Induction motor frequency

An induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor needed to produce torque is obtained by electromagnetic induction from the magnetic field of the stator winding. An induction motor can therefore be made without electrical connections to the rotor. An induction motor's rotor can be either wound type or squirrel-cage type Induction motors, both single and polyphase, are designed for use with a particular frequency of AC power. Occasionally we're confronted with a 'wrong' frequency motor. In this article I'll help you understand the ramifications. There are a large number of interacting relationships in a motor's design Browse other questions tagged motor frequency induction-motor formula-derivation or ask your own question. The Overflow Blog Podcast 283: Cleaning up the cloud to help fight climate change. How to lead with clarity and empathy in the remote world. Featured on Meta. Synchronous speed, frequency, and poles. Synchronous speed, frequency, and poles of the induction motor are related by the formula: η sync = (120 * f e) / P. η sync = Synchronous speed. f e = Frequency of the system. P = Number of poles installed in the machin Induction Motor Speed Control by Changing the Line Frequency If we change the frequency provided to the stator then the change in a rotational magnetic field will be directly proportional to the change in frequency and at the torque-speed curve, the location of no-load point will also vary you can observe this change in a given diagram

Induction Motor Calculator. Calculate the synchronous speed, slip and rated torque for an induction motor. System Frequency (Hz) Number of poles. Rated Speed (rpm): Rated Power (kW): × Motor Starting Time Calculation. Close. Tip: registered users can save calculations. Symbols. f. Synchronous speed is the speed of rotation of the magnetic field in a rotary machine, and it depends upon the frequency and number poles of the machine. The induction motor always runs at speed less than its synchronous speed. The rotating magnetic field produced in the stator will create flux in the rotor, hence causing the rotor to rotate. Due to the lag between the flux current in the rotor.

Induction motor - Wikipedi

  1. al speed of 1500rpm but will run near 1455 rpm
  2. ute (RPM). these values need to be converted to frequency by formula [math]f = rps[/math] and [mat..
  3. Variable Frequency Control of Induction Motor Drive: Variable Frequency Control of Induction Motor Drive - Synchronous speed, therefore, the motor speed can be controlled by varying supply frequency. Voltage induced in stator is proportional to the product of supply frequency and air-gap flux
  4. Let us discuss what is the frequency of the induced emf at the Rotor..
  5. ations)
  6. Speed Control of Induction Motor by Variable Frequency Control Variable Frequency Control is a method which is used to control the speed of an induction motor. The synchronous speed and therefore, the speed of the motor can be controlled by varying the supply frequency.The synchronous speed of an induction motor is given by the relation shown below
  7. The VFD System: The Variable Frequency Device has three parts like an AC motor, a Controller, and an Operating interface. The AC motor used in VFD is generally a three-phase induction motor even though the single-phase motor is used in some systems. Motors that are designed for fixed-speed operation is generally used, but some motor designs offer better performance in VFD than the standard design

Changing an Induction Motor's Power Supply Frequency

3 Phase Induction motor control using variable frequency drive(VFD) Variable Frequency drive or VFD is the most popular and has found widespread use in industrial and domestic applications because of its ease of implementation. They can be used in control of motors used in conveyors and other machinery 50Hz motor will run 20% faster on 60Hz power supply AC motor kilowatt is proportional to Torque times RPM. As the motor's torque is not going to change significantly with the increase of frequency, it will now output 20% more power. A 10kW 50Hz motor will be a 12kW motor on 60Hz power source Induction motor drives with closed-loop control are used in similar applications to d.c. motor drives (i.e. cranes and hoists, winders and un-winders, paper and pulp processing, metal rolling, etc.). These drives are also particularly suited to applications that must operate at very high speeds with a high level of field weakening, for example spindle motors FIGURE 1 Induction motor torque-speed characteristic curves.. Figure 2 showed the equivalent circuit for the stator. We can simplify our calculations by replacing it with a Thevenin's equivalent so that we do not have parallel branches in the equivalent circuit. Figure 3 shows a Thevenin's equivalent of the stator

