Unity Power Factor

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2004 International Conference onPower SystemTechnology - POWERCON2004Slngapore, 21-24 November 2004

Unity Power Factor Rectifier usingScalar Control TechniqueA.G.Visha1Anand, Neeraj Gupta, V.Rammarayanan

Abshct - The widely used Resistance Emulation techniquefor eliminating the problem o f harmonic pollution of the PowerDistribution system is based on the concept that the reemerpresents a pure resistive load to the ac system. In such a case,input voltage and currentwlll have the ssme waveshape and w i l lbe in phase. Over the recent past, many methodologies based onthe Resistance EmuIation technique have been proposed in theliterature. There has been a consistent attempt to introducesimplified control, higher efficiency and cost effectivenesshvarious emerging techniques. Scalar Control Method basedResistance Emulation technique, which is being discussed in thispaper, i s also an endeavor in the same direction. In this paper,the details of Scalar Control theory, analysis, modeling,simulation and erperlmental resnlts obtalned by using thistechnique have been presented.

I. INTRODUCTIONConventional power converters with diode capacitorrectifier front end have distorted input current with highharmonic content in the line currents. It is well known that

these harmonic currents cause several problems such asvoltage distortion, heating, and noises, reducing the capacityof the line to supply energy. Owing to this fact and theadoption of standards such as 1000-3-2 [11, there's a need forpower supplies that draw current with low harmonic content& aIso have power factor close to unity. So far, a variety ofpassive [24] and active PFC echniques have been proposed.While the passive PFC techniques may be the best choice atlow power, cost sensitive applications, the active PFCtechniques are used in majority of the applications owing totheir superior performance.

The active PFC converters can be implemented eitherusing th e two-stage approach [5] or the single-stage approach.Unity power factor and high output voltage regulation areachieved in two-stage approach by the addition of a converterfor input current shaping at the AC line side of theconventional switching power supplies as shown in Fig. 1.The price that is paid for meeting the objectives of sinusoidalinput current& output voItage regulation are

A. G . Vishal Anand is with the Department of Electrical Engg., ndianNeerajGupta is with the Department of Electrical Engg., ndian InstituteV. Ramanarayanan is with th e Department of Electrical Engg., Indian

Institute of Science, 3angdore-560012 ( [email protected])ofScience, Bangalore561H)lZ( [email protected])Institute of Science, BangdoreS6OOl2 [email protected])

Lad.Fig. I TWM age PFC Converter -"

Li-. .r w I - 1

wam7 pmu

Fig. 2 Singre-stage PFC Converter

Fig. 3 Scalar Control based PFC ConverterRequirementof twocontrol loopsBig storage capacitorAdditional DC-DC converterWhile the two-stage approach is a cost effective approach

in high power applications, its cost-effectiveness is reduced inlow power applications due to the additionalPFC ower stageand additional control circuitry. A number of active singlestage PFC techniques [6-91have been introduced in the recentyears as a low cost alternative to this problem. It involvesintegration of the active PFC stage with the isolated DC-DCstage as shown in Fig. 2.

In this approach only one switch and hence only onecontroller is used to shape th e input current and to regulate theoutput voltage. Here, the storage capacitor that's used forstoring the difference between the instantaneous input powerand constant output power is no longer loosely regulated at aconstant value. It happens so because the controller is used toregulate the output voltage and not Vdc. So the downside

0-7803-8610-8104/$20.00 0 2004 IEEE 86 2


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associated with this approach is that the size and the cost ofelectrolytic capacitor is much greater than that used in thetwo-stage approach. So the reduction in cost achieved byusing single switch & controller would be offset byemployinga larger sized capacitor.

The single stage PFC converter, used for obtaining UP F atline side and tight voltage regulation, through scalar controltechnique is as shown in Fig. 3.h the new topology proposed,the front-end diode bridge rectifier circuit is dispensed with.Also the energy storage capacitor is removed because theunbalanced energy is now taken care of by output capacitorCitself. Here the controller employed is DSP based whichsenses input current and output dc voltage for achieving therequisite control. The Scalar Control algorithm used in theDSP controller results in input sinusoidal current and looselyregulated dc voltage at the output if only input current is usedas the sensing signal for DSP controller. While the samealgorithm results in UPF at the line side and tight voltageregulation if both input current and output voltage are fed intothe DSP controller. As voltage across the capacitor isregulakd unlike a conventional single stage PFC converter,the size and cost of capacitor is reduced. In addition to th is,there are other advantages accrued by using this topology.1.Control algorithm is very simple to implement.2. Input voltage need not be measured.3. Control is based on carrier (constant switching kquency)4. At the cost of one extra active device, number of passive5. Efficiency will be higher on account of the fact that only6. The operation is always under CCM.

and is simple to realize.devices is reduced.one device is in the series path ofprocessed power.

