Rating Issues in Fault Tolerant PMSM

Tsarafidy Raminosoa, Chris Gerada, Nazri Othman

Department of Electrical and Electronic Engineering, The University of Nottingham,

University Park, Nottingham, NG7 2RD, UK E-mail of Corresponding Author: Chris.Gerada@nottingham.ac.uk,

Telephone: +44 (0) 115 846 6117

Abstract- The necessary reliability of a safety critical drive

system is often partly achieved by using fault tolerant electrical machines. Although there are various degrees as to what types of faults and to the duration the machine has to tolerate, these generally include open and short circuit winding faults. There are numerous published literatures on the design of fault tolerant machines as well as on control algorithms used to maintain drive operation with an incurred fault. This paper is set to look at the effects of various fault tolerant control methods on the losses in three and five phase surface mount Permanent Magnet (PM) machines when in fault tolerant operation in order to be able to choose the correct rating for such conditions.

I. INTRODUCTION

In a fault tolerant machine, when a phase is disabled as a consequence of an open circuit or short circuit fault the remaining phase currents are controlled in such a way to maintain the same pre-fault positive sequence armature rotating field to interact with the fundamental rotor produced field and thus maintain the same average torque as in healthy operation. Considerable work has been done to investigate the best control methodology to obtain smooth torque in faulted operation [1], [2]. However, to the authors’ knowledge, the effect of the fault tolerant control methodology on the machine losses, particularly in the rotor conducting components, has not been analyzed yet. This issue is quite serious since the amount of power loss will limit the torque capability of the machine in fault tolerant operation mode. In faulted operation, the increased armature current and the unbalanced nature of the phase currents and winding distribution give rise to amplified forward and backward rotating harmonic fields. They induce eddy currents in the sleeve and the magnets. As heat removal is particularly difficult from the rotor, the magnets can heat up and experience irreversible demagnetization, thus diminishing the machine power capability. This paper is set to investigate the effects of fault tolerant control on the copper and rotor eddy current losses of three and five phase surface mount PM machines. Towards this aim effective eddy current loss calculation methods will be used.

In this paper an analytical time stepping as well as a current sheet time harmonic model will be presented able to predict the machine losses in fault tolerant operation. FE models will be subsequently used to verify the proposed modelling approaches. The time harmonic method will give an insight into the losses produced by each of the rotating fields produced by the armature MMF in faulty conditions. Within this paper, a

range of 3 and 5-phase surface mount, fault tolerant, permanent magnet machines with various winding configurations will be looked at in terms of their operating losses. The studied machines are summarized in Table I. The effects of various fault-tolerant control strategies on the machine’s losses will then be investigated.

‐6.00E+05

‐4.00E+05

‐2.00E+05

0.00E+00

2.00E+05

4.00E+05

6.00E+05

10 12 14 16 18 20 22 24

Eddy

 Current Den

sity [A

/m2]

time [ms]

Analytic. Time Stepp. FE Transient

(a)

‐1.50E+06

‐1.00E+06

‐5.00E+05

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

0 2 4 6 8 10

Eddy

 Current Den

sity [A

/m2]

time [ms]

Analytic. Time Stepp.

FE Transient

(b)

Figure 1. 3 phase machine (Machine I): Eddy current densities from the time stepping analytical and FE transient models:

(a) External corner of a magnet in healthy operation; (b) One point of the sleeve in healthy operation.

TABLE I

STUDIED MACHINES

Machine Phases Poles Slots Winding Type

I 3 20 24 Double Layer

II 3 16 24 Double Layer

III 5 18 20 Double Layer

1592978-1-4244-4252-2/09/$25.00 ©2009 IEEE

II. ANALYTICAL TIME STEPPING METHOD

This method is based on an analytical magnetostatic time stepping model [3][4]. It being so, the reaction field of the induced eddy currents is not taken into account. This is however a valid and realistic assumption considering that these currents are mostly resistance limited at relatively low excitation frequencies [5][6][7][8]. The eddy currents created by the armature winding field are derived from the vector potential Az(t) in the magnet region. The eddy current density at any point in the magnet cross section is given by:

