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© 2009 Microchip Technology Inc. DS01299A-page 1
AN1299
INTRODUCTION
A large number of motor control applications are
consistently and continuously looking for methods to
improve efficiency while reducing system cost. These
are the two main factors that are driving the efforts to
improve existing motor control techniques, such as
trapezoidal control, scalar control and Field-Oriented
Control (FOC).
FOC has become more popular in recent years due to
the fact that the cost required to implement this
technique is no longer a constraint. The available
technology and manufacturing process now make it
possible to implement this control technique in a 16-bit
fixed-point machine such as the dsPIC
®
Digital Signal
Controller (DSC).
Efficiency is another reason that has allowed FOC to
gain ground over scalar and trapezoidal control
techniques on low-cost and mid-cost applications. It is
also well suited in applications in which hard
requirements are low noise, low torque ripple and good
torque control over a vast speed range.
Field-oriented control can be implemented using
position sensors such as encoders, resolvers or Hall
sensors. However, not all motor control applications
require such granularity given by a resolver or encoder;
and, in many cases, they do not require control at zero
speed.
These applications are a perfect target for using
sensorless techniques in which the motor position can
be estimated using the information provided by the
currents flowing through the motor coils. There are two
popular approaches to this sensing technique: the
dual-shunt resistor and the single-shunt resistor.
The dual-shunt resistor technique utilizes the
information contained in the current flowing through
two motor coils in order to estimate the motor position.
The single-shunt resistor technique utilizes only the
information contained in the current flowing through the
DC bus to reconstruct the three-phase currents, and
then estimate motor position.
In this application note, the single-shunt approach is
discussed. For information on the dual-shunt resistor
approach, please refer to the application note, AN1078
“Sensorless Field Oriented Control of PMSM Motors”.
CURRENT MEASUREMENT
The information contained in the current flowing
through the motor coils allows a motor control algorithm
to operate the motor in a region where the motor
produces the maximum torque, or to operate the motor
at certain performance, or even to be able to
approximate or estimate internal motor variables such
as position.
Three-phase AC Induction Motors (ACIMs),
Permanent Magnet Synchronous Motors (PMSMs) and
Brushless Direct Current (BLDC) motors in particular
use a three-phase inverter as the topology of
preference. This topology, which is shown in Figure 1,
allows individual control of the energy applied to each
coil, which enables the motor to be efficiently operated.
FIGURE 1: THREE-PHASE INVERTER TOPOLOGY
Authors: Daniel Torres and Jorge Zambada
Microchip Technology Inc.
3-Phase
InverterRectifier
DC Bus
Three-Phase AC
Motor
Single-Shunt Three-Phase Current Reconstruction
Algorithm for Sensorless FOC of a PMSM
AN1299
DS01299A-page 2 © 2009 Microchip Technology Inc.
The three-phase inverter is compounded by three legs.
Each leg contains two electronic switches that are
arranged in such a way that create a half-bridge
topology. Therefore, current can flow in both directions
to and from the legs. The electronic switches can be
either power MOSFETs or IGBTs.
Current MOSFET and IGBT manufacturing
technologies have allowed digital controllers to take
advantage of Pulse-Width Modulation (PWM)
techniques to control the amount of energy applied to
each coil.
The most common techniques used are sinusoidal
modulation, third-harmonic modulation and Space
Vector Modulation (SVM). These PWM techniques are
suitable to operate the electronic switches in saturation
mode, which helps to increase system efficiency.
In order to determine the amount of current flowing
through the coils, a shunt resistor is required on each
coil. A typical three-phase inverter with current
measurement on three phases is shown in Figure 2.
FIGURE 2: CIRCUIT FOR MEASURING
CURRENT IN THREE
PHASES
Assuming there is a balanced load, we can consider
that the sum of the three phases is equal to zero, as
described by Kirchhoff’s Current Law. This law is
shown in Equation 1.
EQUATION 1: KIRCHHOFF’S CURRENT
LAW
Therefore, by measuring only two, the third can be
solved using Equation 1. A simplified version using two
shunt resistors is shown in Figure 3.
