postfault operation of an asymmetrical six-phase induction machine with single and two isolated...

5406 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 10, OCTOBER 2014

Postfault Operation of an Asymmetrical Six-PhaseInduction Machine With Single and Two Isolated

Neutral PointsHang Seng Che, Mario J. Duran, Emil Levi, Fellow, IEEE, Martin Jones, Wooi-Ping Hew, Member, IEEE,

and Nasrudin Abd. Rahim, Senior Member, IEEE

AbstractThe paper presents a study of postfault control foran asymmetrical six-phase induction machine with single and twoisolated neutral points, during single open-phase fault. Postfaultcontrol is based on the normal decoupling (Clarke) transformation,so that reconfiguration of the controller is minimized. Effect of thesingle open-phase fault on the machine equations under this controlstructure is discussed. Different modes of postfault operation areanalyzed and are further compared in terms of the achievabletorque and stator winding losses. Validity of the analysis is verifiedusing experimental results obtained from a six-phase inductionmotor drive prototype.

Index TermsFault-tolerant operation, multiphase machines,variable-speed drives.

I. INTRODUCTION

ONE important advantage of a multiphase machine overits three-phase counterpart is its higher fault-tolerance[1]. Hence, fault-tolerant operation and control are importantresearch topics in this area. Although fault tolerance can beachieved via special machine design [2][6] and the use ofapplication-specific converter topologies [7][10], the majorityof studies [11][26] focus on the postfault control methods forn-phase machines driven by an n-leg voltage source converter(VSC), since this is the most common topology in practice.The discussion here follows this common trend, assuming star-connected stator windings.

Among multiphase machine, those with multiple three-phasewindings, such as six-, nine-, and twelve-phase machines, areoften considered for various applications. Compared with multi-phase machines with prime phase numbers, machines with mul-tiple three-phase windings can benefit from the well-establishedthree-phase technology. Due to the existence of the multiple

Manuscript received September 30, 2013; accepted November 15, 2013. Dateof current version May 30, 2014. Recommended for publication by AssociateEditor F. W. Fuchs.

H. S. Che, W.-P. Hew, and N. A. Rahim are with the Power EnergyDedicated Advanced Center, Wisma R&D, University of Malaya, 59990Kuala Lumpur, Malaysia (e-mail: [email protected]; [email protected];[email protected]).

M. J. Duran is with the Department of Electrical Engineering, University ofMalaga, 29071 Malaga, Spain (e-mail: [email protected]).

E. Levi and M. Jones are with the School of Engineering, Technology andMaritime Operations, Liverpool John Moores University, Liverpool L3 3AF,U.K. (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2293195

Fig. 1. Stator winding magnetic axes in an asymmetrical six-phase machinewith (a) single and (b) two neutral points (positive direction is clockwise).

winding sets, the machine can be configured with single ormultiple neutral points. Fig. 1 shows the connections of statorwindings for an asymmetrical six-phase machine with singleand two neutral points. Each possibility has its own merits. Forinstance, configuration of a six-phase machine with two iso-lated neutrals prevents the flow of zero-sequence currents andreduces the required number of current controllers from five tofour. In addition, it provides isolation between the two wind-ings and allows better dc-bus voltage utilization. On the otherhand, single isolated neutral point connection gives five insteadof four degrees of freedoms, which provides better means forfault-tolerant operation. However, it requires and additional con-troller for regulating the zero-sequence current. Hence, in the lit-erature, discussion on healthy operation of six-phase machinesis usually based on two isolated neutrals, while fault-tolerantcontrol studies are typically based on single neutral connec-tion [12], [13], [20], [27].

The simplest postfault strategy for multiphase machines withmultiple three-phase windings is to disable the whole three-phase winding containing the faulty phase [1]. Such operationhas been reported in [28] for aircraft steering control and in [29]for an elevator application. This approach is addressed as sin-gle VSC operation hereafter, for the specific case of a six-phasedrive. Instead of disabling the whole three-phase winding, whichcauses significant reduction in achievable power/torque, betterperformance can be obtained via suitable postfault control. Suchcontrol has been discussed in [12], [13], [20], and [27], with thesix-phase machine configured with single isolated neutral. Dis-cussion on fault-tolerant control of a six-phase machine with twoisolated neutrals is available in [22] and [23], but is accompa-nied with only simulation studies and very limited experimental

0885-8993 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

CHE et al.: POSTFAULT OPERATION OF AN ASYMMETRICAL SIX-PHASE INDUCTION MACHINE 5407

verification. A more complete study for two-neutral configu-ration was reported in [24], where suitable postfault controlstrategy was shown to give better efficiency than single VSCoperation. However, the control uses PI controllers to regulateac references, which results in poor performance. So far, a com-prehensive discussion covering both configurations has not beenreported.

