Brushless DC motors with permanent magnets are characterized by high efficiency and high torque-to-volume ratio [1, 2]. Therefore, BLDC motors are frequently used in applications where high efficiency and small overall dimensions are the most significant features. Such applications include electric and hybrid drives for vehicles and small aircrafts (unmanned and classic) [3, 4]. In UAV drive systems, low voltage motors with parallel branches are frequently used. Such solution has both advantages and disadvantages. Its advantages include faster reaching of demanded working point and fault-tolerant operation. On the other hand, its disadvantages include possibility of occurring equalizing currents in parallel branches within each phase .
Fault states can be caused by failures in a supply system, a control system or in a machine. In case of failures in a machine, windings short circuits or winding open-circuits can occur [6, 7, 8, 9, 10, 11]. In drives for aircraft applications, higher reliability as well as a possibility of further operation after fault is required [7, 8]. Most of the papers which discuss problems concerning windings faults concern machines with star-connected windings. In machines with delta-connected windings and with parallel branches, there is no possibility of detecting faults as e.g. it is proposed in Ref. .
In the paper, operation under open-winding faults in parallel branches of delta-connected windings was analysed. Waveforms of currents, voltages and electromagnetic torque were determined in the discussed fault states based on the developed mathematical and simulation models. The simulation test results were validated by experiments and conclusions concerning influence of fault states on motor properties were drawn.
2 Analysis of fault states
2.1 Structure of the BLDC motor
The analysed motor (Udc = 52 V, PN = 3.5 kW, nN = 8000 rpm) was designed by the authors for hybrid drive of small unmanned aerial vehicle. The design is a three-phase, external-rotor structure with 24 stator slots and 20 rotor poles (Figure 1). The delta-connected windings with four parallel branches were used in the motor.
2.2 Analysed fault states
Figure 2 shows an electric diagram of the analysed motor. Additional switches which allow obtaining fault states in the machine (by opening them) were placed in phase A in each parallel branch and in phases B and C for chosen branches. The following motor operation variants were analysed: I – regular operation (all switches closed), II- fault in branch Ph1_1 (S1 opened), III – fault in branches Ph1_1 and Ph1_3 (S1 and S3 opened), IV – fault in branches Ph1_1, Ph1_2 and Ph1_3 (S1, S2, S3 opened), V-fault in branches Ph1_1, Ph1_2, Ph1_3, Ph1_4 (S1, S2, S3, S4 opened).
3 Mathematical model
A mathematical model which takes into account the nonlinearity of the magnetic circuit and magnetic couplings between windings has been developed for the discussed BLDC motor.
The voltage-current equation, the equation of rotational motion torques, and the formula expressing angular velocity for the BLDC motor circuit model from Figure 2 can be written down in the form :
where: u - vector of voltages, i - vector of currents, Ψ(θ, i,iPM) - vector of winding fluxes induced by winding currents and permanent magnets, R - matrix of resistances, θ – the rotor position, iPM – the permanent magnet magnetization equivalent current, J – the rotor moment of inertia, D – the coefficient of viscous friction, TL – the load torque, ω = dθ/dt – angular velocity of the rotor.
The expression for the electromagnetic torque (2), can be written down in the form:
where (θ, i,iPM) is the total magnetic field co-energy in the machine air gap.
4 Results of simulation and laboratory tests
4.1 Simulation tests
Simulation tests were carried out for five analysed cases (I – V) under steady-state operation (Udc = 52 V, n = 9000 rpm).
A disconnection of particular branches in phase Ph1 influences on a variation of line currents, phase currents and generated electromagnetic torque. A loss up to two branches (case II and III) causes an expected behavior of the motor. In case of loss of 3 from 4 parallel branches (case IV), slightly higher drop in generated electromagnetic torque is visible. In the case V, phase Ph1 is disconnected and this disconnection of all branches of phase Ph1 does not cause break in connection of remaining phases Ph2 and Ph3 with supply system. However, it significantly influences on a variation of shape and value of line currents as well as electromagnetic torque. The selected simulation results are summarized in Table 1.
After open-winding fault (cases I - IV), electromagnetic torque decreases and torque ripples increase. In the case V, ripples of electromagnetic torque significantly increases. It should be noticed that the motor can continue operation with decreased load despite breaks in supplying of particular parallel branches of phase Ph1 (cases II - V). A diagnostics of fault states can be conducted through FFT analysis e.g. of source current (Figure 6) as it was proposed in [10, 11].
4.2 Laboratory tests
Figure 8 shows a laboratory setup.
The motor operation was tested for cases I, III and V in laboratory conditions. Waveforms of motor line currents and line-to-line voltages were registered at rated voltage and load torque of 1.5 N⋅m (Figures 9-10).
A disconnection of phase Ph1 (case V) at delta-connected windings allows further operation of the motor. However, available torque on the motor shaft is significantly lower in laboratory tests. In two remaining phases Ph2 and Ph3, phase currents increase what leads into increase of line currents i2 and i3 (of value of line current i1).
Overall efficiency of the drive system also decreases noticeably. When at least one branch of phase Ph1 was supplied, there was not observed any significant decrease in overall efficiency of the drive system. Start-ups of the motor were analysed for each case in laboratory conditions and the motor started in each analysed case. However, when phase Ph1 was disconnected (case V), high ripples of generated electromagnetic torque caused oscillations of speed during start-up.
The paper presents the analysis of influence of open-winding faults on properties of brushless DC motor with permanent magnets. Simulation and laboratory tests proved that motor operation is possible after fault in several branches. Nevertheless, it is connected with increase in torque ripples. Thus, start-up with high load torque can be impossible. Depending on a fault type, the resultant efficiency of the drive system decreases (a disconnection of all phase) or remains on a similar level. Therefore, a usage of parallel branches is much more favourable from the viewpoint of the drive system reliability. However, the overall efficiency can be decreased due to equalizing currents.
The research work was supported by The National Centre for Research and Development Project DZP/INNOLOT-1/2020/2013 of Poland and in part by the statutory funds of the Department of Electrodynamics and Electrical Machine Systems, Rzeszow University of Technology.
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Published Online: 2017-12-29