FFT Analysis for Field Oriented Control of SPWM and SVPWM Inverter fed Induction Machine With and Without Sensor

(1)

ISSN (Print) : 2278-8948, Volume-2, Issue-4, 2013

151

FFT Analysis for Field Oriented Control of SPWM and SVPWM Inverter fed Induction Machine With and Without Sensor

Nisha G.K.¹, Z.V. Lakaparampil² & S. Ushakumari³

1&3EEE Dept., College of Engineering, Trivandrum, Kerala, India

2C-DAC (T), Trivandrum, Kerala, India

E-mail : ¹[email protected], ²[email protected], ³[email protected]

Abstract – Adjustable speed drives offer significant energy savings and precise responses in industrial applications.

The indirect field oriented control can provide good dynamic torque response as that obtained from DC motor drives. The concept of indirect field oriented control is based on the effective pulse width modulation pattern generation and effective estimation of rotor flux and speed.

An effective modulation technique can achieve by attaining maximum voltage with lowest harmonic distortion in output waveform. The speed sensors are the most delicate part and often pose serious threats to control issues in the whole drive system. Thus extensive efforts are being made to eliminate the speed sensors from the drive system with an effective speed estimation technique. In this paper, a comparative study of field oriented controlled induction machine with and without sensor using two popular PWM strategies, SPWM and SVPWM. The induction motor drive systems are simulated using MATLAB/Simulink.

The comparative study is based on the harmonic distortion in line-to-line inverter voltage waveforms using an FFT analyzer of MATLAB/Simulink.

Keywords – Induction machine, Field oriented control, Space vector pulse width modulation, Total harmonic distortion.

I. INTRODUCTION

The advancement in microprocessor and power electronics revolution made it possible to implement complex control algorithms of the field oriented control (FOC), which in turn made induction machine as one of the dominating machine in the drives market [1]. The pulse width modulation (PWM) is one of the most widely used techniques applied in the inverter (DC/AC converter) to output an AC waveform with variable voltage and variable frequency for use in mostly variable speed motor drives [2]. The implementation of the complex PWM algorithms have been made easier due to the advent of fast digital signal processors,

microcontrollers, and Field Programmable Gate Arrays (FPGA) [3].

The principle of PWM is based on multiple pulses in each half AC period with the process of modifying the width of the pulses in a pulse train in direct proportion to a small control signal. Among the different types of pulse width modulations, sinusoidal pulse width modulation (SPWM) and space vector pulse width modulation (SVPWM) are the popular ones. In SVPWM, no separate modulators are needed for each of the three phases in comparison with SPWM. The basic concept of SPWM is to achieve symmetrical 3-phase sine voltage waveforms of adjustable voltage and frequency, while in SVPWM, both the inverter and motor are taken as whole using the eight fundamental voltage vector to realize variable frequency of voltage and speed adjustment. SVPWM is increasingly used for AC drives due to the fact that the harmonic current is as small as possible and the maximum output voltage is as large as possible [4]-[7].Space vector modulation is a sophisticated PWM method that provides advantages such as higher DC bus voltage utilization and lower total harmonic distortion [8], [9].

During the past decade, sensorless speed control of induction machine has become a mature technology for a wide speed range [10], [11]. Sensorless control of Induction machine is now attracting wide attention, both in the field of electrical drives and in the field of dynamic control. The advantages of speed sensorless AC drives are reduced hardware complexity, lower cost, elimination of sensor cable, better noise immunity, increased reliability, access to both sides of the shaft, less maintenance requirements and higher robustness [12]. The use of encoders increases the drive‟s price and affects the reliability which is of utmost concern to

(2)

152 many operational situations especially the electric vehicle industry [13], [14].

In the literature, many research efforts have been made for rotor speed estimation in the sensorless speed control. The voltage model flux estimations as proposed in [15] have problems at low frequency regions and is sensitive to leakage inductance. Adaptive observer based approaches [16], [17] using the derived adaptive laws can have better performance with relatively simple computation, but their robustness to parametric uncertainties is never guaranteed. The Kalman filter approaches [18], [19] are known to be able to get accurate speed information and better flux estimation, but have some inherent disadvantages, such as the influence of noise, computational expense and having no specific design and tuning criteria. Recently, extended Kalman filter (EKF) algorithms for estimating stator and rotor resistance are adopted for achieving accurate estimated values [20]. Modal reference adaptive system (MRAS) methods [21] are based on comparison between outputs of two estimates, and the output errors are then used to drive a suitable adaption mechanism, which computes the estimated speed.