This paper aims to provide a unified discussion on the post-fault control of a six-phase induction machine during singleopen-phase fault, by considering both single and two isolatedneutrals configurations. The focus is on asymmetrical six-phaseinduction machine (with two three-phase windings spatially dis-placed by 30) with distributed windings. The discussion pre-sented here differs from previous works in the following aspects:

1) The postfault control uses normal (i.e., not a reduced or-der) decoupling transformation, which allows the use ofthe same controller structure as in the healthy operation.Such control has been discussed in [16] and [21], but notfor an asymmetrical six-phase machine.

2) A unified analysis of postfault control of the six-phase ma-chine, considering both single and two isolated neutrals, ispresented. Results show that the same controller structureis applicable for both configurations, requiring only minoralterations. Quantitative comparisons between the two, interms of the achievable torque and stator winding lossesunder different modes of postfault control, are presentedas well.

The paper is organized as follows. Section II describes themachine equations and control structure of a healthy six-phaseinduction machine. Section III shows the influence of fault onmachine equations when the same decoupling transformationis maintained. Section IV discusses the derivation of currentreferences for different modes of postfault operation. Deratingof the machine is also detailed here. Next, Section V discussesthe current controllers used, and the modifications for postfaultoperation. Experimental verification of the analysis, based ona prototype asymmetrical six-phase induction motor drive, ispresented in Section VI. Finally, concluding remarks are givenin Section VII.

II. MACHINE EQUATIONS AND CONTROL STRUCTURE FORHEALTHY MACHINE

Control of a healthy asymmetrical six-phase induction ma-chine is usually based on the vector space decomposition (VSD)model. Using the VSD model, the machine phase variables [fk ]are related to the new variables [fxy ] via decoupling transfor-mation [T6] (f represents arbitrary machine variables (voltagev, current i or flux ))

[fxy ] = [T6 ] [fk ] (1)

where

[fk ] = [ fa1 fb1 fc1 fa2 fb2 fc2 ]T

[fxy ] = [ f f fx fy f0+ f0 ]T (2)

[T6 ] =13

x

y

0+

0

1 12

12

32

32

0

032

32

12

12

1

1 12

12

32

32

0

0 32

32

12

12

1

1 1 1 0 0 0

0 0 0 1 1 1

.

(3)

For an induction machine with sinusoidally distributed wind-ings and negligible mutual leakage inductance between thethree-phase windings, the machine stator equations in the sta-tionary common reference frame are

vs =(Rs + Ls

d

dt

)is +M

d

dtir

vs =(Rs + Ls

d

dt

)is +M

d

dtir

vxs =(Rs + Lls

d

dt

)ixs

vys =(Rs + Lls

d

dt

)iys

v0+s =(Rs + Lls

d

dt

)i0+s

v0s =(Rs + Lls

d

dt

)i0s (4)

while the rotor equations are

0 =(Rr + Lr

d

dt

)ir + rLr ir +M

d

dtis + rMis

0 =(Rr + Lr

d

dt

)ir rLr ir +M

d

dtis rMis

(5)

where Ls = Lls + 3Lms, Lr = Llr + 3Lms,M = 3Lms , andr is the rotor electrical speed (r = pm , p being the pole pairnumber; m is the rotor angular mechanical speed). Subscriptss and r denote stator and rotor variables, respectively.

For a machine with sinusoidally distributed windings, onlythe components contribute to flux and torque production.As in the three-phase case, rotational transformation [D] canbe used to transform components into the general syn-chronous reference frame dq components (s is the angle oftransformation, which will subsequently be equal to the rotorflux position)

[D] =[

cos s sin s sin s cos s

]. (6)

Indirect rotor flux oriented control (IRFOC) is achieved by us-ing s =r , where rotor flux angler is obtained from measured


Fig. 2. Control structure for IRFOC of a six-phase induction machine.

rotor position (or speed m ) and reference dq stator currents.The controllers structure for IRFOC of a six-phase inductionmachine is shown in Fig. 2. References for ixs , iys , i0+s , andi0s are normally set to zero, to minimize stator copper losses.

Regardless of the neutral point connection (single or twoisolated neutrals), the same controller structure can be used,with a difference that for the two isolated neutrals the zero-sequence current controllers are, since i0+s and i0s cannotflow, disabled by setting v0+s = v

0s = 0.

