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TRANSIENT STABILITY ANALYSIS OF A MULTI MACHINE POWER SYSTEM.
Transient stability analysis has become a major issue in the operation of power systemsdue to the increasing stress on power system networks. This problem requires evaluation of a powersystem's ability to withstand disturbances while maintaining the quality of service.
Multimachine equations can be written similar to the one-machine system connected to the infinite bus.
The first step is to solve the initial load flow and todetermine the initial bus voltage magnitudesand phase angles. The machine currents priorto disturbance are calculated from:
To include voltages behind transientreactances, m buses are added to the n buspower system network. The equivalentnetwork with all load converted to admittances is shown in Fig.1
Fig.1 Power system representation for transient stability analysis
Nodes n+1, n+2, . . ., n+m are the internal machine buses, i.e., the buses behind the transient reactances. The node voltage equation with node 0 as reference for this network, is shown in (4).
Ibus- vector of the injected bus currents
Vbus- vector of bus voltages measured from the reference node.
The diagonal elements of the bus admittancematrix are the sum of admittances connected to it.
The electrical power output of each machinecan now be expressed in terms of the machine’s internal voltages:
The classical transient stability study is basedon the application of a three-phase fault. Asolid three-phase fault at bus k in the network results in Vk = 0. This is simulated by removing the kth row and column from the prefault bus admittance matrix.
Yij-elements of the faulted reduced bus admittance matrix
Hi - inertia constant of machine iexpressed on the common MVA base SB.
If HGi is the inertia constant of machine iexpressed on the machine rated MVA SGi, then Hiis given by:
Fig.2 Flow chart of transient stability analysisfor a multimachine power system
Next,the postfault reduced busadmittance matrix is evaluated and thepostfault electrical power of the ith generator shown by Ppfiis readilydetermined from (14).Using the postfault power Ppfi, the simulation is continued to determine the system stability,until the plots reveal a definite trend as tostability or instability.
(tCCT=0.07s , tc =0.06), the system is
Fig.4Three-phase fault on line 2-18
(tCCT=0.07s tc=0.71), the system is unstable
(tCCT=0.08s, tc=0.7), the system is stable
Fig.6 Three-phase fault on line 3-14
(tCCT=0.08s, tc=0.9), the system is unstable
(tCCT=0.33s, tc=0.3), the system is stable
Fig.8 Three-phase fault on line 12-24(tCCT=0.33s, tc=0.39), the system is unstable
Fig.9 Three-phase fault on line 16-56(tCCT=0.14s, tc=0.1 s), the system is stable
Fig.10 Three-phase fault on line 16-56(tCCT=0.14s, tc=0.18), the system is unstable
Fig.11Three-phase fault on line 19-78(tCCT=0.17s, tc=0.15 ), the system is stable
Fig.12 Three-phase fault on line 19-78
(tCCT=0.17s. tc=0.18), the system is unstable