Among the above strategies, MRAS schemes are popular due to their relative simplicity and less computational effort [22].

The aim of this paper is to compare the performance of field oriented controlled induction machine with and without sensor using both SPWM and SVPWM inverters by analyzing the THD of line voltages. The paper is organized as follows. Section II provides the dynamic model of field oriented controlled induction machine with and without sensor. Section III presents the principles and implementation of SPWM and SVPWM three phase inverters. Section IV describes the concepts of harmonic analysis. Section V explains the simulation of sensor and sensorless FOC of induction machine with SPWM and SVPWM inverters.

Section VI discusses the simulation results generated by MATLAB/Simulink.

II. DYNAMIC MODEL OF FIELD OREINTED CONTROLLED INDUCTION MACHINE WITH

AND WITHOUT SENSOR

The basis of FOC is to use rotor flux angle to decouple torque and flux producing components. The stator currents are transformed to a rotating reference frame aligned with the rotor flux vectors to produce d- axis component of current and q-axis component of current. Torque can be controlled by the q-axis component of stator current space vector and flux controlled by the d-axis component of current vector.

In this paper, indirect FOC is used to control the torque and speed of the machine. Independent control of motor flux and torque are obtained by this method, it is possible by connecting coordinate system with rotor flux vector. To explain the principle of vector control, an assumption is made that the position of the rotor flux linkage, Ψr is at an angle θ from the stationary reference and is referred to as the field angle. Independent control of motor flux and torque can be obtained by this method, it is possible by connecting coordinate system with rotor flux vector. Fig. 1 shows the Park transformation module and the stator current space vector and its component in rotating reference frame by using the transformation as shown in Eq. (1):

Fig. 1 : Current space vector in rotating reference frame

cos sin

sin cos

sd s

sq s

i i





 

    

     

  ⁽¹⁾

Fig. 2 shows the vector diagram of induction motor in stationary α-β and rotating d-q coordinates. The rotor synchronous speed is equal to the angular speed of the rotor flux vector. The reference frame d-q is rotating with the angular speed equal to rotor flux vector angular speed.

Fig. 2: Phasor diagram of field oriented drive system

The applied space vector method as a mathematical tool for the analysis of the electric machines, the complete set of equations can be expressed in the stationary coordinate α-β system. The output signals flux, speed and torque depend on both the inputs, by the orientation of the coordinate system to the stator or rotor

(3)

153 flux vectors decoupling of flux and torque can be achieved. The motor model equations defined with respect to α-β reference frame can be written as given in (2) (3) and (4):

( )

s

s s s

s

s s s

r

r r r r

r

r r r r

d V t R i

dt

d V t R i

dt

d R i p

dt

d R i p

dt



 



 



 



 



  

 

  

  

  

 

(2)

 

2 3 2

r m

s s s s L

r

d P L

J i i T

dt L ^{ } ^{ }

 ^    ^

  (3)

The flux current equation is written as,

s s s m r

r r r m s

L i L i L i L i L i L i L i L i

  

  

  

  



 

(4)

The complete motor dynamic equation is obtained by separating the real and imaginary components of the voltage and current complex space vector. The two phase d-q model of an induction machine rotating at a speed will give the decoupled control concept [23], [24].

The d axis voltage equations expressed at the d-q reference frame rotating with a speed ωe is represented as:

sd

sd s sd s m rd s e sq m e rq

di d

V R i L L i L i L i

dt dt  

    



(5)

   

0 _{r rd} _rdi^rd _m d _sd _r _e _r _rq _m _e _r _sq

R i L L i L i L i

dt dt    

      

(6) The motor torque can be expressed by rotor flux magnitude and stator current component, if the rotor can be kept constant as in the case of DC machine, then the torque control can be accomplished by controlling the current component.

