Experimental comparison of remedial single-channel operations for redundant flux-switching permanent-magnet motor drive.
With the requirements for reducing emissions and improving fuel economy, electric vehicles (EVs) have attracted more and more attentions. High reliability is an essential requirement for electric propulsion of EVs, where any types of fault would lead to disastrous effects on life safety . Hence, fault-tolerant operation of motor drives has been a growing demand .
Permanent-magnet (PM) brushless motor drives are attracting extensive attention in high reliability applications, which are good candidates for EV applications [3-5]. By employing an arrangement of alternately wound teeth in the stator, a fractional-slot concentrated-windings PM machine, termed as rotor-PM machine, was proposed for fault-tolerant operation . To operate the rotor-PM motor at flux weakening mode, an optimal torque control strategy was proposed in . In addition, multi-phase PM motors have received great attention for fault-tolerant operation. In [8,9], a new five phase motor drive was proposed. The proposed control guarantees safe drive operation considering the 3rd harmonic components of back-electro-motive-force (back-EMF). However, since PMs are located in the rotor, these conventional rotor-PM brushless machines, including the surface-mounted, inset and interior topologies, suffer from weak mechanical structure and difficulty of PM cooling .
Recently, a new class of doubly-salient motors having PMs in the stator, termed as stator-PM motors, has been proposed and investigated . These stator-PM motors include the doubly-salient PM (DSPM) type, flux-reversal PM (FRPM) type and flux-switching PM (FSPM) type. Extensive research work has been performed to analyze this class of machines, showing that stator-PM motors incorporate the merits of high power density, strong mechanical integrity and good immunity from thermal problem. It has been identified that the DSPM motors can inherently offer fault-tolerance . Meanwhile, it has been verified that the FSPM motor can offer significantly higher power density than other stator-PM motors [13-15]. Very recently, by introducing the redundant technique to the FSPM machine topology, a new redundant FSPM (R-FSPM) motor has been proposed . It is most viable for fault-tolerant operation of EVs, since it inherently offers high efficiency, high power density, maintenance-free operation, insignificant thermal influence on PMs and mechanically robust. Also in , control strategies for post-fault operation of up to two coils (not in the same channel, e.g., coils-A1 and -B2) have been investigated. However, it can't handle the fault of two or three coils in the same channel, such as coils-A1 and -B1.
The purpose of this article is to propose two remedial control strategies for fault-tolerant operations of the R-FSPM motor drive in the single-channel (SC) operation mode. The structure and electromagnetic features of the R-FSPM motor will be briefly described in Section 2. In Section 3, two remedial operations, namely remedial brushless AC (BLAC) operation and remedial injecting harmonic current (IHC) operation, will be proposed. A co-simulation technique will be adopted in Section 4 to assess the performance of the proposed R-FSPM motor drive at proposed remedial operations. Then, in Section 5, experimental results will be used to verify the proposed remedial operations of the motor drive. Finally, a conclusion will be drawn in Section 6.
2. R-FSPM MOTOR
Figure 1 shows the structure of the 12/10-pole R-FSPM motor, which has 12 salient poles in the stator, 10 salient poles in the rotor, six-coil windings in the stator and 12 PMs in the stator. The coils wound on the diametrically opposite stator poles are connected in series, forming coils-A1 and -A2, and the R-FSPM motor winding configuration is developed by parallel connecting the two coils. Each coil of the R-FSPM motor has its own power converter and controller, which can operate independently. The R-FSPM motor offers the advantages of simple and rugged rotor structure suitable for high speed applications, concentrated stator windings yielding improved space factor and productivity, fault tolerance and increased torque/weight ratio. This motor actually incorporates the merits as follows:
* Similar to the DSPM motor, the R-FSPM motor offers simple rotor structure, easy cooling in PMs and high power density.
* Different from the DSPM motor, the R-FSPM motor has bipolar winding PM flux-linkage, thus achieving higher power density.
