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Abstract Simulink is advanced software by Math Works Inc., which is increasingly being used as a basic building block in many areas of research. As such, it also holds great potential in the area of AC drives system modeling and simulation. In this paper, we have taken a reluctance-machine as an example to demonstrate the features and scope of a Simulink-based model for transient stability analysis of the simulated reluctance-machine. A self sufficient model has been given with full details, which can work as a basic structure for an advanced and detailed study[1].

KeywordsMATLAB simulation; reluctance-machine modeling; Simulink; transient stability

I. INTRODUCTION

HE stability of reluctance-machine has been and continues to be of major concern in the area of AC motor drive. Transient stability of reluctance-machine is the ability of

the motor system to maintain synchronism when subjected to a severe transient disturbance and motor parameters change.

Reluctance motor drive simulation has attracted renewed interest in recent years [1-6). Historically, simulation of motor system and its transient phenomena has been carried out using different programming languages such as C and FORTRAN. The motors simulation using these programming languages is very complicated and hard to achieve.

With the help of simulation software package such as MATLAB & SIMULINK, many kinds of motor-inverter control systems can be easily made, by using the simulating model and control blocks. All parameters can also be changed on line so the better controlling parameters are conveniently determined MATLAB is used in controller design and optimization for different motor drives, but does not include reluctance motor. The model of Synchronous reluctance motor-inverter Control System is a very complete high orders, non-linear, multiple variables and time-varying system, so there is no general implement in form of MATLAB & SIMULINK and report about this is not seen. It is necessary therefore to implement Synchronous reluctance motor-inverter control system using MATLAB & SIMULINK. In order to test the dynamic performance of the reluctance synchronous motor drive, Computer modeling and simulation can be used.

D.E. Abaid is with the Control Engineering department, Faculty of Electronic Technology, Beni-Walid, Libya. Phone No. +218927115265 E-Mail:[email protected].

M.A. Fellani is with the Control Engineering department, Faculty of Electronic Technology, Beni-Walid, Libya. Phone No.+218913774297 Email: Fellani2006 @yahoo.com

This will reduce the expense and length of the design cycle of the real drive system before prototype construction begins. Modeling can be done with the help of mathematical equations.

In this paper, a reluctance synchronous motor model based on the two-axis theory is derived and implemented digitally using SIMULINK Toolbox. The drive system is modeled using MATLAB and SIMULINK. The dynamic equations and simulation results are given. The parameters of an experimental machine are used as base parameters to simulate the system and study the dynamic performance[11].

The simulation is based on the ideal model of the reluctance synchronous motor with saliency ratio of 6. This ratio is a nominal one selected for the simulation purpose, though higher ratio can be achieved with modem designs of RSMs.

In the simulation, the dynamic and transient performances are studied using synchronously rotating reference frame. The inverter (PWM inverter) is digitally modeled using MATLAB.

II. MATLAB SIMULINK MOTOR MODELLING Matlab comprises of a range of toolboxes and block sets

such as Simulink toolbox, communications toolbox, control system toolbox, etc. depending on application requirements. For motor drive system modeling, the Simulink toolbox provides the required components for the drive simulation. Simulink is a program for simulating dynamic systems and Matlab provides powerful evaluation of the simulation results. It follows the principles of modular design, object-oriented design, reusable blocks, support for project hierarchy and self-documentation, because it inherently illustrates the algorithm being performed.

This section will looks at how the modelling and simulation of a synchronous reluctance motor can be carried out using MATLAB/SIMULINK software[12].

As in all system activities, it is useful to split the system into smaller functional blocks and then design and test each individually. The proposed RSM drive system is split into several smaller parts (sub-systems) for the purpose of modeling. These consist of, the reluctance synchronous motor electrical and mechanical block, the vector controller, and PWM inverter. The simulation model of the motor was formed from the dynamic equations, which describe the motor.

In order to simulate any machine the electrical parameters must be known. They can be either measured or calculated. The parameters required for the RSM motor simulation are: the stator resistance Rs, the moment of inertia J, motor friction coefficient K, the number of pole pairs P and the direct and quadrature-axses self inductances Ld and Lq respectively. The

Modeling and Simulation of Reluctance motor using digital computer

Mostafa. A. Fellani, and Daw. and E. Abaid

T

International Journal of Computer Science and Electronics Engineering (IJCSEE) Volume 1, Issue 2 (2013) ISSN 23204028 (Online)

148

64

5

3

2

1

1/s

B

T

-

-

+

1/s 1/J

(3/2)P

-

+*

**

*

1/Lq

-++

-+-

1/s

1/Ld

Rs

Rs

1/s

Current

Speed

Position

Load torque

Current Iq

Flux q

Flux d

Vq

Vd

RSM motor model employed in this simulation is a d-q model in synchronously rotating reference frame. Therefore the stationary three phase system of the motor has to be transformed into synchronously two phase system, i.e. d-q model, or vice versa [5,6].

The equation which describes the behavior of the reluctance synchronous motor can be derived from its d-q axis equivalent circuit figure. 1.

