Key-Words: - MPPT, Sliding mode control, Battery charger, Lyapunov function, Boost converter

Transcription

1 Research on MPPT and Sngle-Stage Grd-Connected or Photovoltac System Department o Electrcal Engneerng Natonal Chang-hua Unversty o Educaton Bao-Shan Campus, Address: No.2, Sh-Da Road, Changhua Cty 520 REPUBLIC OF CHINA.(TAIWAN) y5111@mal.elvs.chc.edu.tw, sdt@cc.ctu.edu.tw, shaong@cc.ncue.edu.tw Abstract: - Ths paper proposes a grd-connected photovoltac (PV) system that s conssted o a boost converter wth maxmum power trackng, battery charge controller, nverter, and the related control crcuts. A sldng mode controller s desgned or controllng the boost converter to output the maxmum power o the solar cells. A control strategy s proposed o a Maxmum Power Pont Trackng (MPPT) mpendence adapter couplng a photovoltac generator to a battery. The proposed strategy s based on the sldng mode control theory o contnung systems to permt a drect control o power converter. The PV generator prce s even relatvely hgh, so the user s nterested o the optmal couplng o PV generator to electromechancal loads. In act, ths system uses the optmal couplng n order to have maxmum power durng the whole operatng perod. A grd-connected nverter s desgned to transorm the maxmum output power nto the load and utlty. The real power control s usng zero-cross and phase-lock crcuts that control the nverter output voltage whch s phase lead and synchronzed wth the utlty. A dgtal crcut s used to detect the phase angles o the load voltage and current to control the nverter output ampltude to acheve the reactve power load compensaton. A montor crcut s desgned to detect the voltage and requency varaton n the utlty. When the photovoltac system encounters a voltage and requency devaton, the montor crcut mmedately dsconnects the photovoltac system rom the utlty to prevent the sland eect. The proposed system s mplemented by usng OP amplers and mcro controller (PIC16F877A). Both the smulaton and expermental results usng MATLAB show the sldng mode controller or maxmum power trackng has good perormance. The phase and ampltude control experments acheve the real and reactve power control. The sland eect experments demonstrate evdence o the solar cell system protecton ablty llustratng the proposed grd-connected photovoltac system has good operatng perormance. Key-Words: - MPPT, Sldng mode control, Battery charger, Lyapunov uncton, Boost converter 1 Introducton Due to depleton o ossl energy and envronmental contamnaton, a renewable energy applcaton such as photovoltac (PV) system has been wdely used or a ew decades. The PV energy s ree, abundant and dstrbuted through the earth. Photovoltac (PV) systems are solar energy supply systems, whch ether supply power drectly to electrcal equpment or eed energy nto the publc electrcty grd. Generally, photovoltacs are consdered as an expensve method o producng electrcty. Moreover, wth the developng o PV technologes, applcaton o photovoltac n grdconnected stuatons has grown rapdly, whch shows that photovoltac are very attractve to pro- duce envronmentally bengn electrcty or dversed purpose [1-3]. Among the PV energy applcatons, they can be dvded nto two categores: one s standalone system and the other s grd-connected system. Stand-alone system requres the battery bank to store the PV energy whch s sutable or low-power system. On the other hands, grd-connected system does not requre the battery bank and has become the prmary PV applcaton or hgh power applcatons. The man purpose o the grd-connected system s to transer maxmum solar array energy nto grd wth a unty power actor. The output power o PV cell s changed by envronmental actors, such as llumnaton and temperature. Snce the characterstc curve o a solar cell exhbts a nonlnear voltage-current characterstc, a controller named maxmum power pont tracker (MPPT) s requred to match the solar cell power to the envronmental changes. Many algorthms have been developed or trackng maxmum power pont o a solar cell. In recent years, the research o the PV MPPT control methods has been pad extensve attenton by many specalst and obtaned some ruts such as: P&O and uzzy control etc. Because the output energy o the PV arrays ISSN: Issue 10, Volume 7, October 2008

