A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

A comparison of basic properties of single-phase serial AC voltage controllersusing bipolar PWM chopper

Zbigniew Fedyczak, Maciej Jankowski, Pawel SzczesniakUNIVERSITY OF ZIELONA GORA, INSTITUTE OF ELECTRICAL ENGINEERING

Ul. Podgo6ma 50, 65-246 Zielona Gora, PolandTel. +48 68 328 25 38, fax. +48 68 324 72 93, fax. +48 68 325 46 15E-mail: Z.Fedycza e.uz.z M.Jan ,

URL:

Keywords<<Converter circuits, Power conditioning, Modelling>>

AbstractThis paper deals with two solutions for single-phase serial AC voltage controllers with bipolar PWMchopper. In these converters, either the bipolar PWM AC matrix chopper (MC) based on full-bridgetopology or the bipolar PWM AC matrix-reactance chopper (MRC) based on Cuk B2 topology andauxiliary transformer is applied. The MRC, in distinction to MC, has a magnitude of voltagetransformation function greater than one. The peak detection method in the control circuit of bothcontroller solutions is applied for fast control of the load voltage changes. The steady state theoreticalanalysis based on averaged models and transient state analysis based on small-signal averaged models ofthe presented controllers are employed. Furthermore, simulation and experimental test results are providedto confirm and verify the theoretical approach. On the basis of these investigations a comparative study ofthe results showing performance ofboth controller solutions is presented.

Introduction

In cases ofAC supply voltage changes, both downward and upward, there is a risk of damage to devices,which are sensitive to changes in voltage, for example: computer equipment, lighting equipment, etc.These kinds of devices need supply sources, which have a stabilized voltage. Serial voltage controllers are

commonly used to supply such sensitive equipment [1] - [6].Serial voltage controllers with unipolar matrix chopper, serial transformer for adding the compensatingvoltage and input transformer with tap changer are proposed in [3] to step-up and step-down AC voltagestabilization. The weight and volume of this controller are large has because of an input transformer withthyristor tap switches, which is a significant inconvenience of this solution. In order to solve this problemseveral other solutions of serial AC voltage controllers are proposed. In works [2], [4] and [6] solutionswith bipolar PWM AC matrix chopper (MC) are proposed. In these circuits full-bridge topology of theMC with four bi-directional switches is used. The bipolar AC voltage transformations achieved by MCenables bipolar compensate voltage shaping without input transformer with secondary coil tap switching.A significant inconvenience of such solutions is relatively greater switching loses in MC. Therefore in [4]a solution for the MC with soft switching of transistors in MC is proposed, however it demands the use oftwo additional transistors. A more universal solution, because of the possibility to input power factorimprovement, is presented in [5]. The AC/DC/AC with three-arm converter topology with bulk capacitoris used in this solution. However, such a circuit solution is a relatively expensive circuit because ofindirect AC/AC converter topology.

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

In an effort to achieve a lower cost solution of AC voltage controller, a new topology with PWM ACmatrix-reactance chopper (MRC) is proposed in [7]. The MRC with Cuk B2 topology is applied, whichhas the possibility to bipolar buck-boost AC voltage transformation [8] - [12]. There are only two bi-directional switches in this topology, which is a favourable feature of the proposed solution. Furthermorethe peak detection method in the control circuit of both controller solutions is applied for fast control of theload voltage changes [1], [13].Steady state theoretical analysis based on averaged models and transient state analysis based on small-signal averaged models of the presented controllers are employed. Furthermore, simulation andexperimental test results of the 3 kVA laboratory model are provided to confirm and verify the theoreticalapproach. On the basis of these investigations a comparative study of the results showing performance ofboth controller solutions is presented.

Description of presented controllers

Schemes for the considered solutions are shown in the Fig. 1. In these schemes the bipolar MC with full-bridge topology (Fig. la) or the bipolar MRC with Cuk B2 topology (Fig. Ic) and auxiliary transformer TRto compensating voltage uc shaping are used. The topologies and operations of the MC and MRC are

similarly to well-known DC/DC converters with full-bridge and Cuk B2 topology respectively, and are

described in detail in works [14], [15] and [7], which is also presented in this EPE conference.

