Comparison and analysis of electromagnetic characteristics of IPMSM with single and double layer PMs

Abstract

For improving torque density, speed range for constant power operation and overload capacity of the interior permanent magnet synchronous machine (IPMSM) with single-layer PMs, a type of IPMSM with double-layer PMs is designed and analyzed in this paper. Under the same stator structure, winding type and the volume of PMs, the models of IPMSM with single and double-layer PMs are built respectively. The electromagnetic properties including torque, inductance, loss and efficiency are calculated and compared for the two types of IPMSM by FEA. The results show that the salient rate, output torque, the area with high efficiency and speed range for constant power with double-layer PMs are improved efficiently compared to the IPMSM with single-layer PMs.

Keywords

Permanent magnet synchronous motor single and double layer permanent magnet electromagnetic properties finite element analysis

1. Introduction

With the rapid development of the performance for permanent magnetic (PM) material, PM motors with NdFeB have been widely applied in ship, aerospace, industrial automation, household applications and electric vehicles, etc [1,2]. PM synchronous machine (PMSM) is a type of special motor, which utilizes PMs to provide the magnetomotive force. It has some advantages including simple structure, high efficiency in the whole working region and good dynamic performance, which has become the main type of driving motor for electric vehicles [3]. Nevertheless, the low torque density and limit speed range of constant power for the traditional PMSM has influenced its further application in the cases of field-weakening for the wider speed range and higher requirement to overload capacity [4–7]. Therefore, it has been one of the interest topics for the electric vehicles to obtain the higher torque density, excellent overload capacity and sufficient speed range for constant power operation [8–17].

Compared with the surface-mounted PMSM under the same stator structure, the IPMSM with four-layer PMs has the larger torque ripple, and a wider speed range due to field-weakening and better output torque characteristic [18]. An IPMSM with double-layer PMs is described in [19], and the salient ratio, operating efficiency and constant power operation area are improved efficiently. Moreover, the IPMSM with three-layer PMs, 14 poles and 18 stator slots is designed in [20–23], which exhibits the advantages of larger reluctance torque, the higher efficiency in the whole working area and a good field-weakening performance, and the harmonic component and torque ripple can be reduced effectively.

Based on the IPMSM with single-layer PMs (IPMSM-SPM), a new type of IPMSM with double-layer PMs (IPMSM-DPM) is designed, which can increase the salient rate, the torque output capacity and overload capability because of the additional reluctance torque. The structure and operating principle of IPMSM are analyzed, and the two types of IPMSM are compared when adopting the control strategy of maximum torque per ampere (MTPA). Finally, a prototype machine was manufactured and some electronic magnetic characteristics are tested to verify the rationality of theoretical analysis.

2. Structure and parameters of IPMSM

2.1. The overall structure of IPMSM

According to the operational performance and the installation space of the electric vehicle, Table 1 gives the partial dimension parameters of IPMSM-DPM. Figure 1 shows the structure model of IPMSM-DPM built by Maxwell. The IPMSM-DPM has 8 poles and the slot number of stator is 48 with the distributed lap winding. Some PMs with the shape of ‘—’ and ‘U’ are arranged in the rotor core, and the magnetic bridge is designed to reduce the flux leakage and improve the utilization of PMs.

Table 1
Part of IPMSM parameters

Item Value Item Value

Rated power (kw) 10.5 Outer radius of stator (mm) 255

Rated voltage (v) 154 Inner radius of rotor (mm) 160.4

Rotor pole number/stator slot number 8/48 Conductors number per slot 8

Rated torque (N m) 33.5 Wire diameter (mm) 0.511

Rated speed (rpm) 3000 Winding connection Wye

Item	Value	Item	Value
Rated power (kw)	10.5	Outer radius of stator (mm)	255
Rated voltage (v)	154	Inner radius of rotor (mm)	160.4
Rotor pole number/stator slot number	8/48	Conductors number per slot	8
Rated torque (N m)	33.5	Wire diameter (mm)	0.511
Rated speed (rpm)	3000	Winding connection	Wye

Fig. 1.

Structure of IPMSM-DPM.