2 changes requently by the surroundngs, mprovng the speed o trackng the PV power system could obvously mprove the system perormance. The exstng trackng control methods or the MPPT can be classed nto ve categores: (.) hllclmbng [1] / perturb and observe (P&O) [2]-[4]. The system then oscllates about the MPP. The oscllaton can be mnmzed by reducng the perturbaton step sze. However, a smaller perturbaton sze slows down the MPPT. Hllclmbng can al under rapdly changng atmospherc condtons. (.) ncremental conductance [5-6]; (.) open-crcut voltage and short-crcut current [7-9]; (v.) uzzy logc control [10]; and (v) neural network control [11]. X. L et al. ntroduced the uzzy trackng control approaches [10] n But t s very dcult to ormulate the uzzy rules, whch are usually obtaned rom the tral-and-error procedure. In 2006, the computatonal expensve neural network was adopted by Tarq et al. [11]. The algorthm requres on-lne learnng n order to make the robot perorm properly. In ths paper, we propose a grd-connected photovoltac system that s conssted o a boost converter wth maxmum power trackng, battery charge controller, nverter, and the requred control crcuts. we come up wth sldng mode control strategy [12-16] to solve the problem o MPPT under the condton o all knds o radaton levels. A grdconnected nverter [4] s desgned to transorm the maxmum output power nto the load and utlty. The real power control s realzed usng zero-cross and phase-lock crcuts that control the nverter output voltage whch s phase lead and synchronzed wth the utlty. A dgtal crcut s used to detect the phase angles o the load voltage and current to control the nverter output ampltude to acheve the reactve power load compensaton. A montor crcut s desgned to detect the voltage and requency varaton n the utlty. When the photovoltac system encounters a voltage and requency devaton, the montor crcut mmedately dsconnects the photovoltac system rom the utlty to prevent the sland eect. Ths paper s organzed as ollows. The DC-DC analyss and mathematcal modelng are presented n Secton 2, and Secton 3 ams at the MPPT controller desgn. Secton 4 s ocused on the charge controller desgn. Secton 5 s devoted to the grd connected Photovoltac system. smulaton and expermental results are presented n secton 6. In Secton 7 concludes ths paper. 2 The Boost Converter o Analyss and Mathematcal Modelng The output energy o the PV arrays s nluenced by the surroundng, such as the surroundng temperature, the solar radaton and the termnal voltage o PV arrays etc, the PV arrays characterstc curve s shown as Fg.1. Mathematcal model o the solar array can be expresses as Equ. (1) [17][18]. q I = I g Isat exp( V ) 1 AKT (1) where I denotes a current o a solar array, g V denotes an output voltage o a solar array, q denotes an electron charge (C), I sat denotes a cell reverse saturaton current (A), K s the Boltzman s constant (J/K), T s a cell temperature (K), A denotes the dealty actor In order to charger the battery, the PV MPPT system adopt step up type DC-DC converter topology system. Fg. 2 presents ts system structure. Fg. 2 shows the Boost Converter to transer power to load rom solar array. In the Fg.2, D represents the swtch uncton o the power swtch devce to control the output energy o the solar array. When D = 0, power wll be swtched to open. When D = 1, power wll be swtched to close. From Fg.2, we can draw the system dynamc model as ollows. Output Power (w) dp < 0 dv 600w 400w 1000w 800w dp dv Output Voltage (V) = 0 Fg.1 The PV arrays characterstc dp dv > 0 ISSN: Issue 10, Volume 7, October 2008

3 Fg. 2 The crcut dagram o PV DC-DC converter system dl V = L + ( 1 D) V0 dt dv C dt = (2) L 1 = ( 1 D C 0 ) L V& = ( ) / C L 1 2 dv dt 0 & = 1 1 L (1 D) V0 V L + (3) L 1 1 V& 0 = (1 D) L 0 C 2 C2 V& x& = & L V& 0 ( L) / C 1 1 ( x) = ( V1 V 0) (4) L 1 ( L 0 ) C 2 0 g( x) = V0 / L L / C 2 x & = ( x) + g( x) D (5) 3 The DC-DC Controller Desgn Based on the solar array characterstc curve shown n Fg.1, when the solar array s operatng n ts maxmum output power state, we can get P / V = 0 (6) Where (6) represents maxmum power acheved. P ( V ) = = V + = 0 (7) V V V From (7), the swtch uncton can be selected, P S( x) = = ( V + ) (8) V V Based on the two states o PV arrays n Fg.1 and the system crcut dagram shown as Fg.2, the swtch control sgnal can be selected as 0 D S 0 = (9) 1 S < 0 Let S S S S & = x = ( x) + g( x) Deq = 0 T T T x & x x (10) Thereore, the equvalent control varable s shown below. 0 Deq = (11) L Theorem: For the system shown n (5) and the swtch uncton (8), the expresson (9) s adopted, they could make the system eventually stablze at the status that swtch uncton s equal to zero rom any ntal state. Proo: Let Lyapunov uncton as ISSN: Issue 10, Volume 7, October 2008