* Similar to the existing fault-tolerant motors, the R-FSPM motor possesses the features of redundant winding structure and independent phases in electric and magnetic circuits, thus offering the possibility of fault-tolerant operation.
* Different from the most of PM brushless motors having PMs and windings magnetically in series, the R-FSPM motor having PMs and windings magnetically in parallel solves the problem of the influence of armature reaction field on the working point of PMs under the short-circuit fault (shown in Figure 2), hence inherently suitable for high reliability applications.
[FIGURE 1 OMITTED]
By using finite element method [17-19], the coil and phase back-EMFs are predicted and shown in Figure 3, comparing with the measured ones. It can be observed that each coil back-EMF has rich harmonic components, but the corresponding phase back-EMF is sinusoidal due to the compensation of harmonic components in the coil back-EMFs. Moreover, back-EMF harmonic analysis is resulted as shown in Figure 4. It can be known that the 2nd harmonic is the main harmonic component, while the 3rd and the higher harmonic can be neglected. Also, the 2nd harmonic amplitude is 15% of the fundamental amplitude and the phase angle is 2[pi]/5. Hence, the back-EMFs of the R-FSPM machine can be expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [E.sub.1] and [[omega].sub.e] are the amplitude and the frequency (the rotor electrical speed) of the fundamental component, respectively.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
3. CONTROL STRATEGIES
For the fault-tolerant operation, the proper fault detectors need to be employed. Detailed discussions on the fault detectors for motor drives have been investigated in [20-22]. This work focuses on how to develop the remedial control strategies for the remedial SC operations of R-FSPM motor drives. Firstly, a simple remedial method is proposed by doubling the healthy-coil currents. Secondly, the relationship between the normal BLAC operation before fault and the remedial IHC operation after fault is derived, and the required harmonic component of the healthy-coil currents are deduced for the torque ripple free operation.
3.1. Normal BLAC Operation
Normally, the R-FSPM motor operates in the dual-channel BLAC operation mode, in which all coils are in work. The six-coil currents can be expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [I.sub.m] is the amplitude of the sinusoidal current. For the R-FSPM motors, the motor torque is predominantly resulted from the PM excitation torque since the reluctance torque is negligible. So, the electromagnetic torque under the normal BLAC operation mode can be calculated as:
[T.sub.en] = (1/[[omega].sub.m])[c.summation over (p=a)]([e.sub.p1] * [i.sub.p1] + [e.sub.p2] * [i.sub.p2]) = [3[E.sub.1][I.sub.m] - 0.45[E.sub.1][I.sub.m] cos(3[omega]t + 2[pi]/5)]/2[[omega].sub.m] + [3[E.sub.1][I.sub.m] + 0.45[E.sub.1][I.sub.m] cos(3[omega]t + 2[pi]/5)]/2[[omega].sub.m] = 3[E.sub.1][I.sub.m]/[[omega].sub.m] (3)
where [[omega].sub.m] is the rotor mechanical speed. It can be known from (3) that a constant electromagnetic torque is achieved during the normal BLAC operation mode because the harmonic torque of coils counteracts each other.
3.2. Remedial BLAC Operation
Similar to the dual-channel switched reluctance motor , the R-FSPM motor can operate in the SC operation mode when its two or three coils in the same channel, such as coils-A1 and -B2, are in fault and disability. In the following analysis, a failure in coils-A2, -B2 and -C2 is considered as an example.
By doubling the healthy-coil currents, the R-FSPM motor can operate in the remedial BLAC operation mode. The currents in the remedial BLAC operation are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Therefore, the remedial BLAC electromagnetic torque can be calculated as:
[T.sub.er1] = ([[omega].sub.m] [c.summation over (p=a)] ([e.sub.p1] * [i'.sub.p1] + 0) = 3[E.sub.1][I.sub.m]/[[omega].sub.m] + 0.45[E.sub.1][I.sub.m]cos(3[[omega].sub.e]t + 2[pi]/5)/[[omega].sub.m] (5)
It can be concluded from the comparison between (3) and (5) that the proposed remedial BLAC operation can maintain the average torque. However, further observation from (5) reveals that there is a pulsating component in the produced electromagnetic torque, which is a function of the rotor position.
