^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

This paper presents a novel five-phase permanent magnet synchronous motor (PMSM), which contains dual rotors and a single stator, equivalent to two five-phase motors working together. Thus, this kind of motor has the potential of good fault tolerant capability and high torque density, which makes it appropriate for use in electric vehicles. In view of the different connection types, the inside and outside stator windings can be driven in series or parallel, which results in the different performances of the magnetomotive force (MMF) and torque under open-circuit fault conditions. By decomposing the MMF, the reason that torque ripple increases after open-circuit faults is explained, and the relationship between MMF and torque is revealed. Then, the current control strategy is applied to adjust the open-circuit faults, and the electromagnetic analysis and MMF harmonics analysis are performed to interpret the phenomenon that the torque ripple is still larger than in the normal situation. The investigations are verified by finite element analysis results.

With the requirements of energy conservation and emissions reduction around the world, electric vehicles (EVs) have been seen as an ideal alternative of transportation, and thus, have got more and more attention from researchers and governments [

The magnetomotive force (MMF) distribution is mainly affected by the winding structure and current waveform. In turn, it influences the motor performances. Thus, much attention has been paid to researching the MMF [

The flux-MMF diagram technique, differing from the analytical method used to study the cogging torque in [

Nowadays, most multiphase PM motors have a single stator and a single rotor, whose structure limits the power density from further increasing. In order to increase the power density, many compound-structure PMSMs integrated by two machines have been proposed [

According to the drive mode, the topologies for four-wheel-drive EVs can be classified into high-speed drive incorporating an additional gear box and low-speed direct drive.

It can be known from

To ensure the coaxial output, the inner and outer rotors are connected by the end flange, as shown in

As there are slots on the inside and outside surfaces of stator iron, two sets of windings (inside winding and outside winding) can be installed, which can be used to improve the fault tolerant ability. In addition, there are two working air-gaps, so the five-phase DRPMSM has a higher torque density, which makes it very suitable for use for EVs. Here, the inner rotor and inside stator winding operates as one motor called inner motor, and the outer rotor and outside stator winding operates as another one called outer motor. Due to the different connections, inside and outside windings can be driven in parallel or series, as shown in

In order to achieve the physical separation and magnetic decoupling between the fault phases and other healthy phases, the armature coils are wound around the alternate stator teeth [

It is assumed that the lengths of inside and outside air gaps along the armature surfaces are uniform. Originating from the winding axis, the winding function of phase “a” can be described by

The Fourier series of the phase “a” winding function can be expressed as:
_{m}

Therefore, the resulting MMF of inner and outer motor is obtained:

It can be concluded from

If defined ϕ=11ψ,

Ideally, the output torque of five-phase DRPMSM is the sum of that of inner and outer motors. Applying the instantaneous power balance theory, the electromagnetic torque of five-phase DRPMSM can be computed by:
_{ij}_{oj}

According to _{i}_{o}_{i}_{o}_{i}_{o}

Let

Furthermore, the net result (black line shown in _{n}

Using the AC standstill test [_{ii}_{ij}

Let the phase current be in phase with the phase EMF, namely, employing the vector control strategy that direct-axis current is equal to zero, the torques are obtained under different working situations, as informed in

It can be found from _{i}_{o}_{n}

In this section, the following open-circuit faults are discussed: one phase open-circuit fault, two adjacent phases open-circuit fault and two non-adjacent phases open-circuit fault.

It is assumed that phase “a” is open circuited. For the star connection without neutral line, the constraint that current vector sum is equal to zero has to be satisfied. By regulating the phase angle, the remaining four phase currents can be depicted as:

From the constraint of star connection, it can be obtained that:

In order to maximize the average torque, basing on

To eliminate the two degrees of freedom existing in

Then,

Taking

According to the instantaneous power balance theory, one can learn that the fault winding can output about 76.1% of the torque acquired when the winding working under normal conditions. For the series drive, as shown in

phase “a” of the inner motor is open circuited in the parallel drive, so the resulting stator MMF of five-phase DRPMSM can be expressed as:

phase “a” of the outer motor is open circuited in the parallel drive, so the resulting stator MMF of five-phase DRPMSM can be expressed as:

phase “a” is open circuited in the series drive, so the total stator MMF can be expressed as:

The MMF distributions under these three fault cases are shown in

It can be seen from

Under these three open-circuit fault cases, the torques are acquired, as shown in

It can be observed from _{n}

It is supposed that phase “b” and “c” occur in an open-circuit fault simultaneously. To satisfy the constraint of star connection, the remaining three normal phase currents are regulated, but their amplitudes are kept unchanged, as follows:

From the condition that current vector sum is equal to zero, it can be obtained that:

For the sake of obtaining the maximum average torque, it can be known from

By solving

Hence, one can learn that the fault winding can output about 46.8% of the normal torque, which is obtained under the case of five phase currents are in healthy state.

