# OPERATION INVESTIGATIONS OF DIFFERENT PERMANENT MAGNET BRUSHLESS DC MOTOR DRIVES.

Byline: Nima Nabizadeh Ahmad Darabi and Morteza AzadiAbstract

Nowadays the applications of permanent magnet brushless DC (PMBLDC) motor drive are growing increasingly but surveys on performance characteristics of the motor drives are not enough. In this paper the performance characteristics of different types of the PMBLDC motor drives with identical fundamental harmonic components of their back electromotive forces are investigated and compared as well as the performance of a sinusoidal-type PMBLDC motor supplied by two- and five-level inverters are investigated and compared to each other. Meanwhile switches for the power inverters are selected based on the motor power and flowed current through switches. The hysteresis and carrier-based pulse width modulation techniques are used respectively for triggering the switches of inverters used in the first comparison and the last comparison. The motor runs a friction load with a torque proportional to the rotor speed and a constant mechanical load. Simulations are carried out by Matlab/Simulink.

The simulations results show that performance characteristics of the sinusoidal-type PMBLDCM are better than the trapezoidal-type PMBLDCM and they would be more improved when the sinusoidal-type PMBLDC motor is supplied by a five-level inverter.

Key Words"Acoustic Noise Hysteresis Modulation Multilevel Inverter Pulse Width Modulation Sinusoidal-type

PMBLDC Motor Drive Torque Pulsations Trapezoidal-type PMBLDC Motor Drive.

I. INTRODUCTION

THE permanent magnet brushless DC (PMBLDC) motor drives are classified as trapezoidal-type and sinusoidal-type according to the waveforms of their back electromotive force (BEMF). Output features of the PMBLDC motors are almost similar to the classic DC motors (brushed DC motor) but the structures are quite different. Using the PMBLDC motor drive the problems related to the mechanical commutations of a conventional DC machine are eliminated [1]. The stator windings of a PMBLDC motor are fed by a three-phase inverter. The switching process of the inverter is done by an algorithm using the signal related to the rotor position sensor and a suitable controller. Due to high efficiency loss free field excitation [2] ease of control simple structure loss free mechanical commutator and down maintenance costs the applications of the PMBLDC motor drive are growing increasingly.

Nowadays the PMBLDC motor drives are employed in so many applications such as the computer disk drivers robotics bodybuilding equipments actuators electrical vehicles and ships propulsion [34]. However the harmonic contents of electromagnetic torque and speed of the PMBLDC motor drives commonly produce some torque pulsations speed ripple and vibrations which are critical and troubling in some applications especially in military equipments. Therefore much effort has been done to reduce the torque pulsations and speed ripples by some modifications of the machine structure and their supplies. In fact there are two main factors for producing the torque pulsations; 1- structural shapes such as pole shape of the rotor PM and stator slots and teeth and 2- harmonic contents produced by voltage source inverter feeding stator windings [5]. Cogging torque ripple is produced by interaction between rotor magnetic field and stator slots. This can be reduced substantially with optimally design of the stator slots

and teeth and using an appropriate shape for the rotor salient poles [6-9]. Based on many investigations carried out in the field of optimization methods no further improvement of the performance is expected by modifications of structural configures unless a big revolution arises in the technology of the conductors or magnetic materials. Due to this recent researches are concentrated on the improvement of the produced voltage quality and modulation techniques of the inverter in order to limit the torque pulsation and speed ripple. Some problems such as vibration bearing failure winding insulation breakdown circulating currents dielectric stress voltage spikes and corona electrical discharge could also be improved using worthy control system for triggering the power switches of an inverter [10].

The wide range applications of the PMBLDC motor drives from ranging ships propulsion to robotics is another motivation of many researchers to investigate new methodologies for reducing the torque pulsation and speed ripple.

In this paper a three-phase PMBLDC motor drive is simulated when the motor is supplied with multilevel inverters and various modulation techniques. The performance of the motor is analyzed in terms of the torque pulsation speed ripple and appeared voltage between mid- point of the inverters and the neutral point of the star- connected of the stator windings and efficiency of the sinusoidal-type PMBLDC motor drive in various conditions. The machine runs a friction load at desired speed from standstill status.

