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INDUCTION MOTOR PERFORMANCE WHEN FED FROM SINGLE TOTHREE PHASE CONVERTERS

P.Pillay, MIEEE and J.BrzezinskiDepartment of Electrical & Electronic EngineeringUniversity of Newcastle upo n Tyn e, NE1 7RU, England

ABSTRACTThe most popular single to three phase converterconsists of a capacitor connected between the motor'sthird phase and either the live or neutral of thesingle phase supply. Proper voltage balance at any onegiven operating point is obtainable with theautotransformer-capacitor converter (ACC), whileproper balance over the entire operating range isobtainable with a variable inductor-variable capacitorconverter (LCC). The appropriate vector diagrams ofthe above mentioned converters are developed toprovide insight into their operation. An assessment ofthe derating necessary in the presence of unbalancedvoltages and currents is presented. A technique forthe measurement of the negative sequence voltage isdiscussed. Measured results when an induction machinestarts directly off a three phase supply, and off theabove converters are included.1. INTRODUCTION

Single to three phase converters are used todrive three phase machines (normally induction motors)from single phase supplies. The need for theseconverters arise in remote locations like farms orhome industries which may only have single phasesupplies, but may have three phase induction motors(IMs) driving pumps, grinders, drills, woodworking andtextile machinery. Electrification in developingcountries is also often based on a single-phase,earth-ret urn system which make these convertersnecessary if three phase machinery is used.

The first type of single to three phase converterdeveloped consisted of a capacitor (capacitor-converter (CC)) connected to an IM fed from a singlephase supply as shown in figure 1.This system hasbeen the subject of a fair amount of analysis, with aheavy reliance on positive and negative sequencetheory as a tool. The magnitude of the capacitanceneeded to provide the best possible balance has beencalculated [ l ] while the transient behavior has alsobeen examined [ 2 - 4 1 . Where several machines are to befed from a single converter, the rotating or"Ferraris-arno"system [ 5 ] has been used as shown infigure 2. This consists of an unloaded IM with a

Figure 1. Capacitor single to three phase converter.

capacitor single to three phase converter acting asthe phase balancer; the hp rating of the so-called"pilot motor" having to be equal to the sum of the hpratings of all the load motors for proper performance.The calculation of the optimum magnitude ofcapacitance for a variety of operating conditions hasalso been presented [6].

When the CC is used, it is not normally possibleto obtain a balanced set of motor terminal voltages atthe operating power factor of most IMs. Proper balanceat any one chosen power factor (except unity), ispossible b y , using an autotransformer in addition tothe capacitor, know n as a autotransformer-capacitorconverter (ACC). A balanced set of terminal voltagesat any power factor is obtainable by using a variableinductor/variable capacitor converter (ICC) [ 7 ] . Thevariability in the inductance can be produced by a n acpower controller using an anti-parallel set ofdevices, while that in the capacitor can be producedby a chopper. This increases the cost and complexitywhile reducing the reliability; the latter beingextremely important in remote locations.

Most of the contributions mentioned above usepositive and negative sequence theory in the analysisor design of the above. This is a powerful tool andits importance should not be underated. On the otherhand, it was found during this investigation thatadditional insight was obtained by using vectordiagrams to obtain a physical understanding of theabove systems. For example, using the positive andnegative sequence equations of the IM, it is possibleto show that perfect balance using the simplecapacitor converter can be obtained only if the motorpower factor angle is 60'. To obtain a physicalunderstanding of why this should be so is difficultusing the sequence equations; the use of appropriatevector diagrams can provide such an insight and is one

Single phase supplyL N

Pilot motor

Figure 2. Rotary single to three phase converter.90/CH 2 9 3 5 - 5 / 9 0 / ~ 5 $ 0 1 . 0 0 @ 1 9 9 0IEEE

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of the purposes of this paper. The appropriate vectordiagrams of the two other types of converter, thecapacitor-autotransformer (figure 3 ) and the inductor-capacitor (figure 4 ) are developed and presented aswell. The vector diagrams show that whereas thecapacitor-only converter can obtain perfect balance atonly a power factor angle of 60, that the capacitor-autotransformer converter can obtain balance at anyone chosen power factor, except unity, but becomesunbalanced at any other operating power factor. Thecapacitor-inductor converter on the other hand, canobtain perfect balance at any operating motor powerfactor provided proper control of the capacitance andinductance is obtained. A comparison of theseconverters is also made. This is the first aim of thepaper.

