Tutorial 1) A 2900 RPM, 380V, 3 phase, 50Hz, 2 pole, delta connected induction motor has a stator resistance of 0.2 Ω. The rotor resistance referred to the stator is 0.3 Ω. The stator and rotor inductive reactance combined is 10 Ω at 50Hz. The hysteresis and eddy current effects can be ignored. Calculate the stator copper loss, rotor copper loss, air gap power, developed power and the developed torque. [Ans: 469W, 704W, 21.1kW, 20.42kW, 67.2Nm] 2) I) The power input to a 3-phase induction motor is 40 kw, and the corresponding stator losses are 1.5 kw. Neglecting the rotor iron loss, calculate: - a) The total developed mechanical power, P d, and the rotor I 2 R loss when the slip is 0.04. <36.96kW, 1.54 kw> b) The output power of the motor if the mechanical losses are 0.8 kw <36.16 kw> c) Efficiency of the motor <90.4%> II) If the speed of the above motor is reduced to 40% of its synchronous speed, calculate a) The total rotor copper loss, <23.1 kw> b) Efficiency of the motor, assuming that the increase in the rotor iron loss is offset by the reduction in friction and windage loss <36.5%> (This question adopted from Hughes, Edward, Electrical Technology) 3) A 2200V, 735 RPM, 50Hz, 8 pole, 3 phase delta connected squirrel cage induction motor has the following per phase parameters: - Stator resistance: 0.075 Ω Stator inductive reactance: 0.45 Ω Rotor resistance referred to the stator: 0.1 Ω Rotor inductive reactance referred to the stator: 0.55 Ω The iron losses and rotational losses can be neglected. K.F. Chan (Mr.) Page 1 of 8 July 2010
i). ii). iii) MEBS 6000 2010 Utilities services Calculate the starting torque and maximum torque as a ratio of the rated full load torque, if the motor is started by star delta starting. What is the maximum value of the line current during starting? Calculate transformation ratio of an auto-transformer so as to limit the maximum starting current to twice the rated line current. What is the starting torque? What will be the value of maximum line current and starting torque if 50% part winding starting method is used? Mechanical losses can be ignored. <0.173, 0.83,1251A> <0.624, 7038Nm> <2590A, 8539 Nm> (This question adopted from DUBEY, Gopal K., Fundamentals of Electrical Drives) 4) A 4-pole, 50Hz induction motor has a mechanical power output of 37.3 kw. The friction and windage torque is 22 Nm. The stator loss is equal to the rotor loss. The iron losses can be neglected. a). Calculate the input power to the stator when delivering full load output at 1440 RPM <44 kw> b). When the motor is used as an induction generator running at 1560 RPM, calculate the gross input torque and the stator output power. The rotor losses, stator losses and windage and friction torque are the same as in (a). <291 Nm, 40.6 kw> (This question adopted from SHEPHERD J., Higher Electrical Engineering) 5) A 380V, 3 phase, 50Hz, 4 pole delta-connected induction motor has a stator resistance of 3 Ω and the rotor resistance referred to the stator is 2 Ω. The equivalent inductive reactance of the stator plus rotor is 10 Ω. Mechanical losses can be ignored. a) Calculate the starting torque and the starting current <44.1 Nm, 34A> b) If both the voltage and frequency of the power supply is reduced to 10%, calculate the starting torque and the stating current. <21.2 Nm, 7.45Amp> K.F. Chan (Mr.) Page 2 of 8 July 2010
6) A SCR is connected between an ac source and a resistive load. The maximum allowable current transient of the SCR is 200 A µ s, the maximum non-repetitive forward blocking voltage is 400V. Maximum allowable voltage transient of the SCR is 1500V µ s. Calculate the value of the resistance, inductance and capacitance of the snubbing circuit to protect the SCR from excessive voltage transient and limit the current transient to half of the maximum rating. [Ans: L s 4µ h, R 15Ω, C s 0.0178µ F ] s 7) Draw a simple AC/DC, DC/AC conversion schematics of a PWM frequency inverter for 3-phase induction motor speed control. Briefly describe function of the components 8) Briefly explain why IGBT is gaining popularity over thyristor in frequency inverter drives. 