Influence of rotor structures on line-start permanent magnet machines electromagnetic characteristics for pumping units application

Abstract

This paper investigates the opportunity to use a proper geometry of Line start permanent-magnet synchronous motor (LSPMSM) that allows the same stator to be used for three different rotor structures, namely, typical, solid rotor and strange rotor. The air-gap flux density, back electromotive force (EMF), cogging torque, efficiency, starting performance and synchronization capability of the three machines are analyzed and compared. It is demonstrated that the typical rotor has the highest air-gap flux density, and the strange rotor has the lowest cogging torque and highest starting torque. In addition, the solid rotor has the lowest total harmonic distortion (THD), the highest efficiency, and the lowest cost. The size of PM and rotor structure are optimized to maximize the starting torque and efficiency of the solid rotor LSPMSM based on response surface method (RSM). Finally, the solid rotor LSPMSM is prototyped to verify the results of the finite element analysis.

Keywords

Finite element analysis LSPMSM rotor structure;starting performance

1. Introduction

Line start permanent-magnet synchronous motors (LSPMSMs) have been increased interest due to self-starting capability, high power factor and high efficiency [1]. Comparing with the induction machine (IM), the high energy rare earth permanent magnet (PM) material can supply high air-gap flux density to reduce the copper loss and offer a high power factor. High power factor, high efficiency and good synchronization capability make the LSPMSM suitable in applications such as pumping units, compressors and some of the energy conservation [2,3]. Meanwhile, the LSPMSM is a type of interior permanent magnet (IPM) machine that can be operated from the fixed frequency direct power supply.

High-efficiency machine can reduce the environmental impact. So in the early years, the researchers have developed LSPMSM by simple modification in IM to improve efficiency. In [4], a 960W LSPMSM is designed and analyzed, and the results show that the proposed machine can keep the high efficiency at synchronous speed, and the efficiency has reached 87.5% compared with IM machine 50.4%. In order to achieve IE4 levels of efficiency, a three phase LSPMSM is proposed in [5] while uses less active material. The efficiency of this machine can achieve 95.4%. Some conclusion comments and remarks are proposed for efficiency improvement, manufacturing, and future research trends of LSPMSM in [6].

The starting performance is one of the most important characteristics for LSPMSM, and it is significantly affected by the rotor cage, air-gap flux density and topological structure. Some of the literatures proved that the rotor configures, PM structures and rotor cage structures can improve the starting and synchronization process of LSPMSM. In order to improve the starting torque, a composite solid rotor is proposed to improve the starting capabilities of the LSPMSM [7], and the results show that the composite solid rotor can reduce the eddy loss and increase the efficiency. Two rotor configurations for the LSPMSM are proposed in [8]. The first configuration is improves starting performance and the second configuration reduces magnet poles, and the results show that the proposed rotor configuration leads to improved steady-state performance, utilizes 10% less magnet volume. In [9], the magnet structure is optimized to get better starting properties, and the experimental results show that the anti-salient pole can improve the starting performance, efficiency and power factor. It can be demonstrated that the increase of rotor cage size leads to the increase of the starting torque. However, it is difficult to increase the starting performance and reduce the loss at the same time.

There is very few technical papers that investigates the influences of the rotor slots and topologies on the starting performance and the air-gap flux density, especially for efficiency and loss at the same PM volume. The finite element analysis (FEA) models are built to calculate the electromagnetic performance and starting performance for the proposed typical, solid rotor and strange rotor. Firstly, the air-gap flux density and cogging torque are calculated by no-load analysis. Then, the starting performance, core loss and efficiency of three machines are analyzed and compared. In addition, in order to improve the starting performance further, the PM and rotor slot are optimized based on the response surface method (RSM) for solid rotor LSPMSM. Finally, a solid rotor LSPMSM machine is manufactured to verify the results of FEA.

2. Proposed the different rotor structure LSPMSM

The most of rotor configurations used in the paper for LSPMSM are interior type rotor, the important research of literature are starting permanence and efficiency. It is found that the spoke type magnet arrangement can offer the higher air-gap density and bigger electromagnetic torque for the same magnet area, stator, rotor and windings. Figure 1 shows three different rotor cage configurations, namely, the typical rotor, the solid rotor and the strange rotor. It can be seen that the solid rotor inner diameter is higher than the typical rotor and strange rotor. Because of the laminated silicon steel is used in the typical rotor and strange rotor, and the entire rotor is composed of each of laminated silicon steel. However, the solid steel is used in the solid rotor, the magnetic bridge shape is complex, and the processing is very difficult for solid rotor. In addition, in order to keep the volume of PMs in the three different rotors same, and the solid rotor inner diameter is higher than the typical rotor and strange rotor.

