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 Total Downloads : 1153
 Authors : Jyoti Agrawal, Sanjay Bodkhe
 Paper ID : IJERTV3IS031945
 Volume & Issue : Volume 03, Issue 03 (March 2014)
 Published (First Online): 31032014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Modeling and Simulation of a Torque Controlled Permanent Magnet Synchronous Motor Drive
Jyoti Agrawal
Department of Electrical Engineering
G. H. Raisoni College of Engineering Nagpur, India
Sanjay Bodkhe
Department of Electrical Engineering
Shri Ramdeobaba College of Engineering & Management Nagpur, India
AbstractThis paper presents the detailed modeling and simulation of a permanent magnet synchronous Motor (PMSM) drive system. The torque control of PMSM is achieved with the help of vector control, which is the widely accepted method. It provides independent control of torque and mutual flux. The
vrds, vrqs d and qaxes stator voltages in rotor reference frame, (V)
vao, vbo, vco inverter midpole voltages, (V)
vas, vbs, vcs input phase voltages, (V)
ds, qs d and qaxes stator flux linkages, (Wb)
switching signals for inverter are generated by two techniques to
test their effect for superior performance of the drive. They are
af
armature flux linkages, (Wb)
hysteresis and sinusoidal pulse widthmodulation (PWM) with current control. The response of the two drives are studied by simulation and evaluated based upon the magnitude of current
*m reference mutual air gap flux linkages, (Vs)
p differential operator, d/dt
r rotor position, (radians)
s
ripples and torque pulsation. Also the effect on Total harmonic *
r
distortion (THD) which is a measurement of harmonic *
stator current command phase angle, (rad) speed reference, (rad/s)
distortion or harmonic components of a distorted waveform is
investigated. The proposed drive is tested at various operating conditions to conclude the effect of different switching techniques on the drive system. The study is carried out with Matlab Simulink software.
KeywordsMathematical model; vector control; torque control; PMSM drive; MATLAB/Simulink.
NOMENCLATURE
B damping constant, (N/rad/s)
fc carrier frequency, (Hz)
H inertial constant in normalized unit, (p.u.)
ids, iqs d and qaxes stator currents in stator reference frame, (A)
r actual rotor speed, (rad/s)
torque angle, (rad)
* torque angle command, (rad)
i hysteresis current window, (A)

INTRODUCTION
Recently, an increased interest in application of permanent magnet synchronous motors (PMSM) in industry for industrial drive application has been observed due to numerous advantages [1][5]. Permanent magnet synchronous machine has overcome the limitations of synchronous motor by using the high energy permanent magnet like NeodymiumIronBoron (NdFeB) instead of electromagnets
irds,
irqs
d and qaxes stator currents in rotor reference frame,(A)
[4]. The use of permanent magnet has replaced the need ofslip rings required for field excitation which results in low maintenance and low losses in the rotor [2]. From literature, it
as, bs cs
i* i* , i* command stator phase currents, (A)
ias, ibs, ics instantaneous stator phase currents, (A)
i
s
* stator current reference, (A)
J total moment of inertia, (kgm2)
Ldd, Lqq stator d and qaxes selfinductances in stator reference frame, (H)
Ldq, Lqd mutual inductances between d and q axes windings, (H)
Ld, Lq stator d and qaxes selfinductances in rotor reference frame, (H)
P number of poles
Rd, Rq stator d and qaxes winding resistances, ()
Rs stator resistance per phase, ()
Tb base torque, (Nm)
Te electromagnetic torque, (Nm)
Te* torque reference, (Nm)
Tl load torque, (Nm)
vds, vqs d and qaxes stator voltages in stator reference frame, (V)
is apparent that for operation of PMSM under closed loop there exist different techniques [2], [6][9]. For proper operation of a PMSM it is necessary to determine the exact rotor position. Commonly, a position sensor, such as optical encoder, Hall Effect sensor or resolver, is fitted to for sensing the rotor position [1]. The vector control of PM motors is much simpler than that of induction motors (IM) because there is no need to consider the slip frequency as in IM drive [7]. This paper describes a simple torque control method for a PMSM drive that provides a highperformance vector control. By using the proposed model, pulse widthmodulated (PWM) current controlled inverter fed PMSM torque drive is simulated in Matlab Simulink environment and the results are then compared with those obtained by using hysteresis current controlled inverter fed PMSM torque drive. In the torque control scheme, three phase currents are regulated by using hysteresis/PWM current controllers, which operate in the rotor reference frame. Before switching the inverter, the modified current errors are transformed to the stator phase currents by inverse Park transformation using measured rotor
position from an encoder [4]. Torque controlled drive system utilizes PMSM model to predict the voltage required for achieving a desired output torque. The dynamic model of PMSM can be derived to evaluate the instantaneous effects of varying current, voltage, stator frequencies and torque disturbance on the performance of machine and drive system [3]. It has been seen from most of the earlier research works that the concept of switching function is a powerful tool which helps in understanding and optimizing the performance of the static power converters/inverters [10, 11]. In this paper a functional simulation model for the voltage source inverter (VSI) fed PMSM using the switching function concept is studied and implemented in Matlab Simulink. The desired
[4]. The model developed for the PMSM drive is using the following assumptions [14].
The saturation effect and changes in parameters are neglected.

