Controller Arrangement for Boost Converter Systems

7/27/2019 Controller Arrangement for Boost Converter Systems

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Contro l ler arrang ement for bo os t conv erter systemssourced from solar ph otov oltaic arrays or o therm ax imu m p ow er sources

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J .A.Gow an d C.D.Manning

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Abstract: Conventional power converter systems, such as boost converters, derive their input fromsources that may be considered to have negligible output impedances, and as such the use of quitesimple conventional control algorithms sufice to give acceptable performance. When the outputimpedance of the source to such a converter is no longer negligible, and moreover if the source has amarkedly nonlinear output impedance, the simple conventional algorithms will no longer be adequateto satisfy the control requirements of the converter. The effect of driving such a converter from a typeof source, for example a photovoltaic array whch has a point of maximum power delivery withm theoperating range is discussed, as is the impact that the use of such a source has upon the controlrequirements of the converter. A novel control arrangement, which includes a complete embeddedmaximum power tracker, is then presented together with results validating the proposed controller.

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List of principal symbols6 = small-signal duty cycleEIl = inductor currentI,,, = converter output currentk,V,, = input voltageV,,, =output voltageA = large-signal duty cycleI,, = converter input currentI lovg= average inductor currentI,, = array short-circuit currentP = array powerV,, = array open-circuit voltagedouble-exponentialmodel parametersIph= array photocurrentZ,,Is 2R, = array series resistanceRp = array parallel resistance1 Introduction

= maximum power tracker output

=gain of maximum power tracker

= array first saturation current= array second saturation current

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A simple step-up DC to DC converter is shown in Fig. 1.This takes power from its input at a voltage V,, and sup-0 EE, 2000IEE Proceedkgs online no. 20000018DO 1 IO. 1049/ipepa:20000018Paper fmt received 10thMarch and in revisedform 2nd August 1 9 9The authors are with the Departmentof Electronic and Electrid Engineering,Loughborough University, Loughborough,UK

1 I to loadrom boostsource I converterHontrolFig.2 voltuge-modecontrol

Several types of control algorithms are used with thistype of converter. The simplest of these, voltage-mode con-trol (Fig. 2), senses the output voltage and compares it witha reference. The result, suitably compensated to avoidinstability, forms the control signal input to the PWMmodulator. A slightly more advanced type, known as aver-age current-mode control (Fig. 3), uses a pair of nestedloops. The inner loop derives an error signal from the dif-ference of the inductor (or output) current and the outputof the outer loop, in which the error signal is derived as forvoltage-mode control. Current-mode control carries a

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number of advantages over voltage-mode control whereselection of component values to optimise loop speed isconcerned, and it is primarily with this form of control thatthis investigation is concerned.

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compFig.3 uu UCurrent-mode control

When such a current-mode controlled system is drivenfrom a conventional power source, it is expected that theinput voltage wdl not change as a function of switchingduty cycle A and therefore small-signal perturbations in Awill normally be around an easily predictable operatingpoint. Thus compensator parameters may be easily calcu-lated based around this operating point to optimise loopperformance.Power sources such as photovoltaic (PV) arrays, how-ever, possess a characteristic whch dlffers from that of aconventional stiff power source. The terminal voltagechanges with current in such a manner as to give the sourcea unique value of terminal voltage and current at which itis providing maximum power. Either side of this point, thepower provided by the source will drop. The general formof the equation relating current to voltage in a photovoltaiccell is known as the double-exponential model (eqn. 1)[I, 21.