frequency - Relationship of Induction Motor Frequencies

Operating principles. The two main types of AC motors are induction motors and synchronous motors. The induction motor (or asynchronous motor) always relies on a small difference in speed between the stator rotating magnetic field and the rotor shaft speed called slip to induce rotor current in the rotor AC winding. As a result, the induction motor cannot produce torque near synchronous speed. Most AC motors are induction motors. Induction motors are favored due to their ruggedness and simplicity. In fact, 90% of industrial motors are induction motors. Nikola Tesla conceived the basic principles of the polyphase induction motor in 1883 and had a half horsepower (400 watts) model by 1888. The speed of a three phase induction motor is given by, N = N s (1-s) and N s = 120f/P This shows the speed of three phase induction motor depends upon synchronous speed (N s) and slip(s).The synchronous speed of induction motor depends upon supply frequency and the number of stator poles. So by changing the supply frequency, the number of stator poles and slip we can change the speed of 3. Effect of Voltage Variation in Induction Motor: The speed-torque characteristic of an induction motor can be modified by Effect of Voltage Variation in Induction Motor. Typical Torque Speed Characteristics of Induction Motor when supplied from variable voltage at rated frequency are given in Fig. 1.24(a)

Induction Motor Formulas with Calculation

The induction motor especially three phase induction motors are widely used AC motor to produce mechanical power in industrial applications. Almost 80% of the motor is a three-phase induction motor among all motors used in industries. Therefore, the induction motor is the most important motor among all other types of motor FLine = Electrical line frequency - normally 60 Hz (3600 cpm) or 50 Hz (3000 cpm). 2 x FLine = Torque Pulse Frequency. This is a common frequency found on a high resolution spectrum. P = # of poles on the motor. The number of poles is how the speed of the motor is controlled. The greater the number of poles, the slower the motor runs When does an Induction motor reach pullout torque? No, more torque causes the rotor frequency to catch up to the stator frequency in less time, faster if u will. Which is the physical insight behind the widely approved 'space vector' notation used in the analysis of the dynamic model of electric machines

What are the Speed Control Method of Induction Motors

Tutorial - Induction Motor and PMSM Models with High-Frequency Effect. 9 . Fig. 7: Top: Induction machine motor drive with high frequency models; Bottom: Motor terminal voltage and common-mode current . The results show the presence of the high frequency components in the common mode curren High frequency heating induction is type of a heating process that uses high frequency electricity to heat the substances that are conductive electrically in nature. This article describes the basics of induction heating, the frequency range used for rapid heating of small parts or the skin of larger parts (mid-frequency 500 Hz to 10 kHz) and high-range (high frequency 100 kHz to 2 MHz) used. Induction motors in practice What controls the speed of an AC motor? In synchronous AC motors, the rotor turns at exactly the same speed as the rotating magnetic field; in an induction motor, the rotor always turns at a lower speed than the field, making it an example of what's called an asynchronous AC motor.The theoretical speed of the rotor in an induction motor depends on the frequency of.

In accordance with NEMA MG 1, 12.44, motors shall operate successfully under running conditions at rated load with variation in the voltage up to the following percentages of rated voltage: Universal motors except fan motors - plus or minus 6 percent (with rated frequency). Induction motors - plus or minus 10 percent (with rated frequency) First off, if you need a variable frequency drive for your AC motor, make sure you check out our web store. Calculating RPM for a three phase induction motor is relatively simple ACThree Phase Induction MotorRPMis determined by the formula: RPM = (120 * Frequency) / # of poles in the motor The synchronous speed. can be adjusted by changing the line frequency and number of poles of an AC motor. Similarly, frequency is the number of positive & negative cycles of input AC supply per second. The required speed can be achieved by adjusting supply frequency of an AC motor In America we use a frequency of 60 Hz while in Europe you will find a frequency of 50 Hz. It may not seem like a big difference, but altering the frequency on a motor can create big changes in how a motor will run. When you alter the frequency of a motor, the strength of the magnets inside the motor will change