The basic parameters are listed in Table 1. It can be seen that the total volumes of the permanent magnets, stator slots and the stator radius in these machines are identical, so the stator material cost is almost the same. For one polar, the typical rotor has seven rotor cage, while the strange rotor has six rotor cage and the solid rotor has only one rotor cage. However, the strange rotor has two different rotor cage structures and the cost of the cage is higher than the typical and solid rotor by 12% and 16%, since the manufacturing process is more complicated. Table 2 lists the cage winding cost of three rotors.

3. Analysis of the characteristics of LSPMSM

3.1. Numerical models of LSPMSM

In general, the working principle of LSPMSM is different from the traditional permanent magnet machine. Due to the fact that LSPMSM works in constant speed, when LSPMSM connects to three-phase balanced AC voltage, the starting process is the same as that of IM and runs up towards synchronous speed with the help of the rotor cage torque [10–12]. The process that pulls the rotor into synchronous speed depends on the balance of three components, which forms part of the total torque acting on the machine shaft: (1) the electromagnetic torque T _e, (2) the asynchronous electromagnetic torque T _a, (3) the load torque T _load. In order to keep the machine running steady, the mechanical equation is expressed as. $\begin{eqnarray}\displaystyle J{\displaystyle \frac{d{\omega}}{dt}}=T_{e}-T_{load}+T_{a} & & \displaystyle\end{eqnarray}$ (1) where J is the total moment of inertia and ω is the angular velocity of the rotor.

Fig. 1.

LSPMSM machines with different rotors.

Table 1

Main parameters of the LSPMSM

Parameters	Typical rotor	Solid rotor	Strange rotor
Rated power/kW		30
Rated speed/rpm		750
Pole pairs		4
Iron core axial length/mm		180
Stator diameter/mm		400
Rotor diameter/mm		283.6
Number of stator slots		72
Number of rotor slots	56	8	48
PMs width/mm		42
PMs thickness/mm		12

Table 2

Rotor cost of three machines

Parameters/dollar	Typical rotor	Solid rotor	Strange rotor
Rotor material	45	49	45
Manufacturing process	16	8	22
Total	61	57	67

Due to the rotor cage, the starting process of the LSPMSM is complex. For typical and strange rotor LSPMSM, the asynchronous run-up rated speed is provided by the rotor cage winding. However, the solid rotor LSPMSM run-up rated speed is provided by the cage and eddy current effect of the solid rotor, the eddy current plays a major role. As the speed approaches the synchronous speed, the slip tends to zero and the LSPMSM comes into the synchronization. So the starting torque can be given as: $\begin{eqnarray}\displaystyle T_{st}=K_{T}{\Phi}_{m}I_{2}\cos {\varphi}_{2} & & \displaystyle\end{eqnarray}$ (2) where K _T is the starting torque constant, I ₂ is the rotor cage winding current and cos φ₂ is the rotor power factor.

As the spoke type LSPMSM, the electromagnetic torque is provided by the summation of the permanent magnet torque and reluctance torque. The equation of the synchronous torque is given by: $\begin{eqnarray}\displaystyle T_{e}={\displaystyle \frac{3pE_{0}U}{2{\omega}_{s}X_{d}}}\sin {\delta}+{\displaystyle \frac{3pU^{2}(X_{d}-X_{q})}{4{\omega}_{s}X_{d}X_{q}}}\sin 2{\delta} & & \displaystyle\end{eqnarray}$ (3) where p is the number of pole pairs, U is the voltage per phase, E ₀ is the back-EMF, X _d, X _q are d-q axis inductances, respectively, δ is the electrical load angle.

The braking torque is mainly due to the increment in magnet flux base on the magnetic saliency enhance that is calculated as : $\begin{eqnarray}\displaystyle T_{b}=-{\displaystyle \frac{mp}{2{\omega}_{s}}}\left[{\displaystyle \frac{R_{S}^{2}+{\omega}_{s}^{2}L_{sd}^{2}(1-s)^{2}}{R_{S}^{2}+{\omega}_{s}^{2}L_{sd}L_{sq}(1-s)^{2}}}\right]\left[{\displaystyle \frac{R_{S}^{2}E_{0}^{2}(1-s)}{R_{S}^{2}+{\omega}_{s}^{2}L_{sd}L_{sq}(1-s)^{2}}}\right] & & \displaystyle\end{eqnarray}$ (4) where R _s is the stator resistance, L _sd and L _sq are the stator self-inductances referred to stator, s is the slip, respectively.

U is the voltage per phase, E ₀ is the back-EMF, X _d, X _q are d-q axis inductances, respectively, δ is the electrical load angle.