11. SCALARCONTROLTHEORYMany UPF Rectifiers [10-121 proposed in recent times,have significant improvement over their predecessor circuits.These UPF Rectifiers have an uncontrolled rectification stagefollowed by a controlled boosthuck-boost topology. In ScalarControl technique, at the cost of increasing the number ofcontrolled devices, the uncontrolled rectification stage can betotally removed. This method has simpler control algorithmand easier implementation to its credit than the existingtechniques.The boost rectifier configuration to which Scalar Control isapplied is as shown in the Fig.4. On applying Volt-sec

balance to the line inductance,Vd,1-2d)2v, =where, the terms are as mentioned in Fig.4.

voltage & input current are related by the relation,where Re s theemulated resistance.From ( 1 ) & (2), he Control Law obtained is,

For obtaining resistance emulation characteristics, he inputV, =I , R, ( 2 )

Load

2Fig. 4 SinglephaseDirect BoostRectifier(3)"dc

By varying the duty ratio in accordance with the aboveControl Law, UP F operation can be achieved. Here, only theinput current & DC bus voltage need to be sensed forachieving the control. The Control Law is very simple toimplement as is evident from (3). The control scheme is alsoindependent of the input voltage.For single phase Scalar Control implementation, theadvantages might not be too marked, since four controlleddevices are used. But when the same technique is extended tothree-phase system, the advantages accrued are quitedistinctive, for the control is decoupled in nature and does notrequire transformations to the stationaryW e f reference asis used for a conventional three-phase PFC converter. Thisconfiguration could also be controlled to obtain bi-directionalpower flow, which might not be possible with a three-phasediode bridge on the AC side.However, the focus of the work reported in chis paper is onsingle-phase Direct Boost rectifier. The same idea could alsoin principle be extended to three-phase operation.III. SYSTEMMODELING

The Block diagram of the scalar controlled PFC controIleris shown in Fig. 5.It can be seen that there are two cascadedcontrol loops in the entire scheme. The outer voltage loopprovides a current reference I,f to the inner current loop.Under steady state, the current reference is a DC quantity. Theinput current is normalized with respect to the referencecurrent, I,f to generate the Normalized current reference. ThePulse width modulator shown in Fig. 5has a standard saw-tooth ramp generator. The switching instants are produced bycomparison of the ramp with the Normalized current referenceas shown in Fig. 6 . On applying Volt-sec balance on the lineinductor,

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vaV =-(1- d)WhereV, is the applied AC voltageV is the DC bus voltaged is the duty ratio of the switch

From (4) & (2) the Control Law for the Sca -2 Control basePFC ontroller is,(5 )

m e r e

J4

%Fig. 5 BlockD i a p f ScaIar ControlPFC Converter

(6 )dc1,.=-Reand is known as the current reference.

412+-

1_ _

IV. STEADY STATE STABILITYThe steady state stability analysis of Scalar ControlledBoost converter is carried out here. Like current mode

controlled converters, it may also exhibit steady state stabilityproblem under certain operating conditions due to thepresence of local feedback in its control structure [13]. Theobjective of the analysis here is to quanti@ the steady statestability condition in terms of circuit parameters and theswitching frequency of the converter.

A=m

bt +

24 T, b

Fig.7 Perturbationanatysis to evaluate steady state stability conditionLet I ,& I ~ b ehe currents at the s t a r t and end of a

switching cycle respectively as shown in Fig. 7. Let AI, ea small perturbation introduced in I1which produces a changeAI 2 in current I2 .From (3,

Differentiating both sides with respect to line current I1Ad 1-= --AI1 2 * 1 d

(7)

From the steady statemodel of the boost converter, we get(91dIdtL-=V, -V,(l-2d)

Differentiating both sideswith respect to d , e get(10)AI2 Vdc (2 *Ts,Ad LWhere,

T, i s the switching ftequencyL is the Line Inductance. Multiplying (8) & (lo), we get

A Converter is said to be stable in steady state if allperturbations die down in subsequent cycles, which impliesthat the expression in (1 1) should be less than 1 . Therefore theFig. 6Duty ratio commandgeneration

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condition or stability of the scalar control method is givenas,

v. SMALL SIGNALANALysrsA linear, low frequency, small signal model of Boostconverter is developed here. It may be noted that, in a dc-dcconverter, when it is operating under steady state, the inputpower is equal b the output power in every switching periodT, of the converter. However the same is not true for single-phase resistor emulator rectifiers. The input voltage V, variesfrom 0 o V in a line cycle and under steady state condition,the input current I, is proportional to the input voltage. Theinstantaneous input power is, therefore v i -A which is

not constant within an input cycle T =- whereas theinstantaneous output power- s constant. So,unlike dcdcRconverter, the power balance condition between input andoutput cannot be satisfied at every switching period of theresistor emulator rectifiers. However, it may be noted that, theinstantaneous input power is equal to the output power only atthe period in which the input voltage is L. herefore thisswitching period is chosen as the equivalent nominaloperating point that represents the entire line cycle for thederivation of the small signal model. The control structure ofthe small signal linear model of the Boost rectifier, switchedby input current shaping modulator, governed by ScalarControl Law, is as shown in Fig. 8

