Electrical Control
Resume:
The Dynamic Simulation of the Three-Phase Brushless Permanent
Magnet AC Motor Drives Using Lab View
Sangam Singh
Dept. of Electrical & Electronics Engineering, SRM University, Chennai, India
E-mail : *****.******@*****.***
Abstract - In this paper, a mathematical model of the three-phase brushless permanent magnet AC motor drives in abc reference
frame is described. A computer simulation of the motor drive is provided which utilized Lab VIEW software. The simulation can be
conveniently used to study the dynamic as well as the Steady-state performance of the three-phase permanent magnet AC motor
drives; with either trapezoidal or sinusoidal back emfs, under various operating conditions. The simulation results have been given in
this paper.
Index Terms: Permanent Magnet AC motor drives, Brushless Trapezoidal Permanent Magnet Motor, Brushless Sinusoidal
Permanent Magnet motor, Lab VIEW,Virtual Instruments.
sinusoidal or rectangular excitation currents
I. INTRODUCTION
respectively. Any deviation from these ideal current
There is a requirement to increase the efficiency of
excitations produces torque pulsations. Computer
AC industrial drives, small or large scale, due to the
simulation is a very useful technique to analyze the
increased awareness about the energy conservation
behavior of the motor drive without implementation of
world-wide. The recent advancements about the
the hardware. In addition to this, the drive simulations
permanent magnet materials, the switching power
can easily be forced to operation under the extreme
devices and the microelectronic technology have greatly
conditions without the fair of damaging the motor drive
contributed to the new energy efficient and high
as in the practical systems.
performance electrical drives, such as Brushless
permanent Magnet AC (PMAC) motor drives. These Although there have been many simulation studies
motors have higher efficiency and higher power factor, in the literature to predict the behavior of the Brushless
and their output power per mass and volume are much PMAC motors, not many studies are user friendly and
greater than their counterparts. Furthermore, they have produce accurate results that can imitate the real drives.
superior dynamic performance, which make them In this paper, the Lab VIEW (Laboratory Virtual
suitable for high performance motor drives . Instrument Engineering Workbench) software is used as
a graphical programming language. In comparison with
Depending upon the stator winding arrangement
the other software tools, the simulation with Lab VIEW
and the shape and the location of the permanent magnets
provides easy debugging features and user-friendly
on the rotor, the motors can be broadly classified into
environment. The main objective of this work is to
two groups. The first group possesses trapezoidal back
create a general Simulation tool for both types of the
emfs and is called Brushless Trapezoidal Permanent
PMAC motors, which can be utilized to study the
Magnet (BTPM) Motor, which is also known as
dynamic as well as the steady-state performance under
Brushless DC Motor. The second type possesses
the various excitation modes and the load conditions.
sinusoidal back emfs and is called Brushless Sinusoidal
Permanent Magnet (BSPM) motor.
II. THE MOTOR DRIVE MODEL
Since BSPM employs a sinusoidal variable
In order to obtain a general dynamic model for the
frequency PWM inverter as a power supply, the motor is
BSTM and BTPM motors, the three-phase abc modeling
also called Brushless Permanent Magnet Synchronous
approach is used in this paper. Since the rotor of a
Motor. The principal differences between the two types
PMAC motor has high receptivity, the effects of the
of motors are the accuracy of the rotor position sensor
stator currents on the total flux distribution may be
and their respective control requirements. In order to
ignored under the normal operating conditions.
produce constant electromagnetic torque, they require
Therefore, a network consisting of a winding resistance,
International Journal of Mechanical and Industrial Engineering (IJMIE), ISSN No. 2231 6477, Volume-1, Issue-2, 2011
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The Dynamic Simulation of the Three-Phase Brushless Permanent Magnet AC Motor Drives Using Lab View
an equivalent winding inductance, can model the three- practical back emf waveforms are always deviate from
phase star-connected PMAC motor and a back emf these ideal assumptions. In these cases, the back emf
source per phase, all connected in series. In this work, it waveforms may be modeled by using a look-up table or
is assumed that the stator resistances of all the windings multiple harmonic components of the real waveform.
are equal and the self and the mutual Inductances are
In Eqns. 4 and 5, Em is the maximum value of the
constant. Therefore, the voltage equations in the matrix
back emfs that can be given by
form of a three-phase PMAC motor are expressed as:
Where ke is the back emf constant, and e is electrical
rotor position that is given by:
Here V1, V2, and V3 are the phase voltages; R is the
winding resistance; i1, i2, and i3 are the line currents; L is Here r is the mechanical rotor position and p is the
the equivalent winding inductance; and e1, e2, and e3 are number of pole pairs of the motor.
the back emfs of the phases.
