Design and Analysis of a Five-phase Flux-Intensifying Fault-Tolerant Permanent-Magnet Motor With Active Sensorless Strategy Under Multimode Operation

In this paper, a new flux-intensifying fault-tolerant permanent magnet synchronous motor (FI-FTPMSM) is proposed to improve sensorless operating capacity under multimode operation including fault conditions. Most previous studies regarding fault-tolerant motors aim to improve fault-tolerant capability but suffer the saliency characteristic problem, which is unfavorable for sensorless control. In this study, an active sensorless strategy is developed by considering the sensorless operating capability under multimode operation in the motor design stage. Based on this novel idea, a new FI-FTPMSM with a high inverse saliency ratio is designed. By carefully choosing slot-pole combination, subtly setting q-axis magnetic barrier shape, and improving air gap waveform, the superior inverse saliency characteristic is obtained, which effectively improves the dynamic and steady-state sensorless operating performance. Through simulation analysis and experimental tests, the rationality and validity of the proposed strategy are verified.


I. INTRODUCTION
R ECENTLY, global problems such as oil shortage and environmental pollution impose ever-increasing challenges for society. With the goal of Carbon Peak and Carbon Neutrality, electric vehicles (EVs) are developing rapidly [1], [2]. The operating conditions of EVs are diverse and compound, including frequent start and stop, low-speed with a heavy load, high-speed cruise, and coping with drive system failures [3]. Consequently, Manuscript  higher requirements of torque density, speed-regulation range, efficiency, short-term overload capacity, fault tolerance, and reliability of the drive motors are demanded for EVs.
Owing to the merits of good fault-tolerant capacity, high torque density, and high efficiency of the five-phase faulttolerant permanent magnet synchronous motor (FTPMSM), it has been extensively investigated in the field of EVs [4]. By adopting the corresponding fault-tolerant control, the FTPMSM is able to operate continuously under power switch fault, opencircuit fault, and short-circuit fault without system performance degradation [5], [6]. To achieve high-precision control for the five-phase FTPMSM, the accurate rotor position is necessary to be acquired. Yet, when the five-phase FTPMSM drive system operates in a harsh driving environment, it is very difficult to obtain an accurate rotor position from the mechanical position sensors. To mitigate this issue, sensorless control technologies are widely paid attention. At present, the existing sensorless control algorithms can be classified as the back-EMF estimated method and the saliency tracking method [7], [8]. To overcome the problem of the back-EMF estimated method that suffers from the zero-/low-speed operation, the high-frequency injection (HFI) algorithms are applied to monitor the rotor saliency for extracting the rotor position information [9]. Typically, to improve the fault-tolerant capacity, the fractional-slot concentrated-windings (FSCWs) [10] are adopted by the existing five-phase FTPMSM. However, the use of FSCWs increase the cross-axis magnetic circuit coupling [11], which will result in a lower saliency ratio for conventional FTPMSM. Then, the estimated accuracy of the rotor position for sensorless control will be greatly reduced. In addition, due to the low saliency ratio, the conventional five-phase FTPMSM, even with an interior PM rotor, still suffers from the low reluctance torque. Correspondingly, the torque performance and flux-weakening speed-regulation range will decrease. Hence, it is important to overcome these shortcomings of the FTPMSM, including poor sensorless operating capacity, narrow speed range, and low efficiency in the high-speed region, while achieving good fault tolerance.
