Optimal design for low iron-loss variable flux permanent magnet memory machine

Abstract

This paper proposes a kind of low iron-loss variable flux permanent magnet memory machine. The proposed memory machine can expand the speed range of machine, guarantee the operation efficiency of machine, avoid the irreversible demagnetization of PMs under high speed, and decrease the iron loss of the machine. Further, Taguchi method is used to optimize the proposed low iron-loss PM memory machine under magnetizing and demagnetizing current pulses respectively. Finally, the final optimum design scheme for the proposed low iron-loss variable flux permanent magnet memory machine is achieved by giving consideration to each optimization objective.

Keywords

Variable flux permanent magnet memory machine iron loss flux linkage Taguchi method magnetizing and demagnetizing current pulses

1. Introduction

Wide speed range is demanded in the permanent magnet synchronous machine (PMSM) used for electric vehicle. For the common PMSM, in order to widen the speed range of machine, a high negative d-axis current is required to decrease the PM flux linkage. The higher the operation speed of the machine is, the larger the negative d-axis current will be. On one hand, the higher negative d-axis current makes the irreversible demagnetization existed in PMs easily[1]; on the other hand, the higher negative d-axis current makes the copper loss and iron loss of the machine higher, which makes the efficiency of machine decreased. In order to avoid these problems, the variable flux permanent magnet memory machine is proposed.

The permanent magnet memory machine is first proposed by Vlado Ostovic in 2001 [2]. The rotor of the firstly proposed memory machine is a “sandwich” structure that is composed of AlNiCo PM, Nonmagnetic interlayer, and rotor core [3,4]. The effects of PM structure in “sandwich” structure on the magnetic field distributions under no-load and negative d-axis current conditions are analyzed in paper [5]. On the basis of the first proposed memory machine structure, some scholars have also proposed several improved structures for PM memory machine. In papers [6,7], a kind of series hybrid variable flux PM memory machine is proposed. Meanwhile, performances of the proposed machine under magnetizing and demagnetizing current pulses are analyzed respectively. In papers [8,9], a kind of hybrid PM memory machine which is excited by both low coercive PM and NdFeB PM is proposed. On this basis, an improved rotor structure is proposed by designing a flux barrier in the rotor core. By improving the rotor structure, the magnetizing characteristic of low coercive PM is improved significantly, and the irreversible demagnetization in low coercive PM under load condition is avoided effectively. In papers [10,11], a kind of PM memory machine with tangential PM structure is proposed, and the d-axis inductance L _d is larger than the q-axis inductance L _q in the machine. Similarly, in papers [12,13], a kind of PM memory machine with radial PM structure is proposed, and the d-axis inductance L _d is larger than the q-axis inductance L _q in the machine. By analyzing performances of the two kinds of PM memory machine structures in papers [10,11] and [12,13], a conclusion that the two kinds of PM memory machines have high torque density under low speed region and high efficiency under expanded speed region is drawn. The hybrid variable flux PM memory machine can be achieved by adding AlNiCo magnets in the common interior PM machine. Therefore, in the design process for hybrid variable flux PM memory machine, a design scheme of common interior PM machine needs to be obtained according to the running demand in constant torque region [14–18]. On this basis, the AlNiCo magnets are added to make the high speed operation range of machine meet the design requirements.