In this paper, it is assumed that the fault only happens in one side winding at the same time, thus the fault cases can be described as:

the inner motor encounters open-circuit fault in the parallel drive, so the resulting MMF of five-phase DRPMSM changes into:

the outer motor encounters open-circuit fault in the parallel drive, so the resulting MMF of five-phase DRPMSM changes into:

the open-circuit fault occurs in the series drive, so the total stator MMF changes into:

Under open-circuit faults, the MMF distributions are shown in

From _{n}

Under the three fault cases, the output torques of five-phase DRPMSM are shown in

It can be seen from _{n}

Supposing that phase “a” and “d” are open circuited. To satisfy the constraint of star connection, the phase angles of remaining normal phases are regulated, whereas their current amplitudes are kept unchanged, as follows:

Accordingly, it can be got that:

In order to maximize the average torque produced by fault winding, based on

By solving

Thus, it can be known that the fault winding can output about 56.5% of normal torque, which is higher than the case of two adjacent phases open-circuit fault. If only considering the fault occurring in one side winding, two non-adjacent phases open-circuit fault can be classified into the following three cases:

the fault occurs in the inner motor in the parallel drive, so the resulting MMF of five-phase DRPMSM becomes:

the fault occurs in the outer motor in the parallel drive, so the resulting MMF of five-phase DRPMSM becomes:

the fault occurs in the series drive, so the total MMF becomes:

The MMF distributions under these three fault cases are shown in

By comparing

Under the three open-circuit fault cases, the torques are obtained by the FEA, as shown in

It can be learned from

By comparing the simulation results, it can be concluded that the performances of torque and MMF are similar,

It can be found from

In order to make clear the relationship between torque and MMF, the following derivation is given. For the vector control that direct-axis current is equal to zero, the electromagnetic torque of five-phase DRPMSM can be computed by:

Where ψ_{f}

When the stator windings encounter open-circuit faults, the PM flux-linkage is not affected at all. Hence, the variation of average torque keeps synchronous with the change of current amplitude, which can be seen from _{n}_{n}

The torques generated by the equivalent currents are shown in

It can be known from Section 4 that the torque ripple is mainly caused by other types of MMF except for the positive rotating component in the 11th MMF harmonic, under open-circuit fault conditions. Therefore, the current control strategy is employed to obtain a disturbance-free MMF (11th harmonic MMF) in this section and the total stator MMF of five-phase DRPMSM is kept constant in pre- and post fault situations.

It is assumed that phase “a” is open circuited. From Section 4.1, one can learn that the ripple current, as depicted in _{m}_{i}/k_{o}_{o}_{i}

As for the fault winding, its currents expression are kept unchanged, as depicted in

For the fault occurring in the series drive, the remaining healthy phase currents are adjusted by applying the current control strategy proposed in [

Under the new current excitations, the torques for the three fault cases (as depicted in Section 4.1) are obtained, as shown in _{n}

It is assumed that phase “b” and “c” are open circuited. Similar to one phase open-circuit, the ripple currents, as depicted in

If the average torque is kept unchanged in pre- and post fault situations for the fault winding, its current amplitude has to become into 2.14 times of _{m}

Under the condition of faults with adjustment, the torques for the three cases (as depicted in Section 4.2) are obtained, as shown in _{n}

It is assumed that phase “a” and “d” are open circuited. When the five-phase DRPMSM is driven in parallel, the current expressions of fault windings are kept unchanged, and the ripple currents (as depicted in

Supposing that the average torque remains unchanged before and after the fault, the current amplitude of fault winding must increase by about 77%. For the series drive, after the fault with adjustment, the remaining normal phase currents can be described as:

Under the three fault cases (as depicted in Section 4.3) with adjustment, the torques are obtained, as shown in _{n}

From the above results, one can learn that the average torque increases to about 91%–98% of normal value, after the open-circuit faults with adjustment. Nevertheless, the torque ripple is still lager than under normal conditions. Taking a one phase open-circuit fault happening in the series drive as an example, this phenomenon is explained as follows: based on the winding function, the MMF harmonics analysis are performed under normal and open-circuit faults with adjustment, as shown in

In addition, it can be known from Section 5.1 that the current amplitudes of fault winding increase by about 31%–38% of _{m}

