BLDCM selected by horizontal well tractor is star connection and the central node is not led out, its equivalent circuit shown in Figure 2.

According to Kirchhoff’s voltage law, the equation of phase voltage can be obtained as follows:

[ V a V b V c ] = [ R 0 0 0 R 0 0 0 R ] [ i a i b i c ] + [ L 0 0 0 L 0 0 0 L ] × d d t [ i a i b i c ] + [ E a E b E c ] + [ V n V n V n ] (1)

in type: V a , V b , V c ―Voltage of each phase to the ground;

i a , i b , i c ―Phase current;

E x = k e ω m ―Back EMF, k e , ω m are back EMF coefficient and rotor mechanical speed;

R ―Phase resistance;

L = L s − L m ―Equivalent inductance of stator winding, L s , L m are self inductance of stator winding and mutual inductance between stator winding;

V n ―Central node voltage of motor armature winding.

The back EMF of BLDCM is a trapezoidal wave, the current is a square wave, and the phase current of each phase winding must be consistent with the back EMF in order for the BLDCM to output the maximum torque. Therefore, Commutation is required for every 60°electric angle in one electric period. Relation of back EMF and current in BLDCM as shown in Figure 3. It can be seen from Figure 3 that back EMF zero crossing point leading the current commutation signal 30˚ in each phase winding, So, The commutation time can be got according to the back-EMF zero crossing point. The motor back EMF can not be measured directly, so, It is necessary to calculate the equivalent voltage by phase voltage.

Set x phase is the non-conducting phase, the phase current is 0, according to Equation (1) can be got:

E x = V x − V n (2)

It can be seen from Equation (2) that the commutation signal can be obtained

indirectly by comparing the relationship between the phase voltage and the central node voltage.

Since the center node of the motor selected by the drive system is not led out, it is necessary to fabricate the motor central node voltage.

As a BLDCM, there are only two phases which have current at the same time, Due to conducting two-phase current equal to the opposite direction, the other a phase current is 0, from Equation (1) can be got:

V a + V b + V c = E a + E b + E c + 3 V n (3)

It can be seen from Figure 2 that the sum of the three phase back EMF is zero when the back-EMF zero crossing, so, the central node voltage at this time can be got as:

V n = V a + V b + V c 3 (4)

Since the back EMF increases with the increase of speed, the back EMF zero- crossing detection is not suitable for motor starting. The drive system adopts three stage start algorithm when the motor is starting, namely, the rotor pre-positioning, external synchronous acceleration, self-synchronization. Figure 5 and Figure 6 are diagrams of rotor position using a three stage start algorithm.

From Figure 5 and Figure 6 shows, the use of three stage start algorithm can be achieved smooth start of the motor. Figure 7 is the motor speed response curve.

It can be seen from Figure 7, the use of three stage start algorithm to start, the speed can be in a relatively short period of time to track the given speed to achieve the desired start effect. Figure 8 is the a phase voltage, PWM and current after switch to self-synchronizing.

Visible, the simulation results consistent with the previous theoretical analysis, the back-EMF zero-crossing lead the phase commutation signal 30˚ electrical angle.

Based on the above analysis, Commutation of sensorless BLDCM based on the back-EMF zero-crossing detection needs to delay 30˚ electric angle time according to speed, therefore, the accuracy of speed detection is crucial for commutation of sensorless BLDCM. The traditional speed detection is calculated by the time difference between two commutation signals. The obtained speed is the average speed between two commutation signals, which is not accurate enough, so commutation can not be performed at the optimum commutation time, So it is

necessary to find a more accurate method of speed detection.

For BLDCM, when the current from phase a to phase b is considered. There are following equations:

{ i a = − i b i c = 0 E a = − E b (5)

According to the formula (1) the line voltage between phase a and phase b can be obtained:

V a b = V a − V b = 2 R i a + 2 L d i a d t + 2 E a (6)

In stable condition, d i d t ≈ 0 . Then, (6) can be rewritten as:

ω m = V a b − 2 R i a 2 k e (7)

According to Equation (7), the motor speed can be calculated according to the line voltage and phase current, but the motor windings resistance could change with the change of temperature. Therefore, BLDCM speed detection based on model reference adaptive control (MRAC) is proposed. As shown in Figure 9.