2.2. The structure of rotor

The rotor structure of IPMSM-DPM is shown in Fig. 2a, and the double-layer PMs are arranged in the rotor core. The thickness of PMs is larger than the width of magnetic bridge. Meanwhile, the width of magnetic bridge is fixed for reducing flux leakage and fixing the PMs. The width of the magnetic bridge (R _ib2) between the first-layer PMs is 2 mm and the width of the magnetic bridge (R _ib1) between the second-layer PMs is 10 mm, respectively. Due to the restricted space and mechanical strength of rotor core, the range of R _ib1 is relatively small while the range of R _ib2 is large, which has the great influence on the flux distribution and the structure of magnetic circuit. The second-layer of PMs is closer to the air gap and the distance (O₂) between the middle magnetic bridge and the shaft has a large impact on the air gap flux density and flux leakage.

For comparative analysis, the structure of single-layer PM with ‘V’ shape after optimized by ANSYS under the same volume of PMs and air gap length is proposed, as shown in Fig. 2b, similar to the rotor structure with double-layer PM in Fig. 2a, the designed magnetic barriers is also used to reduce flux leakage. Meanwhile, there is an iron bridge between the flux barriers and the rotor core near the air gap to guarantee the mechanical strength of the rotor at high speed. Table 2 shows partial parameters of single-layer PMs. In addition, the two rotors have the same stator structure and armature windings.

Fig. 2.

Rotor structure of IPMSM. (a) Rotor structure of IPMSM-DPM; (b) Rotor structure of IPMSM-SPM.

Table 2

Parameters of IPMSM with Single-layer PM

Item	Value
PM (mm³)	6.4844.4440
Outer radius of rotor (mm)	160.4
Thickness of iron bridge (mm)	3.4

3. Electromagnetic analysis

3.1. Control strategy of MTPA

The current vector of IPMSM with the control strategy of MTPA should be satisfied with a system of equations [24,25]. $\begin{eqnarray}\left\{\begin{array}{@{}l@{}}\frac{\partial (T_{em}/i_{s})}{\partial i_{d}}=0,\\ \frac{\partial (T_{em}/i_{s})}{\partial i_{q}}=0,\end{array}\right.\end{eqnarray}$ (1) where $\begin{eqnarray}\displaystyle T_{em}\text{} & =\text{} & \displaystyle p\left[L_{d}i_{f}i_{s}\sin {\beta}+\frac{1}{2}(L_{d}-L_{q})i_{s}^{2}\sin 2{\beta}\right]\nonumber\\ \displaystyle \text{} & =\text{} & \displaystyle p[{\psi}_{f}i_{q}+(L_{d}-L_{q})i_{d}i_{q}]\nonumber\\ \displaystyle \text{} & =\text{} & \displaystyle \frac{p}{{\omega}}[e_{o}i_{q}+(X_{d}-X_{q})i_{d}i_{q}]\end{eqnarray}$ (2) with $\begin{eqnarray}i_{s}=\sqrt{i_{d}^{2}+i_{q}^{2}}.\end{eqnarray}$ (3)

Substituting (2) and (3) into equation (1) yields $\begin{eqnarray}\displaystyle i_{d} & = & \displaystyle \frac{-{\psi}_{f}+\sqrt{{\psi}_{f}^{2}+4(L_{d}-L_{q})^{2}i_{q}^{2}}}{2(L_{d}-L_{q})}\nonumber\\ \displaystyle & = & \displaystyle \frac{{\psi}_{f}-\sqrt{{\psi}_{f}^{2}+4({\rho}-1)^{2}L_{d}^{2}i_{q}^{2}}}{2({\rho}-1)L_{d}},\end{eqnarray}$ (4) where 𝜌 is the motor salient rate, and 𝜌 = L _q∕L _d.

When equation (2) is expressed by the per unit, formula (5) can be obtained $\begin{eqnarray}T_{em}^{\ast }=i_{q}^{\ast }(1-i_{d}^{\ast }).\end{eqnarray}$ (5)