) is C iC

b) error UcT7T3T1T uL d) error T1 T3 u

U~~~~~~~~~~ L cLI~e Fl _T T

Fig. 1: Single-phase serial AC voltage controllers, a), b) using bipolar matrix chopper with full-bridge

topology, c), d) using bipolar matrix-reactance chopper with Cuk B2 topology

The idealized voltage transmittances of the MC and MRC can be described respectively as [7] [14]:

=_2 MRC 2 =(1 2D)

According to (1) and referring to Fig. 1, the idealized voltage transmittances of analysed controllers can be

described as:

_~~~~~t

HT1 and =- ((-l )

The characteristics of the magnitude of voltage transmittances (2) as functions of pulse duty factor D are

shown in the Fig. 2. As it is visible from the Fig. 2a, the voltage controller with the MC has the possibility

to buck-boost load voltage transformation in the range of nominal input voltage +i/lp for changing D from

0 to 1. Whereas in the voltage controller with MRC load voltage can be grater than nominal input voltage

±1lp(Fig. 2b). This is the essential difference between analysed controller solutions.

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

a)

1i-i/p

0-

-1

|1H [V/V] Voltage controller

......

M#t D [-]

0 \ 0.5Mc

b)

1 0.5%

MRC 44

Fig. 2: Idealized characteristics of voltage transmittance magnitudes of a) for presented controller usingbipolar MC, b) for presented controller using bipolar MRC

The schemes for the control circuits of the voltage controllers are shown in the Fig. lb and Id. Bothversions are similar, moreover only the number ofPWM outputs is different depending on the number oftransistors in the main circuit. A detailed description of the control circuit, which is shown in the Fig. Ib, isalso presented in [7].

Mathematical and circuit models of presented controllersThe steady-state averaged state-space equation of the presented controllers is described as [7], [9] -[12]:

(3)

where: x =[i UI iC UL - vector of the averaged state variables for solution from Fig. la or

X = [1i Ui iLC UCC ic UL ]T vector of the averaged state variables for solution fromFig. Ic, A(D) - averaged state matrix and B(D) - input matrix. For both solutions For these matrixes areexpressed by (4) and (5):

0 _ 1

LF11 0

CF0 (2D - 1)

pLF20 0

(1-

0

D

CF1o _(

-D)CC0

p

0

0 0

(2D -1)PCFI

0

0 I

LF21 I

CF2 RLCF2

o o

O (1-D)PCF1

I-D) O

LCFDPCc

?LF20 1

CF2

where: p - voltage transformation ratio and LF2 -

the auxiliary transformer TR.total leakage inductance for the secondary winding of

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B(D)= B =

1LFl01

LF0O

(4)

A(D)=

O _1LFl

1 0

CF1O D

LCo o

O _(1-D)pLF2

o o

0

0

0

0

14I

RLCF2

B(D)= B =

1

LFI0

01

LF20

(5)

JANKOWSKI Maciej

x - A(D)x- + B(D) u,,

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

From (3) one can easily obtain the substitute circuit realization shown in the Fig 3 [7], [15].

a) iI A r

Fig. 3: Averaged circuit models of analysed voltage controllers, a) using bipolar matrix chopper with full-bridge topology, b) using bipolar matrix-reactance chopper with Cuk B2 topology

A - chain matrix of the chopper input filter, Ac - chain matrix of the chopper basic structure, ATRchain matrix of the auxiliary transformer, AF; - chain matrix of the chopper output filter and A - chain

matrix of the complete AC voltage controller

The four-terminal steady state description for the basic properties of the presented controller can bederived by means of well-known expressions, which are collected in mentioned works [7] and [15].Assuming that all variables have two components: a running constant component (the averaged value inthe switching period Ts), which is marked by upper case letter and a perturbation one marked by lowercase letter, which is covered by sign "Al:

us U1+u s is5is+i 9 X+x=IL+lL and d =D+d . (6)

