Analysis of Switched Reluctance Motor Drives for Reduced Torque Ripple

7/27/2019 Analysis of Switched Reluctance Motor Drives for Reduced Torque Ripple

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American Journal of Information Sciences

ISSN (Paper) 2568-5171 ISSN (Online) 2568-5546

Vol.6 No.2 2013 www.congresspress.com

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Analysis of Switched Reluctance Motor Drives for Reduced

Torque Ripple using FPGA based Simulation Technique

Khaldoon Asghar

AMS Engineering College, Namakkal

Abstract

This paper presents real-time simulation results of a switched reluctance motor (SRM) drive with a novel Torque

Distribution Function (TDF) for high-speed applications, in order to reduce torque ripple. The SRM is fed by a

three-phase unidirectional power converter having three legs, each of which consist of two IGBTs and two

freewheeling diodes. The SRM model incorporates all nonlinearities between excitation currents, rotor positionand flux linkages. For the purpose of control SRM drives, an improvement of the TDF method is proposed for

high-speed applications, in order to reduce torque ripple. The real-time simulation of the drive is conducted on

the RT-LAB real time simulation platform. Since the converter is current controlled, simulator latency is critical

to achieving good accuracy and avoiding current overshoot. The paper demonstrates that this type of drive with

simple hysteretic current control can be simulated in real-time at a time-step of 15s, with good accuracy. Thepaper also introduces FPGA-based simulation technology required to test advanced algorithms like TDF

Index Terms -Switched reluctance motor (SRM), Torque Distribution Function (TDF), real-time simulation.

I. INTRODUCTION

Today, before using a motor controller with a real motor drive, it is a common industrial engineering practice to

test a controller against a simulated motor model running in real-time. This has several advantages. For example,the simulated motor drive can be tested with borderline conditions that would damage a real motor, often a costly

prototype. The motor itself may be under development in parallel to the controller and therefore not available for

testing. While testing, a controller is interfaced with the real-time simulated motor drive through a set of proper

I/Os: this approach is called hardware-in-the-loop (HIL) simulation. Such motor drive simulation is required by

hybrid vehicle OEMs and other power electronic motor drive manufacturers to speed up development and testing

time by using real-time simulation before conducting tests on physical prototypes. At the production stage, HILsimulation can also be used to verify code integrity with automated correlation tests. The switched reluctance

motor drive is interesting because of its low manufacturing costs, rugged construction and simplicity of

controller design. Since the rotor has no windings and no magnets, it is a good candidate for drive operation athigh speed and in adverse environments. Position sensor reliability poses a more important problem in the latter

case. A developer or integrator of such drives will want to test the behavior of the drive in case of a position

sensor malfunction, for example. A real-time simulator is the ideal tool to safely test thisscenario. Sensorless drive designs pose other challenges related to sensor accuracy that could be overcome

through the use of a real-time simulator. The real-time simulation of current-controlled drives poses other

challenges, including simulator latency that can create a delay in hysteresis-type current controllers. This, in turn,

can cause current overshoots that are usually not present in real drives. Several SRM models that are ready for

real-time simulation are discussed in detail in references [6], [7], [8]. In these models, a key aspect is the flux-

linkage curve approximations by polynomial functions or tables. The switched reluctance machine has wound

field coils of a DC motor for stator windings and has no coils or magnets on its rotor. A typical 6/4 pole SRM is

shown in Fig. 1. In an SRM, the rotor is aligned whenever diametrically opposite stator poles are excited. At the

same time, when two rotor poles are aligned to two stator poles, another set of stator poles is out of alignment

with a different set of stator poles. Continuous torque production is therefore obtained by sequential excitation ofthe stator phases using a unipolar power converter with 2 IGBTs and 2 diodes for each leg.

Fig. 1. 6/4 pole Switched Reluctance Motor.