The formula of electromagnetic torque can be obtained, when equation (4) is expressed as the per unit value and substituted into equation (5). This leads to $\begin{eqnarray}\displaystyle T_{em}^{\ast }\text{} & =\text{} & \displaystyle \sqrt{i_{d}^{\ast }(1-i_{d}^{\ast })^{3}},\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle T_{em}^{\ast }\text{} & =\text{} & \displaystyle \frac{i_{d}^{\ast }}{2}\left[1+\sqrt{1+4i_{q}^{\ast 2}}\right].\end{eqnarray}$ (7) The functions of $i_{d}^{\ast }$ and $i_{q}^{\ast }$ with respect to the torque can be obtained from equations (6) and (7), which yields $\begin{eqnarray}\displaystyle i_{d}^{\ast }\text{} & =\text{} & \displaystyle f_{1}(T_{em}^{\ast }),\end{eqnarray}$ (8) $\begin{eqnarray}\displaystyle i_{q}^{\ast }\text{} & =\text{} & \displaystyle f_{2}(T_{em}^{\ast }).\end{eqnarray}$ (9) Within the range of maximum output torque, the d- and q-component of the minimum stator winding current can be obtained from the above two formulas for a given load torque by MTPA.

Figure 3 shows the output torque curve by adopting MTPA. The internal power factor angle of 𝛽 corresponding to the maximum output torque at different currents is greater than 0, because of the salient pole effect caused by the difference between the d- and q-magnetic resistance of rotor. Therefore, for a given load torque, it is important to seek the maximum output torque corresponding to 𝛽 by scanning the different current and 𝛽, so as to determine the minimum d- and q-current component in the case of different load.

Fig. 3.

MTPA control trajectory curve.

In order to compare the characteristics of inductance, torque, loss, and efficiency of IPMSM with single-layer and double-layer PMs under the same control strategy of MTPA, the Finite Element Method (FEM) calculation of IPMSM is adopted by Maxwell.

3.2. Output torque and inductance

The output torque of IPMSM is mainly composed of magnetic resistance torque and PM torque, which can be calculated by equation (10) $\begin{eqnarray}T_{em}=P_{n}\left\{{\psi}_{f}i_{s}\sin {\beta}+\frac{1}{2}(L_{d}-L_{q})i_{s}^{2}\sin 2{\beta}\right\}.\end{eqnarray}$ (10) In the coordinate system of d–q, the corresponding formulas are given $\begin{eqnarray}\displaystyle i_{d}\text{} & =\text{} & \displaystyle i_{s}\cos {\beta},\end{eqnarray}$ (11) $\begin{eqnarray}\displaystyle i_{q}\text{} & =\text{} & \displaystyle i_{s}\sin {\beta}.\end{eqnarray}$ (12) The formula (11) and (12) are substituted into equation (10), which leads to $\begin{eqnarray}T_{em}=P_{n}\{{\psi}_{f}i_{q}+(L_{d}-L_{q})i_{d}i_{q}\}=T_{M}+T_{R},\end{eqnarray}$ (13) where $\begin{eqnarray}\displaystyle T_{M}\text{} & =\text{} & \displaystyle P_{n}{\psi}_{f}i_{q},\end{eqnarray}$ (14) $\begin{eqnarray}\displaystyle T_{R}\text{} & =\text{} & \displaystyle P_{n}(L_{d}-L_{q})i_{d}i_{q}.\end{eqnarray}$ (15) Here, T _em is the electromagnetic torque, i _s is the armature current, i _f is the exciting current, P _n is the number of pole pairs, L _d and L _q are d- and q-inductance, X _d and X _q are d- and q-reactance, 𝛽 is the interior power factor angle, i _d and i _q are the d- and q-component of armature current, 𝜓_f and e _o are the flux linkage of the PMs and back EMF, T _M and T _R are the PM torque and reluctance torque.

In order to obtain the relationships between PM toque, reluctance torque and output torque, d- and q-inductances of IPMSM can be calculated by FEM, and then substituted into formula (14) and (15), so the PM torque and reluctance torque can be calculated separately.

Under the same stator structure, air gap length and control strategy, the output torque against 𝛽 is shown in Fig. 4a,b when the armature current is 90 and 100 A respectively. It shows that the output torque increases firstly then decrease with 𝛽, and the maximum output torque deviates from the original point, because of the magnetic resistance torque. Due to differences between d- and q-inductance, the maximum torque and overload capacity of IPMSM with double-layer PMs is larger than that of single-layer PMs under the same excitation.

Fig. 4.

Output torque of IPMSM with single and double-layer PM. (a) I _s = 90 A; (b) I _s = 100 A.

