Chapter 8 Per Unit Representation Sometimes it is more convenient to represent the value

of current, voltage, impedance, power in per unit(pu) value rather than in Amps, Volts, Ohms, kW.

It is unit less.

Ratio of same dimension

Per unit value is the ratio of an actual value to a reference value(Base value)

Apu= (Aactual/Abase)

Some times per unit quantities id mentioned as per cent quantity by multiplying a factor of 100.

pu=actual/base

Apu= (Aactual/Abase)

Ipu= (Iactual/Ibase)

Vpu= (Vactual/Vbase)

Spu= (Sactual/Sbase)

Zpu= (Zactual/Zbase)

Rpu= (Ractual/Zbase)

Xpu= (Xactual/Zbase)

If any two of the I, V, Z, S is known, remaining two can be fix automatically.

Z= V/I

Zbase= (Vbase/Ibase)

Zb= (Vb/Ib)

Zb= (V2b/Sb)

Zpu= (Vpu/Ipu)

Spu= VpuI*pu

Example 8.1 A 5 KVA 400/200 V, 50Hz, single phase transformer

has the primary and secondary leakage reactance each of 2.5 ohm. Determine the total reactance in per unit.

Sb= 5000 VA

Primary Base Voltage Vb1 = 400 V

Secondary Base Voltage Vb2 = 200 V

X1e=X1+a2X2

a=N1/N2=400/200=2

X1e=X1+a2X2=2.5 + 2.5 * 22 =12.5 ohm

Xpu= (Xactual/Zbase)

Zb1= (V2b1/Sb)=4002/5000=32 ohm

Xpu= (Xactual/Zbase)= 12.5/32 = 0.390625 pu

X1pu = X1/Zb1

X2pu = X2/Zb2

Advantages of per unit representation1. ordinary parameters vary considerably with

variation of physical size, terminal voltage and power rating etc. while per unit parameters are independent of these quantities over a wide range of the same type of apparatus. In other words, the per unit impedance values for the apparatus of like ratings lie within a narrow range.

2. It provide more meaningful information.

3. The chance of confusion between line and phase values in a three-phase balanced system is reduced. A per unit phase quantity has the same numerical value as the corresponding per unit line quantity regardless of the three-phase connection whether star or delta.

4. Impedances of machines are specified by the manufacturer in terms of per unit values.

5. The per unit impedance referred to either side of a single-phase transformer is the same.

6. The per unit impedance referred to either side of a three -phase transformer is the same regardless of the connection whether they are ∆-∆, Y-Y or ∆-Y.

7. The computation effort in power system is very much reduced with thee use of per unit quantities.

8. Usually, the per unit quantities being of the order of unity or less can easily be handled with a digital computer. Manual calculation are also simplified. Per unit quantities simply theoretical deduction and give them more generalizes forms.

Advantages of per unit representation