Enhancing the motor's saliency ratio is an effective means of improving the sensorless operating capacity [9]. Studies about enhancing the saliency ratio of the interior permanent magnet (IPM) motors have been conducted [12], [13], [14]. In [12], based on the equivalent magnetic circuit and mechanical phase region, the influence of various dimensional parameters on the d-and q-axes inductances and saliency ratio were analyzed, and then the design principle of increasing the saliency ratio was concluded. In [13], a surface inset permanent magnet machine with unequal d-q axis air-gap length was proposed, in which the high saliency ratio and reluctance torque, as well as the wide-speed range, were obtained. Reference [14] pointed out that the motor's saliency ratio and reluctance torque ratio can be improved by selecting a suitable slot-pole combination. On the whole, these above IPM motors with the effectively enhanced saliency ratio, the steady-state sensorless operating performance can be accordingly improved. It's worth noting that these above motors own the positive saliency feature with L q /L d > 1. Yet, due to the influence of magnetic saturation, the saliency characteristics of the traditional IPM motors may disappear easily when their load increase. Especially for the complex and multiple operating conditions, the changeable load characteristics bring about unpredictable motor's saliency characteristics. Correspondingly, the dynamic sensorless operating performance will deteriorate. In addition, existing fault-tolerant motors generally have a low saliency ratio; thus, their efficiency improvement in a high-speed region is still limited. Typically, to improve the estimated accuracy of the rotor position under multiple operating conditions, the optimized motor control algorithm is adopted. Yet, how to accurately identify the motor's saliency ratio from greater than 1 to less than 1, and change the corresponding estimated method of the rotor position in real-time, which brings great challenges to the sensorless control of the traditional IPM motor. Furthermore, the complexity of the control algorithm is seriously increased.
To solve these above problems, a flux-intensifying interior permanent magnet synchronous motor (FI-IPMSM) is proposed [15]. Owing to the high q-axis reluctance, the flux-intensifying IPM motor has small change of inductance characteristics, which can improve dynamic sensorless control performance. Also, the good power conversion capability can be achieved. In this regard, research has been conducted on achieving the flux-intensifying effect. In [16], the inverse saliency feature with L d > L q was realized by setting q-axis magnetic barrier and segmented permanent magnet. Reference [17] designed two flux-intensifying motors by adding q-axis magnetic barrier and magnetic bridges along the d-axis magnetic circuit, which can reduce the risk of irreversible demagnetization and widen the speed range. To improve the fault-tolerant capacity of the above FI-IPMSMs, a five-phase FI-FTPMSM was proposed in our previous work [18]. Nevertheless, because the permanent magnet with high reluctance is located on the d-axis, its inverse saliency ratio is relatively low. Especially for the use of multi-poles, its rotor size is limited, thus, the enhancement of inverse saliency ratio by adding q-axis magnetic barrier is more difficult. Therefore, the steady-state sensorless operating capacity of the FI-FTPMSM needs to be further improved.
In this article, a new five-phase FI-FTPMSM with an active sensorless control strategy is proposed to achieve the good sensorless operating capacity under multimode operations. The influence of motor parameters on sensorless operation under multiple operating conditions is also comprehensively considered. The main contributions of this article are summarized as below: 1) With the suitable slot-pole combination and q-axis magnetic barrier setup, a remarkable inverse saliency characteristic of the proposed FI-FTPMSM is achieved. Thus, the accuracy of steady-state zero/low-speed sensorless operation can be enhanced. 2) With the stable inductance characteristic of the proposed FI-FTPMSM under different conditions, the dynamic sensorless operating performance can be improved. 3) Owing to the L d > L q characteristic of the proposed FI-FTPMSM, the positive d-axis current is obtained under Maximum Torque Per Ampere (MTPA) control strategy. Hence, the risk of irreversible demagnetization is reduced and the stability of back EMF is improved. Correspondingly, the sensorless operating performance at medium/high speed can be improved. The remainder of this article is organized as follows: In Section II, the multiple operating conditions and the design requirements of sensorless operation under different states will be analyzed. The design idea and the motor structure will be introduced in detail in Section III. Then, the electromagnetic performance of the proposed five-phase FI-FTPMSM will be analyzed in Section IV. Section V will present and analyze the corresponding experimental results. Finally, the conclusions will be drawn in Section VI.