⎥⎦

⎤⎢⎣

⎡ +∂∂

−= )(1)( tCt

AtJ zm

Eddy ρ (1)

Thus, at any point of the magnet, the waveform of the eddy

current density is obtained from the waveform of the vector potential by performing a numerical time derivation. In (1), ρm is the resistivity of the magnet and C(t) is a time dependant function which has to be chosen to impose a zero net current through the cross section of the considered magnet block [5][7]. Actually, C(t) is the spatial average of (dAz/dt) over the magnet cross section [7][9]. Each magnet block is subdivided into several elements and the waveform of the eddy current losses in this magnet is calculated by (2),

[ ]∑=

=elementsmagnetNbr

kkEddykaxialmnetEddyperMag tJtlP

1

2, )(secρ , (2)

where laxial is the axial length of the machine and sectk the

surface of the k-th element. An identical method is used to calculate the eddy current in

the non-magnetic conducting sleeve forming only one component and also subdivided into several elements.

Fig. 1 (a) and (b) compare the waveforms of the eddy current density in one corner of the magnet and in one point of the sleeve obtained from the proposed time stepping method and that obtained from the FE transient simulation for a 3 phase 24slot-20pole motor in healthy operation.

Fig. 2 compares the eddy current losses in one magnet from the analytical time stepping and FE transient methods for a 5-phase machine. Having validated this method, we will now look at the current sheet time harmonic method.

III. CURRENT SHEET TIME HARMONIC METHOD

This modelling method is based on first identifying the field space harmonics present in the air gap due to the armature currents and then, for each harmonic, calculate the sinusoidal distributed current sheet located in the stator surface reproducing the same magnitude of the airgap radial flux density. Similar approaches have been used in [10], [11] and [12]. These approaches, however, do not account for the discrete magnets or, in other words, for eventual circumferential segmentation. They have also not considered faulted operation with various fault tolerant control strategies.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.5 1.5 2.5 3.5 4.5 5.5

Losses in one

 magne

t [W]

Time [ms]

FE Transient

Analytic. Time Stepp.

Figure 2. 5 phase machine (Machine III): Results from the time stepping analytical and FE transient models: Eddy current losses in one magnet in

healthy operation.

Figure 3. Layout of the current sheet model and distribution of the eddy current density due to the 14th space harmonic for a 24 slots 20 poles machine.

In order to consider an unbalanced winding set only one

phase current is enabled at a time and was set equal to the rated peak value (Im). In this way, all the harmonic content of one phase susceptible to persist in any unbalance FT mode are preserved. Some harmonics cancel out under healthy operation.

Unlike healthy operation, each space harmonic field ν will

induce one or two frequencies (clockwise or anticlockwise or both) in the rotor conducting components depending on the nature of the winding and the way it is supplied. These frequencies are given by the following relation:

mechrotor fpf ⋅⋅+= sgn)( νν (3)

Where sgn=+1 or -1 for backward and forward rotating field

respectively. A time harmonic simplified FE model of the machine is built

for each frequency and the corresponding losses are calculated (Fig.3). The analysis is performed according to the following steps:

1. For a given armature space harmonicν : • The frequency induced by each rotating field is determined

using equation (3);

1593

•The magnitudes of the rotating fields for each direction are calculated according to equations (4)-(13);

2. For each rotating field: • An equivalent current sheet is applied to the time harmonic

FE model to replicate the same airgap magnetic field harmonic determined from step 1;

• The model frequency is set according to the considered rotating field;

• Each magnet block was defined as a solid conductor circuit driven by a zero current source (insulated magnet blocks);

The eddy current losses created by each rotating field in one

magnet are then calculated and the eddy current losses attributed to a particular space harmonic is simply the addition of the losses created by its forward and backward rotating fields. The above process is automated using the scripting feature of the FE software MagNet. Figure 3 shows the layout of the time harmonic current sheet model due to 14th space harmonic in healthy mode. Due to the balanced supply in healthy mode, only one travelling wave, and thus one rotor frequency exists for any space harmonic.