II. MATHEMATICAL MODEL OF A PMBLDC MOTOR

The permanent magnet motors are commonly utilized as low and medium power machines (50W-300KW) [11]. The saliency of the rotor poles can be easily neglected [12]. equations

III. MULTILEVEL INVERTER

A conventional two-level inverter is well-known to the power engineers. Each leg of this inverter includes two IGBT implements with anti-parallel diodes. But the type inverter

has some problems such as high common mode voltage and dv/dt and so on. There are some papers on various topologies and advantages of multilevel inverters such as [13]-[17]. In this paper was used a five-level inverter to supply a sinusoidal-type PMBLDC motor. The single-phase diagram of a five-level diode-clamped inverter is shown in Fig. 1.

IV. SIMULATION

The simulated motor is a three-phase four-pole 20Hz 480W PMBLDC motor with Y-connected stator winding. Table II shows the main parameters of the motor drive [11] in which the switch characteristics have been considered ideal; whereas in this paper the Fuji's IGBT module

7MBR30SA060 on the basis power of the motor drive and drown current has been used. This type of transistors is 600V/30A IGBTs [18]. Moreover the amplitude of

fundamental harmonic component of the trapezoidal and the sinusoidal BEMFs is 95.88V.

V. SPEED CONTROLLER AND SWITCHING PROCESS

During rotor acceleration of the PMBLDC motor frequency of the fundamental harmonic component of voltage generated by three-phase inverter corresponding to the frequency of rotor speed must be gradually increased from zero to a desired value. The performance characteristics of the trapezoidal- and the sinusoidal-type PMBLDC motor drives which have been fed by hysteresis inverter are windings generated by permanent magnet (PM) poles of the rotor can be simply written as (14) and the BEMF is calculated by (15).

TABLE I PARAMETERS OF PMBLDC MOTOR DRIVE

Amplitude of fundamental harmonic

###m = 0 .7 6 3 (V.s)

###component of flux linkages

###trapezoidal BEMF Constant###K###e###= 1 .2 5 5 V.s rad

###Self inductance of stator###Laa = 0.026667 (H)

Mutual inductance between stator

###M = 0.006667 (H)

###windings

Phase resistance of stator windings###rs = 1

###2

Total inertia of rotor and load###J = 0.005 (kg.m )

###Friction coefficient###B m = 0.01 (Nm.sec rad)

###Constant load###T l = 7 (N.m)

###Number of poles###P =4

###DC voltage source###V dc = 220 (V)

Collector-emitter saturation voltage###VCE (sat ) = 1 (V)

###Forward on voltage of diode###V F = 0.8 (V)

###IGBT resistance at On state###rIGBT (on ) = 0.06

###diode resistance at On state###rdiode (on ) = 0.001

###Turn-off time###t off = 403.3 (ns)

###Fall time###t f = 88 (ns)

Frequency of carrier triangular

###f = 1 (kHz)

###waveforms

A. Hysteresis Modulation

The motor speed is controlled by a PI controller. Parameters of the PI controller (Kp Ki) are optimized by signal constraint block of Matlab/Simulink. The difference between the reference value of motor speed and the measured actual motor speed is called speed error signal. According to Fig. 2 the speed error signal is an input signal to the PI controller. The PI controller output is the reference electromagnetic torque. Considering that the electromagnetic torque of the motor is proportional to the stator currents the stator currents of the motors should produce an electromagnetic torque equal to the specified torque by speed controller. Thus the inverter switches control signals are generated by current controller technique. The hysteresis modulation (HM) is a motor current control technique.

The hysteresis current controller compares a current error -i.e. the difference between the measured (actual) and the desired (reference) phase currents- with a fixed hysteresis band. As shown in Fig. 3 if the current crosses the upper (lower) limit of the hysteresis band the upper (lower) switch of the inverter leg is turned off; so the currents start to decline (rise). Thus the measured currents stay into the hysteresis band [19]. In Fig.

2 pathways a" and b" are related to the trapezoidal- and sinusoidal-type PMBLDC motor drive respectively. Using Inverse Park's transformation reference qd0"-currents fixed in the rotor frame are transferred to reference three-phase abc"- currents. Inverse Park's transformation is defined as: Equation

B. Pulse width Modulation

As the previous section A the speed error signal enters to the PI controller; but the output of PI control is the amplitude of the reference balanced three-phase sinusoidal voltages of the inverter. The frequency of the fundamental harmonic component of voltage produced by PWM multilevel inverters is exactly equal to the frequency of the rotor speed. So the value varies from zero to a predefined value during the motor operation. The block diagram of speed controller of the PMBLDC motor drive has been shown in Fig. 5. The parameters of PI controller affect the performance characteristics of the motor such as torque pulsations. Thus The Kp and Ki parameters for controlling the sinusoidal-type PMBLDCM fed by two different inverters must be equal for comparison.

