spm

1

Dr. Lazhar BEN-BRAHIM SPRING'11 1

Chapter 1

SINGLE PHASE MOTORSby

Lazhar BEN-BRAHIM

22-Feb-14 Dr. Lazhar BENBRAHIM 2

SINGLE PHASE MOTORS (SPM) SPM are small motors used in homes, offices, shops and factories (washing machines, fans, refrigerators, record players, hand tools, blenders, Mixers, …). SPM are of three main types

1. Single-phase induction motors (SPIM). Resistance-start (split-phase)Capacitor-start.Capacitor-run.Capacitor-start-capcitor-run.Shaded pole

2. Single-phase synchronous motors (SPSM). Reluctance type.Hysteresis type.

3. Single phase series (universal) motors (SPUM).

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SINGLE-PHASE INDUCTION MOTORS

Double revolving field concept

3

Double revolving field theory

cos)( NiF

tIi m cos

bf

mm

m

FF

tNI

tNI

tNIF

)cos(2

)cos(2

coscos)(


Double revolving field Animation

If we take a stator with a single winding, and applya single phase voltage to it, we will have analternating current flowing and thereby anal ternat ing magnet ic f ie ld at each pole .Unfortunately, this does not result in a rotatingmagnetic field, rather it results in two equalrotating fields, one in the forward direction andone in the reverse direction. If we have a shortcircuited rotor within the stator, it will carry rotorcurrent induced by the stator field, but there will betwo equal and counter rotating torque fields. Thiswill cause the rotor to vibrate but not to rotate. Inorder to rotate, there must be a resultant torquefield rotating in one direction only. In the case ofthe single winding and a stationary rotor, theresultant field is stationary. . a’

a

a’a

4


Torque-Speed Characteristics

0stTNo starting torque

Single-phase motors are not self starting.


Slips of SPIM

sn

nns

s

rsf

sn

nnns

n

nn

n

nns

s

rssb

s

rs

s

rsb

22

)(

The forward slip : sf

The backward slip : sb

5

Slip of a Single-Phase IM

Rotor equivalent circuit

6

Torque Speed Characteristics

Torque Pulsation

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Equivalent circuit of a SPIM at standstill #1

R1 = Resistance of the stator windingX1 = Leakage reactance of the stator windingXmag = Magnetizing reactance X’2 = Leakage reactance of the rotor referred to the stator R’2 = Resistance of the rotor referred to the statorV1 = Supply voltageE = Voltage induced in the stator winding (air gap voltage by the stationary air gap flux

fNE 44.4

Equivalent circuit of a SPIM at standstill #2

ff fNE 44.4

bb fNE 44.4

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Equivalent circuit of a rotating SPIM

ff fNE 44.4

bb fNE 44.4

)(5.0/5.0

)/5.05.0(5.0'2

'2

'2

'2

XXjsR

sRXjXjjXRZ

m

mfff

)(5.0)2/(5.0

))2/(5.05.0(5.0'2

'2

'2

'2

XXjsR

sRXjXjjXRZ

m

mbbb

Equivalent circuit of a rotating SPIM

)(5.0/5.0

)/5.05.0(5.0'2

'2

'2

'2

XXjsR

sRXjXjjXRZ

m

mfff

)(5.0)2/(5.0

))2/(5.05.0(5.0'2

'2

'2

'2

XXjsR

sRXjXjjXRZ

m

mbbb

)(

&

&

21

21

21

bfsyn

bf

syn

gbb

syn

gff

bgbfgf

RRI

TTT

PT

PT

RIPRIP

rotmechout

gbgf

bf

synmmech

PPP

sPP

sRRI

sTTP

)1)((

)1)((

)1(2

1

gbgfg

gbgf

gbb

gff

PPP

PssPP

PsP

sPP

)2(

)2(

2

2

2

9

Equivalent circuit of a SPIM

R1 = Resistance of the stator winding

X1 = Leakage reactance of the stator winding

Xmag = Magnetizing reactance

X’2

= Leakage reactance of the rotor referred to the stator

R’2

= Resistance of the rotor referred to the stator

V1 = Supply voltageE = Voltage induced in the stator

winding (air gap voltage by the stationary air gap flux

fNE 44.4

EXAMPLE 1


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Solution for EXAMPLE 1


EXAMPLE 2


For the single-phase induction motor of Example 1, determine the input current,power, power factor, developed torque, output power, efficiency of the motor, air gappower, and rotor copper loss if the motor is running at the rate speed whenconnected to a 120 V supply.

