6 Michal KNAPCZYK Krzysztof PIENKOWSKI 2.pdf

8/10/2019 6 Michal KNAPCZYK Krzysztof PIENKOWSKI 2.pdf

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Prace Naukowe Instytutu Maszyn, Napdw i Pomiarw ElektrycznychNr 59 Politechniki Wrocawskiej Nr 59

Studia i Materiay Nr 26 2006

__________

AC/DC line-side converter, PWM rectifier,

Hysteresis-Band Modulation, Carrier-Based Sinusoidal Modulation,

Space-Vector Modulation, overmodulation, fixed switching frequency

MichaKNAPCZYKF*F, Krzysztof PIEKOWSKIF*

ANALYSIS OF PULSE WIDTH MODULATION TECHNIQUES

FOR AC/DC LINE-SIDE CONVERTERS

The paper presents the analysis of the modulation strategies for the AC/DC line-side converters.The application of the different modulation methods to the control system of the AC/DC converterhas been presented. The operation of the AC/DC converter in different dynamic states strongly de-pends on the modulation method applied. The theoretical background of Hysteresis-Band Modula-tion, Carrier-Based Sinusoidal Modulation and Space-Vector Modulation has been presented. The is-sue of overmodulation has been discussed. Voltage Oriented Control of the AC/DC line-sideconverter has been chosen to examine the presented modulation methods. The influence of the dis-cussed modulation methods on the line current distortion and the switching frequency has been exam-ined. The simulation results of the presented techniques have been demonstrated and concluded.

1. INTRODUCTION

The dynamic development of the power- and microelectronics devices sustains con-tinual progress in design and realization of modern adjustable speed drives. The interestof researchers in the elaboration of advanced control techniques for voltage source in-verters was in last two decades aroused by AC/DC line-side converters called also PWMrectifiers (synchronous rectifiers). These front-end rectifiers due to their properties sys-tematically displace the diode bridges becoming an important part of the modern fre-quency converters for the intelligent motion control applications [1,5]. The three-phasetwo-level AC/DC line-side converters provide sinusoidal line currents and bidirectional

power flow at the unity power factor (UPF). These properties have decided of the use ofthe PWM rectifiers in the applications improving the electrical power quality [7].

*Politechnika Wrocawska, Instytut Maszyn, Napdw i Pomiarw Elektrycznych, 50-370 Wrocaw, ul.Smoluchowskiego 19, [email protected], [email protected].


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The AC/DC converters consist of power electronics devices like Insulated Gate Bipo-lar Transistors (IGBT) or Gate Turn-Off thyristors (GTO) that are characterized byswitch mode operation. The capability of forming sinusoidal currents is provided by theintroduction of the sophisticated technique called Pulse-Width Modulation (PWM). Thistechnique provides the sequences of width-modulated pulses to control power switches.

Many PWM techniques have been developed according to special requirements andoptimization criteria. The choice of the particular PWM technique arises from the de-sired performance of the synchronous rectifiers [2,3]. Generally pulse-width modula-tion techniques for frequency converters may be classified as follows: Carrier-BasedSinusoidal PWM, Hysteresis-Band PWM, Space Vector PWM, Selected HarmonicElimination PWM, Minimum Current Ripple PWM, Sinusoidal PWM with Instanta-

neous Current Control and Random PWM. This paper presents basic assumptions andapplications of selected, most frequently used modulation techniques applied to PWMrectifiers. For the comparative analysis Voltage Oriented Control of the AC/DC line-sideconverter has been chosen to examine the proposed modulation methods.

2. VOLTAGE SOURCE AC/DC LINE-SIDE CONVERTER

The topology of the voltage source AC/DC converter connected to the grid is pre-sented in Fig.1. The power circuit of the synchronous rectifier stems from the topol-ogy of the three-phase PWM voltage inverter.

Fig.1. Voltage source AC/DC line-side converter

The PWM rectifiers bridge consists of six fully-controlled IGBT transistors con-nected to the supply line throughout the three symmetrical line inductors. The voltagedrop over line chokes has to be controlled to provide sinusoidal line currents. Equa-tions (1) describe the dynamic model of the PWM rectifier in natural (A,B,C) coordi-nates. Sa, Sb, Screpresent states [1,0] of power switches in respective converter legs.