A. Sensorless Operation Under Multiple Operating Conditions
With the increasing complexity of urban transportation, vehicle driving cycles have become complex and diverse, which imposes higher requirements for sensorless operation. Fig. 1 shows the relationship between WLTC (Worldwide Harmonized Light Vehicles Test Cycle), driving cycles of EVs, requirements of EV drive system, and requirements of sensorless operation. It can be observed that there are multiple driving cycles in the whole WLTC, including start/stop, acceleration, climbing with a heavy load, high-speed cruise, etc. Additionally, in the presence of faults, the drive motor produces undesirable high torque ripples and even cannot work normally because of its asymmetrical currents caused by faults. Therefore, the performances of high reliability, high torque output capacity, sensorless operation as well as a wide speed range are required for the drive motor.
Furthermore, the motor parameters affect its sensorless operation to some extent. For example, the saliency characteristics and magnetic saturation of the drive motor have an impact on the estimated accuracy of rotor position under sensorless operation. Therefore, the advantageous performances of dynamic and steady-state full-speed sensorless operation are required for multiple operating conditions.

B. Design Requirements of Dynamic Sensorless Operation
For the conventional five-phase FTPMSM, its magnetic saturation is affected by the variations of load current under different operating conditions. Note that the magnetic saturation may lead to the disappearance of the motor's saliency feature and reluctance torque. Correspondingly, the dynamic sensorless operating performance of the conventional five-phase FTPMSM will be greatly influenced by the saliency variation characteristics with the cross-coupling effect.
Sensorless control technology based on saliency tracking can be used to estimate the rotor position at zero/low speed. Owing to the cross-saturation effect, the high-frequency current response trajectory rotates when the high-frequency voltage signal is injected into the stator winding [19], as shown in Fig. 2. Where ΔI dh and ΔI qh are the variation of the d-and q-axis of the high-frequency current response respectively; I max and I min are the major and minor axes of elliptical high-frequency current trajectories, respectively; ε is the angle between the major axis and the d-axis.
The angle offset caused by cross-saturation effect is defined as ε, which can be expressed as: where ε is the angle offset of high-frequency response caused by cross-saturation effect, L dq is the d-and q-axis cross-saturation inductance, L d is the d-axis inductance, and L q is the q-axis inductance.
The angle error is determined by the dq-axis cross-saturation inductance and differential inductance. When the L dq equals to 0, the absolute error |ε| tends to 0. When the differential inductance L q − L d = 0, the absolute error |ε| tends to π/4.Thus, it can be concluded that the magnetic saturation has great impact on the estimated accuracy of rotor position. For the traditional fivephase FTPMSM with interior PM, its saliency ratio is usually greater than 1. Unfortunately, its saliency characteristic deteriorates and even disappears with the increase of load current, which may cause a large position error. Therefore, more stable saliency characteristic is required by improving motor design while ensuring its good basic electromagnetic performance.

C. Design Requirements of Zero/Low-Speed Steady-State Sensorless Operation
In addition to the dynamic sensorless operation performance, more importantly, the estimated accuracy of the steady-state sensorless control operation is affected by the motor's saliency ratio. When the five-phase FTPMSM runs at zero/low speed, its rotor position is usually estimated by HFI algorithms [20]. Among different HFI algorithms, the fluctuating HFI method has the advantages of a high estimation accuracy and less influence of the motor drive system caused by injected signals [21]. Thus, the fluctuating HFI method is utilized to analyze the rotor position error in this paper.
With the injected fluctuating high-frequency voltage signal, the high-frequency response currents are expressed as [22]: where ; I p and I n represent the amplitude of positive sequence and negative sequence current components, respectively; are the amplitude and angular frequency of high-frequency voltage signal, respectively; Δθ is the error between the actual position and the estimated rotor position.
The high-frequency response currentî qh contains the rotor position error term. Then, multiplyingî qh by sinω h t and extracting the position error signal by a low-pass filter, the rotor position error function f(Δθ) can be obtained, which is expressed as: Equation (3) shows that if Δθ is small enough, the error function f(Δθ) and Δθ are approximately linear. Finally, the rotor position can be obtained through the phase-locked loop.
Based on [21], when the rotor position estimation system reaches steady-state, the rotor position error Δθ caused by the fundamental and harmonics introduced by HFI signal is expressed: where ρ = L q /L d is the saliency ratio, λ is the ratio of the amplitude in-phase between the q-axis high-frequency voltage fundamental wave and the injected high-frequency signal, and E is the DC bus voltage. It can be observed from (4) that the estimation accuracy of the rotor position is closely related to the motor's saliency ratio. When the saliency ratio is closer to 1, the (ρ−1) in the denominator of the (4) will be decreased, Correspondingly, the rotor position error of |Δθ| will increase. Therefore, it can be concluded that a better estimated accuracy of rotor position can be obtained when the motor's saliency ratio is much greater than or much less than 1.