9) A high speed VVVF lift system is driven by a 380V, 50Hz, six-pole, delta-connected induction motor. Regenerative braking facility is built in the frequency inverter circuit. The motor has the following parameters: ' R = 0.2Ω, R = 0.1Ω, X = 1. 5Ω 1 2 eq where R 1 is the stator resistance R 2 the rotor resistance referred to the stator X eq the sum of stator reactance and rotor reactance referred to the stator Assume that mechanical losses equal to 5% of the developed power. a) Calculate the outputdeveloped torque at a speed of 960RPM. [1030Nm] b) Calculate the maximum motoring torque outputdeveloped by this motor. What is the speed at maximum torque? [1147Nm, slip of 0.0661, 934RPM] K.F. Chan (Mr.) Page 3 of 8 July 2010
c) Now, the counterweight exerts a 900Nm torque to the motor when the empty lift car is travelling upwards. Regenerative braking is applied to maintain the lift car at a constant speed. Calculate the motor speed and the instantaneous power delivered by regenerative braking to the power supply system. [1021.1PRM, 86kW] 10) In a round trip of a lift in the 5-minute morning uppeak period, the expected number of stops, S, and the expected highest reversal floor, H, can be written as S = P 1 N 1 1, and N H = N N 1 i = 1 i N P where N is the number of floors above the main terminal, and P is the average number of passengers in the lift car. Explain why. State any assumptions made. 11) List any four key safety features in a lift. 12) A multi-tenant prestige office has 48 floors above the ground floor. Each floor is 900m 2 in area. The occupancy is 10m 2 per person and the daily occupancy rate is 90%. The ground floor has a height of 7m. The 24 th floor is a mechanical floor with a height of 3m only. Floor height of the other floors is all 3.5m. 37 th to 48 th floor are grouped into a high zone served by 6 lifts each of contract capacity of 16 persons, 5m/s contract speed, 1m/s 2 acceleration and deceleration. The door opening time and closing time is 0.5 and 2seconds respectively. Both the passenger loading and unloading time are 1.2seconds Calculate the round trip time based on first principles of linear motion, and the % population served in the 5-minute uppeak period with this lift installation. [Jxd f =129m (G/F to 36 th floor, floor to floor height), N=12, H=11.5, S=8.1, RTT=155.8s, K.F. Chan (Mr.) Page 4 of 8 July 2010
%POP=15.2] [Height from G/F to 47 th floor is 1 13) An office has 28 floors above the ground floor. Each floor has an area of 800m 2. The floor to floor height is 3.5m. Assume that the occupancy is 10m 2 /person and the daily occupancy is 90% only. There are 8 lifts each with contract capacity of 20 persons each. The contract speed is 4 m/s, acceleration 1 m/s 2 and deceleration 1 m/s 2 too. The door opening time and closing time is 0.5 and 2seconds respectively. Both the passenger loading and unloading time are 1.2seconds Calculate the round trip time based on first principle of linear motion and the percentage population served in the 5-minute uppeak interval. [H=26.8, S=12.4, RTT=167.6s, 2290pax, %POP=11.4%, lift will not reach contract speed in first jump] 14) Describe the differences between inverter-rated motors and standard motors used for sinusoidal power supply. 15) There is carrier sense multiple access with collision detection, so is there a CSMA/collision avoidance scheme? 16) Briefly describe the functions of the 7 layers in the OSI model. 17) We frequently come across the term broadband, so is there a narrow band? 18) Do wireless networks have physical layer and physical components? 19) What is the difference between a frame and a packet? 20) What is a structured cabling installation? Briefly describe the main components of a structured cabling installation. 21) Explain the differences in functions between repeater, hub, switch, bridge, router and gateway in a communication network. K.F. Chan (Mr.) Page 5 of 8 July 2010