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( )

( )

( )

( )loadgCcgBbgAad

dc

cbadc

gCggC

g

gC

cbadc

gBggB

g

gB

cbadc

gAggA

g

gA

iiSiSiSC

Udt

d

SSSU

iReL

idt

d

SSSU

iReL

idt

d

SSSUiReL

idt

d

++=

+=

+=

=

1

23

1

23

1

23

1

(1)

3. PULSE-WIDTH MODULATION IN APPLICATION TO PWM RECTIFIERS

The major aim of the pulse width modulation in the AC/DC line-side converters isthe control of the amplitudes of the main harmonics of the converter input PWMthree-phase voltages. Besides the appropriate forming of the line current harmonicspectrum should be provided. In general the modulation techniques should be charac-terized by the wide range of the linear operation, fixed switching frequency and lowerinfluence on producing of the higher harmonics in the line currents [6]. The modula-tion process during the operation of the PWM rectifier should provide the maximaluse of the DC-link voltage. The modulation index m expresses the capability of theDC-link voltage utilization in generating the PWM voltages at the input of the AC/DCconverter during the control process.

Fig.2. Range of Pulse-Width Modulation for the AC/DC line-side converters


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Fig. 2 presents the dependence of the converter input voltage on the modulation in-dex with respect to the DC-link voltage. The modulation bandwidth is generally di-vided into the linear and the nonlinear range. The limitation of the modulation regionto the linear range is sufficient for the proper operation of the PWM rectifier. Yet forthe excellent dynamic performance of the synchronous rectifier during the transientsthe operation in the overmodulation range must be provided [1,8]. However this tech-nique introduces the line current distortions due its nonlinearity and may be inadvis-able in the applications of the AC/DC converters improving the electrical power qual-ity. The issue of the modulation index and the modulation range for the basic PWMtechniques will be presented in detail in the next sections of this paper.

3.1.

HYSTERESIS-BAND PULSE-WIDTH MODULATION

The Hysteresis Pulse-Width Modulation, named also bang-bang current controlconsists in direct forcing of the line current flow according to the current referencesignals i*gA, i*gB, i*gC. This kind of the modulation is performed in the nonlinear con-trol circuit with the hysteresis relays [7]. The Voltage Oriented Control of the PWMrectifier with the hysteresis pulse-width modulation is presented in Fig.3.

Fig.3. Voltage Oriented Control with Hysteresis-Band PWM (HB-PWM)

When the instantaneous value of the line phase current exceeds its reference valuethan the respective grid phase is instantly connected to the negative node of the DC-link voltage. Otherwise the grid phase is switched to the positive node in the DC-link.This process is carried out simultaneously and independently for two other phases.


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Equations (2) describe bang-bang current control:

12

02

12

02

12

02

==

==

==

cgCcgC

bgBbgB

agAagA

SH

iSH

i

SH

iSH

i

SH

iSH

i

(2)

where is the line current error and H is the hysteresis bandwidth in [A].ggg iii *=

In result the voltage source AC/DC line-side converter with the hysteresis modula-tion operates as the source of directly formed current. The idea of the hysteresis pulse-width modulation is demonstrated in Fig.4.

Fig.4. The idea and control signals of Hysteresis-Band PWM

The basic problem in the bang-bang modulation is the alternating switching fre-quency that depends on the following significant factors: hysteresis bandwidth, elec-tromagnetic time constant of the grid and chokes circuit, IGBT dead-time and the dif-ference between DC-link voltage and instantaneous value of the respective grid phasevoltage. In order to obtain the privileged switching frequency the additional carriersignal may be added to the current error at the input of the relays. The other solution is


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the synchronization of the switching process i.e. generation of the firing pulses inevery fixed sample step. This type of bang-bang modulation is usually applied in themicroprocessor-based digital control systems and is called -modulation.

The line currents oscillate around the current reference signals within the bounda-ries defined in the hysteresis relays. Fig.5 presents the line phase voltage and the re-spective line phase current for the control system of the AC/DC converter with Hys-teresis-Band PWM depicted in fig.3.

Fig.5. Line voltage (1) and respective line current (2) for Hysteresis-Band PWM

The narrower hysteresis bandwidth is the better reconstruction of the sine-shapedcurrents is obtained. However the absolute reduction of the hysteresis bandwidth isunacceptable due to the restricted values of the switching frequency of the power tran-sistors. Hence the minimal bandwidth of the hysteresis relays should provide nohigher switching frequency as results from the value of dead-time for IGBT devices.