3.3. Remedial IHC Operation
For the torque pulsation free operation, the remedial IHC control strategy is proposed. The key is to operate the R-FSPM motor in the SC operation mode by injecting proper harmonic current to compensate for harmonic torque component in (5).
In the remedial IHC operation mode, the currents are assumed to be:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where [I.sub.1] is the amplitude of fundamental current, and [I.sub.2] and [alpha] are the amplitude and the harmonic angle relative to the fundamental component of 2nd harmonic current, respectively. The electromagnetic torque in the remedial IHC operation can be calculated as:
[T.sub.er2] = (1 / ([[omega].sub.m])[c.summation over (p=a)]([[e.sub.P1] * [i".sub.p1] + 0) = (3 / 2[omega]) * [[E.sub.1][I.sub.1] + [E.sub.1][I.sub.2]cos(3[omega]t + [alpha]) + 0.15[E.sub.1][I.sub.1]cos(3[omega]t + 2[pi] / 5) + 0.15[E.sub.1][I.sub.2]cos(2[pi] / 5 - [alpha])] (7)
To eliminate harmonic torque in (7), a constant electromagnetic torque can be obtained by setting:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
Thus, by substituting (8) into (7), the remedial IHC torque can be calculated as:
[T.sub.er2] = 1.46[E.sub.1][I.sub.1]/[[omega].sub.m] (9)
The torque before and after the fault can be kept the same by setting [T.sub.er2] equal to [T.sub.en], it yields:
[I.sub.1] = 2.05[I.sub.m] (10)
Finally, by substituting (8) and (10) into (6), the remedial IHC operation is achieved as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
Therefore, it can be concluded that by injecting the 2nd harmonic current, the R-FSPM motor can operate in the remedial IHC operation, in which the restructured fault-tolerant torque can effectively displace the normal torque.
This work adopts the co-simulation modeling method of the magnetic circuit and the electric circuit to asses the performance of the R-FSPM motor drive, in which the system-level simulation is provided . Figure 5 shows the co-simulation model of the R-FSPM motor drive.
To assess the level of the torque ripple under various conditions, a torque ripple factor is defined as follows:
[K.sub.T] = ([T.sub.max] - [T.sub.min])/[T.sub.av] x 100% (12)
where [T.sub.max], [T.sub.min] and [T.sub.av] are the maximum, the minimum and the average values of the output torque, respectively.
Under the normal condition, the R-FSPM motor drive operates in the conventional BLAC operation mode. Based on the developed co-simulation model, the motor current and torque waveforms are simulated as shown in Figure 6. It can be seen the corresponding [K.sub.T] of the motor drive is 58.3%.
During the loss of one channel, the R-FSPM motor operates in the remedial SC operation mode. The average torque can be maintained by doubling the currents of the healthy-channel. Without taking harmonic remedial action, the current and torque waveforms of this R-FSPM motor drive are shown in Figure 7. It can be found that the torque ripple at the remedial BLAC operation is slightly worsening, namely [K.sub.T] is 70.6%, which is 12.3% larger than the normal torque ripple factor.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
By injecting the calculated 2nd harmonic current, the proposed remedial IHC operation is activated. As shown in Figure 8, the corresponding [K.sub.T] is 62.1%, which is insignificantly larger than the normal torque ripple factor. It can be concluded that during the loss of one channel, both of the proposed remedial strategies can retain the average torque and that the IHC operation can reduce the pulsating torque. Moreover, it should be mentioned that the torque pulsation for both remedial SC operations is higher than that for normal operation, but the redundant drive system continues operating safely under loss of up to three coils. This feature is very important in traction and propulsion applications where high reliability is of major importance.