On the basis of an averaged state space method the small signal state space equation is expressed as

follows [15], [16]:

d (X + x)2A(D) + B(Dp, + [(Ai A2)X +(B1 B2)US ]d, (7)

where: A1 = A(D = 1), A2 = A(D = O), B1 = B(D = 1) and B2 = B(D = O). Referring to (7), completeaveraged circuit models (canonical averaged models) of the presented controllers can be constructed andare shown in the Fig. 4. In these circuit models additional controlled voltage and current sources occur,

which are expressed by (8) and (9) for a controller with MC or MRC respectively.

j(Us,d)= pPR Usd and e(u ,a)= 2Usd,L P

(8)

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

dd cl 9 ~e~Ud Usd and e U) 1Usd,j, IUd= j2 (U -) 2 (I _ )2R US, e, iU,d )= (1~D dane2 IU,d) Udpw-D)Re 1D) /p((D-D)where: P = p/(2D -i1).

b) is =Is +is

Fig. 4: Complete averaged circuit models (canonical models) of analysed voltage controllers,a) using bipolar MC, b) using bipolar MRC

Laplace transform and solution in complex form of (7) is described by (10) and (11):

Ax(s) = A(D)i(s)+ B(D)ti(s)+ [(A1 - A2)X + (B1 - B2)J]Ud(s),

where:

x(s) = (sI - A(D)) 1t(D)(s) + [(A1 - A2)X + (BI - B2)U]d(s)}= Gi" (s)ss(s) + G,(s)d(s),

GUs(s= ^ (S) and G, (s)= ( )i. ~(s)=-x() x

moreover transmittances (12) are interpreted as:

UL (s) = UL(.S)

A detailed description of these transmittances are inserted in the appendix in tables, tab. A I and tab. A II.

Comparison of simulation and experimental test resultsThe switched model schemes used during simulation and experimental tests are shown in the Fig. 1. Thevalues of the relevant circuit parameters are collected in table A3 (appendix). The simulation andexperimental test results, for purpose of comparison, are collected together with some theoretical

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(9)

(10)

(1 1)

(12)

(13)

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

characteristics obtained for averaged models of the presented controllers, which are shown in the figuresFig. 3 and Fig. 4.In the figures Fig. 5 and Fig. 6 both steady state exemplary simulation and experimental time waveformsof the voltages and currents and steady state magnitude and phase of the voltage transmittances are shownto depict some differences in the operation of the voltage controllers.

a) e") 'US, "L

1.1aU)ina US, UL UL (D = 0.25) 1.5 Usm,,,,, UL (D = 0.75)1. 1 us"", /L D= .0US. )max[- UL (D= 0.50)0.89 Us",ax , 0.86 Usmax__

UL (D = 0.75)

t

US

b) t-13MS}>g UL!,,SAA,

~-s

f) i

lL

''D 0--0.25

c)~fr

iv

NS

j W .'

D = 0.5

d) igi s

. X'\4

IL X-.ZL7=~F-],iv

D 0.25

h) M1'17

h)

I .

D= 0.75

D-0.5

D 0.75

Fig. 5: Exemplary voltage and current time waveforms, a) and e) simulation load voltage time waveformsof the voltage controller using MC or MRC respectively, b), c), d) and f), g), h) experimental voltage and

current time waveforms of the voltage controller using MC or MRC respectively

As is visible from Fig. 5a and Fig.5e of the same circuit parameters of both voltage controller solutions therange of the load voltage change for solution using MRC is greater than for the solution using MC. Thevalues of the load voltage changes are described in the discussed figures. The magnitude and phasetransmittance characteristics obtained both during the theoretical analysis and simulation investigationsdemonstrate good coincidence with what is shown in the Fig. 6. Generally, the experimental resultsobtained for both solutions of the voltage controller confirm the theoretical and simulation ones forchanges of the pulse duty ratio D in full range for the solution with MC (Fig.6a) and in the range betweenO to 0.7 for the solution with MRC. In the last solution, the experimental results, obtained for D greaterthen 0.7, are visibly different from the theoretical and simulation ones (Fig. 6c). In this case the voltagetransmittance is significantly lower. This is caused by the decreasing of the circuit quality factor which isconnected with an influence of the parasitic circuit parameters.

