Electrical Power and Machines

Electrical Power and Machin" rel="nofollow">ines Date: May 2015 Time allowed: 3 hours Instructions to Candidates: This is an unseen examin" rel="nofollow">ination. This exam paper is made up of eight questions. Candidates should answer any five out of the eight questions. All questions are marked out of 20. Materials provided: Graph Paper. Materials allowed: A scientific calculator may be used in" rel="nofollow">in this exam. Unannotated paper versions of general bi-lin" rel="nofollow">ingual dictionaries only may be used by overseas students whose first language is not English. Subject-specific bi-lin" rel="nofollow">ingual dictionaries are not permitted. Electronic dictionaries may not be used. Access to any other materials is not permitted. Turn Over Question 1 A three-phase, 50 Hz, 11kV/415V, transformer with a star connected secondary is used to supply a balanced delta connected in" rel="nofollow">inductive load of 30 kW. This load draws a lin" rel="nofollow">ine current (IL) of 60 A. a) Calculate the system phase to neutral voltage. (Van) (3 marks) b) Calculate the load phase current (IP). (3 marks) c) Calculate the values of R and L in" rel="nofollow">in each branch of the load. (4 marks) The ‘two-wattmeter method’ for measurin" rel="nofollow">ing real and reactive power in" rel="nofollow">in the load is bein" rel="nofollow">ing used. One wattmeter (W1) has its current coil in" rel="nofollow">in the ‘a-phase’ lin" rel="nofollow">ine and its voltage coil connected between the ‘a-phase’ and ‘c-phase’ lin" rel="nofollow">ines. The other wattmeter (W2) has its current coil in" rel="nofollow">in the ‘b-phase’ and its voltage coil connected between the ‘b-phase’ and the ‘c-phase’ lin" rel="nofollow">ines. The phase sequence is abc. d) Sketch a phasor diagram of the voltages and currents supplied to the load highlightin" rel="nofollow">ing the phasors relevant to the two wattmeters. (5 marks) e) Calculate the in" rel="nofollow">individual wattmeter readin" rel="nofollow">ings and thus show that their sum is equal to the total Power supplied to the load. (5 marks) [20 MARKS] Question 2 A factory is supplied at 415 V, 50 Hz and the load at the factory comprises two items. Load one draws a power of 300 kW at a power factor of 0.85 laggin" rel="nofollow">ing. Load two draws an apparent power of 200 kVA and a reactive power of 175 kVAr. The overall power factor at the factory is to be improved by the in" rel="nofollow">installation of capacitor banks totallin" rel="nofollow">ing 100 kVAr. a) Explain" rel="nofollow">in how the capacitor banks should be connected and why. (3 marks) Now calculate: b) The total power supplied. (3 marks) c) The power factor prior to correction. (4 marks) d) The power factor followin" rel="nofollow">ing correction. (4 marks) e) The per-phase value of capacitance (Farads) required to improve the power factor of the origin" rel="nofollow">inal uncorrected system to 0.95. (6 marks) [20 MARKS] Turn Over Question 3 An 11kV overhead lin" rel="nofollow">ine is fed from a busbar with a fault level of 180 MVA. The lin" rel="nofollow">ine is 9 km long with an impedance of (0.1 + j0.6) Ω per km and feeds an 11 kV/415 V, 750 kVA, transformer with an impedance of (0.1 + j0.4) pu based on its own ratin" rel="nofollow">ing. a) Calculate the source impedance as seen from the 11 kV busbars in" rel="nofollow">in: i) Per Unit (Sb = 50 MVA) (3 marks) ii) Ohms (3 marks) b) Convert the overhead lin" rel="nofollow">ine and transformer impedances to per unit values (Sb = 50 MVA). (4 marks) c) If a three-phase short circuit is applied to the transformer secondary termin" rel="nofollow">inals, calculate: i) The fault current (IF) at the short circuit (4 marks) ii) The fault level in" rel="nofollow">in MVA at this poin" rel="nofollow">int (3 marks) iii) The voltage at the 11kV busbars durin" rel="nofollow">ing the fault (3 marks) [20 MARKS] Turn Over Question 4 R1, R2 and R3, shown in" rel="nofollow">in Figure Q4 below, are over-current IDMT relays havin" rel="nofollow">ing a time/psm characteristic given by: a) Usin" rel="nofollow">ing the tabulated data, given in" rel="nofollow">in table Q4, calculate appropriate Plug Settin" rel="nofollow">ings and Time Multiplier Settin" rel="nofollow">ings to ensure min" rel="nofollow">inimum relay operate times and a min" rel="nofollow">inimum gradin" rel="nofollow">ing margin" rel="nofollow">in of 0.4 seconds for the fault conditions given. Show all relevant relay operate times in" rel="nofollow">in your workin" rel="nofollow">ing. (12 marks) b) Recalculate the relay operate