Bus 28 Case

4.5.2 Case 6

A three-phase fault at bus 28 is applied for a 0.1 second. Same as the AC system, generator 9, the closest generator to the fault, tries to retain stability for few seconds after the fault as indicated in the rotor angles Figure 4.25. Then, the oscillations increase and as a result, the system stability deteriorates and generator 9 is separated from the system. The rotor angle oscillations have a frequency around 1 Hz, i.e., local oscillations of generator 9. The proposed first-swing stability algorithm shows that the system is first-swing stable as it does not exceed its CCT, 0.1143 second, as shown in Figure 4.26. The transformer 9-29 energy passed its critical value at 4.178 second, which is higher than the AC system time

Figure 4.26 Total, potential and critical transformer energies for 0.1 second fault at bus 28. Figure 4.27 Transformer 9-29 energy and critical energy.

In contrast with the AC system, generators 14 and 13 go unstable after the separation of generator 9 and then they are followed by generator 16. This response confirms case 5 conclusion that the existence of the nearby HVDC line 50-51 has a great impact on the stability of the three equivalent generators 14, 15 and 16. The second and third separation areas of lines 40-41 and 18-42 and lines18-49 and 18-50 are confirmed at 5.986 and 7.003 seconds as shown in Figure 4.28 and Figure 4.29, respectively.

Figure 4.28 Second separation area energy and critical energy, lines 40-41 and 18-42 energy and critical energy. Figure 4.29 Third separation area energy and critical energy, lines 18-50 and 18-49 energy and critical energy.

4.5.3 Case

The nearest generator, generator 14, lose synchronism due to first-swing instability as indicated in Figure 4. 30. Instead of following by generator 16, generator 15 is separated first. The post-fault rotor angle of generator 14 slowly increases compared to the AC system in Figure 4.14. The system energy and critical energy of the area consists of the two lines, 41-40 and 41-42, are shown in Figure 4.31. The CCT of the system is almost less equal to 0.44 second, i.e., 0.4391 second, hence, this case is barely a first-swing stability. The system passed the UEP at 0.8525 second as indicated in Figure 4.32. The second and third separation areas of lines 18-42 and 18-50 and 18-49 are confirmed at 2.442 and 3.2765 second as shown in Figure 4.33 and Figure 4.34,