The Per-Unit System

           The SI units just described enable us to specify the magnitude of any quantity. Thus mass is expressed in kilograms, power in watts, and electric potential in volts. However, we can often get a better idea of the size of something by comparing it to the size of something similar. In effect, we can create our own unit and specify the size of similar quantities compared to this arbitrary unit. This concept gives rise to the per-unit method of expressing the magnitude of a quantity.

               For example, suppose the average weight of adults in Istanbul is 130 Ib. Using this arbitrary weight as a base, we can compare the weight of any individual in terms of this base weight. Thus a person weighing 160 Ib would have a per-unit weight of 160 Ib / 130 Ib = 1.23. Another person weighing 115 Ib / 130 Ib = 0.88.

             The per-unit system of measurement has the advantage of giving the size of a quantity in terms of a particularly convenient unit, called the per-unit base of the system. Thus in the reference to our previous example, if a wrestler has a per-unit weight of 2.0 we know his weight is far above average. Also, his real weight is 2.0 x 130 Ib = 260 Ib.

       Note that whenever per-unit values are given, they are always pure numbers. So, it would be nonsensical to express that the wrestler weighs 2.0 Ib. His weight is 1.7 per-unit, where the selected base unit is 130 Ib.

Per-Unit System with one base

           If we select the size of only one quantity as our measuring stick, the per-unit system is said to have a single base. The  may be a power, a voltage, a current, or a velocity. For example, suppose that three motors have power ratings of 25 hp, 40 hp, and 150 hp. Let us select an arbitrary base power PB of 50 hp. The corresponding per-unit ratings are then 25 hp / 50 hp = 0.5, 40 hp / 50 hp = 0.8 and 150 hp / 50 hp = 3. Thus, in this per-unit world where the base is 50 hp, the three motors have power ratings of 0.5, 0.8 and 3 pu, respectively.

3500 / 1500 = 2.33

With the using of per-unit system we can easly solve so many problems which are complex.

           We could equally well have selected a base power of 15 hp. In this case the respective per-unit rating would be 25 hp / 15 hp = 1.67, 40 hp / 15 hp = 2.67, and 150 hp / 15 hp = 10. 

          It is therefore important to know the magnitude of the base of the per-unit system. If we do not know its value, the actual values of the quantities we are dealing with cannot be calculated.

          For example, in a circuit there are R1= 3500 Ω, R2= 450 Ω, XL= 4800 Ω, and XC= 3000 Ω

R1(pu) = 3500 / 1500 = 2.33

R2(pu) = 450 / 1500 = 0.30

XL(pu) = 4800 / 1500 = 3.2

XC(pu) = 3000 / 1500 = 2 

           With the using of per-unit system we can easly solve so many problems which are complex.