France



I Introduction&lt;br/&gt;Owing to their characteristics of easy manufacturing, convenient transportation and high fault-tolerant capacity, the modular permanent magnet synchronous machines (PMSMs) are favored by various industrial applications, such as electric vehicle and wind turbine applications [1]. However, due to the manufacturing tolerance, the additional mechanical gaps between the modules are inevitable which will affect the magnetic field distribution and hence the electromagnetic performances. The influences of the inevitable mechanical gaps between the modules in a three-phase PMSM has been investigated in [2-5]. Unfortunately, the influences of the additional gaps between the modules in a six-phase modular machine have not been covered. Moreover, the different influences of the modular structures on PMSMs with symmetrical or asymmetrical six-phase winding layouts are not investigated.&lt;br/&gt;&lt;br/&gt;II Development of the different six-phase winding layouts and the modular machines&lt;br/&gt;The symmetrical and asymmetrical six-phase windings layouts 12-slot/14(10)-pole PMSMs can be obtained by analyzing the the slot star diagram of a conventional 12-slot/14(10)-pole three-phase PMSM with double-layer FSCW as shown in Fig. 1. The mutual inductances between adjacent phases are nonzero as shown in Table I, which will decrease their magnetic isolation capacity. To improve this situation, all the double-layer slots are divided into two single-layer slots so that three 24-slot/14(10)-pole six-phase PMSMs with unequal teeth can be obtained. And, the modular stators are employed. For the asymmetrical six-phase machine, there is only one modular method—one module with one coil (Design A). For the symmetrical six-phase machine, there can be two different modular methods—one modular with one coil (Design B) and one modular with one-phase (Design C) (one phase possesses two adjacent coils). The different modular methods will introduce different additional mechanical gaps which cannot be avoided resulting from the manufacture limitations and tolerances, as shown in Fig. 1. These mechanical gaps will have significant influences on the electromagnetic performances of the modular machine.&lt;br/&gt;&lt;br/&gt;III Influences of the modular stators on the performances&lt;br/&gt;In this section, the performance such as winding factor, no-load air-gap flux density, on-load torque and short-circuit current, are investigated. For the sake of comparison, all the dimensions of the three modular stator PMSMs are the same as shown in Table II and Fig. 2. Since the slot area is fixed, the sum of the width of coil-wound tooth (&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;) and the width of non-wound tooth (&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;) is the same when the width of the coil-wound tooth varies. The additional mechanical gap varies from 0.5 mm to 5 mm.&lt;br/&gt;By injecting rated sine currents, the on-load torques can be obtained as shown in Fig. 3. It can be clearly found that the average torques of the three machines all decrease with the increase in mechanical gap width. When the mechanical gaps are relative small, i.e. 0~1 mm, the average torques are in direct proportion to &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;. However, due to the serious saturation in the non-wound teeth, this rule will disappear. This is why, the average torques drop more rapidly with the increase in mechanical gap width when &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; is relatively large. The average torques of Design C are the most smooth ones, which indicates that the modular method of Design C can avoid deep saturation.&lt;br/&gt;The fault-tolerant machine requires that the short-circuit current should be closed to the rated current. The short-circuit currents of the three modular machines are investigated as shown in Fig. 4. For Design A and B, it can be seen that the short-circuit current decreases with the increase in mechanical gaps when &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; smaller than 24mm, which results from the reduced back-electromagnet force (back-EMF). The short-circuit will rapidly increase with the increase in mechanical gap width when &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; bigger than 24mm, which results from the reduced self-inductance when deep saturation occurs. For Design C, with different winding tooth width, the amplitudes of the short current are almost deprived of the influence of the width of the mechanical gaps.&lt;br/&gt;&lt;br/&gt;IV Conclusion&lt;br/&gt;This paper presents three different modular six-phase PMSMs. For the asymmetrical six-phase machine, there is only one modular method—one module with one coil (Design A). For the symmetrical six-phase machine, there can be two different modular methods—one modular with one coil (Design B) and one modular with one-phase (Design C) (one phase possesses two adjacent coils). For Design A and B, the mechanical gaps between the modules will make the performances bad significantly. While, Design C almost insulates from the influcence of the addtional mechanacal gaps.

**References:**

&lt;br/&gt;[1] B. Bickel, J. Franke, and T. Albrecht, “Manufacturing cell for winding and assembling a segmented stator of PM-synchronous machines for hybrid vehicles,” in Proc. 2nd Int. EDPC, Oct. 2012, pp. 1–5.&lt;br/&gt;[2] Z. Q. Zhu, Z. Azar, and G. Ombach, “Influence of additional air gaps between stator segments on cogging torque of permanent-magnet machines having modular stators,” IEEE Trans. Mag., vol. 48, no. 6, pp. 2049–2055,Jun. 2012.&lt;br/&gt;[3] G. Dajaku and D. Gerling, “Low costs and high-efficiency electric machines,” in Proc. 2012 2nd Int. Electr. Drives Prod. Conf. (EDPC), Oct. 15–18, 2012, pp. 1–7.&lt;br/&gt;[4] G. J. Li, Z. Q. Zhu, W. Q. Chu, M. P. Foster, and D. A. Stone, “Influence of Flux Gaps on Electromagnetic Performance of Novel Modular PM Machines,” IEEE Trans. Energy Convers., vol. 29, no. 3, pp. 716-726, Sept. 2014.&lt;br/&gt;[5] G. J. Li, Z. Q. Zhu, M.Foster, and D. Stone, “Comparative Studies of Modular and Unequal Tooth PM Machines Either With or Without Tooth Tips,” IEEE Trans. Magn., vol. 50, no. 7, 8101610, July 2014.

**Images:**

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 Comparative Studies of Six-Phase PMSMs with Modular Stator Under Pre-Fault and Post-Fault Conditions