5. EXPERIMENTAL VERIFICATION
To verify the theoretical analysis, an experimental test bed for the R-FSPM motor drive has been developed. Figure 9 is the photo of experimental setup. It is composed of an R-FSPM motor supplied by two independent IPM-based converters, a separately excited dc generator used as variable load and a transient torque transducer mounted between the R-FSPM motor and the dc generator to measure the torque of the proposed motor drive.
Firstly, the steady-state performances of the R-FSPM motor drive are evaluated. Figure 10 compares the measured torque and current waveforms in the normal and the proposed remedial operations.
As given in (2), the normal current waveforms in Figure 10(a) are sinusoidal in which both of the channels are in work. In the event of one channel loss, the proposed remedial SC operations are activated. For both of the remedial operations, the currents well agree with the theoretical ones. Table 1 compared the theoretical and experimental torque ripple under normal and remedial operations. It should be noted that the measured torque waveforms have a significant discrepancy with those co-simulated ones since the practical and manufacturing conditions are very difficult to be modeled. Nevertheless, it can be known that the proposed remedial operations can maintain the average torque during the loss of one channel, verifying the effectiveness of the proposed fault-tolerant control strategies. Meanwhile, the torque ripple under the remedial BLAC operation is very more than that under the remedial IHC operation due to the effect of harmonic back-EMFs. Also, the remedial IHC operation can reduce torque ripple in the fault-tolerant mode, slightly inferior to the normal operation.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
Secondly, the system dynamic performance during the fault occurrence is tested, in which the R-FSPM motor operates from the normal mode to the fault-tolerant modes. Figure 11 reports the healthy-channel current responses, verifying that the R-FSPM motor drive can online switch to the proposed remedial operations.
Finally, it aims to assess whether the R-FSPM motor drive can retain the self-starting capability in the remedial SC operation mode, which is essential for those applications such as EVs desiring frequent start-stop. Figure 12 shows the startup healthy-channel current responses under the remedial BLAC operation and the remedial IHC operation, respectively, showing that the motor drive can successfully perform self-starting during the loss of one channel.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
In this paper, the remedial BLAC and the remedial IHC control strategies have been newly proposed and implemented for fault-tolerant operations of the R-FSPM motor drive. By doubling the health-channel currents, the remedial BLAC operation has been achieved, and its pulsating torque component has been analyzed. By injecting the 2nd harmonic current component into the fundamental current, the remedial IHC operation has also been proposed for torque ripple free operation. The validity of the proposed remedial control strategies has been verified by co-simulation and experimental results. Also, it has revealed that the remedial BLAC operation is simple for implementation, meanwhile the remedial IHC operation offers smooth torque. The proposed remedial operations are particularly important to enable continued operation for many practical applications such as EVs.
This work was supported in part by the National Natural Science Foundation of China (Projects 60974060, 50907031 and 51007031), by the Priority Academic Program Development of Jiangsu Higher Education Institutions and by the Professional Research Foundation for Advanced Talents of Jiangsu University, China (Project 10JDG089).
Received 4 November 2011, Accepted 16 December 2011, Scheduled 20 December 2011
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W. Zhao (1), *, M. Cheng (2), R. Cao (2), and J. Ji (1)
(1) School of Electrical and Information Engineering, Jiangsu University, No. 301, Xuefu Road, Zhenjiang, China
(2) School of Electrical Engineering, Southeast University, No. 2, Si-pailou, Nanjing, China
* Corresponding author: Wenxiang Zhao (email@example.com).
Table 1. Comparison of co-simulated and measured torque ripple (%). Normal Remedial Remedial BLAC IHC Co-simulated 58.3% 70.6% 62.1% Measured 43.5% 105.5% 58.8%
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|Author:||Zhao, W.; Cheng, M.; Cao, R.; Ji, J.|
|Publication:||Progress In Electromagnetics Research|
|Date:||Jan 1, 2012|
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