On the control of photovoltic mximum power point trcker vi output prmeters D. Shmilovitz Astrct: A new pproch for trcking the mximum power point of photovoltic rrys is presented. The mximum power point trcker output voltge nd current re used for control purposes, rther thn for its input voltge nd current. It is shown tht using the output prmeters simplifies the mximum power point trcker controller. Moreover, using this pproch, only one out of the two output prmeters needs to e sensed. This oservtion is generl nd pplies regrdless of the power stge or the relistion control lgorithm. Contrry to wht might hve previously een ssumed, it is theoreticlly shown tht the MPPT control tht uses single output control prmeter pplies to nerly ll prcticl lod types, regrdless of the lod nture. 1 Introduction Photovoltic (PV) power genertion hs stimulted considerle interest over the pst two decdes. While solr energy is the only ville energy source in spce, it is n importnt lterntive for mny terrestril pplictions. In the erly 1980s it ws thought to e possile solution to the world s energy crises nd oil shortge. As the PV cell price did not decrese in the mount expected t tht time, PV genertion ws used in restricted pplictions such s in remote terrestril sites not supplied y the utility grid nd on ord ychts in ttery chrgers. In recent yers, s it is n environmentlly renewle energy source, grid-connected photovoltic genertion hs gined incresed importnce, due to dvntges such s the sence of ir pollution nd fuel costs s well s no noise nd low mintennce resulting from the sence of moving prts. Additionlly, in grid-connected pplictions the energy demnd from the grid is reduced, which shves the pek lod demnd [1]. At given temperture nd insoltion level, PV cells supply mximum power t one prticulr opertion point clled the mximum power point (MPP). Unlike conventionl energy sources, it is desirle to operte PV systems t its MPP. However, the MPP locus vries over wide rnge, depending on PV rry temperture nd insoltion intensity. Instntneous shding conditions nd geing of PV cells lso ffect the MPP locus. In ddition, the lod electricl chrcteristics my lso vry. Thus, to chieve opertion t the MPP, time vrying mtching network is required tht interfces the vrying source nd possily the vrying lod. The role of this mtching network, clled the mximum power point trcking network (MPPT) is to ensure opertion of the PV rry t its MPP, regrdless of tmospheric conditions nd lod vritions []. MPPT circuits should ensure extrction of mximum ville r IEE, 004 IEE Proceedings online no. 0040978 doi:10.1049/ip-ep:0040978 Pper first received 5th Septemer 003 nd in revised form 0th July 004. Originlly pulished online: 1th Jnury 005 The uthor is with the Fculty of Engineering, Tel-Aviv University, Tel-Aviv, Isrel power from the PV rry, y its loding t the MPP. MPPT circuits re relised y mens of switched mode DC DC converters, most commonly with pulse width modultion (PWM) control. Mny lgorithms hve een proposed for MPP trcking, the most widely used ones re the pertur nd oserve (P&O) nd the incrementl conductnce lgorithms. In the first, voltge nd current t the PV genertor output (i.e. MPPT converter input) re sensed nd the power is clculted successively y their multipliction. Then, the MPP is pproched in n itertive process. Other lgorithms lso require sensing of the PV rry output voltge nd current, in order to indicte the ctul opertion point. This informtion is thn processed, y vrious possile lgorithms, in order to generte the incrementl correction towrds opertion t the MPP [1 4]. The use of lod voltge nd/or current for MPP trcking ws suggested in just few ppers. Even fewer reserchers proposed to sense only the lod prmeters, while ssuming specil lod types (e.g. mximistion of the lod current when the lod is n electrolysis pool whose production is proportionl to its current [5]). In other cses, pproximtion ttery type of lod y constnt voltge source (neglecting voltge vrition with ttery chrge) ws suggested. Under this ssumption, the lod power is proportionl to its current, so tht lod current cn e mximised rther thn PV rry