vol_3-is-1 jul2010
TRANSCRIPT
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Volume 3 Issue 1 Jul-10 Half yearly
CONTENTS
S.No Title Page No.
1 Direct Torque Control Method of Induction Motor 2
2 Cascaded H-Bridge Multilevel Inverter 10
3 Modern Power Semi-Conductor Devices 15
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Direct Torque Control Method of Induction Motor
S. Swathi, M.Tech Power electronics, Mr. B. S. Krishna Varma department of EEE, GRIET [email protected]
Abstract
Among all control methods for induction motordrives, Direct Torque Control (DTC) seems tobe particularly interesting being independent of machine rotor parameters and requiring nospeed or position sensors. The DTC scheme ischaracterized by the absence of PI regulators,coordinate transformations, current regulatorsand PWM signals generators. Inspite of itssimplicity, DTC allows a good torque control insteady state and transient operating conditions
to be obtained. However, the presence of hysteresis controllers for flux and torque coulddetermine torque and current ripple andvariable switching frequency operation for thevoltage source inverter. This paper is aimed toanalyze DTC principles, control strategies .
1. INTRODUCTION
The history of electrical motors goes back as far as 1820, when Hans Christian Oersteddiscovered the magnetic effect of an electriccurrent. One year later, Michael Faradaydiscovered the electromagnetic rotation and builtthe first primitive D.C. motor. Faraday went on todiscover electromagnetic induction in 1831, but itwas not until 1883 that Tesla invented the A.Casynchronous motor.
Currently, the main types of electricmotors are still the same, DC,AC asynchronous andsynchronous, all based on Oersted, Faraday andTesla's theories developed and discovered morethan a hundred years ago. Since its invention, theAC asynchronous motor, also named inductionmotor, has become the most widespread electricalmotor in use today. At present, 67% of all theelectrical energy generated in the UK is convertedto mechanical energy for utilization. In Europe theelectrical drives business is worth approximately$1.0 Billion/ Annum.
These facts are due to the inductionmotors advantages over the rest of motors. Themain advantage is that induction motors do notrequire an electrical connection between stationaryand rotating parts of the motor. Therefore, they donot need any mechanical commutator (brushes),leading to the fact that they are maintenance freemotors. Induction motors also have low weight and
inertia, high efficiency and a high overloadcapability. Therefore, they are cheaper and morerobust, and less prove to any failure at high speeds.Furthermore, the motor can work in explosiveenvironments because no sparks are produced.Taking into account all the advantages outlinedabove, induction motors must be considered theperfect electrical to mechanical energy converter.However, mechanical energy is more than oftenrequired at variable speeds, where the speed controlsystem is not a trivial matter.
The only effective way of producing aninfinitely variable induction motor speed drive is tosupply the induction motor with three phasevoltages of variable frequency and variableamplitude. A variable frequency is requiredbecause the rotor speed depends on the speed of therotating magnetic field provided by the stator. Avariable voltage is required because the motorimpedance reduces at low frequencies andconsequently the current has to be limited bymeans of reducing the supply voltages.
Before the days of power electronics, alimited speed control of induction motor wasachieved by switching the three-stator windingsfrom delta connection to star connection, allowingthe voltage at the motor windings to be reduced.Induction motors are also available with more thanthree stator windings to allow a change of thenumber of pole pairs. However, a motor withseveral windings is more expensive because morethan three connections to the motor are needed andonly certain discrete speeds are available. Anotheralternative method of speed control can be realisedby means of a wound rotor induction motor, wherethe rotor winding ends are brought out to slip rings.However, this method obviously removes most of the advantages of induction motors and it alsointroduces additional losses. By connectingresistors or reactances in series with the statorwindings of the induction motors, poorperformance is achieved.
At that time the above described methods werethe only ones available to control the speed of induction motors, whereas infinitely variable speeddrives with good performances for DC motorsalready existed. These drives not only permitted the
operation in four quadrants but also covered a widepower range. Moreover, they had a good
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efficiency, and with a suitable control even a gooddynamic response.
With the enormous advances made insemiconductor technology during the last 20 years,the required conditions for developing a proper
induction motor drive are present. These conditionscan be divided mainly in two groups:
The decreasing cost and improvedperformance in power electronic switchingdevices.The possibility of implementing complexalgorithms in the new microprocessors.
However, one precondition had to be made,which was the development of suitable methods tocontrol the speed of induction motors, because incontrast to its mechanical simplicity their
complexity regarding their mathematical structure(multivariable and non-linear) is not a trivialmatter. It is in this field, that considerable researcheffort is devoted.
The aim being to find even simpler methods of speed control for induction machines. One method,which is popular at the moment, is Direct TorqueControl. Historically, several general controllershas been developed:
2. SOME COMMON CONTROL SCHEMESFOR INDUCTION MOTOR (IM):
IM control techniques can be dividedinto scalar and vector control. Scalar control isbased on relationships valid in steady-state.Amplitude and frequency of the controlledvariables are considered.
Figure 2.1. Control schemes of IM
In vector control amplitude and positionof a controlled space vector is considered. Theserelationships are valid even during transientswhich is essential for precise torque and speedcontrol.
2.1. Scalar controllers: Despite the fact that"Voltage-Frequency" (V/f) is the simplestcontroller, it is the most widespread, being in themajority of the industrial applications. It is known
as a scalar control and acts by imposing a constantrelation between voltage and frequency. Thestructure is very simple and it is normally usedwithout speed feedback. However, this controller doesn t achieve a good accuracy in both speedand torque responses, mainly due to the fact that the
stator flux and the torque are not directlycontrolled. Even though, as long as the parametersare identified, the accuracy in the speed can be 2%(except in a very low speed), and the dynamicresponse can be approximately around 50ms .
2.2. Vector Controllers : In these types of controllers, there are control loops for controllingboth the torque and the flux . The most widespreadcontrollers of this type are the ones that use vectortransform such as either Park or Ku. Its accuracycan reach values such as 0.5% regarding the speedand 2% regarding the torque, even when at stand
still. The main disadvantages are the hugecomputational capability required and thecompulsory good identification of the motorparameter
2.3. Field Acceleration method: This method isbased on maintaining the amplitude and the phaseof the stator current constant, whilst avoidingelectromagnetic transients. Therefore, the equationsused can be simplified simplified saving the vectortransformation, which occurs in vector controllers.This technique has achieved some computationalreduction, thus overcoming the main problem with
vector controllers and allowing this method tobecome an important alternative to vectorcontrollers .
