Analysis of Electrical Machines by Richard T. Smith (Auth.)

By Richard T. Smith (Auth.)

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14. Three identical single-phase transformers are connected to form a wye-delta three-phase bank. Accidentally, the polarity of one of the 52 Analysis of Electrical Machines secondary windings is reversed. Balanced three-phase voltages are applied to the wye side. Derive literal expressions for: (a) The voltage across the terminals of the delta if it is opened at one corner. (b) The current that will flow in the closed delta. (c) the current that will flow in the closed delta if a resistance R is inserted in series with it.

Verify the equivalent circuit connections, and solve for the input-output voltage and current relationships for an "ideal" transformer. 10. = ^ * 2 2 \ > e, + 2 £ ^ out — ~ 5 1 1 o u t Two "ideal" transformers, of turns ratios N /N and N /N , are connected as shown. Find the current / (a) when switch a is open; (b) when switch a is closed. The 10 ohms is entirely reactive. N —100, x 2 3 4 } # 2 =300,^3=200,^4=50. 11. For the device shown, consisting of two single phase transformers, interconnected as illustrated, find the voltage across each winding and current through each.

2 0 M = M c o s 0 + ... r and L —L r + L cos2d 0r 2r + ... Thus, dL/d6 = -2L sm26, 2 Msin0; and 2L sin20. 2r The torque is T — — L i sin26 2 e 2 — i i MsmO s r — L i sm20. 2 2r r 28 Analysis of Electrical Machines Assume i — I r and i = / c o s co/; then dc s w T — — L / s i n 2 0 — I I Msm8coscot 2 2r e d c m dc — L I cos 2 2 m co/sin20. If the various functions are expanded, we get T = - L / s i n 2 0 - I I M^ [sin(0 + at) + sin(0 - co/)] 2 2r e d c m dc sin20 + -j- (sin(20 + 2 co/) + sin(20 -2cof)} As before, we see that there is no average torque for positive steady speeds, except when 6 — cot + 8.

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