Power System Analysis (solution) CT-1
Section-A
1. Per Unit value of a given quantity is the ratio of the actual value in any given unit to the
base value in the same unit. the main advantage in using the pu system of computations
is that the result that comes out of the sum, product, quotient, etc. of two or more pu
values is expressed in per unit itself.
In an electrical power system, the parameters of interest include the current, voltage, complex
power (VA), impedance and the phase angle. Of these, the phase angle is dimensionless and
the other four quantities can be described by knowing any two of them. Thus clearly, an
arbitrary choice of any two base values will evidently fix the other base values.
Normally the nominal voltage of lines and equipment is known along with the complex
power rating in MVA. Hence, in practice, the base values are chosen for complex power
(MVA) and line voltage (KV). The chosen base MVA is the same for all the parts of the
system. However, the base voltage is chosen with reference to a particular section of the
system and the other base voltages (with reference to the other sections of the systems, these
sections caused by the presence of the transformers) are then related to the chosen one by the
turns-ratio of the connecting transformer.
If Ib is the base current in kilo amperes and Vb, the base voltage in kilovolts, then the base
MVA is, Sb = (VbIb). Then the base values of current & impedance are given by
Base current (kA), Ib= MVAb/KVb = Sb/Vb
Base impedance, Zb = (Vb/Ib)=(kVb
Hence the per unit impedance is given by
Zpu = Zohms/Zb = Zohms (MVAb/KVb)
In 3-phase systems, KVb is the line-to-line value & MVAb is the 3-phase MVA.
[1-phase MVA = (1/3) 3-phase MVA].




Merits:
The pu value is the same for both 1-phase and & 3-phase systems
The pu value once expressed on a proper base, will be the same when refereed to either side
of the transformer. Thus the presence of transformer is totally eliminated
The variation of values is in a smaller range (0.9 nearby unity). Hence the errors involved
in pu computations are very less.
Usually the nameplate ratings will be marked in pu on the base of the name plate ratings,
etc.
Demerits:
If proper bases are not chosen, then the resulting pu values may be highly absurd (such as 5.8
pu, -18.9 pu, etc.). This may cause confusion to the user. However, this problem can be
avoided by selecting the base MVA near the high-rated equipment and a convenient base KV
in any section of the system.
2. Positive, negative and zero phase sequence components are called symmetrical
components of the original unbalanced system. The subscript 1, 2 & 0 are used to show
positive, negative and zero sequence components respectively.
Let us express the symmetrical components of R-Phase in terms of phase currents



I R, I Y & I B
From fig:












I R  I R1  I R 2  I R 0        (i )





I Y  I Y 1  I Y 2  I Y 0  a 2 I R1  a I R 2  I R 0      (ii )

I B  I B1  I B 2  I B 0  a I R1  a 2 I R 2  I R 0        (iii )
Zero sequence current: (i) + (ii) + (iii)






I R  I Y  I B  I R1 (1  a 2  a)  I R 2 (1  a  a 2 )  3 I R 0        (iv )
Since,
(1  a  a 2 )  0
Therefore,

1   
I R0  ( I R  I Y  I B )
3
Positive Sequence Current: multiply equation (ii) by a & equation (iii) by a2 & then (i) +
(ii) + (iii)



1 
I R1  ( I R  a I Y  a 2 I B )
3
Negative sequence of current: multiply equation (ii) by a2 & equation (iii) by a then adding
to (i)



1 
I R2  ( I R  a 2 I Y  a I B )
3
Thus, Symmetrical components can be expressed as
 I ao 
1 1 1   I a 
 I   1 1 a a 2   I 
 a1  3 
 b 
2
 I a 2 
1 a
a   I c 
3. Current limiting reactors are large coils wound for high self-inductance and very low
resistance.
Application:
 In order to limit the short circuit current to a value which the circuit breaker can
handle
 For the purpose of protecting power plant or power system network
4. Once the fault occurs, the protective devices get activated. A certain amount of time
elapses before the protective relays determine that there is over-current in the circuit and
initiate trip command. This time is called the detection time. The contacts of the circuit
breakers are held together by spring mechanism and, with the trip command, the spring
mechanism releases the contacts. When two current carrying contacts part, a voltage
instantly appears at the contacts and a large voltage gradient appears in the medium
between the two contacts. This voltage gradient ionizes the medium thereby maintaining
the flow of current. This current generates extreme heat and light that is called electric
arc. Different mechanisms are used for elongating the arc such that it can be cooled and
extinguished. Therefore the circuit breaker has to withstand fault current from the instant
of initiation of the fault to the time the arc is extinguished.
Two factors are of utmost importance for the selection of circuit breakers. These are:
 The maximum instantaneous current that a breaker must withstand and
 The total current when the breaker contacts part.
5. The zero-sequence components are the same both in magnitude and in phase. Thus, it is
equivalent to a single-phase system and hence, zero sequence currents will flow only if a
return path exists. The reference point for this network is the ground (Since zerosequence currents are flowing, the ground is not necessarily at the same point at all points
and the reference bus of zero-sequence network does not represent a ground of uniform
potential.
Section-B
6. Positive- and Negative-Sequence Networks: The positive-sequence network is obtained
by determining all the positive-sequence voltages and positive-sequence impedances of
individual elements, and connecting them according to the SLD. All the generated emfs
are positive-sequence voltages. Hence all the per unit reactance/impedance diagrams
obtained in the earlier chapters are positive-sequence networks. The negative-sequence
generated emfs are not present. Hence, the negative-sequence network for a power
system is obtained by omitting all the generated emfs (short circuiting emf sources) and
replacing all impedances by negative-sequence impedances from the positive-sequence
networks. Since all the neutral points of a symmetrical three-phase system are at the same
potential when balanced currents are flowing, the neutral of a symmetrical three-phase
system is the logical reference point. It is therefore taken as the reference bus for the
positive- and negative-sequence networks. Impedances connected between the neutral of
the machine and ground is not a part of either the positive- or negative- sequence
networks because neither positive- nor negative-sequence currents can flow in such
impedances.
Zero-Sequence Networks: The zero-sequence components are the same both in
magnitude and in phase. Thus, it is equivalent to a single-phase system and hence, zero
sequence currents will flow only if a return path exists. The reference point for this
network is the ground (Since zero-sequence currents are flowing, the ground is not
necessarily at the same point at all points and the reference bus of zero-sequence network
does not represent a ground of uniform potential.
7. Symmetrical components can be expressed as
 I ao 
1 1 1   I a 
1
 I   1 a a 2   I 
 a1  3 
 b 
 I a 2 
1 a 2 a   I c 
Therefore,
1   72.133.7 0 


a 2   82.46166 0 
a  63.24  71.56 0 
a  1120 0
 I ao 
1 1
 I   1 1 a
 a1  3 
 I a 2 
1 a 2
 I ao   6.87  j 9.06 
 I   53.07  j 48.88
 a1  

 I a 2  

0
Section-C
8. Choosing 200MVA as base MVA
% reactance of generator G1
5 * 200
G1 
 5%
200
% reactance of generator G2
8 * 200
G2 
 32%
50
% reactance of generator G3
6 * 200
G3 
 4%
300
% reactance of generator G4
8 * 200
G4 
 32%
50
% reactance of transmission line A
5 * 200
A
 25%
40
% reactance of transmission line B
5 * 200
B
 50%
20
% reactance of transmission line C
5 * 200
C
 25%
40
% reactance of transmission line D
5 * 200
D
 20%
50
Fault MVA= Base MVA*
200 *100
100
 361MVA
=
55.31
%reac tan ce