To verify the above theoretical analysis, Fig. 5 shows the variation of d- and q-inductances with the rotor position when armature current is 100 A and the output torque of IPMSM reaches the peak value. It can be seen that the ripple of d- and q-inductances vary with rotor position because of the variable magnetic resistance.

The IPMSM with double-layer PMs can improve the salient ratio and output torque because it has relatively small d-inductance and large q-inductance compared with the single-layer PMs.

Fig. 5.

D- and Q-inductances of IPMSM with Single and double PM. (a) Single-layer PMs; (b) Double-layer PMs.

Based on equations (10)–(15) and figure (5)–(6), the electromagnetic parameters of IPMSM with double and single layer PMs are calculated, respectively, as shown in Table 3, which shows that the motor with double-layer PMs has the larger peak torque and internal power factor angle. Therefore, the IPMSM with double-layer PMs has the better output torque and overload capacity under the same armature current. At the same time, it has the large difference of d and q inductances (L _q–L _d) and saliency ratio (L _q∕L _d), 1.1013 mH and 2.58, respectively. Therefore, the PM torque and the reluctance torque can be calculated by equation (14) and (15), as shown in Table 3.

IPMSM with double-layer PMs has larger reluctance torque and the ratio of reluctance torque to output torque (T _R∕T _max), so the output torque can be increased under the same volume of PMs by adopting the rotor structure with double-layer PMs. Meanwhile, the larger T _R∕T _max can reduce the dependence of output torque on the PM torque with the same load, thus the armature current and the copper loss can be reduced and its efficiency can be improved.

Table 3

The comparison of electromagnetic parameters for IPMSMs with Single and double-layer PMs

Value	Single-layer PM	Double-layer PM
𝛽 (deg)	39.09	47.27
i _d (A)	−63.03	−73.43
i _q (A)	77.64	67.88
L _d (mH)	0.787	0.6952
L _q (mH)	1.6557	1.7965
(L _q –L _d) (mH)	0.8687	1.1013
L _q∕L _d	2.10	2.58
T _max (N m)	84.71	87.39
T _M (N m)	67.71	65.43
(T _M∕T _max) (p.c.)	59.85	49.75
T _R (N m)	17.0	21.96
(T _R∕T _max) (p.c.)	20.06	25.13

3.3. Loss analysis and efficiency

The motor loss is directly related to the parameters such as efficiency and dimensions, so the accurate calculation of loss is of great significance to the motor design [26–28]. Besides, the accurate calculation of core loss is very important due to the saturation influence of magnetic density. The calculation precision is affected by the mesh quality of FEM. Therefore, the encrypted partition is used for the areas, where the magnetic energy varies greatly, such as air gap, while the size of subdivision can increase appropriately and the mesh number can reduce in the areas with smaller magnetic energy varied for increasing the computation speed.

The loss of motor after meshing by FEM can be calculated as follows, $\begin{eqnarray}\displaystyle W_{hi}\text{} & =\text{} & \displaystyle \mathop{\sum }_{e=1}^{n_{elem}}\left\{\mathop{\sum }_{k=1}^{n}a(B_{k})\times f_{k}\right\}\times V_{c},\end{eqnarray}$ (16) $\begin{eqnarray}\displaystyle W_{ei}\text{} & =\text{} & \displaystyle \mathop{\sum }_{e=1}^{n_{elem}}\left\{\mathop{\sum }_{k=1}^{n}b(B_{k},f_{k})\times f_{k}^{2}\right\}\times V_{c},\end{eqnarray}$ (17) $\begin{eqnarray}\displaystyle W_{i}\text{} & =\text{} & \displaystyle W_{hi}+W_{ei},\end{eqnarray}$ (18) $\begin{eqnarray}\displaystyle W_{c}\text{} & =\text{} & \displaystyle 3R_{a}I_{e}^{2},\end{eqnarray}$ (19) $\begin{eqnarray}\displaystyle {\eta}\text{} & =\text{} & \displaystyle \frac{{\omega}T-W_{i}}{{\omega}T+W_{c}}\times 100.\end{eqnarray}$ (20)

Here W _hi is the hysteresis loss, W _ei is the eddy current loss, n _elem is the mesh number, f _k is the harmonic frequency, e is the number of mesh after finite element division, k is the harmonic order, V _c is the mesh volume, B _k is the flux density magnitude of kth harmonics, W _c is the copper loss, R _a is the phase resistance, I _e is the RMS of phase current, 𝜂 is the efficiency, ω is the mechanical angular velocity of rotor, 𝛼(B _k) and b (B _k, f _k) can be obtained by the loss curve of silicon steel material.