The current sheet time harmonic method is then validated by comparison with the previously validated analytical method and with a full time-stepping transient FE simulation for 3 phase and 5 phase machines in both healthy and fault tolerant modes. Figures 4 and 5 show the losses due to each harmonic in one magnet and in the sleeve of a 3 phase machine from the two proposed methods in healthy and fault tolerant mode respectively. Similarly, figures 12 and 13 show the comparison of both methods for a 5 phase machine in healthy and fault tolerant mode respectively. A very good agreement is observed for any machine in any mode of operation.

IV. FAULT TOLERANT CONTROL STRATEGIES FOR THREE PHASE MACHINE

Three fault tolerant strategies are analyzed for 3 phase machines. In all cases, the currents are set so that the rated positive sequence torque is maintained.

Method 3-1: The most straightforward way to operate the machine after

an open circuit fault is just to increase the current magnitude of the remaining healthy phases to compensate for the lost torque contribution of the faulted phase while the phases of the remaining currents are kept identical to the healthy case. The current magnitude overrating is 1.5. This FT control is possible if each phase is fed by separate converter [13]. The relations used to calculate the magnitude of the resulting rotating fields due to each armature harmonic for the current sheet time harmonic method are:

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

2*1 2*5 2*7 2*11 2*13 2*17 2*19 Total

Losses in one

 magne

t [W]

Harmonics

Time stepp. Analytic

Curr Sheet Time Harm.

(a)

0

1

2

3

4

5

6

2*1 2*5 2*7 2*11 2*13 2*17 2*19 Total

Losses in Sleeve [W

]

Harmonics

Time Stepp. Analytic

Curr Sheet Time Harm.

(b)

Figure 4. Machine I: Losses due to each space harmonics in one magnet under healthy operation.

(a): losses in one magnet; (b): losses in sleeve

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

2*1 2*3 2*5 2*7 2*9 2*11 2*13 2*15 2*17 2*19 2*21 Total

Losses in one

 magne

t [W]

Harmonics

Analytic. Time Stepp

Current Sheet Time Harm.

Figure 5. Machine I: Losses due to each space harmonics in one magnet when

one phase is lost and the magnitude of remaining currents scaled by 1.5 (Method 3-1).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2*1 2*3 2*5 2*7 2*9 2*11 2*13 2*15 2*17 2*19 2*21 Total

Losses in one

 magne

t [W]

Harmonics

Analytic. Time Stepp.

Current Sheet Time Harm.

Figure 6. Machine I: Losses due to each space harmonics in one magnet when

one phase is lost and fault tolerant strategy with current shifting is used (Method 3-3).

1594

0

0.1

0.2

0.3

0.4

0.5

0.6

2*1 2*3 2*5 2*7 2*9 2*11 2*13 2*15 2*17 2*19 2*21 Total

Losses in one

 magne

t [W]

Harmonics

Figure 7. Machine I: Losses due to each space harmonics in one magnet when one phase is lost and fault tolerant strategy without neutral connection is used

(Method 3-2).

0

0.05

0.1

0.15

0.2

0.25

8*1 8*2 8*4 8*5 8*7 8*8 Total

Losses in one

 magne

t [W]

Harmonics (a)

0

0.5

1

1.5

2

2.5

3

3.5

8*1 8*2 8*4 8*5 8*7 8*8 Total

Losses in Sleeve [W

]

Harmonics (b)

Figure 8. Machine II: Losses due to each space harmonics under healthy operation.

(a): losses in one magnet; (b): losses in sleeve

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

8*1 8*2 8*4 8*5 8*7 8*8 Total

Losses in one

 magne

t [W]

Harmonics

Figure 9. Machine II: Losses due to each space harmonics in one magnet when

one phase is lost and the magnitude of remaining currents scaled by 1.5 (Method 3-1).

0

0.05

0.1

0.15

0.2

0.25

8*1 8*2 8*4 8*5 8*7 8*8 Total

Losses in one

 magne

t [W]

Harmonics Figure 10. Machine II: Losses due to each space harmonics in one magnet

when one phase is lost and fault tolerant strategy with current shifting is used (Method 3-3).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

8*1 8*2 8*4 8*5 8*7 8*8 Total

Losses in one

 magne

t [W]

Harmonics

Figure 11. Machine II: Losses due to each space harmonics in one magnet when one phase is lost and fault tolerant strategy without neutral connection is

used (Method 3-2).

