NAME: STUDENT NUMBER: Fall 1997 EE361: MIDTERM EXAM 2 This exam is open book and closed notes. Be sure to show all work clearly. 1. 10 points - Mechanical and Electrical Energy Relationships: A dc motor is rotating at 800 RPM with E a =1000 V and I a =10 A. Mechanical rotational losses are 200 W. (a) Find the useful mechanical torque. (Here, useful means that the torque is actually available to do work such as in lifting a weight, turning a fan, etc.) (b) Find the stored rotational energy, if the rotational inertia of the machine is J=0.25 kg-m 2. (Note: kg-m 2 N-m-s 2 )
2. 30 points - General Rotating Machine Relationship: A two pole cylindrical rotor AC motor can be modeled by the circuit parameters given below. The stator is connected to a source so that i s (t)=5sin377t A and the rotor to a source so that i r (t)=5a. The rotor is spinning at a constant rate of 3600 RPM. Neglect winding and rotational losses. Machine Parameters: Armature (stator): L ss =3.2 H N s =50 turns Field (rotor): L rr =0.8 H N r =25 turns Coupling: L sr =1.6cosθ m H (a) What is the stored magnetic energy in the rotating machine as a function of time? (b) What is the torque on the motor shaft? (c) What is the stator voltage as a function of time?
3. 15 points - Three Phase Induction Motor: A three phase 208 V two-pole 60 Hz induction motor when operating at full load has a slip of 5%. Circuit parameters are given below. Neglect core effects. Circuit Parameters (per phase model): Armature: R 1 =1.0 Ω X 1 =2.0 Ω Field: R 2 =0.6 Ω X 2 =1.5 Ω (a) Find the frequency of the rotor current when operating at full load? (b) Find the magnitude of the per phase rotor current referred to the stator when operating at full load?
4. 15 points - DC Machine: A shunt connected 200 V DC Motor has an armature resistance of R a =2Ω and a field resistance R f =200Ω.. When the motor draws 3 A, it is seen to rotate at 1000 RPM. Neglect brush voltage drop and rotational losses in answering the following. (a) What is the motor voltage constant K a? (b) What is the rotational speed if the motor draws 10 A with the same 200 V supply?
5. 15 points - Synchronous Machine: Consider a three phase synchronous generator connected to an infinite bus with the parameters given below. Circuit Parameters (per phase in p.u.): Armature resistance: R a 0.0 Synchronous reactance: X s =0.6 p.u. Internal voltage: E a =1.2 p.u. Infinite bus voltage: V t =1.0 p.u. (a) What is the rotor angle δ if the real power output is 1.5 p.u.? (b) What is the reactive power output for this system in p.u.?
6. (15 points) Short Answer. (a) Why are induction machines seldom used for electric power generation? (b) Why are synchronous machines less frequently used as motors? (c) A four pole single phase induction motor has a 60 Hz signal applied to the stator windings and runs at 5% slip. What is (are) the rotor current frequency(s)?
NAME: STUDENT NUMBER: Spring 2001 EE361: MIDTERM EXAM 2 This exam is open book and closed notes. Be sure to show all work clearly. 1. 25 points - Three Phase Induction Motor: A three phase 25kW 500 V four-pole 60 Hz induction motor when operating at full load has a slip of 2%. Circuit parameters are given below. Neglect rotational losses. Circuit Parameters (per phase model, line to neutral): Stator: R 1 =0.5 Ω (0.05 p.u.) X 1 =1.0 Ω (0.1 p.u.) Rotor: R 2 =0.2 Ω (0.02 p.u.) X 2 =0.75 Ω (0.075 p.u.) Magnetization: X m =80 Ω (8.0 p.u.) (a) Find the frequency of the rotor current when operating at full load? (b) Find the power developed (i.e., the actual electrical power converted to mechanical power) when running at full load. Solution can be given in either per unit or SI units but mark solution clearly. (c) Find the mechanical torque under full load conditions. Solution should be in SI units.
2. 15 points - DC Machine: A shunt connected 200 V DC Motor has an armature resistance of R a =2Ω and a field resistance R f =200Ω.. When the motor draws 3 A, it is seen to rotate at 1000 RPM. Neglect brush voltage drop and rotational losses. What is the motor voltage constant K a?
3. 25 points - General Rotating Machine Relationship: A two pole cylindrical rotor AC motor can be modeled by the circuit parameters given below. The stator is connected to a source so that i s (t)=5sin377t A and the rotor to a source so that i r (t)=5a. The rotor is spinning at a constant rate of 3600 RPM. Neglect winding resistance and rotational losses. Machine Parameters: Armature (stator): L ss =0.8 H N s =25 turns Field (rotor): L rr =3.2 H N r =50 turns Coupling: L sr =1.6cosθ m H (a) What is the average mechanical torque on the motor shaft? Neglect the initial angle of θ m, i.e., let θ m =377t. (b) What is the terminal voltage (voltage across the stator terminals)?
