Effects of harmonics - Overload of equipment

Generators

Generators supplying non-linear loads must be derated due to the additional losses caused by harmonic currents.
The level of derating is approximately 10% for a generator where the overall load is made up of 30% of non-linear loads. It is therefore necessary to oversize the generator.

Uninterruptible power systems (UPS)

The current drawn by computer systems has a very high crest factor. A UPS sized taking into account exclusively the RMS current may not be capable of supplying the necessary peak current and may be overloaded.

Transformers

• The curve presented below (see Fig. M9) shows the typical derating required for a transformer supplying electronic loads

---

Fig. M9: Derating required for a transformer supplying electronic loads

---

Example

• If the transformer supplies an overall load comprising 40% of electronic loads, it must be derated by 40%.
• Standard UTE C15-112 provides a derating factor for transformers as a function of the harmonic currents.

[math]\displaystyle{ k=\frac{1}{\sqrt {1+0.1 \left (\sum_{h=2}^{40} h^{1.6} T_h^2 \right)}} }[/math]
[math]\displaystyle{ T_h=\frac{I_h}{I_1} }[/math]
Typical values:

• Current with a rectangular waveform (1/h spectrum ⁽¹⁾): k = 0.86
• Frequency-converter current (THD ≈ 50%): k = 0.80

(1) In fact, the current waveform is similar to a rectangular waveform. This is the case for all current rectifiers (three-phase rectifiers, induction furnaces).

Asynchronous machines

Standard IEC 60892 defines a weighted harmonic factor (Harmonic voltage factor) for which the equation and maximum value are provided below.
[math]\displaystyle{ HVF=\sqrt {\sum_{h=2}^{13} \frac{U_h}{h^2}} \le 0.02 }[/math]

Example
A supply voltage has a fundamental voltage U1 and harmonic voltages u3 = 2% of U1, u5 = 3%, u7 = 1%. The THDu is 3.7% and the MVF is 0.018. The MVF value is very close to the maximum value above which the machine must be derated. Practically speaking, for supply to the machine, a THDu of 10% must not be exceeded.

Capacitors

According to IEC 60831-1 standard, the rms current flowing in the capacitors must not exceed 1.3 times the rated current.
Using the example mentioned above, the fundamental voltage U1, harmonic voltages u5 = 8% (of U1), u7 = 5%, u11 = 3%, u13 = 1%, i.e. total harmonic
distortion THDu equal to 10%, the result is [math]\displaystyle{ \frac{Irms}{I1}=1.19 }[/math] , at the rated voltage. For a voltage equal to 1.1 times the rated voltage, the current limit [math]\displaystyle{ \frac{Irms}{I1}=1.3 }[/math] is reached and it is necessary to resize the capacitors.

Neutral conductors

Consider a system made up of a balanced three-phase source and three identical single-phase loads connected between the phases and the neutral (see Fig. M10).

---

Fig. M10: Flow of currents in the various conductors connected to a three-phase source

---

Figure M11 shows an example of the currents flowing in the three phases and the resulting current in the neutral conductor.
In this example, the current in the neutral conductor has an rms value that is higher than the rms value of the current in a phase by a factor equal to the square root of 3. The neutral conductor must therefore be sized accordingly.

---

Fig. M11: Example of the currents flowing in the various conductors connected to a three-phase load (In = Ir + Is + It)

---