University of Anbar Power System III
Dr. Omar K. Alazzawi
College of Engineering
4th
Dept. of Electrical Engineering
EX1. For the power system whose one-line diagram is shown in Fig. sketch the zero
sequence network
Solution The zero sequence network is drawn in Fig.
Ex2. A 25 MVA, 1l kV, three-phase generator has a sub transient reactance of 20%. The
generator supply two motors over transmission line with transformers at both ends as shown
in the one-line diagram of Fig. The motors have rated inputs of 15 and 7.5 MVA, both 10 kV
with 25% sub transient reactance. The three-phase transformers are both rated 30 MVA,
10.8/121 kV, connection ∆-Y with leakage reactance of 10% of each. The series reactance of
the line is 100 ohms. Draw the positive and negative sequence networks of the system with
reactance marked in per unit.
Assume that the negative sequence reactance of each machine is equal to its sub transient
reactance. Omit resistances. Select generator rating as base in the generator circuit.
Sol.:
121
Transmission line voltage base= 11𝑥 = 11𝑘𝑣
10.8
10.8
Motor voltage base= 123.2𝑥 = 11𝑘𝑣
121
The reactances of transformers line and motors are converted to pu values
on appropriate bases a s follows
25 10.8 2
Transformer reactance= 0.1𝑥 𝑥( ) = 0.0805𝑝𝑢
30 11
100𝑥25
Line reactance =(123.2)2
25 10 2
Reactance of motor 1=0.25𝑥 𝑥 ( ) = 0.345𝑝𝑢
15 11
25 10 2
Reactance of motor 2=0.25𝑥 𝑥 ( ) = 0.69𝑝𝑢
7.5 11
Positive sequence network is
University of Anbar Power System III
Dr. Omar K. Alazzawi
College of Engineering
4th
Dept. of Electrical Engineering
Negative sequence network is
Ex3. Draw the zero-sequence network for the system described in Example2
Assume zero sequence reactance for the generator and motors of 0.06 per unit. Current limiting
reactors of 2.5 ohms each are connected in the neutral of the generator and motor No. 2. The
zero-sequence reactance of the transmission line is 300 ohms.
Sol.:
Solution The zero sequence reactance of the transformer is equal to its
positive sequence reactance. Hence
Transformer zero sequence reactance: 0.0805 pu
Generator zero sequence reactance : 0.06 pu
25 10 2
Zero sequence reactance of motor 1=0.06𝑥 𝑥 ( ) = 0.082𝑝𝑢
15 11
25 10 2
Zero sequence reactance of motor 2=0.06𝑥 𝑥 ( ) = 0.164𝑝𝑢
7.5 11
2.5𝑥25
Reactance of current limiting reactors= = 0.516
112
Reactance of current limiting reactor included in zero sequence network'
= 3 x 0.516= 1.548pu
300𝑥25
Zero sequence reactance of transmission line = = 0.494𝑝𝑢
123.22
The zero sequence network is shown in Fig.
University of Anbar Power System III
Dr. Omar K. Alazzawi
College of Engineering
4th
Dept. of Electrical Engineering
Q1/ Draw the positive, negative and zero sequence impedance networks for
the power system of Fig. Choose a base of 50 MVA, 220 kV in the 50Ω transmission lines,
and mark all reactance in pu. The ratings of the generators and transformers are:
G1: 25 MVA, 11 kV, X" = 20%
G2: 25 MVA, 11 kV, X" = 20%
Three-phase transformer (each): 20 MVA, 11Y /220Y kV, X = I5%
The negative sequence reactance of each synchronous machine is equal to its sub transient
reactance. The zero-sequence reactance of each machine is 8%. Assume that the zero-
sequence reactance of lines are 250% of their positive sequence reactance.
Q2/ For the power system of Fig. draw the positive, negative and zero
sequence networks. The generators and transformers are rated as follows:
Generator1 : 25 MVA, 11 kV, X" =0.2, X2 = 0.15, Xo = 0.03 pu
Generator2 : 15 MVA, 11 kV, X" =0.2, X2= 0.15, Xo = 0.05 pu
Synchronous Motor 3: 25 MVA, 11 kV, X" = 0.2, X2= 002, Xo = 0.1 pu
Transformer l: 25 MVA, 11∆/120 Y kV, X = 10%
Transformer 2: 12.5 MVA, 11∆/120 Y kV, X = 10%
Transformer 3: 10 MVA, I20Y/11 Y kV, X =10%
Choose a base of 50 MVA, 11 kV in the circuit of generator l.
University of Anbar Power System III
Dr. Omar K. Alazzawi
College of Engineering
4th
Dept. of Electrical Engineering