power [6]. The oservtion tht mny lods might e modelled y their Thevenin equivlent led to control lgorithm sed solely on the lod voltge [7].Inthtpper [7] the output instntneous power ws clculted from the output voltge, which increses complexity nd requires knowledge of system s prmeters. In this pper sensing the MPPT converter s output voltge or current is suggested rther thn its trditionlly used input ones, sing the controller opertion on these quntities. As will e shown, the proposed lterntive implies considerle dvntges in terms of trck ility nd, more significntly, in terms of controller simplicity. It is shown tht sensing of single lod prmeter (either current or voltge) suffices for the trcking of the MPP. Tht results in reduction in the hrdwre involved (sensors) nd simplifiction of the control lgorithm (no multipliction needed for the clcultion of power). It is shown tht trcking of the mximum vlue of the lod current (or voltge) implies opertion of the PV system t its IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005 39
MPP. It should e noted tht, in the mjority of prcticl PV systems with ttery ckup, the MPPT s output voltge nd current re monitored nywy, for the ske of chrge control nd ttery protection. Thus, sensing of the PV rry output voltge nd current is ctully cncelled with no dditionl cost. The suggested pproch does not ssume fmilirity with the lod type or its linerity. It pplies to ny lod type provided it hs non-negtive incrementl impednce. The principle proposed here pplies not only to PV systems ut to ny system in which MPP trcking is needed, such s in wind energy systems [8]. MPPT role in mtching the PV rry nd the lod PV rrys hve nonliner vrying I V chrcteristics. Assume PV rry is composed of evenly illuminted identicl cells, ll t the sme temperture. Its output chrcteristics my e written s: iðvþ ¼I sc 1 exp ð v=v thþ 1 ð1þ expðv oc =V th Þ 1 where i nd v re the PV rry s terminl current nd voltge, nd I sc nd V oc its short circuit current nd open circuit voltge, respectively. V th is the rry s therml voltge. The nonliner chrcteristics of PV cells re depicted in Fig. 1, where R denotes insoltion level nd T the PV rry s temperture. Evidently, the MPP occurs t lower voltge when the insoltion is lower (i.e. R or 1 yields V M (R )ov M (R 1 )). These curves vry with the PV rry mient condition. In prticulr, the MPP locus vries with temperture, insoltion intensity nd shding conditions s well s with the geing of the PV cells. Thus, if directly connected to the lod, opertion of the PV rry t the MPP cnnot e ensured even for constnt lods. Moreover, prcticl lod electricl chrcteristics might vry, due to prmeters such s the chrge condition of tteries nd its geing or the loding nd speed of DC motors powered y the PV rry. Thus opertion t the MPP cnnot e chieved unless tunle mtching network is used tht interfces the lod to the PV rry, see Fig.. The min components of the MPPT circuit re its power stge nd the controller. As the power stge is relised y mens of switched mode power converter, most commonly with PWM control, the control input is denoted y the duty cycle d. Customrily, the power stge input voltge nd current re used y the controller for the purpose of MPP trcking, s depicted in Fig.. In the scheme of Fig., the power stge control prmeter d is continuously tuned until the PV rry is loded t its MPP. It should e noted, however, tht the quntity of ctul interest (the one to e mximised) should e the one power fed to the lod, tht is the MPPT s output power p o. The customrily used mximistion of the MPPT s input power p i vithesensingof nd v in my e justified y the high efficiencies reched y the MPPT s power stge. Thus, mximistion of the input power is equivlent to mximistion of the output power. i PV rry I sc I M MPP(R 1,T) v in MPPT power stge lod R 1 R d MPP(R,T) R 1 = *R control v V M V oc PV rry p (R 1 ) MPPT power stge lod d (R ) v V V (R oc 1 ) M (R 1 ) Fig. 1 The output chrcteristics of PV cells t prticulr temperture nd two insoltion levels, R1 nd R, R1 ¼ R current versus voltge power versus voltge control Fig. Functionl locks of PV system with MPPT trditionl control vi input prmeters v in suggested pproch with control vi output prmeters v out It should e noted tht controlling the input power necessittes the sensing of oth prmeters nd v in, regrdless of the control lgorithm used. For instnce, with the pertur nd oserve lgorithm, the input power is successively clculted y multiplying nd v in. 40 IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005