2.4. Direct Torque Control (DTC):
A new technique for the torque control of induction motors was developed and presented byI. Takahashi as Direct Torque Control (DTC). Theprinciple of Direct Torque Control (DTC) is todirectly select voltage vectors according to thedifference between reference and actual value of torque and flux linkage. Torque and flux errors
are compared in hysteresis comparators.Depending on the comparators a voltage vector isselected from a table.
Advantages of the DTC are lowcomplexity and that it only need to use of onemotor parameter, the stator resistance. No pulsewidth modulation is needed; instead one of the sixVSI voltage vectors is applied during the wholesample period. All calculations are done in astationary reference frame which does notinvolve the explicit knowledge of rotor position.The DTC hence require low computational power
when implemented digitally. The system possessgood dynamic performance but shows quite poor
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performance in steady-state since the crudevoltage selection criteria give rise to high ripplelevels in stator current, flux linkage and torque.
2.5. Direct Self Control : Direct Self Control(DSC) is very similar to the DTC scheme
presented above. It can be shown that the DSC canbe considered a special case of the DTC .Some of the characteristics of DSC are:
1. Inverter switching frequency is lower than inthe DTC scheme. 2. 2.Excellent torque dynamics both in constantflux and in field weakening regions
Low switching frequency and fast torquecontrol over the whole operating range makesDSC preferable over DTC in high power tractionsystems.
3. INDUCTION MOTOR MODEL:
A dynamic model of the machinesubjected to control must be known in order tounderstand and design vector controlled drives.Due to the fact that every good control has to faceany possible change of the plant, it could be saidthat the dynamic model of the machine could be
just a good approximation of the real plant.Nevertheless, the model should incorporate all theimportant dynamic effects occurring during bothsteady-state and transient operations. Furthermore,
it should be valid for any changesin theinver ter s supply such as voltages or currents .Such a model
can be obtained by means of either the space vectorphasor theory or two-axis theory of electricalmachines. Despite the compactness and thesimplicity of the space phasor theory, both methodsare actually close and both methods will beexplained.
Figure 3.1. Cross section of symmetrical 3-phasemachine
Voltage equations: The stator voltages will be
In the stationary reference frame, the equations canbe expressed as follows:
Similar expressions can be obtained for the rotor:
The required transformation in voltages,currents, or flux linkages is derived in a generalizedway. The reference frames are chosen to bearbitrary and particular cases, such as stationary,rotor and synchronous reference frames are simpleinstances of the general case. R.H. Park, in the 1920s, proposed a new theory of electrical machineanalysis to represent the machine in d q model. He transformed the stator variables to asynchronously rotating reference frame fixed in the rotor, which is called P ar k s transformation. He showed that all the time varying inductances that occur due to an electric circuit in relative motionand electric circuits with varying magnetic reluctances could be eliminated.
We know that per phase equivalent circuitof the induction motor is only valid in steady statecondition. Nevertheless, it does not hold goodwhile dealing with the transient response of themotor. In transient response condition the voltagesand currents in three phases are not in balancecondition. It is too much difficult to study themachine performance of the machine by analyzingwith three phases. In order to reduce this complexity the transformation of axes fro 3 to 2 is necessary. Another reason f or transformation is to analyze any machine of n number of phases, an equivalent model is adopteduniver sally, that is d q model.
By using parks transformation we can writethe torque expression
formulated in this section from the motor natural T 3 p Lm ( )
frame, which is the stationary reference frame fixed e 2 2 L L dr qs qr ds s r to the stator. In a similar way, the rotor voltages will be formulated to the rotating frame fixed to therotor.
dr represents d-axis component w.r.t rotor
qr- represents q-axis component w.r.t rotor
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ds- represents d-axis component w.r.t stator No coordinate transforms are needed, all calculations are done in stationary
qs- represents q-axis component w.r.t stator
The torque controlled by controlling d-axis ,q-axisflux linkages.
Flux expression is given by
s = (V s is rs) dt
where V s is one of the voltage vectors produced bythe inverter If resistive drop is neglected
s = V s dt = s0 + Vs t
4. DTC USING SPACE VECTORMODULATION:
Direct torque control (DTC) is one method
used in variable frequency drives to control thetorque (and thus finally the speed) of three-phaseAC electric motors. This involves calculating anestimate of the motor's magnetic flux and torquebased on the measured voltage and current of themotor. Stator flux linkage is estimated byintegrating the stator voltages. Torque is estimatedas a cross product of estimated stator flux linkagevector and measured motor current vector. Theestimated flux magnitude and torque are thencompared with their reference values. If either theestimated flux or torque deviates from the referencemore than allowed tolerance, the transistors of the
variable frequency drive are turned off and on insuch a way that the flux and torque will return intheir tolerance bands as fast as possible. Thus directtorque control is one form of the hysteresis orbang-bang control.
Figure 4.1. DTC-SVM of Induction Motor
This control method implies the followingproperties of the control:
Torque and flux can be changed very fastby changing the references High efficiency & low losses - switchinglosses are minimized because thetransistors are switched only when it is
needed to keep torque and flux withintheir hysteresis bands The step response has no overshoot
coordinate system No separate modulator is needed, thehysteresis control defines the switchcontrol signals directly
There are no PI current controllers. Thusno tuning of the control is required The switching frequency of the transistorsis not constant. However, by controllingthe width of the tolerance bands theaverage switching frequency can be keptroughly at its reference value. This alsokeeps the current and torque ripple small.Thus the torque and current ripple are of the same magnitude than with vectorcontrolled drives with the same switchingfrequency. Due to the hysteresis control the switchingprocess is random by nature. Thus thereare no peaks in the current spectrum. Thisfurther means that the audible noise of themachine is low The intermediate DC circuit's voltagevariation is automatically taken intoaccount in the algorithm (in voltageintegration). Thus no problems exist dueto dc voltage ripple (aliasing) or dcvoltage transients Synchronization to rotating machine isstraightforward due to the fast control;Just make the torque reference zero andstart the inverter. The flux will beidentified by the first current pulse Digital control equipment has to be veryfast in order to be able to prevent the fluxand torque from deviating far from thetolerance bands. Typically the controlalgorithm has to be performed with 10 - 30 microseconds or shorter intervals.However, the amount of calculationsrequired is small due to the simplicity of the algorithm. The current and voltage measuring
devices have to be high quality ones without noise and with low-pass filtering,because noise and slow response ruins thehysteresis control In higher speeds the method is notsensitive to any motor parameters.However, at low speeds the error in statorresistance used in stator flux estimationbecomes critical The direct torque method performs verywell even without speed sensors.However, the flux estimation is usuallybased on the integration of the motor
phase voltages. Due to the inevitableerrors in the voltage measurement andstator resistance estimate the integrals tend
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to become erroneous at low speed. Thus itis not possible to control the motor if the
voltage is applied across the stator terminals of theInduction motor. The accelerating voltage vector,
VoltageVectortable
S B
output frequency of the variable frequencydrive is zero. However, by careful designof the control system it is possible to havethe minimum frequency in the range 0.5
Hz to 1 Hz that is enough to makepossible to start an induction motor withfull torque from a standstill situation. Areversal of the rotation direction ispossible too if the speed is passingthrough the zero range rapidly enough toprevent excessive flux estimate deviation.