The inductance versus rotor position is sinusoidal.

The stator windings are balanced with sinusoidally distributed magnetomotive force.

Windage, friction and drive losses are ignored.
With the above assumptions, the d and qaxes stator voltages in rotor reference frame are:
performance is achieved by implementing vector control
vr
Rs + Lq p
r Ld
ir
technique (normally used in ac machines so as to provide
qs = qs
r af
decoupling between torque and flux producing components)
vr L R + L p ir
0
in Matlab/Simulink and tested under different operating conditions [8]. The main aim of this drive system is to have
ds r q s d
ds
torque control by controlling the torque angle () and the magnitude of current phasor (is) [3]. Due to the implementation of functional modeling, the developed models have various advantages [11].
The torque controlled PMSM drive system is tested under different operating conditions such as load torque disturbance, speed reversal, reduction in torque ripple, varying switching frequency, change in hysteresis current window and change in PWM carrier frequency etc. and the
From (1), it is observed that the voltage equations are equal to the product of the impedance matrix and the current vector, plus an additional component due to the motional emf of the rotor flux linkages. Electromagnetic torque is the most important variable as it determines the rotor position and speed. The expression for the electromagnetic torque developed by the machine can be expessed in d and q components of the currents as,
simulation results are presented. In addition to this study
3 P

r r
effects due to the use of (PWM) and hysteresis current
Te =
af Ld
Lq ids
iqs
controllers on the torque pulsation of motor and drive performance are also evaluated. The main drawback of torque controlled PMSM drive using inverter with hysteresis current control is fast sampling time required and variable switching frequency [12]. Hence, in order to eliminate above disadvantages a new developed control technique called
2 2
Equation (3) represents the electromechanical dynamic equation.
dm
torque control with PWM current control has been introduced [13].
Te = J
dt Tl Bm
This paper is divided into seven sections. Section 1 provides a general introduction and literature review of the PMSM. In section 2, the dynamic modeling of the PMSM is presented. Section 3 contains model of PMSM in the form of Simulink model. Section 4 contains a study of vector control
The stator phase voltages are obtained from (1) by using the inverse Park transformation as,
control strategy of PMSM. Section 5 presents a newly developed torque controlled PMSM drive in the form of
cos r
vas
v
sin r
2
2
1 vr
qs
Simulink model. Section 6 has the simulation results. Also, a
vbs cos r
sin r
1 vr
comparative evaluation of hysteresis and PWM current controller designs used in the proposed PMSM, based upon
cs
3
2
3 ds
2 v0
the magnitude of current ripple and the torque pulsation is
cos r sin r 1
presented in this section. The paper is concluded in section 7.
3
3
The proposed functional modeling of PMSM enables to have an insight into the behavioral characteristics of the machine under different operating conditions.
Similarly, the dqo currents are obtained from abc currents using Park transformation as,