Fig.1. Synchronous reluctance motor d-q axis equivalent circuit

The dynamic model of synchronous reluctance motor in d-q frame can be represented by the following equations:

qrd

dsd dtdIRV += (1)

drq

qsq dtd

IRV

++= (2)

ddd IL= (3)

qqq IL= (4) Where, dL and qL are the direct and quadrature axis

winding self inductance (H), R is the stator winding resistance () and RrR is the rotor angular speed in (rad per second) and it is equal to P*P.

From equations (1) and (2), the rate of change of flux can be obtained as follows:

qrdsdd IRV

dtd

+= (5)

drqsqq IRV

dtd

= (6)

The electromagnetic torque equation for the synchronous reluctance motor in the synchronous reference frame is given by:

)(23 qddqe IIpT = (7)

Ler TT

PJ

dtd

=

(8)

The torque equation in Laplace domain is

*)()(23 JSBiiLLpT qdqd += (9)

dtd r

r = (10)

Where, B and J are the damping fraction and the motor moment of inertia respectively and p is the number of pole pairs and P*P= RrR.

Using the above equations, the motor can be simulated in the SIMULINK software as shown in figure 2.

The transformation from 3-phase to 2-phase and from stationary reference frame (,) to synchronous reference frame (d, q) was accomplished using equation 11 and shown in the transformation block in figure 3.

=

cos

sin

q

d

R

R

sin3

1

cos3

1

sin3

1

cos3

1

c

b

a

RRR

(11)

R in this equation could be voltage, current or flux

Fig.2 Simulated synchronous reluctance motor drive

Rs Lq

rLqiq

rLdid

Vd

Vq

Ld Rs


149

M V

I I

I

Fig. 3 3 to 2-phase and stationary to synchronous reference frame transformation

The transformation for the inverse operation i.e. from

synchronous to stationary reference frame and from 2-phase to 3-phase is obtained using equation 12 and it is as shown in figure 4.

+

+=

q

d

c

b

a

X

X

XXX

)cossin3(21

)cossin3(21cos

)sincos3(21

)cos3(sin21

sin

(12)

Fig. 4. 2to3 phase and synchronous to stationary reference frame

transformation

III. INVERTER MODEL SIMULATION In order to vary the speed in reluctance synchronous motor,

it is necessary to control both the voltage and the frequency applied to the motor terminals. The most common way is to use an inverter bridge, shown in figure 5, that consists of three switches which connect each motor terminal to either the positive or the negative rail of a constant D.C voltage source.

Fig. 5 Voltage source transistor inverter circuit

The implementation of the three phase sinusoidal PWM inverter under SIMULINK environment is as shown in figure 6. The input signals to the inverter are; the fundamental frequency, modulation index, and carrier frequency. Output signals from the inverter are three phase voltages [4].

Fig. 6. SINULINK model of voltage source PWM inverter

IV. MOTOR DRIVE SYSTEM SIMULATION For transient stability study, the complete synchronous

reluctance motor drive system has been represented in terms of Simulink blocks. The Simulated system is as shown in Figure.7. The system consists of main components: a motor,

+

+

1/3 -

- 2/3

+

+

*

-1

cos(u[1])

*

*

*

sin(u[1])

cos(u[1])

sin(u[1])

1

2

1

2

3

Va, I Vb, I

Vd, I

Vq, I

r

* + + * 1 sin(

[1] cos([1])

* + -

2 0

- +

sqrt(3)/2

+ +

*

* - +

+ -

3 * -

+

2 1

3

0

sqrt(3)/2

Va

V

Vd,

Repea seque

+ - Su

+ - Su

+ - Su

2

1

3

2

dc link

-

dc link

Swi

Swit

Swit

Rel

Rel

Rel

+ - -

Su

+ - -

Su

+ - -

Su

2

2

2

1/

1/

3

1/

1

2 signal (b)

signal (c)

Vcn

* + + * 1 sin(

[1] cos([1])

* + -

2 0

- +

sqrt(3)/2

+ +

*

* - +

+ -

3 * -

+

2 1

3

0

sqrt(3)/2

Va

V

Vd,


150

an inverter and controller. The motor is 3-phase synchronous reluctance with damping winding. The converter consists of a three phase voltage source inverter which powers the stator of the motor. The inverter switches are driven by a PWM unit, and the gates are triggered by the 3-line voltage error signal of the motor, and carried by a triangular wave of the PWM source. The current and position sensors are used with a specific references for the feedback control, and the Tow-axis transformation blocks are applied [8].

Fig. 7. indirect current vector control block diagram for RSM motor In order to start simulating the drive system, the parameters

must be known. They can be either calculated or measured as in this investigation. The parameters of the reluctance synchronous motor, used for simulation are as shown in TableI.

TABLE I PARAMETERS OF THE RELUCTANCE SYNCHRONOUS MOTOR

Parameters Values Units. Ld 0.6 H Lq 0.2 H R 4 J 0.0006 K~m K 0.009 I Nm P 1 f 25 Hz

In order to examine the performance of such a drive system

SIMULINK was used to simulate the drive system. A complete dynamic model for transient stability study of a

synchronous reluctance motor drive system was developed using Simulink as shown in figure 8. It is basically a transfer function and block diagram representation of the system equations.

