# A bi-harmonic five-phase SPM machine with low ripple torque for marine propulsion

Abstract: This paper addresses the design of a bi-harmonic five-phase Surface-mounted Permanent Magnet (SPM) machine for marine propulsion. The bi-harmonic characteristic results from the particular 20 slots-8 poles configuration that makes possible high value of third harmonic current injection. Thus the machine performance can be improved in terms of average torque, speed range, losses control and torque quality, this last feature being the scope of the paper. As low ripple torques are wanted at low speed, the magnet layer is defined to reduce the cogging torque and to make third harmonic current injection increasing average torque and reducing pulsating torque in the same time. According to a selection procedure based on the numerical simulations of a high number of machines, it appears that designing the rotor with two identical radially magnetized magnet that cover two-third the pole arc allows to reach this goal. Referring to an equivalent three-phase machine, the torque ripple level of the bi-harmonic five-phase machine is more than three times lower, thus being obtained with a simple control strategy that aims at achieving constant currents in the rotating frames. The time simulations of the drive confirm the significant reduction of the speed oscillation, especially at low speed.

## Summary (3 min read)

### Introduction

- Multi-phase motors are widely used in electrical marine propulsion for reasons such as reliability, smooth torque and distribution of power [1].
- Furthermore, Surface-mounted Permanent Magnet (SPM) rotor facilitates the ripple torque mitigation that is of critical importance at low speed.
- A machine equipped with this winding can be considered as a bi-harmonic five-phase machine since it inherently offers an electronic pole changing effect [10].
- This paper focuses on a characteristic not yet described for 20-8-5 SPM machine.
- The second part addresses the design of the 20-8-5 machine.

### A. Multi-machine decomposition of a five-phase machine

- If the magnetic saturations and the demagnetization issue are not considered, it can be shown that a star-connected five- phase SPM machine behaves as two two-phase virtual machines that are magnetically independent but electrically and mechanically coupled [14].
- Furthermore, as the rotor saliency can be neglected with SPM machines, the space harmonics are distributed among the two virtual machines: the virtual machine sensitive to the fundamental is called Main Machine (MM) whereas the other sensitive to the third harmonic is called Secondary Machine (SM).
- MM and SM are also characterized by their cyclic inductances that will be of the same order with a tooth-concentrated winding, thus making easier the current regulation of the two virtual machines in case of PWM controlled voltage inverter.

### B. Electromagnetic torque calculation

- Therefore the five-phase machine electromagnetic torque T is the sum of the torque produced by the Main Machine T1 and the Secondary Machine T3.
- According to the space harmonic distribution property, the MM pulsating torque t1(γ) results from the interaction of the fundamental of the current with particular back-emf harmonics (1st, 9th, (10k ± 1)th) .
- The same applies for the SM pulsating torque t1(γ) that results from the interaction of the 3rd harmonic of current with particular back-emf harmonics (3rd, 7th, (10k ± 3)th).

### C. Control strategy

- At low speed, Maximum Torque Per Ampere (MTPA) control is wanted, thus meaning that, for both virtual machines, back-emf and current should be aligned.
- The trouble is that the average torque enhancement usually comes with more pulsating torque since the SM pulsating torques t3 add up to the MM ones t1.
- This control strategy is called h1h3-damp: it consists in choosing a particular ratio r that depends of harmonics 7th, 9th, 11th and 13th of the back-emf, that is calculated in order to eliminate the first harmonic of the pulsating torque.
- Therefore the implementation of the control with simple PI controllers can be used since the necessary bandwidth of the controllers does not relate to the frequency of the torque ripple.

### A. Objectives

- The present section focuses on the 20-8-5 machine design to make the two strategies h1h3-boost and h1h3-damp practically similar.
- Hence third harmonic current injection will increase the average torque and reduce the pulsating torque in the same time.
- Due to its particular winding, the 20-8-5 machine should be designed to be supplied with first and third harmonic of current at low speed.
- As it can be observed in Fig-1 that illustrates the electromagnetic circuit of the machine over one pole pair, the magnet arc length τm has to be chosen as a trade-off between cogging and pulsating torque reduction.
- The main machine parameters are listed in table I.

