EE 255 - Chapter 5c

EE 255 - Chapter 5c - 135 5-21 Assume that the generator is...

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Unformatted text preview: 135 5-21. Assume that the generator is connected to a 480-V infinite bus, and that its field current has been adjusted so that it is supplying rated power and power factor to the bus. You may ignore the armature resistance A R when answering the following questions. (a) What would happen to the real and reactive power supplied by this generator if the field flux (and therefore A E ) is reduced by 5%. (b) Plot the real power supplied by this generator as a function of the flux φ as the flux is varied from 75% to 100% of the flux at rated conditions. (c) Plot the reactive power supplied by this generator as a function of the flux φ as the flux is varied from 75% to 100% of the flux at rated conditions. (d) Plot the line current supplied by this generator as a function of the flux φ as the flux is varied from 75% to 100% of the flux at rated conditions. S OLUTION (a) If the field flux in increase by 5%, nothing would happen to the real power. The reactive power supplied would increase as shown below. V φ E A 1 jX S I A Q sys Q G Q 2 Q 1 E A 2 I A 2 I A 1 V T Q ∝ I sin θ A The reactive power 136 (b) If armature resistance is ignored, the power supplied to the bus will not change as flux is varied. Therefore, the plot of real power versus flux is (c) If armature resistance is ignored, the internal generated voltage A E will increase as flux increases, but the quantity δ sin A E will remain constant. Therefore, the voltage for any flux can be found from the expression Ar r A E E g184 g184 g185 g183 g168 g168 g169 g167 = φ φ and the angle δ for any A E can be found from the expression g184 g184 g185 g183 g168 g168 g169 g167 =- r A Ar E E δ δ sin sin 1 where φ is the flux in the machine, r φ is the flux at rated conditions, Ar E is the magnitude of the internal generated voltage at rated conditions, and r δ is the angle of the internal generated voltage at rated conditions. From this information, we can calculate A I for any given load from equation S A A jX φ V E I- = and the resulting reactive power from the equation θ φ sin 3 A I V Q = where θ is the impedance angle, which is the negative of the current angle. Ignoring A R , the internal generated voltage at rated conditions is A S A jX I V E + = φ ( )( ) 277 0 0.899 565.3 31.8 A A j = ∠ ° + Ω ∠ - ° E 137 695 38.4 V A = ∠ ° E so V 461 = Ar E and ° = 5 . 27 r δ . A MATLAB program that calculates the reactive power supplied voltage as a function of flux is shown below: % M-file: prob5_21c.m % M-file to calculate and plot the reactive power % supplied to an infinite bus as flux is varied from % 75% to 100% of the flux at rated conditions. % Define values for this generator flux_ratio = 0.90:0.01:1.00; % Flux ratio Ear = 695; % Ea at full flux dr = 38.4 * pi/180; % Torque ang at full flux Vp = 277; % Phase voltage Xs = 0.899; % Xs (ohms) % Calculate Ea for each flux Ea = flux_ratio * Ear; % Calculate delta for each flux d = asin( Ear ./ Ea .* sin(dr)); % Calculate Ia for each flux...
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EE 255 - Chapter 5c - 135 5-21 Assume that the generator is...

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