issue: May 2005 APPLIANCE Magazine
The Basics of Brushless Motor Drive Design
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by Dal Y. Ohm, consultant, Drivetech, Inc.
Due to the increasing demand for compact and reliable motors and the evolution of low-cost power semiconductor switches and permanent magnet (PM) materials, brushless motors are widely used in every application from home appliances to the aerospace industry.
Figure 1.1. This is an example of a switch configuration for a brushless motor using the six-step drive.
Unlike brushed d.c. motors, every brushless motor requires a drive to supply commutated current to the motor windings synchronized to the rotor position. In other words, some kind of feedback position sensors are necessary to commutate brushless motors, even for sensorless operation where position information is estimated from other variables. Some drives are just commutating while others may include voltage control with or without current-loop.
Instead of the popular three phase six-switch (bipolar drive) configuration, only three (or two) switches (unipolar drive) can be used to drive three-phase (two-phase) brushless motors. Since the direction of winding current cannot be reversed in unipolar drives, windings are not efficiently utilized in this configuration. Unipolar drives are often used in low-power, low-voltage motors due to lower cost and lower voltage drop across semiconductor switches.
Variable Bus Voltage
Similar to brushed d.c. motors, brushless d.c. motors with electronic commutation can operate from a d.c. voltage source, and speed can be adjusted by varying supply voltages. A variable voltage d.c. source may be obtained from rectification of a variable voltage transformer output or from the thyrister bridge. In this configuration, d.c. bus voltage is a function of the firing angle of the thyrister bridge. Instead of varying supply voltage, variable-speed operation can also be realized from a constant bus voltage. In this case, power semiconductor switches are used not only to commutate, but also to control the motor terminal (drive output) voltage via the pulse width modulation (PWM) technique.
The technique generates a fixed frequency (usually 2 to 30 kHz) voltage pulse whose on-time duration is controlled. Since the brushless motor is highly inductive, the motor current produced from this switched voltage would be almost identical, except for current ripples, to that of the fixed voltage whose magnitude is the average of the switched voltage waveform. Although PWM control is now very popular in drives, variable bus voltage control is still used in many applications where dynamic performance is not important.
Figure 1.2. These charts show how voltage affects current. In 1.2 (a), current decay is slow due to a short circuit during PWM off time in Q2 operation, while in 1.2 (b), current decay is fast due to the application of reverse voltage to the winding during PWM off time in Q4 operation.
Since motor speed is roughly proportional to the terminal voltage of the motor, variable-speed operation is possible by changing the terminal voltage via controlling the duty cycle of the PWM. In order to control speed accurately, a closed-loop control may be used where commanded speed is compared with the measured actual speed and the motor is driven by the speed error signal. Without closed-loop control (open-loop drive), motor speed may vary depending on the load, supply voltage, etc.
Commutation, PWM, and Current Control
Dr. Dal Ohm has spent most of his career in applied R&D and product development of diverse a.c. and d.c. motor drives, servo systems, and power electronics. Prior to his full-time consulting at Drivetech, he was with Kollmorgen Motion Technologies Group as technical director, R&D. He received Ph.D. and M.S. degrees in Electrical Engineering from Texas A&M University. If you would like more information on this paper or would like to contact Dr. Ohm, please e-mail firstname.lastname@example.org.
One of the simplest methods of commutating three-phase brushless motors is the six-step drive. In this method, each phase voltage is energized for 120-degree intervals according to its rotor angle. This may be realized by the switch configuration. Each phase voltage is positive when the top switch is on and the bottom switch is off. No voltage is injected when both switches are off, in which case the actual terminal voltage is governed by the motor back electro-motive force (emf) voltage. In other words, each phase voltage at a time takes one of three states—positive, negative, or float.
At every sector, only one phase is energized as positive and one of the other phases is energized as negative to maintain the current path. In order to commutate properly, the controller needs to know the sector (60-degree interval) position of the shaft angle. Three Hall sensor outputs are often used to detect the shaft position. One advantage of this relation is that during the Hall sensor alignment procedure, the engineer can align the Hall sensor board so that each Hall output is in phase with the corresponding back emf (line-to-line) waveform when the rotor is rotated by an external means.