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I Introduction Owing to their characteristics of easy manufacturing, convenient transportation and high fault-tolerant capacity, the modular permanent magnet synchronous machines (PMSMs) are favored by various industrial applications, such as electric vehicle and wind turbine applications [1]. However, due to the manufacturing tolerance, the additional mechanical gaps between the modules are inevitable which will affect the magnetic field distribution and hence the electromagnetic performances. The influences of the inevitable mechanical gaps between the modules in a three-phase PMSM has been investigated in [2-5]. Unfortunately, the influences of the additional gaps between the modules in a six-phase modular machine have not been covered. Moreover, the different influences of the modular structures on PMSMs with symmetrical or asymmetrical six-phase winding layouts are not investigated. II Development of the different six-phase winding layouts and the modular machines The symmetrical and asymmetrical six-phase windings layouts 12-slot/14(10)-pole PMSMs can be obtained by analyzing the the slot star diagram of a conventional 12-slot/14(10)-pole three-phase PMSM with double-layer FSCW as shown in Fig. 1. The mutual inductances between adjacent phases are nonzero as shown in Table I, which will decrease their magnetic isolation capacity. To improve this situation, all the double-layer slots are divided into two single-layer slots so that three 24-slot/14(10)-pole six-phase PMSMs with unequal teeth can be obtained. And, the modular stators are employed. For the asymmetrical six-phase machine, there is only one modular method—one module with one coil (Design A). For the symmetrical six-phase machine, there can be two different modular methods—one modular with one coil (Design B) and one modular with one-phase (Design C) (one phase possesses two adjacent coils). The different modular methods will introduce different additional mechanical gaps which cannot be avoided resulting from the manufacture limitations and tolerances, as shown in Fig. 1. These mechanical gaps will have significant influences on the electromagnetic performances of the modular machine. III Influences of the modular stators on the performances In this section, the performance such as winding factor, no-load air-gap flux density, on-load torque and short-circuit current, are investigated. For the sake of comparison, all the dimensions of the three modular stator PMSMs are the same as shown in Table II and Fig. 2. Since the slot area is fixed, the sum of the width of coil-wound tooth (t1) and the width of non-wound tooth (t2) is the same when the width of the coil-wound tooth varies. The additional mechanical gap varies from 0.5 mm to 5 mm. By injecting rated sine currents, the on-load torques can be obtained as shown in Fig. 3. It can be clearly found that the average torques of the three machines all decrease with the increase in mechanical gap width. When the mechanical gaps are relative small, i.e. 0~1 mm, the average torques are in direct proportion to t1. However, due to the serious saturation in the non-wound teeth, this rule will disappear. This is why, the average torques drop more rapidly with the increase in mechanical gap width when t1 is relatively large. The average torques of Design C are the most smooth ones, which indicates that the modular method of Design C can avoid deep saturation. The fault-tolerant machine requires that the short-circuit current should be closed to the rated current. The short-circuit currents of the three modular machines are investigated as shown in Fig. 4. For Design A and B, it can be seen that the short-circuit current decreases with the increase in mechanical gaps when t1 smaller than 24mm, which results from the reduced back-electromagnet force (back-EMF). The short-circuit will rapidly increase with the increase in mechanical gap width when t1 bigger than 24mm, which results from the reduced self-inductance when deep saturation occurs. For Design C, with different winding tooth width, the amplitudes of the short current are almost deprived of the influence of the width of the mechanical gaps. IV Conclusion This paper presents three different modular six-phase PMSMs. For the asymmetrical six-phase machine, there is only one modular method—one module with one coil (Design A). For the symmetrical six-phase machine, there can be two different modular methods—one modular with one coil (Design B) and one modular with one-phase (Design C) (one phase possesses two adjacent coils). For Design A and B, the mechanical gaps between the modules will make the performances bad significantly. While, Design C almost insulates from the influcence of the addtional mechanacal gaps.

**References:**

 [1] B. Bickel, J. Franke, and T. Albrecht, “Manufacturing cell for winding and assembling a segmented stator of PM-synchronous machines for hybrid vehicles,” in Proc. 2nd Int. EDPC, Oct. 2012, pp. 1–5. [2] Z. Q. Zhu, Z. Azar, and G. Ombach, “Influence of additional air gaps between stator segments on cogging torque of permanent-magnet machines having modular stators,” IEEE Trans. Mag., vol. 48, no. 6, pp. 2049–2055,Jun. 2012. [3] G. Dajaku and D. Gerling, “Low costs and high-efficiency electric machines,” in Proc. 2012 2nd Int. Electr. Drives Prod. Conf. (EDPC), Oct. 15–18, 2012, pp. 1–7. [4] G. J. Li, Z. Q. Zhu, W. Q. Chu, M. P. Foster, and D. A. Stone, “Influence of Flux Gaps on Electromagnetic Performance of Novel Modular PM Machines,” IEEE Trans. Energy Convers., vol. 29, no. 3, pp. 716-726, Sept. 2014. [5] G. J. Li, Z. Q. Zhu, M.Foster, and D. Stone, “Comparative Studies of Modular and Unequal Tooth PM Machines Either With or Without Tooth Tips,” IEEE Trans. Magn., vol. 50, no. 7, 8101610, July 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7d72a6eb79b24e702e24265576ac0d9.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/80cdcd47954ab9f66b951f6c3e7c8a89.jpg)

poster

As the core component of the flywheel energy storage system (FESS), the flywheel energy storage motor requires low self-loss, high power density, and a wide working speed range. This paper proposes a hybrid excitation synchronous machine integrated with magnetic bearing (HESM-IMB), which is suitable for FESS. First, the structure and operation principle of the proposed HESM-IMB are explained. Afterward, the influence of field current on the electromagnetic performance of HESM-IMB is researched by the magnetic equivalent circuit (MEC). Then, the performance of HESM-IMB is present by finite element analysis (FEA). The results indicate that HESM-IMB has the advantages of adjustable air-gap flux density, high integration, and low idling loss. I. Introduction Permanent magnet (PM) synchronous machines are widely used in FESS. However, the PM machine suffers from large idling losses and poor field weakening ability. Besides, the FESS usually requires at least one axial magnetic bearing and two radial magnetic bearings, which causes an influence on rotor dynamics. In order to solve the above problems, this paper proposes a hybrid excitation synchronous machine integrated with magnetic bearing (HESM-IMB), with the advantage of adjustable air-gap flux density, high integration, and low idling loss. II. Structure and operation principle The structure of HESM-IMB is shown in Fig. 1(a). The machine adopts a hybrid excitation structure. The upper section of the out-rotor is a structure in which iron core poles and permanent magnet poles are alternately distributed, and the lower section is a bearing rotor, as a part of radial magnetic bearing. Field wingding, bias permanent magnet, and rotor permanent magnet provide working magnetic flux for the machine at the same time. Fig. 1(b) shows the magnetizing flux path of HESM-IMB. Since the magnetic resistance of the permanent magnet poles is much greater than that of the iron cores, the magnetic flux on the surface of the permanent magnet poles is almost unchanged. On the contrary, the magnetic permeability of the iron core pole is large, by adjusting the magnitude and direction of the field current, the air-gap flux density distribution on the surface of the iron core pole can be changed to meet the needs of the system under different working conditions flexibly. Similarly, the axial air gap magnetic flux on the rotor will also change with field current adjustment, so the axial force on the rotor will change greatly. Thus, an axial magnetic bearing winding at the bottom needs to be used to balance the axial force, keeping the total axial force on the rotor is around zero. As for radial magnetic bearing, the magnetic resistance of the bias permanent magnet is very large, so the flux generated by the permanent magnet poles and the field winding will hardly pass through the core of the radial magnetic bearing, the bias magnetic flux on the bearing rotor is almost unchanged, which provides convenience for control of rotor radial force. III. Simulation and analysis The back EMF waveform of HESM-IMB is shown in Fig. 2(a). In Fig. 2(b), as the field current increases, the RMS of the back EMF increases linearly, which proves that HESM-IMB has a high performance of adjusting air-gap magnetic density. Fig. 2(c) shows the idling loss in the state of field weakening and field increasing. It can be seen that field weakening can reduce the loss of the machine effectively and improve the efficiency of the system. Fig. 2(d) represents the change curve of the axial force on the rotor with the field current when the bottom axial magnetic bearing winding is not energized, which is consistent with the previous analysis. IV. Conclusion The HESM-IMB proposed in this paper can adjust the air-gap flux density flexibly, which increases power during charging and discharging, and reduces idling loss during energy storage standby. Besides, HESM-IMB integrates a radial magnetic bearing and an axial magnetic bearing in the magnetic circuit, with the advantages of high integration.

**References:**

[1] J. A. Tapia, F. Leonardi and T. A. Lipo, "Consequent-pole permanent-magnet machine with extended field-weakening capability," in IEEE Transactions on Industry Applications, vol. 39, no. 6, pp. 1704-1709, Nov.-Dec. 2003. [2] T. D. Nguyen, K. Tseng, S. Zhang, "A Novel Axial Flux Permanent-Magnet Machine for Flywheel Energy Storage System: Design and Analysis," in IEEE Transactions on Industrial Electronics, vol. 58, no. 9, pp. 3784-3794, Sept. 2011. [3] E. Severson, R. Nilssen, T. Undeland, "Magnetic Equivalent Circuit Modeling of the AC Homopolar Machine for Flywheel Energy Storage," in IEEE Transactions on Energy Conversion, vol. 30, no. 4, pp. 1670-1678, Dec. 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/492135431e04d2583404caf965c725ca.jpg)
(a) Topology. (b) Magnetizing flux paths.