The variable flux PM memory machine has wide speed range. When the machine operates under high speed, the alternating frequencies of fundamental and harmonic components in air-gap flux density are high, which makes the iron loss of machine larger. On one hand, the higher iron loss makes the efficiency of machine decreased; on the other hand, the higher loss makes the temperature of machine increased, which will limit the improvement in power density of machine. The harmonic components in the magnetic field caused by harmonic components in PM magnetomotive force and non-sinusoidal distribution of stator magnetomotive force can be weakened effectively by improving the structure of stator or rotor reasonably. In paper [19], the structure parameters in stator teeth and PM cavity in rotor are optimized in order to decrease the copper loss and iron loss of machine. The stator teeth structure in an interior PM machine adopting concentrated winding is improved in paper [20], which decreases the rotor iron loss and PM eddy current loss. Paper [21] proposes three methods to decrease the iron loss of interior PM generator used for vehicle. The three methods include adopting flat stator teeth to expand the stator slot opening width, improving the flux barrier structure in rotor, and improving the stator winding structure (adopting nine-phase single layer winding). Meanwhile, effects of three improved methods on iron loss under no-load and short-circuit conditions are analyzed. In papers [22–24], the rotor structure of interior PM machine is improved to decrease the iron loss of machine. Paper [23] improves the PM cavity structure of an interior PM machine adopting 𝛻 type PM structure. Meanwhile, the optimal structure to make the iron loss least is achieved giving consideration to electromagnetic torque under flux weakening condition. By the improved structure proposed in [23], the stator iron loss is mainly weakened. On the basis of paper [23], the PM cavities between adjacent poles are connected in paper [24], which makes the rotor iron loss and PM eddy current loss weakened to a greater extent. At present, there is no literature to research the iron loss of the PM memory machine. Therefore, this paper will propose a kind of low iron-loss variable flux PM memory machine on the basis of the traditional PM memory machine structure.

In order to achieve the optimum low iron-loss variable flux PM memory machine, it is necessary to conduct optimization for the proposed improved PM memory machine. Taguchi method is a local optimum design method aiming at the multi-objective optimization design problem. This method is founded by Dr. Taguchi G of Japan in 1970s, and it can help engineers to quickly find the optimal combination of design variables with the least number of experiments. At present, Taguchi method has been widely used in the machine field. In paper [25], a six-phase synchronous reluctance machine is optimized by Taguchi method with the lowest cost, the lowest torque ripple, the highest efficiency and the highest power factor as the optimization objectives. In paper [26], an interior PM machine is optimized by Taguchi method with the lowest cogging torque and the highest efficiency as the optimization objectives. In papers [27,28], a line-start PM synchronous machine and a surface mounted PM machine are optimized by Taguchi method respectively. In paper [29], an axial-flux PM generator is optimized by Taguchi method with the highest efficiency, the optimum power quality, and the largest induced voltage as the optimization objectives.

In this paper, a kind of low iron-loss variable flux PM memory machine is proposed. Compared with the common PM machine, on one hand, the proposed memory machine can provide the almost same output torque in constant torque region; on the other hand, it has wider speed range. In addition, compared with the traditional PM memory machine, the iron loss of the proposed low iron-loss variable flux PM memory machine is lower to a great extent. Further, the proposed low iron-loss PM memory machine is optimized by Taguchi method to make it better. Finally, the final design scheme of the proposed low iron-loss PM memory machine to make the iron loss least is achieved giving consideration to other electromagnetic performances.

2. Low iron-loss variable flux PM memory machine

Wide speed range is demanded for PM synchronous machine used for electric vehicle. The method to widen speed range of machine is to reduce PM flux linkage 𝜓_f or to apply larger negative d-axis current. When the PM flux linkage is decreased, the required torque can not be achieved in the constant torque region, which reduces the torque density of machine. When a larger negative d-axis current is applied to winding, on one hand, the irreversible demagnetization exists in PMs easily, which makes the operation reliability of machine decreased; on the other hand, copper loss of machine is larger, which makes the efficiency of machine decreased. Therefore, a kind of machine that can not only ensure the output torque capability in the constant torque region, but also widen speed range on the premise of ensuring the reliability of machine is needed for electric vehicle. Aiming at this demand, the variable flux PM memory machine is proposed, among them, a commonly used PM memory machine structure is shown in Fig. 1.

Fig. 1.

Traditional variable flux PM memory machine.

Figure 2 shows the flux lines distributions of variable flux PM memory machine under magnetizing current pulse and demagnetizing current pulse by using the commercial finite element software Ansys Maxwell 19.0. It can be seen from Fig. 2 that under magnetizing current pulse, almost all of the flux lines produced by NdFeB PM enter the main magnetic circuit except for a small part of magnetic leakage, so the flux linkage is larger, which guarantees the enough output torque in the constant-torque region. In addition, under demagnetizing current pulse, because a considerable part of flux lines produced by NdFeB PM are bypassed by AlNiCo PM, the flux entering the main magnetic circuit is decreased greatly. Therefore, under demagnetizing current pulse, the flux linkage decreases, which makes machine have wide speed range. In conclusion, the variable flux PM memory machine can not only output enough torque in constant torque region, but also operate under wide speed range.