4.1. Schematic of Direct Torque Control of IM using space vector modulation:
which possess maximum rate of change of torqueangle is impressed on induction motor.
The DTC requires the flux and torque estimations,
which can be performed as it is proposed inschematic, by means of two different phasecurrents and the state of the inverter.
4.1.1. Sector Division: The air gap of inductionmotor is divided into 6 sectors each sector spacingfor 60. The sector diagram is as shown in Figure.
s
r _ E +
* s
E * Te r
+G
+
H
S A
H S cTe
S(K)
3 ph supply
Inverter
Figure 4.3. Sector division
4.1.2. Switching Logic Selection Table :
_ Te* _ Te
r Te s
r
Estimator
Single computation
Motor
The switching logic selection table orvoltage selection table , which consists of flux error(dF )& torque error (dT) .The air gap is dividedinto 6sectors , each spanning for 60 starting from -30 to+30 so on all the sectors are divided and
Figure 4.2. Schematic of DTC-SVM of IM
In figure possible schematic of DirectTorque Control is shown. As it can be seen, thereare two different loops corresponding to themagnitudes of the stator flux and torque. Thereference values for the flux stator modulus and thetorque are compared with the actual values, and theresulting error values are fed into the two level andthree-level hysteresis blocks respectively. Theoutputs of the stator flux error and torque errorhysteresis blocks, together with the position of thestator flux are used as inputs of the look up table.
The position of the stator flux is divided into sixdifferent sectors. The stator flux modulus andtorque errors tend to be restricted within itsrespective hysteresis bands .It can be proved thatthe flux hysteresis band affects basically to thestator-current distortion in terms of low orderharmonics and the torque hysteresis band affectsthe switching frequency .
The principle of DTC to control the fluxand torque directly. The appropriate voltage vectoris selected from the voltage selection table basedon torque and flux errors. Based on the voltage
vector selected the switching states of 3 Phasebridge inverter are chosen, The corresponding
denoted as 01..........06 Depending upon theflux error, torque error & the sector in which thestator flux is present that desired amount of voltagewill be chosen and applied to the induction motorin order to obtain desired speeds.
The flux error d can take two differentvalues 1& -1 and torque error dT can take threedifferent values 1, 0, -1. Considering the directionof induction motor in anticlockwise and dependingupon the flux increase or decrease and torqueincrease or decrease will decide the desired amountof voltage.
The way to impose the required stator fluxis by means of choosing the most suitable VoltageSource Inverter state. If the ohmic drops areneglected for simplicity, then the stator voltageimpresses directly the stator flux in accordancewith the following equation :
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Decoupled control of the stator fluxmodulus and torque is achieved by acting on theradial and tangential components respectively of the stator flux-linkage space vector in its locus.These two components are directly proportional(Rs=0) to the components of the same voltage
space vector in the same directions. Figure 4.4shows the possible dynamic locus of the stator flux,and its different variation depending on the VSIstates chosen. The possible global locus is dividedinto six different sectors signaled by thediscontinuous line.
Figure 4.4. Stator Flux vector locus
In Accordance with figure .the generaltable can be written. It can be seen from table 3.1,that the states Vk and Vk+3 , are not considered inthe torque because they can both increase (first 30degrees) or decrease (second 30 degrees) the torqueat the same sector depending on the stator fluxposition. The usage of these states for controllingthe torque is considered one of the aims to developin the present thesis, dividing the total locus intotwelve sectors instead of just six.
Table 1. Selection table for DTCbeing k as a sector number
The sectors of the stator flux space vectorare denoted from S1 to S6 . Stator flux moduluserror after the hysteresis block can take just twovalues. Torque error after the hysteresis block cantake three different values. The zero voltagevectors V0 and V7 are selected when the torqueerror is within the given hysteresis limits, and mustremain unchanged.
Table 2. Lookup table for DTC
FD: Flux decreases.
FI: Flux increases.
TD: Torque decreases.TI: Torque increases.
4.1.3. Three Phase Inverter Switching Modes:
Induction motor stalor terminals are fedfrom 3 F Bridge Inverter. The Bridge inverteremployed here is voltage source inverter with 6switches. ft contains 3 arms each arm includes 2switches. The arms are labeled as a, b, c. Arm 'a
includes 1,4, arm a includes 1,4, arm b includes 3,6& c includes 5,2.
The stator voltage of induction motor ismodeled as Vs(Sa, Sb, Sc).The status of switchesSa;Sb,Sc are obtained from the 3-phase Inverterand the inverter chosen for the project is bridgeinverter with 6switches. Based on conductingmodes of Sa,Sb,Sc the desired voltage is chosenand applied to the induction motor.
Figure 4.5. Voltage Source Inverter Fed Induction Motor
4.1.4. Flux control:
s = (V s is rs) dt
where V s is one of the voltage vectors produced by
the inverterIf resistive drop is neglected
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s = V s dt = s0 + Vs t
Hence the tip of flux vector moves in the directionof the applied voltage vector with a velocityproportional to the amplitude of the non-zerovoltage vector. Application of zero voltage vector
freezes the flux vector.
Figure 4.6. Flux and Torque control
4.1.5. Torque control:
Te = 3 P/4 (L m /sL sLr) { dr qs- qr ds}
=3 P/4 (L m /sL sLr) s r sin
Torque Control is achieved by controlling, i.e., by accelerating or decelerating s with respect to r The angular speed of the stator flux can be modified, in each cycle period, by anopportune choice of the inverter configuration. Thetangential component of the applied voltage vector
determines the instantaneous angular speed of thestator flux in a stator reference frame. The effect onthe flux magnitude of a particular voltage vectordepends on the position of the flux within thesector. The effect on the torque of a particularvoltage vector depends on the position of the fluxwithin the sector and the rotor angular speed.