III. MACHINE EQUATIONS FOR POSTFAULT OPERATION

The fault considered here is an open-phase fault that opencircuits the connection between one of the VSCs legs and themachine. It is assumed that the machines phase winding is notdamaged during the fault.

When an open-phase fault occurs, the corresponding phasecurrent becomes zero, and the machine loses one degree of free-dom. Some of the previous works [11][14] approached theproblem by utilizing new reduced-order decoupling transfor-mations to reflect the loss of one degree of freedom. However,the machine equations obtained from the reduced-order trans-formation have different machine parameters and substantialreconfiguration of the controller is required.

To minimize changes to the control, it appears to be better toretain the same decoupling transformation ([T6] in this case), sothat the same controller structure can be used. Such control hasbeen presented for a seven-phase PM machine in [16], and laterextended for induction machines with odd numbers of phasesin [21]. However, discussions in [16] and [21] only cover theeffect of fault on machines MMF and do not address the changesin machine equations as a whole, which is done here next.

A. Effect of Fault on Machine Equations

If the transformation of machine equations from phase vari-ables to the stationary reference frame variables is analyzed, itis obvious that (4), (5) need not be changed because the ma-chine is not physically affected by the fault. The main effect ofthe open-phase fault is on the currents, where xy0+0components are no longer mutually independent due to the loss

of one degree of freedom. Hence, it is necessary to find thecurrents relationship during fault and the subsequent effects onthe machine equations.

For the purpose of discussion, it is assumed that open-circuitfault occurs in phase-c2, so that ic2 is zero. The , x, and 0+currents, which do not contain phase-c2 term, remain unaffectedby this fault. However, the equations for , y, and 0- currentsare affected and they become

is =13

(32

ib1s 32

ic1s +12ia2s +

12ib2s

)

iys =13

(32

ib1s +32

ic1s +12ia2s +

12ib2s

)

i0s =13(ia2s + ib2s) . (7)

These are the general expressions that are valid regardless ofhow the neutral points are configured.

For two isolated neutrals, the phase currents in each three-phase winding must sum to zero (i0+s = i0s = 0). Hence,when ic2s = 0, ia2s = ib2s , and (7) simplifies to

iys = isi0s = 0. (8)

Since i0+s = i0s = 0 and is is now directly related to iys ,the machine practically has only three degrees of freedom (,, and x) during the single open-phase fault.

Note that there are no changes in the equations for andx components (4). Also, the zero-sequence voltage equations in(4) can be discarded because i0+s = i0s = 0. However, as iysand is are no longer mutually independent, the stator y-axisequation is now

vys =(Rs + Lls

d

dt

) iys =

(Rs + Lls

d

dt

) is . (9)

If the machine is configured with single neutral point, thefollowing relation can be derived:

i0s =13(ia2s + ib2s) = is + iys

i0+s = i0s . (10)

The main difference compared with the two-neutral point caseis that iys is now an independent variable, giving the systemfour degrees of freedom (, , x, and y).

Machine equations for and xy components remain thesame as in (4) and (5). Due to the single neutral point connec-tion, zero-sequence currents can now flow. They are, however,dependent on is and iys due to the fault, as shown in (10). Asa result, the corresponding stator voltage equations are now

v0+s =(Rs + Lls

d

dt

)i0+s =

(Rs + Lls

d

dt

)(is + iys)

v0s =(Rs + Lls

d

dt

)i0s =

(Rs + Lls

d

dt

)(is + iys).

(11)


B. Effect on Torque Equation

The postfault torque equation can be obtained by consideringthe following phase variable equation:

Te = p [iks ]T d

dr[Lsr ] [ikr ] (12)

where r is the rotor position angle and [Lsr ] is the rotor-to-stator inductance matrix.

Since the machine is physically the same, [Lsr ] is consideredto be unaffected by the fault. This also implies that even thoughic2s cannot flow, voltage can still be induced in phase-c2 (ina form of back EMF) due to the variation in stator and rotorcurrents.

By transforming (12), the torque equation during fault resultsin the same form as for the healthy machine

Te = pM (ir is ir is) . (13)This is actually a similar conclusion to the one in [16] and

[21].

C. Conclusion on Postfault Machine Equations

Three important conclusions can be drawn from the postfaultmachine equations based on [T6]:

1) The equations, which are responsible for flux andtorque production, remain unchanged even after the fault.Hence, no modifications of machine parameters are re-quired in the implementation of FOC, unlike in [11][14],where reduced-order transformations are used.

2) The y or zero-sequence components are no longer inde-pendent during fault, as shown by (8) and (10). For ahealthy machine, these current components are usuallycontrolled to zero for loss minimization. However, duringthe fault, an attempt to control them to zero will cause dis-ruption in the current regulation. Hence, the currentreferences need to be adapted during fault.

