MRAS Based Sensorless Speed Control of PMSM for Low Speed and High Torque System

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MRAS Based Sensorless Speed Control of PMSM for Low Speed and High Torque System

Pradeep Kumar Dept. of Electrical Engineering DPG Institute of technology and

management, Gurgaon India

e-mail: [email protected]

Sandeep Dhundhara Department of Electrical and

Electronics Engineering UIET, Panjab University, Chandigarh,

India

Deepak Lakra Dept. of Electrical Engineering

Delhi Technical Campus Bahadurgarh, Haryana

India

Abstract— Due to many advantages of Permanent Magnet Synchronous Motor (PMSM) such as high efficiency, lower in size and better performance in low speed and high torque system, PMSM is an alternative of Induction motor now a day. In this paper performance of PMSM for low speed and high torque system such as an elevator has been evaluated. A position sensor less Model Reference Adaptive System (MRAS) is used with Space Vector Pulse Width Modulation Technique (SVPWM) which reduces the overall cost of PMSM drive and reveals better results. An estimated speed is obtained by MRAS method using two phase stator currents and DC bus voltage. The error between the reference and estimated speed is act as an input to the PI controller. The given proposed algorithm is simulated in MATLAB/Simulink software. The simulation result shows that the MRAS system is feasible and effective for PMSM drive.

Index Terms— Permanent Magnet Synchronous Motor, SVPWM, Low speed and high torque system, Model reference adaptive system.

I. INTRODUCTION

The operation of AC drives in speed open loop requires the estimation of internal state variables of the machine.

This is done by measuring the currents or the voltages on the machine terminals. Low cost, medium performance sensor less drives can be designed using simple algebraic speed estimators. The adjustable speed drives employs various control methods to ensure satisfactory performances considering a specific application. The application with this project deals is low speed control of a current controlled PM motor by means of a Voltage Source Converter (VSC), in open loop. The control strategy should be capable to handle with load.

In works available until now ideal components have been assumed in the inverter feeding the motor and simulations have been carried out. The voltages and currents in different parts of the inverter have not been obtained and hence the losses and efficiency cannot be calculated. In this work, the simulation of a PM motor drive system is developed using Simulink. The simulation circuit includes all realistic components of the drive system. This enables the calculation

of currents and voltages in different parts of the inverter and motor under transient and steady conditions.

Finally the PMSM drive requires two current sensors and an absolute rotor position for the implementation of any control strategy. The rotor position is sensed with an optical encoder or a resolver for high performance applications. The position sensors compares to the cost of the low power motor and also reduce the motor efficiency. Thus making the total system cost very noncompetitive compared to other types of motor drives we are using sensor less speed control of PMSM.

MRAS adaptive speed estimator technique is easy to implement that we are using in this paper. A speed controller has also been designed for closed loop operation of the drive.

A MRAS based sensor less control system is designed using the field oriented control strategy of the PMSM motor in the MATLAB/Simulink. The goal of this paper is to design and implement a drive system of a PMSM which can be implementing on low speed and high torque systems.

This paper structured as follows: Section 2 deals with the modeling of PMSM, space vector pulse width modulation technique is studied in section 3, in section 4 MRAS system has been explained and section 5 and 6 shows the results and conclusion respectively.

II. PERMANENT MAGNET SYNCHRONOUS MOTOR A permanent magnet synchronous motor (PMSM) is a motor that uses permanent magnets to produce the air gap magnetic field rather than using electromagnets. These motors have significant advantages, attracting the interest of researchers and industry for use in many applications. The use of permanent magnets leads significant reduction of copper and iron losses as compared to other motor drives leading to higher efficiency and reduction in machine frame size.

The main features of PMSM as compared to other motors are:

 High efficiency

 High torque to inertia ratio

 High air gap flux density

 High power factor

 Lower maintenance cost

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2

 Higher acceleration and deceleration rates

 Simplicity and ruggedness

PMSM are used in many applications such as lower machine tools (spindle motors, position drives, etc.), robotics applications, ship propulsion, in the field of electricity generation, solar pumping, wind energy applications, pumps, fans, hybrid vehicles etc.

A. Modeling of PMSM

Detailed modeling of PM motor drive system is required for proper simulation of the system. The d-q model has been developed on rotor reference frame as shown in figure 1. At any time t, the rotating rotor d-axis makes and angle θr with the fixed stator phase axis and rotating stator mmf makes an angle α with the rotor d-axis. Stator mmf rotates at the same speed as that of the rotor. The modeling of PMSM is done by taking sinusoidal induced EMF excluding losses such as eddy current and hysteresis are negligible and no cage on rotor [1].

