equivalent circuit for rotor + stator

Question 1

rotor circuit is based on

Answer 1

fr = s*f
sE2 - induced EMF in rotor at slip freq
sXo2 - leakage R at slip freq
R2 - rotor R

Question 2

current

Answer 2

Ir(ph) = (E2)/sqrt( (Xo2)^2 +(R2/s)^2)

EMF = E2
reactance = Xo2
Resistance = r2/s

Question 3

power factor expression

Answer 3

cos 𝜙2 = ( (𝑅2/𝑠) / √( (𝑋𝜎2)^2 + (𝑅2/𝑠)^2)

Question 4

as slip decreases

Answer 4

R2/S increases so rotor R is bigger, lower slip = less current and torque

Question 5

equvicalent circuit for stator

Answer 5

circuit has r1, xo1, Xm = magnetising reactance = represents the previously descibed rotational fields and induction of emf in stator and rotor circuits

Im - magnetising current in Xm

Question 6

we deduce that

Answer 6

following:
𝐸2′ = 𝑚𝐸2, 𝐼2′ =𝐼2/𝑚, 𝑅2′ = 𝑚^2*𝑅2 and 𝑋’𝜎2
= 𝑚^2𝑋𝜎2.

where 𝑚 is the ratio between the number of turns in the stator and rotor windings.

Question 7

what does Rc represent

Answer 7

core loss - and power losses in hystersis and eddy current

Question 8

output mechanical power (fs)

Answer 8

𝑃 = 3(𝐼2’)^2 x ( (1 − 𝑠)𝑅2′/ 𝑠)

3 for 3 phadse current

Question 9

airgap power formula (fs)

Answer 9

power delivered by 𝐼2′ at 𝐸2′ terminal

𝑃𝑔 = 3(𝐼2′)^2 x (𝑅2′/𝑠)
𝑃 = (1 − 𝑠)𝑃𝑔.