D. Design Requirements of Medium/High-Speed Sensorless Operation
The sensorless control technology based on back-EMF estimation can be employed to obtain the rotor position information without additional excitation signal under medium/high speed. Correspondingly, the motor's back-EMF is very important for the precise rotor position estimation. When the fivephase FTPMSM runs at high speed, the flux-weakening control strategy usually needs to be adopted. Then, demagnetization current should be applied to reduce the PM flux and widen the motor speed. However, exorbitant demagnetization current increases the risk of irreversible demagnetization of PM, which inevitably affects its back-EMF.
According to the back-EMF-based sensorless control strategy [23], the estimated rotor position is expressed as: whereẽ α andẽ β represent the estimated back EMF in α-axis and β-axis, respectively. It can be known from (5) that the back-EMF has a decisive influence on the estimation accuracy of rotor position. When the demagnetization occurs in the five-phase PM motor, the five-phase back-EMFs will be asymmetric. At this point, the five-phase PM motor system is in an asymmetric state, which will result in the inability to directly apply the existing traditional sensorless technology at post-fault operation. Then, it can be obtained that the asymmetric back-EMFs caused by PM demagnetization bring a large estimation error in the medium/highspeed for the sensorless control method. Consequently, to obtain the stable back-EMF, the resistance to demagnetization of the FTPMSM is necessary to be improved.