3) The torque equation is not affected by the fault, as indi-cated in (13). Thus, for smooth torque during fault, the stator current references should take the followingform:

is = |I | cos (st)is = |I | sin (st) . (14)

Based on (14), the trajectory of the postfault statorcurrent vector (i = is + jis) should be circular, justlike in the case of a healthy machine.

IV. POSTFAULT OPERATION

A. Derating Factor

If the faulted machine is to generate rated flux and torque,the phase currents will increase above their rated values. Pro-longed operation with such higher than rated phase currents ishazardous as it may violate the thermal limit of the machineand power electronic converter. Hence, for continuous postfaultoperation, the machine should be derated, i.e., run below ratedvalues. This is not a problem for applications like traction and

offshore wind generation, where operation at rated power is notcompulsory and the need for prolonged postfault operation ishighly likely.

To illustrate the amount of derating required, a variabletermed derating factor, a, is considered in the following dis-cussion. The derating factor is the factor by which the flux and/ortorque currents |I | need to be scaled down for derated oper-ation. This variable is defined as the ratio of the postfault (or dq) currents magnitude to the prefault current magnitude(rated phase current rms is denoted by In )

a =|I |post fault

|I |n=

|Idq |post fault|Idq |n

=|Idq |post fault

6In. (15)

A derating factor of 1 implies that the machine is not deratedand is producing rated flux and torque. For any value a < 1,the machine operates with lower than rated flux and/or torquecurrent, and is considered to be derated. While currentmagnitude is important in determining the flux and torque of themachine, it is however the phase current amplitude that needs tobe limited. Thus, a threshold derating factor, ao is defined hereas the derating factor required to keep the maximum postfaultphase current equal to the rated value. The relation betweenmaximum peak postfault phase current and rated phase currentis hence given by

ao = a2In

max(iphase post fault)=

|Idq |post fault3max(iphase post fault)

.

(16)Since the postfault machine equations have identical form as

in the prefault case, the torque equation can be expressed interms of the dq currents, assuming RFOC, as

Te = pM 2

Lridsiqs . (17)

When the fault happens, it may be necessary to derate themachine by reducing the ids and iqs , to keep the maximumphase current within acceptable limits. If both ids and iqs arescaled down by factors ad and aq , respectively, the achievabletorque in terms of rated torque is given by expression

Te post fault = adaqTen . (18)

The achievable torque in derated operation depends on howids and iqs are scaled down. Here, it is suggested to keep ids atrated value, and only derate iqs (ad = 1 and aq < 1) to keep thephase current amplitude at rated, so that

Te post fault = aqTen . (19)

The influence of aq on the overall reduction of the dq currentmagnitude (which is also the derating factor a) is given with

a =

i2dsn + a2q i2qsni2dsn + i2qsn

. (20)

The expressions in (19) and (20) indicate that the achievabletorque during postfault operation depends on the ratio idsn /iqsn .For a special case of idsn /iqsn = 0, applicable to a permanentmagnet machine, the postfault torque varies linearly with a. Foran induction machine, the variation in torque is nonlinear when


the machine is derated with a higher idsn /iqsn ratio giving a morerapid reduction in achievable torque during derated operation.This will be confirmed later in the experimental results.

B. Modes of Operation

While the (dq) stator currents determine the flux andtorque of the machine, the other current components provideadditional degrees of freedom which define the mode of post-fault operation. For this purpose, the xy currents are defined inthe following general form:

ixs = K1is +K2i

s

iys = K3is +K4i

s . (21)

The values of K1 ,K2 ,K3 , and K4 can be chosen based on thedesired modes of operation. In this paper, two different modesof operation are considered, i.e.,

1) Min LossCoefficients are selected to minimize the copper loss in the

stator windings, which is defined as

Ploss = Rs(i2a1s + i

2b1s + i

2c1s + i

2a2s + i

2b2s + i

2c2s

)

= Rs(i2s + i

2s + i

2xs + i

2ys + i

20+s + i

20s

). (22)

This is equivalent to minimizing (i2xs + i2ys + i

20+s + i

20s),

i.e., the sum of squared current components that do not con-tribute to flux and torque production.

2) Max TorqueCoefficients are selected to produce the largest |I | (hence

the maximum torque) with the maximum phase current ampli-tude maintained at the rated value. This is equivalent to findingthe coefficients that give the highest value of ao .