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Solution for EXAMPLE 2



Starting Concept of SPIMIf we now add a second stator winding, physically displaced from the first winding, and apply a voltage equally displaced in phase, we will provide a second set of counter rotating magnetic fields and the net result is a single rotating field in one direction. If we reverse the phase shift of the voltage applied to the second winding, the resultant magnetic field will rotate in the reverse direction.

b’

a

a’

bRotor

Auxiliary Winding

Main winding

VIm

Centrifugal switch (CS)

Ia

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Start (Auxiliary) Winding Once the rotor is up to full speed, it will continue to run with the second windingdisconnected. This is because the rotor circuit is both resistive and inductive. If weconsider the magnetic field rotating in the same direction as the rotor, the frequency ofthe current will be low, so the rotor current will be primarily limited by the rotorresistance. In the case of the counter rotating field, the frequency of the inducedcurrent will be almost twice line frequency and so the inductance of the rotor will play amuch greater role in limiting the rotor current. In other words, once the motor is up tospeed, it will lock on to one field only and the second winding can be disconnected. Ifthe second winding remains in circuit, the displaced field reduces the magneticfluctuations in the gap and therefore provides a more even torque and less vibration.Some "start" windings are only designed for intermittent operation and they must bedisconnected at the end of the start. Continuous operation using these windings wouldcause a winding failure. Most single phase motors are fitted with a centrifugal switch todisconnect the start winding once the motor is close to full speed.

EXAMPLE 3


The currents in the main and the auxiliary windings are as follows:

The effective numbers of turns for the main and auxiliary windings are Nm and Na .The windings are placed in quadrature.

(a) Obtain expressions for the stator rotating mmf wave.(b) Determine the magnitude and the phase angle of the auxiliary winding

current to produce a balanced two-phase system.

tIi mm cos2

)cos(2 ama tIi

13

Solution Example 3



CLASSIFICATION OF MOTORS Single-phase induction motors are known by variousnames. The names are descriptive of the methodsused to produce the phase difference between thecurrents in the main and auxiliary windings.Commonly used types of single-phase inductionmotors are:

Resistance-start (split-phase)Capacitor-start.Capacitor-run.Capacitor-start-capcitor-run.Shaded pole

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This configuration comprises twowindings main and auxiliary and acentrifugal switch CS. The twowindings are wound with a geometricoffset, effectively making a secondset of poles phase shifted within thestator. The auxiliary winding hasresistance to provide a phase shift tothe current flowing in auxiliary andwe therefore have a "two phase"motor while the switch is closed. Themotor can be reversed by reversingthe connections of either main orauxiliary (but not both!)The startwinding provides for a rotatingmagnetic field in one directionenabling the motor to start.

Split Phase IM (Resistance Start)


Capacitor Start

This configuration comprises two windings startW1 and main W2, a centrifugal switch CS and acapacitor. The two windings are wound with ageometric offset, effectively making a second setof poles phase shifted within the stator. Thecapacitor provides a phase shift to the currentflowing in W1 and we therefore have a "twophase" motor while the switch is closed. When themotor is almost up to speed, the switch opensdisconnecting W1 and the capacitor. The motorcan be reversed by reversing the connections ofeither W1 or W2 (but not both!). The start winding(W1) and the start capacitor provide for a rotatingmagnetic field in one direction enabling the motort o s t a r t .

Higher starting torque as the use of acapacitor increases the phase anglebetween the winding currents.

A typical capacitor for a 0.5 hp motor is300F.

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Capacitor Run

The capacitor is left in the circuit all the time. This simplifies the construction and decreases the cost .Motor runs as two-phase motor →The power factor, torque pulsation, and efficiency

are improved and the motor will run more quietly. The capacitor value is of the order of 20-50 F and because it operates continuously,

it is an ac paper oil type. The capacitor is a compromise between the best starting and running values and therefore starting torque is sacrificed.