III. MOTOR DESIGN WITH ACTIVE SENSORLESS STRATEGY
The above analysis shows that the motor with obvious saliency ratio can improve the sensorless operating performance under multiple operating conditions. However, the traditional five-phase FTPMSM still suffers from poor sensorless control performance under multiple operating conditions due to variable saliency characteristics, low saliency ratio, and poor anti-demagnetization capacity. Then, a design idea of active sensorless strategy with the consideration of the influence of motor parameters on the sensorless control performance under multiple operating conditions is proposed in this paper. With the consideration of the sensorless operating capability in the motor design, a new FI-FTPMSM with a high inverse saliency ratio is designed to meet the requirement of high-precise sensorless control under multiple operating conditions.
To obtain the inverse saliency characteristic, the most effective way is to increase the q-axis magnetic barrier. Typically, the 20-slot/18-pole is usually adopted for the traditional five-phase FTPMSM to improve the fault-tolerant capability [18]. However, due to the adoption of multipole, the rotor size is limited and the permeability of the PM located in the d-axis is low. Coupled with the obvious cross-axis coupling phenomenon, the significant inverse saliency ratio is more difficult to be achieved for the traditional five-phase FTPMSM.
To overcome the above problems, a 10-slot/8-pole is selected to provide sufficient space for q-axis magnetic barrier on the premise of ensuring the fault-tolerant performance. Fig. 3 shows the design idea of the proposed FI-FTPMSM. For improving the dynamic sensorless operating performance, a deeper q-axis magnetic barrier is set to reduce the q-axis inductance. Also, the q-axis magnetic barrier adopts concave arc, which is conducive to reducing the saturation of the d-axis magnetic circuit and reducing the rotor iron loss. Furthermore, the permanent magnet with suitable thickness is located near the rotating shaft, which can improve the d-axis inductance and reduce the effect of harmonics. Consequently, the eddy-current loss and demagnetization risk of the permanent magnet of the FI-FTPMSM can be reduced. In addition, the plane stator tooth top is employed to further reduce the q-axis inductance and the coupling of magnetic circuit, which is conducive to further improving the inverse saliency ratio and steady-state sensorless operation performance of the motor. Meanwhile, the plane tooth top can adjust the air-gap reluctance; thus, more sinusoidal back-EMF characteristics and lower torque ripple can be obtained [24]. Noted that the saturation of the flux-bridges is a critical point for the self-sensing characteristics of the machine. Since the proposed FI-FTPMSM has large q-axis barrier, the influence of the q-axis armature magnetic field can be reduced. Therefore, a small variation of q-axis inductance can be achieved, which helps to improve the sensorless operating performance.  With the design idea of the active sensorless strategy, the structure of FI-FTPMSM can be obtained, as shown in Fig. 4. Also, the simplified equivalent magnetic circuit is shown in Fig. 5. From Fig. 5, the d-and q-axis inductances of the five-phase FI-FTPMSM can be obtained, which is expressed as: where R g is the air-gap reluctance, R pm is the reluctance of permanent magnet, R s is the reluctance of stator core, R r is the reluctance of rotor core, and R b is the external magnetic barrier of q-axis.
For the traditional FTPMSM, its d-axis armature magnetic field is always demagnetized with the adoption of the MTPA control strategy below the base speed. At this time, the d-axis armature magnetic field is in reverse series with the permanent magnetic field, as shown in Fig. 5(a). By contrast, the d-axis armature magnetic field of the proposed motor keeps a magnetization characteristic, which is connected in series with the permanent magnetic field, as shown in Fig. 5(b). Consequently, the risk of irreversible demagnetization of PM can be greatly reduced.
Since the proposed FI-FTPMSM also belongs to brushless PM motor, the design theory of brushless PM motor can be used in the initial design of the FI-FTPMSM. According to the design principle of brushless PM motor, the power dimension equation of the FI-FTPMSM can be expressed as: where D s is the stator diameter; l a is the shaft length; P out is the rated output power; k w is the winding factor; n s is the rated speed; A m is the line load; B max is the fundamental amplitude of air gap flux density; η is the motor efficiency; and ϕ is the power factor angle. From (7), it can be known that the output power is closely related to rotor speed and the electromagnetic load. When the motor's rated output is determined, the main dimensions can be designed.
Moreover, the flowchart of optimization process is presented in Fig. 6. According to the flowchart, first, the optimization requirements and model is determined. Second, optimization objectives and design variables are determined, and selecting the variables with high sensitivity based on sensitivity analysis. Finally, the design variables are optimized through design of experimental (DOE) and response surface (RS), and the optimization results were verified by simulation analysis.

IV. PERFORMANCE EVALUATION
To verify the validity of the proposed five-phase FI-FTPMSM, the traditional FTPMSM with 10-slot/8-pole is selected as a benchmark. The electromagnetic performances of the proposed FI-FTPMSM and the traditional FTPMSM are investigated in detail by finite-element analysis (FEA). For a fair comparison, both motors have the same power density and volume. Also, the key parameters and dimensions of both motors are shown in Table I.   FTPMSM, the cogging torque of the proposed FI-FTPMSM increases slightly because of its the saliency characteristic. Then, the back-EMF waveform is analyzed through fast Fourier transform (FFT), as shown in Fig. 8. It reveals that the total harmonic distortion (THD) of the FI-FTPMSM and the traditional FTPMSM is 1.06% and 6.25%, respectively. Since the back-EMF waveform is one of the factors affecting the torque ripple, the sinusoidal back EMF can reduce the torque ripple to a certain extent. Fig. 9 shows the inductance characteristics of the traditional FTPMSM and the proposed FI-FTPMSM under no-load condition. It can be found that the ratio of mutual inductance to self-inductance for the FTPMSM and the FI-FTPMSM is 7.73% and 6.95%, respectively. Therefore, both motors exhibit strong fault-tolerant capability because of their magnetic isolation.   Fig. 10 shows the dq-axis inductances of the two motors at no-load. It can be found that the q-axis inductance of the traditional FTPMSM is greater than the d-axis inductance, which verifies its positive saliency ratio. By contrast, the q-axis inductance is obviously less than the d-axis inductance for the FI-FTPMSM. The inverse saliency ratio of the FI-FTPMSM is 1.2, which verifies the characteristic of L d > L q and the significant flux-intensifying effect.