In effect, a photovoltaic array combines the characteris-tics of a current source with those of a voltage source.Below the maximum power point (MPP), when the currentis low, the source approximates a voltage source. Once themaximum power point is traversed, the source appears as acurrent source. At the maximum power point the sourcemay be considered to be a combination of both. Allsources possess a maximum power point, but in the con-ventional source used to provide power the maximumpower point is outside the normal operating range of thesource; fuses etc. would fall long before the maximumpower point was reached. With a PV source, however, the16

maximum power point is well within the normal operatingregion of the source (and load) and therefore must be takeninto consideration. The class of sources to which PV arraysand other sources exhibiting this characteristic belong maythus be defined as maximum power sources.2 System analysis2.I Boost-converter control schemeIn conventional average current-mode converters, the cur-rent loop conventionally aims to control the average induc-tor current. While average current-mode control can makefor a much faster converter than can voltage-mode control,this approach is not without its problems. One of these isthat the right-hand halfplane zero, a characteristic of thetopology, appears in the voltage loop, whose bandwidthmust be reduced to avoid instability. The current loop con-tains a pair of complex poles which also require carefulcompensation to achieve stability. The net result is thatwith the boost converter topology, the benefits achieved bycurrent-mode control are offset by the reduction in loopbandwidth necessary to acheve stability.In this converter system, a novel approach has beentaken which goes some way to compensate for the prob-lems of inductor current control. The current loop of thissystem controls the average diode current, whch is effec-tively the output current.

The use of linearised time-averaged state-space modelling[3] applied to Fig. 1 operating with continuous inductorcurrent allows small-signal transfer functions and steady-state characteristics to be obtained [4].The small-signaltransfer functions of interest relate the average currentflowing in the diode id to the duty cycle of the switch 6 andthe output voltage v, to the diode current id. The small-signal transfer functions are given in eqn. 2, while thesteady-state characteristics are given in eqn. 3.

A is the steady-state value of the duty cycle of the switch,and represents the magnitude of the input to the PWMmodulator. Note that in the derivation of eqns. 2 and 3 theoutput impedance of the source has been assumed to bezero. Ths is a valid assumption for conventional stiff sup-plies, and is not wildly short of the mark for photovoltaicpower sources in the region close to the array Vac. Control-ling diode current effectively buries the right-hand halfplanezero in the current loop and thus allows the current loopbandwidth to be maximised without excessive concern withthe voltage loop. The transfer function of output voltage todiode current reduces to a single pole, and with the currentloop set for m a x i possible bandwidth the voltage loopbecomes very easy to compensate. A further advantage isthat discontinuous mode operation will result in a smallerdrop in closed-loop bandwidth compared to conventionalcurrent-mode control. Therefore it becomes possible todesign the converter with smaller inductors than wouldotherwise be possible with inductor-current control.

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2.2 PV sourcedboostconverter performanceIf a converter using conventional control algorithms tocontrol output voltage is fed from a PV source, then it willnot operate optimally [5]. This is because the source canappear as either a voltage source or a current sourcedepending upon the position of the operating point. Fig. 5shows the output voltage with respect to A of a convertersourced from a PV array. The curve is generated with theaid of a previously developed PV cell circuit modelling sys-tem [6] and the MATLAB software package [I.'O0O[ \ /900800700600500400

' O C.6 0.7 0.8 0.9del taPV-sourced curve superimposed on constant-voltugemi cOnSimt LUT-ig .5rent curves

In the current fed boost converter the output voltage fallswith increasing A, whereas when voltage-fed, output volt-age rises with increasing A. Ths will require significantlydlfferent controller operation depending upon the region ofthe source characteristic in which operation is taking place.The small-signal dynamics of the converter will also changeradically. The second-order characteristic of the control todiode current transfer function will reduce to the simplefunction I,JS =I3,>(1s>when the converter is current-fed,eluninating dynamic effects from the current loop.

As A increases, so does the average current in L (I,,),and there will come a point A =A, where V ,will start tofall off rapidly as the operating point moves on to the con-stant current portion of the array characteristic. Any fur-ther increase in A will cause V , o fall still further until itreaches zero and V,,, will fall similarly.