5.BENEFITS OF DTC TECHNOLOGY:
There are many benefits of DTC
technology. But most significantly, drives usingDTC technology have the following exceptional
dynamic performance features, many of which areobtained without the need for an encoder ortachometer to monitor shaft position or speed:
Torque response: - How quickly the drive outputcan reach the specified value when a nominal
100% torque reference step is applied. For DTC, atypical torque response is 1 to 2ms below 40Hzcompared to between 10-20ms for both flux vectorand DC drives fitted with an encoder. With openloop PWM drives the response time is typicallywell over 100ms. In fact, with its torque response,DTC has achieved the natural limit. With thevoltage and current available, response time cannotbe any shorter. Even in the newer sensor less drives the torque response is hundreds of milliseconds.
A ccur ate torque control at low frequencies , as
well as full load torque at zero speed without theneed for a feedback device such as an encoder ortachometer. With DTC, speed can be controlled tofrequencies below 0.5Hz and still provide 100%torque right the way through to zero speed.
Torque repeatability: - How well the drive
repeats its output torque with the same torquereference command. DTC, without an encoder, canprovide 1 to 2% torque repeatability of the nominaltorque across the speed range.This is half that of other open-loop AC drives and equal to that of closed-loop AC and DC drives.
Motor static speed accuracy: - Error betweenspeed reference and actual value at constant load.For DTC, speed accuracy is 10% of the motor slip,which with an 11kW motor, equals 0.3% staticspeed accuracy. With a 110kW motor, speedaccuracy is 0.1% without encoder (open-loop).This satisfies the accuracy requirement for 95% of industrial drives applications.
Dynamic speed accuracy: - Time integral of speed deviation when a nominal (100%) torquespeed is applied. DTC open-loop dynamic speed
accuracy is between 0.3 to 0.4%sec.5.1. Practical benefits of DTC:
Fast torque response : - This significantly
reduces the speed drop time during a load transient,bringing much improved process control and amore consistent product quality.
Torque control at low frequencies: - This isparticularly beneficial to cranes or elevators, wherethe load needs to be started and stopped regularlywithout any jerking. Also with a winder, tensioncontrol can be achieved from zero through tomaximum speed.
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Compared to PWM flux vector drives, DTC bringsthe cost saving benefit that no tachometer isneeded.
Torque linearity: - This is important in precisionapplications like winders, used in the paper
industry, where an accurate and consistent level of winding is critical.
Dynamic speed accuracy: - After a sudden loadchange,the motor can recover to a stable stateremarkably fast.
ACKNOWLEDGEMENT:
We acknowledge our special thanks to ourguide Mr. B.S.KRISHNA VARMA, Associateprofessor in Department of Electrical andElectronics Engineering, for his constant
encouragement, valuable guidance and help in thesuccessful completion of the project.
We express our deep sense of gratitude tothe Head of the Department of Electrical andElectronics Engineering, Dr.P.M SARMA for hisconstant encouragement, constructive suggestionsand Inspirations for successful completion of theproject.
REFERENCES
[1] P. Tiitinen, The next generation motor contr ol
method, DTC direct torque control, Proc. of Int. Conf on Power Electronics, Drives and Energy System for Industrial Growth , N. Delhi,India, pp. 37-43, 1996
[2] T. G. Habetler,. F. Profumo, M. Pastorelli andL. M. Tolbert, Direct torque control of induction machines using space vectormodulation, IEEE Trans. Ind. Appl ., Vol. 28,No. 5, pp. 1045-1053, 1992.
[3] Y. Li, J. Shao,. and B. Si, Direct torque control of induction motors for low speed drives
considering discrete effect of control and dead timetiming of inverters, in Conf. Rec. IEEEIAS Annual Meeting , pp. 781-788, 1997.
[4] J. K. Kang. and S. K. Sul, Torque ripple minimization strategy for direct torque controlof induction motor, in Conf. Rec. IEEE-IAS
Annual Meeting , pp. 438-443, 1998
[5] S. Mir , M. E . Elbuluk and D. S.Z inger , F uzzy Implementation of direct self control of Induction motors , IEEE Trans Ind. Appl. , Vol.30, No. 3, pp. 729-735, 1994.
[6] I. G. B ir d. and H. Zelaya DeL a Parra, Fuzzy
logic torque ripple reduction for DTC based:
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Cascaded H-Bridge Multilevel Inverter
Mahesh Babu M.Tech (PE)
Abstract: This paper presents a cascaded H-Bridge multilevel inverter. Among the multilevel converter topologies,
cascaded multilevel H-Bridge inverter is promising one which is an alternative for grid-connected photovoltaic/wind-powerwind power generator ,flexible alternating current systems and motor drive application. A method is presented showing that acascade multilevel inverter can be implemented using only a single DC power source and capacitors. A standard cascademultilevel inverter requires DC sources for 2+1 levels. Without requiring transformers, the scheme proposed here allows the useof a single DC power source (e.g., a battery or a fuel cell stack) with the remaining 1 DC sources being capacitors.
In this paper we are getting 9-level phase voltage waveform with 4-dc sources, as the number of level increases we canget stair case waveform i.e nearly sinusoidal (ac) and harmonics are reduced.
1. INTRODUCTION
Numerous industrial applications have begun to require
higher power apparatus in recent years. Some medium
voltage motor drives and utility applications require
medium voltage and megawatt power level. For a medium
voltage grid, it is troublesome to connect only one power
semiconductor switch directly. As a result, a multilevel
power converter structure has been introduced as an
alternative in high power and medium voltage situations. A
multilevel converter not only achieves high power ratings,
but also enables the use of renewable energy sources.
Renewable energy sources such as photovoltaic, wind, and
fuel cells can be easily interfaced to multilevel converter
system for a high power application.
The concept of multilevel converters has been introduced
since 1975. The term multilevel began with the three-level
converter. Subsequently, several multilevel converter
topologies have been developed. However, the elementary
concept of a multilevel converter to achieve higher power
is to use a series of power semiconductor switches with
several lower voltage dc sources to perform the powerconversion by synthesizing a staircase voltage waveform.
Capacitors, batteries, and renewable energy voltage sources
can be used as the multiple dc voltage sources. The
commutation of the power switches aggregate these
multiple dc sources in order to achieve high voltage at the
output; however, the rated voltage of the power
semiconductor switches depends only upon the rating of the
dc voltage sources to which they are connected.
A multilevel converter has several advantages over a
conventional two level converter that uses high switching
frequency pulse width modulation (PWM). The attractive
features multilevel converter can be briefly summarized as
follows.