![](https://assets.underline.io/uploads/markdown_image/1/image/303ca8289619826542cdfb217438faf4.jpg)
(a) The back-EMF waveform. (b) The RMS of back-EMF versus field current curve. (c) Comparison of idling loss before and after field weakening. (d) The axial force on rotor versus field current curve.

 Research of a hybrid excitation synchronous machine integrated with magnetic bearings

I. Introduction In recent years, with the gradual development of wind power technology from land to sea, the unit capacity of its generating units has developed from low voltage (690V) and medium power (2-3MW) to medium voltage (3.3kV) and high power (5-10MW). For the medium-voltage high-power wind power converters with power level of 5-10MW, the switching frequency of the equipment is usually required to be within 1kHz, which brings many difficulties to the control of the converter [1]. In particular, for semi-direct drive wind power system, the operating frequency of the generator is relatively high, while the switching frequency of the converter is relatively low, which results in the problem of low sampling rate. This further increases the control difficulty of the medium voltage high power converter [2-3]. In addition, in the permanent magnet semi-direct drive wind power generation system, the operating frequency of the generator is usually greater than 100Hz, so the sampling rate is low. It also deteriorates the dynamic and steady-state performance of the traditional model predictive control with low switching frequency, and affects its stability. In order to realize the low switching frequency control of medium-voltage high-power permanent magnet synchronous generator with low sampling ratio, this paper proposes a structure and a control method of a modular frequency-multiplying inverter with low-carrier-ratio. II. System Topology and Principle The modular frequency-multiplying inverter adopts a nested H-Bridge structure. For example, a modular frequency-tripling inverter includes an inner layer, a middle layer and an outer layer. A1-A4 constitute the outer layer module, B1-B4 constitute the middle layer module, and C1-C4 constitute the inner layer module. The outer module uses independent IGBTs, and the middle and inner modules employ bidirectional switches composed of two anti-parallel IGBTs. The two anti-parallel IGBTs share a gate switch signal. The input voltage of the inverter is Vin. The output of the upper module is used as the input of the next module, and so on. The final output voltage of the inverter is Vo. The specific structure is shown in Fig. 1(a). A control signal is applied to each IGBT, where the switch at the diagonal position in the H bridge is turned on and off at the same time, the upper and lower switches on the same arm are turned on complementary, and the phase shift between each layer of modules is 120° electric angle. It can be seen from Fig. 1(b) that the frequency of the inner output voltage Vo of the inverter is three times the frequency of the outer output voltage V1. That is, a triple frequency output voltage is obtained at the fundamental switching frequency. III. Simulation According to Fig. 1(a), a simulation model is established, and the IGBT is controlled by SPWM. The input voltage Vin is 20V, and the fundamental frequency is 50Hz. Assuming that the carrier ratio of the outer switching tube is M, since the switching frequency of the three layer modules is the same, and the output frequency of the inner layer is three times the fundamental wave, the carrier ratio of the entire inverter is reduced to one third of the outer layer, i.e. M/3. The simulation results verify the proposed method. Under the condition that the fundamental frequency is 50Hz and the switching frequency of tube is not increased, an output voltage frequency of 150Hz is achieved. Analyzing the output voltage through FFT, the result shows that the third harmonic component is the highest, which is consistent with the desired result. The output voltage FFT analysis result is shown as in Fig. 2. IV. Discussion and Conclusion The structure and control method of the low-carrier-ratio frequency-multiplying inverter proposed in this paper can output voltages of several times the fundamental frequency without increasing the switching frequency. Simulations and experiments verify the method. The inverter system is simple in structure and easy to implement, and can solve the low carrier ratio control of medium-voltage high-power permanent magnet synchronous generators at low sampling rates. The inverter system can also be expanded to a more layered structure to achieve higher frequency output. The detailed analysis process and experimental results will be provided in the full manuscript.

**References:**

[1] H. Bizhani, R. Noroozian and S. M. Muyeen, IEEE Trans. on Power Electronics., Vol. 34, p. 3407-3417 (2019). [2] X. Zhao, S. Niu and W. Fu, IEEE Trans. on Magnetics., Vol. 56, p. 1-5 (2020). [3] W. Xu, R.D. Lorenz, IEEE Trans. on Industry Applications., Vol. 51, p. 3932-3942 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9d6629a6189646490cf1d18c718f1b23.jpg)
Fig. 1 (a) Low carrier ratio modular frequency-multiplying inverter structure; 
(b) Output of V1 and Vo 

![](https://assets.underline.io/uploads/markdown_image/1/image/f43b1024813a658d4714a6370e017930.jpg)
Fig. 2 Spectrum of load voltage

 Structure and Control of Modular Frequency-Multiplying Inverter with Low-Carrier-Ratio for High Speed Machine

1) Introduction As the use of high-efficiency and high-performance motors as motors for drones and home appliances increases, the use of PMSM (Permanent Magnet Synchronous Motor) type motors is increasing. To this end, many studies are being conducted on speed control in high-speed areas, and studies on sensorless control are also actively being conducted to reduce space constraints and weight and cost. [1][2] However, as the high-speed range increases, the position estimation signal of the sensor becomes unstable due to harmonics and inductance components, and it is greatly affected when small noise and disturbance occur. These errors degrade the performance of the high-speed control algorithm and the reliability of the motor. In this paper, to solve the sensorless error problem from low speed to high speed range, we use the signal output method of line drive method. The line drive output method generates signals that are complementary to each other, and through calculation, it can have strong characteristics against electrical noise and disturbance. Based on this, sensorless control in the high-speed region with high reliability was performed through detection and correction of signal distortion and disturbance in the signal generated at high speed due to inductance and harmonics. The PMSM simulation was configured to compare before and after application of the algorithm and verified its validity. 2) Methodology The sensorless control algorithm of the PMSM method generally includes current-based sensorless control and back EMF-based sensorless control. The current model-based sensorless control is used to estimate the speed and initial position using information of voltage and current, and the back EMF-based sensorless control estimates the position information through the estimated value of the back EMF. For current-based sensorless control, a lambda gamma-axis voltage equation that estimates the position from the existing dq-axis voltage equation is required, and the magnitude of the current is converted into an equation for the change of inductance to detect the position of the rotor. However, as the high-speed region increases, the delay of the current due to the inductance component and the positional error due to harmonics increase, so in the high-speed region, a sensorless control method using a back EMF model is used. Back EMF sensorless control includes a back EMF term as shown in Equation (1), and it is possible to establish voltage equations for lambda and gamma that estimate the position as a difference by θ. Through this, the back EMF equation can be expressed as Equation (2). Using this, you can estimate the position for θ as in Equation (3). Vγ=(R+pLd)iγ-(ωrLq)iδ+eγ, Vδ=(ωrLd)iγ+(R+pLq)iδ+eδ (1) êγ=Eex(-sinΔθ), êδ=Eex(-cosΔθ) (2) Δθ=tan-1(êγ/êδ) (3) However, when the motor reaches the high speed range, the distortion of the waveform becomes severe and it is more affected by disturbances such as vibration. Through this, the accuracy of sensorless control based on back EMF is deteriorated. In order to improve this, there is a harmonic injection method or an extended back EMF method, but the calculation is complicated and the system configuration cost increases due to an increase in the amount of operation. To improve this, we propose a signal correction method of the line drive method applied to the encoder. The basic concept of the line drive method is that the sum of the two signals must always be 1 by calculating the normal signal and the reverse signal at the same time. Therefore, even if an incorrect signal comes into one signal due to interference or disturbance, if a value other than 1 is output through the calculation of the normal component and the reverse component, the instantaneous count is not performed. By applying the method, the A-phase normal signal is processed using the existing signal for the A, B, and C-phase signals, and the reverse-phase signal is made based on the result obtained through the back EMF estimation method. Therefore, even if the A-phase normal signal is changed through disturbance and distortion of the signal, an error of the signal can be detected through comparison of the reverse-phase signal. Fig. 1 briefly shows the disturbed A-phase normal component and reverse phase component, and the resulting error values. As shown in Fig. 1, the position and magnitude of the error value can be detected by calculating the normal and inverse components. Based on this, the accuracy of the sensorless control algorithm can be improved by applying the compensation signal generated with the magnitude of the phase opposite to the error value to the signal generated by the disturbance. 3) Conclusion In order to verify the sensorless control algorithm in the high-speed region using the line drive method, the simulation was conducted after artificially adding noise using Matlab Simulink. In the case of using only the existing sensorless method, control was broken by noise and it was not able to operate properly. On the other hand, when the compensation of the line drive method was performed, the initial error was gradually compensated as shown in Fig 2, and it was confirmed that the motor operates stably after 0.4 seconds. Through this, we verified the validity of the algorithm proposed in this paper.