B. Torque Output Characteristics
The torques of both motors under different current angles over the entire range of current angle from −90°to +90°are given in Fig. 11. It can be observed that the torque current angle characteristics of the two motors are opposite. The maximum output torque of the traditional FTPMSM is obtained when the current angle is greater than 0, while that of the proposed FI-FTPMSM is obtained when the current angle is less than 0. In addition, the waveforms of the reluctance torque of the two motors are also given in Fig. 11. Since the inverse saliency ratio of the proposed motor is obvious, the amplitude of reluctance torque is   comparatively high. And under the current angle corresponding to the maximum torque, the reluctance torque of the proposed motor and the traditional motor are 0.68 N·m and 0.21 N·m, respectively. Fig. 12 provides the torque-speed characteristics of the two motors. It is observed that both motors possess similar output torque in their low-speed regions. Yet, it is worth noting that owing to the inverse saliency design, the FI-FTPMSM exhibits over three times of the speed range of the base speed under the load capacity of 4 N·m. From the amplified waveform of the torque ripples of both motors, it can be known that compared with the traditional motor, the torque ripple of the proposed motor increases by about 0.5%. This is because the increased cogging torque of the FI-FTPMSM with the obvious saliency design. Fig. 13 shows the power-speed characteristics of the two motors. It is obvious that compared with the traditional FTPMSM, the FI-FTPMSM presents a wider constant power area, which demonstrates that the FI-FTPMSM exhibits better torque output capability. Furthermore, from the amplified waveform of the average flux density of PM center varies with the load current at 1500 rpm, it can be clearly seen that when armature current changes from 0 to 7 A, the average flux density of the PM center of the traditional FTPMSM and proposed FI-FTPMSM decreases by 12.29% and 3.4%, which can obtain that the proposed FI-FTPMSM can reduce the risk of irreversible demagnetization of PM.

C. Sensorless Operating Characteristics Under Multiple Operating Conditions
Fig. 14 shows the dq-axis inductance characteristics of both motors vary with q-axis current. The inductance reduces with the increase of q-axis current because of magnetic saturation. The inverse saliency ratio of the traditional FTPMSM changes from 0.93 to 1.23, and its saliency property disappears when the current reaches 2 A. By contrast, the inverse saliency ratio of the proposed FI-FTPMSM changes from 1.2 to 1.4. Therefore, compared with the traditional FTPMSM, the proposed FI-FTPMSM maintains a better saliency characteristic when current changes. Correspondingly, the proposed FI-FTPMSM can achieve better steady-state sensorless operating performance. Fig. 15 gives the saliency ratio map of both motors under different loads. For MTPA operation, the current trajectory is closer to q-axis since the reluctance torque is small. From Fig. 15(a), it can be observed that when the current of the traditional FTPMSM increase from 0 to rated load, its saliency ratio moves across many contour lines, and even experiences saliency characteristic disappearance, which is unfavorable for sensorless control. Yet, as shown in Fig. 15(b), the proposed FI-FTPMSM can obtain a better saliency characteristic because of the small change of saliency ratio with load current. Thus, it is evident that the FI-FTPMSM possesses great dynamic sensorless operating capacity.
To verify the accuracy of sensorless estimation affected by the magnetic saturation effect, Fig. 16 shows variation of the absolute angle offset of both motors on the i d -i q plane. From Fig. 16(a), it can be seen that the feasible range of the traditional FTPMSM is small. Also, the angle offset varies with its load in the range of 0∼45 degrees at MTPA control mode. By contrast, in Fig. 16(b), the angle offset of the proposed motor can keep at a  low level in a large range, which demonstrates that the proposed FI-FTPMSM has a large feasible range. In addition, its angle offset can always keep within 11 degrees at the MTPA control mode. Consequently, it is further verified that the proposed FI-FTPMSM has better dynamic sensorless operating performance.