2g - R e1

2f

V

v&

JZ

Small signal Linearmod el of the Boost

Converter

$Liz;od el of the jeI Modulator IFig. 8 Control structureofLo w frequencysmall signal Boost rectifierHere the control gain transfer function is derived in twosteps [14][15]. First, the low ftequency small signal model ofthe Boost Converter is obtained in the standard form in termsof duty ratio perturbation 2 as the control input. Subsequentlythe small signal model of he modulator is derived to replace2 term in the converter model by the perturbations in and

other state variables 41g~ j,The state variable description of the converter is given by (13)

where, D is the duty ratio of the converter about the operatingpoint & V,is the input voltage to the converter. The linearsmall signal model of the Boost converter is obtained byperturbing the state variables and the duty ratio input. Thegeneralized small signalmodel equation is given as,

& - A --=Ax+Bva + fddt (1 4)* I cWhere, A, B 8 represent system matrices& x, a , are the

perturbed variables. Equation (5) representing the steady staterelationship between the system variables & the duty ratio, dwhen perturbed, will yield the relationship between the smallsignal 2& the other system variablesas given in (15)

Where, i e i s the perturbed value of the emulated resistance,Re-Substituting(15) in (14)yields,

It is observed ftom the system matrix, A of (16) that theproduct of off-diagonal terms is zero which implies that thesystem has real poles. Moreover, the term --me. systemLmatrix A introduces additional damping to the systemresponse,making he system stable.From (16), the transfer function of the converter can beequated as,

(17)

The Bode plot representation of (17) is shown in Fig. 9.For a closed loop control system to be stable, its required thatthe loop gain crosses over 0 dE? (Unity Gain) with a singleslope (-ZOdEVdecade). For a given system, transfer function[GI he design of the closed loop compensator IHI should besuch that the loop gain IT1 (lGllHl) satisfies the aboverequirement. As per the system transfer function given in (17)

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the bode plot of the Compensator (PI controller) shown inFig. 10satisfies the requisite condition of single slope 0 dBcrossover.

tRC

Fig. 9 Rode plot of ystem "fer function

\

I bI 2 b g w-RCFig. 10 Bodeplot of Compensat01

VI. SIMWLATION & EXPERIMENTAL RESULTSThe Scalar Controlled UPF ectifier is simulated in OrcadPspice. The simulation results obtained, as shown in Fig. I 1

are taken with an input voltage of 230 V @k) and loadresistance of 250 !2. Th e Line inductance is kept small at 3mH in order to have IOW voltage drop across it at full load.The switching frequency is chosen o be 10ICHZ.The DCbusvoltage is maintained constant at 360 V.

Fig. 1 1 (a) lnput Voltageand hput Currentinphase

The Control algorithm is tested for experimentalverification on a 1 kW single-phase Boast rectifier unit. TheAC line input is 138 V (rms] nd the DC Bus voltage of therectifier is regulated at 400 V. The measured value of boostinductance is 11 mH. The switching fkquency of the lGBTbased (IPM Module) converter is chosen to be 10 kHz. Theload resistance is fixed at 250 R.

Fig. 12(a) Chl: Input Voltage ; h2:nputCurrentVoltage scale : 0 0 V/div. Current Scale : 10 mV/A

Fig.12@) Chl: Input Voltage ;Cb2:nputcumntVoltage scale : 100Vidiv. Cumnt Scale :10mV/A

Fig. 12(c) Cbl : DC Bus VoltageVoltage scale :100 V/div.Fig. 12(a) shows UF'F operation at the line side. Underconstant load conditions, Fig. 12(b) shows an increase in the

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Hc- ,111 r..,

Fig. 1 (bl DC Bus Voltage regulated at360V 866


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input current with the decrease in line voltage. Tightregulation of the DC bus voltage under the same condition isevident fiom Fig, 12(c). The THD of the input currentwaveform calculated from the FFT shown in Fig. 12(d) isfound to be 12%, which indicates a very high input powerfactor.

Frequency (Hz)Fig. 12 (d) FFT of Input Current

W. ONCLUSIONIn th i s paper, a novel active power factor correctiontechnique named Scalar control is proposed and analyzed.With the proposed method, the power factor of the single-phase fiont-end converter is made unity without sensing theinput voltage. The control is extremely simplified & the samecontrol technique could be extended to a three-phase system.The conditions for steady-state stability & the small-signalmodel are derived.T h e proposed method has the disadvantageof instability under certain conditions because of the nature ofthe control. The results obtained from the simulation of theconverter are also verified experimentally,

WI. REFERENCESIEC 1000/3/2 InternationalStandard,Limits orharmonic current emissions (equipment input current

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