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EE304
SYNCHRONOUS GENERATOR TRANSIENT ANALYSIS
Instructed By: Mr. B.S. Madushanka
Name
: G.R. Raban
Index Number
: 070384P
Field
: EE
Group
:8
Date of Performance
: 15/10/2009
Date of Submission
: 13/11/2009
Observations
Variation of the current waveform
Variation of field current with time
Variation of phase voltage with time
The following readings were also obtained during the practical Pre short circuit line voltage
=
90 V
Steady short circuit current
=
0.4 A
Generator speed
=
1500 rpm
Number of generator pole pairs
=
2
Steady state field current
=
0.2 A
Calculations (i)
Step 1 Using the phase current oscillogram, the following values were obtained and the graph of Ipk-pk versus time (graph-1) was drawn. T (ms) 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 175 185
By the graph of I pk-pk verses time, the following values were obtained; (Since I have not used the t he peak-to-peak half value, I have divided the values by 2)
A
=
B
=
79.2 2 17 2
A
A
Pre S/C line to neutral voltage,
∴
Xd
”
X
d
=
=
2V 2V s B
2V 2V s A
=
39.6 A
=
8.5 A
Vs =
90
V 3
Ω Ω 2×
=
8.5
2×
=
90 3
90 3
39.6
=
8.64
Ω
=
1.86
Ω
Step 2 By using using the ∆X components of graph-1, the following values were obtained and graph-2 was drawn; ∆X (A) 62.2 45.0 33.0 25.0 20.2 16.6 13.8 11.4 9.4 7.4 6.6 5.8 4.6 4.2 3.4 2.6 1.8 1.4 1.0 0.6 0
Step 3 By using using the ∆Y components of graph-2, the following values were obtained and graph-3 was drawn; T (ms) 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72
Step 4 By using the values of graph-1, the following values were obtained and the envelope mean was plotted against time to obtain the armature time constant; T (s) 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 175 185
Using short circuit field current expression, arriving at short circuit field current wave form
If = If 0 + If 0
(X d
−′ ′ − ′ − − ′′ − ′′ − Xd )
Xd
e
t/T d
1
Since it is assumed zero damping,
If = If 0 + If 0
(X d
Tkd Td
and
e
t/T d
′′
Tkd Ta
−
e
t/T a
ω
cos ( t)
is zero.
−′ ′ − ′ − − ′′ Xd )
t/T d
e
Xd
e
t/T d
− − − − − − −
If = 0.4 + 0.4 ×
8.64
If = 0.4 + 2.92 e
1.04
1.04
t/28
e
× e
t 28
e
t 21
t/21
The above function is plotted below; 0.8
0.7
0.6
0.5 ) A ( 0.4 a I
0.3
0.2
0.1
0 0
50
100
150
Time (ms)
200
250
300
(iii)
Open circuit line voltage
Va = 2V 2Vs cos ωt + θ0
Assuming
Va
0
− − − 2V 2Vs
X d′
Xd
X d′′
e
′ t/T d0
cos ωt + θ0
2V 2Vs
X d′
X d′′
e
Xd
t/T d′ 0
cos ωt + θ0
is zero,
− e− = 2V 2V cosωt − 2V 2V s
s
Va = (73. (73.48 48
− − −
−
293.29e
X d X d′
−
X d′′
t/232.62
t/T d′ 0
− e− cosωt − 2V 2V s
X d′ X d′′ Xd
t/T d′ 0
cos ωt
)cos (314.16t)
The above function is plotted below; 250
200
150
100
50 ) V ( a
0
V
0
100
200
300
400
500
-50
-100
-150
-200
-250
Time (ms)
600
700
800
900
Discussion Comparison of the theoretical and observed oscillogram of short circuit field current and
open circuit line voltage The practically observed oscillogram and the theoretically calculated waveform are relatively similar in shape. But the actual time they take to arrive at steady state are different. This is because we have assumed that there is zero damping when calculating the expression for the short circuit field current, whereas in the practical case, a small amount of damping may exist. We have used practically calculated X and T values to establish the theoretical expressions. This may introduce some errors to the expression. The theoretical graphs are smooth. But the practically obtained oscillogram may have been affected by noise introduced by external devices. Therefore, we can observe a slight difference in practical and theoretical observations.
Features of short circuit oscillogram of phase and field currents
In short circuit oscillogram we can identify four components in the field currents. They are, a. Transient b. Sub transient c. DC offset d. Steady state component Generally sub transient fades away by completion of several cycles although transient is quite unlikely to disappear rapidly and may last for quite a number of cycles.
The importance of short circuit study Generator parameters such as synchronous reactance, transient reactance, sub transient reactance and other relevant parameters can be determined through a short circuit study. These parameters are necessary when designing protection schemes in synchronous generators. Therefore, the short circuit study of a synchronous generator is essential.