In this paper, the MMF and torque performances of a novel five-phase DRPMSM, with both advantages of good fault tolerant capability and high torque density, have been investigated. Due to the different connection types, the inside windings and outside windings can be driven in series or parallel. Through analysis, it can be concluded that the inner motor and outer motor are magnetic decoupling, so they can be controlled independently in the parallel drive. Comparing with the series drive, the motor is able to exhibit better MMF and torque performances in the parallel drive,

Under the condition of open-circuit faults without adjustment, the remaining normal phase currents of the faulty winding are regulated to meet the constraint of star-connection and the maximum average torque is obtained. By comparison, it is found that the characteristics of torque and MMF magnitude edge are similar,

Then, the open-circuit faults are adjusted to obtain an undisturbed rotating MMF. For the parallel drive, this objective is achieved by injecting the ripple currents into the normal working winding, whereas the fault winding currents expression are kept unchanged except increasing the amplitude; for the series drive, this objective is achieved by keeping the total MMF unchanged in pre- and post fault situations. After adjustment, one can discover that the average torque can increase to about 91%–98% of normal torque, but the torque ripple is still larger than in a normal situation. One reason is that the current amplitudes of the faulty winding improve a lot, as compared with the normal situation, which causes the local magnetic saturation, thus results in larger torque ripple. Another reason is that the 33rd order stator MMF space harmonic still exists and its amplitude increases. Due to the asynchronous velocity, the ripple torques of second and fourth order are generated, when it interacting with the 33rd rotor MMF harmonic.

This work was supported in part by the National Natural Science Foundation of China under Project 51307008 and 11372034, in part by Ph.D. Programs Foundation of Ministry of Education of China under Project 20121101120024, in part by Basic Research Foundation of Beijing Institute of Technology under Grant 20110642015 and 20120642013, and in part by Excellent Young Scholars Research Fund of Beijing Institute of Technology.

The authors declare no conflict of interest.

The Component diagram of five-phase DRPMSM.

Finite element model of five-phase DRPMSM.

Drive mode of five-phase DRPMSM: (

Phase “a” winding function.

MMF distribution under normal conditions: (

MMF distribution under one phase open-circuit fault case a: (

MMF distribution under one phase open-circuit fault case b: (

MMF distribution under one phase open-circuit fault case c: (

Torque comparison under one phase open-circuit fault without adjustment: (

MMF distribution under two adjacent phases open-circuit fault case a: (

MMF distribution under two adjacent phases open-circuit fault case b: (

MMF distribution under two adjacent phases open-circuit fault case c: (

Torque comparison under two adjacent phases open-circuit fault without adjustment: (

MMF distribution under two adjacent phases open-circuit fault case a: (

MMF distribution under two adjacent phases open-circuit fault case b: (

MMF distribution under two adjacent phases open-circuit fault case c: (

Torque comparison under two adjacent phases open-circuit fault: (

Stator MMF harmonics analysis under open-circuit faults conditions: (

Simulation results under no-load conditions: (

Torque comparison between direct and equivalent output: (

Torque comparison under one phase open-circuit fault with adjustment.

Stator MMF harmonics analysis under normal and one phase open-circuit faults with adjustment: (

Flux density in the stator inside teeth: (

Flux density in the stator outside teeth: (

Some design parameters of Prius PMSM and five-phase DRPMSM.

Peak power (kw) | 60 | 18@750 rpm |

Maximum speed (rpm) | 13,500 | 1500 |

Peak torque (nm) | 207 | 210 |

Outer rotor out diameter (mm) | - | 320 |

Outer rotor in diameter (mm) | - | 300 |

Stator outer diameter (mm) | 264 | 298 |

Stator inner diameter (mm) | 161.9 | 130 |

Inner rotor out diameter (mm) | 160.4 | 128 |

Inner rotor inner diameter (mm) | 51 | 100 |

Rotor stack length (mm) | 50.165 | 60 |

Stator stack length (mm) | 50.8 | 60 |

Air gap (mm) | 0.73 | 1 |

Number of stator slots | 48 | 40 |

Number of rotor poles | 8 | 44 |

Current density (A/mm^{2}) |
40.1 | 20 |

Torque density (kNm/m^{3}) |
74.15 | 43.52 |

The inductances of inside and outside windings.

L_{AA} |
750 μH | M_{Aa} |
0.888 μH | L_{aa} |
775 μH |

M_{AB} |
1.157 μH | M_{Ab} |
0.1 μH | M_{ab} |
0.076 μH |

M_{AC} |
3.765 μH | M_{Ac} |
0.286 μH | M_{ac} |
1.177 μH |

The torque performance of the five-phase DRPMSM under normal conditions.

