Result
The actual waveform is the mathematical sum of the fundamental and harmonic components.
The actual waveform is the mathematical sum of the fundamental and harmonic components.
4. Effect of Different Phase Differences
| Phase Difference | Typical Waveform Effect | Important Observation |
|---|---|---|
| 0° | Maximum reinforcement at some points | Harmonic distortion follows a particular alignment |
| 45° | Waveform shape changes | Peaks and zero crossings shift differently |
| 90° | Different portions reinforce/cancel | Waveform becomes noticeably asymmetric in shape |
| 120° | Different harmonic contribution | Distortion pattern changes |
| 180° | Harmonic is inverted | Opposite harmonic phase can produce cancellation at some points |
| 270° | Equivalent to -90° phase | Distortion pattern changes again |
| 360° | Equivalent to 0° | Waveform repeats the 0° phase relationship |
5. Mitigation
High Harmonic Level
Large harmonic currents can increase equipment heating, losses, vibration, electromagnetic interference and waveform distortion.
Large harmonic currents can increase equipment heating, losses, vibration, electromagnetic interference and waveform distortion.
Passive Filters
LC filters can provide a low-impedance path for selected harmonic frequencies and reduce harmonic current.
LC filters can provide a low-impedance path for selected harmonic frequencies and reduce harmonic current.
Active Harmonic Filters
Active filters measure harmonic components and generate compensating currents to reduce distortion.
Active filters measure harmonic components and generate compensating currents to reduce distortion.
Reduce Harmonic Sources
Improved power-electronic designs, suitable rectifiers, multipulse converters and low-harmonic drives can reduce harmonic generation.
Improved power-electronic designs, suitable rectifiers, multipulse converters and low-harmonic drives can reduce harmonic generation.
Effective harmonic after filter =
Original harmonic × (1 − Filter Reduction)
6. Live Measurements
Fundamental Frequency
50 Hz
50 Hz
Harmonic Frequency
250 Hz
250 Hz
Original Harmonic
20%
20%
After Mitigation
20%
20%