1. Staircase waveform quality: Multilevel
converters not only can generate the output
voltages with very low distortion, but also can
reduce the dv / dt stresses; therefore
electromagnetic compatibility (EMC) problems
can be reduced.
2. Input current: Multilevel converters can draw
input current with low distortion.
3. Switching frequency : Multilevel converters can
operate at both fundamental switching
frequency and high switching frequency PWM. It
should be noted that lower switching frequency
usually means lower switching loss and higher
efficiency.
Unfortunately, multilevel converters do have some
disadvantages. One particular disadvantage is the greater
number of power semiconductor switches needed.
Although lower voltage rated switches can be utilized in a
multilevel converter, each switch requires a related gate
drive circuit. This may cause the overall system to be more
expensive and complex.
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Plentiful multilevel converter topologies have been
proposed during the last two decades.
Contemporary research has engaged novel converter
topologies and unique modulation schemes.
Moreover, three different major multilevel converter
structures have been reported in the literature: cascaded H-
bridges converter with separate dc sources, diode clamped
(neutral-clamped), and flying capacitors (capacitor
clamped). Moreover, abundant modulation techniques and
control paradigms have been developed for multilevel
converters such as sinusoidal pulse width modulation
(SPWM), selective harmonic elimination (SHE-PWM),
space
vector modulation (SVM), and others. In addition, many
multilevel converter applications focus on industrial
medium-voltage motor drives , utility interface for
renewable energy systems , flexible AC transmission
system (FACTS) , and traction drive systems .
This chapter reviews state of the art of multilevel power
converter technology. Fundamental multilevel converter
structures and modulation paradigms are discussed
including the pros and cons of each technique. Particular
concentration is addressed in modern and more practical
industrial applications of multilevel converters. A
procedure for calculating the required ratings for the active
switches, clamping diodes, and dc link capacitors including
a design example are described. Finally, the possible future
developments of multilevel converter technology are noted.
2. TYPES OF MULTILEVEL INVERTERS
The general structure of the multilevel converter is to
synthesize a near sinusoidal voltage from several levels of
dc voltages, typically obtained from capacitor voltage
sources. As the number of levels increases, the synthesized
output waveform has more steps, which produce a staircase
wave that approaches a desired waveform. Also, as more
steps added to the waveform, the harmonic distortion of the
output wave decreases, approaching zero as the number of
levels increases. A s the number of levels increases, the
voltage that can be spanned by summing multiple voltage
levels also increases. The output voltage during the positive
half-cycle can be found from
Vao
Where SFn is the switching or control function of nth node
and it takes a value of 0 or 1. Generally, the capacitor
terminal voltages E1,E2 ,.. all have the same value Em.
Thus, the peack output voltage is
Vao(peak) = (m-1)Em = Vdc.
To generate an output voltage with both positive and
negative values, the circuit topology has another switch to
produce the negative part Vob so that Vab = Vao +Vog =
Vao-Vbo.
The multilevel inverters can be classified into three types.
1. Diode-clamped multilevel inverter;
2. Flying-capacitors multilevel inverter;
3. Cascade multilevel inverter.
3. CASCADED MULTILEVEL INVERTER
A cascaded multilevel inverter consist of a
series of H-bridge (single-phase, full-bridge) inverter units.
The general function of this multilevel inverter is tosynthesize a desired voltage from several separate dc
sources (SDCSs), which may be obtained from batteries,
fuel cells, or solar cells fig(1) shows the basic structure of a
single phase cascaded inverter with SDCSs. Each SDSCS
is connected to an H-bridge inverter. The ac terminal
voltages of different level inverters are connected in series.
Unlike the diode-clamped or flying-capacitors inverter, the
cascaded inverter does not require any voltage-clamping
diodes or voltages-balancing capacitors.
A single-phase structure of a 9-level cascaded inverter is
illustrated in . Each separate dc source (SDCS) is
connected to a single-phase full-bridge, or H-bridge,
inverter. Each inverter level can generate three different
voltage outputs, +V dc, 0, and Vdc by connecting the dc
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source to the ac output by different combinations of the
four switches, Sa1, Sa2, Sa3, and Sa4.
To obtain +V dc, switches S a1 and Sa 4 are turned on, whereas
Vdccan be obtained by turning on witches Sa 2 and Sa 3. By
turning on Sa 1 and Sa 2 or Sa3 and Sa 4, the output voltage is0. The ac output of each of the different full-bridge
inverter levels are connected in series such that the
synthesized voltage waveform is the sum of the inverter
outputs. The number of output phase voltage levels m in
a cascade inverter is defined by m = 2s+1 , where s is the
number of separated sources. An example phase voltage
waveform for an 9-level cascaded H-bridge inverter with 4
SDCSs and 4 full bridges is shown in Figure(1)
The phase voltage van = v1 + v2 + v3+ v 4
Fig1. Single-phase multilevel cascaded
H-Bridge Inverter
Fig 2: Output wave form of 9-level phase voltage.
Fig3.The connection diagram of Y-configured 9-level
converter using cascaded inverter with 4 SDC capacitors..
A 9-level phase voltage cascaded inverter needs four
SDCSs and four full bridges. Controlling the conducting
angels at different inverter levels can minimize the
harmonic distortion of the output voltage.
The output voltage of the inverter is almost is sinusoidal,
and it has less than 5% total harmonic distortion (THD)
with each of the H-bridges switching only at fundamental
frequency. If the phase current is, as shown in fig (2), is
sinusoidal and leads or lags the phase voltage van by 90,
the average charge to each dc capacitor is equal to zero
over one cycle. Therefore, all SDCS capacitor voltages can
be balanced.
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The major advantages of the cascaded inverter can be
summarized as follows:
1. Compared with the diode-clamped and flying-
capacitors inverters, it requires the least number
of components to achieve the same number of voltage levels.
2. The number of possible output voltage levels is
more than twice the number of dc sources ( m =
2s + 1).
3. Optimized circuit layout and packing are possible
because each level has the same structure and
there are no extra clamping diodes or voltage-
balancing capacitors. This will enable the
manufacturing process to be done more quickly
and cheaply.4. Soft-switching techniques can be used to reduce
switching losses and device stresses.
The major disadvantage of the cascaded inverter is as
follows:
1. It needs separate dc sources for real power
conversions, thereby limiting itsapplications.