The phase currents are related to the VSD variables via theinverse decoupling transformation [T6 ]1 :

[iks ] = [T6 ]1 [ixys ]T . (23)

The relationship between stator phase and currents can beobtained by substituting (8) and (21) or (10) and (21), for twoand single isolated neutral points, respectively, into (23) and

Fig. 3. Threshold derating factor (in %) as a function of K1 and K2 , forasymmetrical six-phase induction machine with two isolated neutrals.

rearranging the expression. Hence, for two isolated neutrals

ia1s

ib1s

ic1s

ia2s

ib2s

=

13

1 +K1 K2

12(1 +K1)

3 1

2K2

12(1 +K1)

3 1

2K2

32

(1K1) 32

K2

32

(1K1)32

K2

[is

is

]

(24)while for a single isolated neutral (25) is obtained, as shown atthe bottom of this page.

The relationship between the coefficients and the thresholdderating factor can be obtained by iteratively varying the co-efficients based on (24) and (25). Fig. 3 shows the plot of aoagainst K1 and K2 for the machine with two isolated neutrals.The coefficients and threshold derating factors that define dif-ferent modes of postfault operation with different neutral pointconfigurations are summarized in Table I. Using the coefficientslisted in Table I, the theoretical mean stator winding losses fordifferent modes of postfault operation can be calculated basedon (22). The losses, normalized with respect to the stator wind-ing loss of the healthy machine, are given in Table II. These

ia1s

ib1s

ic1s

ia2s

ib2s

=

13

1 +K1 K3 1 +K2 K4

12 K1

2(

32

+ 1

)K3

32

1 K22

(

32

+ 1

)K4

12 K1

2+

(32

1)K3

32

1 K22

+

(32

1)K4

32

3K12

+3K32

32

3K22

+3K42

32

+3K12

+3K32

32+

3K22

+3K42

[is

is

]. (25)


TABLE ISUMMARY OF COEFFICIENTS FOR DIFFERENT MODES OF POSTFAULT

OPERATION (OPEN-PHASE FAULT IN PHASE-C2)

TABLE IINORMALIZED MEAN STATOR WINDING LOSSES FOR DIFFERENT MODES OF

POSTFAULT OPERATION

TABLE IIISUMMARY OF COEFFICIENTS FOR DIFFERENT MODES OF POSTFAULT

OPERATION (OPEN-PHASE FAULT IN PHASE-a1)

losses are calculated assuming a = 1 (without derating), thusthe losses can go up to as high as twice the nominal value.

All the discussions and derivations so far were based onthe open-circuit fault in phase-c2. Using the same principles,a set of machine equations that are similar to those presented inSection III can be obtained for fault in phase-a1. Instead of hav-ing coupling between , y, and 0 components, the couplingnow exists between , x, and 0+ components.

Corresponding coefficients for postfault operation can be ob-tained from Table I, by swapping with , y with x, and 0with 0+ components. The results are shown in Table III. Notethat the result obtained for Max Torque mode of single isolatedneutral case is identical to the one given in [22].

Due to the symmetry of the phases within each three-phasewinding, the results in Tables I and III can be made readilyapplicable to other phases by reordering the phase sequence.For fault that occurs in phase-a1, b1 or c1, postfault strategy forphase-a1 can be adopted; for fault in phase-a2, b2 or c2, thestrategy developed for phase-c2 can be used with correspondingphase rearrangement.

V. CONTROLLER FOR POSTFAULT OPERATION

In order to maintain the same controller structure for bothhealthy and faulted operation (as in Fig. 2), it is necessary tochoose appropriate current controllers. For an n-phase machine,supplied using an n-leg VSC, the inverters leg voltages and ma-chine phase voltages are no longer related by a constant matrixduring fault [11]. Instead, neutral point voltage of the statorwinding is influenced by the back-EMF voltage of the faulted

Fig. 4. Current controllers of a six-phase induction machine. Red dotted boxshows the negative sequence PI controller which is only activated during fault.

phase [15]. This introduces disturbance in the form of negativesequence voltage in plane. To overcome this disturbance,dual PI controller is used for dq current control during fault, asshown in Fig. 4. The negative sequence PI controller (dotted redbox) is only activated during fault. For the xy currents, sincetheir references can be ac quantities, dual PI controller is used(see Fig. 4) to enable effective regulation of the xy currents.

From (9) and (11), it appears that, during the fault, there is anoverlapping controller action for, y, and zero-sequence currentcontrollers due to the coupling of the components. However,this is not the case because connection of phase-c2 is lost duringthe fault, and vys (v0+s and v0s , respectively) is no longercontrollable by the VSC for the two (single) isolated neutralscase. To reflect the loss of the degree of freedom on control,y (zero-sequence, respectively) current controller is disabledduring the fault for the two (single) isolated neutral case, bysetting vys = 0 (v0+s = v0s = 0). Note that the zero-sequencecurrent controllers are only enabled during healthy operation ofthe machine with single neutral point connection.

