Why does a three-phase system not produce third harmonics?
Power quality is an estimate of how stable the electrical system is, often this is described as “power quality health.” The primary effects of poor power quality effects include:
- Dips and swells — voltage lower or higher than expected
- Harmonics — frequency effects caused either by the power supply or by equipment operating within the system
- Unbalance — the effect of voltage or current variations on each of the electrical phases
So, A harmonic is a sinusoidal wave (voltage or current waveform) whose frequency is an integer multiple of the fundamental frequency. Harmonics are bad for the power system due to its non-fundamental components because it downgrades the quality of the power supply.
Considering a 3-phase system, the currents in the different phases will be:
Ir = Iₘₐₓ sin(ωt)
Iy = Iₘₐₓ sin(ωt+2π/3)
Ib = Iₘₐₓ sin(ωt-2π/3)
The third harmonic of these currents will be,
3rd Harmonic of Ir = Iₘₐₓ sin 3(ωt) = Iₘₐₓ sin (3ωt)
3rd Harmonic of Iy = Iₘₐₓ sin 3(ωt+2π/3) = Iₘₐₓ sin (3ωt+2π) = Iₘₐₓ sin (3ωt)
3rd Harmonic of Ib = Iₘₐₓ sin 3(ωt-2π/3) = Iₘₐₓ sin (3ωt-2π) = Iₘₐₓ sin (3ωt)
In the above expression, the third-order harmonic currents of all three phases are equal. However, it is observed that if there is no neutral conductor, the sum of the third-order harmonic currents is zero
(Ir + Iy + Ib = 0), which is only possible if each of the components is zero. Thus, we can understand that in a star connected alternator, third harmonics never appear in the line voltages.
