This chapter discusses per unit representation, which expresses values like current, voltage, impedance, and power as a ratio of an actual value to a reference or base value. This makes the quantities unitless and independent of physical size or ratings. The document provides examples of converting actual values to per unit values and explains the advantages, which include representing apparatus values consistently over a wide range, simplifying computations, and specifying machine impedances in per unit values according to manufacturers.

2. 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.

3. 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.

4.  Z= V/I
 Zbase= (Vbase/Ibase)
 Zb= (Vb/Ib)
 Zb= (V2
b/Sb)
 Zpu= (Vpu/Ipu)
 Spu= VpuI*
pu

5. 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

6.  Xpu= (Xactual/Zbase)
 Zb1= (V2
b1/Sb)=4002/5000=32 ohm
 Xpu= (Xactual/Zbase)= 12.5/32 = 0.390625 pu
 X1pu = X1/Zb1
 X2pu = X2/Zb2

7. Advantages of per unit representation
1. 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.

8. 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