In order to achieve higher reluctance torque, the difference value of d-q axis inductances are often designed. The maximum electromagnetic torque occurs at the load angle which is between an electrical angle of 90° and 180°. When the load torque is constant, the point of intersection between the load line and the electromagnetic torque curve define the operating electrical load angle.

The efficiency of LSPMSM is the ratio of the output power to the input power, it can be expressed as: $\begin{eqnarray}\displaystyle {\eta}={\displaystyle \frac{P_{out}}{P_{out}+P_{loss}}}={\displaystyle \frac{P_{out}}{P_{out}+P_{cu.stator}+P_{Fe}+P_{cu.rotor}+P_{mec}}}. & & \displaystyle\end{eqnarray}$ (5) Where P _{cu. stator} is the loss of stator windings, P _Fe is stator and rotor core loss, P _{cu. rotor} is the loss of rotor cage, and P _mec is the machine loss.

3.2. Analysis of no-load performance

The two-dimensional finite element model (FEM) of three types rotors LSPMSM are established, and the Fig. 2 shows the flux density distribution of three different rotors at no load. It can be seen that solid rotor LSPMSM flux density is much lower than the typical rotor and strange rotor. The strange rotor saturation point occurs between the magnetic separation bridge and rotor cage, and the maximum saturation point of typical rotor is located on the junction of air gap and bridge. In addition, the solid rotor saturation point is far less than the others. It can be speculated that the rotor loss of solid rotor is lower than the typical rotor and strange rotor.

Fig. 2.

Flux density of three kinds rotor.

Figure 3 shows the FE-predicted air-gap flux density and the spectral components of three types rotor LSPMSM at no load. It can be seen that the air-gap flux density can achieve 1.0T, due to spoke-type PM. In Fig. 3(b), it can be noted that 5th, 11th, and 13th harmonics of solid rotor LSPMSM machine are reduced. It also can be obtained that the fundamental flux density of solid rotor is reduced as compared to the other two rotor machines. The solid rotor has the lowest THD of air-gap flux density, and the typical has the highest THD of air-gap flux density.

Figure 4 shows the no-load phase EMF and the spectral components of three types rotor of LSPMSM at 750 r/min. In Fig. 5(a) it can be noted that the no-load back EMF of solid rotor machine is similar to sinusoidal waveform, but the amplitude of typical is larger than solid rotor and strange rotor . It can be also seen that the fundamental back EMF of solid rotor machine is slightly decreased as compared to the other two rotor machines.

Fig. 3.

Air-gap flux density distributions of three LSPMSM machines.

Fig. 4.

No-load phase EMF of three LSPMSM machines.

Fig. 5.

Waveform of cogging torque of three LSPMSM machines.

The cogging torque is another important parameter of LSPMSM machines, and the cogging torque of three different rotor machines are shown in Fig. 5. It can been noted that the cogging torque of typical LSPMSM machine is the highest, and the amplitude value is about 28 N ⋅ m. The cogging torque of solid rotor is about 20 N ⋅ m, and cogging torque of strange rotor is lowest, it only about 10 N ⋅ m.

3.3. Starting performance and synchronization capability

In order to obtain the accurate dynamic performance of LSPMSM, a quasi-dynamic analysis model is built. The cage torque (T _cage), the magnet braking torque (T _b) and the average cage torque (T _av) for different rotor structure are shown in Fig. 6. It is observed that magnet braking torque for different rotors is nearly equal, since the volume of PMs and stator core used for three types rotors are kept same.

It can be seen that the starting torque of typical rotor is about 985 N ⋅ m, and 1540 N ⋅ m with solid rotor, and 1678 N ⋅ m with strange rotor. It can be deduce that the strange rotor presents better starting performance, and the starting performance of typical rotor is lower than solid rotor. Under rated load condition, starting processes of the LSPMSM with the three types rotor are obtained by the 2-D time-step finite-element model, as shown in Fig. 7. It can be noted that the strange rotor LSPMSM reaches the synchronous speed fastest, followed by the solid rotor. The less time the LSPMSM requires to reach the synchronous speed, the higher the synchronous capability and the lower rotor copper loss at the asynchronous period.

Fig. 6.

Run up torque–speed curves assuming quasi dynamic condition for each speed.

Fig. 7.

Simulated speed-time responses.

3.4. Electromagnetic loss and efficiency

Compare with the traditional PM machine, the LSPMSM electromagnetic loss contains the stator copper loss, the rotor copper loss, the core loss and the PM eddy loss. The rotor copper loss is mainly determined by the rotor cage and resistance, and the core loss is mainly determined by the flux density waveform of stator core and rotor core.

