Exam 3 Instructions: Closed book, closed notes, no crib sh…
Exam 3 Instructions: Closed book, closed notes, no crib sheet, no calculator. Put your student ID on each page. You must show work for credit on the first two problems. Answers must be reasonably simplified. Honorlock must remain running until you finish submitting your work. For your trigonometric convenience: Exam 3 – Problem 1. (25 pts) Understand Time Varying Transformations. Consider a two-phase induction machine. Recall that the rotor and stator voltages can be represented as follows: Also recall the following transformations: Derive expressions for vqdss{“version”:”1.1″,”math”:”vqdss”} and vqdr’s{“version”:”1.1″,”math”:”vqdr’s”}. vqdss should be in terms of rs{“version”:”1.1″,”math”:”rs”} and qd variables only. vqdr’s should be in terms of rr'{“version”:”1.1″,”math”:”rr'”}, ωr{“version”:”1.1″,”math”:”ωr”}, and qd variables only. Note: Exam 3 – Problem 2. (25 pts) Consider the phasor model of a wye-connected 3-phase induction machine rs, lls{“version”:”1.1″,”math”:”rs, lls”}, and llr'{“version”:”1.1″,”math”:”llr'”} can be ignored. It is fed with a balanced 3-phase AC voltage of Vs{“version”:”1.1″,”math”:”Vs”} (RMS) with a frequency of f.ωe=2πf{“version”:”1.1″,”math”:”f.ωe=2πf”} . Derive an expression for the a-phase stator current and the electromagnetic torque in terms of Vs, LM, P, ωr, ωe, {“version”:”1.1″,”math”:”Vs, LM, P, ωr, ωe, ”}and rr'{“version”:”1.1″,”math”:”rr'”}. Note: torque = something * Re(jIasIar'{“version”:”1.1″,”math”:”jIasIar'”}). (The overbar denotes the complex conjugate). You may leave Re in your final expression. Exam 3 – Problem 3. (5 pts) What is the optimal voltage phase angle for maximum torque for a PMSM? Exam 3 – Problem 4. (5 pts) When do we use flux weakening and how is it implemented? Exam 3 – Problem 5. (5 pts) Draw one phase leg of a 3-phase bridge converter and label ixdc, ixs, vdc, vxg. {“version”:”1.1″,”math”:”ixdc, ixs, vdc, vxg. ”} Exam 3 – Problem 6. (5 pts) What are two features of sine-triangle modulation? Exam 3 – Problem 7. (5 pts) Give two downsides of induction machines. Exam 3 – Problem 8. (5 pts) Draw the phasor equivalent circuit for a balanced two-phase induction machine. Include voltage and component labels/values. Exam 3 – Problem 9. (5 pts) An inverter fed PMAC machine is fed from a 100V source. The fast averages of the q-axis voltage, d-axis voltage, q-axis current, and the d-axis current are 40V, 10V, 10A, and -10A respectively. Estimate the fast average of the DC current into the inverter. Exam 3 – Problem 10. (5 pts) An ideal PMAC machine is fed from an inverter which is PWM controlled. The DC voltage is 100V, duty cycle is 0.5, and ϕv=0{“version”:”1.1″,”math”:”ϕv=0″}. Find vqsr{“version”:”1.1″,”math”:”vqsr”} and vdsr{“version”:”1.1″,”math”:”vdsr”}. Exam 3 – Problem 11. (2 pts) (T or F) The QD equivalent circuit is valid for both balanced and unbalanced machines. Exam 3 – Problem 12. (2 pts) (T or F) In a squirrel cage induction machine, the number of rotor poles will automatically be the same as the number of stator poles. Exam 3 – Problem 13. (2 pts) Solid rotor induction machines are often used in wind power. Exam 3 – Problem 14. (2 pts) (T or F) For one phase leg of a 3-phase bridge converter, if the upper switch is on and no current is flowing, then vxg=vd{“version”:”1.1″,”math”:”vxg=vd”}. Exam 3 – Problem 15. (2 pts) (T or F) When performing the blocked rotor test on an induction machine, slip is equal to 1. Exam 4 Instructions: Closed book, closed notes, no crib sheet, no calculator. Put your student ID on the front of the exam, not your name. You must show work for credit on the first two problems. Answers must be reasonably simplified Honorlock must remain running until you finish submitting your work. Exam 4 – Problem 1. (25 pts) Ability to Analyze / Design Electromagnetic Devices. Consider the UU core inductor below. This inductor has two coils. Each coil is wound in a direction such that positive current will cause flux to flow in a clockwise direction. Each coil has N turns. The air has permeability μ0{“version”:”1.1″,”math”:”μ0″}. Each U core has a permeability of μrμ0{“version”:”1.1″,”math”:”μrμ0″} . Assume wu=du=w{“version”:”1.1″,”math”:”wu=du=w”}. Draw the MEC. Find inductance in terms of N, μ0, μr, w, l, g, ws, ds. {“version”:”1.1″,”math”:”N, μ0, μr, w, l, g, ws, ds. ”} Find the absolute value of force using co-energy in terms of N, μ0, μr, w, l, g, ws, ds, i. {“version”:”1.1″,”math”:”N, μ0, μr, w, l, g, ws, ds, i. ”} Exam 4 – Problem 2. (25 pts) Understand Principals of Electromagnetic Energy Conversion. Consider a conservative electromechanical system with the flux linkage equations The currents are positive and a{“version”:”1.1″,”math”:”a”} is a constant for you to determine. Find an expression for force in terms of i1, i2, {“version”:”1.1″,”math”:”i1, i2, ”}and x{“version”:”1.1″,”math”:”x”}. Exam 4 – Problem 3. (25 pts) Analysis/Understanding of DC, Brushless DC, and Induction Machines. Consider an induction machine. All angles are defined to be positive in the counterclockwise direction. The winding functions of the rotor of a machine are given by The rotor currents are given by If the rotor is moving at a mechanical speed of 100 rad/s in the clockwise direction, what is the velocity of the stator MMF relative to an observer on the stator? Your answer should be positive if it is moving CCW relative to the observer. Exam 4 – Problem 4. (5 pts) Analysis of Power Converters for DC Machines. Consider a permanent magnet DC machine operating fed from a single quadrant chopper under hysteresis current control. Derive an expression for the switching period in terms of h, LAA, Vdc, Vfsw, Vfd, ra, ia*, kv, ωr. {“version”:”1.1″,”math”:”h, LAA, Vdc, Vfsw, Vfd, ra, ia*, kv, ωr. ”} Hint: Find the time that the switch is on, then the time when the switch is off and add them together. Congratulations, you are almost done with Exam 3 & Exam 4. DO NOT end the Honorlock session until you have submitted your work to Brightspace. When you have answered all questions: Use your smartphone or scanner to scan your answer sheet, and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDFs as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Submit your exams to these assignments: Exam 3 Submission Exam 4 Submission Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. 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