Brushless DC motors are known for their high performance and reliability, as well as their high torque and high power per volume unit [1, 2], that is why they are widely used in the automotive industry, industrial automation, computer drives, medical and military technology as well as in special purpose devices [1, 2, 3, 4, 5, 6, 7, 8]. Rotational speed of BLDC motors is proportional to power supply voltage, therefore it can be regulated by pulse width modulation (PWM) using an inverter [1, 2, 9, 10, 11]. Such operation results in phase currents pulsations and pulsations in torque with a frequency range of up to several dozen kHz. It can be particularly unfavorable for low inductance machines [6, 12]. Magnetic flux density pulsations in an air gap caused by stator slotting and motor phase currents pulsations resulting from commutation and inverter PWM operation, are responsible for power losses in permanent magnets and the rotor iron [13, 14]. Phase currents pulsations lead to the increase in power losses in the stator iron and in the winding. Currents changes result in a different magnetic flux density distribution within the magnetic circuit of the machine. It affects the change in power losses in the motor and the change of the winding inductance; and therefore it has an impact on the instantaneous values of electrical quantities in the drive system. In the available literature these phenomena are not sufficiently presented. Only field-circuit modelling using the finite element method can show a correlation between phenomena appearing in the magnetic circuit and electrical circuit of the motor along with the power converter.
This paper presents the field–circuit analysis of electromagnetic phenomena in a drive system with a new design solution of PM BLDC motor which speed is controlled using PWM method. The essence of the solution is presented in Figure 1. The magnetic circuit of the motor consists of a stator with a three-phase winding, and a rotor with neodymium magnets on its surface. Inside of the rotor there is a built-in inverted action high pressure vane pump. To prevent the pump from the incoming magnetic flux, a nonmagnetic sleeve was used between the rotating part of the pump and the yoke of the rotor.
The stator of the motor is a part of the body of the integrated motor-pump device. The pump external casing rotates along with the rotor of the electric motor. The internal part of the pump (with the vanes) is immovable [3, 8, 11]. The flow of the vane pump is controlled through the change in rotational speed of the motor by the PWM method.
The BLDC motor power is P = 2,5 kW at maximum speed nmax = 3000 rpm. The motor is supplied (Figure 2) from the single-phase 230 VAC, 50 Hz network through the converter that consists of a rectifier, a smoothing capacitor and an inverter. The construction of the motor was shown in detail in  Both the motor and the converter were designed and built at the Department of Electrical Machines, Drives and Measurements at the Wroclaw University of Science and Technology .
2 Field – circuit model
In order to analyze electromagnetic phenomena in the motor, it was necessary to develop a field-circuit model of the whole analyzed electromechanical system, i.e. the electric circuit (Figure 2), the motor magnetic circuit (Figure 3), and the waveform of the load torque generated by the vane pump. The model was developed using the ANSYS software.
geometrical dimensions of the machine magnetic circuit,
axial direction of the magnets magnetization,
magnetization characteristics and conductivity of the stator sheet and rotor yoke,
demagnetization characteristics and conductivity of permanent magnets,
eddy currents and hysteresis power losses in the stator and in the rotor,
source voltage waveform (u1) and parameters of the power supply network (R1, L1),
parameters of the converter (rectifier, smoothing capacitor, inverter),
resistance and inductance of the winding,
commutation of the winding phases,
the unipolar H_PWM_L_ON  speed control method,
limiting instantaneous values of motor phase currents to the level which does not lead to demagnetization of the magnets,
the load torque waveform generated by the vane pump experimentally determined.
The field-circuit model is described in details in Ref. .
3 Results of computations of the waveforms of electrical and mechanical quantities
4 Analysis of the electromagnetic phenomena in the system: single-phase AC network – converter – PM BLDC motor
The magnetic circuit computations of the integrated motor-pump device showed correct magnetic flux density values of its particular elements (Figure 3). The magnetic induction value at the rated motor torque does not exceed 1.6 T, and 2.0 T during overloading. This means that the magnetic circuit is used, but not oversaturated. The magnetic induction module value of the external (rotating) element of the pump reaches a few mT only. This means that the used non-magnetic sleeve successfully protects the inside of the pump from the magnetic flux generated by the magnets.
The converter input voltage waveform is a distorted sine wave. This is a result of source voltage deformation, and voltage drops in the single-phase AC network (Figure 4). The converter input current is drawn from the network during a time interval, when the instantaneous value of the converter input voltage is higher than the one of the capacitor (Figure 4). The converter input current charges the capacitor which smoothens the input voltage of the inverter.
As a result of the rectifier operation, the capacitor voltage (the input voltage of the inverter) has a ripple waveform with the frequency of 100 Hz. These ripples and pulsations result from converter input voltage deformations are transferred to the waveforms of: phase voltages and currents of the motor, inverter input current, and the motor torque (Figures 6-8, 10).
Waveform of the capacitor current (Figure 5) has two components: rectified current drawn from the single-phase AC network which charges the capacitor, and the inverter input current (Figure 6) which discharges it. The inverter input current waveform is a result of the load torque and rotational speed, commutation of the motor winding phases, the PWM operation of the inverter and the voltage ripples at its input.