 

2 3 2

m

d r sq

r

T P L i

L 



(7) where,

L_s = L_m(1+s) : Stator self Inductance L_m : Magnetizing Inductance

s : Stator leakage factor L_r = L_m(1+r) : Rotor self Inductance

_r : Rotor leakage factor R_s : Stator resistance R_r : Rotor resistance T_d : Electromagnetic torque T_L : Load torque

r : rotor speed in electrical rad/sec

P : Number of poles

θ : Angle between d and stator a axis τr : Rotor time constant

i_mr : Rotor magnetizing current

_slip : Slip angular frequency

_e : Rotor flux speed

Block diagram of field oriented control of induction motor with sensor is shown in Fig. 3. The most accepted reference frame is the frame attached to the rotor flux linkage where the torque can be instantaneously controlled by controlling the current i_qs after decoupling the rotor flux and torque producing component of the current components. The flux along the q axis must be zeroas given by,

rq 0 d

dt

 

⁽⁸⁾

Fig.3: Block diagram of FOC inductions machine with sensors The fundamental equations for field oriented control which allows the induction motor to act like a separately excited DC machine with decoupled control of torque and flux making the induction motor to operate as a high performance four quadrant application.

Up to rated speed, rotor magnetizing current is kept constant to get the fast control over electromagnetic torque of the machine because the dynamics of the

(4)

154 magnetizing current involves a big time constant. From the voltage loop equation, the magnetizing current dependency on the d component of stator current and slip angular frequency in terms of the rotor flux linkage and q axis current is represented as:

mr 0

m r rd

L di R i

dt   ⁽⁹⁾

mr

sd mr r

i i di

 dt

  ₍₁₀₎

r sq

e r

r mr

R i

  L i ₍₁₁₎

The expression for the electromagnetic torque of the machine becomes:

2

3 2 (1 )

m

d mr sq

r

P L

T i i

 



(12) where

r r

r

L

 R

In MRAS scheme, with two independent machine models, speed estimation is obtained by comparing the output of the reference model with the output of the adaptive (adjustable) model until the error between the two models disappear [25]. Figs. 4 and 5 describe the classical rotor flux MRAS and sensorless FOC with MRAS speed estimator. The reference value of the rotor flux components are generated from the monitored stator voltage and current components [3], [26] which are given by,

( )

r

r s s s s s

m

L v R i dt L i

 L   

  



  

(13)

( )

r

r s s s s s

m

L v R i dt L i

 L   

  



  

(14) 1 1

(1 _s)(1 _r)

^{ }   (15)

Fig.4 : Bock diagram of conventional MRAS speed estimator The adaption mechanism of conventional rotor flux MRAS is a simple fixed gain linear PI controller. The adaptive values of rotor flux components are given by,

ˆ_r 1 ( _{m s} ˆ_r ˆ_{r r}ˆ_r )

r

L i T dt

 T   

 



   ⁽¹⁶⁾ ˆ_r 1 ( _{m s} ˆ_r ˆ_{r r}ˆ_r )

r

L i T dt

 T   

 



   ⁽¹⁷⁾

ˆ ˆ

r r r r

e_ _ _ _ _ ⁽¹⁸⁾ The adaptive scheme for the MRAS estimator can be designed based on Popov‟s criteria for hyper stability concept [27], The expression for estimated rotor speed is given by,

ˆ_r K e_p _ K e dt_i _

  



⁽¹⁹⁾

Fig.5 : Block diagram of sensorless FOC induction machine with MRAS speed estimator

III. SPWM AND SVPWM BASED THREE PHASE INVERTERS

The three phase two level voltage source inverter is used for driving the motor by accepting the control signals generated by the controller. The modulation technique used here are sine triangle and space vector pulse width modulation. In sin PWM the controlled sine waves for the three phases are compared with a carrier triangular waveform to obtain PWM pulses for the three phases and in SVPWM the required pulses can be generated by comparing the modulating functions with the triangular waveform. These PWM pulses are given to the gate of the inverter switches to get a controlled three phase output voltage which can be given to the motor input. In three phase system, each pole voltage node can apply a voltage between +V_DC/2 and –V_DC/2.

The relationship between the pole voltage and line-to- line voltage vector is given by Eq. 20.

