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# Power system Stability, Equal area criteria

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Questions for practice

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• 1. Unit V Practice QuestionsQ1. Find the steady state power limit of a system consisting of a generator with a synchronousreactance of 0.4 pu connected to an infinite bus through a series reactance of 1.0 pu. The terminalvoltage is held at 1.0 pu and the infinite bus voltage is 1.0pu [0.957]Q2. A 30 MVA, 15KV, 4 pole, 50 Hz turbo-generator has an inertia constant of 10KW-sec/KVA. If theinput power and the output power are 25MW and 20MW respectively, find the acceleration inrpm/sec [12.5]Q3. A 50Hz synchronous generator having H constant as 5MJ/MVA is supplying 1.2pu power to aninfinite bus. The emf of the generator is 1.6pu in magnitude and the voltage at the infinite bus is1.0+j0 pu. The reactance through which the power is getting transmitted is 0.8pu. Calculate thefollowing:(i) The shaft power(neglecting the rotational losses)[1.2](ii) The rotor angle for stable and unstable operation [36.86, 143.13](iii) The frequency with which the generator oscillates during a disturbance[1.128Hz]Q4. A generator is supplying 1.5pu power to an infinite bus. There is a 3 phase fault occurring at a pointwhich reduces the steady state power limit. The fault is cleared by a circuit breaker and the powertransmission is resumed but the maximum limit is different from the pre-fault conditions. The powerangle equation pertaining to the three conditions are :Pre – fault: 2.1 sinδ; During– fault: 0.8 sinδ ; Post – fault: 1.8 sinδFind the critical clearing angle [57.6]Q5. A 60 Hz generator is supplying 60% of maximum power to an infinite bus through a reactive network.A fault occurs which increases the reactance of the network between the generator internal voltageand the infinite bus to 400%. When the fault is cleared the maximum power that can be delivered is80% of the original maximum value. Determine the critical clearing angle for the conditionsdescribed. [61.64]Q6. A 60 Hz turbo alternator rated 500MVA, 22KV has H=7.5MJ/MVA. Find:(i) K.E. stored in the rotor at synchronous speed[3750](ii) The angular acceleration if the electrical power developed is 400MW when the input less therotational losses is 740,000HP [36.5rpm/sec].