0

0.1

0.2

0.3

0.4

0.5

0.6

1 3 5 7 9 11 13 15 17 19 21 total

Losses in one

 magne

t [W]

Harmonics

Analytic. Time Stepp.

Current Sheet Time Harm.

(a)

0

1

2

3

4

5

6

7

8

1 3 5 7 9 11 13 15 17 19 21 total

Losses in Sleeve [W

]

Harmonics

Analytic. Time Stepp.

Current Sheet Time Harm.

(b)

Figure 12. Machine III: Losses due to each space harmonics in under healthy operation.

(a): losses in one magnet; (b): losses in sleeve

1595

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 3 5 7 9 11 13 15 17 19 21 total

Losses in one

 magne

t [W]

Harmonics

Analytic. Time Stepp.

Current Sheet Time Harm.

Figure 13. Machine III: Losses due to each space harmonics in one magnet

when one phase is lost and the magnitude of remaining currents scaled by 1.25 (Method 5-1).

0

0.2

0.4

0.6

0.8

1

1.2

1 3 5 7 9 11 13 15 17 19 21 total

Losses in one

 magne

t [W]

Harmonics

Analytic. Time Stepp.

Current Sheet Time Harm.

Figure 14. Machine III: Losses due to each space harmonics in one magnet

when one phase is lost and without neutral connection is used (Method 5-2).

Forward field:

⎥⎦

⎤⎢⎣

⎡ −⋅−⎥⎦

⎤⎢⎣

⎡ −−+= 3

2)1(23

2)1()(

21)(

πνπννν

jjonephaserotatfield eeBB (4)

Backward field:

⎥⎦

⎤⎢⎣

⎡ +⋅−⎥⎦

⎤⎢⎣

⎡ +−+= 3

2)1(23

2)1()(

21)(

πνπννν

jjonephaserotatfield eeBB (5)

For this control strategy, all space harmonics exist and each of them creates rotating fields in both directions (Table II).

TABLE II HARMONIC ROTATING FIELDS OF MACHINE I UNDER METHOD 3-1

+: FORWARD; -BACKWARD; 0: CANCELLED

ν 2*1

2*3

2*5

2*7

2*9

2*11

2*13

2*15

2*17

2*19

2*21

Hlth - 0 + - 0 + - 0 + - 0 Met 3-1

+/- +/- +/- +/- +/- +/- +/- +/- +/- +/- +/-

Method 3-2: If the three phases are fed by a single inverter and the neutral

point of the machine is not accessible operation is still possible by controlling the current of the two remaining healthy phases

which are now connected is series. Assuming phase A is lost, the resulting phase of B and C currents are shifted 300 toward the phasor of the pre-fault A current, i.e. iC=-iB. Only one current is effectively controlled. The current overrating in this case is 1.732. The relations used to calculate the magnitude of the rotating fields due to each harmonic for the current sheet time harmonic method are:

Forward field:

⎥⎦

⎤⎢⎣

⎡ −−⋅−⎥⎦

⎤⎢⎣

⎡ +−−+= 63

2)1(263

2)1()(

21)(

ππνππννν

jjonephaserotatfield eeBB (6)

Backward field:

⎥⎦

⎤⎢⎣

⎡ ++⋅−⎥⎦

⎤⎢⎣

⎡ −+−+= 63

2)1(263

2)1()(

21)(

ππνππννν

jjonephaserotatfield eeBB (7)

We can notice, from (6) and (7) that the resultant tripplen harmonics due to the two remaining phases are reduced to zero and do not create any rotating fields. Any non tripplen harmonic creates rotating fields in both directions (Table III).