DYNAMIC MODEL OF PMSM
cos
2
2
r r
cos r
3
cos r +
3
The detailed modeling of three phase PMSM drive system
iqs
ias
is required for proper simulation and analysis of the system.
r
2
2
The model of the PMSM is developed using a two phase
ids = sinr
sin r
3
sin r +
3 ibs
configuration along direct and quadrature axes. This provides
i 1
1 1
ics
simplicity of only one set of windings on the stator. The rotor has no windings but consists of permanent magnets only [3],
0
2 2 2
In a balanced threephase system, the sum of three phase currents is zero, leading to i0 of zero value. Hence, if any two phase currents are measured, the thirdphase current can be obtained by algebraic manipulation of the other twophase currents. This eliminates the need for additional current sensors.
In order to have a meaningful interpretation in the modeling, analysis and simulations, the power input to the three phase machine has to be equal to the power input to the two phase machine. From (1) and (3) the complete dynamic model of PMSM in rotor reference frame is derived and is expressed by (6).
and vector control [2]. The vector control method allows to change and control stator currents or voltage both in magnitude and phase at the same time which helps in achieving high dynamic performance. A proposed vector control scheme for PMSM is shown in Fig. 3. The first block is current and torque angle calculator, here in this block using Te* and *m, the i*s and * signals are calculated. The next block is the stator reference current synthesizer where reference current signals are generated by using Equations (12)(14). The rotor position is sensed by using a position transducer. On comparing the respective reference current to the actual phase current switching pattern for the power devices are produced [17]. The most popular vector control is known for decoupling as it allows independent control of
s d
R L
– Lq – Lq r
af 0
Lq
1 0 0
torque and mutual flux from each other [18]. Vector control to PMSM is normally used to get the control, in the same way
ir
ir L
r
as that of the separately excited dc motor, which has high
qs
Lq R
qs q
vqs
desirable controlcharacte ristics [18]. Thevector control can
r r – s
0 0 r
1
p ids Ld Ld
ids
0 0 vr
be implemented either by using Field Oriented Control (FOC)
L ds
r
af
L L ir
r
d T
or Direct Torque Control (DTC) [19]. By using (7), the
d q qs B 0
0 0
1
l
electromagnetic torque in PMSM can be expressed as,
r 2H
2H 2H
r
0 0 1 0
It gives the information of rotor position which is of crucial
e af is sin
Ld Lq is
sin 2
Equation (6) is used for the simulation of PMSM model.
importance in determining the current and voltage in each phase of the machine.

SIMULATION OF PMSM
The functional model of PMSM is built in several steps through the construction of d and qaxes stator currents in rotor reference frame, electromagnetic torque, rotor speed and rotor position.
T * = 3 P
2 2
* * 1
2
* 2 *

dq axis stator current in rotor reference frame
By using (6), the daxis and qaxis model is constructed as shown in Fig. 1 and Fig. 2 respectively.

Electromagnetic torque
The electromagnetic torque Te developed on the rotor can be obtained as given by (7). From (7), it is seen that the torque of PMSM can be calculated in terms of the estimated stator flux linkage and motor current [15].
Fig. 1. Simulink model for irds
3 P
r r
Fig. 2. Simulink model for irqs
2 2
Te =
Ld Lq ids af iqs

Rotor position
To implement vector controlled PMSM drive system the information of rotor position is necessary. The speed of the machine is maintained at a certain speed. By using (6) the rotor position (r) is calculated.