The core loss of IPMSM-SPM is given in Fig. 6a, which shows that the core loss increases with the speed. Figure 6b is the core loss distribution of IPMSM-DPM, and the field weakening starts when the speed is up to 3000 r/min in the constant torque mode and the core loss is increased with the speed. Compared with Fig. 6a, the core loss of IPMSM-SPM is greater than that of IPMSM-DPM due to the good magnetic accumulation effect with the ‘V’-shape for the single-layer PMs, and causes serious saturation for the stator tooth.

The copper loss distributions of IPMSM are given in Fig. 6c,d, which shows that the copper loss increases with the output torque gradually. Compared with Fig. 6d, the same copper loss under low torque can be found due to the same stator structure and winding type, while the armature current is reduced and the copper loss distribution is improved for IPMSM-DPM because of its higher reluctance torque under the larger load torque.

Fig. 6.

Core loss and copper loss for IPMSM with single and double-layer PMs. (a) Core loss for IPMSM with Single-layer PMs; (b) Core loss for IPMSM with double-layer PMs; (c) Copper loss for IPMSMs with Single-layer PMs; (d) Copper loss for IPMSMs with double-layer PMs.

Figure 7 shows the efficiency distribution of IPMSM. The mechanical friction loss is set to 100 W when calculating the efficiency. Meanwhile, the eddy-current loss of PMs is neglected. According to the efficiency distribution of IPMSM-SPM in Fig. 7a, it has the better efficiency distribution in the whole working area and the maximum efficiency is about 95.34%, while the maximum efficiency of IPMSM-DPM is about 96.4% shown in Fig. 7b. Comparing with the IPMSM-SPM, it has the larger region with constant torque and higher efficiency ( >90%), while the domain for the efficiency of IPMSM-SPM above 95% is significantly less.

Fig. 7.

Efficiency for IPMSMs with Single and double layer-PMs. (a) Efficiency for IPMSMs with Single layer-PMs; (b) Efficiency for IPMSMs with double layer-PMs.

4. Experiment and analysis

According to the comparative analysis, the output torque, loss and efficiency of the IPMSM-DPM is superior to that of IPMSM-SPM, etc. A prototype was manufactured according to the design scheme of IPMSM-DPM, and the test platform was set up to carry out the relevant experiment.

The design parameters of IPMSM-DPM are shown in Table 4.

Table 4
Part size parameters of the motor

Item Value Item Value

Rated power (kw) 10.5 Outer radius of stator (mm) 255

Rated voltage (v) 154 Inner radius of rotor (mm) 160.4

Rotor pole number/stator slot number 8/48 Number of conductors per slot 8

Rated torque (N m) 33.5 Wire diameter (mm) 0.511

Rated speed (r/min) 3000 Winding connection Wye

Unilateral air gap length (mm) 0.6 Coercively (KA/m) 915

Number of turns per slot 20 Remanence (T) 1.2

Item	Value	Item	Value
Rated power (kw)	10.5	Outer radius of stator (mm)	255
Rated voltage (v)	154	Inner radius of rotor (mm)	160.4
Rotor pole number/stator slot number	8/48	Number of conductors per slot	8
Rated torque (N m)	33.5	Wire diameter (mm)	0.511
Rated speed (r/min)	3000	Winding connection	Wye
Unilateral air gap length (mm)	0.6	Coercively (KA/m)	915
Number of turns per slot	20	Remanence (T)	1.2

Figure 8 shows the pictures of the prototype, which includes (a) rotor lamination, (b) rotor of IPMSM-DPM, (c) the rotor with shaft and (d) stator core.

Fig. 8.

Manufactured IPMSM-DPM. (a) rotor lamination; (b) rotor; (c) rotor with shaft; (d) stator core lamination.

The prototype test platform is shown in Fig. 9. The resistance, inductance, electromotive force and output torque are tested and compared with the simulation results.

Fig. 9.

Test platform.