times and the gradin" rel="nofollow">ing margin" rel="nofollow">in for all relevant faults with only one transformer in" rel="nofollow">in service. (5 marks) c) Discuss the advantages and disadvantages of ‘Time-Graded’ and ‘Current-Graded’ protection systems. (3 marks) Figure Q4 Maximum Feeder Load (Amperes) Fault Level T1 & T2 in" rel="nofollow">in Service (MVA) Fault Level One Transformer in" rel="nofollow">in Service (MVA) R1 380 240 130 R2 290 180 110 R3 190 180 110 Table Q4 [20 MARKS] Turn Over Question 5 Tests on a three-phase, 100 kW, 2 kV, 4-pole, 50 Hz in" rel="nofollow">induction motor produced the results shown in" rel="nofollow">in table Q5: No load test @ 50 Hz Locked rotor test @ 15 Hz DC Test Voltage(V) 2000 250 20 Current (A) 5.0 27 3.7 Power (W) 1620 9100 Table Q5 a) Draw the approximate equivalent circuit for this in" rel="nofollow">induction motor and calculate the relevant component values from the data given in" rel="nofollow">in table Q5 above. (10 marks) b) For the above motor, usin" rel="nofollow">ing the component values determin" rel="nofollow">ined in" rel="nofollow">in (a) above, calculate the followin" rel="nofollow">ing parameters when slip = 2.5%: i) Rotor current referred to stator (Is) (3 marks) ii) Gross electromagnetic torque (Te) (3 marks) iii) Motor losses (2 marks) iv) Motor efficiency (2 marks) [20 MARKS] Question 6 a) Usin" rel="nofollow">ing diagrams and appropriate graphs, explain" rel="nofollow">in briefly how a sin" rel="nofollow">ingle-phase, full-wave half-controlled rectifier bridge, can be used to effect speed control of a permanent magnet dc motor. (5 marks) b) A 150 V, shunt connected, dc motor has an armature resistance of 0.17 Ω and a field resistance of 75 Ω. At no load the motor runs at 1000 rpm takin" rel="nofollow">ing a lin" rel="nofollow">ine current of 5A. At full load the electrical power in" rel="nofollow">input to the motor is 7.5 kW. If armature reaction is considered negligible, calculate for full load conditions: i) Motor speed (3 marks) ii) Speed regulation (2 marks) iii) Gross torque (3 marks) iv) Gross mechanical power developed (3 marks) c) If armature reaction reduces the air gap flux by 6% when full load current flows in" rel="nofollow">in the armature recalculate the values for part (b) above. (4 marks) [20 MARKS] Turn Over Question 7 a) Explain" rel="nofollow">in how two 3-phase, fully-controlled, 6-pulse rectifier bridges, operatin" rel="nofollow">ing in" rel="nofollow">in circulatin" rel="nofollow">ing current mode, may be used as a 4-quadrant drive to control the speed of a dc machin" rel="nofollow">ine. Illustrate your answer with appropriate sketches. (8 marks) For a p-pulse, controlled rectifier bridge, without a flywheel diode, the average dc voltage presented to the load, is given by: Where VS = the supply voltage IL = the lin" rel="nofollow">ine current L = the source in" rel="nofollow">inductance (per phase) P = the number of pulses per cycle α = the delay angle beyond the natural commutation poin" rel="nofollow">int It is required to provide variable speed control of a 400 V, separately excited, dc motor usin" rel="nofollow">ing a 6-pulse converter. The motor armature current ratin" rel="nofollow">ing is 600 A, its speed ratin" rel="nofollow">ing is 1200 rpm and the armature resistance is 20.0 mΩ. The supply frequency is 50 Hz and the source impedance is j0.06 Ω per phase. b) Calculate the min" rel="nofollow">inimum lin" rel="nofollow">ine voltage required to operate the motor at its ratin" rel="nofollow">ing with the above arrangement. (6 marks) c) Determin" rel="nofollow">ine the value of α when the motor is operated at 700 rpm drawin" rel="nofollow">ing two thirds rated current with a supply voltage of 350 V. (6 marks) [20 MARKS] Turn Over Question 8 a) Explain" rel="nofollow">in fully, usin" rel="nofollow">ing circuit diagrams and appropriate graphs of voltage and current waveforms, how the speed of a permanent magnet, dc motor may be controlled from a dc supply usin" rel="nofollow">ing a chopper drive. (10 marks) b) A simple chopper circuit is used to control the speed of a permanent magnet dc motor. The dc supply voltage is 48V and the motor armature resistance is 0.5 . The motor drives a constant torque load which takes an average current of 10 A. The motor torque constant KM is 0.27 Nm/A. If the motor current is contin" rel="nofollow">inuous determin" rel="nofollow">ine: i) The duty cycle (on /off ratio) of the chopper such that the motor rotor just starts to turn. (6 marks) ii) The speed of the motor when the duty cycle is 2:3. (4 marks) [20 MARKS]