1 1 0

0 1 1

1 0 1

ab ao

bc bo

ca co

V V

      

      

     

     

     

(20)

(5)

155 Also, the relationship between the pole voltage and output line-to-neutral voltage (phase voltage) vector can be expressed by Eq. 21.

2 1 1

1 1 2 1

3 1 1 2

an ao

bn bo

cn co

V V

 

     

      

     

      

     

(21)

where, V_an, V_bn and V_cn are the three phase voltages which are applied to the stator of the induction machine.

A. Sinusoidal Pulse Width Modulation

Sinusoidal PWM has relatively unsophisticated method employs a high-frequency carrier triangular wave compared with three sinusoidal reference wave of the desired frequency. The intersection of the carrier and reference waves determine the PWM signals for the three phases, which define the switching instants of the power devices in the inverter. The carrier and reference waves are mixed in a comparator, when sinusoidal wave has magnitude higher than the triangular wave, the comparator output is high, otherwise it is low. The inverter output voltage is explained as,

control carrier

V V





2 2

DC AO

V V

 

  ⁽²²⁾

The modulation index (m) is the ratio of V_m/V_c, where V_cis the peak value of the carrier wave and V_m that of the modulating wave and it controls the harmonic content of the output voltage waveform. The modulation index can be varied between 0 and 1 to give a linear relation between the reference and output wave. The asymmetrical nature of the PWM switching characteristics produces relatively high harmonic distortion in the supply [28].The magnitude of the fundamental component of output voltage are controlled by changing the magnitude of the modulating signal, but it can never be more than unity. This method is unable to make full utilization of the inverter‟s supply voltage.

B. Space Vector Pulse Width Modulation

The three phase symmetric system represented in a natural coordinate system by phase quantities such as currents, voltages and flux linkages of AC motors can be analyzed in terms of complex space vectors [29].

Any three time varying quantities, which always sum to zero and are spatially separated by 120 can be expressed as space vector. A three phase system defined by V_a(t), V_b(t), V_c(t)) can be represented uniquely by a rotating vector as,

2 /3 2 /3

( ) ( ) ^j ( ) ^j

a b c

V V t V t e ^ V t e^ ^ ⁽²³⁾

where,

V_a(t) = V_msinωt

V_b(t) = V_msin(ωt-2/3) V_c(t) = V_msin(ωt+2/3)

In space vector pulse width modulation, the three phase stationary reference frame voltages for each inverter switching state are mapped to the complex two phase orthogonal α-β plane known as the Clark‟s transformation as shown in (24). The reference voltage is represented as a vector in this plane.

1 1

1 2 2

3 3

0 2 2

an bn cn

V V V V

V





 

 

 

   

     

      

(24)

Fig. 6 shows a typical two-level three phase Voltage Source Inverter (VSI) configuration. The three legs of the three phase inverter can connect the phases of the motor to positive or negative terminal of the DC bus voltage. In order to generate a rotating field, the inverter has to be switched in six of the eight states. When the upper switch is „ON‟, the corresponding lower switch is in „OFF‟ position which can be used to determine the output voltage. Only one switch in an inverter leg can be turned on at a time to avoid short circuit in the DC link.

In three phase system, each pole voltage node can apply a voltage between +V_DC/2 and –V_DC/2. Six non-zero vectors (V₁ and V₆) shape the axis of hexagonal called the active vectors and the angle between any adjacent two non-zero vectors is 60 [30]. Two of these states (V₀ and V₇) correspond to a short circuit on the output called the zero vectors, while the other six can be considered to form stationary vectors in the - complex plane as shown in Fig. 7.

The transition of reference vector moving from one sector in the space vector diagram to the next requires minimum number of switching in order to reduce the switching losses

Fig. 6. Three phase voltage source inverter configuration

(6)

156

Fig. 7: Space vector hexagon

[31]. Any space vector lies in the hexagon can be constructed by time averaging of the adjacent two active space vectors and zero vectors. If T₁ and T₂are the time for which space vector V₁ and V₂ are applied, for each switching period T_s, the geometric summation can be expressed by applying volt-second balancing as,

0

1 2

1 2 0

ref

s s s

T

T T

V V V V

T T T

  



(25) The space vector, V_ref is normally represented in complex plane and the magnitude as,