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Well-known algorithms for controlling an SRM, such as advanced rise and commutation angles, adaptive control,

fuzzy logic control, and neural network control have been proposed in the literature. Torque Distribution

Function may be the most well-known method. There are many kinds of TDFs; developed by Husain [3]

(denoted as TDF-I), Ilic-Spong [4] (denoted as TDF-II), and Krishnan [1] (denoted as TDF-III). In this paper, the

authors present the topic of real-time simulation of switched reluctance motor drives using TDF-III, and also

propose a novel Torque Distribution Function, based on TDF-III, for high-speed model applications. Next, areal-time simulation system for switched reluctance motor drives is demonstrated. It is implemented using a

novel TDF for high-speed applications, in order to reduce torque ripple.

II. TORQUE PRODUCTION STRATEGY

In SRM control strategies, each phase winding is excited separately in the rising slope of the inductance for the

positive torque, and in the falling slope for negative torque. The overall torque of the motor is the sum of the

phase torques. The inductance profile, phase current and voltage are shown in Fig. 2.

A. Model of the SRM

In the SRM, there is a three-dimensional relationship between excitation current, rotor position and flux

linkages [2]. Therefore, electromagnetic torque depends on both

Fig. 2. Inductance profile, phase current and voltage.

excitation current and rotor position. Those relationships are presented in Fig. 3. The machine under study also

has a stator winding resistance equal to 0.2 and a rotational inertia of 0.1 kg.m2.

This SRM model integrates its flux at each winding, considered as uncoupled. Its equation is

( RI)dt= (1)whereIabc is the stator current inside the winding, R is the stator resistance and Vabc is the voltage across thestator windings. The current is then derived from the machine flux characteristics abc (I,).


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Fig. 3. Three-dimensional relationship between excitation current, rotor position and flux linkages.

The phase flux linkage depends on both rotor position and phase current. The model of an SRM can be described

as follows:

Fig. 4. Model of SRM used for simulation.

The produced electrical torque is also derived from the flux-current characteristic, pre-computed and stored in

tables prior to the real-time simulation in a normalized form (dK/d ).

(, ) = (,)(,) = 2(,) B. Torque Distribution Functions

In many machines, such as ac and dc machines, the air gap torque is directly proportional to the excitation

current (in a DC machine) or the transformed current variable (qaxis current in an AC machine). However, in thecase of an SRM drive system, a three-dimensional non-linear relationship exists between the flux linkages,

excitation current and rotor position. This means that the air-gap torque depends on both excitation current and

rotor position. Therefore, in the SRM drive system, it is necessary to add the torque control to the control loop.The control configuration for an SRM drive system using TDF is shown in Fig. 5. The extraction of the

excitation current reference from air-gap torque reference is made using a three-dimensional relationship. The

equation for extracting the current reference is shown as follows:

1 = 2!(,) (2)C. Torque Distribution Function Methods


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The method of torque control depends on how many phases are excited at a given time. If, in an SRM drive

system, only one phase is excited at a given time, the torque ripple produced is very large. So, it is necessary to

excite more than one phase at a given time to reduce torque ripple. In this paper, the TDF method is used. When

using the TDF method, it is necessary to make certain assumptions: (1) Neglect the mutual coupling effect

between phases, (2) The current controller is idealized (without tracking error). Working based on these

assumptions, the torque command will be divided into two parts, one for the incoming phase (called phase x forshort) and another for outgoing phase (phase y). This division makes the current commands vary more slowly so

that the actual ones can keep up. There are many ways to get Tx* and Ty* in the commutation interval,

depending on the inductance profile of a given machine [1], [3], [4]. The TDF III that was developed by

Krishnan [1] is shown in the following equations:

Fig. 5. SRM drive control system diagram

"# = (, #) "$ = %&(,')% (3)

! = #!$! #! = *+*++ $! = +*++where x y g ,g are pre-calculated and stored in a table and extracted by linear interpolation method. The torque

commands during a commutation interval are illustrated in Fig. 6. In this method (TDF III), the saturation andmutual coupling between the phases are neglected. In reference [1], Krishnan has also proposed the method TDF IV,

which takes the mutual coupling into consideration and the TDF V, which includes both saturation and mutual

coupling. The practical implementation of methods TDF IV and TDF V is however very difficult, due to the fact

that the mutual coupling between the phases is not easily determined. Therefore, we prefer to consider only the

method TDF III, and try to improve its drawback (Section III).