**References:**

[1] X. Song, J. Fang, B. Han, and S. Zheng, “Adaptive compensation method for high-speed surface PMSM sensorless drives of EMF-based position estimation error,” IEEE Trans. Power Electron., Vol. 31, No. 2, pp. 1438-1449, Feb. 2016. [2] G. Wang, H. Zhan, G. Zhang, X. Gui, and D. Xu, “Adaptive compensation method of position estimation harmonic error for emf-based observer in sensorless IPMSM drives,” IEEE Trans. Power Electron., Vol. 29, No. 6, pp. 3055-3064, Jun. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/76f075f49ab706ea99c61b8f10ce32c1.jpg)
Fig. 1 A,A-,Err graph using line drive method

![](https://assets.underline.io/uploads/markdown_image/1/image/2607ae6609735773963af48240233c1c.jpg)
Fig. 2 Actual angle and angle of line drive method

 A Study on High Reliability Sensorless Control of High Speed Permanent Magnet Synchronous Motor Using Line Drive Method

—Electrically excited homopolar inductor machine (EE-HIM) has good application in the field of flywheel energy storage system (FESS) due to its merits of simple structure, brushless exciting and little idling electromagnetic losses. However, the copper loss of field winding in the charge/discharge operation state would decrease the efficiency of energy conversion. To improve the efficiency of charge/discharge and inherit the merit of little idling electromagnetic losses, a novel HIM with flux memory (HIM-FM) is proposed. Firstly, the structure and operation principle of HIM-FM are illustrated. Then, the key structure parameters, including the rotor tooth width and slots depth are optimized. Finally, the electromagnetic performance, including the air-gap flux density, flux linkage, back-EMF and output torque and losses of HIM-FM are analyzed by finite element method. The result indicates that the proposed HIM-FM has the merit of little idling electromagnetic losses and no copper loss, which can be help to improve the energy conversion efficiency. I. Introduction An electrical machine is the key component of flywheel energy storage system (FESS), whose performance would directly affect the ration of energy conversion of FESS. Among the various electrical machine topologies, an electrically excited homopolar inductor machine (EE-HIM) has attracted much attention in the FESS due to its merits of robust rotor structure, brushless exciting. Moreover, the idling electromagnetic loss of EE-HIM can be eliminated by cutting off the field current [1]. However, the copper loss of field winding would decrease the charge/discharge efficiency of EE-HIM. Addressing this issue, a NdFeB permanent magnet (PM) HIM is proposed in [2]. While the idling loss would be caused due to the no-load high frequency magnetic field generated by PM. To improve the efficiency of charge/discharge and inherit the merit of little idling electromagnetic losses, a novel HIM with flux memory (HIM-FM) is proposed in this paper. II.Topology and operation principle The topology of proposed HIM-FM is shown in Fig. 1. As shown, the rotor is made of solid steel and has teeth on its both ends. The left and right teeth axes are differed by 180o electrical degree. Two stator cores are made of laminated steels and sandwich a magnetizing coil, which is used to demagnetize and magnetize the circular Al-Ni-Co permeant magnet (PM). Two segment shells are placed on both sides of Al-Ni-Co PM and provide the flux path for fluxes generated by the PM or the magnetizing coil. The PM would be magnetized when the HIM-FM works at charge/discharge state and demagnetized when the HIM-FM works at idling state. III.Performance evaluation Fig. 2(a) shows the air-gap flux density distribution of HIM-FM when the Al-Ni-Co PM has different remanence. It can be found that the maximum and minimum air-gap flux density is 0.848 and 0.021T. Fig. 2(b) gives the phase back electromotive force (EMF) of HIM-FM under different demagnetization. The amplitude of back-EMF can be regulated by 97.2% compared with the zero demagnetization. The stator core loss of HIM-FM are respectively 13.3 W and 0.0284W and the rotor eddy current loss of HIM-FM are respectively 0.85 W and 0.00197W under zero and severe demagnetization. Compared with the zero demagnetization, the stator core loss and eddy current loss can be reduced by 99.91% and 99.77%, which indicates that the proposed HIM-FM can be greatly reduced the idling electromagnetic loss. IV.Conclusion This paper proposed a novel HIM with flux memory (HIM-FM) for the application of flywheel energy storage system. The performance of HIM-FM is evaluated, which indicates that the proposed HIM-FM helps to reduce the idling electromagnetic loss and improve the efficiency of charge/discharge. The other electromagnetic performance of HIM-FM, such as the flux linkage, output torque and losses, would be presented in full paper.

**References:**

 [1] P. Tsao, M. Senesky, and S. Sanders, “An integrated flywheel energy storage system with homopolar inductor motor/generator and high-frequency drive,” IEEE Trans. Ind. Appl., vol. 39, no. 6, pp. 1710–1725, Nov./Dec.2003. [2] Z. Q. Liu, K. Wang and F. Li, "Design and Analysis of Permanent Magnet Homopolar Machine for Flywheel Energy Storage System," IEEE Trans. on Magn., vol. 55, no. 7, pp. 1-6, Jul. 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3382740e74094ea148be468a3449ecde.jpg)

 Investigation of a Novel Homopolar Inductor Machine with Flux Memory for the Flywheel Energy Storage System