VI. SIMULATION RESULTS

A. Trapezoidal- and sinusoidal type PMBLDC motor drives As mentioned earlier the values of fundamental harmonic components of BEMFs induced in stator windings for the both motors are equal to 95.88 and hysteresis modulation technique with identical hysteresis band width is used for the both motors as well as optimized identical parameters (Kp Ki) related to PI controller for the both motors are equal to

0.7453 and 22.9516 respectively. The reference electrical angular speed of these motors is 40p rad/s.

Figures 5(a) and 6(a) show the trapezoidal BEMF and the sinusoidal BEMF waveforms for the PMBLDC motor respectively. TABLE II represents harmonic contents of the trapezoidal BEMF. Regarding Table II after the fundamental harmonic component third order harmonic is the largest than the other harmonics. So in some papers the trapezoidal BEMF has been approximated to the first and third order harmonics such as in [20].

Figures 5(b) and 6(b) illustrate the steady state of line-to-line voltage produced by the two-level three-phase HM inverter which supplying the trapezoidal- and the sinusoidal-type PMBLDC motor respectively. Figures 5(c) and 6(c) show quasi-rectangular and sinusoidal phase currents waveforms. The fundamental harmonic component amplitudes of the line-to-line voltage and the phase current of the trapezoidal- and sinusoidal-type PMBLDC motor drive are equal to

173.1V 172.5V and 3.36A 3.33A respectively. Total harmonic distortions of the line-to-line voltage of the trapezoidal- and sinusoidal-type PMBLDC motor drive are

85.26% and 87.42% respectively. High order harmonics of line-to-line voltage of the sinusoidal-type PMBLDC motor drive are larger whereas low order harmonics of line-to-line voltage the trapezoidal-type PMBLDC motor drive are larger. The motor drives mostly are employed in underwater vehicle and consequently the high order frequencies generated by inverters lead to be produced electrical noises that damped in water environment. Moreover the high order harmonics are filtered easily. So the sinusoidal-type PMBLDC motor drive could have proper performance using suitable filters. However the RC filters make troubles in order to detect the rotor position in sensorless PMBLDC motor drives [21].

The trapezoidal-type PMBLDC motor drive in each p /3 electrical angle two phases are conducting and last phase is floating. The commutation period of the phase

currents the motor drive is p /3 electrical angle and conducting period of each phase is 2p / 3 electrical angle.

The detailed phase current flows according to the 6 operating modes are represented in TABLE III. The positive sign means that the direction of the flowed current is from the

output of three-phase HM inverter to the motor terminals.

The motor speed and speed ripples are shown in figures 7(a) and 7(b) respectively. The amplitude of speed ripples of the trapezoidal-type PMBLDC motor varies within 598.5rpm and

600.75rpm whereas it varies just between 599.7rpm and 600.3rpm for the sinusoidal-type PMBLDC motor. Another more important performance characteristic is torque pulsations. The amplitude of torque pulsations related to the trapezoidal-type PMBLDCM varies within 5N.m and

8.8N.m whereas it varies just between 7.05N.m and 8.2N.m for the sinusoidal-type PMBLDCM as shown in Figures 8 and 11. As mentioned before the trapezoidal-type PMBLDC motor drive two phases conduct current at any time leaving the third phase floating. The trapezoidal-type PMBLDC motor drive has a significant torque pulsation due to commutating current during the phase commutation of the switch devices as shown in Fig. 9.

Acoustic noises are dependant of torque pulsations. One of the most important applications of the PMBLDC motor drive is in the field of autonomous underwater vehicles used in the military industries. An effective factor in the military equipments especially underwater vehicles is proceeding without recognition of its position by the enemy. One important factor in recognition of an underwater vehicles position is the acoustic noises that they depend on torque pulsations.

As a conclusion performance characteristics of the sinusoidal-type PMBLDC motor drive are better than the trapezoidal-type PMBLDC motor drive. However the quality of voltage produced by the three-phase two-level HM inverter is not good.