. Figure.1. Motor axis

In the rotating d-q reference frame, the stator current equations can be written as given below:-

1 .

^q

d d d q

d d d

s r

d R L

i u i i

dt  L  L   L

(1)

1

^d ^f

q q q d

q q q q

s

r r

d R L

i u i i

dt L L L L

  

   

(2)

^T

^e

^ ^1.50 ^{P i} ^ _

^q

^

^f

^ ^{i i L}

^{d q}



^q

^ ^L

^d

 ^ _

(3)

^m

¹ 

^e L ^m



d T T B

dt   J   

(4)



r

 p 

m (5) Equations (1-3) are electrical equations which describe the direct and quadrature axis current change and electrical torque, while equation (4) is a mechanical equation giving angular speed change. Here,



f



Magnetic flux of the rotor,

L

d



d- axis inductance of the stator,

L

q



q-axis inductance of the stator,

R

s



Resistance of the stator,

T

e



Electromagnetic torque of the drive,

T

L



Load torque of the drive,



m



Mechanical speed of the rotor,



r



Angular speed of

the rotor,

J 

Moment of inertia,

B 

Friction Coefficient,

p 

No. of poles

Surface mounted PM motors have a surface mounted permanent magnet rotor. Each of the PM is mounted on the surface of the rotor, making it easy to build, and specially skewed poles are easily magnetized on this surface mounted type to minimize cogging torque. These motors are considered to have small saliency, thus having practically equal inductances in both axes [4]. The permeability of the permanent magnet is almost that of the air, thus the magnetic material becoming an extension 0f the air gap. For a surface permanent magnet motor Ld = Lq.

Figure.2. Surface permanent magnet motor

Interior PM motors have interior mounted permanent magnet rotor as shown in figure2[1]. Each permanent magnet is mounted inside the rotor. It is not as common as the surface- mounted type but it is a good candidate for high-speed operation. There is inductance variation for this type of rotor because the permanent magnet part is equivalent to air in the magnetic circuit calculation. These motors are considered to have saliency with q axis inductance greater than the d axis inductance ( Lq > Ld ) [2].

Figure.3. Interior mounted permanent magnet motor

This section presents the theoretical review of permanent magnet motors drives which includes permanent magnet materials, classification of permanent magnet motors, the construction and advantages. A dynamic mathematical modeling of a permanent magnet synchronous motor from three phase stator reference frame to equivalent two phase

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rotor reference frame called d-q model of a permanent magnet synchronous motors also derived which can be easily implemented in MATLAB/Simulink.

III. SVPWM A. Introduction

SVPWM is accomplished by rotating a reference vector around the state diagram, which is composed of six basic non- zero vectors forming a hexagon. A circle can be inscribed inside the state map and corresponds to sinusoidal operation.

The area inside the inscribed circle is called the linear modulation region or under-modulation region. As seen in Figure 4, the area between the inside circle and outside circle of the hexagon is called the nonlinear modulation region or over-modulation region. The concepts in the operation of linear and nonlinear modulation regions depend on the modulation index, which indirectly reflects on the inverter utilization capability [3].

Figure.4. Under-modulation and Over-modulation Regions in Space Vector Representation.

B. Principle of space vector PWM

A three-phase mathematical system can be represented by a space vector. For example, given a set of three-phase voltages, a space vector can be defined by

2 4

0 3 3

( ) 2 ( ) ( ) ( )

3

j j

a j b c

V t V t e V t e V t e

 

 

    

 

(6) where Va(t), Vb(t), and Vc(t) are three sinusoidal

voltages of the same amplitude and frequency but with

±120o phase shifts. The space vector at any given time maintains its magnitude. As time increases, the angle of the space vector increases, causing the vector to rotate with a frequency equal to that of the sinusoidal waveforms. When the output voltages of a three-phase six-step inverter are converted to a space vector and plotted on the complex plane, the corresponding space vector takes only on one of six discrete angles as time increases. The central idea of SVPWM is to

generate appropriate PWM signals so that a vector with any desired angle can be generated. In the space-vector modulation, a three-phase two-level inverter can be driven to eight switching states where the inverter has six active states (1-6) and two zero states (0 and 7). The basic principle of SVPWM is based on the eight switch combinations of a three- phase inverter [4]. The switch combinations can be represented as binary codes that correspond to the top switches S1, S3, and S5 of the inverter as shown in Figure5.