If the incrementl conductnce lgorithm is used, [4], nd v in re used or clcultion of the incrementl nd solute conductnces. The high efficiency power stge my e relised nd modelled y one of three power-conservtive networks: controllle trnsformer [9], loss free resistor [10] or gyrtor [11]. I M k=1 k=k* 3 DC trnsformer nd loss-free resistor models of the MPPT 3.1 MPP trcking y mens of controllle trnsformers It hs een shown in mny pieces of reserch tht stedystte opertion of pulse width modulted power converters in continuous conduction mode cn e well modelled y time vrile trnsformers [10 14]. Time vrile trnsformers modelling of the power stge is therefore used in this description. In PV system, the time vrile trnsformer couples the PV rry to the lod. This trnsformer trnsfers n unmtched lod t its output, into mtched one t its input (where it connects to the PV rry). As mentioned erlier, the PV rry conditions s well s the lod my vry, therefore this trnsformer hs tunle turns rtio, see Fig. 3 [10]. The trnsformer model implies: v out ¼ k 1 0 vin 0 k ðþ p in k=1 k > k* V M k=k* k > k* v in PV rry MPPT k:1 k control lod Fig. 4 PV rry nd trnsferred lod chrcteristics during vrition of the trnsfer rtio, k in the v in in the p in v in plne V M v in Fig. 3 vs The controller sets the trnsfer rtio k, sed on the sensed prmeters v s nd i s (which re, trditionlly, the MPPT s input voltge, nd current v in nd ). This model trnsformer couples DC voltges nd currents nd is commonly relised y mens of PWM switched-mode highefficiency converters. The effective trnsfer rtio k is controlled vi the duty cycle d t which the converter is operted [1 14]. Consider lod typiclly pplied in PV systems, which my e represented s series connected voltge source E nd resistor R: v out ¼ E þ R ð3þ This lod hs liner lod line in the v in plne, determined y the trnsformer turns rtio. v in ¼ k E þ k R ð4þ Figure 4 shows the interction of the lod (referred to the MPPT s input) nd the PV rry (where V M, I M nd denote the MPP) for three vlues of trnsfer rtio k. An unmtched lod is ssumed in this exmple, which if connected directly, would lod the PV rry t voltge lower thn V M. At k ¼ 1 the PV rry opertes s if directly connected to the lod. In this cse the resulting opertion point is t i s The tunle trnsformer model of the MPPT power stge voltge lower thn V M (see Fig. 4). The power consumption yield is lower thn,sseeninfig4, where the lod line is prolic. p in ¼ v in k E v in k ð5þ R As k increses, v in increses nd so does p in.whenk reches k *, mtching is chieved nd mximum power is supplied y the PV rry. If k is further incresed (k4k * ) v in keeps rising ut p in decreses, due to the rupt fll of. Thus p in (k) hs mximum point t k * where k * cn e expressed in terms of the PV rry nd lod chrcteristics: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k E ¼ þ 4 R ð6þ I M R In prcticl pplictions (6) cnnot e used to set k ecuse, I M nd E re not constnts nd R might e unknown. Thus control lgorithm is itertively pplied until mximum ville power is otined. Therefore, p in must e successively clculted y multiplying nd v in. 3. MPP trcking y mens of loss-freeresistors Other power conservtive tunle circuits might e used s MPPT, for instnce, converters with resistive input chrcteristics [3]. Such converters my e relised either y mens of closed loop control [10], or y the converter inherent properties, such s flyck converter operted in IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005 41