TABLE III

HARMONIC ROTATING FIELDS OF MACHINE I UNDER METHOD 3-2 +: FORWARD; -BACKWARD; 0: CANCELLED

ν 2*1

2*3

2*5

2*7

2*9

2*11

2*13

2*15

2*17

2*19

2*21

Hlth - 0 + - 0 + - 0 + - 0 Met 3-2

+/- 0 +/- +/- 0 +/- +/- 0 +/- +/- 0

Method 3-3: To get a smooth output torque, the fault tolerant control

strategy presented in [14] can also be used. This control needs a separate converter for each phase or a neutral point connection to mid-point of the DC link capacitor. Assuming phase A is lost, then, phase B and C currents are shifted 300 away from the phasor of the pre-fault phase A current. The magnitude overrating is again 1.732. This control strategy cancels the negative sequence field produced by the torque converting harmonic. The relations used to calculate the magnitude of the rotating fields due to each harmonics for the current sheet time harmonic method are:

Forward field:

⎥⎦

⎤⎢⎣

⎡ +−⋅−⎥⎦

⎤⎢⎣

⎡ −−−+= 63

2)1(263

2)1()(

21)(

ππνππννν

jjonephaserotatfield eeBB

(8) Backward field:

1596

⎥⎦

⎤⎢⎣

⎡ −+⋅−⎥⎦

⎤⎢⎣

⎡ ++−+= 63

2)1(263

2)1()(

21)(

ππνππννν

jjonephaserotatfield eeBB

(9) It can be observed from (8) and (9) that for any non tripplen

space harmonic, either only forward or only backward field exists. But tripplen harmonics create rotating fields in both directions. Table IV summarises those observations.

TABLE IV

HARMONIC ROTATING FIELDS OF MACHINE I UNDER METHOD 3-3 +: FORWARD; -BACKWARD; 0: CANCELLED

ν 2*1

2*3

2*5

2*7

2*9

2*11

2*13

2*15

2*17

2*19

2*21

Hlth - 0 + - 0 + - 0 + - 0 Met3-3

- +/- + - +/- + - +/- + - +/-

V. FAULT TOLERANT CONTROL STRATEGIES FOR FIVE PHASE MACHINES

The fault tolerant control strategies analyzed in this section are limited to 2. Similarly to the previous section the post-fault currents are regulated to produce the rated DC output torque.

Method 5-1: Just like for the 3 phase machines, the most straightforward

FT method is to just overrate the magnitude of the remaining healthy phases’ currents. This method is possible if each phase is fed by a separate converter. This will involve a current overrating of 1.25. The phases of the remaining currents are kept identical to the healthy case. For the current sheet time harmonic method, the relation used to calculate the magnitudes of the harmonic rotating fields are given below for this FT control strategy:

Forward field:

++=⎥⎦

⎤⎢⎣

⎡ +⋅−⎥⎦

⎤⎢⎣

⎡ +−5

2)1(25

2)1()(

21)(

πνπννν

jjonephaserotatfield eeBB

⎥⎦

⎤⎢⎣

⎡ +⋅−⎥⎦

⎤⎢⎣

⎡ +⋅−++ 5

2)1(45

2)1(3 πνπν jjee (10)

Backward field:

++=⎥⎦

⎤⎢⎣

⎡ −⋅−⎥⎦

⎤⎢⎣

⎡ −−5

2)1(25

2)1()(

21)(

πνπννν

jjonephaserotatfield eeBB

⎥⎦

⎤⎢⎣

⎡ −⋅−⎥⎦

⎤⎢⎣

⎡ −⋅−++ 5

2)1(45

2)1(3 πνπν jjee (11)

For this control strategy, all space harmonics exist and each of them creates rotating fields in both directions (Table V).

TABLE V

HARMONIC ROTATING FIELDS OF MACHINE III UNDER METHOD 5-1 +: FORWARD; -BACKWARD; 0: CANCELLED

ν 1 3 5 7 9 11 13 15 17 19 21 Hlth - 0 0 0 + - 0 0 0 + - Met 5-1

+/- +/- +/- +/- +/- +/- +/- +/- +/- +/- +/-

Method 5-2: The second method considered is that for no zero-sequence

current as in the case when using a single inverter for the machine without a neutral point connection [1][2]. Assuming phase A is lost, the phases of C and D currents are kept identical to the healthy case and B and E currents are set to iB = -iD and iE = -iC. The magnitude overrating in this case is 1.382 to keep the same pre-faulted fundamental positive sequence field. For the current sheet time harmonic method, the relation used to calculate the magnitudes of the harmonic rotating fields are given below for this FT control strategy:

Forward field:

++=⎥⎦

⎤⎢⎣

⎡ +⋅−⎥⎦

⎤⎢⎣

⎡ −+−5

2)1(255

2)1()(

21)(

πνππννν

jjonephaserotatfield eeBB

⎥⎦

⎤⎢⎣

⎡ ++⋅−⎥⎦

⎤⎢⎣

⎡ +⋅−++ 55

2)1(45

2)1(3 ππνπν jjee (12)

Backward field:

++=⎥⎦

⎤⎢⎣

⎡ −⋅−⎥⎦

⎤⎢⎣

⎡ +−−5

2)1(255

2)1()(

21)(

πνππννν

jjonephaserotatfield eeBB

⎥⎦

⎤⎢⎣

⎡ −−⋅−⎥⎦

⎤⎢⎣

⎡ −⋅−++ 55

2)1(45

2)1(3 ππνπν jjee (13)

It can be derived from (12) and (13) that this control strategy

cancels the backward field due to the torque converting harmonic as well as the fields due to any harmonic multiple of 5. Table VI summarises the existing rotating fields and their directions under this control strategy.

TABLE VI

HARMONIC ROTATING FIELDS OF MACHINE III UNDER METHOD 5-2 +: FORWARD; -BACKWARD; 0: CANCELLED

ν 1 3 5 7 9 11 13 15 17 19 21 Healthy - 0 0 0 + - 0 0 0 + - Method

5-2 - +/- 0 +/- + - +/- 0 +/- + -

1597

VI. LOSSES DURING FAULT TOLERANT OPERATION OF THE THREE PHASE MACHINE

From the analysis done on a number of machines the eddy current losses in magnets and sleeve during faulted operation are higher or equal to the losses during healthy operation for the same output torque. This depends on the winding configuration and the control method as will be discussed in this section. The loss computation was done up to the 21st harmonic for the Machine I and till the 64th for the Machine II since the losses due to higher order space harmonics was found to be very low.

The losses are the highest for the FT control without neutral

connection mode (Method 3-2) despite the cancellation of tripplen harmonic fields. Moreover the torque ripple is extremely high (Fig. 15 and 16). The reason is the high magnitude of the negative sequence field of the torque converting space harmonic (high losses due to harmonic 10 for Machine I in Fig.7 and 8 for Machine II in Fig.11). The main advantage of such a system would be the reduced component count from the converter point of view.

As to the two other methods (Methods 3-1vs. 3-3), Method

3-3 creates higher losses in Machine I and lower in Machine II. The reason is the presence of tripplen harmonics in the field created by one phase of the Machine I which do not cancel out in unbalanced operation. We can compare the losses due to each harmonic for the Machine I in healthy and in the FT control with zero fundamental negative sequence (Method3-3) (Fig. 4 and 6 respectively). The losses due to each harmonics are the same except for the tripplen harmonics which appears in the faulted mode creating additional losses. For the Machine II, there aren’t any tripplen harmonics in the phase MMF under both healthy and faulty operation due to the coils being pitched by 2/3. Thus, the losses in healthy mode and in this FT control strategy are exactly identical. The torque waveform is also identical to the healthy case as shown in Fig.16.

Although current phase shifting (Method 3-3) produces

lower torque ripple (Fig.15), for machines having tripplen harmonics in their armature phase field (Machine I), just increasing the phase current magnitude by 1.5 (Method 3-1) to keep the same average torque as in healthy mode appears to be interesting from losses point of view. Such a control method needs a lower current overrating than the two others and thus lower copper losses and in addition lower eddy current losses in the rotor conducting components (magnets and sleeve)(Fig. 5, 6 and 7).

For machines not having any tripplen harmonics present in the armature field of a single phase (Machine II), the losses in the rotor conducting components as well as the torque waveform are exactly identical to the healthy case when Method 3-3 is used. This is quite interesting since there is no

increase in the torque ripple and no increase in the losses in any rotor conducting components.

