Effect of Harmonics on Pitch and Distribution Factors
(a) If the short-pitch angle or chording angle is a degrees (electrical) for the fundamental flux wave, then its values for different harmonics are
Example 37.8. The stator of a 3-phase, 16-pole alternator has 144 slots and there are 4 conductors per slot connected in two layers and the conductors of each phase are connected in series. If the speed of the alternator is 375 r.p.m., calculate the e.m.f. inducted per phase. Result- ant flux in the air-gap is 5 ´ 10– 2 webers per pole sinusoidally distributed. Assume the coil span as 150° electrical.
(Elect. Machine, Nagpur Univ. 1993)
Example 37.11. A 4-pole, 50-Hz, star-connected alternator has 15 slots per pole and each slot has 10 conductors. All the conductors of each phase are connected in series’ the winding factor being 0.95. When running on no-load for a certain flux per pole, the terminal e.m.f. was 1825 volt. If the windings are lap-connected as in a d.c. machine, what would be the e.m.f. between the brushes for the same speed and the same flux/pole. Assume sinusoidal distribution of flux.
Example 37.14. A 3-phase alternator has generated e.m.f. per phase of 230 V with 10 per cent third harmonic and 6 per cent fifth harmonic content. Calculate the r.m.s. line voltage for (a) star connection (b) delta-connection. Find also the circulating current in delta connection if the reactance per phase of the machine at 50-Hz is 10 W .
(Elect. Machines-III, Osmania Univ. 1988)
Solution. It should be noted that in both star and delta-connections, the third harmonic components of the three phases cancel out at the line terminals because they are co-phased. Hence, the line is composed of the fundamental and the fifth harmonic only.
(a) Star-connection
Tutorial Problems 37.1
1. Find the no-load phase and line voltage of a star-connected, 4-pole alternator having flux per pole of 0.1 Wb sinusoidally distributed; 4 slots per pole per phase, 4 conductors per slot, double-layer winding with a coil span of 150°.
[Assuming f = 50 Hz; 789 V; 1366 V] (Elect. Technology-I, Bombay Univ. 1978)
2. A 3-f, 10-pole, Y-connected alternator runs at 600 r.p.m. It has 120 stator slots with 8 conductors per slot and the conductors of each phase are connected in series. Determine the phase and line e.m.fs. if the flux per pole is 56 mWb. Assume full-pitch coils.
[1910 V; 3300 V] (Electrical Technology-II, Madras Univ. April 1977)
3. Calculate the speed and open-circuit line and phase voltages of a 4-pole, 3-phase, 50-Hz, star-connected alternator with 36 slots and 30 conductors per slot. The flux per pole is 0.0496 Wb and is sinusoidally distributed.
[1500 r.p.m.; 3,300 V; 1,905 V] (Elect. Engg-II, Bombay Univ. 1979)
4. A 4-pole, 3-phase, star-connected alternator armature has 12 slots with 24 conductors per slot and the flux per pole is 0.1 Wb sinusoidally distributed.
Calculate the line e.m.f. generated at 50 Hz.
[1850 V]
5. A 3-phase, 16-pole alternator has a star-connected winding with 144 slots and 10 conductors per slot.
The flux per pole is 30 mWb sinusoidally distributed. Find the frequency, the phase and line voltage if the speed is 375 rpm.
[50 Hz; 1530 V; 2650 V] (Electrical Machines-I, Indore Univ. April 1977)
6. A synchronous generator has 9 slots per pole. If each coil spans 8 slot pitches, what is the value of the pitch factor ?
[0.985] (Elect. Machines, A.M.I.E. Sec. B. 1989)
7. A 3-phase, Y-connected, 2-pole alternator runs at 3,600 r.p.m. If there are 500 conductors per phase in series on the armature winding and the sinusoidal flux per pole is 0.1 Wb, calculate the magnitude and frequency of the generated voltage from first principles.
[60 Hz; 11.5 kV]
8. One phase of a 3-phase alternator consists of twelve coils in series. Each coil has an r.m.s. voltage of 10 V induced in it and the coils are arranged in slots so that there is a successive phase displacement of 10 electrical degrees between the e.m.f. in each coil and the next. Find graphically or by calculation, the
r.m.s. value of the total phase voltage developed by the winding. If the alternator has six pole and is driven at 100 r.p.m., calculate the frequency of the e.m.f. generated.
[ 108 V; 50 Hz]
9. A 4-pole, 50-Hz, 3-phase, Y-connected alternator has a single-layer, full-pitch winding with 21 slots per pole and two conductors per slot. The fundamental flux is 0.6 Wb and air-gap flux contains a third harmonic of 5% amplitude. Find the r.m.s. values of the phase e.m.f. due to the fundamental and the 3rd harmonic flux and the total induced e.m.f.
[3,550 V; 119.5 V; 3,553 V] (Elect. Machines-III, Osmania Univ. 1977)
10. A 3-phase, 10-pole alternator has 90 slots, each containing 12 conductors. If the speed is 600 r.p.m. and the flux per pole is 0.1 Wb, calculate the line e.m.f. when the phases are (i) star connected (ii) delta connected. Assume the winding factor to be 0.96 and the flux sinusoidally distributed.
[(i) 6.93 kV (ii) 4 kV] (Elect. Engg-II, Kerala Univ. 1979)
11. A star-connected 3-phase, 6-pole synchronous generator has a stator with 90 slots and 8 conductors per slot. The rotor revolves at 1000 r.p.m. The flux per pole is 4 ´ 10-2 weber. Calculate the e.m.f. generated, if all the conductors in each phase are in series. Assume sinusoidal flux distribution and full- pitched coils.
[Eph = 1,066 V] (Elect. Machines, A.M.I.E. Summer, 1979)
12. A six-pole machine has an armature of 90 slots and 8 conductors per slot and revolves at 1000 r.p.m. the flux per pole being 50 milli weber. Calculate the e.m.f. generated as a three-phase star-connected ma- chine if the winding factor is 0.96 and all the conductors in each phase are in series.
[1280 V] (Elect. Machines, AMIE, Sec. B, (E-3), Summer 1992)
13. A 3-phase, 16 pole alternator has a star connected winding with 144 slots and 10 conductors per slot.
The flux/pole is 0.04 wb (sinusoidal) and the speed is 375 rpm. Find the frequency and phase and line
e.m.f. The total turns/phase may be assumed to series connected.
[50 Hz, 2035 Hz, 3525 V] (Rajiv Gandhi Technical University, Bhopal, 2000)
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