4 1 V S 2 ds dp d dp V& = S = ( ) dt dd dt dd 2 = > 0 (12) eq Substtutng equaton (1) nto (8), then P S = = ( V + ) V V qv qisatv qv = I g Isat exp( ) 1 exp( ) AKT AKT AKT qv qisatv qv = I g + Isat Isat exp( ) exp( ) AKT AKT AKT qv qv = ( I g + Isat ) Isat (1 + ) exp( AKT AKT (13) 3.1 When S > 0 Base on (8) (9) and Fg. 1, the system s operatng n let, the swtch uncton D = 0, and V s ncrease. dv > 0 (14) dt ds qi sat qv dv = exp( ) dt AKT AKT dt qv qv q dv Isat (1 + ) exp( ) AKT AKT (15) AKT dt ds Brng (14) nto (15), then 0 dt <, so ds S < 0 (16) dt 3.2 When S < 0 The system s operatng n rght, the swtch uncton D = 1, V s decreasng, so dv < 0 (17) dt Fnally, substtutng equaton (17) nto (15), then ds 0 dt > and ds S > 0. dt Obvously, the system could reach global stablty and the swtch uncton s tendng to zero whether the system s operatng n let or n rght. eq And the swtch unctons as: P S( x) = = ( V + ) V V (19) 4 The Charge Controller Desgn Ths paper uses pulse charge model to save the power on the lead-acd battery. The pulse wdth o power transton swtch s by the voltage o lead-acd battery to control the charge current. The voltage o battery ull-charged or every cell s about 2.43V so that total ull-charged battery s about 29.16V.Fg. 3 shows the measurement crcut o lead-acd voltage s measured by current sensor. The measurement o Battery voltage s put nto mcrochp, PIC16F877A, to control the pulse wdth o power transton swtch and also to control the charge current. As Fg.4 shows, durng the current charged, the current generated by booster converter s provded to battery va pulse charge mode. Accordng to the voltage o lead-acd battery and maxmum power o solar cell, the battery charged wll be the best adjusted. 5 The Grd-Connected Photovoltac System Ths paper proposes the grd-connected photovoltac system as shown n the Fg.5 whch ncludes solar cell, boost converter and grdconnected nverter. In the grd-connected cty power mode, cty power s a constant AC and nverter s a voltage source. Thereore, by the technology o Phase-Locked Loop, t wll lock the requency and phase o cty power to acheve the synchronzaton wth the cty power. The phase and ampltude o output voltage s controlled by nverter to acheve the real power and the reactve power. Besdes, n normal condton, SW2 and SW3 are shorted. As the cty power s out o order, SW2 and SW3 are o to prevent sland eect. 3.3 Control Algorthm The system control rules can be present as ollows. 0 D S 0 = (18) 1 S < 0 Fg.3 Crcut o Charger Control ISSN: Issue 10, Volume 7, October 2008

5 Fg. 4 Flow Chart o Charger Control Fg.5 Archtecture o Grd Connected Photovoltac System 5 ISSN: Issue 10, Volume 7, October 2008