The voltage command signals which are obtained in the synchronous rotating d-q reference frame are transformed back to the stator reference frame and then used to switch the voltage source PWM inverter [3,7].

Fig. 8 Simulation block diagram for the SRM drive system

In the simulation, the various parameters are obtained from

a practical synchronous reluctance machine. The control aspects are studied using synchronously rotating reference frame.

Using the simulation diagrams of figure 8, the effects of controller on the drive transient performance are studied.

V. DRIVE SIMULATION RESULTS This section presents simulation results for the synchronous

reluctance motor drive. The drive system with vector control method has been simulated using Matlab & Simulink software packages and the dynamic responses have been obtained as shown in Figures (9,10,11). The simulation results are based on a 2-pole ALA-rotor RSM model, whose Ld and Lq inductances are measured experimentally [2,10].

To test the transient stability of the proposed synchronous reluctance motor drive system, the motor run at different reference speed of r=200,400,600and 800 rad per second. Figures 9 shows the response of the motor drive for speed references of 200 and 400 rad/sec for a nominal values of motor inductance of Ld=0.6. Figure 10 shows the responses of the motor drive for speed references of 600 and 800 rad/sec for a nominal values of motor inductance of Ld=0.6.

Fig. 9 motor speed responses for reference speed values of 200 and

400 rad/sec with nominal value of motor inductance Ld=0.6.

r

PWM voltage source inv.

RSM

2 to 3 phase and synchronous to stationary transformation

Current controllers

*dI & *qI

currents calculat

PI speed

ll

*dI

*qI

*aI

*bI

*cI

*T

*r

r


151

Fig. 10 motor speed responses for reference speed of 600 and 800 rad/sec with nominal value of motor inductance Ld=0.6.

Figure 11 shows the speed response when step load torque is applied to the motor at nominal value of Ld=0.6 and Rs=18 at reference speed of r=400 rad per second.

Fig. 11 motor speed responses to step load change

VI. CONCLUSIONS This paper has considered simulation of the synchronous

reluctance machine drive systems using Matlab/Simulink software. The main motivation was due to the numerous advantages, the matlab has over the other programming

languages, such as C, FORTRAN and other competitive software. In this paper the robustness and flexibility of the SIMULINK/MATLAB modeling package has been shown.

The transient performance of reluctance motor drive system has been analyzed by using MATLAB & SIMULINK. Although the model of the reluctance motor is complicated, the implement produced in this paper is accurate and useful.

With MATLAB & SIMULINK facilities, reluctance motor-inverter control drive systems can be directly implemented and simulated. The configuration and all parameters of control systems can be easily changed on line.

The simulation results shows that the reluctance motor has good responses over a wide speed range and therefore simulation results give more confidence in using SIMULINK as a simulation tool for the RSM drives.

REFERENCES

[1] Betz. R.E, Theoretical aspects of control of synchronous reluctance machines Proc IEE. Vol B-1 39, no 4, 1992, pp 355-364.

[2] Boldea, I. and Nasar, S.A Emerging electric machines with axially laminated anisotropic rotors a review, ibid Elect Mach. Power Sys, 19 (6), 673-703, 1991.

[3] Boldea, I. and Nasar, S A, Vector Control of AC Dives, CRC Press, Boca Raton, USA, 1992.

[4] Boldea, I, Fu, Z.X. and Nasar, S.A, Digital simulation of a vector controlled rotor synchronous motor servo-drive, Elect Mech. axially-laminated anisotropic (ALA) Power Sys., Vol 19.1991, pp 415-424.

[5] Fletcher, J.E Green, T C and Williams, T.J.E., Vector control of a synchronous reluctance motor utilizing an axially laminated rotor, IEE Power Elect. and variable speed drives, 26-28 Oct., 1994.

[6] Fratta, A. and Vagati, A., A reluctance motor drive for high dynamic performance applications, Record of IEEE 4AS. 1987, Annual Meeting, pp.295-302.

[7] Lawrenson P.J and Gupta, S.K, Developments in the performance and theory of segmental rotor reluctance motors, Proc. JEE. Vol 114, No 5, May. 1967, pp.645-53.

[8] Liang, L., Xu, L. and Lipo, T.A., d-q analysis of variable speed doubly A.C excited reluctance motor, Elect Mach Power Sys. Vol.19. no.2.1991, pp 125-138.

[9] Boldea, Z. I., and Nasar, S.A., Torque vector control (TVC) of axially-laminated anisotropic (ala) rotor reluctance synchronous motors, Electric Machines and Power Systems, vol. 19, pp. 381398, 1991.

[10] Sawata, T., Kjaer, PC., Cossar C., Miller THE., A study on operation under faults with the single-phase SR Generator, 13th Annual Applied Power Electronics Conference, Anaheim, USA, 15-19 February 1998, Vol.2, pp.1040-1046, 1998.

[11] The Math Works Inc., SIMULINK Users Guide, April 1996. [12] Math Works Inc., MATLAB Users Guide, March 1997.

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