FIGURE 3: CIRCUIT FOR MEASURING
CURRENT IN TWO PHASES
The intention of the algorithm presented in this
application note is to be able to measure all three
phases with a single-shunt resistor and a single
differential amplifier. A circuit showing a single-shunt
resistor is shown in Figure 4.
FIGURE 4: CIRCUIT FOR MEASURING
CURRENT FLOWING
THROUGH DC BUS
VBUS
3 ~
I
C
IB
IA
IA + IB + IC = 0
VBUS
3 ~
I
B
IA
IC = -IB -IA
VBUS
3 ~
IBUS
© 2009 Microchip Technology Inc. DS01299A-page 3
AN1299
ADVANTAGES AND
DISADVANTAGES OF USING A
SINGLE-SHUNT RESISTOR
Advantages
As previously mentioned, one of most important
reasons for single-shunt three-phase reconstruction is
cost reduction. Which in turn, simplifies the sampling
circuit to one shunt resistor and one differential
amplifier.
In addition to cost reduction benefits, the single-shunt
algorithm allows the use of power modules that do not
provide individual ground connection of each phase.
Another benefit of single-shunt measurement is that
the same circuit is being used to sense all three
phases. Gains and offset will be the same for all
measurements, which eliminates the need to calibrate
each phase amplification circuit or compensate in
software.
Disadvantages
During single-shunt measurements, a modification on
the sinusoidal-modulation pattern needs to be made in
order to allow current to be measured. This pattern
modification could generate some current ripple. Due
to modification of patterns and correction of the same
modifications, more CPU is used to implement this
algorithm.
IMPLEMENTATION DETAILS
In order to drive the motor with AC signals, PWM
methods are used to drive the switching transistors
shown in the three-phase inverter. This modulation and
resulting modulated waveform are shown in Figure 5.
A sinusoidal waveform can be generated by loading a
series of duty cycle values into the PWM generator
module. The values in the lookup table represent a
modulated sine wave, so once these duty cycles are
fed into the motor windings through the inverter, the
motor windings will filter the switching pattern. The
resulting sine wave is shown Figure 5.
The downside of a lookup table with sine values is the
maximum value that can be achieved. This value is
limited to 86% of the input voltage. Another sinusoidal
modulation method is Space Vector Modulation, which
is used to overcome this limitation. SVM allows 100%
utilization of input voltage. SVM is described and used
in several application notes such as AN908 “Using the
dsPIC30F for Vector Control of an ACIM” and AN1017
“Sinusoidal Control of PMSM Motors with dsPIC30F
DSC”. The typical voltage shape generated using SVM
is shown in Figure 6.
FIGURE 5: SINUSOIDAL MODULATION
AN1299
DS01299A-page 4 © 2009 Microchip Technology Inc.
FIGURE 6: SPACE VECTOR MODULATION (SVM)
When calculating the resulting voltage from line-to-line,
we get three sinusoidal waveforms phase shifted 120°,
as shown in Figure 7.
FIGURE 7: CALCULATED LINE-TO-LINE VOLTAGE
PWM1
PWM2
PWM3
100%
50%
0%
II I III IV V VI
SVM
Sector
VA - VB
VB -VC
VC - VA
+VBUS
0V
-V
BUS
II I III IV V VI
SVM
Sector
© 2009 Microchip Technology Inc. DS01299A-page 5
AN1299
SVM and Current Measurement
Relationship
When measuring current through a single-shunt
resistor, the state of the bottom switches is critical. To
show this, Sector I of SVM is magnified in Figure 8. In
addition, PWM waveforms on each switching transistor
are also shown.
To observe the relationship between PWM modulation
and current measurement through a single-shunt
resistor, let us consider PWM Cycle 2 as an example.
Since we are only interested in the low-side switch
PWM, we will only show the PWMxL components of the
PWM (Figure 9).
FIGURE 8: PWM SIGNALS ON SWITCHING TRANSISTORS IN SECTOR I
FIGURE 9: SAMPLING TIME WINDOWS FOR MEASURING CURRENT
100%
50%
0%
PWM1
PWM2
PWM3
PWM1H
PWM1L
PWM2H
PWM2L
PWM3H
PWM3L
PWM
CYCLE
12 5634 78
PWM1L
PWM2L
PWM3L
T0 T1 T2 T3 T2 T1 T0
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