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ISSUE: December 2010
Current Flow Analysis in Permanent Magnet Brushless DC (BLDC)
Motor Control Using PSpice
by Amitabh Mallik and Rakesh Dhawan, Strategic Technology Group, Pune, India
Brushless direct current (BLDC) motor drives are widely used in automotive, aerospace, consumer, automation,
instrumentation, and other applications. The development of advanced magnetic materials, power electronics
and digital control systems has made the permanent magnet (PM) BLDC motors an effective solution for a wide
range 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 of 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 that 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. Simulation could offer a convenient
means for determining the optimum sequence for energizing the windings. However, methods for performing
this type of simulation using popular tools such as Spice are not widely known in the industry. In this article, we
describe a step-by-step procedure for simulating a BLDC motor control system using PSpice. To apply this
procedure effectively, it is helpful for engineers to understand some basic concepts underlying motor operation
and the historical development of permanent magnet materials.
Permanent Magnet BLDC Motor Control: Concepts, Operation And Modeling
The first experiment involving rotation of electromagnetic components was conducted in the early 1900s. The
development of the 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, interest in the PM motor has increased due to the advancement of power electronics,
semiconductor materials, and digital control.
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 the permanent
magnet was the compass. But it was not until the nineteenth century that the relationship between magnetism
and electricity was first discovered by Orsted, Sturgeon and Faraday. Then, in the twentieth century, the
development of commercially available PM materials began with the production of magnetic steel. In the 1930s,
the first PM aluminum-nickel-cobalt alloy (AlNiCo) was developed for electromechanical systems. However, it
had a very limited use due to its low coercive force.
Coercive force is defined as the amount of reverse magnetic field that 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 Fig. 1.
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Fig. 1. Hysteresis loop. (Note: Point C on the hysteresis curve is also labeled “Coercivity.”)
In the 1950s, low-cost ferrite permanent magnets with high coercive force were developed. Even today these
magnets remain the most useful PMs because of their superior price-performance ratio.
The next introduction of a PM occurred when 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. However, there have been more recent introductions of other PMs with even better
performance.
In the 1980s, neodymium-iron-boron (NdFeB) was invented, offering higher performance and lower cost than
SmCo. However, NdFeB is not always superior due to its lower thermal stability. There is significant research
activity in the area of metallurgy to invent new and powerful PMs. Today, high-performance rare-earth magnets
are widely used in small motors like hard disk drives, servo drives, etc. But great care is needed at all times to
handle these permanent magnet materials because of their brittle nature.
Basic Operating Principle, BLDC Motor Control. 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, it does not directly operate the motor. A BLDC motor is a PM synchronous motor that uses position
sensors 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. In these applications, the
armature can be located in the center of the motor and the magnets are on the outside.
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 a BLDC motor, the armature
does not rotate, instead the PMs rotate. In a 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 motor, six-step commutation is the simplest method of driving the motor. One set of
sequences represents a full electrical rotation. The number of electrical cycles is equal to the number of pole
pairs. An 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 the energized winding. Also, it is
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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. Fig. 2 shows the closed-loop representation of the BLDC motor
for speed and torque control.
Fig. 2. Basic BLDC motor control system.
BLDC Motor Control—Rotation. Fig. 2 shows a basic block diagram of a 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 degrees. It is necessary to know the precise 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 a 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, the hall sensors provide six unique position values. Table 1 shows the hall
sensor table for a three-phase BLDC motor. It lists the six unique values for the hall sensors (H1, H2, and H3)
along with the active phase voltages and switch connections associated with these hall sensor values. (The
phase voltage and switch terms shown in Table 1 will be defined in subsequent figures.)
Table 1. Commutation sequence from Hall sensors.
Hall sensor values
(H3, H2, H1)
Phases
Switches
100
Va-Vb
AT-BB
101
Va-Vc
AT-CB
001
Vb-Vc
BT-CB
011
Vb-Va
BT-AB
010
Vc-Va
CT-AB
110
Vc-Vb
CT-BB
Generally the hall table is provided by the motor manufacturer. Depending on the current hall sensor values,
the firing signal is routed to the corresponding switches of the inverter as per Table 1.
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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. The speed of a BLDC motor is proportional to the applied voltage across its windings. A precise
speed can be controlled using a conventional proportional-integral (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 obtain 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.
Mathematical Modeling Of BLDC Motors
The three-phase star-connected BLDC motor can be described by the following basic equations. These are perphase-modeled equations. A per-phase model is also shown in Fig. 3.
dia
+ ea
dt
di
Vb = RI b + L b + eb
dt
di
Vc = RI c + L c + ec
dt
dω
Te = K f ωm + j m + TL
dt
Va = RI a + L
(1)
(2)
(3)
(4)
where V, I and e are the voltage, current and back-EMFs of phases a, b and c; R and L are the resistance and
inductance of each phase respectively; Te and TL are electrical torque and load torque; j is the rotor inertia; Kf
is the friction constant; and ωm is the rotor speed.
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Fig.3. Per-phase model.
Back-EMF Modeling
Fig 4 shows the back-EMF model in PSpice. The model has parameters like frequency (Freq), rise time (Tr), fall
time (Tf), pulse width (Pw) and amplitude (A).
Fig. 4. Back-EMF model in PSpice.
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Fig. 5 shows the simulated trapezoidal back EMF from the model in Fig. 4.
Fig. 5. Trapezoidal Back-EMF produced by the PSpice model of Fig. 4.