What happens very much depends on the type of load attached to it. In some cases, the load is proportional to speed, e.g. fans. If we reduce voltage, the generated torque reduces, and so the speed reduces. The load torque due to air resistance als.. For an induction motor, if you change the frequency more than a little bit, you really want to change the voltage in unison. For example, if the motor is happy running at 240V and 60Hz, it will also be happy at 120V and 30Hz or 60V and 15 Hz. As long as the Volts over Frequency. Induction motors with squirrel cage rotors are relatively simple, very reliable, and low maintenance machines. Induction motors operate under the principle of electromagnetic induction and are also known as asynchronous motors since their rotation speed (RPM) does not reach the synchronous frequency of the electromotive field Starting of an Induction Motor A three phase Induction Motor is Self Starting. When the supply is connected to the stator of a three-phase induction motor, a rotating magnetic field is produced, and the rotor starts rotating and the induction motor starts. At the time of starting, the motor slip is unity, and the starting current is very large Frequency converter is most commonly used. It converts standard plant power (220V or 380 V, 50 Hz) to adjustable voltage and frequency to power AC motor. The frequency applied to AC motor determines motor speed. The AC motors are usually same standard motors that can be connected across AC power line

Comparison of Soft Starting and Frequency Converter Motor

machines, the behavior of induction motor fed by frequency inverter and methods on how to evaluate the performance of motors under non-sinusoidal supply as well This is an induction motor not a synchronous motor. Torque is only generated when slip exists between the rotor RPM and the stator's rotating magnetic field. The frequency needs to be slightly higher, typically around 5% to develop rated torque Variable Voltage Variable Frequency Speed Control of Induction Motor Using FPGA-Xilinx 1Ravi Prakash , 3Prof. Rishi Kumar Singh2, Rajeev Ranjan Kumar 1Ravi Prakash,Department of Electrical Engineering, Maulana Azad National Institute of Technology Bhopal, MP, Indi APPLICATION OF AC INDUCTION MOTORS WITH VARIABLE FREQUENCY DRIVES Barton J. Sauer, Consulting Applications Engineer Patrick A. Brady, Principal Business Developer Siemens Energy & Automation ABSTRACT Variable Frequency drives (VFD's) have been available to the cement industry for a number of years

<br>It is a detailed article on the Induction Motor Torque-Speed Characteristics I have explained every point related to an induction motor. this site had a lot of answers for your questions: I saw that but there is not a single formula related to my question. Contact us for feedback, legal purposes, adverstisement or just throw a Hi to us! In this picture, it is stated that the angle (S) is. Applied frequency and synchronous speed are equivalent, so going a step further; torque may be defined in terms of speed. In the constant voltage range then, motor torque drops off as the inverse of synchronous speed squared, or 1/(N squared). This is shown in the accompanying graph. Torque = (line frequency/extended frequency)squared. O Electric Motor Wiring - 480 Volt - Electrical motor wiring data - NEMA amps, starter size, HMCP size for motors ranging 1/2 to 500 hp; Electrical Induction Motors - Synchronous Speed - The speed at which an induction motor operates depends on the input power frequency and the number of electrical magnetic poles in the motor

Keywords: Induction Motor, Faults, Instantaneous frequency signature analysis I. INTRODUCTION Three-phase induction motors are the most widely used electrical machines. In an industrialized nation, they can typically consume between 40 to 50% of its generated capacity. Consequently, they have to be safe and reliable The equivalent inductance of three-phase induction motors is experimentally investigated in this paper, with particular reference to the frequency range from 1 kHz to 20 kHz, typical for the switching frequency in inverter-fed electrical drives. The equivalent inductance is a basic parameter when determining the inverter-motor current distortion introduced by switching modulation, such as rms. Induction motor high frequency model Abstract: In this paper, an accurate high frequency model of an induction motor is presented. The proposed model allows analysis, at the same time, of both high frequency phenomena up to some MHz due to the static supply, and low frequency phenomena usually analyzed by means of the dq motor model An induction motor operates at the frequency of the supply feeding it. One may vary the speed by varying the applied frequency. To operate, the motor requires flux in the iron -- or more specifically in the gap between the rotor and stator

Induction Motor Equations ENGN1931F - Spring 2017 2 Let ω ω ω L R S and be the angular velocities of the magnetic field (line frequency), rotor, and slip respectively. For convenience we assume that ϕ= 0 at t = 0, which implies ϕ ω= R t and ω ω ω S L R= −. The flux in the single-turn coil on the rotor surface i The two motors are mechanically coupled together to drive a common load. The starter of slip ring induction motor is connected to three-phase supply and its rotor is connected to stator of the other machine. There are four possible speeds can be obtained by this arrangement. Where f = supply frequency P1 = No of poles in slip ring motor It should always be understand that, for large Motor of rating more than 20 kW if the Induction Motor characteristics is required near s=1 i.e. for getting an idea of starting torque, then Blocked Rotor Test shall be performed at line frequency as the rotor frequency sf = f =line frequency. But if we need Induction Motor characteristics near. Induction Motor: Almost 70% of the machines used in industries now a days are 3 phase induction motors. It works on the principle of induction where electro-magnetic field (emf) is induced in to the rotor conductors when rotating magnetic field of stator cuts the stationary rotor conductors Speed control of induction motor is possible in two sides. stator side and rotor side. We can change the speed at the stator by, changing the supply frequency, changing the supply voltage and changing the number of stator poles.Speed control at the rotor side -We can change the speed at the rotor by,By adding some external resistance in the rotor circuitby cascade connection of the motor