Figure.5. Three phase bridge inverter

Each switching circuit generates three independent pole voltages Vao, Vbo, and Vco, which are the inverter output voltages with respect to the mid-terminal of the DC source marked as „O‟ on the same figure. These voltages are also called pole voltages [5-7].

Space Vector Switching State On-state Switch V e c t o r

D e f i n i t i o n

V

0 [000] S4,S6,S2 →−

V

0

=

0

V

1 [100] S1,S6,S2 →−

V

1

=

2

V d c

e

j

V

2 [110] S1,S3,S2 →−

V

=

2

V e

j

π 2

V

3 [010] S4,S3,S2 →−

V

=

2

V e

j

2

V

4 [011] S4,S3,S5 →−

V

=

2

V e

j

V

5 [001] S4,S6,S5 →−

V

=

2

V e

j

V

6 [101] S1,S6,S5 →−

V

=

2

V e

V7 [111] S1,S3,S5 →−

V

7

=

2

V Table.1. Space Vectors, Switching States, and On State Switches

The reference voltage vector

V

_ref rotates in space at an angular velocity ω = 2πf, Where f is the fundamental frequency of the inverter output voltage. When the reference voltage vector passes through each sector, different sets of switches in Table. 1 will be turned on or off. As a result,

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4 when the reference voltage vector rotates through revolution in space, the inverter output varies one electrical cycle over time. The inverter output frequency coincides with the rotating speed of the reference voltage vector. The zero vectors (

V

0 and

V

₇) and active vectors (

V

1 to

V

₆) do not move in space. The switching times are arranged symmetrical around the center of the switching period s h o w n in Figure 6. The zero vector

V

₇ (1,1,1) is placed at the center of the switching period, and the zero vector

V

₀

(0,0,0) at the start and the end, and the total period for a zero vector is divided equally among the two zero vectors. In the under-modulation region, as the modulation index increases, the reference voltage vector grows outward in magnitude. It reaches the inscribed circle of the hexagon and T0 will reduce to zero whenever the tip of the reference voltage vector is on the hexagon. From figure 6, a zero state vector is applied followed with two adjacent active vectors in half of the switching period.

The next half of the switching period is symmetrical to the first half. To generate the signals that produce the rotating vector, an equation is required to determine the time intervals for each sector [8].

Figure.6. Construction of Symmetrical Pulse Pattern for Three-Phase

This chapter deals with the mathematical and theoretical concepts of control technique used for producing gate pulses for voltage source inverter and space vector pulse width modulation control. The mathematical modeling is provided which is easily designed and implemented in matlab/Simulink by using the simpowersystem tool.

IV.MODEL REFERENCE ADAPTIVE SYSTEM

The MRAS method depends on two models. These are shown in the diagram viz. reference and adjustable model. The reference model is taken as PMSM and the adjustable model is taken as the current model of PMSM. The current model of PMSM is discussed in the section of modeling of PMSM. The

difference signal is generated from the output of the two models and a PI controller is employed to ensure that the system output is converged. The reference model does not depend on rotor speed while adaptive model is rotor speed dependent as shown in figure 7. The output of both models are I_d and I_q .Now, we can estimate the speed of rotor by certain adaptive model.

The stator current equations can be written in the matrix form [9-11].

Fig.7. Typical model reference control system.

Figure.8. shows the model formed by the stator current equations of PMSM in the rotating d-q reference frame. The rotor speed is included in these equations.

s d

d d q

s s

R u

d i i i

dt   L    L

(7)

s r q

q q d

s s s

R u

d i i i

dt L L L

  

    

(8)

Figure.8. Stator current model of PMSM

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1

s

d d s d

q q s q

s

R

i i u

d L

i i R u

dt L

L



  

 

     

   

        

          

(9)

Let

i

d ^r

i

d

L

   

;

i  

q

i

q (10) d ^r d

u R u

L

   

^;

u  

^q

u

^q (11) The speed estimation process can be described as:

ˆ ˆ ˆ 1

ˆ ˆ

ˆ

d d d

q q q

R i i u

d L

R u

dt i i L

L



  

  

           

             

      

 

(12)

The error of the static variable is e=

i    i ˆ

Equation (9) can be written as

d ˆ ˆ ˆ i i A u B

dt     

(13)

From the equations shown above

 ˆ

can be obtained as

2

ˆ ˆ

1

ˆ ˆ

ˆ k i i (

q d

i i

d q

) k i i (

d q

i i d

d q

) ˆ (0)

                

⁽¹⁴⁾

When k₁ and k₂ ≥0

By replacing

i

d,

i

q with

i

d,

i

q we get the estimates speed as

1

ˆ ˆ ˆ

ˆ k i i [

q d

i i

d q

( i

q

i

q

)

^r

] d L

          ^ ^{k i i}

²

^[

^{d q}

^ˆ

ˆ

^{d q}

(

^q

ˆ

^q

)

^r

] ˆ (0)

s

i i i i L

 

   

(15)

Figure .9. Estimated speed of MRAS

ˆ

_d

i

and

i ˆ

_q are of adjustable model in this equation and

i

d,

i

qcan be obtained from the stator current transformation.