Note that if the output load is fned, then the point ofmaximum voltage must also be the point of maximumpower, therefore AI is the value of A to give maximumpower when sourced by an array under these conditionsinto a load of the specified value. AI also marks the transi-tion between constant-voltage and constant-current opera-tion.In the region A AI it would appear that it is necessary tochange the sign of the current error signal such that anincrease in error causes A to fall. The requirement is for acontroller which for loads below maximum power operatesnormally, but as A traverses A , will reverse the sign of thecurrent error signal. The net result will be for loads exceed-ing maximum power, that the output voltage of the con-verter will fall to a level supplyingmi"power to theload and the operating point will oscillate around the max-imum power point; in effect a maximum power tracker.IE E Proc -Eleclr Power Appl Vo l 147, N o I January 2000

There are a number of problems with th s arrangement.One is that if the load is reduced while A >AI then the con-troller will reduce the throughput power by increasing Aand operating in the constant-current region, remaining inthis region until A, is once again traversed. This is not thebest way of using the PV array for low powers, the highcurrents in this region leading to inefficient operation of theconverter being only one of the reasons for this.The second problem is associated with the action of thecontroller while the system is oscillating about the maxi-mum power point. The source is unable to completely meeta h gh demand which is causing the system to enter theconstant-current region; it can only provide maximumpower. The amplitude of the oscillations about the maxi-mum power point are controlled by the output of the cur-rent loop controller. If the system cannot meet the demand,the output of the integrator in the controller will rise andcontinue to do so until it reaches its saturation limit. Thiswill not only result in large excursions around the maxi-mum power point during tracking but will also take longerto recover when demand falls, resulting in a possibly cata-strophic rise in output voltage.To avoid these problems, the controller can contain anembedded maximum power tracker which comes into effectif the load exceeds that for maximum power at the speci-fied rail voltage. Therefore, instead of implementing themaximum power tracker by changing the sign of the cur-rent error, a maximum power tracker could form an inte-gral part of the controller, only coming into effect fordemands at or exceeding maximum power.The subject of maximum power tracking systems hasbeen treated extensively in published literature, since toobtain maximum efficiency from photovoltaic arrays sucha system is essential [7-121. However, most published maxi-mum power tracking systems possess significant disadvan-tages owing to the manner in which they are implemented.To determine the position of an operating point on thearray characteristic it is necessary to determine the slope ofthe array characteristic at this point. This requires the oper-ating point to move slightly so that a comparison of differ-ences may be used to determine the slope. The method bywhich the operating point is moved can limit the converter.Some methods [SI require an AC inverter as a load as theymake use of the fluctuating currents, while others [10-12]have speed disadvantages. As part of this system a type ofmaximum power traclung system was developed whchwould be very fast and would address the problems andlimitations of existing maximum power tracking systems.The method to be described makes use of a characteristicof the boost converter itself to provide the necessary oper-ating point variation and thereby determine the array oper-ating point. Since the calculations are performed on a per-cycle basis, the only limiting factor to the speed of maxi-mum power tracking is the bandwidth of the converter.The method is independent of load type and does not pro-duce any extraneous signals superimposed upon the con-verter output that are a function of the maximum poweralgorithm that would otherwise require filtering.3 Comp lete embedded MPP control lerA discrete version of the above mentioned controller wasimplemented, together with a converter power chain, as asimulation model using the 'Saber' [13] simulator. A blockdiagram of the complete embedded maximum power track-ing controller is shown in Fig. 6 , and this details the linksbetween the maximum power tracker and the PI currentloop controller together with the conditions evaluated to

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2* 1/25000delay inductor current

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(PWM modulated) boostconverterf omp2{+st \ IFig.6 Comjdete embedd ed-MP P controllercontrol the algorithm selection. The two-switchmg cycledelay in the current measurement is a function of calcula-tion delays when a per-cycle average current is required in adigital implementation of the system. The conditions forthe switch are also given in the Figure where P1 is thepower sample taken just before the start of the switch on-time and P2 is the sample taken just before the switch turnsOf f .

