deequivalent circuit model

Question 1

vph (per phase terminal voltage)

Answer 1

𝑣𝑝ℎ = (𝑑𝜓𝑝ℎ/𝑑𝑡) − 𝑅𝑠*𝑖𝑝ℎ
voltage drop across winding (stator) R

vph = terminal V
𝜓𝑝ℎ = magnetic flux linkage of the phase winding
iph = phase current

voltage representing affect of faradays law is given by 𝑑𝜓𝑝ℎ/𝑑𝑡

Question 2

what affects the V at the output terminals of a stator phase winding

Answer 2

EMF induced by the rotor’s magnetic field
V drop due to stator R
V drop due to inductance

Question 3

what is 𝑑𝜓𝑝ℎ/𝑑𝑡

Answer 3

self inductance - magnetic flux from the same phase
mutual - inductance - flux from other phases
simplified into one term

e(𝑑𝜓𝑝ℎ/𝑑𝑡) = 𝑒𝑝ℎ − 𝐿𝑠 (𝑑𝑖𝑝ℎ/dt)
eph = induced emf

Question 4

termina voltage equation (forms)

Answer 4

𝑉𝑝ℎ arrow = 𝐸𝑝ℎ arrow − (𝑗𝜔𝑠𝐿𝑠 + 𝑅𝑠)𝐼𝑝ℎ arrow

eph and iph have sinusoidal waveform with angular freq of 𝜔𝑠 = 2𝜋𝑓𝑠

Question 5

synchronous impedance formula sheet

Answer 5

𝑍𝑠arrow= 𝑗𝜔𝑠𝐿𝑠 + 𝑅𝑠 = 𝑗𝑋𝑠 + 𝑅𝑠

Question 6

equivalent circuit model

Answer 6

draw circuit
combined effect of ls and RS leads to ZS

Question 7

what happens to current if there is a resistive and inductive load

Answer 7

current iph is drawn lagging vph

Question 8

how does jXS lead RS

Answer 8

by 90 deg so ZS*Iph is resultant force

Question 9

draw full phasor diagram

Answer 9

nsfjs

Question 10

what does phi phase mean

Answer 10

load power factor = cosphi

Question 11

what does theta mean in phasor diagram

Answer 11

load angle theata

Question 12

draw simplified equivalent circuit

Answer 12

rs is very small compared to xs so no rs

Question 13

conductor with negligle loss (forms)

Answer 13

𝒁𝒔 arrow = 𝒋𝑿𝒔