6 5.1 Grd Connecton Inverter on Real Power Reactve Power Controller Desgn In the Fg.5 grd connecton nverter s a sngle phase ull-brdge nverter. When M1 and M4 s shorted, the load o the current s passed rom M1 to M4. Smlarly, as M2 and M3 are shorted, the load o the current s passed rom M2 to M3. By the power swtch, M1 ~ M4, the output DC voltage o boost converter s transormed to AC output. The selecton on PWM swtches requency o M1~M4 s by the phase-lock crcut and requency doubler. It uses the requency, 60Hz, o the cty power to rase the requency to 24kHz and makes the output AC o nverter synchronze wth the cty power. However, the PWM modulaton sgnal o 24kHz can reduce the value o nductor, L2, and capactor, C2, o lter. In order to lter the hgh requency o PWM to acheve 60Hz, the L2 and Io need to be adjusted. I the value o the nductor s too small, the value o rpple current gets larger. These wll nluent both ncreasng swtch and nductor power lost. Also, the value o the nductor s too large, the dynamc response o nverter wll be reduced especally or the non-lnear load. Thereore, the selecton o capactor depends on the operaton current and swtchng requency. Moreover, the equvalent Seres Resstor, ESR, wll drectly nluent the value o output voltage rpples. That s because ESR s one o consumpton actor o capactor. The nner power consumpton generates heat and the letme o the capactor s reduced. Thereore, the selecton o the capactor depends on the value o the seral resstor. So, the requency selecton o nductor and capactor s less than 10 1 o 10 tmes o as shown n Equ. (20). 1 PWM 10 output 2π L C 10 Parameters or ths paper s pwm and s greater than output (20) =60Hz, pwm =24kHz, L2=2mH and C2=5µF. Ater the solar cells are traced by boost converter wth MPPT, the nverter and the cty power wll be paralleled. Thereore, output ampltude and phase o nverter wll drectly nluent the real power and reactve power o the cty power. Fg. 5 shows the system crcut or the output voltage control mode o nverter s paralleled wth cty power. The cty voltage V s (t) s shown below. V ( t) = V snωt (21) s m where V m s the peak o the cty power voltage,ω s the angle requency o the cty power voltage. The output voltage o grd connecton nverter V out (t) s shown below. Vout ( t) = Vc sn( ω t + δ ) (22) Where V s the peak o the grd connecton c nverter. The ω s the angle requency o grd power. The δ s the phase derence o the grd connecton nverter output voltage and cty voltage. The real power o nverter P S s shown below. VmVc / 2 P S = snσ (23) X The reactve power o nverter Q S [ V / 2 ( V / 2) cosσ ] Q S s shown below. VC / 2 = (24) C m X where X s nductve reactance o L. By Equ. (23), to control the angle,δ, o V S (t) can control the P S, the real power. By Equ. (24), to control the ampltude, V C, can control the reactve power, Q S.6 Smulaton and Experment Results 6.1 Smulaton Ths paper used Matlab/Smulnk to smulate P&O, uzzy and sldng mode control. Fg. 7 shows comparson o the trackng maxmum power whch reveals the sldng mode controller only needs 0.06s, uzzy controller needs 0.24s and P&O controller needs 1.74s. Thereore, the proposed sldng mode controller s mproved ts perormance o MPPT. Fg. 8 shows the trackng condton o the sldng mode controller as the llumnaton changes. As the tme changes rom 1 second to 1.2 second and the 2 2 solaton changes rom 0.6 kw / m to 1 kw / m. Hence, the MPPT changes rom 14W to 24.5 W. Fg.9 shows the trackng condton o the controller as the temperature changes. As the tme changes rom 2 second to 2.2 second and the temperature changes rom 25 C to 50 C. Hence, the MPPT changes rom 25 W to 23 W. Fg.10 shows the trackng condton o the controller as the llumnaton changes. ISSN: Issue 10, Volume 7, October 2008

7 Fg. 6 The achevement o real power and reactve power 2 Fg. 7 The system output power (1 kw / m, 25 C ) ISSN: Issue 10, Volume 7, October 2008

8 Fg. 8 The system output power (llumnaton change) Fg.9 The system output power (temperature change) 8 ISSN: Issue 10, Volume 7, October 2008

9 Fg. 10 Sldng algorthm o trackng maxmum power pont tracker Fg. 11 Dagram o photovoltac charger system ISSN: Issue 10, Volume 7, October 2008