D. Simulation Results

The performance of the SRM drive system was evaluated by using Torque Distribution Function, TDF-III. The

torquecommand was set to 100 Nm and the motors speed was set to 1000 rpm and 3000 rpm. In commutation

intervals, the torque command was divided into two parts so that two phases could reduce torque ripple. Simulation

results illustrate that at 1000 rpm, the torque ripple is very small. However, at a speed of 3000 rpm, torque ripple isvery large.

III. PROPOSED TORQUE DISTRIBUTION FUNCTION

Because of the non-idealized current controller, the actual currents need a specified time to track their commands.

As a result, actual phase torques cannot track commands that produce torque ripple, especially in high speedapplications; in other words, the higher the speed of the motor, the larger the torque ripple that will be produced. For

this reason, a new TDF is proposed to reduce torque ripple, especially in SRM drive high-speed applications.


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Fig. 6. Torque commands in commutation interval.

Fig.7. Phase current, phase torques and total torque at 1000rpm (upper) and 3000 rpm (lower) and torque

reference of 100Nm (red line real torque and green line command torque).

In the proposed Torque Distribution Function [14], the torque command is actively compensated for in each

phase,

resulting in a flat total command torque. The following equations describe this method. In the table, Ta*,Tb* and

Tc*are the phase torque commands, and Te is the torque command.


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TABLE I. EQUATIONS OF PROPOSED TDF

angle 0---

#

"

""

# 0#

""" (# 12")angle -- /--# "

" (# 1

2")

# """ # 0angle /-- 0--# "

"" (# 12")# 0# """ As illustrated in the simulation results, the torque command is not flat (green curve). However, the actual torque

(red curve) is quite flat, thereby significantly reducing torque ripple.

IV. REAL-TIME SIMULATION OF SRM DRIVES

A. RT-LAB real-time simulation platform

RT-LAB, from Opal-RT Technologies, is a real-time simulation platform that enables HIL simulation of

controllers, electric plants or both, through automatic code generation methods. The entire process occurs

without the need for handwritten C code, enabling very rapid deployment of prototyped controllers or HIL-

simulated plants. The process is notably very efficient when applied to I/O code because RT-LAB provides a set

of Simulink blocks that automatically configure common I/O functions, like analog inputs/outputs and time-

stamping capable digital I/Os, with a 10 nanosecond resolution. Special interpolating models use this timing

information to greatly increase simulation accuracy [10]. RT-LAB simulators can also be equipped with a userprogrammable FPGA card. The FPGA card can be programmed with the Xilinx System Generator blockset for

Simulink enabling implementation of complex sensor models like resolvers, Resolver-To-Digital and FM

resolvers or even complex motor drives [11], [12].


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Fig. 8. Phase current, phase torques and total torque at speed of 3000 rpm and load torque of 100 Nm (red line

real torque and green line command torque).

TABLE II. RT-LAB SIMULATOR CHARACTERISTICS

HardwarePC with dual Quad-Core Intel

processor (2.3 GHz)

Real-time OS QNX or RedHawk Linux

RT-LAB version 8.2.5

Digital I/O 16 Din-16 Dout (Time Stamped)

Analog I/O 16 Analog Inputs and 16 Outputs

B. Test case: constant turn-on and turn-off angles and 10A dead band.

The SRM drive discussed in this paper is simulated in real-time on the RT-LAB real-time simulation platform,

using 2 cores of a dual quad-core PC. Table II summarizes the characteristics of the RT-LAB system used in this

paper. A very basic type of SRM control with fixed turn on and turn-off angles will be used as an example. The

task separation for the experiment is shown in Fig. 9. A sample time of 13 s was reached with an I/O interfaceconsisting of 6 digital inputs for the IGBT gates, 3 digital outputs (used for quadrature encoder emulation) and 5

