abstract

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Goal of my project: Over the years induction motor has been utilized as a workhorse in the electrical industry Due to its easy construction, high robustness and generally satisfactory efficiency with the invent of high speed power semiconductor devices three-phase inverter play the key role for variable speed ac motor drives. Traditionally six switches, 3 phase inverters have been widely utilized for variable speeds induction motor drives. This involves the losses of the six switches as well as the complexity of the control algorithms and interface circuits to generate six PWM logic signals. In the past researches mainly concentrated on the development of the efficient control algorithms for high performance variables speed induction motor drives, however the cost, simplicity and flexibility of the overall drive system which becomes some of the most important factors did not get that much attention to the researchers in this area most of the developed control system failed to attract the industry. 1

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Page 1: Abstract

Goal of my project:

Over the years induction motor has been utilized as a workhorse in the electrical industry

Due to its easy construction, high robustness and generally satisfactory efficiency with

the invent of high speed power semiconductor devices three-phase inverter play the key

role for variable speed ac motor drives. Traditionally six switches, 3 phase inverters have

been widely utilized for variable speeds induction motor drives. This involves the losses

of the six switches as well as the complexity of the control algorithms and interface

circuits to generate six PWM logic signals.

In the past researches mainly concentrated on the development of the efficient control

algorithms for high performance variables speed induction motor drives, however the

cost, simplicity and flexibility of the overall drive system which becomes some of the

most important factors did not get that much attention to the researchers in this area most

of the developed control system failed to attract the industry.

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Page 2: Abstract

INTRODUCTION:

Induction motors are being used for many industrial and commercial applications because

it its easy build, high robustness, and generally satisfactory efficiency. AC induction

motors, which contain a cage, are very popular invariable-speed drives. They are simple,

rugged, inexpensive and available at all power ratings. Progress in the field of power

electronics and microelectronics enable the application of induction motors for high-

performance drives. The speed of the induction motor can be controlled by varying its

input AC voltage and frequency using an Inverter. A standard six - switch three phase

voltage source inverter has six switches in three legs with a pair of complementary power

switches per phase. A reduced switch count voltage source inverter i.e. four switch three-

phase inverter (FSTPI)] uses only two legs, with four switches. The advantage of this

inverter due to the use of 4 switches instead of conventional 6 switches is lesser

switching losses, lower electromagnetic interference (EMI), less complexity of control

algorithms and reduced interface circuits. Several articles report on FSTPI structure.

Power semiconductor devices constitute the heart of the modern power electronics, and

are being extensively used in power electronic converters in the form of a matrix of on -

off switches, and help to convert power from one form to another. There are four basic

conversion functions that can be implemented namely; ac to ac, ac to dc, dc to ac and dc

to dc. The switching mode power conversion gives high efficiency but the disadvantage

is that due to the non- linearity of the switches, harmonics are generated in both the

supply and load sides. The switches are not ideal and they have conduction, turn-on and

turn off switching losses. Although the cost of the power semiconductor drives, may

hardly exceed 20-30 percent, the total equipment cost and performance may be highly

influenced by the topology of the circuit used for power conversion. Owing to the

development of power electronics in power conversion, AC adjustable speed drives are

becoming more and more popular for industrial applications. This equipment improves

energy efficiency, but there are key issues, like efficiency and harmonic injection into the

line, which affects the power factor, and the overall cost of the system, and these issues

need to be considered before any drive is used for industrial or commercial purpose.

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Page 3: Abstract

One way to increase the efficiency of the drive is by reducing the losses at possible places

such as in the converter used along with the ac motor. These losses are computed as

switching losses and conduction losses. It may also be improved as the number of circuit

elements is minimized, because as the number of devices reduces the associated amount

of switching reduces and so the losses are minimized.

Proliferation of nonlinear loads, such as three-phase rectifiers, adjustable speed drives

and uninterruptible power supplies are prone to high harmonic injection into the utility,

which powers them. To reduce harmonic injections, improvement in displacement factor

is considered and so power factor correction equipment like capacitors and filters are

installed in the system. Harmonic currents cause resonance between utility and

harmonic–producing loads or among multiple harmonic producing loads. These harmonic

related phenomena result in de-rating of the system equipment such as transformers,

higher transmission line loss and reduced system stability margin. Since electrical motors

consume around 56% of the total consumed electrical energy the improvement in power

factor of electrical drives as seen by the utility connection has been of major concern.