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

a) IHu [V/VI p= i Calculation

2 _/ ~~p= 2 Simulation1.5= Experiment

0.5

0,5p

p =230/48

arg( H ) [radi

21/4

-n4 D

-n/20 0.25 0.5 0.75

b) 4ILU IIVNV p=2 p=i p-=4\3 Calculation

2 Simulation

-I p=10

n/2

arg( H ) [radi

-1l/4 ~~~~D21l/2

0 0.25 0.5 0.75 1

c) iflu I [V/V] p = 230/48 p=104- Calculation -

Simulation

12

IExperiment _ :

0

71/2arg( H ) [radl p = 230/48 P=10Il| \ .\

iT/40

-7/4-71/2

D

0.25 0.5 0.75 1

Fig. 6: Magnitude and phase of the controller voltage transmittances for different transformer TR voltagetransformation ratios p, a) for voltage controller using MC, b) for voltage controller using MRC with load

matching condition, c) for voltage controller using MRC at value RL= const (Tab. A III)

As is visible from Fig. 6c, in the controller with MRC at constant load resistance, the value of the loadoutput voltage can be more then two times greater than supply voltage for p = 230 V/48 V. This means

that the nominal load voltage can be obtained even for 50% step-down of the supply voltage. It is theessential distinction in comparison with solutions based on bipolar matrix choppers. Exemplary timewaveforms of the voltages for 15% and 10% step-down and step-up changes of the supply voltageobtained during experimental investigations are shown in the Fig. 7.

1500 step-down

.fiE QUL,(pe=A)ergri

111 1_ 1 i ff S

b) = Ss10% stcp up'

1 I-Nt \

c) g}Wt;tS UC 15%X step-down

1 U3 UL(peA)

ul ak) l

d) UC oo step-up

'5 \

c~rror,~ u

-(l o,,vA

3 g 31 A

U' error

Fig. 7: Exemplary experimental time waveforms of the voltages for a 15% step-down and 10% step-up inthe supply voltage, a) and b) for voltage controller using MC, c) and d) for voltage controller using MRC

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING JANIIWRKI PWMciej CHOPPER

In Fig. 8 there are exemplary voltage time waveforms obtained during simulation investigations of thedynamic behaviour of presented controllers. As is visible from Fig. 8, for both topologies, the load voltagetime response is less than one period of supply voltage in step down/up changes in supply voltage and instep changes of the control signal.

a4) Us [V], d? 1100 [-] =~us00

200 r

-- --- --t---- ---- - ----

l to t [MS]-400 \

b)

'TOO 120 140 160 180

Topology Calc. Sim.uL [V] with MC _

500 Wltn lVlm-I

0 /

Zoom

-500 tm-500 ~~~~~~~t[imSI100 120 140 160 180 120

180E' o__ t[ImIs] -550L

100 120 140 160 180 120

to130

t[ms]

140

Fig. 8: Exemplary voltages and pulse duty factor time waveforms, a) and c) at 25% supply voltage step-down forD = 0.5, b) and d) with pulse duty factor step change from 0.5 to 0.25 for topology with MC or

from 0.5 to 0.75 for topology with MRC for Us= 230 V

The comparative results of the analysed controller with MC or MRC are shown in Tab. I. There isconfirmation in Tab. I that the results obtained for the voltage controller with MRC, both in steady stateand in transient state, are not worse than for one with MC. Whereas it should be noted that in a circuit withMRC, only two bipolar and bidirectional switches (4 transistors) are used. Furthermore, as mentionedearlier, the voltage controller with MRC has a more enhanced possibility of load voltage stabilization witha greater variation in the supply voltage.