Fig.6. Line current harmonic spectrum for Hysteresis-Band PWM


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In case of non-synchronized Hysteresis-Band PWM the line current harmonic spec-trum contains all higher harmonics including sub-harmonics (fig.6). The Total Har-monic Distortion ratio of the line current from fig.5 is equal THDigA=9.3%.

The Hysteresis-Band Pulse-Width Modulation technique is mostly used in the ana-log control systems of the PWM rectifiers. The hardware implementation of the hys-teresis relays can be realized using simple circuit applications with the operationalamplifiers [1]. The dynamic performance of the PWM rectifiers control system withthe bang-bang modulation technique applied is excellent since the hysteresis relays donot require tuning and provide robustness to line disturbances or parameter mismatch.

3.2.

CARRIER-BASED SINUSOIDAL PULSE-WIDTH MODULATION

Carrier-Based Sinusoidal Pulse-Width Modulation is based on the comparison ofthe converter voltage reference signals with the carrier signal of the triangular shape[4]. Unlike Hysteresis-Band PWM with the reference current signals, this modulationtechnique provides the firing pulses upon the converter voltage reference signals. TheVoltage Oriented Control of the PWM rectifier with Carrier-Based Sinusoidal Pulse-Width Modulation is presented in Fig.7.

Fig.7. Voltage Oriented Control with Carrier-Based Sinusoidal PWM (CB-SPWM)


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The reference voltage signals U*A, U*B, U*Care usually sinusoidal of the grid fre-quency. Their amplitudes are proportional to the expected amplitudes of the mainharmonic of the converter input PWM three-phase voltages. The frequency of thecarrier signal is usually hundredfold higher then the frequency of reference signals.The modulation index mis defined by the mutual rate of the reference signals and thecarrier signal amplitudes (3):

carrier

CBA

U

Um

,,*= (3)

The converter voltage reference signals U*d, U*qare provided by two linear line

current controllers operating in the (d-q) rotating frame. The idea of the Carrier-BasedSinusoidal Pulse-Width Modulation is demonstrated in Fig.8.

Fig.8. The idea and control signals of Carrier-Based Sinusoidal PWM

The range of the Carrier-Based Sinusoidal Pulse-Width Modulation is constraineddue to the fact that the modulation index can reach the maximal value of m=1. Thenthe amplitudes of the sinusoidal converter voltage reference signals and the carriersignal are equal. The equation (4) describes the amplitude of the main harmonic of theconverter input PWM phase voltage by the unity modulation index m=1.

2*max

dcconvA

UUU == (4)


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According to the equation (4) the RMS value of the line-to-line converter inputPWM voltage is described by the following expression:

dcdcRMSconvARMSconvAB UUUU === 612.02

32

2

3)()( (5)

The maximal utilization of the DC-link voltage in case of Carrier-Based SPWM isabout 83%. Due to the fact that the DC-link is not connected with the neutral node ofthe grid it is admissible to modify the sinusoidal converter voltage reference signals byadding so called Zero Sequence Signals of the third harmonic frequency [9].

Fig.9. Line voltage (1) and respective line current (2) for Carrier-Based Sinusoidal PWM

This solution extends the linear range of the modulation up to m=2/3=1.15. Thenthe utilization of the DC-link voltage increases to 91%. Fig.9 presents the line phasevoltage and the respective line phase current for the control system of the AC/DCconverter with the Carrier-Based Sinusoidal PWM depicted in Fig.7.

Fig.10. Line current harmonic spectrum for Carrier-Based Sinusoidal PWM


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Fig.10 demonstrates the line current harmonic spectrum for the Carrier-Based Si-nusoidal Pulse-Width Modulation. The higher harmonics are located in the vicinity ofthe carrier frequencyfs=5 kHz and its multiple. The Total Harmonic Distortion ratio ofthe line current presented in Fig.9 is equal THDigA=6.1%.

The Carrier-Based Sinusoidal Pulse-Width Modulation is acknowledged as theclassical type of the modulation for the power converters. The analog realization isrelatively simple and is based on the application of the operational amplifiers and themonolithic carrier signal generators. For the digital implementation a slightly differenttype of the Carrier-Based Sinusoidal PWM technique has been elaborated. It is calledRegular Modulation and consists in the fixed sampling of the sinusoidal convertervoltage reference signals. In result the sequences of the pulses of the precisely defined

widths are obtained. The modern evaluation boards with the Digital Signal Processorsare equipped with the hardware implementation of Carrier-Based Sinusoidal Modula-tion. These digital devices are purpose-dedicated to control the power converters.