Fig. 2.

Flux lines distribution of variable flux PM memory machine under magnetizing and demagnetizing current pulses.

PMSM used for electric vehicle requires not only a wide speed range, but also a high power density. When the machine operates under high speed, the harmonic contents in air-gap flux density increase, which makes the iron loss of machine increased. On one hand, the higher iron loss makes the efficiency of machine decreased; on the other hand, the higher iron loss makes the temperature of machine rise, which makes the increment of power density limited. Therefore, it is necessary to decrease the iron loss of machine in designing process. In this paper, a kind of low iron-loss variable flux PM memory machine is proposed by improving the structure of traditional PM memory machine shown in Fig. 1. An expanded air flux barrier structure is added to the traditional PM memory machine to achieve the low iron-loss variable flux PM memory machine, as shown in Fig. 3. The distribution of rotor magnetomotive force becomes more sinusoidal by adding the expanded air flux barrier structure, which decreases the harmonic contents in air-gap flux density effectively. Therefore, the iron loss of machine can be decreased effectively, and further the efficiency of machine can be effectively improved, meanwhile, the temperature of machine can be effectively decreased. The related parameters of machine are shown in Table 1.

Fig. 3.

Proposed low iron-loss variable flux PM memory machine.

Table 1

Related parameters of the machine

Symbol	Quantity	Value	Unit
p	Pole pair number	4	–
Q	Slot number	48	–
R _ra	Outer radius of rotor	64	mm
δ	Length of air gap	1	mm
R _sy	Outer radius of stator	100	mm
B _rNdFeB	Remanence of NdFeB	1.125	T
H _cNdFeB	Coercive force of NdFeB	886	kA/m
B _rAlNiCo	Remanence of AlNiCo	0.6	T
H _cAlNiCo	Coercive force of AlNiCo	40	kA/m
h _NdFeB	Thickness of NdFeB PM	6.5	mm
w _NdFeB	Width of NdFeB PM under one pole	39	mm
h _AlNiCo	Thickness of AlNiCo PM	6.9	mm
w _AlNiCo	Width of AlNiCo PM under one pole	10	mm
l	Axial length of PM	140	mm

The same magnetizing and demagnetizing current pulses are applied to the common PM machine and the proposed low iron-loss variable flux PM memory machine respectively. The waveforms of flux linkage in two machines are achieved, as shown in Fig. 4. Further, the fundamental magnitudes of flux linkage are achieved by Fourier decomposition for flux linkage waveforms in Fig. 4, as shown in Table 2. It can be seen from Fig. 4 and Table 2 that under the same magnetizing current pulse, the proposed low iron-loss variable flux PM memory machine has the almost same flux linkage with common PM machine. Therefore, the proposed low iron-loss memory machine can provide the almost same output torque with the common PM machine in constant torque region. In addition, under the same demagnetizing current pulse, compared with the common PM machine, the proposed low iron-loss variable flux PM memory machine has lower flux linkage. Therefore, the proposed low iron-loss PM memory machine can effectively expand the speed range of machine.

Fig. 4.

Comparison of flux linkage between the proposed low iron-loss memory machine and common PM machine under magnetizing and demagnetizing current pulses.

Table 2

Comparison of flux linkage between the proposed low iron-loss memory machine and common PM machine

Flux linkage (Wb)	Common PM machine	Low iron-loss PM memory machine
Under magnetizing current pulse	0.1008	0.09892
Under demagnetizing current pulse	0.03979	0.02988

Meanwhile, the iron loss of the traditional PM memory machine and the proposed low iron-loss variable flux PM memory machine are calculated respectively under the same magnetizing and demagnetizing current pulses, as shown in Table 3. It can be seen from Table 3 that the loss of the proposed low iron-loss variable flux PM memory machine is lower than that of the traditional PM memory machine to a large extent.