V. EXPERIMENTAL VALIDATIONS
To further validate the theoretical analysis, the proposed FI-FTPMSM is designed and manufactured. Fig. 17 shows the corresponding silicon steel sheet, the prototype motor and the experimental platform. The dSPACE1007 and inverter are employed to control and drive the experimental prototype. A magnetic powder brake is applied as the load. A torque sensor and an encoder are used to measure the torque and the rotor position, respectively.

A. Back-EMFs
With the adoption of traditional back-EMF test method, the back-EMFs of the FI-FTPMSM can be obtained. It is worth noting that for achieving the back-EMFs under phase-A shortcircuit fault, a small resistor is connected at both ends of the phase-A winding for the experimental safety reasons. The measured no-load back-EMF waveforms at 1500 rpm are shown in Fig. 18(a). Also, the corresponding harmonic analysis of the proposed motor is depicted in Fig. 18(b), where the THD of the measured back-EMF is 3.21%. The measured back-EMFs and the corresponding THD are consistent with the simulation results aforementioned in Figs. 7 and 8. Moreover, to illustrate the fault-tolerant capability of the proposed FI-FTPMSM, the measured short-circuit current of one phase (i a ) and its influence on the back-EMF of adjacent phases (e b and e e ) are shown in Fig. 18(c). Because of its large self-inductance, the short-circuit current amplitude is only 3.5 A, which can be restrained. Also, the amplitudes of back-EMFs of adjacent phases are unaffected by the short-circuit phase. Hence, it can be concluded that the FI-FTPMSM possesses high phase independence and high fault-tolerant capacity. while i z is always zero. i z is the zero-sequence current, and it should be controlled to be zero to suppress the torque ripple under single-phase fault condition [25]. Hence, the healthy and fault-tolerant currents are nearly identical, which verifies the excellent fault tolerance of the FI-FTPMSM.

B. Fault-Tolerant Operation
The transient variable-load response of the proposed FI-FTPMSM at 300 rpm is shown in Fig. 20. The load torque changes from 3.5 N·m to 6 N·m and back to 3.5 N·m. Under healthy operation, the i q1 changes from 1.86 A to 3.12 A and then back to 1.86 A, while the i d1 changes from 0.3 A to 0.5 A and then back to 0.3 A. During this process, the i q3 and i d3 are always kept as zero. Due to the characteristic of L d > L q , a positive current of i d1 can be obtained, which can achieve the flux-intensifying effect and reduce the risk of irreversible demagnetization. Additionally, the speed can maintain at a nearly constant with small fluctuation. Furthermore, the fault-tolerant currents are nearly identical to the healthy ones, and i z at fault-tolerant operation is always zero. Therefore, it can be summarized that the FI-FTPMSM with fault-tolerant  operation exhibits good dynamic performance under variable load conditions.

