Which is the method for sizing a generator working with distortion loads?

Simplified method for the sizing of electrical machines working with distortion loads.

In order to avoid problems with the overheating of alternators with distortion loads, precise calculations should be made with regard to the sizing. By distortion load, we mean any type of load producing current harmonics. Generally, such loads are: diode rectifiers, thyristor converters, inverters, uninterruptible power systems (UPS), etc.

If there are not accurate specifications about the distortion load that the alternator has to feed, Mecc Alte bases the sizing of the electrical machine purely from a thermal point of view that leads to a machine over-sizing. Considering the different types of distortion, it is generally assumed that 20% over-rating should be applied to the machine.

Over-sizing is necessary to obviate the temperature increase of the windings, due to the current harmonics introduced by the distortion load.

If it is necessary to meet a specification on the overall voltage distortion, it is necessary to know the individual value of the current harmonics amplitude introduced by the load.

The total harmonic distortion (THD) is defined as follows:

(1) THD% = 100 • SQRT(Σ Un²/U²)

Where Un is the RMS amplitude of the n-th voltage harmonics and U is the RMS amplitude of the first voltage harmonic. In a three phase generator, if the neutral is not distributed, multiples of 3^rd harmonic must not be considered. Thus, the previous equation becomes:

(2) THD% = 100 • SQRT ((U5²+U7²+U11²+ … Un²)/U²)

In a synchronous machine the voltage droop produced by the current harmonics is determined by the direct - axis sub-transient reactance (X"d):

(3) Un = X”d • n • In

Where In is the component of the n-th current harmonic. Unsaturated sub-transient reactances should be taken into account.

If all the quantities are expressed in percentage of the rated values, the equation 2 becomes:

(4) THD% = SQRT ((U5%)²+(U7%)²+(U11%)²+ … +(Un%)²)

and the equation 3:

(5) Un% = (X”d%/100) • n • In%

If it is known the relative amplitudes of the current harmonics, the components of the voltage harmonics can be easily calculated. These amplitudes in a converter are a function of the commuting configuration. If the THD is specified, it is possible to calculate the required X"d from a given content of current harmonics.

Combining together equation 4 and from the equation 5 it comes:

(6)THD%=SQRT (((X”d%/100) • 5 • I5%)²+(((X”d%/100) • 7 • I7%)+ … +(((X”d%/100) • n • In%)²)

(7) THD% = (X”d/100) • SQRT ((5 • I5%)²+(7 • I7%)²+ … +(n • In%)²)

and finally:

(8) X”d% = (100 • THD%)/ SQRT ((5 • I5%)²+(7 • I7%)²+……………+(n • In%)²)

By means of the formula n. 8, it is possible to calculate the correct value of X"d (direct - axis sub-transient reactance) that is needed to suit the THD voltage distortion specification. As it has been proved, it is necessary to know current harmonic content of the load.

As an example, let's consider a distorted load of 70 kVA at 400 V, 50 Hz.

If there is not any other specification given, it is advisable to select an alternator of the size ≥84 kVA (+ 20%) at 400 V, 50 Hz (=> ECP34-1S/4). This is necessary to obviate the temperature increase of the windings, due to the current harmonics introduced by the distortion load.

Let's suppose that the same load has to meet a maximum voltage distortion specification. The specs for such a load are:
- Maximum voltage THD of 10%.
- 6 pulse distortion load characterized by the following individual current harmonics:

Applying the equation n. 8, it is possible to get:

(9) X”d%=(100 • 10)/ SQRT ((5 • 20)²+(7 • 14)²+(11 • 9)²+(13 • 8)²+ … +(23 • 4)²+
+(25 • 4)²)

X”d% = 3,58%

Then it is calculated an X"d equal to 3.58%, that results to be met by the model ECP34-2L/4. The X"d of this alternator is equal to 6.8% at 150 kVA, 400 V, 50 Hz and, then, it will be equal to 3.2% (< 3.58%) at 70 kVA, 400 V, 50 Hz. The reactance expressed in percentage (%) changes proportionally in respect to the power.

The use of a damped caged rotor is strongly suggested when power supplying a distorted load. The damping cage on the rotor is a standard supply for all the machines of series 32, 34, 38, 40, 43 and 46.