Table 3

Comparison of iron loss between the proposed low iron-loss memory machine and traditional PM memory machine

Iron loss (W)	Traditional PM memory machine	Low iron-loss PM memory machine
Magnetizing current pulse	406.5	379.8
Demagnetizing current pulse	130.8	68.2

3. Optimal design for the proposed low iron-loss PM memory machine based on Taguchi method

3.1. Selecting optimization objective, optimization variables, and constraint condition

It is necessary to optimize the proposed low iron-loss variable flux PM memory machine to make its performances better. The optimization objectives are that the least flux linkage under demagnetizing current pulse, the lowest iron loss under demagnetizing and magnetizing current pulses. The constraint condition is that flux linkage of the optimized low iron-loss PM memory machine is less than 5% lower than that of common PM machine under magnetizing current pulse, so as to ensure the enough output torque of machine in constant torque region. The corresponding optimization objective functions and constraints are shown in formula (1). $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}\text{Objective Function}:[\text{Min}({\psi}_{\text{fd}}),\text{Min}(P_{\text{Fe}})]\\ \text{Constraint}:{\psi}_{\text{f}\text{m}}\geq 0.95{\psi}_{\text{PM}}.\end{array}\right. & & \displaystyle\end{eqnarray}$ (1) Where 𝛹_fd is the flux linkage of the proposed low iron-loss PM memory machine under demagnetizing current pulse; P _Fe is the iron loss of machine; 𝛹_fm and 𝛹_PM are the flux linkage of low iron-loss PM memory machine and common PM machine under the same magnetizing current pulse respectively.

The optimization variables are shown in Fig. 5, and are represented by A, B, C and D respectively. Among them, A represents the distance between the vertex of expanded air flux barrier structure and the center of rotor; B represents the angle between the vertex of expanded air flux barrier structure and the center line of corresponding magnetic pole; C represents the width of the opposite side of the vertex of expanded air flux barrier structure; D represents the position of the opposite side of the vertex of expanded air flux barrier structure. The value range of each optimization variable is determined according to the structure parameters of machine, and further the factors and levels of each optimization variable are achieved, as shown in Table 4.

Fig. 5.

The sketch map of the optimization variables in the proposed low iron-loss PM memory machine.

Table 4

Factors and levels

Level	Factor
	A (mm)	B (°)	C (mm)	D (mm)
I	62	3	1	0
II	60	6	2	1
III	58	9	3	2

The L ₉ (3⁴) orthogonal table is established according to the factors and levels in Table 4, as shown in Table 5.

Table 5

L ₉ (3⁴) orthogonal table

Experiment number	A	B	C	D
1	I	I	I	I
2	I	II	II	II
3	I	III	III	III
4	II	I	II	III
5	II	II	III	I
6	II	III	I	II
7	III	I	III	II
8	III	II	I	III
9	III	III	II	I

3.2. Experimental results and results processing

Flux linkage and iron loss of the proposed low iron-loss PM memory machine under magnetizing and demagnetizing current pulses are calculated by Ansys Maxwell 19.0 according to the orthogonal table in Table 5. Experimental results of each experiment under magnetizing and demagnetizing current pulses are listed in Table 6 respectively.

Table 6
Experimental results under magnetizing and demagnetizing current pulses

Experiment number Under magnetizing current pulse Under demagnetizing current pulse

𝜓_f (Wb) P _Fe(W) 𝜓_f(Wb) P _Fe(W)

1 0.09913 382.4 0.02465 69.73

2 0.1001 391.4 0.02733 47.87

3 0.1026 412.5 0.03369 61.1

4 0.099 383 0.0248 71.24

5 0.09892 379.8 0.02988 68.2

6 0.1011 399.5 0.0259 98.82

7 0.09744 370.1 0.02534 83.22

8 0.1006 396.9 0.02523 106.7

9 0.1009 398.6 0.02787 118.4

Experiment number	Under magnetizing current pulse	Under demagnetizing current pulse
1	0.09913	382.4	0.02465	69.73
2	0.1001	391.4	0.02733	47.87
3	0.1026	412.5	0.03369	61.1
4	0.099	383	0.0248	71.24
5	0.09892	379.8	0.02988	68.2
6	0.1011	399.5	0.0259	98.82
7	0.09744	370.1	0.02534	83.22
8	0.1006	396.9	0.02523	106.7
9	0.1009	398.6	0.02787	118.4

In order to achieve the effects of each optimization variable on each optimization objective, it is necessary to analyze the average values of the experimental results. Further, in order to achieve the relative importance of the effects of the optimization variables on each optimization objective, it is necessary to analyze the variance of experimental results.