In this way, the slip power of main motor is fed to the auxiliary induction motor at a frequency of f 2 = s 1 f 1.. Let us now assume that P 1, P 2 and s 1, s 2 be the number of poles and slips respectively. Then for the main motor, synchronous speed is 120f 1 /P 1.Therefore, its speed of rotation will b induction motor and this application lem alone. How amplitude modulation suits' are often seen in association note applies to this type of electric components and beat frequency com- with some of the 'magnetic' vibration motor. Engineers should be able to re- ponents can appear in the induction problems, because 'mechanical' prob In frequency controlled processes this is the voltage supplied by the variable frequency drive. The induction motor asks a certain current I. The induction motor has an inductive character because of the use of the different coils. This means that current and voltage through and over the windings are not in phase

Induction Motor Calculator - myElectrical

Home >> Category >> Electrical Engineering (MCQ) questions and answers >> 3 - Phase Induction Motors 1) The frequency of the induced emf in an induction motor is a The Polyphase Induction Motor The polyphase induction motor is the most commonly used industrial motor, finding application in many situations where speed regulation is not essential. It is simple and relatively inexpensive, and the absence of sliding contacts in the squirrel-cage machine reduces maintenance to a minimum An induction motor is practically a constant speed motor, that means, for the entire loading range, change in speed of the motor is quite small. Speed of a DC shunt motor can be varied very easily with good efficiency, but in case of Induction motors, speed reduction is accompanied by a corresponding loss of efficiency and poor power factor.As induction motors are widely being used, their. Speed Control of Variable Frequency Induction Motor: Further, the operation of the motor is eco­nomical and efficient, if it operates at very small slips. The speed of the motor is, therefore, varied by varying the supply frequency and maintaining the rotor frequency at the rated value or a value corresponding to the required torque on the linear portion of the torque-speed curve An induction motor is fed from a balanced three phase supply at rated voltage and frequency through a bank of three sing... GATE EE 1995. GO TO QUESTION. Skew is used in induction motors in order to reduce torque due to. A three phase squirrel cage induction motor has a starting current of seven times the full load current and full load sl..

There are a few key differences between AC induction Motors and Permanent Magnet Synchronous Motors. Permanent magnet motors MUST operate with a drive. AC induction motors can be used without a VFD to drive a pump or fan, but are often installed with variable frequency drives (VFD) in pump systems or fan systems in an effort to improve system efficiency Since an induction motor does not have a self-governing field circuitry, its circuit will not comprise an interior voltage source like the inner produced voltage E A, in a synchronous motor that exists. lt is probable to design the correspondent (equivalent) circuitry of an induction motor from the information of transformers (i) When a 3-phase induction motor is in normal operation, the rotor frequency f '= s f where f is the supply frequency) is low and so is the rotor reactance. The current that flows is then largely limited by rotor resistance rather than reactance For a given motor, the number of poles is fixed so the only way to change speeds is to change the frequency of the power supply to the motor. Because electrical grids run at a fixed frequency, induction motors generally run at a constant speed, with only slight variation as the load changes This project is about variable frequency drive for three phase induction motor using pic microcontroller. In this project voltage frequency control ( V/F ) method is used to control the speed of three phase induction motor. Induction motors have many industrial and domestic applications