The maximum power trackmg operates as follows: if thedemand increases, so the algorithm attempts to adjust A toprovide power to meet it. If A1 is exceeded, the sign of thecurrent error is changed and A is reduced, whereas belowA1 A is increased. The result is that if the demand increasesbeyond the maximum power point the PV array operatingpoint oscillates about the maximum power point.

The maximum power tracker essentially provides anerror signal used for modulating A by solving eqn. 4.

E =k,1($) t (4)Note that dPldV instead of dPldI may be used. Note alsothat k , is the gain of the integrator. The differences lie inthe way dPldV or dPldI is calculated; in every case thisimplies tracing a portion of the PV array characteristic todetermine slope information. In this system a very fastmethod was developed using the input current waveform ofthe boost converter. This is a ramp. Samples of array cur-rent and voltage were taken at the start of the switch-ontime and also at the end. Input current is rising throughoutths period independent of the position of the average valueon the characteristic, and thus the required slope informa-tion is obtained by multiplying voltage and current andthen subtracting the later of the two samples from theearlier [6].The result is integrated to form the power errorsignal.4 ResultsA Saber template was written embodying the entirety ofFig. 6 so that a set of simulation results could be obtained.PI controller constants were selected for a voltage-fed con-verter system with a 110V voltage source input and a 400VDC output using an inductor of 1.2mH and a capacitor oflOOOpF at a switching frequency of 25kHz, by making use18

conditions:on each cycle:IF (P~=PI)& (IerrO)

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tracker gives considerably superior performance in terms ofspeed of response compared with the controller using PIcompensators alone, reaching its output voltage muchquicker. The action may be seen in the time domain curvesof array power over the same period of time (Fig. 9) wherethe action of the maximum power tracker may be seen.

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The output voltage transient response for step loadchanges forms the second set of results, as shown inFig. 10. Load changes used wereIEE Proc.-Electr. Power Appl . , Vol. 147, N o. 1. January 2000

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The 35M00ms region clearly exhibits maximum powertracking in the system containing the embedded MPP,where the array is supplying maximum power to the load.Without the embedded MPP the PI-only system cannotsupply enough power to sustain voltage across the loadapproaching demand voltage. The differences here betweenthe embedded MPP system and the PI-only system are verymarked, the PI system displaying the anticipated problemsof integrator windup in the constant current portion of thearray I-V characteristic. As the array operating pointpasses the maximum power point and enters the constantcurrent region, so the power, and hence output voltage, falloff. The difference between the demand and reference atthe inputs to the PI compensators becomes increasinglypositive, and the integrators within the compensators rampup and effectively bring about a duty cycle increase. In thlsregion of operation, increases in duty cycle actually bringabout a fall in output power. The error at the input of thePI compensators thus increases further, and the integratorsquickly ramp up into saturation. The output voltage clearlyfalls off as seen in Fig. 10. The time histories of the arraycurrent (Fig. 11) and power (Fig. 12) serve to show thedifferences between the two systems.

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A hardware prototype of the controller was constructedbased around a TMS320C50 DSP as the control element.As only low-power PV arrays were available with which totest the system, it was designed to provide a regulated out-put voltage of 15V for loads below maximum power. Thearray used was illuminated to provide a maximum powerof 1.88W. Fig. 13 shows the array power as a function ofload current, while Fig. 14 shows the converter output volt-age as a function of load current. The three curves inFig. 13correspond to three different values of the maxi-mum power tracker integrator gain and show that, for thisinstance, variation of this parameter has limited effect.

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Fig.13Track power: 1.76W(i) kc =1.953x lo=?(ii) k, =0.5(iii) k, =128

Array power characteristicfor h r d vu r e prototype

00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40load current,A

Converter output voltage characteristic o r llardvare prototypeig. 14The behaviour of the system can clearly be seen. Where

the system operates in voltage-regulating mode for loadsbelow maximum power, once the demand from the loadexceeds maximum power the converter switches to maxi-mum power tracking mode. The actual value of powerthroughput is slightly below actual array maximum, in thelow-power prototype. This is due to the inductor currentramp being large in comparison with the array short-circuitcurrent. In a high-power system, the track power will bemuch closer to the array maximum. The array power fallsoff at very high loads as the converter is operating then inregions of inefficiency at high boost ratios.

