approximate equivalent circuit Flashcards
(27 cards)
what approximations do we make
the magnetising branch 𝑋𝑚 is transferred to the supply terminals;
* the stator and rotor leakage reactances can be simply added together to form
the total leakage reactance 𝑋𝜎;
new rotor current formula (fs)
𝐼2′ =𝑉1 / √( (𝑅1 + (𝑅2′/𝑠) )^2 + 𝑋𝜎^2 )
why do we keep R1
v drop is significant
what is sm (fs)
critical slip
what is Tm (fs)
maximum torque
when do we consider motor operation
Tm and Sm have a positive val
we consider generator operation when
Tm and Sm have negative val
relationship between torque and slip
linear function in region of small slips (normal motor operation) and first order hyperbola in regions of higher slips
at small slips or rotor close to synchronous speed
R2’/S is much higher than Xo
at standstill condition (s=1, rotor speed = 0)
impedance in rotor is much smaller than magnetizing branch
frictionless motion equation
𝐽 (𝑑Ω/𝑑𝑡) = 𝑇 − TL
TL = load torque
J = moment of inertia
what does frictionless motion equation mean
T > TL - motor accelerate
T < TL - motor slows down
T = TL - motor reaches steady-state speed
what happens when there is a small load increase
motor is running stable and when it increases initially TL>T -> motor slows down
eventually it reaches new equilibrium system quickly settles
large load increas
Load torque is raised close to max torque Tm, Motor decelerates, a tiny speed drop makes 𝑇<𝑇𝐿. The motor enters uncontrollable deceleration → stalls
This is why Tm is also called the stall torque.
Motoring mode
Normal operation: 0<s<1
Rotor speed Ω<Ω0
Torque opposes load torque and drives the load
Power flows: electrical → mechanical
generating mode
Occurs when rotor is driven faster than synchronous speed s<0
E.g., by a turbine or another machine
Rotor speed Ω>Ω0
Torque still opposes motion, but power flows mechanical → electrical
Acts like a generator
Pg and P -ve
braking mode
Rotor turns opposite to the rotating field → Ω<0
Slip s>1
Torque is still developed, opposing rotor motion
Both electrical and mechanical input → converted to heat
Rotor slows down → used as an electric brake
what happens as a result of variation in stator V
change in rotor speed and reduced max torque for a give T but it doesnt affect critical slip
if Stator V is too low
max T could be lower than load T so motor will stall, so has to be in certain magnitude
stator V regulation
achieved by using a variable transformer
increasing R to control speed
only possible in wound-rotor machine where external R is connected across its circuit however more power losses as Rext is higher
varying stator V and frequency f for
speed control
RMS val of induced emf
ϕm = E1/ 4.44N1*f
ϕm peak of sinosoidally varying air-gap flux and f = freq of stator V
if f decreases and V is constant
higher ϕm -> higher magnertic flux, exceeds rated flux of core