The three different rotors loss at rated power are shown in Fig. 8. It can be note that the stator copper loss and rotor loss are much lower than strange rotor and typical rotor. The reason for this phenomenon is that the position of PMs for solid rotor is different with strange rotor and typical rotor, and the stator phase current of solid rotor is the lowest in three rotors. Meanwhile, the rotor slot of solid rotor is open slot, but the rotor slot of strange rotor and typical rotor are closed slot. In addition, the volume of rotor cage for solid rotor much lower than strange rotor and typical rotor, so the rotor loss of solid rotor is much lower than strange rotor and typical rotor.

The efficiency of three rotor LSPMSM machines at different output power are shown in Fig. 9. It can be seen that the efficiency of typical and strange rotor are almost the same, but the solid rotor machine is higher than strange rotor and typical rotor machine. The maximum efficiency of solid rotor machine can achieve 95%. Meanwhile, the cost of solid rotor is lower than the typical rotor and strange rotor. Therefore, the solid rotor machine is selected as the prototype machine.

Fig. 8.

The stator and rotor loss for three different rotors.

Fig. 9.

Efficiency of three LSPMSM machines at different output power (at 750 r/min).

Fig. 10.

Proposed optimum design flowchart.

4. Optimal design of the LSPMSM

As can be seen from the analysis of the electromagnetic performance, the solid rotor LSPMSM has good starting performance, low cost and high efficiency. In order to improve the starting performance, the synchronization ability and efficiency for solid rotor LSPMSM, a flowchart for the optimal design is depicted in Fig. 10. Setting two target functions as: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \text{Efficiency}:(\max (\text{efficiency}(x)))\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \text{Starting torque}:(\max (T_{\text{st}}(x))).\end{eqnarray}$ (7)

According to the initial size in Table 1, the optimization analysis model is built based on FEA model, with the given five design variables in sensitivity analysis (x ₁, x ₂, x ₃, x ₄, x ₅), the design variable are 0.15 ≥ x ₁ ≥ 0.3, 2 ≥ x ₂ ≥ 8.5, 5 ≥ x ₃ ≥ 15, 23 ≥ x ₄ ≥ 40, 20 ≥ x ₅ ≥ 12, as shown in Fig. 11. The results of multi-objective sensitivity are obtained, as shown in Fig. 11. It can be seen that the influence of the parameters of LSPMSM machine on the starting torque and efficiency is different. The ratio of PM width and length (x ₁) has the greatest influence on the efficiency and starting torque, and the distance between PM and shaft is x _5. Since the rotor slot size are the main factors that affects starting torque, and the distance between PM and shaft has an influence on the efficiency.

In step I of basic optimal design and according to previous research, the main factors that affect the starting performance and efficiency are the ratio of PM thickness to length (x ₁) and the distance between PM and shaft (x ₅). The mentioned design in LSPMSM is optimized efficiently with the help of response surface method (RSM). RSM is a set statistical and mathematical techniques to find the best fit response of the physical system through simulation. With the given two design variables, there are 12 different simulation models that are built to be analyzed, which are listed in Table 3.

Fig. 11.

Design values of each design variable.

Fig. 12.

Sensitivity of solid rotor LSPMSM.

Table 3

Design of LSPMSM basic RSM model

	x ₁	x ₅	Efficiency (%)	Starting torque T _st (N ⋅ m)
1	0.15	16	93.3	1649.7
2	0.18	12	94.6	1345.4
3	0.2	15	94.2	1669.8
4	0.22	14	95.4	1327.5
5	0.26	17	92.4	1549.7
6	0.16	18	91.7	1340.9
7	0.25	14	96.5	1735.6
8	0.3	18	95.9	1327.5
9	0.24	20	93.7	1621.2

Based on the results of FEA, the regression coefficient is obtained and the RSM model of efficiency and starting torque are given by: $\begin{eqnarray}\displaystyle {\eta}\text{} & =\text{} & \displaystyle 89.84163+0.00735x_{1}+0.9231x_{2}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle -∼9.02\times 10^{-5}x_{1}x_{2}-4.7379\times 10^{-4}x_{1}^{2}+0.021283x_{2}^{2}\end{eqnarray}$ (8) $\begin{eqnarray} \displaystyle T_{st}\text{} & =\text{} & \displaystyle 1251.487+0.386629x_{1}-0.88612x_{2}-9.275\times 10^{-5}x_{1}x_{2}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle -∼0.02282x_{1}^{2}-0.013721x_{2}^{2}. \end{eqnarray}$ (9)