The magnitude of the negative sequence voltageprovides insight into the performance of theconverter. A technique for the measurement of thisvoltage is presented. This circuit can however be usedin a more central role in the closed loop control ofthe system. This is the second aim of the paper.When the capacitor-only or the autotransformer-

capacitor converter is us ed, some unbalance wouldexist whenever the motor power factor deviates fromthe value chosen for balance. This implies a negativesequence voltage which when impressed upon thenegative sequence IM network, produces a correspondingnegative sequence current and hence torque. Thenegative sequence current increases the copper losswhile the negative sequence torque subtracts from thepositive sequence value so as to enforce a torquederating of the machine. The second contribution ofthis paper is therefore an assessment of the deratingnecessary in the presence of unbalanced voltages andcurrents. Normalised curves are produced so that for agiven level of voltage or current unbalance, thecorresponding torque derating can be determined.Theoretical predictions are supported by practicalmeasurements. This is the third aim of the paper.The run-up performance of an IM fed from suchconverters is o f course of crucial importance in apractical application. Measured results of the motor'sperformance is presented when starting directly off athree phase supply, off a CC and a ICC. Theperformance results when operating off a capacitor-inductor converter has already been presented

elsewhere [ 7 ] . This is the fourth aim of this paper.

Figure 3. Autotransformer-capacitor converter

'L

Figure 4 . Inductor-capacitor converter

2. VECTOR DIAGRAMS OF SINGLE TO THREE PHASE CONVERTERSThe vector diagram of the convertersystem shown in figure 1is drawn in figure 5. Fromfigure 5, clear that the vector va is equal tothe vector sum of vc and icXc, Alternately, vector vcis defined by the vector difference between v and

icXc. Given that vc should make an angle of 120' withthe horizontal under balanced conditions and that itshould be of the same tagnitude as va, this forces thevector icXc to be 30 from the horizontal so that ican terminate on va. This means that ic must be 60from the horizontal since icXc is perpendicular to ic.Of course, most induction motors operatefactor angle significantly larger than p:;::running and hence proper balance cannot normally beachieved with this simple converter. Note however thatin the Ferraris-arno system the pilot IM is requiredto be unloaded when the power factor can be quiteclose to 0 . 5 . This enables the system to achieve amore balanced supply.

it is

s

For a given magnitude and angle of ic , thereare an infinite number of vc, depending on themagnitude of the Xc chosen. Xc may be chosen tosatisfy the magnitude criterion of vc (ie = va) orparticular case of the lattera special case of the ICC, ie

some other criterion. Ais to consider the CC aswith no inductor.

'b

Figure 5. Vector diagram o f the capacitor converter.46

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VCk - .I \ .

i, '

Figure 6 . Vector diagram of theVb inductor-capacitor converter.

Figure6 shows the vector diagram of the ICC.The idea here is force the capacitor current tooperate at factor angle of 60' by adding thecorrect contribution from the inductor. The voltageacross the inductor is vbc and hence iL, which mustlag vbc by 90, lies along va. The magnitude of thiscontribution is controlled by varying the effectiveinductance by using an antiparallel pair of devices17). The magnitude of the icXc vector is controlled byvariation of the effective capacitance. Both thechopper and the ac power controller generate harmonicsinto the system, which in addition to the increasedcomplexity is a disadvantage of this scheme.

a power

From symmetrical component analysis [6 ], thecapacitance required for balance as a function of slipis given in figure 7 from which the capacitance usedin the CC is taken. Note that ideally, the capacitanceshould vary continuously as a function of slip. It isalso clear however, that between a slip of 1 and 0.3,that the required capacitance is approximatelyconstant. Minimization of the number of capacitancesrequired can be obtained by switching in thecapacitance required at full load at some slipgreater than 0 . 3 . This limits the number of discretecapacitances to two, although some commercial designsuse several.

80 -30 -60- PF

50 -40-30 -

SLIPI I 1 I I I 3

0 0.1 02 03 0.4 05 06 0.3 0.8 09 1.0

' Figure 8 . Vector diagram oft'/ capacitor converter.N

banV

the autotransformer-

Figure 8 shows the vector diagram o f acapacitor-autotransformer converter for a power factorangle of approximately 30'. The vector icXc is alsoshown. While it does not reach va, it does reach anextension of the vector Vba. But Vba is the singlephase input line voltage and an extension of it can beproduced through an autotransformer; this is the basisof the operation of this converter. It is evident thatthe closer the power factor of the motor is to 60,the lower is the required autotransformer outputvoltage. Of course no autotransformer is necessary at60'. At unity power factor, the vector icXc isparallel to that of the input supply voltage and hencea balanced terminal voltage set cannot be obtainedwith this converter. However this is not a practicalproblem since IMs do not operate at unity powerfactor.