I Introduction Owing to high efficiency, high power density and inhererly high fault-tolerant capacity, multiphase permanent magnet synchronous machines (PMSMs) equipped with the fractional-slot concentrated windings (FSCWs) have been drawing much attention [1]. Unfortunately, they are still limited by the excessive armature magnetomtive force (MMF) harmonics which will produce high eddy current loss in the PMs. To improve this situation, some new stator and winding arrangements, which can reduce the content of armature MMF harmonics, are proposed. But, it should be noted that the amplitude of the winding short-circuit current of these new topologies will increase due to the reduction of the harmonic leakage inductance. In this paper, the winding short-circuit faults of three six-phase PMSMs with different stator configurations whose contents of armature MMF harmonics are different are compared. II Six-Phase PMSMs with Different Armature MMF Distributions The well-known six-phase 12-slot/14-pole PMSM with traditional single-layer FSCW is shown in Fig. 1(a). The MMF distribution produced by the troditional single-layer FSCW contains a large content of harmonics as shown in Fig. 1(d). The two harmonics of order υ=1 and υ=5 are the main components, which are both the main contributors to PM eddy loss and harmonic leakage inductance. To improve the quality of armature MMF distribution produced by the traditional single-layer FSCW, two low armature MMF harmonic topologies are proposed, as shown in Fig.1 (b) and (c). By employing modular stator as shown in Fig. 1(b), the amplitude of the harmonic of order υ=1 can be significantly reduced. By using the concept of stator shifting [5], a double-layer 2-pitch 24-slot/14-pole six-phase PMSM can be obtained, as shown in Fig. 1(c). It can be seen that the main harmonic components, i.e. harmonics of order υ=1 and υ=5, are significantly reduced in the 24-slot/14-pole six-phase PMSM. In this way, three six-phase PMSMs with different contents of armature MMF harmonics are obtained for the comparison studies. III Winding Short-Circuit Currents and Demagnetization Analyses The winding short current will contain a transient component and a steaty component when the winding short current occurs in a PM machine. In orde to compare the surface-mounted PM demagnetization withstand ability of the three six-phase PMSM, the peak negative d-axis current during the whole short-circuit fault should be firstly obtained. The transit short current trajectories are shown in Fig. 2. It can be found that for the three six-phase PMSMs, the peak d-axis components of the winding short currents are -29.8 A, -39.5 A and -74.8 A, respectively. The amplitudes of the peak d-axis currents are increase with the decrease of the content of the armature MMF harmonics. A high winding short-circuit current will destroy the balance thermal distribution, which is the main drawback of the low armuture MMF harmonic designs. Futunately, owing to more even armature MMF distributions, even with higher negative d-axis current, the minimum flux densities of the PMs of the low armature MMF harmonics designs will be lower than the traditional one, as shown in Fig. 3.

**References:**

 [1] F. Barrero and M. J. Duran, “Recent advances in the design, modeling, and control of multiphase machines—Part I,” IEEE Trans. Ind. Electron., vol. 63, no. 1, pp. 449–458, Jan. 2016. [2] P. B. Reddy, K.-K. Huh, and A. M. El-Refaie, “Generalized approach of stator shifting in interior permanent-magnet machines equipped with fractional-slot concentrated windings,” IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 5035–5046, Sep. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/03b46be4fba1176ff03595252310aead.jpg)
Fig. 1 Three six-phase PMSMs and MMF distributions

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 Comparative Studies of Winding Short-Circuit Currents of Six-Phase PMSMs with Different Armature Magnetomovtive Force Distributions

—In order to reduce the cogging torque of the permanent magnet (PM) machine more effectively, a novel conception of the regional magnetic compensation (RMC) is introduced. An effective approach from the perspective of dynamic control for cogging torque reduction based on RMC is then proposed, by which the cogging torque could be reduced. Index Terms—Cogging torque, permanent magnet machines, dynamic reduction method, regional magnetic compensation. I. Introduction The cogging torque is an significant issue of the PM machines, which is an inherent shortcoming of PM machines. It leads to mechanical vibration, noise, and deteriorate the performances of the PM machines [1]. A wide variety of design methods for minimizing the cogging torque of PM machines have been comprehensively studied [1-3]. The existing cogging torque reduction methods can be mainly divided into two types: stator design and rotor design techniques. Undoubtedly, these methods can weaken the cogging torque but may result in the degradation of other machine performances, such as the unnecessary harmonics introduction, cost increase, and efficiency reduction, etc. On the other hand, it is impossible to weaken the cogging torque of a PM machine that has already been manufactured. Therefore, weakening the cogging torque from the perspective of dynamic control is worth considering, but few scholars have carried out related research on this. In this paper, a novel cogging torque reduction method based on regional magnetic compensation (RMC) has been proposed. The imbalance property of the magnetic field between adjacent stator teeth has been investigated and the compensation strategy of the regional magnetic field has been researched. The case studies of interior and surface-mounted PM machines show that the proposed method could help to dynamic minimize the cogging torque. II. Finite Element Analysis Of Cogging Torque Cogging torque is caused by the construction of the magnetic circuit of the machine, which is the interaction between the rotor magnetic flux and variable permeance of the air gap due to the geometry of stator slots [4], and it also exists when the machine is not energized. By making accurate analysis and calculation of the cogging torque, the basis for its compensation of the PM machines is created. The net cogging torque at any rotor position, which produced by a surface/interior PM machine can be calculated by [5] TC=∑k=1QS(La∫0hs((Bθb12(rt)−Bθb22(rt))/(2μ0)) (1) where Bθb1 and Bθb2 are the tangential components of flux densities near the adjacent stator teeth, respectively; QS is the number of slots; La is the effective length; hS is the radius of the slot opening. The cogging torque calculation of PM machines will be illustrated and analyzed in this part. III. Regional Magnetic Compensation Strategy According to the analytical formula of cogging torque, it can be known that the tangential flux density on both sides of the slot wall can be compensated by supplying current or voltage on the stator side, the magnetic close component of the cogging torque can be balanced, thus weakening the cogging torque. The cogging torque analytical calculation and the regional magnetic field compensation is shown in Fig. 1. Take a 2-pole, 12-slot surface-mounted PM machine as an example, the current injection scheme for different slots is illustrated in Fig. 2. Further detailed regional magnetic compensation schemes of different machine topologies and their cogging torque reduction results will be reported in the full paper.

**References:**

 [1] W. Fei and Z. Q. Zhu, “Comparison of cogging torque reduction in permanent magnet Brushless machines by conventional and herringbone skewing techniques,” IEEE Trans. Energy Convers., vol. 28, no. 3, pp. 664–674, Mar. 2013. [2] J. Gao, G. Wang, X. Liu, W. J. Zhang, S. D. Huang, and H. M. Li, “Cogging Torque Reduction by Elementary-Cogging-Unit Shift for Permanent Magnet Machines,” IEEE Trans. Magn., vol. 53, no. 11, p. 8208705, Nov. 2017. [3] L. Zhu, S. Z. Jiang, Z. Q. Zhu, and C. C. Chan, “Analytical methods for minimizing cogging torque in permanent-magnet machines,” IEEE Trans. Magn., vol. 45, no. 4, pp. 2023–2031, Apr. 2009. [4] E. H. Abd-Elhameed and M. Iwasaki, "Pulsating torque modeling and compensation for high precision positioning control," 2009 IEEE International Conference on Mechatronics, Malaga, 2009, pp. 1-5. Z. Q. Zhu and D. Howe, “Analytical Prediction of the Cogging Torque in Radial-field Permanent Magnet brushless motors,” IEEE Trans. Magn., vol. 28, no. 2, pp. 1371–1374, Mar. 2009.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/9e00f76d4a91dc15460041f836e5411e.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/50410699d8d89d71f2ac6c6235d0902d.jpg)

