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Current Flow Analysis in Permanent Magnet Brushless DC (BLDC) Motor Control using PSpice: Part 1

1. Introduction:

Brushless Direct Current (BLDC) motor drives are widely used in Automobiles, Aerospace, Consumer, Automation equipment, Instrumentation etc. The development of advanced magnetic materials, power electronics and digital control systems make the Permanent Magnet (PM) BLDC motors an effective solution for wide rage of inverter fed variable speed drives. BLDC use in electric vehicles has increased substantially in the recent years due to its high power and torque density and ease in controllability.

A Brushless DC motor has a permanent magnet rotor and a wound stator. The windings are connected to an inverter. The inverter energizes the windings in a pattern which rotates the magnetic field around the stator. The energized stator winding causes the PM rotor to rotate in a synchronous fashion around the stator. So it is important to know the perfect sequence to energize the stator windings. In this paper we have shown the simulation results and step by step procedure to simulate a BLDC motor control system.

Keywords: Motor Control, Permanent Magnet Motors, BLDC motor, Back EMF, Inverter, Simulation, Spice, PSpice, Brushless, Motor Drive, Torque Control, PWM Motor Control

2. Permanent Magnet BLDC Motor Control: Concepts, Operation and Modeling:

The first experiment involving rotation of electromagnetic components was conducted in early 1900s.The development of first practically useful PM motor started with the invention demonstrated by Edison around 1900. The improvements were mainly driven by the development of better magnetic materials. However, in the last decade the interest has increased due to the advancement of power electronics, semiconductor materials, and digital control.

2A. Magnet Materials:

The magnetic phenomenon was discovered more than 2500 years ago. For the longest time, the only known magnetic material was lodestone (Fe3O4). The most significant early use of Permanent Magnet was the compass. The relation between magnetism and electricity was first discovered by Orsted, Sturgeon and Faraday in the 19^th century. The development of commercially available PM materials began in the 20^th century with production of magnetic steel. In 1930s the first PM aluminum-nickel-cobalt alloy (AlNiCo) was developed for electro mechanical systems. However it had a very limited use due to its low coercive force.

Figure 1: Hysteresis Loop for Permanent Magnets used in Motor Control Applications

[Definition of Coercive Force - The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero. It is the value of H at point c on the hysteresis curve.]

In 1950s the low cost ferrite permanent magnets with high coercive force were developed. Until today this remains the most useful PM because of its superior price-performance ratio.

The next introduction of PM was sintered rare-earth cobalt magnets developed around 1970. These are also known as Samarium Cobalt alloy (SmCo). These magnets have higher performance and coercive force than the ferrite magnets. There have been recent introductions of other PMs with better performance. In 1980s Neodymium-Iron-Boron (NdFeB) was invented with higher performance and less cost than SmCo. However, NdFeB is not always superior due to its lower thermal stability. There is a significant research activity in the area of metallurgy to invent new and powerful PM. Today the high performance rare-earth magnets are widely used in small motors like hard disk drive and servo drives etc. Great care is needed at all times to handle the permanent magnet materials because of their brittle nature.

2B. Basic Operating Principle, BLDC Motor Control:

Figure 2: Basic block diagram of permanent magnet motor drives

Brushless DC motors are also known as Magnet Synchronous motors. The question is whether BLDC can be classified as an AC or a DC motor. Though the supply is DC and does not directly operate the motor. BLDC is a PM synchronous motor that uses position sensor to detect the position of the rotor and an inverter to control the armature currents. BLDC motors can also be configured as an inside-out motor for direct-drive electric vehicle applications when armature can be located in the center of the motor and the magnets are on the outside.

[Definition of Trapezoidal Motor: In a trapezoidal motor the back-EMF induced in the stator windings has a trapezoidal shape and its phases must be supplied with quasi-square currents for ripple free torque operation.]

In BLDC motor the armature does not rotate, instead the PMs rotate. In brushed DC motor, windings are in the rotor. So it becomes difficult to transfer the current to the moving rotor.