In the waveforms of phase currents (Figure 7), the greatest part is played by ripples caused by winding phases commutation process and ripples caused by PWM operation of the inverter. Ripples, with the frequency of 100Hz, resulting from the rectifier operation are smaller.
Using the unipolar H_PWM_L_ON method of rotational speed control, the upper group of inverter transistors are switched on/off with the PWM frequency of 15625 Hz. When one of them is switched off (e.g. the transistor Q1 while supplying phases ‘a’ and ‘b’ – Figure 1) the current decreases in the circuit: one of the winding phase (phase ‘a’) – second of the winding phase (phase ‘b’) – a transistor of the inverter lower group of the second winding phase (transistor Q4) – a flyback diode of the first winding phase (diode D2) – first of the winding phase (phase ‘a’). This circuit is marked in red in Figure 2.
In some time periods e.g. from approximately 292,9 ms to around 294 ms - Figure 7) there is a current flow in the “non-powered” phase ‘c’ when the upper group of inverter transistors are switched off due to the PWM system operation. The electric circuit diagram presenting this phenomenon (current flow in the “non –powered” phase ‘c’) is shown in Figure 15. The current in the phase ‘c’ begins to flow when the inverter diode D6 becomes conductive. It can happen when the transistor Q1 is switched off (which is caused by the PWM system operation) and the instantaneous value of the induced electromotive force ec is negative (with direction towards node ‘W’ in the electric circuit -Figure 15). Because of the fact that the ‘upper’ group transistors (Q1, Q3, Q5) of the inverter are switched off, electrical energy is not transferred to the motor. Magnetic energy accumulated in the winding phases ‘a’ and ‘b’ maintains the direction of currents flow ia and ib discharging itself within the circuit: phase ‘b’– transistor Q4 – flyback diode D2 – phase ‘a’ and the parallel circuit with the flyback diode D6 and phase ‘c’ (the circuits marked in red in Figure 15).
The current flow in the phase ‘c’ of the winding leads to a faster discharging of energy accumulated in phase ‘a’, so it decreases the instantaneous value of the current flowing in phase ‘a’. For this reason the current pulsations of the phase ‘a’, which are the result of the PWM system operation, are higher than in the phase ‘b’. The difference becomes higher with the growth of the instantaneous value of the phase ‘c’ current.
Waveforms of the phase voltages are not symmetrical to the time axis (Figure 8). This is a result of changes in the steepness in increase and decrease of currents during the current flow in the “non-powered” winding phase.
During the winding phases commutation process there are considerable changes of the instantaneous values of the phase voltages. These changes are caused by the changes in the steepness in the decrease and increase of phase currents, and by resulting from this the changes of the self-induced emfs.
Waveforms of flux linkage with the winding phases (Figure 9) are distorted sine waves. In these waveforms the deformations during winding phases commutation process, and to a much lesser degree ripples which results from phase currents ripples with PWM frequency can be noticed.
In waveform of the motor torque, the greatest part is played by both: the ripples resulting from the winding phases commutation, and the pulsations caused by the inverter PWM operation (Figure 10). These pulsations are much higher than the load torque pulsations generated by the vane pump. Despite high amplitude of the torque pulsations, rotational speed pulsations (Figure 11) do not exceed 1.3%.
In the waveforms of power losses in the stator iron, rotor and the winding, there are pulsations caused by the operation of the rectifier, as well as commutation of the motor winding phases and the inverter PWM operation (Figure 12-14). The main reason for power losses in the stator iron, in both eddy currents and hysteresis, lies in the magnetic flux pulsations with the PWM frequency (Figure 12). Power losses in the rotor also depends heavily upon the magnetic flux pulsations with the PWM frequency. The instantaneous values of power losses in the rotor during the commutation of the winding phases are higher than their average value (Figure 13). Waveforms computations of the electrical and mechanical quantities in the system: single phase AC network – converter – PM BLDC motor – vane pump enabled operating parameters of the designed drive system to be determined, including motor efficiency and converter efficiency. These efficiencies reached 87.1% and 97.3% respectively at the rated motor torque. The results of computations were verified and confirmed by experimental analyses. The differences between average values of computations and measurements do not exceed a few percent.
Due to the developed field-circuit model it was possible to determine the waveforms of electrical and mechanical quantities in the drive system with BLDC motor and PWM speed control.
The determined waveforms take into account interactions between electromagnetic and electromechanical phenomena in the: single phase AC network – converter – BLDC motor system. The analysis of electromagnetic phenomena in the drive system showed their complexity and that it is necessary to consider their mutual interactions. Computations of electrical and mechanical quantities waveforms at different values of the load torque allow the electromechanical characteristics and drive system performance to be determined. The developed drive system with the developed BLDC motor reached a high performance of 84.7%.
Computations were made using resources of the Wroclaw Centre for Networking and Supercomputing (http://wcss.pl). Grant No. 400.
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Published Online: 2017-12-29