 Cogging Torque Dynamic Reduction Based on Regional Magnetic Compensation

1. Introduction In recent wind power generation systems, a permanent magnet synchronous generator(PMSG) using rare earth magnets has been widely used for high power density and miniaturization per unit volume[1]. However, rare earth magnets have the disadvantage of high prices and high instability in supply and demand due to the characteristics of resources produced mostly in specific countries[2]. On the other hand, ferrite magnets have the advantage of stable material supply and demand and low cost compared to rare earth magnets. However, ferrite magnets have a low magnetic flux density, about 1/3 of that of rare earth magnets, and a spoke-type structure was developed to compensate for this. The spoke-type is a structure in which magnetic flux is concentrated by arranging two magnets in a radial direction on the rotor. By combining the magnetic fluxes of two magnets facing each other, the magnetic flux can be increased to obtain a high airgap magnetic flux density[3]-[4]. Currently, various research and development of spoke-type are carried out and used in the motor field, but application cases, research and development are still insufficient in generators. In this paper, a 10-pole 36-slot spoke-type PMSG was designed using a 3kW class wind turbine as a model, and a hybrid magnetic flux intensive PMSG with improved performance of the conventional spoke-type was proposed. 2. Conventional spoke-type shape and features A spoke-type rotor structure typically has two feature types, as shown in Figure 1 (a) and (b). There are types of non-conductors, such as (a), that are designed to prevent magnetic flux from flowing into the inside of the rotor, and (b), such as the inside of the rotor is designed extremely small, to rapidly saturate the inner core of the rotor to reduce the leakage magnetic flux. For the first method, high output density can be expected because it essentially removes passes from the leakage magnetic flux, but it has the disadvantage of high manufacturing difficulty and production costs due to the need for another material component inside the rotor. Additional structures are also needed for binding to non-elastic bodies and cores to support the release of the pole piece. The second method is advantageous in terms of manufacturability and production cost, but even though the rotor shape has an extremely small inner side, leakage magnetic flux occurs and the output density decreases. If the inner side is too shortened, there is a limit to reducing the inner side because it is disadvantageous in terms of rigidity.[5]-[6]. 3. Hybrid spoke-type permanent magnet synchronous generator design and characteristic analysis In this paper, the shape of a hybrid spoke-type permanent magnet synchronous generator for wind power generation system is proposed. The hybrid spoke-type PMSG is a shape in which the inner and outer bridges of the rotor are arranged in zigzag as shown in Fig. 1(c), and they are intersected when stacked. Since it does not require additional components, it has better fabrication than the (a) type, and the inner leakage magnetic flux is reduced by using only half of the inner bridge, and the stiffness is supplemented by adding an outer bridge. Cogging torque related to the starting performance of wind turbines, efficiency during load operation, and voltage fluctuation rate are compared and analyzed for each model using finite element analysis(FEA). The cogging torque was 3.6, 3.5, and 2.3[Nm], respectively, and the proposed model had the best cogging torque performance. During load operation, the efficiency was 96.2, 95.7, and 95.6[%], respectively, and there was a difference of about 0.6%P between the (a) model and the proposed model, in which the internal leakage was blocked. As a result of the 3D analysis, the voltage fluctuation rate during load operation occurred above the target specification value of 15% for each model[7]. As the voltage fluctuation rate increases, the target output and efficiency cannot be satisfied. The voltage decrease during load operation is due to the armature reaction, so the number of turns and the voltage drop are proportional. Therefore, the number of turns was reduced by applying the overhang model, and as a result, the voltage fluctuation rate was reduced, and the final model was designed that satisfies the target specifications of cogging torque, voltage fluctuation rate, efficiency, and output. 4. Performance test and Conclusion To confirm the validity, a prototype was produced based on the final design model and a performance test was performed. The comparison of the test values with the FEA analysis results is shown in Table 1 and shows that the test values are similar to the analysis results. In this paper, a hybrid spoke-type PMSG for wind turbines was designed. By comparing the performance with the existing spoke-type models, it was confirmed that the cogging torque, an important performance specification of the wind turbine, was reduced, and the final model with overhang was designed to reduce the voltage drop that occurs during load operation. The performance was reviewed through 2D and 3D FEA, and a prototype was produced to verify the validity of the analysis results. Acknowledgments This work was supported in part by Technology Innovation Program (No. 20000401) funded By the Ministry of Trade, Industry & Energy(MOTIE), Korea and in part by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1A2C1013724).

**References:**

[1] Zaijun Wu, Xiaobo Dou, Jiawei Chu and Minqiang Hu, “Operation and Control of a Direct-Driven PMSG-Based Wind Turbine System with an Auxiliary Parallel Grid-Side Converter”, Energies 2013, pp. 3405-3421, 12. July. 2013. [2] J. Seaman, “Rare Earths and Clean Energy: Analyzing China’s Upper Hand,”2010. [3] W. Zhao, T. A. Lipo, and B. I. Kwon, “Torque pulsation minimization in spoke-type interior permanent magnet motors with skewing and sinusoidal permanent magnet configurations,” IEEE Trans. Magn., vol. 51, no. 11, Nov. 2015 [4] S. I. Kim, S. Park, T. Park, J. Cho, W. Kim, and S. Lim, “Investigation and experimental verification of a novel spoke-type ferrite-magnet motor for electric-vehicle traction drive applications,” IEEE Trans. Ind. Electron., vol. 61, no. 10, pp. 5763–5770, Oct. 2014. [5] Sandra M. Castano;Ehab Sayed;James Weisheng Jiang;Jianbin Liang, " Design of a Spoke-Type Ferrite Magnet Generator for a Hybrid Electric Vehicle Application," 2019 IEEE Transportation Electrification Conference and Expo (ITEC), 08 August 2019 [6] Mohammad Kimiabeigi; James D. Widmer; Raymond Long; Yi Gao; James Goss, On Selection of Rotor Support Material for a Ferrite Magnet Spoke-Type Traction Motor," IEEE Transactions on Industry Applications Volume: 52, Issue: 3, May-June 2016 [7] Sung Gu Lee;Jaenam Bae;Myungchin Kim;Won-Ho Kim, ” Study on the Improvement of the Correction Coefficient Considering the 3-D Effect of Spoke-Type Permanent-Magnet Synchronous Motor “ IEEE Transactions on Magnetics, Volume: 56, Issue: 3, March 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4c46d14717a099bee2f8b8c899a7f2ba.jpg)
Fig.1 Shape cross section for each rotor type

![](https://assets.underline.io/uploads/markdown_image/1/image/f373b2142d465bd6377247713506e6f2.jpg)
Table.1 Comparison of FEA and Test results

 Hybrid Spoke-Type Permanent Magnet Synchronous Generator for Wind Power Generation System