4. APPLICATIONS
There is considerable interest in applying voltage sources
inverters in high-power applications such as in utility
systems for controlled sources of reactive power. In the
steady state operation, an inverter can produce a controlled
reactive current and operates as a static volt-ampere
reactive (VAR) compensator (STSTCON). Also, these
inverters can reduce the physical size of the compensatorand improve its performance during power system
contingencies. The use of a high-voltage inverter makes
possible direct connection to the high-voltage (e.g,13-
kv)distribution system, eliminating the distribution
transformer and reducing system cost. In addition, the
harmonic content of the inverter waveform can be reduced
with appropriate control techniques and thus the efficiency
of the system can be improved. The most common
applications of multilevel converters include
(1).Reactive Power compensation.
(2).Back-to-back intertie and
(3).Variable speed drives.
5. FEATURES OF MULTILEVEL INVERTERS
A multilevel inverter can eliminate the need for the step-up
transformer and reduce the harmonics produced by inverter.
Although the multilevel inverter structure was initially
introduced as a means of reducing the output waveform
harmonic content.
The key features of a multilevel structure follow:
1. The output voltage and power increase
with number of levels. Adding a voltage
level involves adding a main switching
device to each phase.
2. The harmonic content decreases as the
number of levels increases and filtering
requirements are reduced.
3. With additional voltage levels, the voltagewaveform has more free-switching angles,
which can be pre selected for harmonic
elimination
4. In the absence of any PWM techniques, the
switching losses can be abided. Increasing
output voltage and power does not require
an increase in rating of individual device.
5. Static and dynamic voltage sharing among
the switching devices is built into the
structure though either clamping diodes or
capacitors.
6. The switching devices do not encounter
any voltage-sharing problems. For this
reason, multilevel inverters can easily be
applied for high-power applications such as
large motor drives and utility supplies.
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7. The fundamental output voltage of the
inverter is set by the dc by bus voltage
Vdc, Which can be controlled through a
variable dc link.
6. CONCLUSION
Multilevel converters can be utility interface
systems and motor drives. These converters offer a low
output voltage THD, and a high efficiency and power
factor. Using this we are getting harmonics less sinusoidal
waveform The main advantage of multilevel converters
includes the following:
1. They are suitable for high-voltage and high-
current applications.
2. They have higher efficiency because the devices
can be switched at a low frequency.
3. Power factor is close to unity for multilevel
inverters used as rectifiers to convert ac to dc.
4. No EMI problem exists.
5. No charge unbalance problem results when the
converters are in either charge mode
(rectification) or drive mode (inversion).
The multilevel converters require balancing the voltage
across the series-connected dc bus capacitors. Capacitors
tend to overcharge or completely discharge, at which
condition the multilevel converter reverts to a three-level
converter unless an explicit control is devised to balance
the capacitor charge. The voltage-balancing technique must
be applied to the capacitor during the operations of the
rectifier and the inverter. Thus, the real power flow into a
capacitor must be the same as the real power flow out of
the capacitor, and the net charge on the capacitor over one
cycle remains the same.
REFERENCES
[1] J. Rodriguez, J. S. Lai and F. Z. Peng, Multilevel
Inverters: Survey of Topologies, Controls, and
Application s, IEEE Transactions on Industry
Applications, vol. 49, no. 4, Aug. 2002, pp. 724-738.
[2] J. S. Lai and F. Z. Peng, Multilevel Converters-A new
Breed of Power Converters , IEEE Trans. Ind. Applicat.,
vol.32,pp. 509-517, May/June 1996.
[3] L. M. Tolbert, F. Z. Peng, and T. Habetler, Multilevel
Converters for Large Electric drive s, IE EE Trans. Ind.
Applicat.,vol.35,pp. 36-44, Jan./Feb. 1999.
[4] R. H. Baker and L. H. Bannister, Electric Power
Conve rter, U. S. Patent 3 867 643, Feb. 1975.
[5] A. Nabae, I. Takahashi, and H. Akagi, A New Neutral-
point Clamped PWM inve rter, IEEE Trans. Ind. Applicat.,
vol. IA-17, pp. 518-523, Sept./Oct. 1981.
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Modern Power Semi-Conductor Devices
Vicharapu Bharat Kumar (09241D4301), Department of Electrical Technology, GRIET, Hyd.
Abstract - This paper presents information about various modern power semi-conductor devices availableand used extensively in various converter circuits (ac-ac, ac-dc, dc-dc, dc-ac). Due to its superior advantagessuch as high power rating and its usefulness in eliminating commutation circuit in DC-DC converters, IGBTis universally adopted in almost all converter circuits over other semiconductor devices. So, IGBTs basicstructure, principle of operation, advantages and their characteristic are briefly discuss along with its application in Boost Chopper (DC-DC Converter) .
I. Introduction 1) Triac
2) GTO (Gate Turn-off Thyristor)Electrical power is processed by power electronics to 3) BJT (Bipolar Power Transistor)make it suitable for various applications, such as DCand AC regulated power supplies, Electro chemicalProcess, heating and lighting control, electrical
4)
5)
MOSFET ( Metal Oxide SemiconductorField Effect Transistor)IGBT (Insulated Gate Bipolar Transistor)
machine drives etc 6) SIT (Static Induction Transistor)7) SITH (Static Induction Thyristor)
The processing involves conversion 8) MCT ( MOS controlled Th ristor) (dc-ac, ac-dc, dc-dc and ac-ac) and control usingpower semi conductor switches. By using PowerElectronics, we can achieve a high level of productivity in Industry and product quality
enhancement that cannot be possible by using Non-Power Electronic methods. Hence these devicesconstitute the heart of Modern Power Electronics.Power Semiconductor Devices are indeed mostcomplex, delicate and fragile element in conversionfrom one form of energy to another or usable form.A Power Electronic engineer needs to understand thedevice thoroughly for efficient, reliable and costeffective of a converter. Hence in further chapters wewould deal with various power semi conductordevices and their application in brief. The age of modern power electronics stared by the invention of the thyristor since then we have seen the gradualemergence of other power semiconductor devicessuch as:
The last four devices which appeared in the 1980 scan be defined as Modern Power SemiconductorDevices and these are reviewed briefly in further
chapters.