When the output voltage should also be controlled, in addition to commutation, PWM control may either be applied to both sides or lower side switches only. When PWM is applied only to the low side switches (Q2, Q4, and Q6), a short-circuited current path is established through one of the free-wheeling diodes of the upper switches during PWM off time. For instance, assume that switches Q1 and Q4 are turned on for commutation, and the current is established through A and B winding. While Q4 is performing the PWM, the current path is still established through Q1 to the A winding then to the B winding, and while Q4 is briefly off, the current moves through D3 path (see Figure 1.1). Since this configuration cannot control the current at fast torque reversal, it is only used when the directions of torque and speed are identical (1-quadrant or 2-quadrant operation).
When PWM is applied on both upper and lower side switches, current decay during PWM off times are quicker. In the previous example, since both Q1 and Q4 are controlled by PWM, negative bus voltage is applied through D2, A winding, C winding, and D3 when both Q1 and Q4 are briefly off. This condition is similar to when a reverse bus voltage is applied to the winding, and the current decays fast. A full 4-quadrant operation is possible at this configuration, where the directions of torque and speed are arbitrary (see Figure 1.2). This configuration is preferred when fast speed reversal is required, such as in a servo application.
Note that there are additional penalties in applying the 4-quandrant switching, in addition to higher PWM switching loss. First, the fast decaying current must flow through the bus capacitance, and one should select the capacitor with higher capacitance and higher ripple current rating. Second, during fast torque reversal condition, there might be a chance of shoot-through—a short-circuited condition when both upper and lower switches are both turned on during switching transition. Therefore, turn-on dead-time of several microseconds has to be applied for safe operation. In 2-quadrant switching, dead-time is normally not necessary. Several other 4-quadrant PWM schemes are possible and are discussed in previous works .
When the brushless motor is operated from a six-step voltage source drive, permanent magnet d.c. motor equations of Eq. 2.1, 2.2, and 2.3 are applicable.
V = R Ia + L dIa/dt + Ke (2.1)
T = Kt Ia (2.2)
T - Tload = J d/dt + B (2.3)
In the above equation, applied voltage V produces armature current Ia, resulting in torque T. The produced torque, then, starts to accelerate the motor to a speed , where the above three equations are satisfied in steady-state (dIa/dt = 0 and d/dt = 0). Constants R (armature resistance), L (armature inductance), Kt (torque constant), and Ke (voltage constant) are determined by motor design while J (rotor and load inertia) and B (viscous friction) are system constants.
Unlike the six-step mode operation in which only one upper and one lower switch are turned on at a time, the square-wave mode operation allows more than two switches to be on at a time. In fact, each phase voltage is either positive or negative, without allowing floating condition, except during a brief moment of switching to eliminate shoot-through condition. Although this square-wave mode operation is not popular in practice, it is the basis of the sinusoidal and the space vector PWM operation [2, 3].
When the motor is controlled by a voltage source, the armature current is solely determined by Eq. 2.1, and over-current situation may occur. In order to protect motors and drives from a destructive over-current, it is common to limit the maximum allowable current. In addition, wanting to regulate torque (current) or shorten dynamic response time, motor current may be regulated. In either case, one needs to measure the current.
Although measurements of all three-phase currents are ideal, in many applications, it is too costly to be justified. One of the simplest methods of measuring current is inserting a low value resistor (Rs) in the d.c. link path. This method is very economical up to about 20 A and does not require isolation in most cases. When operated by 2-quadrant switching, positive current is detected during the PWM “on” period and can be used to limit the current by turning PWM off as soon as current limit is detected. For 4-quadrant switching, positive current is detected during the PWM “on” period, while the negative state of one of the phase current is detected during the PWM “off” period. Therefore, an absolute value circuit is normally necessary to limit or regulate the current in this case. An alternative method is to capture the current only during the PWM “on” time using digital drives with A/D converters.
This is an edited version of a paper that was presented at the Electrical Manufacturing Conference, owned by the Electrical Manufacturing & Coil Winding Association, Inc.
 D. Y. Ohm and R. J. Oleksuk, “Influence of PWM Schemes and
Commutation Methods for DC and Brushless Motors and Drives,”
P.E. Technology 2002 Conference, Stephens Convention Center
(Rosemont, IL, U.S.), Oct. 27-31, 2002.
 Dal Y. Ohm, “The Basics of Brushless Motor Drive Design,”
Proceedings of Electrical Manufacturing Expo 04, Indiannapolis,
IN, U.S., Sept. 20-22, 2004.
 D. Y. Ohm and J. H. Park, “About Commutation and Current
Control Methods for Brushless Motors,” 28th Annual Symposium
on Incremental Motion Control Systems and Devices, San Jose,
CA, U.S., July 26-29, 1999.