Another consideration is the need to increase the VA capacity of motor drives, so that the

full utilization of the isolated real power is possible.

In order to solve some of these problems, a large variety of control techniques and

converter topologies have appeared in the literature. Since good quality power factor

systems are becoming more and more mandatory, power factor improvement is one of the

key issues in designing a system.

Several methods have been attempted in order to obtain a satisfactory

power quality from the supply mains. The use of terminal capacitors

across the machine windings is very common, due to its low cost and

simplicity. However, this method is often not often recommended for

the adjustable speed drives employing inverters which are PWM operated, as

the capacitor may draw high harmonic currents due to the harmonics present in the PWM

terminal voltages, and the motor may experience self-excitation, which might cause over-

voltages in its terminals.

In rural electric systems, the cost of bringing three-phase power to a remote location is

often high due to high cost for a three-phase extension. Furthermore the rate structure of a

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Page 4: Abstract

three-phase service is higher than that for single-phase service. Therefore, single-phase to

three-phase power converters are excellent choices for situations where three-phase

power is not available. Such converters have a wide range of applications in which a

three-phase motor is a main component and the available supply is single-phase. Other

factors that influence the choice of a static converter and three–phase motor combination

are listed as follows:-

1. Three–phase motors are more efficient and economical than their single-phase

counter parts.

2. Starting and inrush currents in a three-phase motor are less severe than in a single-

phase motor.

Owing to wide applications of power converters, it is essential to

develop single to three-phase converters, which are efficient, cost

effective and give high quality performance. Presently, available

converters for such applications are classified as rotary type;

autotransformer with switched capacitors and lastly, the static

converter type. The first two types of converters as given in employ

bulky magnetic components of considerable size and weight. The third

category that employs static semiconductor devices for direct

conversion of single-phase to three-phase is by far the most active

research area in which the bulky magnetic part can be eliminated and

embedded control of the line and the load can be achieved. The superiority of static

converters is further reinforced with the advances in power semiconductor devices and

their control logic.

Previous work on static single-phase converters involves the use of thyristors in

combination with L, C components, as in. The disadvantage of this scheme is the limited

control range and the L-C values must be matched with the load impedances. Moreover

the circuit topology is bulky due to the reactor used with the input. In a number of

reduced switch count converter topologies for generating high quality three-phase

voltages from single-phase mains have been presented, in which the converters were

classified as active input current shaping feature ones and those without the active input

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Page 5: Abstract

current shaping feature. The converters, which do not employ the input current shaping

feature have reduced number of switches when compared to ones in which this feature

was included, but in both types the converter size is large due to the inductor, in series

with the single-phase supply.

In a new single-phase to three phase converter for low cost ac motor

drive was presented, which employed only six switches and

incorporates an active input current shaping feature that results in

sinusoidal input current close to unity power factor. This converter has

the capability of bidirectional power transfer, an improvement on all

the previously proposed converters. In new topologies for single to

three-phase power conversion was proposed in which the zero

sequence voltage was used to control the supply side parameters. This

allowed the integration of the load and supply control, and with this

class of converters unity power factor operation was possible. Low power

drive systems typically in the range of fractional horse-power (hp) to 1 hp, due to their

massive emerging applications in appliances and in industrial processes have been of

great interest for researchers to explore their performance while improving the same. For

these low power drives it is very common to use the single-phase to three-phase type of

converter to drive the motor. The usual approach for these adjustable speed drives is to

implement the power factor correction (PFC) feature in the power converter itself, which

normally requires additional circuitry and controls. Some analysis has been done in order

to evaluate the impact of these PFC schemes in the drive system in terms of performance

and costs. It was concluded that, though a good system input power factor improvement

can be achieved, the used of additional PFC control feature may not be very attractive for

induction motor drives, due to cost and packaging factors. Hence, in order to make this

scheme more cost effective, it is important to develop power converters with PFC

schemes using a reduced number of components and more integrated controls.

Due to the variety of the topologies and control strategies, the

converter topologies have been differentiated as Conventional

converters and Sparse converters. In Conventional circuits the

numbers of switching devices are sufficient enough to achieve

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independent control of both the converter and the three-phase

inverter. In sparse converters the number of switching devices are not

sufficient enough to achieve this independent control, thus the

converter and inverter control actions are dependent on each other. As

the number of switching devices are reduced the name sparse

converters has been given.