discontinuous opertion mode [10]). A loss-free-resistor (LFR) network models these converters. The model is two-port network consisting of n emulted resistnce R e t the input nd power source t the output, s shown in Fig. 5. The power source is defined s n element, which outputs certin power regrdless of the lod chrcteristics, with tht of the power sored t the resistive input port. The equtions descriing the LFR model re: ν i i i R e (ν c (t)) controlled LFR p = i i R e p out i o ν o v i ðþ¼r t e i i ðþ t p 0 ðþ¼r t e i i ðþ t 8Z L ; 8t ð7þ V c (t) i i P = i i R e i o i o ν i R e P out ν o p out (ν c (t)) LFR i o ν o Fig. 6 The controlled LFR model () nd the output chrcteristics () P hs power source chrcteristics [3]. The trcking process is descriedinfig.7. Even though n idel voltge source type of lod E is ssumedinthisexmple,thepvrry sees pure resistive ν o R e1 Fig. 5 The LFR model s two port element () nd the power source chrcteristics () I M R e > R e R e3 This eqution descries power conservtive two-port network in which the input terminls hve pure resistive chrcteristic, which is uffered from the output. To pply for MPPT, the vlue of the emulted resistnce R e must e controllle. In this cse, the LFR model should e ugmented y control terminl to which control signl v c (t) is pplied, see Fig. 6. In this cse the emulted resistnce is determined y the control signl. In principle, this control terminl does not supply or consume power, so controllle LFR is descried y: 8 >< >: v i ðþ¼r t e i i ðtþ R e ¼ R e ðv c ðtþþ p c ¼ 0 P 0 ðþ¼r t e i i ðtþ 9 >= 8t 8Z >; L; 8t ð8þ p 3 p 1 p R e > V M where p c is the power t the control terminl. A fmily of constnt power hyperoles descries the output chrcteristics of the controllle LFR. The effective hyperole is determined y the control signl v c (t). In such MPPTs, the vlue of the resistnce, emulted y the MPPT, is tuned so s to drw mximum power from the PV rry. This power is trnsferred to the output, which E Fig. 7 MPP trcking process with n LFR sed converter s viewed t the converters input t the lod side 4 IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005
lod. The emulted resistnce is vried until it is equl to the PV rrys optiml lod R*, when mximum power is drwn from the PV rry. R¼ V M ð9þ I M The vlue of R e defines the PV opertion point nd the input power. Suppose the initil vlue of R e is R e1,itis incresed until mximum input power is reched t R e (R e ¼ R*). If the emulted resistnce is further incresed (R e ¼ R e3 ), the input power decreses. Ech input-emulted resistnce sets corresponding hyperole of constnt power in the output plne, Fig. 7. The prticulr lod opertion point is determined y the intersection of the hyperole p(r e ) nd the lod line (in this exmple constnt voltge type of lod). As in the controllle trnsformer cse, (9) cnnot e used in prctice to set R e ecuse V M nd I M re not constnts, so control lgorithm is itertively pplied until mximum ville power is otined. Thus, in this cse too, nd v in must e sensed nd p in successively clculted y multiplying nd v in. A 350 wtt LFR sed MPPT circuit is descried [3], in which the resistive input chrcteristics were chieved y operting flyck converters in discontinuous current conduction mode. The emulted resistnce ws controlled vi the duty rtio t which these converters were operted. 4 Control vi output prmeters The potentil control of MPPT converters vi output prmeters hs een noticed in the pst [6, 15 17]. In[16] the possiility of sensing only output current ws shown for constnt voltge lod. This method, however, uses power derivtive sign, which might cuse inccurcies nd unrecoverle stte from error. Positive current feedck is used in [17], which is sed on curve fitting. It is reveled in this pper tht this method results in which is restricted to situtions in which only smll vritions in the insoltion level nd PV pnel temperture re present nd where the PV genertors chrcteristics re precisely known. In the present work it is stressed tht true-mximumpower-point-seeking is chieved for nerly ll prcticl lods (not only for constnt voltge lod types) nd the PV genertors chrcteristics do not need to e known. Two incentives cll for control pproch sed on the output prmeters nd v out rther thn on the input ones. First, the power converter used might hve n efficiency curve tht yields mximum output power