Table I: Comparative study of the presented voltage controllers

Feature Topology with MC Topology with MRCNumber of transistors 8 4

Number of reactive elements (without aux. TR) 3 5Calculation: 83 126 Calculation: 51 126Supply voltage variation at setting load voltage as Simulation: 83 126 Simulation: 57 150

L a [/o] of US(nom)7rinal) Experiment: 84 134 Experiment: 76 135Calculation: -3.4 -3.6 Calculation: -3.8 -25

Maximal load voltage phase shifting [0] Simulation: -3.3 -3.7 Simulation: -2.9 -27Experiment: - Experiment: -2.5 -27

Step function response [s] One supply voltage period TLoad voltage over-voltage at transient state 14 14

as a [%] of US(nominal)

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-300 Io130

14[is]140

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

ConclusionsIn this paper a comparative study of basic properties of the single-phase serial AC voltage controller usingbipolar MC or MRC with Cuk B2 topology has been presented. It should be noted that the controller usingMRC consists of half the number of transistors than in case of the voltage controller using MC. Furthermore,the voltage controller with MRC has an enhanced possibility of load voltage stabilization with a greatervariation in the supply voltage. In this solution, the nominal load voltage can be obtained even for 50% step-down of the supply voltage. The dynamic proprieties for both solutions are similar; moreover the voltagecontroller using MRC is more sensitive to the load change in mismatching conditions. Further research isfocused both on the experimental investigations and development of the presented solution for the purposeof decreasing commutation loses and obtaining robust faster response to step-down/up changes in supplyvoltage across a wide range of load changes.

AppendixTable A I: Small signal transfer functions of analyzed AC voltage controller with MC.

Definition Formula1?L (S) s~~~~~1 2

+P1-

G (s)=aL(s) L2 2- F, L FICFILF2Cf2a5(s) det(sI - A(D))

sL(s ) 1 4 LF(C)-2 22 2(P- ) F- F2 2Go ( () pdLLF2CF2 PpRLCCFCLF2CFL2 pLFCILFCF2 C C

G ( ) fid(s) + LSSH1DLFF+LC 2

det(sI - A(D))

d 15 3 + P2 (LFI CF1J±LF2CF2)+(LFlCF2 +2 + L F2 ±LFl

RL CF2 P LFICFILF2CF2 PRLLFICFILF2CF2 LFICFILF2CFTable A II: Small signal transfer functions of analyzed AC voltage controller with MRC.

Definition Formnula

a(s) P2((DC4+ p(D2LFlCc+ (I D2LFICFI + - D)2 (i DX 2D)GoL-S ?(S>L LF2C2 pLFICFLcCcLF2C2 pLF CFLcCLF2C2

det (sI A (Ds)) XFRL2LFFl2cFlLclcclLFt2cF21 4 p(+ DXDCFI (1 D)C) (1-2DXDCFl (ID)C2)3 +

p(1 D)LF2CF2 p 3(1 D)RLCFlCCLF2CF2

(S) O(S>) +DLFlCC±(I1 D)LFlCFl+LcCcC 52GILd LXJ + p(1 D)LF1lCF LcCcLF2CF2a- spP( - DF DXDLc (I- 2D)LF) (1 -2DXDLc (I 2D)LF)

3(1 RDCRLLFCLCCcL CpLfCFLcLp ~ ~ Fl C CF2CF2 PFl CC F2CF2det(slI A(D))

s6 ± RC 5 ± p2((D2CC + (I D)2CFJL~FlLF2CF2 + (LFICF2 + LF2CF2)LCCC)± (D2cF, + (i D Cc)LFjLcCC2 s4RLF2 p2LFjC LcCL 2C2

+P2((D2c ±(i D)2CFlLFl+±LCCC)LF2 ±(D2cF, +(i DD2CC)LFlLc s3 +det(slI-A(D)) +P2RLL 1C 1LCCLF2C2+ p2 (D2LFlCC I- Df (LFICQi ± LF2CF2) Lc CC+D ±+( - 22LF 2 2+

p2LF1CFlLcCCLF2Cf2+ p2(1 -DYLF2±+(D2Lc±+(I 2DYLF, ) + (i-Df

To2RLLF1CF1LCCCLF2CF2 LCFLcCcL2C2

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A COMPARISON OF BASIC PROPERTIES OF SINGLE-PHASE SERIAL AC VOLTAGE CONTROLLERS USING BIPOLAR PWM CHOPPER

