Problem 1
Consider the classical power system discussed in the lectures where one generator is connected to the infinite bus through two transmission lines. We want to study the transient stability for a fault on one of the two lines. The generator parameters are as follows: Pm = 1. H = 6. KD = 5. x'd = 0.25, E' = 1.5 The transmission line where the fault occurs has a line reactance of 0.7 pm The other transmission line that remains in service has a line reactance of 0.8 pu.
a) Suppose the fault occurs at the middle of the line. Mite out the swing equations for the pre-fault, fault-on and post-fault systems.
b) Suppose the clearing time is stated as 4 cycles. Use the Euler algorithm with a step size of one millisecond to compute the trajectory during the fault-on period and compute the clearing state. Carry out the Euler algorithm for 20 seconds into the post-fault period assuming an integration step size of one millisecond. Is the system transient stable or not'?
c) Repeat Part b) after changing the fault clearing time to be 5 cycles. Is the system transient stable? Repeat the study by increasing the clearing time in steps of one cycle. The largest value of the clearing time when the system is still transient stable is known as the critical clearing time. Keep repeating the simulation while increasing the clearing time by one cycle at a time till the system becomes transient unstable. What is the critical clearing time?
d) Apply the equal area criterion to check for the transient stability of the system for part (a) the instantaneous clearing case.
Problem 2: bus Power System Simulation
Fig. Six bus power system
In this simulation project, you will use the Power World simulator to solve the power flow. For each case, provide a powerworld 5-bus power system state, tabulate your results and comment as needed Take the base voltage to be 230 kV.
Problem 2: 6 bus Power System Simulation
Table 1: Day time bus data:
|
Bus
|
Generation
|
Loads
|
|
Name
|
Type
|
V(pu)
|
P(MW)
|
Q(MVAR)
|
P(MW)
|
Q(MVAR)
|
|
1
|
SL
|
1.0∠0°
|
|
|
|
|
|
2
|
PV
|
1.0∠0°
|
100
|
|
60
|
35
|
|
3
|
PQ
|
1.0∠0°
|
|
|
40
|
25
|
|
4
|
PQ
|
1.0∠0°
|
|
|
60
|
40
|
|
5
|
PQ
|
1.0∠O°
|
|
|
30
|
10
|
|
6
|
PQ
|
1.0∠0°
|
|
|
40
|
25
|
Table 2: Night time bus data:
|
Bus
|
Generation
|
Loads
|
|
Name
|
Type
|
V(pu)
|
P(MW)
|
Q(MVAR)
|
P(MW)
|
Q(MVAR)
|
|
1
|
SL
|
1.0∠0°
|
|
|
|
|
|
2
|
PV
|
1.0∠0°
|
100
|
|
40
|
25
|
|
3
|
PQ
|
1.0∠0°
|
|
|
30
|
20
|
|
4
|
PQ
|
1.0∠0°
|
|
|
50
|
35
|
|
5
|
PQ
|
1.0∠0°
|
|
|
15
|
5
|
|
6
|
PQ
|
1.0∠0°
|
|
|
30
|
15
|
Table 3: Line data (All Shunt admittance capacitance are ne li ible
|
Transmission Line
Number
|
From/to
(bus to bus)
|
Series impedance
Z(pu)
|
Rated MVA
|
|
1
|
1-2
|
0.010+j0.080
|
200
|
|
2
|
2-3
|
0.010+j0.080
|
200
|
|
3
|
3-4
|
0.008+0.064
|
200
|
|
4
|
4-5
|
0.020+j0.150
|
100
|
|
5
|
5-6
|
0.008+0.064
|
200
|
|
6
|
6-1
|
0.010+j0.080
|
200
|
The base apparent power of the power system is 100 MVA and the tolerance on each bus voltage is 5%. Answer the following questions about the power system in figure 2 on page 4.
1. Answer the following questions about the above power system:
a. Find the voltages at each bus of the power system under day time conditions
b. Find the voltages at each bus of the power system under night time conditions
c. Find the real and reactive power flows in each transmission line in each case
d. Are any of the bus voltages out of tolerance in the power system ?
e. Are any of the transmission lines overloaded ?
2. If there are any problems with the bus voltages under typical day time loads, propose a solution for this problem. Define a set of capacitors at various buses in the system to compensate for out-of-tolerance voltage variations.
3. What happens to the bus voltages under night time conditions if the capacitors proposed in part (2) are left attached to system at night? Is it OK to permanently connect the capacitors to the power system or must they be switched off?
4. Suppose the power system is operating under typical daytime loads, and the transmission line between bus 4 and bus 5 open circuits.
a. What happens to the voltages on each bus now
b. Are any of the transmission lines overloaded?
5. Suppose a new transmission line is to be added to the power system bus 1 and bus 4. The line is rated at 200 MVA and its series impedance is 0.008+ j 0.064 pu. Assume no capacitors have been added to the system and determine the daytime and nighttime voltages at every bus. Did the new transmission line resolve the voltage problems?