(1) Analysis of average value

The average analysis for experimental results includes overall average analysis and average analysis under each level of each factor.

(a) Overall average analysis

The overall average values of experimental results in each column of Table 6 are calculated respectively, and the corresponding calculation formula is listed as follow $\begin{eqnarray} \displaystyle m={\displaystyle \frac{\displaystyle\sum _{i=1}^{n}m_{i}}{n}}. & & \displaystyle \end{eqnarray}$ (2) Where m is the overall average value of experimental results in certain column of Table 6; n is the experiment number; m _i is the experimental result of certain experiment in Table 6.

The overall average values of experimental results in each column of Table 6 are calculated by formula (2), and the corresponding results are listed in Table 7.

Table 7

Overall average values

Operate point	m _{𝜓_f} (Wb)	m _{P_Fe}(W)
Under magnetizing current pulse	0.09998	390.467
Under demagnetizing current pulse	0.02719	80.587

(b) Average analysis under each level of each factor

The average value of the flux linkage 𝜓_f under each level of factor A under magnetizing current pulse is set as an example to be calculated, and the corresponding expressions are shown in formula ((3))–((5)). $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle m_{{\psi}_{\text{f}}\text{A}(\text{I})}={\displaystyle \frac{{\psi}_{\text{f1}}+{\psi}_{\text{f2}}+{\psi}_{\text{f3}}}{3}}\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle m_{{\psi}_{\text{f}}\text{A}(\text{II})}={\displaystyle \frac{{\psi}_{\text{f4}}+{\psi}_{\text{f5}}+{\psi}_{\text{f6}}}{3}}\end{eqnarray}$ (4) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle m_{{\psi}_{\text{f}}\text{A}(\text{III})}={\displaystyle \frac{{\psi}_{\text{f7}}+{\psi}_{\text{f8}}+{\psi}_{\text{f9}}}{3}}.\end{eqnarray}$ (5)

Similarly, the average values of the flux linkage, iron loss under each level of each factor at magnetizing and demagnetizing current pulses can be achieved respectively. The corresponding results are listed in Table 8.

Table 8

Average values of experimental results under each level of each factor under magnetizing and demagnetizing current pulses

Factor	Level	Under magnetizing current pulse		Under demagnetizing current pulse
		m _{𝜓_f} (Wb)	m _{P_Fe}(W)	m _{𝜓_f}(Wb)	m _{P_Fe}(W)
	I	0.10061	395.43	0.0286	59.57
A	II	0.09967	387.43	0.02686	79.42
	III	0.09965	388.53	0.0261	102.77
	I	0.09852	378.5	0.02493	74.73
B	II	0.09987	389.37	0.02748	74.26
	III	0.1015	403.53	0.0292	92.77
	I	0.1003	392.93	0.02526	91.75
C	II	0.1	391	0.0267	79.17
	III	0.09965	387.47	0.0296	70.84
	I	0.09965	386.93	0.0275	85.44
D	II	0.09955	387	0.02619	76.64
	III	0.1007	397.47	0.0279	79.68

Under the magnetizing current pulse, it can be achieved from Table 8 that the larger the value of variable A is, that is, the smaller the distance between the vertex of expanded air flux barrier and rotor surface is, the larger the stator flux linkage will be, but at the same time, the larger the iron loss will be. The larger the value of variable B is, that is, the farther the vertex of expanded air flux barrier away from the center line of magnetic pole is, the larger the stator flux linkage will be, but at the same time, the larger the iron loss will be. The larger the value of variable C is, that is, the larger the width of the opposite side of the vertex of the expanded air flux barrier is, the smaller the iron loss will be, but at the same time, the smaller the stator flux linkage will be. As the value of variable D increases, that is, as the distance between the opposite side of the vertex of the expanded air flux barrier and the rotor surface increases, the iron loss will increase gradually, and at the same time, the flux linkage will also present an increasing trend.