BLDC Motor: Basic Model
In our simulation technique, we have modeled a BLDC motor similar to the BN-23 from Moog. Some of the key
specifications for this motor are listed in Table 2.
Table 2. BN‐23 motor specifications.
Frequency
133.33 Hz
Back EMF (A)
6.3 V
Back-EMF constant
3.15 V/1000 rpm
Motor/Terminal resistance (R_mot)
0.181 Ω
Motor/Terminal Inductance (L_mot)
242 µH
The complete motor model is shown in Fig. 6.
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Fig. 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 value of the text file is that it includes all the parameters of interest, so it
provides a convenient way to change parameters and re-run analysis. The parameter file is shown in appendix
A. Fig. 7 shows the three-phase trapezoidal back-EMF waveforms generated by the three-phase BLDC model
shown in Fig. 6.
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The Inverter
Fig. 7. Three‐phase trapezoidal back-EMF waveforms.
An inverter is used to energize the stator windings 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.
Fig. 8. Inverter and motor model in PSpice. Inverter legs are denoted as A, B and C and the
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 appendices B and C,
respectively.
Fig. 9 shows the 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, and CB are connected to
the gates of leg B-top switch, leg B-bottom switch, leg C- top switch, and leg C-bottom switch, respectively.
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Fig. 9. Gate-drive model for six‐step control of a BLDC motor.
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 article, we will show the simulation results of a
BLDC motor control system without any PWM to highlight the simulation technique and the basics of the firing
sequence.
Analysis Of Current Flow In BLDC Motors
When switch AT and switch BB are on, current flows through 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 coil C by switching on switch CB and switching off switch BB. Consequently, there will be no further
current flow through coil B. However, the current in phase B cannot 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.
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Fig. 10. Three‐phase motor currents simulated by PSpice model of BLDC motor-control system.
There are 18 different states of current flow in the three-phase BLDC motor in a 360-degree electrical cycle.
The different steps are listed here with a brief description of the current flow and energy storage associated
with these steps.
Step 1. AT and BB are on (0 degrees)  Current starts to increase in coil A (+ve) and comes out from coil B (ve).
Step 2. AT and BB are on (0 to 60 degrees)  Current still flows in coil A (+ve) and B (-ve).
Step 3. AT is on and BB is off (60 degrees)  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 are on (60 degrees)  Current 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 to 120 degrees)  Current flows in coil A (+ve) and C (-ve).
Step 6. AT is off and CB is on (120 degrees)  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 degrees)  Current starts to increase through coil B (+ve)
while flowing through coil C (-ve).
Step 8. BT and CB are on (120 to 180 degrees)  Current flows in coil B (+ve) and C (-ve).
Step 9. BT is on and CB is off (180 degrees)  Current still flows in coil B (+ve) and energy stored in coil C
flows through the freewheeling-diode D5.
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Step 10. BT and AB are on (180 degrees)  Current still flows in coil B (+ve) and A (-ve).
Step 11. BT and AB are on (180 to 240 degrees)  Current flows in coil B (+ve) and A (-ve).
Step 12. BT is off and AB is on (240 degrees)  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 degrees)  Current starts to increase in coil C (+ve) and it also
flows through coil A (-ve).
Step 14. CT and AB are on (240 to 300 degrees)  Current flows in coil C (+ve) and A (-ve).
Step 15. CT is on and AB is off (300 degrees)  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 degrees)  Current flows through coil C (+ve) and Coil B (-ve).
Step 17. CT and BB are on (300 to 360 degrees)  Current flows through coil C (+ve) and coil B (-ve).
Step 18. CT and BB are on (360 degrees)  Energy stored in coil C flows through the freewheeling-diode D6
and coil B (-ve).
Conclusion
Understanding BLDC motor operation and firing the proper stator winding are important in the 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
subsequent articles. In 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
180-degree phase shift, and PWM activation of all inverter legs at all times. These strategies impact the
performance, cost, efficiency and volume of a motor-control system.
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Appendix A: Parameter Text File
Appendix B: Switch Sub-Circuit
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Text File:
Appendix C: Diode Implementation with Snubber
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Text File: Ideal Switch Diode
References
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About The Authors
Rakesh Dhawan is a twenty-year veteran of the power electronics industry. Rakesh has
a BTech in Electrical Engineering from the Indian Institute of Technology, Kharagpur, a
Masters of Electrical Engineering (MSEE) from the University of Minnesota, and an MBA
from Old Dominion University, Virginia. Rakesh has been an entrepreneur who has built
several high-quality technology businesses. Rakesh has six approved and filed patents
and twenty five conference and journal publications to his credit. Rakesh founded
Strategic Technology Group to further his passion in power electronics. His interests
include electric bicycles, electric vehicles, permanent magnet brushless motor drives,
switch-mode power supplies, solar inverters, simulation, statistics, project management
and new and ultra-fast product development. Rakesh has built and managed several
high-technology product development teams in his career. He has been directly
responsible for over twenty five product launches.
Amitabha Mallik received his Bachelors of Engineering from Visveswaraiah Technological
University, Belgaum, India in 2008. He is pursuing his MTech at MIT, Manipal University,
Manipal, India, in Power Electronics Systems and Control. He is currently working at
Strategic Technology Group, Pune, India. His areas of interests are power semiconductor
devices, motor drives and control, PWM dc-dc converters, and OrCAD/PSPICE (systemlevel simulations).
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