Induction Motor: Basics & Types Electrical4

3 Phase Induction Motor speed Control VFD - YouTube

F = Supply Frequency (Hz) P = Number of poles. Motor Torque. The torque produced by an induction motor is a function of the shaft power and the shaft speed where the torque reduces with speed for constant power. T = 9.5493 x P / RPM. T = Torque (Nm) P = Power (KW) T = 5252 x P / RPM T= Torque (lb-ft) P= Power (HP Induction Motor General-purpose motors and vector variable frequency drive (VFD) dedicated motors are three-phase induction motors. These motors mainly consist of a rotary shaft, bearings, stator winding and connection terminals. Vector VFD dedicated motors have an encoder at the rea 3 phase Induction Motor frequency of induced emf current and power factor - problems 1. Three Phase Induction Motors Contents : Frequency of Rotor Rotor EMF Rotor Current and Power Factor Related Problems Kongunadu college of Engineering & Technology Three phase Induction - Frequency, Rotor EMF, Current and Power factor related Problem Soln: Frequency of supply to the induction motor f = pn/120 = 12 x 500 / 120 = 50 Hz . Speed of Induction motor = 1440 rpm, Number of poles of induction motor = p = 120 f / n = 120 x 50/1440 = 4.16 . The number of poles are to be even, selecting the nearest even number as th

How to determine the pole number of an induction motor

Increased induction motor losses, noise and vibrations, detrimental impact on the induction insulation system, and bearing failure are examples of frequency converter related systems' issues. Increased induction losses mean a de-rating of the induction output power to prevent overheating Frequency controlled motors These motors are optimized exclusively for variable speed applications. Compared to standard induction motors they offer improved characteristics such as energy efficiency, compactness, control performance and reliability Induction Motor Testing and Evaluation Summary As energy costs rise, more emphasis is being placed 2 * line frequency number of motor poles For a four pole AC motor operating on 60 Hz power, the syn-chronous motor speed is calculated as: 2 * 60 Hz 4 = 30 Hz or 1800 RP controller, and frequency counter. Power up the motor normally and determine the no-load * rpm when the motor, as viewed from the front, is rotating clockwise (CW); repeat with the motor spinning counter clockwise (CCW). BE CAREFUL !! It can hurt to tangle with a three-phase motor. A successful salesman for General Electric's motor division onc

My January 2013 Pumps & Systems' column focused on the reduction in motor horsepower (HP) as frequency is reduced by a variable frequency drive (VFD). I had several requests to revisit this subject and explain the relationship between HP and torque across a broad range of frequencies Digital control of induction motors results in much more efficient operation of the motor, resulting in longer life, lower power dissipation. Although various induction motor control techniques are in practice today, the most popular control technique is by generating variable frequency supply, which has constant voltage to ratio frequency ratio 4 Technical guide - Induction motors fed by PWM frequency inverters The number of industry applications in which induction motors are fed by static frequency inverters is growing fast and, although much has already been done within this fi eld, there is still a lot to be studied/understood regarding such applications

What is meant by rotor frequency? - Quor

3 Phase Induction Motor Speed Controller Circuit

Induction Motor Equivalent Circuit From the preceding, we can utilise the equivalent circuit of a transformer to model an induction motor. In the equivalent circuit R 1 represents, the resistance of the stator winding and X 1 the stator leakage reactance (flux that does not link with the air gap and rotor) Answer 1. Less than 1% . Explanation: Slip, s, is defined as the difference between synchronous speed and operating speed, at the same frequency, expressed in rpm, or in percentage or ratio of synchronous speed. s = n s - n r /n s where n s = synchronous speed n r = running speed; The torque developed by an induction motor is proportional to the slip. At synchronous speed, the slip is zero. RETURN HOME. VOLT PER HZ SPEED CONTROL OF AN INDUCTION MOTOR. The speed of an induction motor can be easily controlled by varying the frequency of the 3-phase supply; however, to maintain a constant (rated) flux density, the applied voltage must also be changed in the same proportion as the frequency (as dictated by Faraday's law).This speed control method is known as Volts per Hz Introduction Three-phase induction motors are the most common and frequently encountered machines in industry - simple design, rugged, low-price, easy maintenance - wide range of power ratings: fractional horsepower to 10 MW - run essentially as constant speed from no-load to full load - Its speed depends on the frequency of the power source • not easy to have variable speed control.

1. A double squirrel-cage induction motor has two rotors moving in opposite direction two parallel windings in the stator two parallel windings in the rotor two series windings in the stator 2. The starting torque of a squirrel-cage induction motor is low negligible same as the full-load torque slightly more than full-load torque 3. The <a title=Three Phase Induction Motor MCQs class. AC 3 phase induction motor with a frequency drive ! This is genius . First the the tree phase motor allows very fast starting with near zero lag time . Also AC 3 phase motors have lots of torque this why your S takes off like a slot car on steroids!

