Multiple Stator Connections in a Three-phase Alternator

Question 1

Consider now twelve stator slots. The slots are all inserted with the same number of conductors. So, their induced
e.m.f.s, i.e., 𝐸1, 𝐸2, …, 𝑐𝐸11 and 𝐸12, have equal magnitude which we will now call E

Answer 1

Due to their arrangement in the stator, the induced e.m.f.s are lagging each other by
30°, i.e., 𝐸1 lags 𝐸2, 𝐸2 lags 𝐸3, 𝐸3 lags 𝐸4, …, 𝐸11 lags 𝐸12, and 𝐸12 lags 𝐸1 all by
30°, as shown in the phasor diagram shown below. exmaple

Question 2

how to know which phasor is leading or lagging

Answer 2

imgine all phasors are rotating in anti clockwise (conventtion) and decedie

Question 3

how to group the 12 induced emfs into 3 components

Answer 3

EA = E1 - E7 +E2 -E8
EB = E9 - E3 +E10 - E4
EC = E5 - E11 +E6 -E12

Question 4

this can be displayed in phasor diagram

Answer 4

EA, EB, EC have diff phases with each other, EA is set as reference so eb lags ea by 120 and ec leads ea by 120

Question 5

resolve magnitude

Answer 5

𝐸𝑝ℎ =
2 + 2 cos 30°
cos 15° 𝐸 ≈ 3.86E so set of 3 power supplies gives nearly 4x more than ori emf