As can be seen from Figure 9, the main module of speed detection is a model reference adaptive regulator, S p e _ e s t is speed estimated by line voltage and phase current, S p e _ c e is speed calculated by the commutation signal, The input of regulator is the deviation of the two speed, the output of the regulator is a correction variable quantity k c to estimate the speed.

When the motor stator winding resistance increases from 11.9 Ω to 15.9 Ω, the actual motor speed, the speed calculated based on the fixed resistor value, the

Figure 9. BLDCM speed detection based on model reference adaptive.

speed detected based on the commutation signal and the estimated speed based on the MRAC are shown in Figure 10.

It can be seen from Figure 10 that after the change of the resistance of the stator winding of the motor, the estimated speed based on the MRAC is the closest to the actual speed.

Drive system of sensorless BLDCM includes two parts: software and hardware, the software part includes the main program and several subroutines and interrupt service functions, the main function is to achieve BLDCM without position start, commutation, PWM duty cycle setting and communicate with the upper computer. The hardware part includes the controller, drive circuit, three phase inverter, voltage and current sampling circuit. and the overall structure of the drive system is shown in Figure 11.

As the actual working environment temperature of the horizontal well tractor is too high, there are high requirements on the controller. Therefore, the controller of the drive system adopts the dsPIC series chip of the MICROCHIP company.

Figure 11. The overall structure of the drive system for sensorless BLDCM.

The control chip is a kind of motor-specific control chip with digital signal processor (DSP) computing function. It can withstand underground high temperature environment and meet the actual working conditions of horizontal well tractors. As the IGBTs that form the three phase inverter need certain voltage and power to trigger, Therefore, a driving circuit composed of the driver chip IR2233 and its corresponding peripheral circuits is added between the controller and the three phase inverter. The specific design of the driving circuit and the inverter circuit is shown in Figure 12.

As the drive system uses PWM technology, which results in a large number of chopping components in the detected voltage and current, which will interfere with the sampling, therefore, It is necessary to add a filter capacitor in the sampling circuit.

As can be seen from Figure 11, the drive system uses double closed-loop speed and current control, the controller receives commands through the communication with the upper computer to obtain the desired speed of the motor, after the motor is started and switched to self-synchronous by the three stage start algorithm, Estimate the actual motor speed based on MRAC, DC bus current obtained through the current sampling circuit, and then through the speed regulator and current regulator to obtain the corresponding PWM duty cycle, so that the motor speed reaches the desired speed.

After switch to self-synchronizing, through the ADC interrupt service function to complete the acquisition of phase voltage, and then according to equation (4) fictitious motor central node voltage and compared with each phase voltage, and then by the PWM interrupt service function using majority functions to detect the back-EMF zero point, if true then calculate the 30˚ electrical angle of time according to speed and start the timer for commutation of sensorless BLDCM. As the sampling circuit introduces a filter capacitor nonlinear element, Resulting in a phase shift between the detected zero crossing point of the back EMF and the actual zero crossing point. Therefore, the delay phase needs to be compensated according to speed.

Figure 12. Design of specific driving circuit and inverter circuit.

The structure of the body, rotor and stator of the motor used in the drive system are shown in Figure 13 and Figure 14.

In order to facilitate the test of the drive system, we designed a monitoring and control software for upper computer based on the serial port, which can monitor the motor speed and PWM duty cycle. Figure 15 shows the Phase voltage waveform diagram before and after filtering. Figure 16 the modulation signal of the upper bridge and phase voltage waveform. Figure 17 and Figure 18 are motor speed and PWM duty cycle obtained by the software at a temperature of 150˚C. Figure 19 is the modulation signal of the upper bridge and phase voltage waveform when the motor speed is 6000 rpm.

From the experimental results, it can be seen that the drive system for sensorless BLDCM based on DSC can realize the smooth start of BLDCM in high temperature environment and can track the given speed rapidly.