Main advantages of the four-switch converter compared to the

conventional six-switch converter can be summarized as

bellow ;

The number of the power semiconductor switches and the fly-wheel diodes are

reduced, resulting in cost and space savings. Besides, the control and drive

circuits are reduced which itself brings more savings.Due to a reduced number of

switches, the conduction and switching losses in the semiconductor devices will

be reduced.

Eliminating some semiconductor devices from the topology, directly leads to

more reliability.

DC link voltage is as twice as a six-switch converter. Although it is an advantage

in the rectifier operation mode, but it may not be desired in some inverter

applications.

This topology also has some drawbacks;

The third phase current flows through the DC link capacitors. So they are

exposed to low frequency harmonics which calls for bigger values for the DC link

capacitors.

A controller is needed to balance the capacitors voltages. It is proved that the

balanced voltages can be readily achieved by a simple proportional controller.

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Page 7: Abstract

Since the four-switch converter does not eliminate the third-order harmonics

automatically, so a bigger value for switching frequency is expected.

Literature survey:

1. M.B.R. Correa, C.B. Jacobina, E.R.C. Silva, A.M.N. Lima: A General PWM

Strategy for Four-switch Three-phase Inverters, IEEE Transactions on

Power Electronics, Vol. 21, No. 6, Nov. 2006, pp. 1618 – 1627.

This paper presents a method to generate PWM signals for control of

four-switch three-phase inverters. With the proposed approach, it was

possible to study several PWM schemes using three or four vectors to

synthesize the desired output voltage during the switching period. The

scalar version of the proposed modulation technique can be

implemented by software and may be easily included in drive software

with a negligible increase in the computational effort. The effects of

capacitor unbalance have been evaluated, and compensation

procedures have been proposed. The THD analysis shows that the

PWM pattern based on three vectors, in which two are small, presents

the lowest harmonic distortion. However, the common-mode voltage

analysis points out that use of the two greatest vectors, , is more 7

Page 8: Abstract

adequate for common-mode voltage reduction. The paper also

presented suitable PWM strategies to be applied when the motor

windings are delta connected.

2. M.N. Uddin, T.S. Radwan, M.A. Rahman: Fuzzy-logic-controller-based

Cost- effective Four-switch Three-phase Inverter-fed IPM Synchronous

Motor Drive System, IEEE Transaction on Industry Application, Vol. 42,

No.1, Jan/Feb. 2006, pp. 21 – 30.

A cost-effective 4S3Ph-inverter-fed IPMSM drive incorporating an FLC

has been developed, simulated, and successfully implemented in real

time using the DSP TI TMS320C31 for a prototype 1-hp motor. The

proposed 4S3Ph-inverter-based drive reduces the cost of the inverter,

the switching losses, and the complexity of the control algorithms as

well as interface circuits as compared to the conventional 6S3P-

inverter-based drive. The vector control scheme has been incorporated

in the integrated drive system to achieve high performance. The

incorporation of FLC as a speed controller enhances the robustness of

the drive. In order to verify the robustness of the proposed approach,

the performances of the proposed FLC-based 4S3Phinverter- fed IPMSM

drive have been investigated both theoretically and experimentally at

different operating conditions. A comparison of performances for the

proposed 4S3Ph-inverterfed IPM motor drive with a conventional

6S3Ph-inverter-fed drive has also been made in terms of THD of the

stator current and speed response under identical operating

conditions. The proposed 4S3Ph-inverter-fed IPMSM drive has been

found robust and acceptable for high-performance industrial variable

speed- drive applications considering its cost reduction and other

inherent advantageous features.

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Page 9: Abstract

3. F. Blaabjerg, D.O. Neacsu, J.K. Pedersen: Adaptive SVM to Compensate

DC-link Voltage Ripple for Four-switch Three-phase Voltage-source

Inverters, IEEE Transactions on Power Electronics, Vol. 14, No. 4, July 1999,

pp.743 – 752.

