Problem

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: P_m = 1. H = 6. K_D = 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.