3.3. SPACE VECTOR PULSE-WIDTH MODULATION

The power transistors of the three-phase two-level synchronous rectifier during itsoperation provide eight different states of the conduction (Fig.11).

Fig.11. Conduction states of the AC/DC line-side converter


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The converter input voltage can be represented by the space vector U [8,9]. Thespace vector Uonce can take one of eight different positions resulting from the per-missible combinations of the conduction states. Fig.12a presents the diagram of thepossible locations of the space vector U decomposed over (-) orthogonal coordi-nates oriented with the line phase A. Vectors U1 toU6have fixed modulus of (2/3)Udcand are phase-shifted by /3. They are called active vectors and refer to the conduc-tion states of the power switches during which the respective phases are supplying theDC-link load. While the three upper or three lower transistors are conducting simulta-neously, the supply line is short-circuited. These states are described by twozero vec-tors U0 and U7. The zero vectors are located in the origin of (-) coordinates andthey are represented by the two concentric points.

Fig.12. Space Vector representation of the converter input voltage (a) and control signal pattern (b)

If six active conduction states were successively forced in the rectifier, the con-verter input PWM voltage space vector would change its position every /3 inside thehexagon. Hence active vectors allocate six equal sectors. During the SV-PWM theconverter input voltage vector Ushould be appropriately formed in order to map thereference vector U*. The (d-q) components of the reference vector U*are generatedby two PI current controllers in the control system depicted in Fig.13. The optionalposition of the reference vector U*inside the sector can be reached by providing thesymmetrical control pulses represented by the following switching sequence:

U0-U1-U2-U7-U2-U1-U0 (6)

in case when the reference vector U*is moving throughout the first sector. In the othersectors two next adjacent vectors should be considered. The period TSof each sym-metrical control sequence is fixed and corresponds to the frequencyfSas follows:


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S

ST

f 1= (7)

Fig.12b presents the control sequence for the first sector. During the TScycle theadjacent and zero vectors are applied for unambiguously determined times t1, t2, t0.These durations are calculated with the help of the trigonometrical relationships (8).

( )

( )210

2

1

2

sin3

3

3sin

3

3

ttT

t

tTmt

tTmt

S

gS

gS

+=

=

=

(8)

where 0 gt /3 (in the first sector). The argument of the sinfunctions should beappropriately modified according to the range of the other sectors every /3.

Fig.13. Voltage Oriented Control with Space-Vector PWM (SV-PWM)

The reference vector U*rotates with mains pulsation g. To achieve the smooth ro-tation of the reference vector U* a relatively small value of period TSis necessary. Inpractice the switching frequency of fS=5 kHz is sufficient to obtain the sinusoidal line


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currents with the minimum ripple. Fig.14 presents the line phase voltage and the re-spective line phase current for the control system of the AC/DC converter with theSpace Vector Pulse-Width Modulation depicted in Fig.13.

Fig.14. Line current and respective line voltage for Space Vector PWM

The Total Harmonic Distortion ratio of the line current presented in Fig.14 is equalTHDigA=5.7%. For the linear modulation the maximal length of the reference vectorU* is restricted to the radius of the circle inscribed into the hexagon (Fig.12a) and is

equal U*max= Udc/3. The modulation index can reach the maximal value m=1.15 andthe utilization of the DC-link voltage equals 91%. The Space Vector Modulation cor-responds to the sinusoidal modulation with the additional Zero Sequence signals.

Fig.15. Line current harmonic spectrum for Space Vector PWM

Fig.15 presents the line current harmonic spectrum for the Space Vector Pulse-Width Modulation. The higher harmonics are located in the vicinity of the switchingfrequencyfs=5 kHz thus have no practical influence on the grid.


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3.4.

OVERMODULATION

The nonlinear Pulse-Width Modulation occurs when the modulus of the referencevector U* exceeds the radius of the hexagons incircle. Then the hodograph of theconverter input voltage vector U is not circular any more since the top of the vectorremains at the hexagon being unable to cross its boundaries.

Fig.16. Regions beyond linear modulation: a) overmodulation; b) six-step operation

Fig.16 presents the regions of the nonlinear modulation. The overmodulation pro-ceeds when the modulation index is located in the range of 1.15


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Fig.17. Converter input phase voltage by: a) linear modulation, m=0.85; b) overmodulation, m=1.9; c)six-step operation, m=20

4. CONCLUSIONS

The paper presents the comprehensive analysis of the selected pulse-width modula-tion techniques in the applications to the AC/DC line-side converters. The Hysteresis-Band PWM technique provides the excellent dynamics through the direct line currentstracking. This feedback PWM technique allows the switching pattern to be realizedon-line. This method despite the simplicity of the implementation is corrupted by thevarying switching frequency accounting for the high current ripple.