This paper introduces a new adaptive SVM approach for compensating the dc-link ripple

in a B4 inverter. To achieve this goal, both dc-link voltages are sensed and the equations

corresponding to the time portions allocated to the switching vectors by the SVM method

are modified accordingly. The theory, design, and performance of this PWM method are

presented, and the method effectiveness is demonstrated by extensive simulations and

experiments. The quality of the inverter output waveforms is demonstrated to be the same

as for the ripple-free case. Furthermore, this adaptive SVM method allows reducing the

size of the dc-filter capacitors. However, assuming the presence of the dc-ripple leads to a

more reduced value of the maximum rms phase voltage and to additional stress of the

power devices and the induction machine which have to be weighted against the

advantages.

4. C.T. Lin, C.W. Hung, C.W. Liu: Position Sensorless Control for Four-switch

Three-phase Brushless DC Motor Drives, IEEE Transactions on Power

Electronics, Vol. 23, No. 1, Jan. 2008, pp. 438 – 444.

This paper has presented a novel FPGA-based sensorless control

scheme for four-switch three-phase brushless dc motor drives. In the

scheme, a novel asymmetric PWM scheme using six commutation

modes in the FSTP inverter is proposed. The position information is

estimated from the crossings of voltage waveforms in floating phases,

and a low cost FPGA is utilized to implement the algorithm. Because

the stator current waveforms of the FSTP inverter using this novel

voltage PWM scheme are rectangular, the motor will operate smoothly

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Page 10: Abstract

and the torque ripple will be at the same level. However, the two

estimated commutations maybe cause commutation torque ripple. The

experimental results show that the scheme works very well. With the

developed control scheme and the lowest cost implementation, the

proposed scheme is suitable for commercial applications.

5. J. Kim, J. Hong, K. Nam: A Current Distortion Compensation Scheme for

Four-switch Inverters, IEEE Transactions on Power Electronics, Vol. 24, No.

4, April 2009, pp. 1032 – 1040.

It was investigated that the source impedance unbalance and the

center tap voltage fluctuation were the major reasons for the phase

current distortion of the four-switch inverters. Both of them originated

from the limited (finite) capacity of dc-link capacitors. Hence, the

motor phase current distortion becomes ignificant as the frequency

decreases, load increases, and the capacitance decreases. The

corresponding errors were derived as the functions of the capacitive

variable , and a compensation method was proposed based on . The

effectiveness of the proposed method was supported by the simulation

and experimental results. The proposed method, just requiring

measurements of -phase current, can be easily implemented.Thus, the

proposed method is believed to be a viable tool for four-switch

inverters.

6. Stanislav Bartos, Ivo Dolezel, Jakub Necesany, Jiri Skramlik and Viktor

Valouch Institute of Thermomechanics ASCR, Dolejskova, Electromagnetic

Interferences in Inverter-Fed Induction Motor Drives, Institute of

Thermomechanics ASCR, olejskova 5, 182 00 Praha 8, Czech Republic.

The equivalent models of the feeding cable as well as the IM suitable

for the determination of stray current disturbances in the common and

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Page 11: Abstract

differential modes have been suggested. The frequency characteristics

of selected parts of the system and their contributions to the resultant

harmonic spectra have been evaluated as well. The responses

obtained on this model well correspond with the responses captured on

the real drive system. This holds even at the very beginning of the

transients, where the variables variables (mainly currents) are

characterized by steep changes (peaks) and high frequencies. As for

the IGCT inverters, it has to be expected that these inverters may

produce similar voltage waves traveling along the cables connecting

the inverters and ac motors and resulting phenomena as those

produced by the IGBT inverters, although IGCT total switching times

are substantially longer. The paper summarizes also the experience

acquired during laboratory experimental operation of the IGBT and

IGCT inverter feeding a 3-phase induction machine (IM) as well as

practical knowledge gained from the employment of these switching

devices in vehicles of city mass transportation.

7. M. Nasir Uddin, T. S. Radwan, and M. A. Rahman, Performance Analysis of

a Cost Effective 4-Switch 3-Phase Inverter Fed IM Drive, IRANIAN

JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL.