22) What are the differences in the role of a hub and a switch in a structured cabling installation? 23) a. Briefly discuss the type of technologies used in broadband connections in Hong Kong. b. What is the role of an ISP? Briefly describe the services an ISP can offer to a consumer. 24) A 440V, 4 pole, 3 phase, 50Hz induction motor has an effective stator to rotor turns ratio of 3.49. The stator winding is delta connected. The measured stator resistance per phase is 0.6 Ω, and the stator reactance per phase is 3 Ω at 50 Hz. The measured rotor resistance per phase is 0.05 Ω and the rotor reactance per phase is 0.25 Ω, at 50Hz. a. Calculate the maximum torque and the slip at which it occurs. [277Nm, 0.1] b. If the ratio of full load to maximum torque is 1:2.5, find the full load slip and the power output. [0.02, 17.1kW] (This question adopted from SHEPHERD J., Higher Electrical Engineering) 25) A VVVF lift system is driven by a 380V, 50Hz, 8-pole, delta-connected induction motor. Regenerative braking facility is built in the frequency inverter circuit. The motor has the following parameters: ' R = 0.15Ω, R = 0.1Ω, X = 2Ω 1 2 eq where R 1 is the stator resistance R 2 the rotor resistance referred to the stator X eq the sum of stator reactance and rotor reactance referred to the stator Assume that mechanical losses equal to 5% of the developed power. a) Calculate the outputdeveloped torque at a speed of 720RPM. [1188Nm] b) Calculate the maximum motoring torque outputdeveloped by this motor. What is the speed at maximum torque? [12791215Nm, slip of 0.0499, 713RPM] K.F. Chan (Mr.) Page 6 of 8 July 2010
c) Now, the lift car exerts an 800Nm torque to the motor when the fully loaded lift car is travelling downwards. Regenerative braking is applied to maintain the lift car at a constant speed. Calculate the motor speed and the instantaneous power delivered by regenerative braking to the power supply system. [760.8PRM, 58.5kW] 26) A skyscraper is equipped with high speed VVVF lifts. A lift in the system serving the skyscraper is driven by a 380V, 50Hz, six-pole, delta-connected induction motor. Regenerative braking facility is built in the frequency inverter circuit. The motor has the following parameters: ' R = 0.025Ω, R = 0.025Ω, X = 1Ω 1 2 eq where R 1 is the stator resistance R 2 the rotor resistance referred to the stator X eq the sum of stator reactance and rotor reactance referred to the stator The fully loaded lift car exerts an 1800Nm torque to the motor during its downward travel. Regenerative braking is applied to maintain the lift car at a constant speed. Calculate the motor speed and the instantaneous power delivered by regenerative braking to the power supply system. Mechanical losses can be assumed to be 5% of the developed power. [Ans: 1012.8RPM, 177.2kW] K.F. Chan (Mr.) Page 7 of 8 July 2010
Values of H, average highest reversal floor, calculated by conventional formulae. Cars assumed to carry 80% of contract capacity. CC 6 8 10 12 16 20 24 P 4.8 6.4 8.0 9.6 12.8 16.0 19.2 N H H H H H H H 5 4.6 4.7 4.8 4.9 4.9 5.0 5.0 6 5.4 5.6 5.7 5.8 5.9 5.9 6.0 7 6.2 6.5 6.6 6.7 6.8 6.9 6.9 8 7.1 7.4 7.5 7.6 7.8 7.9 7.9 9 7.9 8.2 8.4 8.6 8.7 8.8 8.9 10 8.7 9.1 9.3 9.5 9.7 9.8 9.9 11 9.6 10.0 10.2 10.4 10.6 10.7 10.8 12 10.4 10.8 11.1 11.3 11.5 11.7 11.8 13 11.2 11.7 12.0 12.2 12.5 12.6 12.7 14 12.1 12.6 12.9 13.1 13.4 13.6 13.7 15 12.9 13.4 13.8 14.0 14.3 14.5 14.7 16 13.7 14.3 14.7 14.9 15.3 15.5 15.6 17 14.5 15.2 15.6 15.8 16.2 16.4 16.6 18 15.4 16.0 16.5 16.8 17.1 17.4 17.5 19 16.2 16.9 17.4 17.7 18.1 18.3 18.5 20 17.0 17.8 18.2 18.6 19.0 19.3 19.4 21 17.9 18.6 19.1 19.5 19.9 20.2 20.4 22 18.7 19.5 20.0 20.4 20.9 21.1 21.3 23 19.5 20.4 20.9 21.3 21.8 22.1 22.3 24 20.3 21.2 21.8 22.2 22.7 23.0 23.2 (Adopted from table 2.13 of CIBSE Guide D) K.F. Chan (Mr.) Page 8 of 8 July 2010