B. Sinusoidal-type PMBLDC motor fed by two- and five- level inverters Figures 12 and 13 illustrate the steady state voltages appeared between phase and mid-points (Van) of two-level and five- level inverters and phase and neutral point Y-connected stator windings (Vas) a-phase and b-phase (Vab) and mid- point of two-level and five-level inverters and neutral point Y-connected stator windings(Vnn) respectively. On the basis of rules of multilevel inverters the number of levels of Van and Vab of an m-level inverter are m and 2m-1 respectively. So the number of levels of Van and Vab are 2 5 and 3 9 for the two-level and five-level inverter as shown in Figures

12(a) 12(c) and Figures 13(a) 13(c). The fundamental harmonic component amplitudes of the line-to-line voltage produced by the two-level and the five-level inverters are

202.58 and 192.29 respectively. Amplitudes of the fifth seventh eleventh and thirteenth and forty-ninth order harmonics of the line voltage are given for the two various inverters in Table IV. For the two-level inverter feeding the filtered easily. So the sinusoidal-type PMBLDC motor drive could have proper performance using suitable filters. However the RC filters make troubles in order to detect the rotor position in sensorless PMBLDC motor drives [21].

The trapezoidal-type PMBLDC motor drive in each p /3 electrical angle two phases are conducting and last phase is floating. The commutation period of the phase

currents the motor drive is p /3 electrical angle and conducting period of each phase is 2p / 3 electrical angle.

The detailed phase current flows according to the 6 operating modes are represented in TABLE III. The positive sign means that the direction of the flowed current is from the

output of three-phase HM inverter to the motor terminals.

The motor speed and speed ripples are shown in figures 7(a) and 7(b) respectively. The amplitude of speed ripples of the trapezoidal-type PMBLDC motor varies within 598.5rpm and

600.75rpm whereas it varies just between 599.7rpm and 600.3rpm for the sinusoidal-type PMBLDC motor. Another more important performance characteristic is torque pulsations. The amplitude of torque pulsations related to the trapezoidal-type PMBLDCM varies within 5N.m and

8.8N.m whereas it varies just between 7.05N.m and 8.2N.m for the sinusoidal-type PMBLDCM as shown in Figures 8 and 11. As mentioned before the trapezoidal-type PMBLDC motor drive two phases conduct current at any time leaving the third phase floating. The trapezoidal-type PMBLDC motor drive has a significant torque pulsation due to commutating current during the phase commutation of the switch devices as shown in Fig. 9.

Acoustic noises are dependant of torque pulsations. One of the most important applications of the PMBLDC motor drive is in the field of autonomous underwater vehicles used in the military industries. An effective factor in the military equipments especially underwater vehicles is proceeding without recognition of its position by the enemy. One important factor in recognition of an underwater vehicles position is the acoustic noises that they depend on torque pulsations.

As a conclusion performance characteristics of the sinusoidal-type PMBLDC motor drive are better than the trapezoidal-type PMBLDC motor drive. However the quality of voltage produced by the three-phase two-level HM inverter is not good.

B. Sinusoidal-type PMBLDC motor fed by two- and five- level inverters Figures 12 and 13 illustrate the steady state voltages appeared between phase and mid-points (Van) of two-level and five- level inverters and phase and neutral point Y-connected stator windings (Vas) a-phase and b-phase (Vab) and mid- point of two-level and five-level inverters and neutral point Y-connected stator windings(Vnn) respectively. On the basis of rules of multilevel inverters the number of levels of Van and Vab of an m-level inverter are m and 2m-1 respectively. So the number of levels of Van and Vab are 2 5 and 3 9 for the two-level and five-level inverter as shown in Figures

12(a) 12(c) and Figures 13(a) 13(c). The fundamental harmonic component amplitudes of the line-to-line voltage produced by the two-level and the five-level inverters are

202.58 and 192.29 respectively. Amplitudes of the fifth seventh eleventh and thirteenth and forty-ninth order harmonics of the line voltage are given for the two various inverters in Table IV. For the two-level inverter feeding the

motor total harmonic distortion (THD) of the line-to-line voltage is 61.91% whereas for five-level inverter it is just 17.06%. In fact the output voltage waveform of five-level inverter is almost sinusoidal and any extra filters are not required. Consequently there are not any problems related to the RC filters.

