ES2C6 – Power Electronics 5 – Induction Machines
Induction Motor
The induction machine is a very important machine in the modern world – more than half of all the
power generated on Earth is used to power them. A motor is essentially a generator in reverse,
taking electrical power and transferring it to mechanical.
In an electrical car, the DC voltage from the battery – around 200𝑉 – is passed through a DC-DC
converter which raises it to 600𝑉 and then a DC-AC inverter which converts it to 3 phase AC.
All electrical currents have a magnetic field which follows the right-hand rule.
All motors and generators have a stator and a rotor. The stator is a stationary electromagnet and the
rotor is a rotating one. Most induction machines have three sets of stator coils displaced by 120°.
The magnetic field strength is dependent on the placement and timings of the AC through the stator
coils:
𝐻𝑚𝑓 = 𝐻𝑎𝑎 cos(𝜔𝑡) ∠0° + 𝐻𝑏𝑏 cos(𝜔𝑡 − 120°) ∠120° + 𝐻𝑐𝑐 cos(𝜔𝑡 − 240°) ∠240°
where the first angle is the timing angle and the second angle is the displacement around the stator.
Resolving this gives:
𝐻𝑚𝑓 = 𝐻𝑎𝑎 cos(𝜔𝑡)[cos 0 + 𝑗 sin 0] + 𝐻𝑏𝑏 cos(𝜔𝑡 − 120°)[cos 120 + 𝑗 sin 120]
+ 𝐻𝑐𝑐 cos(𝜔𝑡 − 240)[cos 240 + 𝑗 sin 240]
1 1
= [𝐻𝑎𝑎 cos 𝜔𝑡 − 𝐻𝑏𝑏 cos(𝜔𝑡 − 120) − 𝐻𝑐𝑐 cos(𝜔𝑡 − 240)]
2 2
√3 √3
+ 𝑗 [ 𝐻𝑏𝑏 cos(𝜔𝑡 − 120) − 𝐻 cos(𝜔𝑡 − 240)]
2 2 𝑐𝑐
Frequency and Rotation
An induction machine can have any number of stator coil pairs. For a machine with a two-pole
stationary magnet and three pairs of stators, two stators are connected to each of the phases 𝐴, 𝐵
and 𝐶. The frequency of the AC determines the speed of the rotational output of the motor:
𝑝𝑛𝑠
𝑓= (9)
120
where 𝑓 is the frequency, 𝑝 is the number of poles and 𝑛𝑠 is the synchronous speed in RPM.
𝑑𝜙
Due to Faraday’s Law of Electromagnetic Induction, 𝐸 = −𝑁 , an emf is induced as the flux cuts
𝑑𝑡
through the wire or squirrel cage. This flux linkage originating from the revolving flux from the stator
causes the rotor to gain emf and rotate, following the magnetic field. The speed of the rotor will not
catch up to the synchronous speed, otherwise the magnetic flux will no longer be cut by the rotor
and therefore will not experience any emf so won’t rotate. The difference between the synchronous
and rotor speed is slip:
𝑛𝑠 − 𝑛𝑟
𝑆= (10)
𝑛𝑠
When the rotor is stationary, 𝑛𝑟 = 0, the slip is 1, this is called a locked rotor. When the rotor speed
is equal to the synchronous speed, 𝑛𝑟 = 𝑛𝑠 , slip is 0 as there is no flux linkage so no torque or power
is produced.
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Induction Motor
The induction machine is a very important machine in the modern world – more than half of all the
power generated on Earth is used to power them. A motor is essentially a generator in reverse,
taking electrical power and transferring it to mechanical.
In an electrical car, the DC voltage from the battery – around 200𝑉 – is passed through a DC-DC
converter which raises it to 600𝑉 and then a DC-AC inverter which converts it to 3 phase AC.
All electrical currents have a magnetic field which follows the right-hand rule.
All motors and generators have a stator and a rotor. The stator is a stationary electromagnet and the
rotor is a rotating one. Most induction machines have three sets of stator coils displaced by 120°.
The magnetic field strength is dependent on the placement and timings of the AC through the stator
coils:
𝐻𝑚𝑓 = 𝐻𝑎𝑎 cos(𝜔𝑡) ∠0° + 𝐻𝑏𝑏 cos(𝜔𝑡 − 120°) ∠120° + 𝐻𝑐𝑐 cos(𝜔𝑡 − 240°) ∠240°
where the first angle is the timing angle and the second angle is the displacement around the stator.
Resolving this gives:
𝐻𝑚𝑓 = 𝐻𝑎𝑎 cos(𝜔𝑡)[cos 0 + 𝑗 sin 0] + 𝐻𝑏𝑏 cos(𝜔𝑡 − 120°)[cos 120 + 𝑗 sin 120]
+ 𝐻𝑐𝑐 cos(𝜔𝑡 − 240)[cos 240 + 𝑗 sin 240]
1 1
= [𝐻𝑎𝑎 cos 𝜔𝑡 − 𝐻𝑏𝑏 cos(𝜔𝑡 − 120) − 𝐻𝑐𝑐 cos(𝜔𝑡 − 240)]
2 2
√3 √3
+ 𝑗 [ 𝐻𝑏𝑏 cos(𝜔𝑡 − 120) − 𝐻 cos(𝜔𝑡 − 240)]
2 2 𝑐𝑐
Frequency and Rotation
An induction machine can have any number of stator coil pairs. For a machine with a two-pole
stationary magnet and three pairs of stators, two stators are connected to each of the phases 𝐴, 𝐵
and 𝐶. The frequency of the AC determines the speed of the rotational output of the motor:
𝑝𝑛𝑠
𝑓= (9)
120
where 𝑓 is the frequency, 𝑝 is the number of poles and 𝑛𝑠 is the synchronous speed in RPM.
𝑑𝜙
Due to Faraday’s Law of Electromagnetic Induction, 𝐸 = −𝑁 , an emf is induced as the flux cuts
𝑑𝑡
through the wire or squirrel cage. This flux linkage originating from the revolving flux from the stator
causes the rotor to gain emf and rotate, following the magnetic field. The speed of the rotor will not
catch up to the synchronous speed, otherwise the magnetic flux will no longer be cut by the rotor
and therefore will not experience any emf so won’t rotate. The difference between the synchronous
and rotor speed is slip:
𝑛𝑠 − 𝑛𝑟
𝑆= (10)
𝑛𝑠
When the rotor is stationary, 𝑛𝑟 = 0, the slip is 1, this is called a locked rotor. When the rotor speed
is equal to the synchronous speed, 𝑛𝑟 = 𝑛𝑠 , slip is 0 as there is no flux linkage so no torque or power
is produced.
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