t n opertion point tht does not coincide with mximum input power in which cse mximum output power is the choice of preference. Second, the output prmeter-sed controller is simpler nd requires fewer sensors. Regrdless of the prticulr control lgorithm employed, input prmeter-sed controller requires sensing of nd v in. It is shown tht, in contrry, output prmeter-sed controllers requires sensing of only one output prmeter or v out. This is generl feture of output prmetersed controllers, which pplies to wide rnge of lod types, including nonliner ones, provided tht the lod does not encompss negtive impednce chrcteristics. 4.1 MPP trcking y mens of controllle power conservtive mtching network in cse of liner lod Consider PV rry nd liner lod coupled y tunle power-conservtive mtching network s shown in Fig. 8. It is well known tht this type of lod, consisting of resistor in series with voltge source, models wide rnge of PV rry p in power conservtive mtching network α(ν c ) lod Fig. 8 PV rry nd liner lod coupled y tunle powerconservtive mtching network prcticl lods vi their Thevenin equivlent scheme. Any comintion of liner DC lods, such s resistors, tteries nd motors cn e represented y its Thevenin equivlent, descried in (3) [7]. It is ssumed tht this mtching network hs n internl controllle prmeter (v c ) tht ffects the power flow through the network. The mtching network might e controllle trnsformer, loss-free resistor, or gyrtor or even nonliner power conservtive network. For instnce, if the mtching network is implemented y controllle trnsformer, is its trnsfer rtio k. wheres if implemented y loss-free-resistor,! is its emulted resistnce R e. In gyrtor-sed mtching network, the internl controllle prmeter would e its gyrtion conductnce g. As the controllle prmeter is vried, the input power chnges nd peks t prticulr vlue of the controllle prmeter (v c ) ¼ *, see Fig. 9. Since the mtching network is ssumed to e power conservtive, the output power equls the input power. The vrition of lod power implies vrition of lod current nd voltge: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 R p out þ E ¼ E ; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ð10þ 4 R p out þ E v out ¼ þ E Evidently, nd v out monotoniclly increse s the output power increses, thus mximum output current (or voltge) implies mximum output power. In other words, mximum output current (or voltge) trcking is equivlent to MPP trcking. As (v c ) chnges (sy increses), the opertion point chnges long the curve in Fig. 9, from point 1 to the MPP (point 3). If (v c ) keeps incresing, the power decreses s the opertion point ecomes point numer 4, Fig. 9. This process is lso shown on the current-power plne (Fig. 9) nd voltge-power plne (Fig. 9c). Since the power chnges, the output current lso chnges (10). Mximum current is reched t mximum power. As (v c )isfurther incresed the opertion point chnges from point 3 to point 4, returning on the sme i p curve (Fig. 9). For instnce, opertion points nd 4, though different, coincide on the i p curve (Fig. 9). The sme explntion holds for lod voltge vrition s shown in Fig. 9c. Thus control strtegy, different from the conventionl one, cn e pplied. It is possile to continuously chnge (v c )while oserving. As long s increses s result of the (v c ) vrition, it should still e chnging in the sme direction. If decreses s result of chnging (v c ), the tendency of (v c ) vrition should e reversed. In this mnner the opertion point should converge to the MPP (mx, ). Thus n MPPT lgorithm my e sed on single output prmeter. In this lgorithm the output current or output voltge is mximised rther thn the power. The ν c p out R E IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005 43