Generally, three-phase brushless PM motors are
In the PMAC motors, because of the large air gap powered from the three-phase inverters. Therefore, to
between stator and rotor, the saturation is neglected. obtain a complete drive simulation, the inverter should
Therefore, the flux linkages become a linear function of also be modeled.
the phase currents, and hence the electromagnetic torque
The inverter that is controlled by the switching
is given by:
signal provides the desired terminal voltage to each
phase winding of the motor. In practical motor drives,
the Motor is normally connected the star, and the star
point is normally left floating (which means that the star
point is not linked to anywhere in the power circuit).
Here is the angular speed of the rotor.
Therefore, due to the inverter switching the star
However, in order to study the transient behavior of
point Voltage varies and the effective winding voltage
the PMAC motors, the mechanical state equation must
depends on the star-point voltage, which should also be
be also known, that is given as
determined in the simulation. Due to the symmetry in
the motor windings, only one of the phase (Phase 1)
voltages is analysed below, which can be repeated for
the other two phases. If Va is the terminal voltage of the
Here Tl is the load torque; J is the inertia of the motor and Vs is the floating star-point voltage of the
motor and the connected load. motor, both relative to the mid point of the DC link
voltage of the inverter, the phase voltage V1 can be
As mentioned earlier the two groups of motors (BTPM
given as
and BSPM) posses different back emf waveforms.
If the stator windings of the three-phase motor are
symmetrically displaced, the ideal back emf equations
of the BSPM motor can be given by
The terminal voltage Va is determined by the
switching states of the phase, which can be either Vdc/2.
For the star-connected PMAC motor, it is always true
For the BTPM motors, however, the back emf that the summation of the line currents equals to zero.
Waveform of one phase is given in piecewise linear Therefore, when all three phases conduct current, the
form as: floating star-point voltage of the motor can be easily
derived from the three-voltage equation that is given in
Note that Eq. 5 should be repeated to define the
Eq.1.
other two phases of the motor simply by shifting 120
degree electrical. Moreover, please remember that the
International Journal of Electronics Signals and Systems (IJESS), ISSN:2231- 5969, Volume-1, Issue-2, 2011
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The Dynamic Simulation of the Three-Phase Brushless Permanent Magnet AC Motor Drives Using Lab View
Similarly, if only two of the phases (say Phase 1 and 2) the other sub-VIs in the program. One of the inputs is
are conducting currents, the floating star-point voltage the array of the inputs for the switching signals, which
of the motor can be derived as are used to link the control signals of the power devices
in the inverter. The parameters of the motor and the
calculation interval are the other two inputs in the sub-
VI. In order to set the initial values at the top-level VI,
the final step values of the currents and the rotor
position also provided as the inputs to the "motor" sub-
The Table 1 summarizes the estimated star point and
VI. An input signal named "mode" is defined to select a
phase voltage values of the inverter driven motors [2, 3],
BTPM or a BSPM motor to be simulated. The outputs of
which are also used in the simulation model of the
the "motor" sub-VI include the line currents, the phase
motor drive.
voltages, the torque and the rotor position. Similar to the
TABLE 1 practical motor drive system, the" control" sub-VI is
implemented as the current controller of the motor.
The summary of the star point and the phase voltages
From the control point of view, both the BSPM and
BTPM motors can accommodate the identical current
controller. The only difference is that they need either
sinusoidal or rectangular current reference signals
respectively. Therefore, the first function of the
"control" sub-VI is to generate the three-phase current
reference signals. The reference current waveforms can
be either as ideal sine waves or as piecewise rectangular
waveforms, which can be expressed per phase as shown
below.
III. THE VIRTUAL INSTRUMENT OF THE
DRIVE
The programs in Lab VIEW applications are called
Virtual Instruments (VI). Similar to a subroutine used in
the C language, any VI in Lab VIEW can be used as a
sub-VI in the block diagram (where the programming is
done) of a high-level VI. The sub-VIs can also be called
from the inside of another sub-VI, and there is no limit
Here Im is the amplitude of the stator current
to the number of sub-VI used in Lab VIEW. This
command. As stated previously, because of the three-
hierarchical nature provides a very flexible and powerful
phase symmetry, only one phase of the current reference
programming environment. A number of sub-VIs is
signal is given above. The other two phases can be
implemented in this study. The VI named "motor" is
obtained by shifting Eqns.11and12, 120degree electrical
based on the motor's functions that are summarized in
angle. Although there are various current control
the previous sections. The "motor" sub-VI consists of
schemes used in practice, which force the actual current
four-computation subsection. The first section calculates
to follow the reference signal, only two of the
the electrical rotor position according to the Equation.7.
commonly used schemes are implemented here: the
The second section produces the back emfs by using the
Hysteresis Current Controller and the PWM Current
Equation.4 or 5. The three phase voltages are estimated
Controller. The "control" sub-VI also contains the
in the third section based on the formulas given in Table
Hysteresis Current Controller and the PWM Current
1. Finally, the section four solves the differential
Controller, which to produce the switching signals
equations (Equation.1) and computes the
required by the "motor" sub-VI.
electromagnetic torque of the motor (Equation.2).