Under the demagnetizing current pulse, it can be achieved from Table 8 that the larger the value of variable A is, that is, the smaller the distance between the vertex of expanded air flux barrier and rotor surface is, the larger the stator flux linkage will be, and at the same time, the smaller the iron loss will be. The larger the value of variable B is, that is, the farther the vertex of expanded air flux barrier away from the center line of magnetic pole is, the larger the stator flux linkage will be, but at the same time, the iron loss will also present an increasing trend. The larger the value of variable C is, that is, the larger the width of the opposite side of the vertex of the expanded air flux barrier is, the larger the stator flux linkage will be, and at the same time, the smaller the iron loss will be.

The combinations of the level taken by each factor to make optimization objectives optimal can be achieved by the average analysis results in Table 8. Under magnetizing current pulse, the combination of the level taken by each factor to make iron loss least is A (II)B (I)C (III)D (I). Under demagnetizing current pulse, the combination of the level taken by each factor to make flux linkage least is A (III)B (I)C (I)D (II), and the combination to make iron loss least is A (I)B (II)C (III)D (II). It can be achieved from the above analysis results that the combinations of the level taken by each factor to make each optimization objective optimal are different. Hence, in order to obtain a combination of the level taken by each factor taking into account all the optimization objectives, it is necessary to analyze the variance of experimental results to achieve the relative importance of the effects of the optimization variables on each optimization objective.

(2) Analysis of variance

It is necessary to analyze the variance of experimental results to achieve the relative importance of the effects of the optimization variables on each optimization objective. The corresponding calculation formula is as follow $\begin{eqnarray} \displaystyle S_{A}={\displaystyle \frac{\displaystyle\mathop{\sum }_{j=I}^{Q}(m_{A(j)}-m)^{2}}{Q}}. & & \displaystyle \end{eqnarray}$ (6) Where S _A is the variance of certain optimization objective under factor A; m _{A (j)} is the average value of certain optimization objective under level j of factor A; m is the overall average value of certain optimization objective; Q is the number of levels taken by each factor, and Q = 3 in this paper.

The results of variance analysis for experiment results under magnetizing and demagnetizing current pulses are achieved, as listed in Table 9 and Table 10.

Table 9

Variance of experimental results under magnetizing current pulse

Factor	S _{𝜓_f}	S _{𝜓_f}(%)	S _{P_Fe}	S _{P_Fe}(%)
A	2e-7	9.87%	12.536	8.52%
B	14.847e-7	73.28%	105.02	71.35%
C	0.706e-7	3.49%	5.11	3.47%
D	2.707e-7	13.36%	24.52	16.66%

Table 10

Variance of experimental results under demagnetizing current pulse

Factor	S _{𝜓_f}	S _{𝜓_f}(%)	S _{P_Fe}	S _{P_Fe}(%)
A	1.095e-6	13.75%	311.72	65.88%
B	3.077e-6	38.64%	74.254	15.69%
C	3.2577e-6	40.91%	73.87	15.61%
D	0.5334e-6	6.7%	13.318	2.82%

It can be achieved from Table 9 and Table 10 that, under magnetizing current pulse, the variable B has the largest effect on flux linkage and iron loss. Under demagnetizing current pulse, variable C has the largest effect on flux linkage. At the same time, variable B has the second largest effect on flux linkage, and its relative importance is slightly smaller than variable C. Meanwhile, variable A has the largest effect on iron loss of machine.

3.3. Optimal structure of the low iron-loss variable flux PM memory machine

It can be achieved from the analysis results of average value that under magnetizing current pulse, the combination of the level taken by each factor to make iron loss least is A (II)B (I)C (III)D (I). Under demagnetizing current pulse, the combination of the level taken by each factor to make flux linkage least is A (III)B (I)C (I)D (II), and the combination to make iron loss least is A (I)B (II)C (III)D (II). Combinations of the level taken by each factor to make three optimization objectives optimal respectively are different. Further, it can be achieved from the variance analysis results in Table 9 and Table 10 that, under magnetizing current pulse, the relative importance of the effects of each factor on the iron loss is BDAC from the largest to smallest. Under demagnetizing current pulse, the relative importance of the effects of each factor on the flux linkage is CBAD from the largest to smallest, and the relative importance of the effects of each factor on the iron loss is ABCD from the largest to smallest.