As noted, the current control structure is shown in Fig. 4. Theoverall control structure remains unchanged and as in Fig. 2,with no modifications of the machine parameters or transforma-tion matrix. Transition from healthy to postfault operation in-volves enabling of the negative sequence PI current controllersin the d-q path, and disabling of y and/or zero-sequence currentcontrollers depending on the neutral point configuration.

VI. EXPERIMENTAL RESULTS

The experimental results were all obtained for the fault inphase-c2. The tests are conducted on a prototype six-pole asym-metrical six-phase induction machine, which is obtained byrewinding a 1.1 kW, 50-Hz three-phase machine. The machineis controlled in speed control mode with IRFOC. A dc machine,


TABLE IVEXPERIMENTAL SYSTEM PARAMETERS

controlled using ABB DCS800 drive, is coupled to the six-phase machine and functions as a variable load. The machine,converter, and control parameters used in the experiments aredetailed in Table IV.

A six-leg VSC is used to control the six-phase machine.Switching frequency is selected as 2 kHz, and the currents aresampled at twice the switching frequency. Carrier-based pulsewidth modulation is used, without any zero-sequence injection.The control is implemented using DS1006 dSpace system withControlDesk control environment. Experimental data, displayedin this section, are obtained by using the data capture functionin ControlDesk and processed using MATLAB. The results,presented here, focus only on the steady-state behavior of themachine under different modes of operation. The dynamic per-formance of the machine, including transition from healthy tofaulted operation, is beyond the scope of this paper.

A. Healthy Operation

Fig. 5(a) shows the operation of the healthy asymmetrical six-phase machine when running at 250 r/min with no load. Syn-chronous PI current controllers (only the positive sequence part)are used for dq current regulations, while dual PI controllersare used for controlling the xy currents, with ixs = i

ys = 0.

As seen from the figure, the phase currents are a balanced set ofsinusoidal signals, while the current space vector describesa circular trajectory. The xy currents are controlled to zero tominimize losses. Under such healthy operation, the machinesspeed is regulated at 250 r/min, with slight oscillations causedby the mechanical imperfections.

B. Single Open-Phase Fault

Single open-phase fault is emulated by removing the connec-tion from VSC to phase-c2. Fig. 5(b) shows the correspondingoperation of the machine without any modification to the currentreferences and the controllers. Since iys is still set to zero, thecontroller tries to minimize iys . This causes the disruption ofthe current due to the coupling between stator y and com-ponents. Instead of being regulated to the proper reference, current is now almost zero. As a result of the improper control,the machines speed shows significant oscillations.

Fig. 5(c) illustrates the case when the faulted machine op-erates with single active VSC. With connections to winding-a2b2c2 open-circuited, the machine is practically a three-phasemachine with two degrees of freedom, and only currentscan be controlled. Hence, the xy current controllers are dis-abled by setting vx = v

y = 0. The currents now track their

references well, producing a circular trajectory that is the sameas in the healthy case. The machine now operates with constantspeed identical to that of the healthy machine. Even though thisprovides a simple means of postfault control, the phase cur-rent amplitude in the remaining phases has now doubled. Aswill be shown later, better performance in terms of achievabletorque and stator losses can be obtained using postfault controlstrategies discussed in Section IV.

C. Postfault Operation (Two Isolated Neutrals)

Fig. 6 shows the postfault operation of the machine, con-figured with two isolated neutrals. The , , and x cur-rents are now regulated with dual-PI controllers, while y andzero-sequence current controllers are disabled (vys = v

0+s =

v0s = 0). Fig. 6(a) and (b) shows the Min Loss and MaxTorque modes of postfault operation, respectively. For the MinLoss mode, the phase currents in the remaining five phases haveunequal amplitudes. For the Max Torque mode, currents onlyflow in four of the remaining five phases, and all have the sameamplitude. It can be observed that the maximum phase currentamplitude in Max Torque mode is slightly lower than that ofthe Min Loss mode, which is in agreement with the theoreticalanalysis in Section IV (regarding the values of ao ). Despite thedifference in phase current waveforms, both modes of operationhave their currents well regulated to the references and themachines speed remains practically constant, as in the healthycase. The maximum phase current amplitudes for both modesare also lower than in the single VSC mode, suggesting abetter performance.