### B. Design exploration

- The best design is found by using a numerical two-dimensionnal field calculation (Finite Elements Analysis FEA software FEMM, [17]).
- Skewing the rotor or the stator would be necessary to mitigate the cogging torque, thus making the manufacturing more complex.
- Finally, the investigated 20-8-5 machines with two magnets per pole is compared with an equivalent 12-8-3 one, thus meaning that the equivalent 3- phase machine is also equipped with a rotor made with two identical radially magnetized magnets per pole.
- One can observe that the peak cogging torque can be minimized by choosing τm equal to 0.33 for the 5-phase machine and by choosing τm equal to 0.36 for the 3-phase one: nevertheless, according to the FEA predictions, the minimum cogging torque for the 5-phase machine is about two times lower than the 3-phase machine one.
- For 20-8-5 machine, it is worth mentioning that the h1h3-boost control reduces the pulsating torques referring to h1 control if the magnet arc length is between 0.29 and 0.40 the pole pitch, which is quite compliant with the analytical predictions reported in Fig-2.

### C. Results

- The resulting electromagnetic circuit is depicted in Fig.1.
- For the designed 20-8-5 machine, the average values of the 1-q and 3-q are almost equal, which complies with the back-emf spectrum analysis.
- For the 5-phase machine, the FEA torque estimations with the three possible control strategies are shown: h1h3-boost, h1 and h3.
- It is also worth mentioning that, with these two controls (h1 and h3), the resulting ripple torques are almost equal to the one obtained with the best 12- 8-3 machine (whereas h1 and h3 controls are not the proper control for the optimal 20-8-5 machine).

### B. Results

- Fig.-8 shows the resulting torque waveforms for the 12-8-3 and 20-8-5 machines according to the simulation of the drives (in steady state).
- The torque ripple reduction with the 5-phase machine is about three times which complies with the FEA results given in Fig-4.
- The significant speed oscillation reduction is then illustrated.
- In particular, at low speed (250rpm), the difference between the maximum speed and the minimum speed is about 70 times lower with the 20-8-5 machine (against 8 times at 1000rpm).

### V. CONCLUSION

- This paper addresses the design of a bi-harmonic fivephase SPM machine for marine propulsion.
- As low ripple torques are wanted at low speed, the magnet layer is defined to reduce the cogging torque and to make third harmonic current injection increasing average torque and reducing pulsating torque in the same time.
- Designing the rotor with two identical radially magnetized magnets that cover two-third the pole arc appears as a possibility to reach this goal.
- Numerical simulations of the five-phase machine confirm this approach and show a significant torque quality improvement: referring to an equivalent three-phase machine, the torque ripple level is reduced by more than three times.
- The possibility to eliminate the ripple torques with a simple control that aims at achieving constant currents in the rotating frames is evaluated with a time simulation of the drive.

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4 citations

### Cites background from "A bi-harmonic five-phase SPM machin..."

...5 slot per phase and per pole is studied in [7] and [8] (with 4 poles): referring to an equivalent 3-phase machine (12 slots and 4 poles), the possible advantages of this bi-harmonic 5-phase machine regarding the ripple torques, the magnet losses limitation and the speed range enlargement for given Volt-Ampere inverter are discussed....

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2 citations

### Cites background from "A bi-harmonic five-phase SPM machin..."

...Five-phase machines have been studied the most [3]–[16]....

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...3007053 [2], marine [3], and aerospace [4] industries....

[...]

...In contrast to, say, [3], where a fractional slot PMSM was considered, the machine is with an integer slot number per phase per pole....

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...A 5-phase 20-slot 8-pole dual-harmonic machine with surface magnets was developed in [3] in order to reduce torque ripple....

[...]

2 citations

##### References

1,559 citations

### "A bi-harmonic five-phase SPM machin..." refers background in this paper

...Multi-phase motors are widely used in electrical marine propulsion for reasons such as reliability, smooth torque and distribution of power [1]....

[...]

1,065 citations

### "A bi-harmonic five-phase SPM machin..." refers background in this paper

...In addition, the slot filling can also be improved with this solution [8]....

[...]

822 citations

712 citations

### "A bi-harmonic five-phase SPM machin..." refers background in this paper

...The following hypotheses are taken: • the inverter is made with perfect switches and the DC bus voltage continuously equals 60V • an intersective modulation based on a carrier signal at 10kHz is considered • dq-axis currents (classical dq-axis currents for the 3-phase machine and d1q1-axis (MM) and d3q3-axis (SM) for the 5-phase machine) are regulated with PI controllers tuned according to [18] with back-emf compensation • the mechanical load increases with the square of the rotating speed (such as, at full speed, the load torque is the rated machine torque) • the rotating speed is not regulated....

[...]

171 citations

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##### Frequently Asked Questions (2)

###### Q2. What have the authors stated for future works in "A bi-harmonic five-phase spm machine with low ripple torque for marine propulsion" ?

Designing the rotor with two identical radially magnetized magnets that cover two-third the pole arc appears as a possibility to reach this goal. The possibility to eliminate the ripple torques with a simple control that aims at achieving constant currents in the rotating frames is evaluated with a time simulation of the drive.