In a three phase BLDC six step commutation is the simplest method to drive the motor. One set of sequence represents a full electrical rotation. Number of electrical cycle is equal to the number of pole pairs. Increase in pole pairs may decrease the torque ripple. The speed and torque of the motor depend on the strength of PMs and in certain instances the magnetic field generated by energized winding. Also it is necessary to know the exact position of the rotor magnet to start the motor. The two main objectives are to control the speed and torque of the BLDC motor. In figure 2 it shows the closed loop representation of the BLDC motor for speed and torque control.

Brushless DC Motor Control

Rotation

Figure 2 shows a basic block diagram of BLDC motor control system. A flux is generated by an energized stator which interacts with the rotor magnet flux. Maximum flux is generated when the angle between the stator and rotor flux is close to 90 degree. It is necessary to know the proper position of the rotor magnet to ensure alignment of the stator flux close to this angle. Generally in low cost systems, three hall sensors are placed on the stator with 60 or 120 electrical degree phase shift to provide the position feedback. Six step commutation requires that the windings be switched every 60 electrical degrees. Three hall sensors read the rotor position every 60 electrical degrees of rotation. So in one complete electrical rotation hall sensors provide six unique position values. Table 1 shows hall sensor table for a three-phase BLDC motor with six unique values along with active phase voltages and switches.

Hall Sensor Values (H3,H2,H1)	Phases	Switches
100	V_a-V_b	AT-BB
101	V_a-V_c	AT-CB
001	V_b-V_c	BT-CB
011	V_b-V_a	BT-AB
010	V_c-V_a	CT-AB
110	V_c-V_b	CT-BB

Table 1: Commutation sequence from Hall sensor

Generally the hall table is provided by the motor manufacturer. Depending on the current hall value, firing signal is given to the corresponding switches of the inverter as per Table 1.

[Definition of BACK EMF: Back-EMF is a voltage that occurs in electric motors when there is a relative motion between the armature of the motor and the external magnetic field].

Speed Control:

Speed of a BLDC motor is proportional to the applied voltage across its windings. A precise speed can be controlled using a conventional PI controller. A well designed PI controller generates a duty cycle command based on the difference between the actual and commanded speed. Depending on the duty cycle command, PWM pulses are generated that vary the gate drive of the inverter switches to get the required speed.

Torque Control:

Torque is directly proportional to the motor current. In this mode of control, a current reference proportional to the desired torque is generated. Current feedback is compared with this reference and the error is fed to a PI. A duty cycle is generated proportional to the output of the PI amplifier.

3. Mathematical Modeling of BLDC Motors:

The three phase star connected BLDC motor can be described by the following basic equations. These are per phase modeled equation. A per phase model is also shows in figure 3.

Modeling of Brushless DC Motor

Where V, I and e are the voltage, current and back-emfs of phase A, B and C. R and L are the resistance and inductance of each phase respectively. T_e and T_L are electrical torque and load torque, j is the rotor inertia, K_f is the friction constant and ω_m is the rotor speed.

Figure 3:Per phase modeling of star BLDC Motor

4. Back EMF modeling:

Fig 4 shows the back EMF model in PSpice. The model have parameters like frequency (F_req), rise time (T_r), fall time (T_f), pulse width (P_w), amplitude (A), motor inductance (L_mot) and motor resistance (R_mot).

Figure 4:Back EMF model of Brushless DC Motor

Fig 5 shows simulated trapezoidal back emf from the model in fig 4.

Figure 5: Simulation result of trapezoidal Back EMF

5. BLDC Motor: Basic Model

In our simulation technique we have modeled a BLDC motor similar to BN-23 from Moog (http://www.moog.com). Some of the key specifications are listed below:

Frequency	133.33 Hz
Back EMF (A)	6.3V
Back EMF constant	3.15V/1000rpm
Motor/Terminal resistance(R_mot)	0.181 ohm
Motor/Terminal Inductance(L_mot)	242 uH

The complete motor model is showing in figure 6.