It is not surprising to find that this type of electric motor is so popular, when one considers its simplicity, reliability and low cost. In the last decade, it has become increasingly common practice to use 3-phase squirrel cage AC induction motors with variable voltage variable frequency (VVVF) converters for variable speed drive (VSD) applications Formulas and Equations for Linear and Induction Motors . The following equations and formulas related to linear and induction motors can be used to calculate the basic parameters while analyzing and designing a single phase and three phase induction motor induction motor are the fans and the rotor bars in the vents areas and at the rotor ends. Open Motors: These have a free exchange of internal and external air as shown in Figs. 1 and 2. The numbers on the figure refer to the parts of the motor: 1) Extended rotor bars, 2) rotor end rings, 3) rotor laminations, 4) rotor vents, 5

Traditionally induction motors only run well at a given stable speed and torque, however if used with a VFD - variable-frequency drive their uses can be increased. Parts: Stator - consists of an electro magnet around the outside of the motor This is a simple version of speed control of induction motor using V/F control method. This method is implemented on hardware using embedded coder and Texas instruments C2000 microcontroller using embedded coder. It done at inQbe innovation pvt ltd cochin, INDIA. see at www.inqbe.i In case of induction motor, any speed other than the synchronous one will be fine, and offer you an output, while for a synchronous machine, the only way to change speed is to change the frequency

Frequency converter also plays a major role in 3-phase induction motor, as it is responsible for feeding the 3-phase induction motor with the 3-phase power supply. Estimations show that rotor related faults account for 8-10% of motor faults while that of stator windings accounts for 26-37% An AC induction motor is one of the simplest and most reliable types of electric AC motor, with the power ranging from a few watts to many kilowatts. There are many different ways to design and control such motors, from low cost with a single-phase input to high accuracy with a polyphase approach, and this type of system is the most widely used motor across the consumer and industrial markets Full load torque formula for induction motor is as follows:. Starting Torque Formula for Induction Motor The starting torque of a motor is that torque which is produce by it at start. It is denoted by T st and corresponds to s = 1. So by substituting s = 1 in above expression, we get the expression for starting torque

Variable Frequency Control of Induction Motor Drive

Choose a VFD base on motor rated current | GoHz

The Induction Motor cannot run at Synchronous speed because the Slip is never zero in an Induction Motor. Now the question is arise, why slip is never zero in an induction motor. So in this article, we will discuss the total concept of What is Synchronous speed, What is Slip in induction motor, etc Induction Motor. RkTiwary Induction Motor. Why induction motor (IM)? Robust; No brushes. No contacts on rotor shaft High Power/Weight ratio compared to Dc motor Lower Cost/Power Easy to manufacture Almost maintenance-free, except for bearing and other mechanical parts Disadvantages Essentially a fixed-speed machine Speed is determined by the supply frequency Stator Construction Squirrel Cage. natural frequency due to em effects is presented. Systems with very soft couplings can be extremely sensitive to the em effect. INTRODUCTION: AC polyphase induction motors produce rotating electromagnetic fields in the stator windings, which in turn induce currents in the rotor bars and thereby caus Download this complete Project material titled; Open-Loop Variable Voltage Variable Frequency Control Of Three (3) Phase Induction Motor For An Electric Vehicle Drive with abstract, chapters 1-5, references, and questionnaire. Preview Abstract or chapter one below Format: PDF and MS Word (DOC) pages = 65 ₦ 3,00 Stator frequency control . The expression for the synchronous speed indicates that by changing the stator frequency also it can be changed. This can be achieved by using power electronic circuits called inverters which convert dc to ac of desired frequency DOI: 10.1109/TIA.2009.2023483 Corpus ID: 15597272. Induction Motor Rotor Temperature Estimation Based on a High-Frequency Model of a Rotor Bar @article{Cho2009InductionMR, title={Induction Motor Rotor Temperature Estimation Based on a High-Frequency Model of a Rotor Bar}, author={Kyung-Rae Cho and J. Seok}, journal={IEEE Transactions on Industry Applications}, year={2009}, volume={45}, pages.

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