Analog Outputs for motor currents and resolver signals. The final simulation time of 15 s was chosen to leave

margin available for a more complex model. In this test, however, the sensors are idealized, and only the

numerical value of the angle is transmitted between cores. The most important difference is the current ripple

amplitude during current regulation. The 15 s simulation run exhibits higher ripple (as much as 2 times the

nominal 10A gap) because of the increased delay in the current loop. In an SRM, this component of the torqueripple is a magnitude lower than the overall torque ripple and may therefore minimally affect the overall testing

purpose of the real-time simulator. As previously mentioned, the SRM drive was simulated on an RT-LAB

system with Hardware- In-the-Loop capability. This section shows the model signals obtained during real-time

simulation. A 100 N.m torque is applied so that the SRM runs in current regulation mode in steady state.


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Fig. 9. Real-time simulation of an SRM drive: task separation.

Fig. 10. Simulation runs at 1 us and 15 us (with zoom in the lower).

Fig. 11. shows the currents for the 3 phases of the motor, with an analog output scaling of 1/50 V/A. The lower

oscilloscope grab of Fig. 11 shows the current of phase A, along with the corresponding IGBT gate signals. The

correspondence between the IGBT gate level and current slope sign is clearly apparent in this figure.


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Fig. 11. Motor currents: all 3 phases (upper); phase A with gate signals

(lower).

V. REAL-TIME SIMULATION OF AN SRM WITH FPGAS AS COMPUTATIONAL ENGINE.

Real-time simulation of SRM drives on a CPU-based real-time simulator can produce accurate results, but can

also have the undesirable effect of causing current overshoots because of model latency. In this case, this latency

has prevented the testing of the proposed TDF method in real-time. To remedy this problem, an FPGA

implementation is desirable because it offers a very low calculation and I/O latency. FPGA implementations of astandard Park-model PMSM drive [6] and a Finite- Element Analysis (FEA) based PMSM drive [7] have been

demonstrated, and have a total latency just above 1 microsecond, including I/Os. The SRM model has a

calculation structure very similar to an FEA-based PMSM, as follows: flux integration, followed by the

multiplication by inductance inverse to compute machine currents. However, in the case of the SRM, the flux

current characteristic is two-dimensional, while in [11] a 3-D table was necessary to store inductance values as a

function of current amplitude and sector, as well as rotor position. Consequently, the SRM implementation on anFPGA should be easier. Simulation results similar to Fig. 11. (1 microsecond curves), but with minimal

overshoot, are expected. The RT-LAB system comes with a user programmable FPGA card based on the Virtex

II-Pro (11K cells, 44 multipliers, PCI interface). An improved FPGA card based on the SPARTAN-3 chip from

Xilinx has recently become available (77K cells 104 multipliers, PCIe interface). The support for the

SPARTAN-3 chip provides an undeniable boost to the capability of the system. Logic cells, the standard

measure of FPGA resource availability, are increased 7 fold with the SPARTAN-3. A more subtle advantage, the2.5 times increase in hardware multiplier, greatly increases FPGA drive design possibilities, since multiplication

operations are very common in drive models. The increased I/O number also enables the possible connection of

several drives implemented on the chip. Finally, RT-LAB can also be interfaced with a Virtex-5 board with 288

multiplier units and PCIe interface.


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Fig. 12. Design flow in RT-LAB

The interface to the CPU-side of the simulator is also very important. A typical RT-LAB application (automotive

applications, for example) will have several motor drives interacting electrically, as well as through a mechanical

system. The latter, for example, is typically complex and relatively slow, and therefore best implemented usingSimulink on a regular CPU, using a standard code generation technique. Consequently, a fast data exchange

mechanism is required to conduct mixed type simulation (CPU-FPGA). The PCI Express (PCIe) support

available on the SPARTAN-3 design greatly increases the data exchange rate between CPU and FPGA. Finally,

the I/O access time is minimal with FPGA implementations because the FPGA card is hardwired with the Digital

I/Os and Analog converters. The most important objective is to make the whole design process easy and

straightforward. With RT-LAB, this process follows the Model-Based Design paradigm in which the userdevelops specifications, and conducts model design and test simply by interacting with the high level model,

usually designed in Simulink. When FPGA design is involved, the same process flow, described in Fig. 12, ismaintained except that Xilinx ISE FPGA code generation tools are involved in the process.