VECTOR CONTROL LED PMSM TORQUE DRIVE
Control of PMSM is based on the information of rotor position and speed which has been always a challenging task. The main problem lies in accurate and rapid estimation of rotor position [16]. Various types of closedloop control techniques are proposed and validated for PMSM, like scalar
Fig. 3. Proposed vector controlled PMSM drive
In (8) if is assumed to be zero, then the expression for torque of PMSM becomes similar to torque of separately excited dc machine. The magnitude of reference mutual flux linkage is given by (9).
the torque and mutual flux linkages directly. An inverse Park transformation is used which transforms the twophase signals into threephase which are then used as feedback as shown in the scheme. The reference torque angle () can be obtained from (8) and (11) assuming the machine parameters to be constants. Each functional block is elaborated in detail in the following sections.
* = L i* cos * L i* sin * 2
m af d s q s
The stator current phase angle command is obtained by summing the rotor position and torque angle as given by (10).

Current and torque angle Calculator
If the rotor has a surface mounted design (SMPMSM), where Ld = Lq, then the stator current reference obtained from the expression in (9) is given as
* = + *
* 2
2
* *
s
s r


IMPLEMENTATION OF VECTORCONTROLLED
i*
m
– – 2af is cos
af
Ld
PMSM TORQUE DRIVE
The vector controlled PMSM torque drive is implemented using the software Matlab/Simulink. By combining Fig. 1, 2 and Fig. 5 to Fig. 8 the complete torque drive for PMSM fed from Hysteresis/PWM current control inverter has been developed as shown in Fig. 4. It consists of five functional blocks. They are current and torque angle calculator, stator current synthesizer, inverter with hysteresis/PWM current control, PMSM model and signal conditioner. A PMSM drive with external inputs of torque and mutual flux linkages known as references are considered. The actual phase
This is shown in Fig. 5. The torque reference value of 5.5631 Nm and the flux linkage reference with 0.1546 Vs is put on the motor drive [14]. The process of obtaining current (i* ) and torque angle (*) by using (8) and (9) is the heart of vector controller [4, 14, 21].
s

Reference currents
The reference currents are generated by using (12)(14).
currents are firstly calculated based on the PMSM model and in the third functional block which is hysteresis/PWM current regulator, here the calculated phase currents are compared with the references. The outputs of the comparators are the switching signals which are used to select the appropriate stator voltage vector so as to minimize the current errors [11, 20].
The stator windings of the PMSM are fed by a PWM/Hysteresis current controlled inverter which controls
ias = issin rt +
i = i sin t + – 2
bs s r 3
i = i sin t + + 2
cs s r 3
Fig. 4. Block diagram of simulation model for inverter fed vectorcontrolled PMSM torque drive using hysteresis/PWM current control
s
Fig. 5. Current (i* ) and torque angle (*) calculator block

Current Controlled Inverter Model
Fig. 4 show that the PMSM is fed from a voltage source inverter with current control. A comparative study is carried out by using two different current controllers to generate gate
specified bands all the time. The hysteresis window i, can be set externally. In this controller the reference current of a respective phase is summed with the negative of the actual or measured current. The error thus obtained of respective phase is then fed to a comparator having a tolerance band around the reference current associated with that phase. The hysteresis current controller reacts instantaneously to changes in the current command; hence there is no delay [27]. The benefits of hysteresis current controllers are good accuracy, simple design and high robustness. The major drawback with this controller is that it does not have a fixed switching frequency as in PWM current control and varies continuously but it is related with the i. Simulink model is shown in Fig. 8.
and Hysteresis Current Controller. Proper selection of the
as as
ao 2
signals for the inverter i.e. Pulse Width Modulation (PWM)
inverter power devices (such as IGBT, MOSFET, GTO etc.)
and selection of the current control technique will guarantee
if i – i i,
else if i – i i,
set v
set v
= Vdc
= – Vdc
in improving the efficiency of the drive [20, 22].