Table A III: Simulation and experimental tests circuit parameters

ValueParameter Symbol MC MRC

Simulation Experiment Simulation ExperimentSupply voltage / frequency Us If 230 V / 50 Hz 230 V / 50Hz 115 V/ 50HzFilter inductances LFI, LF2 5.4 mH, 4.35 mH 10.8 mil, 4.35 mHFilter capacitances CF1,CF2 6.2 ,uF, 6,uF 1.6 ,uF, 6,FInductance in the chopper Lc 1.6 RFCapacitance in the chopper Cc 10.8 mHLoad resistance RL 23 Q 23 QTransformation ratio p 230/48 V/V 230/48 V/VSwitching frequency fs 5 kHz 5 kHzProportional factor kp 0.005 0.005Integration time constant Ti 0.05 s 0.05 s

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shunt and a serial regulator. EPE'97, pp. 2.186 - 2.191. Trondheim 1997.[3]. D H. Jang, G. H. Choe. Step-up/down AC voltage regulator using transformer with tap changer and PWM AC

chopper. IEEE Transaction on Industrial Electronics, Vol. 45, No. 6, pp. 905 - 911, December 1998.[4]. J. C. Oliveira, V. J. Farias, L. C. Freitas, J. B. Vieira. A serial regulator using a soft switching PWM AC/AC

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Of2nd Conff on Power Electronics Devices Compat. PEDC'01, pp. 144 - 155, Zielona G6ra, Poland, Sept 2001.[7]. Z. Fedyczak, M. Jankowski. Single-phase serial AC voltage controller using bipolar matrix-reactance chopper.

llth EPE'05 Conrference, (in process) Dresden, Germany, 2005.[8]. A. Ikriannikov, S. Cuk. Direct AC/DC conversion without input rectification", Proc. ofIEEE 30th PESC'99,

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Zielonogdrskiego. Uniwersytet Zielonog6rski, Zielona G6ra, Poland, 2003.[10]. Z. Fedyczak. Steady state modelling of the bipolar PWM AC line matrix-reactance choppers based on the Cuk

topologies. Archive ofElectrical Engineering, Vol. LII, No 3, pp. 303-316, 2003.[11]. Z. Fedyczak, I. Y. Korotyeyev. Bipolar PWM AC line matrix-reactance choppers - the steady state basic

energetic properties. Proc. ofthe EPE'03 on CD. Toulouse Sept. 2003.[12]. Korotyeyev I. Y., Fedyczak Z. Steady-state modelling of basic unipolar PWM AC line matrix-reactance

choppers, The Int. Journal for Comp. and Mat. in Electrical and Electronic Eng., COMPEL, Vol. 24 No. 1,2005, pp. 55 - 68.

[13]. D. M. Lee, T. G. Habetler, R. G. Harley, J. Rostron, T. Keister. A voltage sag supported utilizing a PWM-switched autotransformer", 35th Annual IEEE PESC '04, pp. 4244 - 4250, Aachen, Germany 2004.

[14]. E. Lefeuvre, T. Meynard, P. Viarouge. Robust Two-Level and Multilevel PWM AC Choppers. Proc of 9thEPE'01, CD, DS.1-23, pp. 1-8. Gratz, Schwitzerland 2001.

[15]. Z. Fedyczak, M. Jankowski. Modelling And Analysis Of The Quadrature-Booster Phase Shifter With PWMAC Bipolar MC And Passive Load", 4th International Workshop Compatibility in Power Electronics - CPE2005. Gdafnsk-Zielona Gora, Poland, 2005 .- Zielona Gora (In progress).

[16]. R. D. Middlebrock, S. Cuk. A general unified approach to modelling switching-converter power stages, Proc.ofPESC'76, pp. 18 - 34. 1976.

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