10 6.2 Experment Fg.11 shows the control archtecture, the control system comprses Mcrocontroller PIC16F877A, MOSFET, L etc. Fg.12 shows the photovoltac system. DC/DC s the charge trackng the maxmum power. The storage battery s as the load. Fg.12 shows the photovoltac system o MPPT. T = 85.9 P& O sec, T = 16.3sec, T = 8.2sec. Fg.13 shows Fuzzy sldng pulse wdth module s 0.2 and charge current s 0.1A. Fg.14 shows pulse wdth module s 0.8 and charge current s 0.5A. By adjust the pulse wdth module t can get the best charger method. Fg.15 shows zero-cross crcut o output plot. The phase-lock crcut demonstrates the crcut can track or the cty power o requency 63Hz (n Fg. 16). Fg. 16, 17, 18 show the phase-lock crcut the crcut can track the cty power o 60 Hz, 57Hz, 63Hz.. Fg.12 shows the photovoltac system o MPPT. T & = 85.9sec, T = 16.3sec, P O T = 8.2sec sldng Fuzzy Fg. 12 P&O, Fuzzy, Sldng charge curve ISSN: Issue 10, Volume 7, October 2008

11 Fg. 13 D=0.2 and charge current=0.1a Fg. 14 D=0.8 and charge current=0.5a ISSN: Issue 10, Volume 7, October 2008

12 Fg. 15 The zero-cross crcut o output plot Fg. 16 The phase-lock crcut trackng or 60 Hz plot 12 ISSN: Issue 10, Volume 7, October 2008

13 Fg. 17 The phase-lock crcut trackng or 57 Hz plot Fg. 18 The phase-lock crcut trackng or 63Hz plot ISSN: Issue 10, Volume 7, October 2008

14 7 Conclusons Ths paper presents the sldng mode controller rom VSC that controls Booster type converter o solar array and battery charger to compete the trackng o MPP. Ater usng Matlab/Smulnk to smulate P&O control, uzzy control and sldng control, compare ts response tme. Accordng to the g.3, the PV maxmum power pont trackng (MPPT) speed s aster apparently comparng the P&O and uzzy control method. Seen rom the smulatng result, gure 4, 5 and 6, t s obvous that the ecency o the PV MPPT s greatly mproved the system shown mplements the sldng control algorthm. In order to prove the easblty o the sldng control method; a system o PV arrays was desgned as g.7 and 8. In the control system comprses Mcro-controller, IC16F877A, IGBT, L etc. Expermental results show the response tme o the proposed sldng control s better than P&O and uzzy control. Ths paper, consstng o a Boost type dc/dc converter, whch mcro-processor, PIC16F877A, s used to mplement the sldng mode controller. Comparng wth other technques used n the past, the use o the proposed MPPT control mproves the PV system perormance. The results o smulaton and experment are present. A grd-connected nverter s desgned to transorm the maxmum output power nto the load and utlty. The real power control s usng zero-cross and phaselock crcuts that control the nverter output voltage whch s phase lead and synchronzed wth the utlty. A dgtal crcut s used to detect the phase angles o the load voltage and current to control the nverter output ampltude to acheve the reactve power load compensaton. A montor crcut s desgned to detect the voltage and requency varaton n the utlty. When the photovoltac system encounters a voltage and requency devaton, the montor crcut mmedately dsconnects the photovoltac system rom the utlty to prevent the sland eect. The proposed system s mplemented by usng OP amplers and mcro controller (PIC16F877A). Both the smulaton and expermental results usng MATLAB show the sldng mode controller or maxmum power trackng has good perormance. The phase and ampltude control experments acheve the real and reactve power control. The sland eect experments demonstrate evdence o the solar cell system protecton ablty llustratng the proposed grd-connected photovoltac system has good operatng perormance. Reerences: [1] W. Xao and W. G. Dunord, A moded adaptve hll clmbng MPPT method or photovoltac power system,, n 35th Annual IEEE Power Electron. Specalsts Con., 2004, pp [2] N. Fema, G. Petrone, G. Spagnuolo, and M. Vtell, Perturb and Observe MPPT Technque Robustness Improved, IEEE Internatonal Symposum on Industral Electroncs, vol. 2, May 2004,pp [3] N. Fema, G. Petrone, G. Spagnuolo, and M. Vtell, Optmzaton o Perturb and Observe Maxmum Power Pont Trackng Method, IEEE Transactons On Power Electron., vol. 20, July 2005, pp [4] N. Kasa. T, Ida. and L, Chen, Flyback Inverter Controlled by Senseless Current MPPT or Photovoltac Power System, IEEE Trans. Ind. Electron., vol, 52, pp, ,AUG, [5] K. Kobayash, I. Takano, and Y. Sawada, A study on a two stage maxmum power pont trackng control o a photovoltac system under partally shaded nsolaton condtons, n IEEE Power Eng. Socety General Meetng, 2003, pp [6] W. Wu, N. Pongratananukul, W. Qu, K. Rustom, T. Kaspars, and I. Batarseh, DSPbased multple peak power trackng or expandable power system, n Eghteenth Annual IEEE Appl. Power Electron. Con. and Exposton, 2003, pp [7] T. Noguch, S. Togash, and R. Nakamoto, Short-current photovoltac power generaton system, n Proc IEEE Internatonal Symp. on Ind. Electron., 2000, pp [8] N. Mutoh, T. Matuo, K. Okada, and M. Saka, Predcton-dada-based maxmum-power-ponttrackng method or photovoltac power generaton system, n 33rd Annual IEEE Power Electron. Specalsts Con., 2002, pp [9] M. A. S. Masoum and H. Dehbone. E. F. Fuchs, Theoretcal and Expermental Analyses o Photovoltac Systems wth Voltage and Currentbased Maxmum Power-pont Trackng, IEEE Transactons on Energy Converson. vol. 17, Issue 4, Dec. 2002, pp [10] B. M. Wlamowsk and X. L, Fuzzy System Based Maxmum Power Pont Trackng or PV System, IEEE Annual Couereuce o the Industral Electroncs Socety, Vol4, Nov. 2002,pp ISSN: Issue 10, Volume 7, October 2008