VII. LOSSES DURING FAULT TOLERANT OPERATION OF THE FIVE PHASE MACHINE

As expected, the eddy current losses in magnets and sleeve are higher in any fault tolerant mode compared to healthy operation due to the amplified harmonic rotating fields. For the five phase Machine III, the loss computation was stopped at the 21st harmonic since the losses due to higher order space harmonics was found to be very low.

Eddy current losses are the highest for the no neutral

connection FT control strategy Method 5-2 (Fig.14). Moreover, the current overrating (1.382) is the highest and consequently the increase in the copper losses is the highest as well. Thus for the Machine III, the only advantage of this control strategy is the slightly lower torque ripple and the fact that only two currents are controlled (Fig. 17).

The control strategy consisting in simply scaling the

remaining currents by 1.25 of the healthy current magnitude is very attractive (Method 5-1). The torque ripple is not significant compared to the previous one and both copper losses and rotor losses in fault tolerant operation are lower (Fig.13).

VIII. CONCLUSION

This work presents some of the issues to consider when rating fault tolerant PM machines to work with various remedial control methods. The increase of copper and rotor eddy current losses were compared for various fault tolerant control strategies for three and five phase machines. Table VII and VIII summarise the results discussed.

Three phase machines that have no tripplen harmonics in their single phase airgap field can be controlled using Method 3-3 to operate in faulty conditions with the same torque ripple and rotor loss as during healthy operation. This comes at the expense of doubling the copper losses. If torque ripple and an increase on rotor losses is acceptable, then using Method 3-1 can give the minimum overall loss. On the other hand, machines which have tripplen harmonics in their single phase MMF always show higher torque ripple in FT mode of operation.

For the machines considered, Method 3-1 always gives the best efficiency.

For a five phase machine, if the phases are fed by separate converters, the simple current scaling strategy (Method 5-1) appears also to be the most interesting in terms of copper losses and rotor losses. The resulting torque ripple is just slightly higher than the FT strategy without neutral connection (Method 5-2).

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The approaches developed to determine the rotor eddy current losses which have been validated through FE results, should be used at the design stage of the machine alongside an appropriate thermal model to ensure the magnet temperatures do not exceed the allowable values. Whilst this work has been limited to open circuit faults, future work will focus on the loss aspects with short circuit faults.

TABLE VII

LOSS DISTRIBUTION OF 3 PHASE MACHINES [W]

Healthy Method 3-1 Method 3-2 Method 3-3 Machine Stat. Rot. Stat. Rot. Stat. Rot. Stat. Rot.

I 441 9.26 661 14.67 882 21.50 882 18.68

II 516 6.70 774 13.55 1032 34.13 1032 6.70

TABLE VIII LOSS DISTRIBUTION OF 5 PHASE MACHINE [W]

Healthy Method 5-1 Method 5-2 Machine Stator Rotor Stator Rotor Stator Rotor

III 441 17.45 551 22.48 673 28.66

0 10 20 30 40 50 60 70 80 90-20

0

20

40

60

80

100

Mechanical Angle [°]

Torq

ue [N

m]

24s20pDL: Healthy24s20pDL: Current scaling by 1.5 (Method 3-1)24s20pDL: Without neutral (Method 3-2)24s20pDL: Current shifting (Method 3-3)

Figure 15. Torque of Machine I under healthy and various fault tolerant mode.

0 10 20 30 40 50 60 70-20

0

20

40

60

80

100

Mechanical Angle [°]

Torq

ue [N

m]

24s16p: Healthy24s16p: Current scaling by 1.5 (Method 3-1)24s16p: Without neutral (Method 3-2)24s16p: Current shifting (Method 3-3)

Figure 16. Torque of Machine II under healthy and various fault tolerant

mode.

0 20 40 60 80 100 120 140 160 1800

10

20

30

40

50

60

70

Mechanical Angle [°]

Torq

ue [N

m]

20s18p: Healthy20s18p: Current scaling by 1.25 (Method 5-1)20s18p: Without neutral connection (Method 5-2)

Figure 17. Torque of Machine III under healthy and various fault tolerant

mode.

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