2 2

tan 1

Vref V V V V

 





 ^

 



(26)

The six active vectors are of equal magnitude and are mutually phase displaced by π/3, these vectors divide the complex plane into the six sectors [32]. The general expression is represented by,

( 1) /3

2 . , 1, 2,...., 6 3

j n

n DC

V  V e ^ ^ n (27) The reference vector could be synthesized by the adjacent switching state vectors V1 and V2, the duty cycle of each being d_α and d_βrespectively and the zero vector duty cycle d₀ are given by,

0

sin( / 3 ) sin

1

d m

d d d





 

 



 



  

(28)

where, 1 2 0

, , 0

s s s

T

T T

d d d

T T T

     ^Vref

DC

m V

V

This gives switching times T₀, T₁and T₂ for each inverter state for a total switching period, Ts. The dwell

times for the seven segment add up to the sampling period T_s. The four modulating functions, m₀, m₁, m₂ and m₃, in terms of the duty cycle for the space vector modulation scheme is expressed as,

0 0

1 0

2 1

3 0

2 m d

m m d







 

(29)

Switching time for each sector is shown in Fig. 8.

Fig. 8: Switching tmes for each sector

The required pulses are generated by comparing the modulating functions with the triangular waveform [29].

A typical seven segment switching sequence for generating reference vector in sector six is shown in Fig. 9.

Fig. 9: Switching logic signals for sector- 6

IV. HARMONIC ANALYSIS TECHNIQUE The concept of harmonic distortion is used as the performance index to compare various PWM algorithms. The most important aim of the modulation strategies is to achieve the maximum voltage with the lowest harmonic distortion. Total harmonic distortion

(7)

157 (THD) and weighted total harmonic distortion (WTHD) are the commonly used performance evaluation methods [2], [3]. To measure the harmonic performance, Total Harmonic Distortion (THD) method is used and is expressed as,

2

3,5... 1 n n

THD V

V





 

  

 



(30) where, V_n is the harmonic component for the n^th harmonic and V₁ is the fundamental component.

V. SIMULATION

Simulation models for i) FOC with sensor using SPWM inverter, ii) FOC with sensor using SVPWM inverter, iii) sensorless FOC with SPWM and iv) sensorless FOC with SVPWM have been developed using MATLAB/Simulink. The switching frequency selected for both the inverters is 5 kHz. The induction machine used for the simulation is a 1.5 kW having the motor parameters as given in Table I.

TABLE I : PARAMETERS OF INDUCTION MOTOR

R_s 4.850 

R_r 3.805 

L_s 0.274 H

L_r 0.274 H

L_m 0.258 H

P 4

J 0.03 Nm

B 0.00334 Nm.s

VI. RESULTS AND DISCUSSION

In the simulation, for comparing the harmonic performance of line-to-line voltage, the motor starts from a standstill state with reference speed 104 rad/sec and application of a load torque, T_L = 5 N.m at time, t = 1 sec for all cases. Figs. 10 and 11 show the responses of rotor speed and electromagnetic torque for FOC with and without sensor respectively feeding with SPWM and SVPWM inverters. The motor torque has a high initial value in the speed acceleration zone, then the value decreases to zero and increases to the applied load torque and performed well in all cases.

(a) SPWM

(b) SVPWM

Fig.10 : Torque and speed response of the drive system with sensor

(a) SPWM

(b) SVPWM

Fig.11 : Torque and speed response of the drive system without sensor

Figs. 12 and 13 gives the output waveforms of line- to- line voltages at time, t = 0.4 sec and FFT analysis spectrum of SPWM and SVPWM strategies in field oriented controlled induction machine with and without sensor. In Fig. 12, it is observed that THD for FOC with sensor using SPWM and SVPWM are 125.47% and 95.32% respectively and for sensorless FOC as shown in Fig. 13, it is seen that 214.01% and 119.42%.

By comparing and observing all the simulation results, it ensures that the developed simulation models work well and shows that the total harmonic distortion of line-to-line voltages by SVPWM inverter is less compared to that of SPWM in both cases of FOC, with and without sensor.

