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Assignment Submission Last Date: Exam day of Power System

Analysis For each day delay, 5 marks will be reduced

Problem: The one line diagram of an unloaded power system is shown in the following figure. Reactances of the three sections of the transmission line are shown on the diagram. The generators, motor and the transformers are rated as follows: Generator 1 and: 20 MVA, 20 kV, X=20% Motor: 30 MVA, 13.8 kV, X= 20% Transformers T1, T3: 20 MVA, 140-Y/20-Y kV, X=10% Transformers T2, T4: Composed of three single-phase transformer each rated 80.83/11.55 kV, 10 MVA, X= 10% Transformers T5, T6: 15 MVA, 140-Y/13.8- kV, X=10% Draw the reactance diagram with all reactances marked in per unit. Choose a base of 100 MVA, 280 kV in the 40- line.

Problem: The source voltage v = 141.14sin(314t+) V is applied in the following circuit where R = 0.5 , L = 15 mH. Find the current response after closing the switch S for the following cases: (i) no dc-offset, and (ii) maximum dc-offset. Sketch the current waveform up to 3 cycles corresponding to case (i) and (ii). Problem: A 500 MVA, 20 kV, 60 Hz synchronous generator with Xd=0.20, Xd=0.4, Xd=1.2 pu and time constant Td=0.03, Td= 1.5, TA=0.2 s is connected to the circuit breaker. The generator is operating at 10% above rated voltage and at no-load when a bolted three-phase short-circuit occurs on the load side of the breaker. The breaker interrupts the fault 3 cycles after fault inception. Determine (i) the subtransient fault current in pu and kA rms, (ii) the maximum dc-offset as a function of time; and (iii) rms asymmetrical fault current, which the breaker interrupts, assuming maximum dc-offset. Problem: A synchronous generator and motor are rated 50 MVA, 15 kV, and both have subtransient reactances 20%. The line connecting them has a reactance of 20% on the basis of the machine ratings. The motor is drawing 30 MW at 0.9 power factor leading and a terminal voltage of 12.8 kV when a symmetrical three-phase fault occurs at the motor terminals. Find the

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subtransient current in the generator, motor, and fault by using the internal voltage of the machine. Problem: The one-line diagram as shown in the following figure is of a simple three-bus power system. Line impedances are marked in per-unit on a 100 MVA base. (a) Determine the admittance (Ybus) matrix for the following one-line diagram. (b) Using the Gauss-Seidel method, determine (i) the phase angle and reactive power at generator buses 2 and 3, and (ii) the voltage magnitude and phase angle at the load buses 4 and 5 up to the second iteration. (c) Calculate the real and reactive power of slack bus by using Gauss-Seidal method after second iteration. (d) Derive the Jacobian Matrix for load flow studies by using Newton Raphson method.

Problem: Two generators are connected in parallel to the low-voltage side of three-phase -Y transformer as shown in the following figure. Before the fault occurs, the voltage at pint F is 68 kV. The transformer is unloaded, and there is no circulating current between generators. Find the subtransient current in each generator when the three-phase short-circuit occurs at point F. G1: 50 MVA, 16 kV, Xd= 25% G2: 75 MVA, 16 kV, Xd= 25% T1: 75 MVA, 16/69Y kV, X = 10%

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Problem: A synchronous generator and motor are rated 30 MVA, 12 kV, and both have subtransient reactances 20%. The line connecting them has a reactance of 10% on the basis of the machine ratings. The motor is drawing 20 MW at 0.8 power factor leading and a terminal voltage of 12.8 kV when a symmetrical three-phase fault occurs at the motor terminals. Find the subtransient current in the generator, motor, and fault by the using of Thevenins theorem.. Problem: A 25 MVA 13.8 kV generator with Xd =15% is connected through a transformer to a bus which supplies four identical motors, as shown in Fig. 10.15. The subtransient reactance Xd of each motor is 20% on a base of 5 MVA, 6.9 kV. The three-phase rating of the transformer is 25 MVA, 13.8/6.9 kV with a leakage reactance 10%. The bus voltage at the motors is 6.9 kV when a three-phase fault occurs at point P. For the fault specified, determine (i) the subtransient current in the fault, (ii) the subtransient current in breaker A and (iii) the symmetrical short-circuit interrupting curent (as defined for circuit breaker application) in the fault and in breaker A.

Fig. 10.15 One-line diagram for Example 10.5.

Problems: Two synchronous motors having subtransient reactances of 0.80 and 0.25 per unit, respectively, on a base of 480 V, 2000 kVA are connected to a bus. This motor is connected by a line having a reactance of 0.023 to a bus of a power system. At the power system bus the short-circuit megavoltamperes of the power system are 9.6 MVA for a nominal voltage of 480 V. When the voltage at the motor bus is 440 V, neglect load current and find the initial symmetrical rms current in a three-phase fault at the motor bus.