MRAS is one of the most widely accepted speed regulation scheme since it is simple and require least extra hardware to implement [12].

This section deals with the theoretical concepts of sensor less technique used for the speed control of PMSM. A detailed mathematical modeling of model reference adaptive system (MRAS) is provided which can be easily designed and implemented in MAYLAB/Simulink using simpowersystem tool.

V.SIMULATION AND RESULTS

Simulation is performed in the matlab Simulink software version 7.10. Simulation time is kept 0.6sec. Result is verified under low speed (300rpm) and high torque (150Nm) system.

Fig.10. shows the result of real and reference speed and fig.11 shows the result of estimated speed obtained by MRAS estimation algorithm. It is clear from the figure that the actual speed will follow the reference speed after 0.2sec.

Figure.10. Reference and Actual speed of PMSM

Figure.11. Estimated speed obtained by MRAS system

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6 VI. CONCLUSION

This paper shows that the sensor less speed control of PMSM using SVPWM technique based on MRAS method is very effective. Overall performance of PMSM for low speed and high torque systems is good. The estimated speed is calculated by the adjustable and reference model and thus compared with the reference speed. The error is calculated by the comparator and reduced with the help of PI controllers and SVPWM technique. The overall performance of the controlled algorithm is checked in matlab simulation and the results shows that MRAS based PMSM derive has good dynamic response for low speed and high torque system. The implementation of additional control techniques such as direct torque control (DTC), other sensor less control schemes can be taken up for future research, performance calculation and practical implementation of PMSM drives.

References

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[3]. B.Wu High-Power Converters and AC Drives. IEEE Press, John Wiley and sons, Inc., 2006.

[4]. R.Krishnan, Electric Motor Drives Modeling, Analysis, and Control Pearson Education 2001.

[5]. O. Saadaoui, A. Khlaief, A. Chaari, M. Boussak, “A new approach rotor speed estimation for PMSM on sliding mode observer,” Journal of Automation & Systems Engineering (JASE), vol. 9, pp. 66-78, 2015.

[6]. S. Dhundhara, P. Kumar, and Y. P. Verma, “Sensor less speed control of PMSM using Space Vector Pulse Width Modulation based on MRAS method,” 2015 2nd Int. Conf. Recent Adv. Eng. Comput. Sci., no.

December, pp. 1–6, 2015.

[7]. Z. Wa.ng, J. Chen, M. Cheng, and K. T. Chau, “Field-oriented control and direct torque control for paralleled VSIs Fed PMSM drives with variable switching frequencies,” IEEE Trans. Power Electron., vol. 31, no. 3, pp. 2417–2428, 2016.

[8]. E.Hendawi, F.Khater and A.Shaltout, “Analysis, simulation and implementation of space vector pulse width modulation inverter,”

International Conference on application of electrical engineering, pp.124-131, 2010.

[9]. S. Mohamed, M. S. Zaky, A. S. Zein El Din, and H. A. Yasin,

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Innov. Syst. Des. Eng., vol. 2, no. 5, pp. 44–66, 2011.

[10]. X.Xi, LI Yongdong, Zhang Meng, Liang Yan, “A Sensorless Control Based on MRAS Method in Interior Permanent-Magnet Machine Drive”, pp 734-738, PEDS 2005.

[11]. Z. Bingy, Cen Xiangjun et al. “A position sensor less vector control system based on MRAS for low speeds and high torque PMSM drive”

Railway technology avalanche, vol.1, no.1, pp.6, 2003

[12]. Z.Bingyi, C.Xiangjun, S.Guanggui, F.Guihong, “A Position Sensorless Vector-control System Based on MRAS for Low Speed and High Torque PMSM Drive” , International Conference on electrical machines and system (ICEMS (Volume:2 ), pp 1682 – 1686,sept 2005.

MRAS Based Sensorless Speed Control of PMSM for Low Speed and High Torque System