5 ConclusionsThis paper has discussed the effects of supplying a boostDC-DC converter from maximum power sources such as aPV array. Using state-space modelling and analysis tech-niques, a stable converter system has been proposed whchincludes an MPP tracker together with conventional cur-rent and voltage loops in the controller. It has been demon-strated that the PI with embedded MPP approach to PVconverter control gives far superior results when comparedwith a pure PI-compensated controller, where fuced-voltageDC outputs are required. For values of power demandfrom the load at or exceeding array maximum power point,the converter tracked the array maximum power point andsupplied the load with this level of power. Once the loadwas shed the constant-voltage output was restored. As ageneral purpose front-end converter, allowing PV arraysto supply many different types of load through the samepiece of hardware, this system could find a place in manyapplications where photovoltaic power, or any other formof maximum-power energy source, has been considered buthas been previously thought to be impractical owing to thelack of general purpose power conversion systems designedto handle such sources with the minimum of installation-specific requirements. A hardware prototype has been con-structed to show that the system behaves as expected and isa viable proposition in these applications61

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ReferencesENEBISH, N., AGCHBAYAR, D., DORJKHAND, S., and BAA-TAR, D.: Numerical analysis of solar cell current-voltage characteris-tics, Sol. Energy Mater. Sol. Cells, 1993,29, (3), pp. 201-208PROTOGEROPOULOS, C., BRINKWORTH, B.J., MARSHALL,R.H., and CROSS, B.M.: Evaluation of two theoretical models insimulating the performance of amorphous silicon solar cells. Proceed-ings of the 10th European Photovoltaic Solar Energy conference,8-12Lisbon, Portugal, April 1991, pp. 412415MOHAN, UNDELAND, and ROBBINS: Power electronics: Con-verters, applications and design (Wiley Intemational)SEVERNS, R., and BLOOM, G.: Modem DC-DC switchmodepower converter circuits (Van Nostrand Reinhold, 1985)COW, J.A.: Modelling, simulation and control of photovoltaic con-verter systems. Thesis submitted to Loughborough University, Eng-land for the degree of PhD, May 1998GOW, J.A., and MANNING, C.D.: Development of a model forphotovoltaic arrays suitable for use in simulation studies of solarenergy conversion systems. Proceedings of the Sixth international con-ference on Power electronics and variable speed drives, NottinghamUniversity, United Kingdom, 2>25 September 1996, pp. 69-74THE MATHWORKS Inc, MATLAB mathematical simulation soft-wareCOCCONI, A., CUK, S., and MIDDLEBROOK, R.D.: High fre-quency isolated 4kW photovoltaic inverter for utility interface. Pro-ceedings of the Seventh intemational PCI83 conference, Geneva,Switzerland, 13-15 September 1983DECKER, B., and GENTZ, M.: Development and evaluation of a20W MPP tracking charge controller for PV supplied remote monitor-ing stations. I991 international Solar Photovoltaics conference, Lis-bon, Portugal, 8-12 April 199110 BODUR, M., and ERMIS, B.: Maximum power point tracking forlow-power photovoltaic solar panels. Mediterranean Electrotechnicalconference MELECON, 1994, Vol. 2, pp. 758-76111 SNYMAN, D.B., and ENSLIN, J .H.R.: Simplified maximum powerpoint controller for PV installations. IEEE Photovoltaics Specialistsconference, 1993, pp. 124C124S12 SPEER, J.H.: Microprocessor control of power sharing and solararray peak power tracking for high power (2.SkW) switching powerconverters. PESC Record - IEEE Power Electronics Specialists con-ference, 1981, Vol. 3, pp. 6C89I3 ANALOGY Inc SABER circuit modelling and simulation software

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Controller Arrangement for Boost Converter Systems