I. Introduction PM machines have become more and more popular in various applications due to high torque density and efficiency. There are two typical winding connection methods for PM machines, of which star connection is more widely used. Delta connection is the other one, which leads to higher line current yet smaller line voltage compared to star connection. Therefore, delta connection is usually employed in high-voltage applications. However, circulating currents are likely to occur in delta connection, which can lead to additional copper loss and thus reduced efficiency. In addition, a hybrid star-delta connection has been proposed in the past few years [1]. Compared to star connection, the winding factor is maximized and thus torque density is enhanced by approximate 5.2%. Nevertheless, little literature is found regarding short circuit (SC) and demagnetization for these winding connections. SC and demagnetization are detrimental to the reliabilities of PM machines. SC currents are usually several times larger than working currents, which can generate more heat and accelerate winding insulation aging. In addition, SC can lead to large torque ripple, which can result in vibration and further damage machine components. Moreover, SC current can yield huge magnetic fields against PMs and thus cause irreversible demagnetization. Average torque can be reduced and torque ripple can deteriorate once demagnetization happens [2]. Therefore, comparing SC currents and demagnetization between different winding connections helps determine which connection should be selected when designing PM machines, especially those for safety-critical applications. In this digest, three-phase SC (3PSC) and two-phase SC (2PSC) for star and delta connections are investigated, together with their resultant demagnetization. II. Finite Element Model and Drive Schemes for Star and Delta Connections Finite element method coupled with circuit is employed. A 10-pole/12-slot surface-mounted PM machine is selected for investigation. Practically, SC faults are more likely to happen in the converter than the SPM machine itself because the power electronic devices are usually easier to be damaged than the well-insulated windings. Therefore, the drive schemes for both connections are shown in Fig. 1(a) and (b) for the following analysis. III. Three-Phase Short Circuit and Demagnetization It is assumed that 3PSC happens when all upper switches in Fig.1 (a) and (b) are closed whilst all lower ones are opened to prevent shoot-through. The equivalent circuits are shown in Fig. 1(c) and (e). The 3PSC starts at the rotor position π/2 from open-circuit state and the rotor speed is assumed to be 500rpm during 3PSC. As shown in Fig. 2(a), the star connection shows slightly larger peak currents. Since SC current usually produces a voltage against the back-EMF, the terminal voltage of each phase is approximately 0V during 3PSC for star connection. Therefore, when only the fundamental back-EMF is considered, the 3PSC currents for both winding connections are almost the same. For the star connection, the 3rd back-EMF harmonics are compensated in each loop and does not contribute to the 3PSC currents. However, the 3rd harmonic cannot be compensated in the delta connection and leads to additional 3PSC current component, which reduces peak currents in this 10-pole/12-slot SPM machine. In addition, the demagnetization level is evaluated by torque loss, which is defined as the ratio of the reduction of average torque to pre-demagnetization value. The torque loss for the star and delta connection are 1.84% and 1.53%, respectively. IV. Two-Phase Short Circuit and Demagnetization It is assumed that 2PSC happens when the switches VT1 and VT3 in Fig.1 (a) and (b) are closed whilst the others are opened. The equivalent circuits are shown in Fig. 1(d) and (f). 2PSC heavily depends on start rotor position and only SC currents starting from rotor position π/2 are analyzed as an example. As shown in Fig. 2(b), for the delta connection, the phase B current is approximately twice the SC currents of phase A and C in the opposite directions. This is because the SC loop of winding A and C has twice larger impedance than that of winding B, as shown in Fig.1 (f). Compared to the star connection, the phase B and C peak currents are larger and the phase A current is smaller under this start rotor position. The 2PSC peak currents under different start rotor positions are shown in Fig. 2(c). In addition, the torque loss after 2PSC for delta connection is larger under most start rotor positions, as shown in Fig. 2(d). V. Conclusions It can be concluded which winding connection causes larger 3PSC peak currents and severer demagnetization heavily depends on the 3rd back-EMF harmonic. In addition, delta connection exhibits larger 2PSC peak currents and severer demagnetization under most start rotor positions. In the full paper, hybrid star-delta connection and single-phase SC will be considered. In addition, more analytical analysis and experimental validation will be presented.

**References:**

[1] M. N. F. Ibrahim, A. S. Abdel-Khalik and E. M. Rashad, IEEE Transactions on Energy Conversion, vol. 33, pp. 1015-1024 (2017). [2] L. Wu, Y. Du and Z. Chen, IEEE Transactions on Industry Applications, vol. 56, pp. 2427-2440 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2d5e681b6a76738fef42a8cf2aa839f.jpg)
Fig. 1. Drive schemes for star and delta winding connections and SC equivalent circuits. (a) Drive scheme, star. (b) Drive scheme, delta. (c) 3PSC equivalent circuit, star. (d) 2PSC equivalent circuit, star. (e) 3PSC equivalent circuit, delta. (f) 2PSC equivalent circuit, delta.

![](https://assets.underline.io/uploads/markdown_image/1/image/072d4c8f3f2cf29649904f0936930c75.jpg)
Fig. 2. SC currents and torque loss. (a) 3PSC current waveforms. (b) 2PSC current waveforms. (c) 2PSC peak currents under different start rotor positions. (d) Torque loss due to 2PSC under different start rotor positions.

 Comparison of Short Circuit and Irreversible Demagnetization between Different Winding Connections in Surface-Mounted PM Machines

Permanent magnet synchronous machines (PMSMs) are widely used in transmission and air-conditioning systems owing to several advantages such as high power density, high efficiency, and compact structure. However, PMSMs have the drawbacks of noise, vibration, and harshness (NVH) caused by the interaction between the magnetic motive force (MMF) of the stator winding and rotor magnets having a high coercive force, significantly affecting the machine characteristics. The NVH of PMSMs is influenced by serious machine operation problems such as eccentricity, rotor mass asymmetry, and axis misalignment, which causes machine faults and breakage. Therefore, it is necessary to consider these problems during the initial design stage. However, among these problems, the rotor mass asymmetry and axis misalignment have an influence on the change in mechanical characteristics, while eccentricity affects the change in the electromagnetic characteristic, which causes an increase in the electromagnetic NVH sources. Previous research has shown that eccentricity affects not only electromagnetic performance but also NVH sources that are related to the machine’s characteristics. Electromagnetic NVH sources can be divided into two types: torque and electromagnetic force characteristics. The torque characteristics are classified as cogging torque and torque ripple. Previous research has shown that NVH characteristics are improved by reducing the torque characteristics. The electromagnetic force characteristics are classified as unbalanced electromagnetic force (UMF) and magnetic pull force (MPF). The MPF is the distribution of the magnetic flux density owing to the MMF of the stator winding, rotor magnets, and slotting effect. Numerous studies emphasizing MPF symmetry have been published. The UMF is caused by changing the magnetic flux density according to the rotating operation, which has been actively studied as the primary cause of NVH along with rotor eccentricity in induction machines. There are a few studies on the UMF of PM machines. Wu, et al. analyzed the UMF harmonic orders using an analytical method along with experimental results. Zhu, et al. analyzed the UMF generated in the models according to different winding patterns with equal specifications and changes in the current waveform according to the shape of the machines. However, the electromagnetic source influence on the NVH caused by eccentricity was not confirmed. Therefore, to analyze the eccentricity influence on each electromagnetic NVH source, we proposed the design of a PMSM with a fractional pole/slot combination, derived the dominant model of the pole/slot combination for each electromagnetic NVH source through a finite element analysis, and carried out a comparative results analysis of the results of the electromagnetic characteristic analysis. The derived pole-slot combination of the models are 8-pole/9-slot. The dominant components of 9-slot is electromagnetic force characteristics, respectively. However, if it is applied eccentricity conditions that increased the torque characteristics. Thus, we analyzed the influence of each NVH source by conducting experiments and electro-mechanical coupled analysis using FEM, and then compared the results with two different operating conditions. The analysis model and concept of eccecntricity used for the electromagnetic excitation analysis are shown in Fig. 1(a). The derived pole-slot combination is the 8-pole/9-slot and 8-pole/12-slot. The concept of the NVH experimental system is shown in Fig. 1(b), to generate eccentricity, an apparatus for moving the stator is applied to the test motor. The characteristic analysis results of electromagnetic excitation are shown in Figs. 1(c) and (d). The NVH source, in the eccenctricity condition is higher than that in a healthy condition. Therefore, the influence on each source can be analyzed. Figs. 2(a) and (b) show the electro-mechanical NVH characteristic analysis results of PMSMs according to the eccentricity. Figs. 2(c) and (d) show the measurement NVH results. This indicates that eccentricity significantly influences the NVH of the PMSMs. Detailed analysis and measurement results are discussed in the full paper.