Figure 6: A BN-23 Motor Model

Figure 6: A BN-23 motor model

Every parameter of interest has been defined in this simulation example. In our simulation technique we generate a parameter text file. The importance of the text file is that it includes all the parameters of interest. It is a convenient way to change parameters and re-run analysis. The parameter file is shown in appendix A.

Fig. 6 shows the 3-phase BLDC model. Fig. 7 shows the three phase trapezoidal BackEMF waveforms from the model shown in figure 6.

Figure 7: Back EMF simulation result

6. The Inverter:

An inverter is used for energizing the stator winding based on the rotor position. The current in any two energized phases can be turned ON and OFF anytime during every 60 electrical degrees. The inverter and motor model are shown in Fig 8.

Figure 8:Inverter and Motor Model in PSpice. Inverter legs are donated as A, B and C and corresponding switches are referred to as AT for A-top, AB for A-bottom etc

In the above model we assume that switch and diode are ideal in nature. It is important to use ideal components at the beginning of any simulation activity to reduce unnecessary complexity and build any system model one step at a time.

The sub-circuits used for the switch and diode are shown in appendix B and C respectively.

Figure 9: Gate Drive Modeling for Six-Step Control of a BLDC

Fig 9 shows PSpice model related to the gate drive circuits. AT is connected to the gate of the top switch of leg A. AB is connected to the gate of the bottom switch of leg A. Similarly BT,BB,CT,CB are connected to the gates of leg B-top switch, leg B-bottom switch, leg C- top switch and leg B-bottom switch respectively.

A phase current that is being turned OFF will flow through its complementary freewheeling diode while the current in the phase which is turned ON will start rising from zero. We have implemented six step firing of the stator winding current in this simulation example. It is important to know the current flow in the system at every instance of time and how the off phase winding current flows through the complementary freewheeling diode when a switch is turned off in a particular interval. In this paper we have shown the simulation results of BLDC motor control system without any PWM to highlight the simulation technique and the basics of the firing sequence.

7. Analysis of Current Flow in BLDC Motors:

When switch AT and switch BB are on, current flows through the coils A and B. This is shown in fig. 10. It is clear from the simulation results that when switch AT is on, current flows through coil A and it is positive whereas current through coil B is negative while flowing through switch BB. When Switch AT is on and BB is off, we start to energize the coil C by switching ON the switch CB and switching OFF the switch BB. Consequently, there will be no further current flow through coil B. However, the current in phase B can not come to zero instantly. It has to flow through the complementary diode D3. Current in Phase A once again starts to increase as the switch CB starts conducting soon after the current in Coil B finishes through Diode D3.

Figure 10: 3-Phase Motor Currents with PSpice model of BLDC Motor Control System

There are 18 different states of current flow in the 3-phase BLDC motor in a 360 degree electrical cycle. The different steps are illustrated here with a brief discussion and simulation results.

Step 1: AT and BB are ON (0 degree)à Current starts to increase in coil A (+ve) and comes out from coil B (-ve)

Step 2: AT and BB are ON (0-60 degree)à Current still flows in coil A (+ve) and B (-ve).

Step 3: AT is ON and BB is OFF (60 degree)à Current flows in coil A (+ve) and energy stored in coil B flows through the freewheeling diode D3. There is a slight drop in the phase current.

Step 4: AT and CB is ON(60 degree)àCurrent flows in coil A(+ve) and once again starts to increase and comes out from Coil C(-ve)

Step 5: AT and CB are ON (60-120 degree)à Current flows in coil A (+ve) and C (-ve).

Step 6: AT is OFF and CB is ON(120 degree)à Energy stored in coil A flows through the freewheeling diode D2 and current flows through coil C(-ve)

Step 7: BT is just ON and Switch CB is ON (120 degree)à Current starts to increase through coil B (+ve) while flowing through in coil C (-ve)

Step 8: BT and CB are ON (120-180 degree)à Current flows in coil B (+ve) and C (-ve).

Step 9: BT is ON and CB is OFF (180 degree)à Current still flows in coil B (+ve) and energy stored in coil C flows through the freewheeling diode D5.