D. Postfault Operation (Single Isolated Neutral)

Postfault operation of the six-phase machine configured withsingle isolated neutral point is depicted in Fig. 7, with Fig. 7(a)and (b) showing Min Loss and Max Torque mode, respectively.The controller structure is the same as used for the two neutralscase. As discussed in Section V, all four , , x, and y currentsare controlled, so only zero-sequence current controllers aredisabled (v0+s = v

0s = 0).

Similar to the two neutrals case, the currents are wellregulated under both modes and the machine runs at constantspeed without obvious oscillations. For the Min Loss mode,the phase currents in the remaining five phases have differentamplitudes, with the maximum phase current amplitude slightlyhigher than in the previous section. On the other hand, operationin Max Torque mode yields phase currents of the same amplitudeflowing in all the five remaining phases. The maximum phasecurrent amplitude under this mode is found to be the lowestamong all the discussed modes.


Fig. 5. Stator phase currents, currents (blue trace = i ; green trace = i ), xy currents (blue trace = ixy , green trace = ixy ) and speed (blue trace

= m , green trace = m ) for (a) healthy machine and faulted machine (b) without modifications of current references(ix = i

y = 0), (c) with single VSC

operation (winding-a2b2c2 disconnected). The machine is configured with two isolated neutrals and operates at 250 r/min without load.

Fig. 6. Stator phase currents, currents (blue trace = i ; green trace = i ), xy currents (blue trace = ixy , green trace = ixy ), and speed (blue trace =

m , green trace = m ) for faulted machine configured with two isolated neutrals, and controlled using (a) Min Loss and (b) Max Torque mode. The machineoperates at 250 r/min without load.

E. Derated Operation

So far, the results given in Sections VI-AD only show thatdifferent modes of postfault operation can be achieved usingthe current references and controllers discussed in Sections IV

and V. Next, the performance in different modes is compared interms of the achievable torque and stator winding losses.

Fig. 8 shows the relationship between the normalized max-imum phase current amplitude and the normalized torque,


Fig. 7. Stator phase currents, currents (blue trace = i ; green trace = i ), xy currents (blue trace = ixy , green trace = ixy ), and speed (blue trace =

m , green trace = m ) for faulted machine configured with single isolated neutral, and controlled using (a) Min Loss and (b) Max Torque mode. The machineoperates at 250 r/min without load.

Fig. 8. Experimental () and theoretical (solid line) plot of the normalizedmaximum phase current against normalized torque for the asymmetrical six-phase induction machine operating under different postfault operation modes(idsn /iq sn = 0.294).

obtained based on (16), (19), and (20). With this plot, the achiev-able torque for different modes can be compared. As discussedearlier, the postfault torque varies as the machine is derated. Forsingle VSC mode, the maximum achievable torque at ratedphase current is found to be only approximately 43% of its ratedvalue. As emphasized in Section IV, this depends on the ratioidsn /iqsn of the machine, which in this case is 0.294. This isdifferent from a six-phase permanent magnet machine, where50% of the rated torque remains for single VSC operation.Better performance can be obtained if the machine is controlledin Min Loss or Max Torque mode with two isolated neutrals,giving around 50% and 53%, respectively. The improvement

Fig. 9. Instantaneous (dotted lines) and theoretical mean (solid lines) of thenormalized stator winding losses, for healthy and faulted asymmetrical six-phaseinduction machine under different modes of postfault operation (the theoreticalmeans for single VSC and Max Torque (two neutrals) overlap).

provided by Max Torque is only marginal compared to MinLoss mode and the advantage in terms of additional torque canbe easily outweighed by the increase in stator losses, as dis-cussed shortly. Finally, the achievable torque is significantlyimproved, to approximately 66% of the rated value, when op-erating in Max Torque mode with single isolated neutral. Thenormalized stator losses of the faulted machine under differ-ent modes of operation are shown in Fig. 9. For each modeof operation, the phase currents of the machine under no-loadcondition are measured and transformed to the decoupled vari-ables using transformation [T6]. The stator winding losses arethen calculated based on (22) and normalized using the meanstator winding loss for healthy case. The experimental results


(dotted lines) are in full accordance with the theoretical mean(solid lines) values shown in Table II. In terms of stator losses,Min Loss mode for the machine with single neutral gives thebest performance. On the other hand, the Max Torque mode inconfiguration with two neutrals gives the worst performance,with mean stator winding losses being twice higher than for thehealthy case. This is the same as operating the faulted machinein single VSC mode. For the machine configured with twoisolated neutrals, Min Loss mode gives lower stator windingloss, which is 25% lower than in the Max Torque mode. Con-sidering that the difference of achievable torque between thetwo modes is small (only approximately 3%), Min Loss modeis more favorable mode of operation for the configuration withtwo neutrals.

