A 50 Hz synchronous generator is connected to an infinite bus through a line. The p.u. reactances of generator and the line are j0.3 p.u. and j0.2 p.u. respectively. The generator no load voltage is 1.1 p.u. and that of infinite bus is 1.0 p.u. The inertia constant of the generator is 4 MW-sec/MVA. Determine the frequency of natural oscillations if the generator is loaded to 60% of its maximum power transfer capacity and small perturbation in power is given.

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The necessary equation to be solved during the load flow analysis using Fast-Decoupled method is given below:<br/>where B' and B'' are formed using the imaginary part of the bus admittance matrix, Ybus. If the system consists of 6 buses of which one of the bus is slack bus and 2 bues are voltage regulated buses, then then the matrix B' is of order ____and the matrix B'' is of order____, respectivity.<br/>∆P/|Vi| = - B'∆δ<br/>∆Q/|Vi| = - B''∆|V|

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