**References:**

[1] J. Zou, H. Lan, Y. Xu, and B. Zhao, “Analysis of Global and Local Force Harmonics and Their Effects on Vibration in Permanent Magnet Synchronous Machines,” IEEE Trans. Energy convers., vol. 32, no. 4, pp.1523-1532, Dec. 2017. [2] D. Torregrossa, F. Peyraut, B. Fahimi, J. MBoua, and A. Miraoui, “Multiphysics finite-element modeling for vibration and acoustic analysis of permanent magnet synchronous machine,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 490–500, Jun. 2011. [3] H. Yang and Y. Chen, “Influence of radial force harmonics with low mode number on electromagnetic vibration of PMSM,” IEEE Trans. Energy Convers., vol. 29, no. 1, pp. 38–45, Mar. 2014. [4] P. Beccue, J. Neely, S. Pekarek, and D. Stutts, “Measurement and control of torque ripple-induced frame torsional vibration in a surface mount permanent magnet machine,” IEEE Trans. Power Electron., vol. 20, no. 1, pp. 182–191, Jan. 2005. [5] Z. Q. Zhu, Y. Liu, and D. Howe, “Minimizing the influence of cogging torque on vibration of PM brushless machines by direct torque control,” IEEE Trans. Magn., vol. 42, no. 10, pp. 3512–3514, Oct. 2006. [6] D. Y. Kim, M. R. Park, J. H. Sim, and J. P. Hong, “Advanced Method of Selecting Number of Poles and Slots for Low-frequency Vibration Reduction of Traction Motor for Elevator,” IEEE/ASME Trans. Mechatro., vol. 22, no. 4, pp. 1554-1562, Aug. 2017. [7] J. F. Gieras, C. Wang, and J. C. Lai, Noise of Poly-phase Electric Motors. New York, NY, USA: Taylor & Francis, 2006.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/84a39008bc4ccc70facb277b81e18897.jpg)
Figure 1 (a) Analysis model (b) the concept of experimental system (c) UMF analysis results according to Eccentricity (d) Back EMF analysis results according to Eccentricity

![](https://assets.underline.io/uploads/markdown_image/1/image/4eee758d9a0e9c24b511c0483b44bfbf.jpg)
Figure 2 Experimental and analysis results of NVH according to eccentricity: (a) healthy conditions analysis results (b) eccentricity conditions analysis results (c) healthy conditions measurement results (d) eccentricity conditions measurement results

 Analysis and Experimental Study for Electromagnetic and Mechanical Characteristic of Permanent Magnet Synchronous Machines according to Eccentricity

this paper proposes segmented asymmetrical stator design to reduce torque ripple for permanent magnet synchronous motor (PMSM). By changing the design parameters of the segmented stator, a specific phase difference of the two torque ripples can be generated by two sections of the stator, so the ripples can offset each other to reduce the torque ripple. A 14-pole 12-slot PMSM is carried out to analyze the proposed stator design, and the correctness of the method is verified by finite element analysis (FEA). I. Introduction Permanent magnet synchronous motor (PMSM) is widely used in industrial fields because of the advantages of high power density and high efficiency [1]. However, torque ripple of PMSM can cause vibration and noise, which are not conducive to the smooth operation of the motor. So, it’s of great necessity to reduce the torque ripple. Generally, magnet shape optimization is carried out to reduce torque ripple, but this method also decreases the average torque [2]- [3]. Consequently, this paper proposes segmented asymmetrical stator design, which can reduce torque ripple without significant drop of average torque. II. Mechanism of Torque Ripple Electromagnetic torque is generated by back EMF and current. Assuming that the input current is a standard sinusoidal wave, then average torque is generated by the current and the fundamental of back EMF, while torque ripple is generated by the current and the harmonics of back EMF. The conventional method is to optimize the shape of permanent magnet. In this way, the amplitude of back EMF harmonics can be reduced so as to achieve the decrease of the torque ripple. However, the fundamental of back EMF is also reduced so the average torque decreases obviously. The proposed method is not to reduce the back EMF harmonics, but to create two groups of harmonics which are staggered by a certain phase to make them cancel each other. In this way, the torque ripple is reduced and the average torque can be maintained. III. segmented stator design A 14-pole 12-slot PMSM is carried out to analyze the proposed stator design. For the conventional symmetrical structure, the average torque is 53Nm and the torque ripple is 3.05%. Then segmented asymmetrical design is carried out to optimize the stator. The main parameters are θ and W. θ is the degree from the middle of teeth to the middle of slot opening. W is the width of the slot opening. Given several θ and W, finite element analysis (FEA) is used to calculate the performance of the motor. A total of 120 schemes are calculated by FEA and the results are analyzed. Fast Fourier Transform (FFT) are applied to the torque results to obtain the harmonics distribution of the torque ripples. From the analysis, it’s easy to find two torques which have similar ripple amplitude and opposite phase. The model A is that when θ is 12° and W is 4.4, and the model B is that when θ is 18° and W is 4.4. The details of the torque results are shown as Fig.1. It can be seen from Fig.1 that the amplitudes of sixth torque ripple are 0.4664 and 0.7719, and the phases are -109° and 74°. The amplitudes of twelfth torque ripple are 0.1484 and 0.1512, and the phases are -165° and 28°.Both the sixth and the twelfth torque ripples of the two models have similar amplitude and opposite phase. So the torque ripple can be reduced sharply if the two torque waveforms are superimposed. According to the above analysis, the stator core can be designed in sections. The stator core can be divided into two parts in the axial direction, and the laminations of the two parts are made according to model A and model B respectively. Then the segmented stator is used for FEA calculation, the average torque is 52.5 Nm and the torque ripple is 0.93%. The torques of segmented stator and relevant comparison models are shown in Fig.2. It can be seen from Fig.2 that although the FEA results of segmented stator structure are not entirely consistent with the average results of model A and model B, the torque ripple of the motor can be effectively reduced without obvious reduction of average torque. The torque ripple is obviously reduced from 3.05% to 0.93%, and the average torque is only reduced from 53Nm to 52.5Nm. IV. Conclusion This paper proposes a segmented asymmetric stator structure. By segmenting the stator and designing each section, the torque ripples generated by different sections can cancel each other, so as to weaken the torque ripple. This method doesn’t require permanent magnet shape optimization, so the torque will not decrease significantly. The validity and accuracy of the segmented asymmetrical stator structure are verified by FEA calculation.

**References:**

1. J. Si, S. Zhao, H. Feng and R. Cao, Chinese Journal of Electrical Engineering, vol. 44, p. 67-73(2018) 2. W. Zhao, T. A. Lipo and B.-I. Kwon, IEEE Transactions on Industrial Electronics., vol. 61, p. 5779-5787(2014) 3. D. Wu and Z. Q. Zhu, IEEE Transactions on Magnetics, vol. 51, p. 1-4(2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3e74da84394619607f70d0edbc605b1e.jpg)
Fig.1 Structures and torque analysis of asymmetrical models

![](https://assets.underline.io/uploads/markdown_image/1/image/753d00020fd38f4003146832df524af2.jpg)
Fig.2 Segmented asymmetrical stator structure and torque results of the models

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