Overall, the experimental results clearly show that, in an eventof a fault, single isolated neutral configuration is significantlybetter than two isolated neutrals case, both in terms of achievabletorque and stator loss minimization. Nevertheless, if configura-tion with two isolated neutrals is required, say, for safety orelectrical isolation purposes, it is better to operate the machineunder Min Loss mode.

VII. CONCLUSION

This paper analyzes postfault operation of an asymmetricalsix-phase induction machine, configured with single and twoisolated neutrals. Using the same decoupling transformation, theeffects of a single open-phase fault on the machine equations areaddressed. It is pointed out that the fault only affects the mutualrelationship between axis current components, so that the samemachine equations, based on healthy decoupling transformation[T6], can still be used for postfault control. Regardless of theneutral point connection, the same controller structure can stillbe used, with only minor modifications of current referencesand the enabling/disabling of the controllers.

Based on the decoupling transformation [T6] and the currentcomponent interdependencies during the fault, different modesof postfault operation have been analyzed. The performance ofthese different modes of control, in terms of achievable torqueand stator losses, has been compared, with an overall conclu-sion that better postfault behavior results for the single isolatedneutral configuration.

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Hang Seng Che received the B.Eng. degree in electri-cal engineering from the University of Malaya, KualaLumpur, Malaysia, in 2009. He received the Ph.D. de-gree under auspices of a dual Ph.D. program betweenthe University of Malaya and Liverpool John MooresUniversity, Liverpool, U.K., in 2013.

He is currently a Postdoctoral Research Fel-low at Power Energy Dedicated Advanced Center(UMPEDAC), University of Malaya. His researchinterests include multiphase machines, fault tolerantcontrol, and renewable energy.

Dr. Che received the 2009 Kuok Foundation Postgraduate Scholarship Awardfor his Ph.D. study.

Mario J. Duran was born in Malaga, Spain, in 1975.He received the M.Sc. and Ph.D. degrees in electricalengineering from the University of Malaga, Malaga,Spain, in 1999 and 2003, respectively.

He is currently an Associate Professor with theDepartment of Electrical Engineering, University ofMalaga. His research interests include modeling andcontrol of multiphase drives and renewable energyconversion systems.

Dr. Duran received the Best Paper Award from theIEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

in 2009.

Emil Levi (S89M92SM99F09) received theM.Sc. and Ph.D. degrees from the University ofBelgrade, Belgrade, Yugoslavia, in 1986 and 1990,respectively.

From 1982 till 1992, he was with the Departmentof Electrical Engineering, University of Novi Sad. Hejoined Liverpool John Moores University, U.K., inMay 1992 and since September 2000 has been a Pro-fessor of Electric Machines and Drives. He serves asthe Co-Editor-in-Chief of the IEEE TRANSACTIONSON INDUSTRIAL ELECTRONICS, as an Editor of the

IEEE TRANSACTIONS ON ENERGY CONVERSION, and as an Editor-in-Chief ofthe IET Electric Power Applications.

Dr. Levi received the Cyril Veinott Award of the IEEE Power and EnergySociety for 2009.

Martin Jones received the B.Eng. degree (First ClassHons.) in electrical engineering from the LiverpoolJohn Moores University, Liverpool, U.K., in 2001,and the Ph.D. degree in 2005.

He received the IEE Robinson Research Scholar-ship for Ph.D. studies. He is currently a Reader withLiverpool John Moores University. His research in-terest includes the area of high performance ac drives.

Wooi-Ping Hew (M06) received the B.Eng. andMasters degrees in electrical engineering from theUniversity of Technology, Malaysia. He received thePh.D. degree from the University of Malaya, KualaLumpur, Malaysia in 2000.

He is currently a Professor in the University ofMalaya Power Energy Dedicated Advanced Center(UMPEDAC), University of Malaya, Kuala Lumpur,Malaysia, where he is also the Director of centre. Hisresearch interests include electrical drives and elec-trical machine design.

Dr. Hew is a Member of IET and a Chartered Engineer.

Nasrudin Abd. Rahim (M89SM08) received theB.Sc. (Hons.) and M.Sc. degrees from the Univer-sity of Strathclyde, Glasgow, U.K., and the Ph.D. de-gree from Heriot-Watt University, Edinburgh, U.K.,in 1995.

He is currently a Professor with the Faculty ofEngineering, University of Malaya, Kuala Lumpur,Malaysia, where he is also the Director of the PowerEnergy Dedicated Advanced Center.

Prof. Rahim is a Fellow of the IET, U.K., and theAcademy of Sciences Malaysia.

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