As shown in Figures 14(b) and 15(b) when the five-level inverter is used to replace the two-level inverter the amplitude of torque pulsations reduce from 3N.m (6.12N.m

9.12N.m) to 2.25N.m (6.5N.m 8.75N.m). In other words if the sinusoidal-type PMBLDCM is fed by the five-level PWM inverter torque pulsations are reduced up to 25% as compared to the two-level PWM inverter.

The average of input instantaneous power to the two- and five-level inverter is 610W and 583W respectively shown in Fig. 16(a) and Fig. 17(a). The average of input instantaneous power to the PMBLDC motor fed by two- and five-level inverter is 575W and 530W respectively shown in Fig. 16(b) and Fig. 17(b). The average power of motor load is equal to

479.3W for both cases. But considering that the value of harmonic component of the produced voltage and drawn current by the five-level inverter are less than the two-level inverter less power is required to run the specified mechanical load and the motor efficiency is better. However the power loss related to the five-level inverter is larger due to increase of the number of switches. The efficiency of the five-level inverter the PMBLDC motor and the motor drive are equal 90.91% 90.43% and 82.21% respectively as well as for the PMBLDC motor drive fed by two-level inverter are

94.26% 83.33% and 78.57% respectively. In other words the efficiency of the sinusoidal-type PMBLDC motor drive fed by the five-level inverter is increased up to 4.6%. As mentioned before for both cases the controllers and their parameters KP and Ki modulation technique and the parameters of motor are quite identical. So it can be

expressed in confidence that existing differences is due to the number of levels of the inverters.

Motors are usually damaged earlier that their useful life due to being fed by inverters that produce high-frequency stepped waveforms of voltage and high dv/dt. Such produced voltage by an inverter may put a relatively large voltage between the neutral point of stator windings and the mid-point of inverter. This voltage is known as common mode voltage. The voltage induces a voltage on the rotor shaft via existing capacitors and nonlinear impedances between rotor and stator. The amplitude of the voltage is considered as a symbol of circulating bearing currents [22].

There is a significant difference in the voltage appeared across the neutral of stator windings to the mid-point of both inverters. Figures 12(d) and 13(d) illustrate the appeared voltage between the mid-point of two-level and five-level inverters and the Y neutral pint of the stator windings for the sinusoidal-type PMBLDC motor drive. The amplitude of voltages varies between -110V 110V for the two-level inverter and -55V 55V for the five-level inverter. Therefore in cooperation with other above verified benefits the five-level inverter is preferable regarding common mode voltage and less circulating bearings current too.

TABLE II HARMONIC COMPONENTS OF BEMF WAVEFORM

Harmonic

###1st###3rd###5th###7th###9th###11th###13th

order

###21.###3.###1.###2.

BEMF in volt###95.9###0.8###0.6

###3###8###9###4

TABLE III PHASE CURRENT FLOWS ACCORDING TO THE OPERATING MODES

Mode###1###2###3###4###5###6

ia###+###+###0###-###-###0

ib

###-###0###+###+###0###-

ic###0###-###-###0###+###+

TABLE IV HARMONIC COMPONENTS OF LINE-TO-LINE VOLTAGE RELATED TO SINUSOIDAL-TYPE PMBLDC MOTOR SUPPLIED BY TWO-LEVEL AND FIVE-LEVEL INVERTER

Harmonic

###5th###7th###11th###13th###49th

Order

Two-Level Inverter

Line-to-Lin

###7.23###1.18###0.73###0.3###51.92

voltage

Five-Level Inverter

Line-to-Lin

###7.34###0.97###0.71###0.25###0.55

Voltage

VII. CONCLUSION

Optimum design of a PMBLDC motor and select an inverter with appropriate number of the levels and its proper control system are the ways to decrease torque pulsation and speed ripple and consequently to reduce vibration and acoustic noises. The simulation results illustrate that when the amplitudes of fundamental harmonic component of their BEMFs are quite identical the sinusoidal-type PMBLDC motor drive have better performance than the trapezoidal- type. On the other hand it normally required a high resolution encoder to trace the rotor position. So the sinusoidal-type PMBLDC motors drive more expensive and the control is more complicated. It also shows that the five- level PWM inverter in comparison with the two-level PWM inverter reduce amplitude of the torque pulsation more than

20 percent and consequently acoustic noise will mitigate. In the five-level inverter the appeared voltage between neutral point of the star-connected stator windings and mid-point of the inverter and dv/dt and consequently the stress settled on the motor bearings would be significantly small in comparison with the two-level inverter.

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