4.1. Resistance characteristics

Table 5 shows the measured data of winding resistance. The measured phase resistance is slightly higher than that of simulation, and the average value of three-phase winding resistance is 9.14% larger than the simulation value. It is mainly due to the inaccuracy of the equivalent model for the end winding by 2D FEA, and there are some errors between theoretical calculation and measurement of armature winding copper wire and insulation properties. Therefore, the measured winding resistance is increased, the loss of the prototype is increased and the efficiency is reduced.

Table 5
Resistance of IPMSM-DPM

Measured Simulation

A phase B phase C phase Average value

Resistance (𝛺) 0.04717 0.05293 0.05458 0.05156 0.0472404

	Measured	Simulation
	A phase	B phase	C phase	Average value
Resistance (𝛺)	0.04717	0.05293	0.05458	0.05156	0.0472404

4.2. Inductance characteristic

In the test platform shown in Fig. 9, a digital bridge instrument is used to measure d- and q-inductances of prototype given in Fig. 10a. The two inductances are not equal due to the asymmetry of the rotor magnetic circuit. Compared with Fig. 10b, there are significantly difference between the simulation and measured value because of the serious saturation for the q-axis magnetic circuit. The number of the measured q-axis inductance is equal to the positions of q-axis magnetic circuit.

Fig. 10.

Inductance characteristics of IPMSM-DPM. (a) measured inductance; (b) simulation inductance.

The average d- and q-inductances within a mechanical cycle is reported in Table 6. The measured d-inductance is smaller while the q-inductance is larger than the calculated value because the error in machine prototype and the end-winding effect is ignored by 2D FEM. There are 14.9% and 14.3% errors for the d- and q-inductances calculation, respectively. Therefore, 3D FEM can be applied in order to improve the accuracy of calculation.

Table 6

The average of d- and q-inductances

	Simulation value		Measured value
d∕q inductance	d-axis	q-axis	d-axis	q-axis
Average (mH)	0.6208	1.6012	0.543641	1.869149

4.3. EMF at No-load and Output torque

The electromotive force of the prototype at no load was tested when the rotor speed is 1000 r/min, as shown in Fig. 11a. It can be found that the measured EMF is slightly less than the simulation value due to the equivalent end winding and errors from mechanical process compared with Fig. 11b.

Figure 11c gives the comparison of output torque between the measurement and theoretical calculation for the prototype, and it can be found that the output torque increases with the armature current. The experimental result of the torque is slightly less than the simulation value because of the mechanical process and end winding effect. At the same time, the IPMSM-DPM has the better capability of output torque and the reliability of FEA is verified through the experimental results.

Fig. 11.

Induced electromotive force waveform and output torque of IPMSM-DPM (1000 r/min). (a) Measured; (b) Simulation; (c) Output torque.

5. Conclusions

In this paper, the structures of IPMSM-SPM and IPMSM-DPM are proposed under the same of stator outer diameter, air gap length and permanent magnet dosage. Some electromagnetic characteristics such as output torque, inductance, loss and efficiency of the two IPMSM are compared and the better characteristics of IPMSM-DPM are obtained. A prototype of IPMSM-DPM was manufactured and the related tests were carried out. The electromagnetic design and finite element calculation are verified by the test results of prototype. The IPMSM-DPM is a good candidate for electric-vehicle applications because of the good torque capacity and the wide speed range.

Footnotes

Acknowledgements

This work was supported in part by National Natural Science Foundation of P.R. China (No. 51267006, 51767009), Plan Project of Jiangxi Province of P.R. China (GJJ160598, 20151442040049, 20151BBE50109, 20181BAB206035), Qingjiang youth talents support program of Jiangxi University of science and technology.

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Comparison and analysis of electromagnetic characteristics of IPMSM with single and double layer PMs

Abstract

Keywords

1. Introduction

2. Structure and parameters of IPMSM

2.1. The overall structure of IPMSM

3.1. Control strategy of MTPA

Table 5 Resistance of IPMSM-DPM Measured Simulation A phase B phase C phase Average value Resistance (𝛺) 0.04717 0.05293 0.05458 0.05156 0.0472404

Footnotes

Acknowledgements

References

Table 5
Resistance of IPMSM-DPM

Measured Simulation

A phase B phase C phase Average value

Resistance (𝛺) 0.04717 0.05293 0.05458 0.05156 0.0472404