Pulse Width Modulation Current Controller
Sinusoidal pulse width modulation (SPWM) is the most commonly used technique for controlling inverter output voltage and harmonic reduction. The Simulink model of SPWM current control strategy for phase a is shown in Fig. 6.
The functional model of a three phase PWM current controlled inverter is shown in Fig. 7. The error of the controlled signal is then compared against a common high frequency triangular carrier wave of desire switching frequency. The comparison will result in a pulse when the error signal is greater than the triangular wave which is then used to trigger the respective power devices [23]. The speed at which inverter switches are turned on and off depends on the switching frequency is usually fixed at carrier frequency (fc).
The output linetoline voltages can be defined by following equations
as as ao 2
Fig. 6. Simulink model of SPWM current control strategy for phase a
vab = vao – vbo ,
vbc = vbo – vco and vca = vco – vao
Fig. 7. Simulink model of PWM current controlled inverter
Assuming the system to be balanced the phase voltages are computed in terms of linetoline values with the help of (16) [2, 24, 25].
v = vab – vca , v
= vbc – vab and v
= vca – vbc
as 3
bs 3
cs 3
The threephase voltages of the inverter are converted to twophase by using Park transformation (refer (4) and (5)).

Hysteresis Current Controller
The basic implementation of hysteresis current control technique is based on deriving the switching patterns to the inverter from the comparison of the current error within a fixed hysteresis band [26]. The inverter midpole voltage is determined by the logic given in (17). The hysteresis current control keeps the actual value of the currents within the
Fig. 8. Simulink model of Hysteresis current controlled inverter


SIMULATION RESULTS AND DISCUSSION
To study the performance of torquecontrolled PMSM drive system using hysteresis/PWM current control the simulation model has been developed in MATLAB environment. The behavior of torquecontrolled system is analyzed and the response of PMSM is observed for load torque disturbance, speed reversal, reduction in torque ripple,
varying switching frequency, change in hysteresis current window and change in PWM carrier frequency etc. The simulation is carried out using two current control methods
i.e. hysteresis and PWM to study the performance of PMSM drive system. The plots of torque, speed, current and flux linkage are given for all the cases. From the simulation results it is observed that the commanded torque is tracked very well (refer Fig. 9 to Fig. 11 and Fig. 13 to Fig. 15). The plotted variables are in normalized units (p.u.). The parameters for PMSM are given in the appendix. In all the simulations rated speed of 628.6 rad/s is selected as base speed.

VectorControlled PMSM Torque Drive with Hysteresis current control
The torque controlled PMSM drive is tested under different operating conditions as follows (a) change in load torque (b) speed reversal (c) change in hysteresis current window.
Fig. 9 to Fig. 11 reveal simulation results of the PMSM drive when fed through threephase hysteresis current controlled inverter.

Disturbance in torque:
Fig. 9.a. gives the simulation results of the torque response of the PMSM under the condition of a step change of torque command. A torque of 0.4 p.u. is added and then increased to 1 p.u. at 0.005s. From Fig. 9.a. it can be seen that the torque response is very fast. In this test the motor speed is assumed constant, which is chosen as 314.3 rad/s and the hysteresis current window is set at 0.1 p.u. Simulated three phase currents are shown in Fig. 9.c. (reference) and Fig. 9.d.(actual) respectively.