Figure 9 shows figure 8 with relevant anglesincluded. From simple trignometry it is easy to showthat the angle between nV and i X is the power factorangle d. The magnitude of nV EsCcalculated using thesine rule as follows:sin( 4)/vca - sin( 60-d)/nVsin(6O0)/iCXc = sin(4)/vbc ( 2 )

(1)Similarly, the magnitude of icXc is calculated from

"Ct:

Figure 7. Capacitance vs slip Figure 9. Detailed representation of figure 8.47

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3. MEASUREMENT OF NEGATIVE SEQUENCE VOLTAGEThe magnitude of the negative sequence voltage is

of importance in assessing the ability of theconverter to obtain balance. It can however, perform amore useful function. The magnitude of the capacitancein the converter should ideally vary as a function ofthe slip. However, for the machine used, the startingcapacitance can remain essentially constant up to slip= 0.5, when the capacitance should then reduce rapidlyas the slip reduces.

With the fixed value of starting capacitance,the magnitude of the negative sequence voltageincreases as the speed increases. The negativesequence detector can therefore be used to decide whento start decreasing the capacitance, instead of usinga more expensive slip detector as proposed in [6]. Aschematic of the negative sequence detector used isshown in figure 10 with the corresponding phasordiagram in figure 11. When the line voltages arebalanced, IA + IB = 0 and no current flows through theampmeter M. It can be shown [ 8 ] that this current isdirectly proportional to the magnitude of the negative

N =r -

'A I BFigure 10. Negative sequence voltage detector.

Figure 11. Vector diagram o f the negativesequence detector.

sequence voltage. Also, it is necessary that ZB - aZA.A l s o , ZA must provide a leading current of 60' whileZB must provide a lagging current of 60 ' . The valueschosen were RA = 185 Ohms, LB - 1.02 H and CA -9.95 pF. In order to obtain a voltage signal from thecurrent flowing in the negative sequence detector, a 1Ohm resistor was inserted in place of the ampmeter

RB =

The output of the negative sequence detectorduring run-up with the starting capacitance only isshown in figure 12.Clearly, the output can be used tocontrol the switching-in of the run capacitance. Thisis done in figure 13where at a slip of 0.13, the ru ncapacitance is inserted. The effect is to reduce themagnitude of the negative sequence voltage since therun capacitance creates a more balanced supply nearthe full load slip. This technique removes the needfor a centrifugal switch to control the connection ofthe run capacitance.

a CO V / C IV i o o m s / o I v5.00 V / C I V I c c m s / O I vI

I

Figure 12. Negative sequence detector output.

2.00 V / OI V I o o m ~ / o I vI I 1

Figure 13. Negative sequence detector output duringswitching.

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4. STEADY-STATE RESULTSThe well known IM equivalent circuit, in the

presence of unbalanced supply voltages is used tocalculate the derating of the machine used in thisinvestigation. The positive sequence voltage isapplied to the positive sequence network (figure 14a)to produce the positive sequence current and hencetorque. The negative sequence voltage is applied tothe negative sequence network (figure 14b) to producethe negative sequence current and hence torque. Thenet machine torque is the difference between thepositive and negative sequence components. Thederating is based on the most conservative approach,ie when any one phase current reaches its rating. Inpractice, there is thermal conduction between the mostheavily loaded phase an d' the more lightly loadedphases which allows the former to be loaded beyond itsrated value. The calculation of this degree ofoverloading is complicated because it depends forexample on the thermal conductivity of the slotinsulation and the degree of contact between the slotinsulation and teeth. It is therefore heavilydependent on the motor's construction and size.

The motor parameters were measured using thelocked rotor and zero-slip tests and are shown inTable 1. This was used to calculate the full loadperformance which was verified experimentally.Unbalanced voltages were also applied to the networksand the performance calculated and verifiedexperimentally. Having verified the model, it was thenused to determine the torque derating for a series ofunbalanced voltages and currents. Two derating curveswere produced, figure 15, assuming the machine issupplied with unbalanced voltages and figure 16 forthe derating necessary for a given level of currentunbalance, The standard torque equation of aninduction motor was used in the calculation.Table 1.R1 - 4.58 OhmsR2 - 5.60 OhmsX1 - 7.18 OhmsX2 .. 10.78 OhmsXm - 115.78 OhmsRm - 695.65 Ohms

Figure 15 shows the torque deratlng as afunction of vb , with va held constant at lpu and vcvarying between 0.2 and 1 . 2 pu. Hence for anyunbalance in the phase voltages between 0. 2 and 1.2puin two phases, with the third phase at l pu , the torquederating can be calculated. Figure 16 can be usedcorrespondingly if the level of unbalanced currentsare known.5. TRANSIENT RESULTS

The run -up performance of IMs is of importancein a practical application. A long run-up time implieslonger voltage dips, and more severe operation of themotor. The performance of other equipment on the samebus can also be adversely affected.

