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Unformatted text preview: EE321 Exam 4 Spring 2009 Notes : There are five questions. You must show work for credit, except for problem 1. Some problems have more information than is needed. The last two pages have trigonometric identities. You can tear these off if more convenient. You may also need these for Exam 5. A score of 60% on this exam satisfies ABET objectives 3 and 4. Good luck ! The following questions should be answered true or false. They are worth 2 pts. each. You do not need to show work. 1a) The induction motor model is more accurate than the brushless dc model. 1b) In a squirrelcage induction machine, the number of rotor poles will automatically be the same as the number of stator poles. 1c) Induction machines are always connected directly to the utility bus. 1d) The machine variable rotor and stator currents are generally at different frequencies. 1e) In the induction machine, the qd rotor currents and the qd stator currents are always at the same frequency in the steadystate with balanced conditions. 1f) The stator and rotor MMFs move at different speeds when viewed from the same place. 1g) Squirrel cage induction machines are often used in wind power generation. 1h) Referring rotor variables to the stator by the turns ratio eliminates rotor position from the machine equations. 1i) The qd model of the machine is only valid for balanced steadystate operation. 1j) The instantaneous qaxis rotor current is equal to the aphase rotor current (when using the stationary reference frame as discussed in class). On the remaining problems, show your work! 2.) 20 pts. The conductor density of the stator of a machine is given by ) 4 cos( 100 sm as n = ) 4 sin( 100 sm bs n= The stator currents are given by ) 50 cos( 5 ) 50 sin( 5 t i t i bs as = = If the rotor is moving at a mechanical speed of 100 rad/s in the clockwise direction, what is the mechanical speed and direction of the rotor MMF relative to an observer on the rotor ? What is the absolute value of the frequency of the rotor currents in Hz? 3.) 20 pts. A single phase induction machine has a single winding on the stator and a single winding on the rotor. The flux linkage equations are ar r sr as ss as i L i L ) cos( + = as r sr ar rr ar i L i L ) cos( + = where r is electrical rotor position, and ss L , sr L , and rr L are constants. Derive an expression for torque in terms of a number of poles P , ss L , rr L , sr L , as i , ar i , and r . Not all of these variables will necessarily be needed. Your answer should be in the form of a single scalar equation (i.e. fully multiplied out). 4.) 20 pts. Consider a wyeconnected 3phase machine with the following parameters: = s r , ' = = lr ls L L mH, 1 . 20 = M L mH, = m r r 3 . 41 ' , and 4 = P . A balanced 3phase, 60 Hz, 460 V ll voltage is applied to the machine. If the speed is 1795 RPM, compute the rms value of the aphase stator current and the electromagnetic torque. 5.) 20 pts. Consider a machine with a 2pole stator winding and a 4pole rotor winding. 20 pts....
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 Spring '08
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