The appliance of the Carrier-Based Sinusoidal PWM technique may reduce thehigher harmonics content in the line currents since the carrier signal imposes roughlyconstant switching frequency of the power transistors. Unlike bang-bang current con-

trol carrier-based modulation directly enforces adequate converter input PWM volt-ages to track their reference values. Hence the main problem is the efficiency of theDC-link voltage conversion into the PWM scheme at the input of the AC/DC con-verter. The deliberate distortion of voltage reference signals by the third harmonics isthe most effective method to extend the linear range of the carrier-based modulation.

The Space Vector PWM technique provides the wide range of the linearity and theimproved harmonic performance although the high computational effort and the com-


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plexity of the implementation. The space vector modulation likewise the carrier-basedmodulation is the feedforward PWM technique. The PWM voltage may be thenformed via an open-loop control scheme. Hence the control system of the synchronousrectifier does not exhibit the high dynamic performance and the effects of disturbancesare not automatically reduced.

REFERENCES

[1] BOSE B.,Modern Power Electronics and AC Drives, Prentice Hall PTR, 2002[2] BUSO S., MALESANI L., MATTAVELLI P., Comparison of Current Control Techniques for Active

Filter Applications, IEEE Transactions on Industrial Electronics, vol.45, no.5, October 1998.

[3] CICHOWLAS M., KAMIERKOWSKI M. P., Comparison of Current Control Techniques for PWMRectifiers, 2001 IEEE International Symposium on Industrial Electronics, June 2001.

[4] KIM J.-H., SUL S.-K., A Carrier-Based PWM Method for Three-Phase Four-Leg Voltage SourceConverters, IEEE Transactions on Industrial Electronics, vol.19, no.1, January 2004.

[5] KRAH J.-O., HOLTZ J., High-Performance Current Regulation and Efficient PWM Implementationfor Low Inductance Servo Motors, IEEE Transactions on Industry Applications, vol.35, no.5,Sept./Oct. 1999.

[6] KWASINSKI A., KREIN P. T., CHAPMAN P. L., Time Domain Comparison of Pulse-Width Modu-lation Schemes, IEEE Power Electronics Letter, vol.1, no.3, September 2003.

[7] LIN B.-R., WU D.-P., High Power Factor Correction Circuits with Space Vector and HysteresisControl Methods, Electric Power Systems Research 43, March, 1997.

[8] MONDAL S. K., BOSE B. K., OLESCHUK V., PINTO J. O., Space Vector Pulse Width Modulationof Three-Level Inverter Extending Operation into Overmodulation Region , IEEE Transactions on

Power Electronics, vol.18, no.2, March 2003.[9] ZHOU K., WANG D., Relationship Between Space-Vector Modulation and Three-Phase Carrier-Based PWM: A Comprehensive Analysis, IEEE Transactions on Industrial Electronics, vol.49, no.1,February 2002.

ANALIZA METOD MODULACJI SZEROKOCI IMPULSW W UKADACHSTEROWANIA PRZEKSZTATNIKW SIECIOWYCH AC/DC

Artyku prezentuje analizwybranych metod modulacji szerokoci inpulsw (MSI) w ukadach ste-rowania przeksztatnikw sieciowych AC/DC, zwanych take prostownikami PWM. Zdolno prze-ksztatnika AC/DC ksztatowania sinusoidalnych prdw sieci jest zapewniona przez uporzdkowan se-kwencj zacze poszczeglnych kluczy tranzystorowych, zwan modulacj szerokoci impulsw (MSI).

W artykule przedstawiono teoretyczne zaoenia metody histerezowej modulacji nadnej z bezpored-nim formowaniem przebiegw prdu, modulacji sinusoidalnej z sygnaem nonym oraz modulacji wekto-rowej. Do celw analizy porwnawczej strategii modulacji zastosowano metodVoltage Oriented Con-trol w ukadzie sterowania przeksztatnika sieciowego AC/DC. Przedstawiono wybrane wyniki badasymulacyjnych i omwiono wpyw przedstawionych metod modulacji na znieksztacenia prdw sieci isposb przeczania pprzewodnikowych kluczy tranzystorowych.

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