Speed reversal:
Fig. 10 give the simulation results under the condition of applying constant amplitude of roto flux linkage. Fig. 10.b. shows the response of speed of the PMSM under a step change of reference speed from 0.5 p.u. (314.3 rad/s) to 0.7 (440 rad/s) p.u. at the time 0.005s. It is seen from Fig. 10.a. that the torque under any circumstances is able to follow the reference quite well. Fig. 10.a. shows the reference and actual
technique for varying hysteresis bands. Table I shows that when the hysteresis band is selected as i=4%, it provides the lowest THD of 17.57 %, 20.22 %, 25.68 % for current of all the three phases i.e. a, b and c respectively.
TABLE I. THD ANALYSIS OF THE PMSM DRIVE USING HYSTERESIS CURRENT CONTROLLED INVERTER
Sr.
No.
Hysteresis Current Control Technique
Hysteresis band (i )
Phase
THD in current %
1.
i = 0.48 p.u.
a
17.57
b
20.22
c
25.68
2.
i = 1.2 p.u.
a
21.6
b
23.76
c
28.49
3.
i = 2.4 p.u.
a
33.53
b
35.07
c
34.49
Fig. 9. Torque control of a PMSM with constant reference speed and step change of torque command 0.4 p.u. is added and then increased to 1 p.u. at
0.005s. (a) Torque response (b) Speed response (c) Reference phase currents response (i* i* , i* ) (d) Phase current response (i i , i ). (e) Mutual flux
torque. Mutual flux linkages increases with the increase in
stator current magnitude (refer Fig. 10.d and Fig. 10.e). In this test i is set at 0.3 p.u.

Change in hysteresis current window:
Fig. 11 reveals the torque and flux waveforms for three different hysteresis bands (i=4%, i=10% and i=20% respectively). Step change in reference torque is applied two times i.e. at 0.002 s, from 2 Nm (30% of the rated torque) to 5.5631 Nm (100% of the rated torque) and viceversa at 0.0045 s. Torque and flux tracking performance analysis allows selection of the optimal hysteresis current window in accordance with the respective power switches.

Calculation of total harmonic distortion:
In Fig. 12 it is seen that the total harmonic distortion (THD) of current waveform for phase a under hysteresis current control technique is 21.6%. Table I shows the THD analysis for currents using the hysteresis current control
as, bs cs
linkages response.
as, bs cs
as, bs cs
Fig. 10. Torque control of a PMSM with with step change in reference speed from 314.13 rad/s to 440 rad/s at 0.05s (a) Torque response (b) Speed response (c) Reference phase currents response (i* i* , i* ) (d) Phase current response (ias, ibs, ics). (e) Mutual flux linkages response.
Fig. 11. Torque step and flux response for three different hysteresis bands (i=4%, i=10% and i=20% respectively). (a) Torque tracking performance (b) Flux tracking performance.
Fig. 12. Stator phase a current and its spectrum for hysteresis bands ( i=10%) (a) phase a current waveform (b) current spectrum.


VectorControlled PMSM Torque Drive System with PWM current Control
Fig. 13 to Fig. 15, the simulation results are observed for torque, speed, motor currents and flux linkage for the PMSM drive when fed by PWM current control inverter instead of a Hysteresis current control inverter. The torque response in Fig. 13.a. shows considerable drop in torque and current ripples after using a PWM current controlled inverter.

Disturbance in torque:
In this test, the drive is operated with a constant speed and there is a step change in reference torque. At 0.005 s (see Fig. 13.a.), a motor reference torque is increased to 1 p.u. (5.5631 Nm). It is seen from Fig. 13.a. that the response of torque is improved. The increase in torque causes increase in stator current magnitude which in turn increases the mutual flux linkages [22]. (see Fig. 13.a, 13.d and 13.e).

Speed reversal:
In this test, the drive is analyzed with a disturbance in speed command that is the reference speed is step changed from 314.3 rad/s to 440 rad/s at 0.005 s, under constant load torque of 5.5631Nm. From figure 14.c and 14.d it is seen that in this test the phase sequence reverses to rotate the motor in reverse direction.

Change in carrier frequency:
Fig. 15 represents the motor actual torque response due to the torque controlled drive for change in carrier frequency. The torque step response and flux response for varying carrier frequency fc =20 kHz, 10 kHz, 2.5 kHz is shown in Fig. 15. Also it is seen that the actual torque response contains ripples. In this test, step change in reference torque is applied two times i.e. at 0.002 s, from 2 Nm (30% of the rated torque) to 5.5631 Nm (100% of the rated torque) and viceversa at 0.0045 s, as it is shown in Fig. 15.a.