Capacitor Start/Run

Theoretically, optimum starting and running performance can be achieved byhaving two capacitors.

The starting capacitor Cs, is larger in value and is of the ac electrolytic type.The running capacitor Cr ,permanently connected in series with the starting

winding, is of smaller value and is of the paper oil type.Typical values of these capacitors for a 0.5 hp motor are Cs=300F, Cr=40 F.Expensive , however, it provides the best performance.

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Induction Start (Split Phase)Salient pole type motor. A shaded band consisting of a short-circuited copper turn, known as a shading coil, isused on one portion of each pole.The main single-phase winding is wound on the salient poles. The result is that the current induced in the shadingband causes the flux in the shaded portion of the pole to lag the flux in the unshaded portion of the pole.Therefore the flux in the shaded portion reaches its maximum after the flux in the unshaded portion reach itsmaximum. This is equivalent to a progressive shift of the .flux from the unshaded to the shaded portion of thepole. It is similar to a rotating field moving from the unshaded to the shaded portion of the pole. As a result, themotor produces a starting torque.Shaded pole motors are the least expensive of the fractional horsepower motors and are generally built for lowhorsepower rating, up to about 1/20 hp.

SINGLE-PHASE INDUCTION MOTORS

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STARTING WINDING DESIGN


Objectives:Starting (auxiliary) winding → to develop a starting torqueStarting winding design → maximum starting torque or

→ optimize starting torque per ampere of the starting current

sinams IKIT Im→E2m=4.44fN2m→ m & I2a→Tm

Ia→E2a=4.44fN2a → a & I2m→Ta

Starting Torque

sinam

ams

II

TTT

The cage rotor can be represented by an equivalent two-phasewinding, represented by the coils a-b and c-dAssume that each of these coils has an effective number ofturns N2, resistance R2, and reactance X2 (at the statorfrequency f).The current flowing thro through the main winding producesflux that induces voltage e2m (by transformer action) andcurrent i2m in the a-b coil of the rotor.The current i2m flows in such a direction as to oppose flux m.Similarly, flux a in the auxiliary winding induces voltage e2aand current i2a in the c-d coil of the rotor.

SPLIT PHASE STARTING WINDING DESIGN


Objectives:Main winding is designed to satisfy the running operation of the motorStarting winding is designed so that together with the main winding produces the desired starting torque → How? Assume a number of turns of starting coil (Na), calculate Ra to maximize the starting torque.

Maximum Starting Torque

)( mmm

aa ZX

X

XR

)()(2

mma ZXmNaNR

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DESIGN OF CAPACITOR START MOTORS


Objectives:Main winding is designed to satisfy the running operation of the motorHow to select the starting capacitor to to maximize the starting torque.

Maximum Starting Torque

)(

1

mm

ma

ZXRR

aXC

2

90 ma

Sine Im is fixed, Ts ∝ IaSinα ∝ length CK

the length CK is maximum when it passes through the center of the circle.

DESIGN OF CAPACITOR START MOTORS #2


Objectives: How to select the starting capacitor to maximize the starting torque per ampere of starting current.

Maximizing the starting torque per ampere of starting current is the most desirable criterion.

Starting current is represented by OCStarting torque is represented by CK. The ratio CK/OC is maximum when OC is tangential

to the circle ABCD, which is the locus of Ia and I.

Maximum Starting Torque per ampere of starting Current

m

maamamaC R

RRRZRXX

CX

)(1

19

Example 4



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EQUIVALENT CIRCUIT OF A CAPACITOR-RUN MOTORS


a = Na/Nmfm →Efm &fa→Efa

bm→Ebm & ba→Eba

fa → -jEfa/aba → jEba/afm → jaEfm

bm → -jaEbm

EQUIVALENT CIRCUIT OF A CAPACITOR-RUN MOTORS


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Example 5



Switched Reluctance Motors (SRM)•saliency in both stator and rotor•winding only on the stator•rotor pole align with the stator pole to maximize the stator flux -> torque

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HW#1


7.17.57.67.87.97.12

Course Projects


Simulation & Control of Single-phase motors

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