Capacitors, Magnetic Circuits, and Transformers is a free introductory textbook on the physics of capacitors, coils, and transformers. See the editorial for more information.... 
Home The Transformer Per Unit Quantities  
Search the VIAS Library  Index  
Per Unit Quantities
The performance of a line of machines can be readily compared, and the analyses of complex power systems involving transformers of different ratios can be facilitated, by means of per unit quantities. Per unit quantities are decimal fractions that relate current, voltage, impedance, admittance, and power to certain base values of these respective quantities, i.e.
The values of the base quantities are dictated by convenience. In dealing with a specific piece of apparatus by itself, as in the case of a transformer, the rating of the transformer is generally taken as the base. In the transformer of Example 62, the following are the base quantities on the lowvoltage side
Similarly, the base quantities on the highvoltage side are 150000 v, 2400 v, 62.5 amp, 38.4 ohms, and 0.02604 mho. The leakage impedance of this transformer was found in Example 64 to be 1.008 ohm referred to the highvoltage side, and the per unit impedance from Eq. 699 is
On the other hand, when the analysis is applied to a number of equipments in combination, a larger kva base is used. The leakage impedance of the transformer referred to the low side is that referred to the high side divided by the impedance ratio, and, in this case, is 1.008 / (10)^{2} = 0.01008 ohm. The per unit impedance of the transformer referred to the low side is, therefore, 0.01008 ohm divided by the transformer leakage impedance referred to the low side, i.e., 0.384 ohm, which results in the same value as before, namely, 0.0263 per unit. This brings out an important advantage of the per unit system with regard to transformers, in that the per unit impedance has the same value whether referred to the high side or to the low side, regardless of the turns ratio of the transformer. In the analysis of power systems encompassing several pieces of equipment of similar or of different ratings, it is generally more convenient to use a relatively large kva base, which may be several times the rating of any one of the generators or transformers in the system. The per unit values of generators and transformers are generally known in terms of their own rating and can be conveniently converted to any other base on the principle that the per unit value of an impedance, for a given base voltage, is proportional to the voltampere base. Thus, if an impedance has a per unit value of Z_{pu1} for a base of VA_{1} va, then its per unit value for a base of VA_{2} va for the same voltage base, is expressed by
Thus, the per unit impedance of the transformer in Example 62 for a base of 10000 kva would be


Home The Transformer Per Unit Quantities 