It can be seen from analysis results of variance that variable A has the largest effect on iron loss under demagnetizing current pulse, so the level of A should be selected I to make iron loss under demagnetizing current pulse least, namely A (I). Variable B has the largest effect on the iron loss under magnetizing current pulse, so the level of B should be selected I to make iron loss under magnetizing current pulse least, namely B (I). Variable C has the largest effect on the flux linkage under demagnetizing current pulse, so the level of C should be selected I to make stator flux linkage under demagnetizing current pulse least, namely C (I). Variable D has the largest effect on iron loss under magnetizing current pulse. Therefore, the level of D should be selected I to make iron loss under magnetizing current pulse least, namely D (I). In conclusion, the final optimization scheme of the proposed low iron-loss PM memory machine is achieved, and the final combination of the level taken by each factor in the optimization scheme is A (I)B (I)C (I)D (I). The optimal memory machine structure is shown in Fig. 6.

Fig. 6.

The final structure of the proposed low iron-loss PM memory machine.

Comparison diagram of flux linkage between the optimal low iron-loss variable flux PM memory machine and the common PM machine is shown in Fig. 7. Meanwhile, the fundamental amplitudes of the waveforms in Fig. 7 are obtained by Fourier decomposition, as listed in Table 11. It can be seen from Fig. 7 and Table 11 that under the same magnetizing current pulse, the flux linkage of optimal low iron-loss PM memory machine only decreases 1.67 percent compared with the common PM machine, which satisfies the requirement of the constraint condition. Further, it shows that the output torque can be guaranteed in the optimal low iron-loss PM memory machine under the constant torque region. Further, under the same demagnetizing current pulse, the flux linkage of optimal low iron-loss PM memory machine significantly decreases compared with the common PM machine. Hence, the proposed low iron-loss PM memory machine can have a wide speed range. Meanwhile, the iron loss of the optimal low iron-loss PM memory machine is compared with that of the traditional PM memory machine, as shown in Fig. 8. It can be seen from Fig. 8 that the iron loss of the optimal low iron-loss PM memory machine decreases significantly compared with the traditional PM memory machine. Among them, iron loss decreases 46.67 percent under demagnetizing current pulse, and 5.95 percent under magnetizing current pulse.

Fig. 7.

Comparison of flux linkage between the optimal low iron-loss PM memory machine and common PM machine.

Fig. 8.

Comparison of iron loss between the optimal low iron-loss PM memory machine and traditional PM memory machine.

Table 11

Performances comparison of common PM machine, traditional PM memory machine and optimal low iron-loss PM memory machine under magnetizing and demagnetizing current pulses

	Performance	Common PM machine	Traditional PM memory machine	Optimal low iron-loss PM memory machine
Under magnetizing current pulse	Flux linkage (Wb)	0.1008	0.1019	0.09912
	Loss (W)	407.7	406.5	382.3
Under demagnetizing current pulse	Flux linkage (Wb)	0.03979	0.02488	0.02464
	Loss (W)	207.5	130.8	69.76

4. Conclusion

This paper proposes a kind of low iron-loss variable flux PM memory machine based on the structure of traditional PM memory machine. When the magnetizing current pulse is applied to the winding, the flux linkage of the proposed low iron-loss PM memory machine is basically the same as that of the common PM machine. So the torque density of the proposed low iron-loss PM memory machine can be guaranteed. When the demagnetizing current pulse is applied to the winding, the flux linkage of the proposed low iron-loss PM memory machine is much smaller than that of the common PM machine. So the proposed low iron-loss PM memory machine has wide speed range. Meanwhile, the iron loss of the proposed low iron-loss PM memory machine is lower than that of the traditional PM memory machine to a large extent under both demagnetizing current pulse and magnetizing current pulse. So the proposed low iron-loss PM memory machine has higher efficiency and lower temperature rise. Further, the Taguchi method is used to optimize the proposed low iron-loss PM memory machine to make its performances better. Finally, the final optimal design scheme of the proposed low iron-loss PM memory machine is achieved.

Footnotes

Acknowledgements

This work was supported in part by the project supported by Major Program of National Natural Science Foundation of China under Grant 51690183, and in part by the project supported by National Natural Science Foundation of China under Grant 51577134.

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