The responses to the design efficiency and starting torque with all the design variables are shown in Fig. 13. It can be seen that the efficiency and starting torque increases firstly and then deceases with the increase of the ratio of PM thickness to length, however, the starting torque increases obviously first and then decreases linearly with the increase of the ratio of PM thickness to length and the distance between PM and shaft. At the end of the optimization, the ratio of PM thickness to length x ₁ and the distance between PM and shaft x ₅ are selected as 0.25 and 14 mm, respectively. The results of the optimal LSPMSM are shown in Table 4. The efficiency of optimal model can achieve 96.5% as compared to the basic model 94.4%, and the optimal design improves starting torque by 10.6% Compared with basic model, non-synchronized ratio is increased by 6.5% for optimal model, due to the effect of rotor slot and PM.

5. Experimental verification

5.1. No-load test

In order to reduce the processing difficulty and cost, the aluminum conducting bar is used in the rotor cage, and the insert processing is selected for the rotor cage and PMs. In addition, to realize the fixation of PM and rotor cage expediently, and the round copper plate is selected as end ring to connect the rotor cage. The end ring is welded together by tin

Based on the FEA analysis and optimization results, a 30 kW prototype machine with solid rotor is manufactured considering the manufacturing conditions for optimal model. The experimental setup is shown in Fig. 14. The measured solid rotor LSPMSM is driven by the control cabinet. The phase current is tested by tong-type ammeter, and the load is a 50 kW induction motor.

Due to the limitation of experimental conditions, the minimum phase current method is applied to obtain no-load characteristic of machine. The relationship between current and voltage is shown in Fig. 15. It can be seen that the no-load back EMF is about 216 V, and the result of FEA analysis is about 224 V. The error is about 3.7%. Then, the back-EMF is tested at no load when the speed is 750 r/min, as shown in Fig. 16. It can be noted that the experimental results agree well with the FEA results.

Fig. 13.

Characteristics according to x ₁ and x ₂.

Table 4

Results for basic model and optima model

Item	Basic model	Optimal model
Efficiency/%	94.4	96.5
Starting torque/N ⋅ m	1540	1725
Non-synchronized/%	6	12.5
Rated torque/N ⋅ m	356	382
Cogging torque/N ⋅ m	11.5	9.4

Fig. 14.

Experimental setup.

Fig. 15.

The phase current versus voltage.

Fig. 16.

No-load back-EMF waveforms.

Fig. 17.

FEA calculated and tested torque values with current at 750 r/min.

Fig. 18.

FEA calculated and tested efficiency values with output power.

Fig. 19.

Pull-out torque and power test.

Fig. 20.

Torque characteristic with FEA result.

5.2. Load test

During the load test, the voltage of the LSPMSM machine is kept constant, and the input power of the machine is changed through the electrical control cabinet. The changes of current and output torque under 750 r/min is shown in Fig. 16. It can be noted that the measured torque is lower than FEA analysis with the increase of phase current, because the PM flux linage is reduce with the arise of PM temperature and the measured error. In addition, good agreement between FEA prediction and experimental test is achieved.

The tested efficiency is obtained by the input power divided by output power. The simulated and measured efficiency of the sloid rotor LSPMSM are shown in Fig. 17. It can be seen that the FEA analysis and optimization results in this paper is useful to estimate the efficiency and starting performance of the LSPMSM.

Pull-out torque represents the overload capacity of the LSPMSM. In the experiment, the phase current is constantly increased, and the torque and power are increased. When the switch sound occurs for machine, and the pull-out torque is obtained, as shown in Fig. 19. It can be seen that the pull-out torque of the LSPMSM is about 840 N ⋅ m and the power is about 65.8 kW. Meanwhile, the torque characteristic curve of the prototype is shown in Fig. 20. It can be noted that the pull-out torque is about 853 N ⋅ m, and the error is about 1.6%.

6. Conclusion

In this paper, three different rotor structures LSPMSM are proposed to improve the machine starting ability and decrease the cost for pumping units applications. A solid rotor LSPMSM is proposed to compare the electromagnetic performance with typical and strange rotor, including the magnetic field, cogging torque, starting performance and synchronization capability. It is demonstrated that the solid rotor LSPMSM machine can make the no-load back EMF more sinusoidal, higher efficiency, good starting performance and low cost. Based on FEM analysis results, the optimal method is proposed to improve the solid rotor LSPMSM, and the results show that the efficiency and starting torque can be improved. Finally, the optimal prototype machine with solid rotor is manufactured and the results of FEA are verified by experiments.

Footnotes

Acknowledgements

This work was supported by the Natural Science Foundation of Anhui Province, China (NO. KJ2017A752, KJ2018A0865, KJ2019A1156).

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