15 [11] A. Tarq and M. S. Jam Asghar, Development o an Analog Maxmum Power Pont Tracker or Photovoltac Panel, Internatonal IEEE Annual Conerence on Power and Electroncs and Drves Systems, Vol.1, Jan. 2006, pp [12] R. A. Decarlo and S. H. Zak. G. P. Matthews, Varable Structure Control o Nonlnear Multvarable System: A tutoral, Proceedngs o the IEEE, Vol.76, March. 1988,pp [13] J. J. Negron; C. Meza; D. Bel; F. Gunjoan; Control o a buck nverter or grdconnected PV systems: a dgtal and sldng mode control approach, Industral Electroncs, ISIE Proceedngs o the IEEE Internatonal Symposum on Volume 2, June 2005 Page(s): vol. 2 [14] A. F. Flppov, Derental Equaton wth Dscontnuous Rghtsdes, Kluwer Academc, Dordrecht, Boston, London, [15] E. Baly and A. Arapostaths, Smple sldng mode control scheme appled to robot manpulator, Int. J. o Systems Scence, Vol. 17, pp , [16] I. Lagrat, H. Ouakka, and I.Boumhd, Sldng Mode PI Controller or Nonlnear Systems, Proceedngs o the 6th WSEAS Internatonal Conerence on Smulaton, Modellng and Optmzaton, Lsbon, Portugal, September 22-24, [17] T. J.Mabnoto, K. Sopan, W. R. W. Daud, M. Agoul and A. Zaharm, Mathematcal Model or Determnng the Perormance Characterstcs o Mut-Crytallne Photovotac Modules, Proc. o the 9th WSEAS Int. Con. on Mathematcal and Computatonal Methods n Scence and Engneerng, Trndad and Tobago, November 5-7, [18] D. Wu and Z. Wang, Study on Model and Control System o Varable-Speed Ptch- Controlled Wnd Turbne, Proceedngs o the 7 th WSEAS nternatonal Conerence on Smulaton, Modelng, and Optmzaton, Bejng, Chna,, September 15-17, 2007 ISSN: Issue 10, Volume 7, October 2008