When employing the per-unit system, it is usual to work with a base voltamperes, or base
VA, usually given by the MVA rating of the transformer. Other powers can be expressed in
per cent or per unit of this base power.
The base VA must be the same throughout the network being studied.
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27 EEE8044: Fundamentals
3.2.3 Base Current
The rated current of any power device is of course determined by its rated voltamperes VA
and rated voltage. Similarly, the base current must be defined in terms of the already
defined base values for voltage and power
3 base voltage
base current base
×
Ibase = VA (3.3)
3.2.4 Base Impedance
The base impedance Zbase is given by:
base 3 base voltage
base voltage 3
base current
base voltage 3
line current
line voltage 3
phase current
phase voltage
×
= = = =
VA
Zbase
Hence, in terms of the already defined base VA and voltage,
( )
VA
V
Z base
base base
2
= (3.4)
One of the main reasons for using the per unit method is that transformer impedances are
identical on both sides of the transformer when expressed in terms of their per unit values.
This is the case as long as the voltage bases used in the calculations are related by the turn
ratios of the transformers. If this is not the case, the whole basis for the method breaks
down. We will demonstrate this by examining the p.u. impedance values of a single-phase
transformer on both sides.
Fig. 3.2 shows a single-phase transformer with the total series impedance Z1 referred to the
primary side. The p.u. impedance on the primary side is thus given by (Z1 ⁄ Zbase) or (I1 Z1 ⁄
V1), where I1, V1 are transformer rated (or base) current and voltage on the primary side.
Z1
V1 V2
I1 I2
1 : N
Fig. 3.2 equivalent circuit of single-phase transformer referred to the primary side
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28 EEE8044: Fundamentals
The total impedance refereed to the secondary is given by (V2 ⁄ V1)2 Z1. Thus, the p.u.
impedance on the secondary side is (V2 ⁄ V1)2 Z1 (I2 ⁄ V2) = (I1 Z1 ⁄ V1).
Hence the p.u. impedance of the transformer is the same whether considered from the
primary or the secondary side.
3.2.5 Change of MVA Base
Having calculated the p.u. impedances on one VA base, this can be converted to any other
VA base using the following relationship
old base
new base
(calculated on old base)
(calculated on new base)
p.u.
p.u.
VA
VA
Z
Z
= (3.5)
This follows from (3.1) and (3.4) which shows that the Zp.u. is proportional to the base VA.
3.2.6 Stages of calculation when using per unit values
When performing a calculation using per unit values, the required steps can be summarised
as follows:
i) Select VA base value (voltage base values are the circuit nominal line to line voltages).
This will fix the current and impedance base values.
ii) Convert all known quantities to per-unit values
iii) Make calculations using per-unit values
iv) Convert back to actual values for quantities of interest
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29 EEE8044: Fundamentals
3.3 Fault Level Calculations
3.3.1 General
The design of a power network is influenced to a large extent by the currents that flow in
its various components under fault conditions. Fault current calculations can help us
dete
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