p out 3 strt 4 red 1 d(0), d α sense i o (0) d = d d mx /4 3 1 yes d >1 p out d =1 no sense i o (k1) v out v outmx /4 3 yes i o (k1) > i o (k) E 1 no p out d = d d Fig. 9 Output power versus the controllle prmeter output current versus output power output voltge versus output power (c) c Fig. 10 Flowchrt of the control lgorithm mximistion of output power follows utomticlly, thus eliminting the need for sensing second prmeter s well s the multiplier. The derivtive of (or v out ) with respect to the control vrile or the duty cycle d my e used in serch of the MPP. The MPP is found vi the simple itertive lgorithm whose flowchrt is plotted in Fig. 10. It cn e seen tht, unlike in previously reported MPPT controllers, the power is never clculted in this flowchrt, nor is multipliction pplied. 4. Sensor choice Some liner lod exmples re descried in Fig. 11: voltge source, pure resistive, series comintion of voltge source nd resistor nd current source types (represented y lines 1 4 respectively). Hyperoles representing lines of constnt power re lso plotted. The lods might operte t ny point, drwing power tht is not greter thn,thepv rry mximum ville power. Consider the voltge source type of lod (lod line 1 ). When k ¼ 0, neither current nor power is fed to the lod. As k increses lso increses. This process continues until MPP is reched (when the lod line hits the mximum power hyperole). Further increse of k yields reduction in the current s well s in the power p out. Thus mximum output current implies mximum power. This conclusion is vlid for other lod types ut current source type of lods in which power my e mximised y mximistion of output voltge. It should e noted tht 44 IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005
most of the prcticl lods pplied in PV systems cn e modelled y voltge source, or resistor, or y comintion of oth (such s relistic ttery with internl resistnce or DC motors). Thus the MPP my e reched y mximistion of either v out or without sensing of the second prmeter, nor multipliction (s would hve een required with conventionl input power control). Thus, with voltge-source type lods, MPP cn e reched vi mximistion of the output current, wheres with currentsource type of lods it would e reched vi mximistion of the output voltge. With other lod types such s resistors or voltge source nd resistor (see Fig. 11), either output current or output voltge cn e chosen. The sensed prmeter is then chosen for ese of implementtion (usully voltge sensing is esier to implement) nd sensing ccurcy. To evlute the ccurcies, the sensitivity of the power to the sensed prmeter should e compred. Sensitivity is defined s: S p out ¼ @p out @ p out ; S p out v out ¼ @p out @v out v out p out ð11þ For instnce, pplying the sensitivity comprison to the voltge source nd resistor comintion (3), yields: S p out P 1 P 4 3 P 1 < P < Fig. 11 Different lod types in the v out. 1-voltge-source type lod, -resistive lod, 3-resistive & voltge source type lod, 4-current source type lod 1 ¼ E þ R ; S p out v E þ R ¼ v out E out v out E ð1þ It cn e esily shown tht S p out v out 4S p out. Therefore, it is preferle to sense the output current (s the sme reltive error in sensing output voltge will cuse higher error in the power). 4.3 Generlistion for nonliner lods So fr, lod linerity hs een ssumed when developing the single output prmeter control. However, nonliner lods re not rre in PV systems such s gs dischrge lmps nd electronic circuits. In this Section, it is shown tht the single output prmeter control lso pplies to nonliner lods, on condition tht it exhiits nonnegtive impednce chrcteristics. This condition is expressed in (13): dv o di o 0; 0 8ðv o ; i o Þ ½p o Š ð13þ di o dv o where dv o /di o ¼ 0 descries n idel voltge source nd di o / dv o ¼ 0 n idel current source (which is quite rre, yet current sink type lods do exist, for instnce, current fed converters lods). The ove is true for nerly ll prcticl lods (unless the lod shows negtive resistnce or oscilltory chrcteristics). Eqution (13) implies tht v o (i o ) nd i o (v o ) re monotoniclly nondecresing functions. Tht mens tht incresing just one of the output prmeters (v o or i o ) gurntees n ssocited rise in the output power: ( dp o ; dp o 40 8ðv di o dv o ; i o Þ ½p o Š o p o ¼ v o ði o Þi o ¼ i o ðv o Þv o ð14þ At given opertion point (v o, i o ), the output power is p o. p o ¼ v o ði o Þi o ð15þ Suppose i o hs incresed y Di o, the new opertion point determined y the lod yields new output power: p o ði o þ Di o Þ¼v o ði o þ Di