(8)

158

(a) SPWM

(b) SVPWM

Fig.12 : FFT analysis of line voltage with sensor

(a) SPWM

(b) SVPWM

Fig.13: FFT analysis of line voltage without sensor

VII. CONCLUSIONS

In this paper, simulation models of field oriented controlled induction motor were developed with and without sensor feeding with both SPWM and SVPWM inverters. For sensorless FOC, the speed estimation technique adopted is the MRAS observer with the classical PI controller. The performance of the developed models is verified with the speed and torque responses. Simulation results ensure that the SVPWM scheme performs better in terms of THD of the output line voltage and also it is observed that THD in sensorless FOC is more compared to FOC with sensor.

In sensorless field oriented controlled induction motors, SVPWM inverter is the suitable one as it generates less harmonic distortion in addition to the more effective bus voltage utilization.

(9)

159 VIII. ACKNOWLEDGMENT

The first author acknowledges support from SPEED- IT Research Fellowship from IT Department of the Government of Kerala.

IX. REFERENCES

[1] J. Holtz, ”Sensorless control of induction machines: with or without signal injection” IEEE Trans. Ind. Elect., vol. 53, no. 1, pp. 7-30, Feb.

2006.

[2] D. G. Holmes and T. A. Lipo, “Pulse Width Modulation for Power Converters: Principles and Practice,” New Jersey: Wiley IEEE Press, 2003.

[3] H. Abu Rub, Atif Iqbal and Jaroslaw Guzinski,

“High performance control of AC Drives,”

NewYork: Wiley, pp. 375-388, 2012.

[4] D. P. Marcetic and S. N. Vukosavic, ”Speed sensorless AC drives with the rotor time constant parameter update,” IEEE Trans. Ind. Elect., vol.

54, no. 5, pp. 2618-2625, May 2007.

[5] J. Holtz, “Pulse width modulation - a survey,”

IEEE Tran. Ind. Elect., vol. 39, no. 5, pp. 410- 420, Oct. 1992.

[6] G. K. Nisha, S. Ushakumari and Z. V.

Lakaparampil, “Harmonic Elimination of Space Vector Modulated Three Phase Inverter”, in Proc.

Multi-conference of Engineers and Computer Scientists, IMECS 2012, pp. 1109-1115, Mar.

2012.

[7] G. K. Nisha, S. Ushakumari and Z. V.

Lakaparampil, “Method to Eliminate Harmonics in PWM: A Study for Single Phase and Three Phase”, International conference on Emerging Technology, Trends on Advanced Engineering Research, vol. 2, pp. 598-604, Feb. 2012.

[8] A. Mehrizi-Sani and S. Filizadeh, “An optimized Space Vector Modulation Sequence for Improved Harmonic Performance,” IEEE Trans. Ind. Elect., vol. 56, no. 8, pp. 2894-2903, Aug. 2009.

[9] H. W. Van der Broeck, H. C. Skudelny and G.V.

Stanke, " Analysis and realisation of a pulse width modulator based on voltage space vectors", IEEE Trans. Ind. Appl., vol. 24, pp. 142-150, Jan./Feb. 1988.

[10] J. Quan and J. Holtz, “Sensorless vector control of induction motors at very low speed using a non linear inverter model and parameter identification,” IEEE Trans. Ind. Appl., vol. 38, no. 4, pp. 1087-1095, Jul./Aug. 2002.

[11] H. Tajima, Y. Hori, “Speed sensorless field orientation control of the induction machine”, IEEE Trans. Ind. Appl., vol. 29, no.1, pp. 175- 180, Jan./Feb.1993.

[12] F. Z. Peng and T. Fukao, “Robust speed identification for speed-sensorless vector control of induction motors,” IEEE Trans. Ind. Appl., vol. 30, pp. 1234–1240, Sept./Oct. 1994.

[13] H. Tajima, G. Guidi and H. Umida,

“Consideration about problems and solutions of speed estimation method and parameter tuning for speed sensorless vector control of induction motor drives,” IEEE Trans. Ind. Appl., vol. 38, no. 5, pp. 1282-1289, Sept./Oct. 2002.

[14] B. K. Bose, “Adjustable speed AC drives - A technology status review,” in Proc. IEEE- IECON, vol. 70, pp. 116-135, Feb. 1982.

[15] H. Abu Rub, M. R. Khan, A. Iqbal and S. M.