5, NO. 2, SUMMER-FALL 2006 1682-0053/06$10 2006 JD, 97

A cost effective 4S3P inverter fed IM drive has been simulated and successfully

implemented in real-time using TI TMS320C31 DSP for a prototype 1 hp induction

motor. The proposed control approach reduces the cost of the inverter, the switching

losses, and the complexity of the control algorithms and interface circuits as compared to

the conventional 6S3P inverter based drive. However, the proposed inverter based drive

suffers from slight unbalance in the phase currents which cause relatively higher speed

vibrations as compared to the conventional 6S3P inverter fed drive. The vector control

scheme is incorporated in the integrated drive system to achieve high performance. The

performance of the proposed drive is investigated both theoretically and experimentally

at different operating conditions. A performance comparison of the proposed 4S3P

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Page 12: Abstract

inverter fed drive with a conventional 6S3P inverter fed drive is also made in terms of

total harmonic distortion (THD) of the stator current and speed response. The proposed

4S3P inverter fed IM drive is found acceptable for high performance industrial variable

speed drive applications considering its cost reduction and other advantageous features.

Proposed Topology

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Page 13: Abstract

In the simulation and experimental work, the single phase half bridge rectifier converts

AC power to DC. The DC power is fed to FSTPI. The FSTPI converts the DC power to

controlled 3-phase AC power. The 3-phase induction motor is driven by the FSTPI.

Microcontroller is used to generate the controlled PWM pulse for FSTPI. The controlled

PWM pulses of microcontroller are fed to the gate of MOSFETs of FSTPI through the

driver circuit to drive the IM.

Fig1: circuit diagram of four switch three phase inverter

Principle of FSTPI operation

The power circuit of the FSTPI fed IM drive is shown in Fig. 1. The circuit consists of 4-

switches S1 , S2 , S3 and S4 and split capacitors C1 and C2 . The 3-phase AC input,

which is of fixed frequency, is rectified by the rectifier switches. The power circuit is the

three-phase four-switch inverter. Two phases ‘a’ and ‘b’ are connected to the two legs of

the inverter, while the third phase ‘c’ is connected to the center point of the dc-link

capacitors, C1 and C2 .The 4 power switches are denoted by the binary variables 1 S to

4 S , wherethe binary ‘1’ corresponds to an ON state and the binary ‘0’ corresponds to an

OFF state. The states of the upper switches ( S1 , S2 ) and lower switches ( S3 , S4 ) of

a leg are complementary that is S3 =1− S1 and S4 =1− S2 . T he terminal voltages Vas

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Page 14: Abstract

,Vbs and Vcs of a 3-phase Y-connected Induction Motor can be expressed as the function

of the states of the upper switches as follows:

Since, there is no control on the third phase, the middle point of the DC

link (point C) is taken as the reference, so:

where Vas , Vbs , Vcs are the inverter output voltages,V c is the voltage across the

dc link capacitors, Vdc is the voltage across the capacitors C1 and C2 (V c =V dc / 2 ).

In matrix form the above equations can be written as:

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Page 15: Abstract

Block diagram of FSTPI fed closed loop induction motor drive:

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Page 16: Abstract

The block diagram of the proposed FSTPI fed induction motor drive system is shown in

figure 2.

The drive system consists of:

Three phase AC supply,

Three-phase diode bridge rectifier,

Three-phase four switches Inverter (FSTPI),

3-phase induction motor.

The controlled equipments are:

Control logic,

Processor board.

The standard AC supply is converted to a DC voltage by a three-phase diode bridge

rectifier. A voltage source FSTPI is used to convert the DC voltage to a variable AC

voltage. The output of the FSTPI is fed to the three-phase induction motor. PC is loaded

with software and code composer software. The software consists of several external

modules used for different engineering applications. The values of each block are

adjusted according to the need of drive system. codes are generated and these codes are

targeted (loaded) to the processor. The processor generates the required PWM pulses

according to the user’s setting blocks in PC. The sensor is connected at the shaft of the

motor to sense the actual speed of the induction motor. The sensor output is fed to the

processor through the ADC of processor. The processor compares the reference speed

(set speed) with actual speed through software loaded. The generated error signal is fed

to the PI controller in the processor. Based on the output of PI controller, the processor

generates the required controlled PWM pulses for FSTPI to control the speed of the

induction motor.

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Page 17: Abstract

Limitations of FSTPI:

Due to the inherent voltage vector limitation in the four-switch inverter, three-phase 120˚

balanced current can only be obtained by using 60˚phase shifted PWM control strategy.

In order to properly utilize the four-switch inverter topology in a certain application, it is

very important to understand its operational limitations. The main limitations are lower

voltage utilization and higher harmonic components. Consequently, it can result in an

increased harmonic copper losses and torque pulsations. Therefore, the four-switch

inverter cannot be an alternative to the six-switch inverter configuration in all application

areas, but can be a good choice in middle power range application, in which a certain

harmonic level can be tolerated. For this circuit to be more effectively utilized advanced

PWM control strategies should be developed for wide application in industry.