II. IGBT
The Insulated Gate Bipolar Transistor (IGBT) is aminority-carrier device with high input impedanceand large bipolar current-carrying capability. Manydesigners view IGBT as a device with MOS inputcharacteristics and bipolar output characteristic that isa voltage-controlled bipolar device. To make use of the advantages of both Power MOSFET and BJT, theIGBT has been introduce d. Its a functionalintegration of Power MOSFET and BJT devices in
monolithic form. It combines the best attributes of both to achieve optimal device characteristics [2].The IGBT is suitable for many applications in powerelectronics, especially in Pulse Width Modulated(PWM) servo and three-phase drives requiring highdynamic range control and low noise. It also can beused in Uninterruptible Power Supplies (UPS),Switched-Mode Power Supplies (SMPS), and otherpower circuits requiring high switch repetition rates.IGBT improves dynamic performance and efficiencyand reduced the level of audible noise. It is equally
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suitable in resonant-mode converter circuits.Optimized IGBT is available for both low conductionloss and low switching loss.
III. Basic Structure of IGBT
The basic schematic of a typical N-channel IGBTbased upon the DMOS process is shown in Figure 1.
This is one of several structures possible for thisdevice. It is evident that the silicon cross-section of an IGBT is almost identical to that of a verticalPower MOSFET except for the P + injecting layer. Itshares similar MOS gate structure and P wells withN+ source regions. The N + layer at the top is thesource or emitter and the P + layer at the bottom is thedrain or collector. It is also feasible to make P-channel IGBTs and for which the doping profile ineach layer will be reversed. IGBT has a parasiticthyristor comprising the four-layer NPNP structure.Turn-on of this thyristor is undesirable.
Schematic view of a generic N-channel IGBT
Some IGBTs, manufactured without the N+ bufferlayer, are called non-punch through (NPT) IGBTswhereas those with this layer are called punch-
through (PT) IGBTs. The presence of this bufferlayer can significantly improve the performance of the device if the doping level and thickness of thislayer are chosen appropriately. Despite physicalsimilarities, the operation of an IGBT is closer to thatof a power BJT than a power MOSFET. It is due tothe P+ drain layer injecting layer) which isresponsible for the minority carrier injection into theN--drift region and the resulting conductivitymodulation.
Equivalent circuit model of an IGBT
Based on the structure, a simple equivalent circuitmodel of an IGBT can be drawn as shown in Figure2. It contains MOSFET, JFET, NPN and PNPtransistors. The collector of the PNP is connected tothe base of the NPN and the collector of the NPN isconnected to the base of the PNP through the JFET.The NPN and PNP transistors represent the parasiticthyristor which constitutes a regenerative feedback loop. The resistor R B represents the shorting of thebase-emitter of the NPN transistor to ensure that thethyristor does not latch up, which will lead to the
IGBT latchup. The JFET represents the constrictionof current between any two neighboring IGBT cells.It supports most of the voltage and allows theMOSFET to be a low voltage type and consequentlyhave a low RDS(on) value. A circuit symbol for theIGBT is shown in Figure 3. It has three terminalscalled Collector (C), Gate (G) and Emitter (E).
IGBT Circuit Symbol
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IXYS has developed both NPT and PT IGBTs. Thephysical constructions for both of them are shown inFigure 4. As mentioned earlier, the PT structure hasan extra buffer layer which performs two mainfunctions: (i) avoids failure by punch-through actionbecause the depletion region expansion at applied
high voltage is restricted by this layer, (ii) reduces thetail current during turn-off and shortens the fall timeof the IGBT because the holes are injected by the P +
collector partially recombine in this layer The NPTIGBTs, which have equal forward and reversebreakdown voltage, are suitable for AC applications.The PT IGBTs, which have less reverse breakdownvoltage than the forward breakdown voltage, areapplicable for DC circuits where devices are notrequired to support voltage in the reverse direction.
NPT type IGBT
PT-type IGBT
IV. IGBT Operation Modes Forward-Blocking and Conduction Modes
When a positive voltage is applied across thecollector-to-emitter terminal with gate shorted toemitter, the device enters into forward blocking modewith junctions J1 and J3 are forward-biased and
junction J2 is reverse-biased. A depletion layerextends on both-sides of junction J2 partly into P-base and N-drift region.
An IGBT in the forward-blocking state can betransferred to the forward conducting state byremoving the gate-emitter shorting and applying apositive voltage of sufficient level to invert the Sibelow gate in the P base region. This forms aconducting channel which connects the N+ emitter tothe N-drift region. Through this channel, electronsare transported from the N+ to the N- drift. This flowof electrons into the N- drift lowers the potential of the N-drift region whereby the P+ collector/ N-driftbecomes forward biased. Under this forward-biasedcondition, a high density of minority carrier holes is
injected into the N- drift from the P+ collector. Whenthe injected carrier concentration is very much largerthe background concentration, a condition defined asa plasma of holes builds up in the N- drift region.This plasma of holes attracts electrons from theemitter contact to maintain local charge neutrality. Inthis manner, approximately equal excessconcentrations of holes and electrons are gathered inthe N- drift region. This excess electron and holeconcentrations drastically enhance the conductivity of
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N- drift region. This mechanism in rise inconductivity is referred to as the conductivitymodulation of the N-drift region.
Reverse-Blocking Mode
When a negative voltage is applied across thecollector-to-emitter terminal shown in fig, the
junction J1 becomes reverse-biased and its depletionlayer extends into the N- drift region. The break down voltage during the reverse-blocking isdetermined by an open-base BJT formed by the P+collector/ N- drift/ P- base region. The device isprone to punch-through if the N-drift region is verylightly-doped. The desired reverse voltage capabilitycan be obtained by optimizing the resistivity andthickness of the N-drift region. The width of the N-drift region that determines the reverse voltagecapability and the forward voltage drop which
increases with increasing width can be determined by
Lp= minority carrier diffusion length
Vm= maximum blocking voltage
0 = Permittivity of free space
Safe Operating Area (SOA)
The safe operating area (SOA) is defined as thecurrent-voltage boundary within which a powerswitching device can be operated without destructivefailure, For IGBT, the area is defined by themaximum collector-emitter voltage V ce and collectorcurrent I c within which the IGBT operation must be
confined to project it from damage. The IGBT has thefollowing types of SOA operations: forward-biasedsafe operating area (FBSOA), reverse-biased safeoperating area (RBSOA) and short-circuit safeoperating area (SCSOA).
Forward-Biased Safe Operating Area
(FBSOA)
The FBSOA is an important characteristic forapplications with inductive loads. It is defined by themaximum collector-emitter voltage with saturatedcollector current. In this mode, both electrons andholes are transported through the drift region, whichis supporting a high collector voltage. The electronand hole concentrations in the drift region are relatedto the corresponding current densities by:
Where V sat,n and V sat,p are the saturated driftvelocities for electrons and holes, respectively. Thenet positive charge in the drift region is given by,
This charge determines the electric field distributionin the drift region. In steady-state forward blockingcondition, the drift region charge is equal to N D. InFBSOA, the net charge is much larger because thehole current density is significantly larger than theelectron current density.