_{av} |
||
---|---|---|

Inside winding-inner rotor | 63.8 | 214.6 |

Outside winding-outer rotor | 150.8 | |

Inside winding-inner and outer rotors | 64 | 214.7 |

Outside winding-inner and outer rotors | 150.7 | |

Inside and outside windings-inner and outer rotors | 214.7 | - |

The performances of MMF amplitude edge under one phase open-circuit fault conditions.

_{av} |
_{av}_{n} |
||
---|---|---|---|

Case a | 0.4156 | 92.6 | 7.98 |

Case b | 0.3741 | 83.3 | 19.9 |

Case c | 0.3424 | 76.3 | 30.8 |

The torque performances under one phase open-circuit fault without adjustment.

_{av} |
_{av}_{n} | |||
---|---|---|---|---|

Case a | 199.2 | 31.4 | 7.87 | 92.8 |

Case b | 178 | 65.7 | 18.4 | 82.9 |

Case c | 162.7 | 93.6 | 28.8 | 75.8 |

Current 1 | 165.8 | 5.74 | 1.73 | 77.2 |

Current 2 | 0 | 105.3 | - | - |

Resultant | 166 | 103.9 | 31.2 | 77.3 |

The performances of MMF amplitude edge under two adjacent phases open-circuit fault conditions.

_{av} |
_{av}_{n} |
||
---|---|---|---|

Case a | 0.3765 | 83.9 | 7.12 |

Case b | 0.2768 | 61.6 | 23.2 |

Case c | 0.2079 | 46.3 | 42 |

The torque performances under two adjacent phases open-circuit fault without adjustment.

_{av} |
_{av}_{n} | |||
---|---|---|---|---|

Case a | 180.3 | 30.4 | 8.44 | 84 |

Case b | 133.4 | 77.5 | 29 | 62.1 |

Case c | 98.8 | 98.1 | 49.5 | 46 |

Current 3 | 100.1 | 4.27 | 2.07 | 46.6 |

Current 4 | 0 | 70.2 | - | 0 |

Current 5 | 0 | 51.4 | - | 0 |

Resultant | 100 | 92.4 | 45.2 | 46.6 |

The performances of MMF amplitude edge under two non-adjacent phases open-circuit fault conditions.

_{av} |
_{av}_{n} |
||
---|---|---|---|

Case a | 0.3896 | 86.8 | 5.76 |

Case b | 0.3117 | 69.4 | 15.9 |

Case c | 0.2538 | 56.5 | 27.8 |

Torque performances under two non-adjacent phases open-circuit fault without adjustment.

_{av} |
_{av}_{n} | |||
---|---|---|---|---|

Case a | 186.7 | 24.5 | 6.55 | 87 |

Case b | 148.7 | 32.9 | 11.1 | 69.3 |

Case c | 120.7 | 51.6 | 21.3 | 56.2 |

Current 6 | 124.1 | 8.98 | 3.6 | 57.8 |

Current 7 | 0 | 58.4 | - | 0 |

Current 8 | 0 | 42.8 | - | 0 |

Resultant | 124 | 73.8 | 29.5 | 57.8 |

The coefficients of equivalent stator current amplitude function under open-circuit faults without adjustment.

λ | η | θ | |
---|---|---|---|

One phase | 0.763 | 0.235 | 90 |

Two adjacent phases | 0.463 | 0.1944 | 210 |

Two non-adjacent phases | 0.565 | 0.157 | 73 |

The torque characteristics of direct and equivalent output under open-circuit faults conditions.

_{av} |
|||
---|---|---|---|

One phase | direct | 162.7 | 28.8 |

equivalent | 167.9 | 29.4 | |

| |||

Two adjacent phases | direct | 99 | 49.5 |

equivalent | 98.5 | 43 | |

| |||

Two non-adjacent phases | direct | 120.7 | 21.3 |

equivalent | 124.2 | 28.4 |

The torque performances under one phase open-circuit fault with adjustment.

_{av} |
_{av}/_{n} | ||
---|---|---|---|

Case a | 209.9 | 4 | 97.8 |

Case b | 206.9 | 8.49 | 96.4 |

Case c | 206.5 | 10.4 | 96.2 |

The torque performances under two adjacent phases open-circuit fault with adjustment.

_{av} |
_{av}_{n} | ||
---|---|---|---|

Case a | 203.3 | 4.9 | 94.7 |

Case b | 200.8 | 10.6 | 93.5 |

Case c | 195.7 | 15.4 | 91.1 |

The torque performances under two non-adjacent phases open-circuit fault with adjustment.

_{av} |
_{av}_{n} | ||
---|---|---|---|

Case a | 207.3 | 3 | 96.5 |

Case b | 205.4 | 4.85 | 95.7 |

Case c | 202 | 8.2 | 94.1 |