Measurements when an IM is fed from a balancedthree phase supply, a capacitor only converter and acapacitor-autotransformer converter are presentedhere. (The performance when fed from a capacitor-inductor converter being already presented in [6].)Figures 17, 18 and 19 show the speed when the IM isstarted off a balanced supply, a CC and an ACC. In thecase of the converter starting, only the startcapacitance is used. The motor takes approximately325111sto run up on a balanced suppl y, and 40 0 ms with

the capacitor only or autotransformer converter. Thisis an 23 %when compared to starting on abalanced supply. Although the ACC can provide betterbalance at ful l-l oad , the start-up time is essentiallythe same as that for a CC , indicating approximatelythe same level of unbalance during run-up.

increase of

P x2'Figure 14a. Positive sequence network of the IM

I v 2Figure 14b. Negative sequence network of the IM

1.2

1 .o

0.8

0.6

0.4

0.2

Te

/ = l 2 p-u*= 1.0 p.u.= 0.8 p.u.

v =1 p . u .A

vc= 0.6 p.u.= 0.4 p.u.

= 0.2 p.u.

"B

0.2 0.4 0.6 0.8 1.0 1.2Figure 15. Derating for unbalanced voltages.

Figure 16. Derating for unbalanced currents.

I,= 1.2 p.u.

I = 1.0 p.u.

I = 0.8 p.u.

IC = 0.6 p.u.

IC = 0. 4 p . u .

I C = 0.2 p.u.

0.2 0 .4 0. 6 0.8 1.0 1 . 2L

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6. CONCLUSIONS

Figure 17. Startup speed from a balanced 3 phaseSUPP1Y.

Figure 18. Startup speed from a CC converter

The vector diagrams of the capacitor-onl y, theautotransformer-capacitor and the inductor-capacitorconverters supplying 3-phase IMs have been presented.Physical insight into the operation and performance ofthe mo tor-converter set was obtained.

A circuit for the detection of the negativesequence voltage was presented and used to switch inthe run capacitance. This avoided the use of a slipdetector or centrifugal switch.

The steady-st ate derating of the machine waspresented when fed from a CC OK a ACC. Unbalance inthe terminal voltages or currents could be used todetermine the derating.Finally the start-u p results of the IM when fedfrom a 3-phase supply, a CC and an ACC were presented.It was shown that the run-up time was increased whenthe CC or ACC was used. This indicates a more onerousoperation of the motor as well as associated equipmentconnected to the motos's bus.

ACKNOWLEDGEMENTSThe authorswith measurement of the motor parameters.acknowledge the assistance of D.J.Whitley

REFERENCES[ l ] R.Habermann, "Single phase operation of a 3-phasemotor with a simple static phase conve rter", AIEETransactions, August 1 954, pp 833-837.[2] J.E. Brown and C.S.Jha, "The starting of a threephase induction motor connected to a single -phas esupply system", Proc.IEE, April 1959, pp 183-190.[3] K.A.Ahmed, A.M.Osheiba and M.A.Rahman, "Dynamicperformance o f a three phase induction motor fed froma single phase sup ply", IEEE IAS Annual Meeting, 1989,(41 S . S . Murthy, G.J.Berg, B.Singh, J.S.Jha andB.P.Singh, "Transient analysis of a three phaseinduction motor with single phase supply", IEEETrans., vol. P AS-10 2, No. 1, January 1983.[ 5 ] A.H.Maggs, "Single-phase to three-phase conversionby the Ferraris-A rno system", Proc IEE[6] A.L. Mohamadein, A.Al-Ohaly and A.Al-B ahrani, "Onthe choice of phase balancer capacitance for inductionmotors fed from a single phase supply ", IEEE Tran s.,[7] P.G.H olmes , "Single to 3 phase transient phaseconversion in induction motor drives", Proc IEE, vol132, Pt. B, No. 5, Sept 1985, pp 289-296.[8] C.F.Wagner and R.D.Evans, "Symmetrical componentsas applied to the analysis of unbalanced circuits".

pp 137-146.

V O ~EC-2, No.3, pp 458-464.

L + --.+ - - * --+ -.-- --. ---,AFigure 19 Startup speed from a ACC converter.

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