Ahmed , “MRAS based sensorless control of a five phase induction motor drive with a predictive adaptive model,” in Proc..IEEE Ind.

Elect. Conf., pp. 3089-3094, Jul. 2010.

[16] H. Kubota, K. Matsuse, and T. Nakano, “DSP- based speed adaptive flux observer of induction motor,” IEEE Trans. Ind. Appl., vol. 29, no.2, pp.

344-348, Mar./Apr. 1993.

[17] G. Yang, and T. H. Chin, “Adaptive-speed identification scheme for a vector controlled speed sensorless inverter-induction motor drive,”

IEEE Trans. Ind. Appl., vol. 29, no.4, pp. 820- 825, Jul./Aug.1993.

[18] Y.-R. Kim, S.-K. Sul, and M.-H. Park, “Speed sensorless vector control of an induction motor using an extended kalman filter,” IEEE Trans.

Ind. Appl., vol. 30, no. 5, pp. 1225-1233, Sept./Oct. 1994.

[19] Y. S. Kim, S. U. Kim, and L. W. Yang,

“Implementation of a speed sensorless vector control of induction machine by reduced-order Kalman filter,” in Proc. IEEE APEC 95 Conf., Dallas, TX, pp. 197–203, Mar. 1995.

[20] M. Barul, S. Bogosyan and M. Gokasan,

“Experimental evaluation of braided EKF for sensorless control of induction motors,” IEEE Trans. Ind. Elect. , vol. 55, no. 2, pp. 620-632, Feb. 2008.

[21] L. Zhen and L. Xu, “A mutual MRAS identification scheme for position sensorless field orientation control of induction machines,” in

(10)

160 Proc. IEEE-IAS Conf., Orlando, pp. 159–165.

Oct. 1995.

[22] M. Rasheed and A. F. Stronach, “A Stable back- EMF MRAS based sensorless low speed Induction motor drive insensitive to stator resistance variation, ”in Proc. IEE Elect. Pow.

Appl., vol. 151, no. 6, pp. 685-693, Nov. 2004.

[23] W. Leonhard, “Control of Electrical Drives,”

New York: Springer, pp. 163-180, 1996.

[24] Z. V. Lakaparampil, K. A Fathima and V.T.

Ranganathan, ”Design modeling simulation and implementation of vector controlled induction motor drive,” in Proc. Power Electronics, Drives and Energy Systems for Industrial Growth 1996 Conf., vol. 2, pp. 862-868, Jan.1996.

[25] B. K. Bose, “Modern Power Electronics and AC drives,” Prentice Hall of India Pvt. Limited, New Delhi, pp. 390-392, 2009.

[26] C. Schauder, “Adaptive speed identification for vector control of induction motors without rotational transducers,” IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1054-1061, Sept./Oct. 1992.

[27] Y. D. Landau, “Adaptive Control-The Model Reference Approach,” Marcel Dekker, 1979.

[28] Chen Y.M. and Cheng Y.M., “PWM control using a modified triangle signal”, IEEE Trans.

Ind. Elect., vol. 29, no. 1, pp. 312-317, Feb. 1999.

[29] K. Zhou and D. Wang, “Relationship between Space Vector Modulation and three phase carrier based PWM: A Comprehensive Analysis,” IEEE Trans. Ind. Elect., vol. 49, no. 1, pp. 186-196, Feb. 2002.

[30] A. Mehrizi-Sani and S. Filizadeh, “Digital Implementation and Transient Simulation of Space Vector Modulated Converters,” IEEE Power Engineering Society General Meeting, Montreal, QC, Canada, Jun. 2006.

[31] J. Holtz, P. Lammert and W. Lotzkat, “High speed drive system with ultrasonic MOSFET PWM inverter and single-chip microprocessor control,” IEEE Trans. Ind. Appl., vol. 23, no. 6, pp. 1010-1015, Nov. 1987.

[32] V. G. Agelidis, A. I. Balouktsis, and M. S. A.

Dahidah, “A five level symmetrically defined selective harmonic elimination PWM strategy:

Analysis and experimental validation,” IEEE Trans. Pow. Elect., vol. 23, no. 1, pp. 19-26, Jan.

2008.