o Þði o þ Di o Þ ð16þ Eqution (16) implies: v o ði o Þv o ði o þ Di o Þ ð17þ Therefore: p o ði o þ Di o Þ4p o ði o Þ ð18þ A similr procedure with respect to incresed output voltge would show: p o ðv o þ Dv o Þ4p o ðv o Þ ð19þ Figure 1 illustrtes how incresed current implies incresed voltge nd vice vers. The ssocited power consumption is proportionl to the re defined y the opertion point. Evidently, it is incresed s well. i o i o i o Fig. 1 Thus, it cn e stted tht, for non-negtive impednce lods (except for the voltge source nd current source type of lods), the power is monotoniclly incresing function of oth lod voltge or lod current. In the mrginl cse of voltge source type of lod (corresponding to n incrementl impednce tending to 0 ), the lod power is proportionl to the lod current, wheres, in the cse of current source type of lod (corresponding to n incrementl impednce tending to N ), the power consumption is proportionl to the lod voltge. 5 Experimentl results ν o ν o ν o The experimentl setup consists of 00 wtt PV rry with I sc ¼ 10 mp, V oc ¼ volt nd ¼ 00 wtt (@ 1 Sun, 81C). A synchronous-uck converter ws used for the power stge, which cn e modelled s tunle trnsformer s discussed previously. The converter scheme is shown in Fig. 13. Both switches were implemented y FDB035AN06A0 power MOSFETs (Rds(on) ¼ 3. mo). The converter ws operted in continuous conduction mode An ritrry, nonliner nonnegtive impednce lod line IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005 45
D1 L iout C in Q1 Q D C out lod r s Fig. 13 The experimentl power stge with PWM control. To reduce switching losses, the switching frequency ws chosen to e 5 khz. Indeed power conversion efficiency up to 98.5% ws chieved (typicl efficiency in the rnge of opertion ws 97.0%). The inductor vlue L is 70 mh nd it hs negligile losses. Input cpcitnce C in is.8 mf nd output cpcitnce C out is 1.88 mf. Voltges were sensed using 1% ccurcy resistor voltge dividers nd currents y LA 55-TP/SP7 current sensors. Four control strtegies were compred: () conventionl input prmeter-sed pertur nd oserve () output power mximistion (similr to (), ut where output prmeters re used) (c) output current mximistion (s descried in Fig. 10) (d) output voltge mximistion, (similr to (c), ut where output voltge is sensed). These control lgorithms were implemented in microcontroller with 10-it ADC (microchip, PIC18F45). Trcking effectiveness of the different controllers ws compred. Trcking effectiveness TE is defined s TE ¼ p * /,wherep * is the power ctully supplied to the lod, due to the MPPT controller ction. is defined s the mximum ville lod (output) power. ws found y disling the MPPT s controller nd mnully vrying the duty rtio (y pulse genertor) until mximum output power ws reched. Results typicl for resistive lod relistedintle1forlodresistor:r lod ¼ 1 O. The second lod type tested ws led cid 1 V ttery feeding resistor in prllel, see Fig. 14. This lod represents PV system with ttery ckup. The ttery internl resistnce r s ws 0. O nd the prllel lod R p ws 1. O. Experimentl results for the second lod type re given in Tle. It cn e seen tht quite high trcking efficiency ws chieved with oth lod types under ll control strtegies. Also, it cn e seen tht use of the simpler single-output Fig. 14 The experimentl lod representing d PV system with ttery ckup prmeter control does not scrifice trcking efficiency. On the contrry, in oth lod cses the est results re chieved y output current control. It my e noted tht the duty rtio reding does not exctly comply with the input output voltge rtio. Tht is ecuse the ctul duty rtio vries continully during the trcking opertion nd the reding presented in the Tle represents some verge vlue (performed y oscilloscope). Since the focus t this stge ws trcking efficiency in the stedy stte, the duty-cycle increment Dd ws set to 50 ns, llowing fine-tuning ner the MPP. This is illustrted in Fig. 15, which shows the voltge cross Q (Fig. 13). The different triling edges show the vrition in duty cycle while operting ner MPP (in increments of Dd). Another performnce criterion is the trnsient MPPT