C. Sensorless Operating Capability
The sensorless control technique based on the HFI is well suited for the IPM motor, taking advantage of its saliency characteristic. The HF voltage components with amplitude 35 V and frequency 500 Hz are added on the source voltages, then the corresponding HF currents are generated which contain information about the rotor position. And the center frequency of the bandpass filter is 1000π + ω e . Fig. 21 presents the sensorless operating performance of the FI-FTPMSM under the HFI method with the changed speed from 60 rpm to 120 rpm and then back to 60 rpm. The results confirm that the estimated speed and position can track the actual speed and position with a high accuracy. It is also evident that the estimated error of rotor position is less affected by the speed changes, demonstrating a good sensorless operating capacity of the FI-FTPMSM.
To realize the high-performance sensorless control operation of five-phase FI-FTPMSM in the full speed range, the sensorless composite control combined with fluctuating HFI method and sliding mode observer [5] is used. In the low-speed range, the fluctuating HFI method is used, the composite control is used to estimate the rotor position and speed in the transition region, and the sliding mode observer is used in the high-speed range. Fig. 22 shows the experimental results of sensorless composite control strategy for the five-phase FI-FTPMSM. The fluctuating HFI method is used at low speed, the composite control method is used in the transition region (250∼350 rpm), and the sliding mode observer is used at medium speed. Also, the speed change rate during acceleration and deceleration is 100 rpm/s. From Fig. 22, it can be known that the acceleration and deceleration operation during the transition region is steady and smooth. In addition, the five-phase FI-FTPMSM can maintain stable sensorless operation under different speed ranges. Thus, the effectiveness of the sensorless composite control strategy for the five-phase FI-FTPMSM can be further verified. To clearly demonstrate the advantage of dynamic sensorless operation performance of the FI-FTPMSM, the traditional FTPMSM with positive saliency characteristics is selected as the benchmark. The comparison results of the angle offset variation with q-axis current for both the motors are depicted in Fig. 23(a). The angle offset of the proposed FI-FTPMSM tends to be stable with the increase of the q-axis current, and its value of the angle offset remains relatively small during the q-axis current change. By contrast, the angle offset of the traditional FTPMSM increases with the increase of the q-axis current, which demonstrates that the FI-FTPMSM possesses a better capability for sensorless operation. Additionally, the sensorless operating performance of the FI-FTPMSM with the load variation from no-load to 6 N·m and then back to no-load at 500 rpm is shown in Fig. 23(b). It reveals that the estimated speed precisely tracks the actual speed. Also, the speed error changes little with the load variation and remains near zero. Therefore, it can be concluded that the FI-FTPMSM has good dynamic sensorelss operating performance.
Furthermore, Fig. 24 presents the experimental waveforms of the five-phase FI-FTPMSM from normal to phase-A opencircuit fault-tolerant operation with the speed of 500 rpm and the torque of 2 N·m. It can be found that the current of phase-A instantly decreases to 0 A when phase-A open-circuit fault occurs. Yet, the average torque can be remained, and only 3% of torque ripple increased. In addition, the rotor position error can remain almost unchanged at 0.125 rad under both healthy and fault-tolerant conditions, which demonstrates that the rotor position can still be accurately tracked even under fault conditions.  The starting capability of proposed FI-FTPMSM is investigated in Fig. 25. It can be observed that the speed changes from 0 to 500 rpm in 1 s. The current increases slightly caused by friction etc. Additionally, the speed and torque with low ripple can be achieved after speed changes, which indicates that the proposed motor possesses a good starting capability with load.

VI. CONCLUSION
In this article, a novel five-phase FI-FTPMSM suitable for multiple sensorless operating conditions was proposed based on the design idea of the active sensorless strategy. The performances of the proposed FI-FTPMSM and the traditional FTPMSM were analyzed and compared. The following conclusions were obtained: 1) The proposed FI-FTPMSM greatly enhances the sensorless operating performance under multimode operation, including acceleration, high-speed cruise, and even fault operation. 2) With the full consideration of the influence of motor parameters on sensorless operating performance in the motor design stage, a superior inverse saliency characteristic of L d > L q was obtained through a modified design, which can simplify the senorless control algorithms and improve the estimated accuracy of rotor position. 3) In addition to the improved accuracy of sensorless operation, the proposed FI-FTPMSM exhibits excellent torque output capability compared with the traditional FTPMSM.
The FI-FTPMSM obtains maximum torque at inverse d-axis current, which reduces the risk of irreversible demagnetization. Moreover, the prototype motor was fabricated and tested. The experimental results validated the feasibility of the proposed five-phase FI-FTPMSM in achieving strong fault-tolerant capacity and superior sensorless operating capacity.
Finally, a five-phase FI-FTPMSM was proposed based on sensorless strategy in this paper, which can simplify the complexity of sensorless control algorithm and improve the safety and reliability of motor drive system. Additionally, for the FTPMSMs with multiple pole-pairs, their flux-intensifying effect is relatively more difficult to be achieved. Therefore, how to achieve more obvious inverse saliency ratio for the FTPMSMs still needs to be further researched and explored.