The breakdown voltage limit in the FBSOA isdefined by
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Reverse-Biased Safe Operating (RBSOA)
The RBSOA is important during the turn-off transient. The current which can be turned-off islimited to twice the nominal current of the IGBT.This means a 1200A IGBT is able to turn-off amaximum current of 2400A. The maximum current is
a function of the peak voltage which appears betweencollector and emitter during turn-off. The peak valueof VCE is the sum of the DC link voltage and theproduct of L dI C / dt where L is the stray inductance of the power circuit. The relation between maximum I C and V CE can beseen in the RBSOA
RBSOA of IGBT
In this mode, the gate bias is at zero or at a negativevalue thus the current transport in the drift regionoccurs exclusively via the holes for an n-channelIGBT. The presence of holes adds charge to the driftregion, resulting to the increase in the electric field atthe P-base/N drift region junction. The net charge inthe space charge region under the RBSOA conditionis given by
where Jc is the total collector current. The avalanchebreakdown voltage for RBSOA is given by:
Short-Circuit Safe Operating Area (SCSOA )
A very important requirement imposed onthe power switching device, when used in motorcontrol applications is that be able to turn-off safelydue to a load or equipment short circuit. When acurrent overload occurs, collector current risesrapidly until it exceeds that which the device can
sustain with the applied gate voltage. The key tosurvivability for the power device is to limit thecurrent amplitude to a safe level for a period of timethat is sufficiently long to allow the control circuit todetect the fault and turn the device off.
A circuit diagram for SCSOA test is shown in Figure12. The short-circuit inductance value determines themode of operation of the circuit. When it is in therange of uH , theoperation is similar to normal switching of inductiveload. When IGBT is turned on, V CE drops to itssaturation voltage. The IGBT is saturated and I C isincreasing with a dIc/dt of Vcc/Lsc. It is not allowedto turn-off the IGBT from the saturation region at acollector current higher than 2 times rated currentbecause this is an operation outside the RBSOA. Incase of short-circuit; it is necessary to wait until theactive region is reached. The IGBT must be turned-off within 10 us to prevent destruction due tooverheating.
V. Characteristic of IGBT
Output CharacteristicsVI.
The plot for forward output characteristics of anNPT-IGBT is shown in Figure 5. It has a family of curves, each of which corresponds to a different gate-to-emitter voltage (V GE). The collector current (I C) ismeasured as a function of collector-emitter voltage(VCE) with the gate-emitter voltage (V GE) constant.
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A distinguishing feature of the characteristics is the0.7V offset from the origin. The entire family of curves is translated from the origin by this voltagemagnitude. It may be recalled that with a P + collector,an extra P-N junction has been incorporated in the
IGBT structure. This P-N junction makes its functionfundamentally different from the power MOSFET.
Transfer Characteristics
The transfer characteristic is defined as the variationof ICE with V GE values at different temperatures,namely, 25 oC, 125 oC, and -40 oC. A typical transfercharacteristic is shown in Figure 6. The gradient of transfer characteristic at a given temperature is ameasure of the transconductance (g fs) of the device atthat temperature
A large g fs is desirable to obtain a high currenthandling capability with low gate drivevoltage. The channel and gate structures dictate thegfs value. Both g fs and R DS(on) (on-resistance of IGBT)are controlled by the channel length which isdetermined by thedifference in diffusion depths of the P base and N +emitter. The point of intersection of the tangent to thetransfer characteristic determines the thresholdvoltage (V
GE(th)) of the device.
Switching Characteristics
The switching characteristics of an IGBT arevery much similar to that of a Power MOSFET. Themajor difference from Power MOSFET is that it has atailing collector current due to the stored charge inthe N --drift region. The tail current increases the turn-off loss and requires an increase in the dead timebetween the conduction of two devices in a half-bridge circuit. The Figure 8 shows a test circuit forswitching characteristics and the Figure 9 shows thecorresponding current and voltage turn-on and turn-off waveforms. IXYS IGBTs are tested with a gatevoltage switched from +15V to 0V. To reduceswitching losses, it is recommended to switch off thegate with a negative voltage (-15V).
Switching time test Circuit of IGBT
The turn-off speed of an IGBT is limited by thelifetime of the stored charge or minority carriers inthe N --drift region which is the base of the parasiticPNP transistor. The base is not accessible physicallythus the external means can not be applied to sweepout the stored charge from the N --drift region toimprove the switching time. The only way the stored
charge can be removed is by recombination withinthe IGBT. Traditional lifetime killing techniques oran N+ buffer layer to collect the minority charges atturn-off are commonly used to speed-uprecombination time.
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VII. Application of IGBT in Boost Chopper
The Switch used in the above circuit is IGBT, Themain purpose for using IGBT over SCRs and otherswitching devices is because it is set to ON whensupplied is given, when supply is taken off the switchwill be OFF automatically without any ForcedCommutation.
Where as in SCRs since the supplied is DC which
does not vary with time and phase once SCR is set toON it wont get turned off when the supply is takenoff it will remain in ON state forever since a negativepulse is given to gate. Hence need ForcedCommutation circuit.
Source Current Waveform
VIII. Conclusion:
This paper present brief idea of various modernpower semi-conductor devices available and IGBT istaken as example for its good features and explainedin detailed the basic structure, operation principle,safe area operations and its characteristics such asoutput characteristics, transfer characteristics,switching characteristics are discussed along withwaveforms. It also have application of IGBT in Boostchopper.
IX. References
B. Jayant Baliga, Power Semiconductor DevicesPWS Publishing Company, ISBN: 0-534-94098-6,1996.
Vinod Kumar Khanna, Insulated Gate BipolarTransistor (IGBT): Theory and Design IEEE Press,Wiley-Interscience
IXYS, Power Semiconductors Application Notes,2002 IXYS Corporation, 3540 Bassett Street, SantaClara CA 95054, and Phone: 408-982-0700
Ned Mohan, Tore M. Undeland, William P. Robbins,Power Electronics: Converters, Applications andDesign John Willey & Sons, Inc.
Ralph E. Locher, Abhijit D. Pathak, SeniorApplication Engineering, IXYS Corporation, Use of BiMOSFETs in modern Radar Tra nsmitters IEEEPEDS 2001-Indonesia
Ralph Locher, Introduction to Power MOSFETs andtheir Applications Fairchild Semiconductor,Application Note 558, October 1998.
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