Homework 5

Homework 5 - 10.26.2004 Homework 5 Randall Robert 9771...

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10.26.2004 Randall Robert Homework 5 9771 Problem 1 Calculate the parameters of a 20kVA, 480/120V transformer equivalent model recalculated to the primary side, if the short circuit voltage is V ISC =7% ovV 1r , short- circuit power P sc =2.5% of S r , open circuit current I 1o =4% of I 1r and trhe open circuit power P o =1.5% of S r . Calculate transformer supply voltage V 1 needed to provide voltage V 2 =120V to the load if the transformer is loaded with the power *Draw the diagram of the complex RMS values of voltages and currents for each case of the load. a. S 2 = P 2 = 20kW b. S 2 = 20e^(j45)kVA c. S 2 = 20e^(-j45)kVA Part a. Rated primary current RMS value; I 1r = S r /V 1r = 20000/480 = 41.7A Open circuit admittance; Y 1o = I 1o /V 1o = (.04*41.7A)/480 = .003475[S] Magnetizing circuit conductance; G Fe = P o /U 1r ² = (.015*20000)/480² = .001303[S] Magnetizing circuit susceptance; B m = -√ (Y 1o ²-G Fe ²) = -√(.00347²-.001303²) =3.222 E -3 [S] 1
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Short circuit impedance; Z 1sc = V 1sc /I 1r ² = (.07*480)/41.7A = 0.806Ω Series resistance; R 1 + R’ 2 = P sc /I 1r ² =(0.015*20000)/41.7² = .1725Ω Series reactance; X 1l + X’ 2l = √ (Z 1sc ²-( R 1 + R’ 2 )²) = √ (0.806² - 0.1725²) = 0.7871Ω R 1 + R’ 2 = 0.0863Ω
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Homework 5 - 10.26.2004 Homework 5 Randall Robert 9771...

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