Step 10: BT and AB are ON (180 degree)à Current still flows in coil B(+ve) and A(-ve).

Step 11: BT and AB are ON (180-240 degree)à Current flows in coil B (+ve) and A (-ve).

Step 12: BT is OFF and AB is ON(240 degree)à Energy stored in coil B flows through the freewheeling diode D4 and it also flows through coil A(-ve)

Step 13: Switch CT and Switch AB are ON(240 degree)à Current starts to increase in coil C (+ve) and it also flows through coil A(-ve)

Step 14: CT and AB are ON (240-300 degree)à Current flows in coil C (+ve) and A (-ve).

Step 15: CT is ON and AB is OFF (300 degree)à Current flows in coil C (+ve) and energy stored in coil A flows through the freewheeling diode D1.

Step 16: CT and BB are ON (300 degree)à Current flows through coil C (+ve) and Coil B (-ve)

Step 17: CT and BB are ON (300-360 degree)à Current flows through coil C (+ve) and coil B (-ve).

Step 18: CT and BB are ON (360 degree)à Energy stored in coil C flows through the freewheeling diode D6 and coil B (-ve)

Concluding Remarks:

Understanding the BLDC motor operation and firing the proper stator winding are important in simulation and development of any BLDC motor control system. This article lays down the basic foundation of a BLDC motor control model which will be used to analyze torque and speed control along with advanced PWM techniques in the subsequent articles. In the future articles, we will also explore various control strategies such as High Side PWM, High and Low Side PWM, High and Low Side PWM with two active inverter legs, High and Low Side PWM with 180o phase shift, PWM activation of all inverter legs at all times. These strategies impact performance, cost, efficiency and volume of a motor control system.

Appendix A: Parameter Text File

******* Modeling Moog Brushless Motor BN23 ******

.Param Freq=133.33

.Param A = 6.3

* A = Back EMF Voltage

.PARAM Tr= {1/Freq/12}

.PARAM Tf= {1/Freq/12}

.PARAM Pw= {1/Freq/3}

.PARAM R_MOT =0.181

.PARAM L_MOT =242u

.PARAM GATE_Tr =10uS

.PARAM GATE_Tf = 10uS

.PARAM 180_DEGREE = {1/Freq/2}

.PARAM 120_DEGREE = {1/Freq/3}

.PARAM 240_DEGREE = {2/Freq/3}

.PARAM 30_DEGREE = {1/FREQ/12}

.PARAM OFFSET = 0

*PARAM DLY1 = {1/FREQ/12}

.PARAM DLY1 = 0

*DLY1 = 30 Degrees

.PARAM DLY2 = {DLY1+1/Freq/2}

*DLY2 = DLY1+180 Degrees

.PARAM DLY3 = {DLY1+ 1/Freq/3}

*DLY3 = DLY1+ 120 Degrees

.PARAM DLY4 = {DLY1+ 1/Freq/3+1/Freq/2}

*DLY4 = DLY3+180 Degrees

.PARAM DLY5 = {DLY1+2/Freq/3}

*DLY5 = DLY1+240 Degrees

.PARAM DLY6 = {DLY1+2/Freq/3+1/Freq/2}

*DLY6 = DLY5+180 Degrees

*** Gate Drive Voltage

.PARAM GATE_DRV_V = 5

**END**

Appendix B: Switch Sub-Circuit

**** Idle Switch Spice subckt*****

*********** CONNECTIONS:

**** DRAIN

**** | SOURCE

**** | | GATE

**** | | | GATE GND

**** | | | |

.SUBCKT SWITCH D S G GG

Switch_Idle D S G GG IDLE_SWITCH

.MODEL IDLE_SWITCH VSWITCH (RON=0.005)

.ENDS SWITCH

*** End of sub-circuit definition.

*** Adapted from Power Electronics: Computer Simulation, Analysis and Education using PSpice by Ned Mohan

Text File:

Appendix C: Diode Implementation with Snubber :

Text File: Ideal Switch Diode

**** Idle Switch Diode Spice sub-ckt ***