Phase-SplittingSplit-Phase Induction Motor

Main Winding contributes “Direct-Axis” flux, d

Auxiliary Winding contributes “Quadrature-flux”, q

Auxiliary Winding is also known as the “Starting Winding”

Equivalent Circuit

Purpose of the “Phase-Splitter”

• Make the current in the Auxiliary Winding out of phase with the current in the Main Winding.

• This results in the quadrature field and the main field being out of phase.

• The locked-rotor torque will be given by

sin

mw aw

lr sp mw aw

i i

T k I I

Example 6-1

• The main and auxiliary windings of a hypothetical 120 V, 60 Hz, split-phase motor have the following locked-rotor parameters:– Rmw=2.00 Ω Xmw=3.50 Ω

– Raw=9.15 Ω Xaw=8.40 Ω

• The motor is connected to a 120 V system. Determine

Example 6-1 continued

• The locked-rotor current in each winding

2.00 3.50 4.0311 60.2511

9.15 8.40 12.4211 42.553mw mw mw

aw aw aw

Z R jX j

Z R jX j

120 029.8 60.3

4.0311 60.2511120 0

9.66 42.612.4211 42.5530

T

mw

mw

T

aw

aw

VI A

ZV

I AZ

Example 6-1 continued

Example 6-1 continued

• The phase displacement angle between the main and auxiliary currents

60.3 42.6 17.7mw awi i

Example 6-1 continued

• The locked-rotor torque in terms of the machine constant

sin

(29.8)(9.66)sin17.7 87.52

lr sp mw aw

lr sp sp

T k I I

T k k

Example 6-1 continued

• External resistance required in series with the auxiliary winding in order to obtain a 30 phase displacement between the currents in the two windings.

Example 6-1 continued

• Phasor diagram for the new conditions

' 60.3 30 30.3awi

Example 6-1 continued

' '

' '

'

'

030.3

'

30.3aw

aw

T T

aw aw

aw aw Z

Z

aw x aw aw

V VI I

Z Z

Z R R jX

Example 6-1 continued

'

'

tan

tan

8.409.15 14.38 9.15 5.23

tan30.3

aw

aw

aw

Z

aw x

aw

x aw

Z

XR R

XR R

R

Example 6-1 continued

• Locked-rotor torque for the condition in d

'

'

'

sin

120 09.15 5.23 8.40

7.2 30.29

(29.8)(7.2)sin30 107.1

107.1

lr sp mw aw

T

aw aw

aw

aw

lr sp sp

lr sp

T k I I

VI I

Z jI

T k k

T k

Example 6-1 continued

• % increase in locked-rotor torque due to the adding of additional resistance

107.1 87.52100% 22.37%

87.52sp sp

sp

k kX

k