ehviour. Optimistion for trnsient response is out of the scope of this pper, yet simple comprison will demonstrte the superiority of the proposed output prmeter-sed control over the conventionl one. Output current, voltge nd power vrition for sudden lod chnge re shown in Fig. 16. A resistor lod ws stepped from B1.6 O to twice this vlue. It cn e seen tht the overll recovery time is 6.4 s. Some time periods my e noted during which the MPPT does not progress towrds the MPP (periods of constnt output current, voltge nd most evidently power). Similr ehviour ws oserved when stepping the lod in the opposite direction with n overll convergence time of 6.5 s. The response to the sme step for output voltge-sed control is shown Fig. 17. Evidently the convergence process is smooth nd continuous, yielding n overll settling time of less thn s. It should e stressed tht other system prmeters re the sme (controller smpling time 0 ms, duty cycle chnge step of 50 ns). E R p Tle 1: Trcking efficiency Control strtegy v * in [V] i * * in [A] v out [V] * [A] Duty cycle [%] TE [%] 1. Input prmeter. Output prmeter 3. Output current 4. Output voltge 19.75 8.7 1.67 13.10 66 97.6 19.70 8.80 1.69 13.14 65.7 98.0 19.6 8.9 1.77 13. 67.0 98.8 19.96 8.56 1.6 13.7 64.7 98.3 Resistive lod, R 1 D1 O, ¼ 170 wtt. 46 IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005
Tle : Trcking efficiency Control strtegy v * in [V] i * * in [A] v out [V] * [A] Duty cycle [%] TE [%] 1. Input prmeter. Output prmeter 3. Output current 4. Output voltge 18.1 9.64 1.3 13.80 68.5 99.3 19.9 9.14 1.1 13.87 65.8 99.6 19.1 9.1 1.5 13.86 66. 99.9 17.74 9.76 1.0 13.81 70.8 99.1 Bttery lod, ¼ 170 wtt. Tek Stopped 1 Acqs 4 Jun 04 05:59:09 Fig. 15 Experimentl results during opertion in stedy stte Voltge cross Q, upper trce 10 V/div, 10 msec/div. Zoom on triling edge, lower trce, 5 V/div, 100 nsec/div. Tek Stopped power current voltge M1 Ch1 5V Ch1 00mV B w M 400ms 1.5KS/s 800us/pt Mth1 141 mvv 400ms A Ch \ 37mV φ 6 Conclusions 1 Acqs 4 Jun 04 06:53:40 Fig. 16 Response to lod step (1.6 O-3.65 O) with conventionl PV pnel voltge nd current control. Output current-lue trce 1 A/ div, 1 sec/div. Output voltge-yellow trces.5 V/div, 1 sec/div. Output power vrition-red trce 4.5 W/div, 1 sec/div. It hs een shown nlyticlly nd vlidted experimentlly tht MPPT control vi output prmeters is possile nd dvntgeous. It hs een shown tht controlling MPPTs power current voltge M1 Ch1 5V Ch 100mV B w M 400ms 1.5KS/s 800us/pt Mth1 45.4 mvv 400ms A Ch \ 476mV φ Fig. 17 Response to lod step (1.6 O-3.65 O) with output voltge sed control. Output current-lue trce 1 A/div, 1 sec/div. Output voltge-yellow trces.5 V/div, 400 sec/div. Output power vrition-red trce 4.5 W/div, 400 sec/div. vi its output prmeters fcilittes sensing of single output prmeter nd removes the need for multiplier in the controller. A mjor contriution of this work is showing tht single output prmeter control is, in generl, possile for nerly ll prcticl lod types, regrdless of lod nture. In ddition, it hs een experimentlly shown tht no deteriortion in the systems stedy-stte trcking-efficiency results from the single output prmeter control. Moreover, single output prmeter control is significntly superior to conventionl input prmeters control in terms of dynmic response. In smll PV systems with n nlogue controller, omission of the multiplier provides mjor dvntge s it simplifies the hrdwre. In PV systems with digitl controller, omission of the multiplier implies lgorithm simplifiction. In oth cses one of the usul employed sensors (voltge or current) is sved. Issues relted to the MPPT system trnsient response such s the influence of converter dynmics nd its interctionwiththecontrollerhvenoteenexplorednd cll for further investigtion. 7 Acknowledgements This work ws supported in prt y the Isreli ministry of Industry nd trde, within the frmework of the Lrge Scle Rurl Telecommuniction Consortium, under grnt 1956. Mr Ozeri Shul is cknowledged for his dedicted nd competent technicl support. IEE Proc.-Electr. Power Appl., Vol. 15, No., Mrch 005 47
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