Calculation of total harmonic distortion:

After using the SPWM current control technique, the THD is effectively reduced to 14.53% (when fc =20 kHz) as shown in Fig. 16. The waveform of stator current for phase a is better than that obtained with hysteresis current controller (refer Fig. 12.a. and Fig. 16.a). Table II shows the THD analysis for currents using the PWM current control technique for two different carrier frequencies [28]. It also shows the comparison of THD levels for all the three phases.
Fig. 13. Torque control of a PMSM with constant reference speed and step change of torque command 0.4 p.u. is added and then increased to 1 p.u. at 0.005s. (a) Torque response (b) Speed response (c) Reference phase currents
Fig. 15. Torque step and flux response for three varying carrier frequency (fc =20 kHz, 10 kHz, 2.5 kHz respectively). (a) Torque tracking performance
(b) Flux tracking performance.
Sr.
No.
SPWM Current Control Technique
Carrier frequency (fc ) kHz
Phase
THD in current %
1.
fc = 2.5
a
27.54
b
25.69
c
15.42
2.
fc = 20
a
14.53
b
21.84
c
18.69
TABLE II. THD ANALYSIS OF THE PMSM DRIVE USING PWM CURRENT CONTROLLED INVERTER
response (i*
i* , i* ) (d) Phase current response (i
i , i ). (e) Mutual flux
as, bs cs
linkages response.
as, bs cs
Fig. 16. Stator phase a current and its spectrum for carrier frequency (
fc=20kHz) (a) phase a current waveform (b) current spectrum.
Fig. 14. Torque control of a PMSM with with step change in reference speed from 314.13 rad/s to 440 rad/s at 0.05s under constant load torque of
5.5631 Nm. (a) Torque response (b) Speed response (c) Reference phase currents response (i* i* , i* ) (d) Phase current response (i i , i ). (e)


CONCLUSION
The dynamic modeling and simulation study of PMSM drive using two different techniques for generation of switching signals is presented in this paper. A comparative evaluation based upon the ripple content in stator currents
as, bs cs
as, bs cs
and torque pulsation is carried out to determine the
Mutual flux linkages response.
effectiveness and performance wise superiority of hysteresis an sinusoidal PWM technique. The THD analysis of the PMSM drive for current waveform under both the techniques is presented. A comparison of THDs at various hysteresis bands and different carrier frequency is made and it has been concluded that THD under SPWM technique is lowest as compared to the hysteresis current control technique.
It is seen from the simulation results that the pulsation in torque, ripples in current and hence flux characteristics are considerably lower when the PWM current control technique is used as compared to the hysteresis current controller. Also it is concluded from the simulation results that whether a
PWM or hysteresis current controller is used on an average the nature of torque and flux linkages curve remains same. This study confirms that PWM current control technique is superior to hysteresis current controllers when compared with large hysteresis window. The main advantage of using hysteresis current controllers are good accuracy, simple design and high robustness. But the major drawback with this technique is that it does not have a fixed switching frequency as in PWM current control. Simulation results indicate that the proposed scheme is effective in obtaining fast torque response. The simulation results confirm that the design of vector controlled PMSM drive is valid. The general theory of switching functions was reviewed for implementing proposed function model.
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APPENDIX
Parameter Values of PMSM used in Simulation
P=6 poles; Rs= 1.4; Ld = 5.6mH; Lq = 9mH; J = 0.006
kgm2; B = 0.01 Nm/rad/s; *m = af = 0.1546 V/rad/s; * =
implementation of carrier based sinusoidal PWM inverter, Int. Journal of Advanced Research in Electrical, Electronics and Instrumentation
314.3 rad/s; Te*
r
= Tb = 5.5631 Nm; Vdc=285 V; i=1.2, fc=20
Engineering, vol. 1, no. 4, pp. 230236, October, 2012.
kHz. These parameters were taken from reference [3].