Applying the component minimization concept of the four switch inverter to the

conventional three-phase to three-phase PWM converter system, we can reduce the

number of switches from the conventional configuration and come up with the eight

switch based configuration.

The desirable functions of an active power factor correction scheme are line voltage

rectification, bus voltage regulation and line current wave shaping. To perform these

tasks an additional circuitry, based on a dc-dc converter, is added to the front-end

rectifier. Among a number of dc-dc topologies proposed in the literature, the use of a

boost converter has been considered very appropriate for many applications due to the

following reasons.

1) The dc bus voltage is higher than the conventional diode bridge rectified ac

voltage. This is very convenient to increase the range of operation of single-phase

to three phase motor drive inverters.

2) It has an inductor in the input and a capacitor at the output, which is very

convenient for filtering.

Figure 1.3 shows the conventional active power factor correction scheme based on the

boost converter. The input current shaping is done by the boost action of the inductor and

the switch‘s’.

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Page 18: Abstract

For efficient operation of the above scheme the circuit needs to be operating at a high

switching frequency in tens of kHz range. At higher switching frequencies the switching

losses increase, and the cost of high voltage diodes with fast reverse recovery

characteristics prove to be costly.

This configuration does not provide bi-directional power flow between the dc bus and the

ac mains, which is a very desirable feature for ac motor drives. Moreover, though the

boosted dc bus improves the drive operating range, when compared to the conventional

system, still there is a limitation for the system speed range. Several single-phase to

three-phase topologies were proposed in [7] with bidirectional power flow and input

current shaping capabilities and with reduced component count.

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Page 19: Abstract

References

[1] J. Kim, J. Hong, K. Nam: A Current Distortion Compensation Scheme for Four-

switch

Inverters, IEEE Transactions on Power Electronics, Vol. 24, No. 4, April 2009, pp. 1032

– 1040.

[2] M.B.R. Correa, C.B. Jacobina, E.R.C. Silva, A.M.N. Lima: A General PWM Strategy

for

Four-switch Three-phase Inverters, IEEE Transactions on Power Electronics, Vol. 21,

No. 6,

Nov. 2006, pp. 1618 – 1627.

[3] M.N. Uddin, T.S. Radwan, M.A. Rahman: Fuzzy-logic-controller-based Cost-

effective

Four-switch Three-phase Inverter-fed IPM Synchronous Motor Drive System, IEEE

Transaction on Industry Application, Vol. 42, No.1, Jan/Feb. 2006, pp. 21 – 30.

[4] C.T. Lin, C.W. Hung, C.W. Liu: Position Sensorless Control for Four-switch Three-

phase

Brushless DC Motor Drives, IEEE Transactions on Power Electronics, Vol. 23, No. 1,

Jan.

2008, pp. 438 – 444.

F. Blaabjerg, D.O. Neacsu, J.K. Pedersen: Adaptive SVM to Compensate DC-link

Voltage

Ripple for Four-switch Three-phase Voltage-source Inverters, IEEE Transactions on

Power

Electronics, Vol. 14, No. 4, July 1999, pp.743 – 752.

[6] Microchip Technology, 2001, PIC16F877A Data sheet, www.microchip.com.

[7] M. Vasudevan, R. Arumugam, S. Paramasivam: High-performance Adaptive

Intelligent

Direct Torque Control Schemes for Induction Motor Drives, Serbian Journal of Electrical

Engineering, Vol. 2, No. 1, May 2005, pp.93 – 116.

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Page 20: Abstract

[8] M. Bounadja, A. Mellakhi, B. Belmadani: A High Performance PWM Inverter

Voltage-fed

Induction Machines Drive with an Alternative Strategy for Speed Control, Serbian

Journal

of Electrical Engineering, Vol. 4, No. 1, June 2007, pp.35 – 49.

[9] K. Rathnakannan, V. Ranjan: The Modeling and the Analysis of Control Logic for a

Digital

PWM Controller based on a Nano Electronic Single Electronic Transistor, Serbian

Journal

of Electrical Engineering Vol. 5, No. 2, Nov. 2008, 285 – 304.

[10] MATLAB, Simulink User Guide, Math Works Inc., 2007

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