The "control" sub-VI has six inputs and one output.
The "motor" sub-VI is customized and six inputs
The rotor position and the amplitude value of the current
and four outputs are defined, which are used to link to
command are the two inputs that are used to generate
International Journal of Electronics Signals and Systems (IJESS), ISSN:2231- 5969, Volume-1, Issue-2, 2011
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The Dynamic Simulation of the Three-Phase Brushless Permanent Magnet AC Motor Drives Using Lab View
the reference current signals. The line current inputs are All of the above mentioned three sub-VIs are linked
used as the current feedback signals (which simulate the to obtain a closed loop drive VI for the PMAC motors
current transducers in practice) for the controller. The (Figure. 2). This final VI can be used to study the
parameters of the controller and the calculation interval various operating modes of the PMAC motor drives as
are two other inputs. In order to distinguish the motor mentioned previously.
and controller types, two "mode" input signals are also
implemented. IV. SIMULATION RESULTS
Figure. 1 shows the block diagram of the VI that can The simulation results presented in this paper have
be used to simulate the steady-state operation of the been specifically chosen to demonstrate some of the
PMAC motor drives. There are four "waveform graphs" typical operations that occur in the operation of the
in this block diagram, which display the line currents, motors. The results provide a confirmation of the
the phase voltages, the electromagnetic torque Per-phase validity of the current, the voltage, and the torque
or all three phase currents and voltages can be displayed estimation of the drive in both the steady state and the
in the graph. transient operation.. The below motor parameters are
used to simulate both the BTPM and BSPM motor
drives in this paper.
The test motor name plate data and measured
parameters:
Torque constant, Kt = 0.310 Nm/A
Back emf constant, ke = 0.417 V/rad/s
Moment of inertia, J = 0.0008 kgm2
Number of poles P=8
Winding resistance, R = 0.8 W
Equivalent winding
In order to simulate the transient performance of the
Inductance, L= 3.12 mH
motor drive while maintaining the simplicity, the VI
shown in Figure.1 is integrated into the "drive" sub-VI Firstly, the "drive" VI was used to simulate the
that has five inputs and three outputs. The inputs are the steady-state operation of the motor. To obtain the
current command, the angular speed, the rotor position, simulation results, the parameters of the drive must be
the currents and the calculation interval. The outputs set on the Front Panel (the user interface) of the VI. The
include the torque, the rotor position and the currents. input parameters are classified into three groups.
The inputs and outputs of rotor position and currents are The first group is the motor parameters, which
used to set the initial values. Furthermore, two include the number of pole pairs, the winding resistance
additional sub-VIs are built to solve the mechanical R, the equivalent winding inductance L, the back EMF
equation (Equation.3) and to simulate a PI speed constant ke, and the DC link voltage of the inverter. The
regulator. second group contains the current controller's
parameters, which are the modulation frequency of the
PWM Current Controller, the hysteresis bandwidth of
the Hysteresis Current Controller and the phase
advance/delay angle of the current command. The third
group is called the "mode" parameters, which are used
to select the type of the back emf (trapezoidal or
sinusoidal), the wave shape of the reference current
(rectangular or sinusoidal), and finally the type of the
current controller (hysteresis or PWM). In addition to
the above parameters, the reference speed, reference
current and integration time step are set on the Front
Panel of the VI.
Figure. 3 shows the simulated results under the steady
state operating condition of the test motor. Phase1
International Journal of Electronics Signals and Systems (IJESS), ISSN:2231- 5969, Volume-1, Issue-2, 2011
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The Dynamic Simulation of the Three-Phase Brushless Permanent Magnet AC Motor Drives Using Lab View
voltage, Line 1 current and the total electromagnetic bandwidth of 0.2A, Im(ref) = 5A, no phase advance or
torque of the BTPM motor. delay angle
Figure. 4 shows the simulated results under the
steady state operating condition of the test motor.