Fig. 13. Experimental setup.

VI. CONCLUSION

The paper has presented modeling, simulation and control SRM using Torque Distribution Function, developed

by R.Krishnan, to reduce torque ripple. In this paper, the authors have also proposed a novel Torque Distribution

Function to reduce torque ripple at high speed. The simulation results have confirmed excellent response of the

torque by novel TDF. This paper has also demonstrated the feasibility of real-time simulation of a SRM drive,

based on the RT-LAB simulator. The real time simulation was conducted on 2 cores of an 8-core standard PC at

a sample time of 13 s, including digital and analog I/O access time. Acceptable results have been produced,despite some overshoot when the current converter hysteresis gap is not too small. However, for a very

demanding control algorithm, such as Torque Distribution Function method, the


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standard CPU-based approach presents input-output latency issues at the I/O level that will prevent an accurate

simulation from being performed. In this case, an implementation of the SRM drive on the FPGA should solve

the problem. This FPGA-implementation was not presented in the paper. It is believed that the FPGA

implementation should not be problematic because a machine of similar complexity, a FPGA-based PMSM with

FEA-based inductance profile, has already been designed using RT-LAB.

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[1] R. Krishnan, Switched Reluctance Motor Drives, CRC Press LLC, 2001.

[2] T.J.E. Miller, Switched Reluctance Motors and Their Control, Magna Physics, Oxford, 1992.

[3] Husain, I. and M. Ehsani, Torque ripple Minimization in Switched Reluctance Motor Drives by PWM

Control,IEEE Trans. on Power Electronics, Vol. 11, No. 1, 1996, pp. 83-88.

[4] M. Ilic-Spong, T. J. E. Miller, S. R. MacMinn, and J. S. Thorp, Instantaneous torque control of electric

motor drives,IEEE Trans. on Power Electronics, vol. 2, no. 1, 1987, pp. 5561.

[5] B.K Bose,Power Electronics and Variable Frequency Drives, IEEE Press, 1997.

[6] Le-Huy, H.; Brunelle, P. A versatile nonlinear switched reluctance motor model in Simulink using realistic

and analytical magnetization characteristics,Proceedings of the 31st IEEE Annual Conference of the Industrial

Electronics Society 2005 (IECON-2005), 6-10 Nov. 2005

[7] I. Boldea, S.A. Nasar,Electric Drives, CRC Press, ISBN 0-8493- 2521-8[8] T.J.E. Miller, et al., Ultra-fast model of the switched reluctance motor, IEEE Industry Applications

Conference Proceedings, Vol. 1, 1998, pp. 319-326.

[9] D.A. Torrey, X.M. Niu, E.J. Unkauf, Analytical modeling of variable-reluctance machine magnetisationcharacteristics,IEEE Proceedings- Electric Power Applications, Vol. 142, No. 1, January 1995, pp. 14-22.

[10] M. Harakawa, H. Yamasaki, T. Nagano, S. Abourida, C. Dufour and J. Blanger, Real-Time Simulation of

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[11] C.Dufour, J. Blanger, V. Lapointe, FPGA-Based Ultra-Low Latency HIL Fault Testing of a Permanent

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[12] C. Dufour, J. Blanger, S. Abourida, V. Lapointe, FPGA-Based Real-Time Simulation of Finite-Element

Analysis Permanent Magnet Synchronous Machine Drives, Proceedings of the 38th

Annual IEEE Power

Electronics Specialists Conference (PESC 07), Orlando, Florida, USA, June 17-21, 2007.[13] M. Ehsani, Y. Gao, S. E. Gay, A. Emadi, Modern Electric, Hybrid Electric and Fuel Cell Vehicles, CRC

Press, ISBN 0-8493-3154-4[14] L. V. Do and M. C. Ta, Modeling, Simulation and Control of Reluctance Motor Drives for High-Speed

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Analysis of Switched Reluctance Motor Drives for Reduced Torque Ripple