4. 20 points - Synchronous Machine: Consider a three phase 10MVA 12kV synchronous generator connected to an infinite bus with the parameters given below. Solution can be given in either per unit or SI units but mark solution clearly. Circuit Parameters (per phase model, line to neutral): Armature resistance: R a 0.0 Synchronous reactance: X s =23 Ω (1.6 p.u.) Internal voltage: E a =8.31kV (1.2 p.u.) Infinite bus voltage: V t =6.93kV (1.0 p.u.) (a) What rotor angle(s), δ (0<δ<180 o ), will give a three phase real power output of 5 MW (0.5 p.u.)? (b) If there is more than one solution to (a), which of the angles can the generator actually operate at? (c) What is the reactive power output for this generator at this operating point?
5. (15 points) Short Answer. (a) A two pole single phase induction motor has a 60 Hz signal applied to the stator windings and runs at 5% slip. What is (are) the rotor current frequency(s)? (b) Match the following rotating machines to a typical application. (Just draw a line matching the machine to the application) Machine type Synchronous paper) Induction Brushless DC Stepper motor Typical application Paper feeder in printer (precise positioning of Hard disk drive (constant speed spinning of disk) Compressor or pump Large hydro generator unit
ECE 325: MIDTERM EXAM II Fall 2013 NAME: STUDENT NUMBER: There are 6 problems be sure to show all work clearly. 1. Three phase Induction Motor (20 points). For a three phase 381V, 60 Hz, 6 pole induction motor, you are given the per phase parameters below. When operating at full load, this motor has a slip of 4%. Find: (a) the frequency (or frequencies) of the rotor current at full load, and (b) the mechanical power output neglecting any rotational losses. Motor parameters: R X 1 1 = 0. 2 W = 0. 6 W R X 2 2 = 10. W = 2. 0 W X m = 80 W
2. DC Motor and Mechanical/Electrical Energy Relationships (15 points). A series connected 250 V DC motor has a total armature and field winding impedance of R a + R f =50 W. A lab test reveals that the motor draws 1.5 A when operating at 1000 RPM. Neglect any brush voltage drop. Find: (a) the electrical torque developed under this operating condition, (b) the stored rotational energy, if the rotational inertia of the machine is J=0.25 kgm 2. (Note: kg-m 2 º N-m-s 2 ).
3. General Rotating Machine (20 points): A two pole cylindrical rotor AC generator can be modeled by the parameters given below. The field is connected to a source with i r (t)=10 A. The rotor is spinning at a constant rate of 1800 RPM and the stator is open circuited. Neglect winding and rotational losses. Machine Parameters: Armature (stator): L ss =0.4 H N s =40 turns Field (rotor): L rr =1.6 H N r =80 turns Coupling: L sr =0.8cosq m H (a) Find the stored magnetic energy in the machine as a function of time. (b) Find the open circuit stator voltage as a function of time.
4. Synchronous Machine (15 points): A three-phase synchronous generator is connected to a load (infinite bus) as sketched in the one-line diagram below. Circuit Parameters: Armature resistance: R a» 0.0 Synchronous reactance: X s =0.3 p.u. Internal voltage: E a =1.2 p.u. Terminal voltage: V t =1.0 p.u. (a) At what rotor angle d will the generator operate if the real power output is 1.5 p.u.? (b) What is the maximum possible power output for this generator in p.u.? ~ X s = 0. 5 V load = 1. 0 E a Ð d = 1. 3Ðd
5. Three phase fundamentals (10 points). Three 69 kv voltage sources are connected in a balanced wye configuration as sketched below. These are then connected to an unbalanced delta load with the values indicated in circuit below. Find the total real and reactive power delivered to the 3 phase load. V an + -- -j100 W 50 W V cn + -- -- V bn + j100 W
6. Short Answer (20 points). (a) True or false. A three-phase induction motor (connected to a positive sequence three phase voltage source) can operate either clockwise or counterclockwise depending on the initial direction of rotation? Explain your answer, don t merely answer true or false. (b) What type of rotating machine is most commonly used for power generation? (c) A two pole single phase induction motor has a 50 Hz signal applied to the stator windings and runs at 5% slip. What is (are) the rotor current frequency(s)? (d) Select ONE of the motors listed below, identify a typical application, and then state why this motor is good for such an application. Stepper Permanent magnet Brushless DC Induction