Phase1 voltage, Line 1 current and the total
electromagnetic torque of the BSPM motor
Figure 3: The simulated waveforms under the steady-
Figure 5: The simulated waveforms under steady-state
state operations of the BTPM motor: 500 rpm, Vdc = 50
operation for the similar settings for BTPM motor as in
V, Hysteresis Current Controller with a bandwidth of
Fig. 3 but without the current control.
0.2A, Im(ref) = 5A, no phase advance or delay angle.
Figure 6: The simulated waveforms under steady-state
Figure 4: The simulated waveforms under the operation for the similar settings for BSPM motor as in
steady-state operations of the BSPM motor: 500 rpm, Fig. 4 but without the current control.
Vdc = 50 V, Hysteresis Current Controller with a
International Journal of Electronics Signals and Systems (IJESS), ISSN:2231- 5969, Volume-1, Issue-2, 2011
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The Dynamic Simulation of the Three-Phase Brushless Permanent Magnet AC Motor Drives Using Lab View
Figure 8: The simulated waveforms under the transient
operation of the BSPM motor drives, Vdc = 56 V
Figure.7 &8 illustrates the results obtained under
the transient operation of the motor drives. In this test,
the motor accelerates from standstill up to the constant
speed of 500 rpm. In this mode of operation, since the
current demand was set to a maximum, and DC link
voltage was kept constant, after starting of the motor,
the current profile reduces as the speed increases.
V. CONCLUSIONS
The paper demonstrated that the complex drive
structure that exist in the BTPM and BSPM motor
drives can be simplified by using the graphical
programming language Lab VIEW. The simulation
structure in Lab VIEW provides easy debagging and a
very friendly user interface. The simulation tool can
work under the steady state as well as the dynamic
operating conditions and can provide an accurate
analysis tool for the brushless PMAC motor drives. In
addition, the simulation tool can be used to study further
control and parameter estimation Concepts in the motor
drives.
Figure 7: The simulated waveforms under the transient REFERENCES
operation of the BTPM motor drives, Vdc = 56 V
[1] Jacek F. and Mitchell W., "Permanent Magnet
Motor Technology," Marcel Dekker, Inc., New
York, 1997.
[2] Ertugrul N.,"Position Estimation and
Performance Prediction for Permanent-Magnet
Motor Drives, Ph.D. Thesis, University of
Newcastle upon Tyne, UK, 1993.
[3] Ertugrul N., Eric Chong, "Modeling and
Simulation of an Axial Field Brushless
Permanent Magnet Motor Drive, " European
Power Electrical Conference, Trondheim,
Norway, 1997.
[4] Azizur M. R. and Ping Z., "Analysis of Brushless
Permanent Magnet Synchronous Motor, IEEE
Transactions on Industrial Electronics, Vol.
43,No.2, April 1996.
[5] Lab VIEW Tutorial Manual, National
Instruments 1996.
[6] T.M. Jahns, Torque production in permanent
magnet synchronous motor drives with
rectangular current excitation, EEE
Trans.Industry Application, Vol. 20, No. 4,
July/Aug., 1984, pp. 803-813.
[7] G.R. Slemon, Achieving a constant power speed
range for PM drives, IEEE Trans. on Industry
International Journal of Electronics Signals and Systems (IJESS), ISSN:2231- 5969, Volume-1, Issue-2, 2011
62
The Dynamic Simulation of the Three-Phase Brushless Permanent Magnet AC Motor Drives Using Lab View
Applications, Vol. 31, No. 2, pp.368-372, March [10] K.i. Korzine, S. D. Sudhoff, and H.J. Hegner,
April 1995. Analysis of a current regulated Brushless DC
drive, IEEE Trans. Energy Conversion, Vol. 10
[8] S.D. Sudhoff, E.L. Zivi, and T.D. Collins, Start
No. 3, Sept. 1995, pp. 438-445.
up performance offload-commutated inverter-fed
synchronous machine drives, IEEETrans. [11] ]illay, R.Krishnan, Modeling,simulation, and
Energy Conversion, Vol. 10, No. 2, June 1995, analysis of Permanent-magnet motor drives, Part
pp. 268-274. II; The brushless DC motor drive, IEEE Trans.
Industry Applications, Vol. 25,No. 2,Marc April
[9] S.D. Sudhoff, K.A. Corzine, and H.J. Hegner, A
1989, pp.274-279.
flux-weakening Strategy for current-regulated
surface mounted permanent-magnet machine [12] B.R. Pelly, Thyristor phase controlled converters
drives, IEEE Trans. Energy Conversion, Vol. and cycloconverters,Wiely Interscience, 1971.
10, No. 3,Seut. 1995. DD. 431-437.
International Journal of Electronics Signals and Systems (IJESS), ISSN:2231- 5969, Volume-1, Issue-2, 2011
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