Energy-balance and Sliding Mode Control Strategies of a Cascade H-Bridge Multilevel Converter for Grid-connected PV Systems

Transcription

1 Energy-balance and Sldng Mode Control Strateges of a Cascade H-Brdge Multlevel Converter for Grd-connected PV Systems Juan José Negron Domngo Bel Francesc Gunjoan Carlos Meza Unversdad Tecnológca Metropoltana, Electronc Engneerng Department Santago, Chle UPC- Electronc Engneerng Department Vlanova la Geltrú, Span UPC- Electronc Engneerng Department Barcelona, Span Costa Rca Insttute of Technology, Electronc Engneerng School Cartago, Costa Rca juan.negron@utem.cl bel@eel.upc.edu gunjoan@eel.upc.edu cmeza@etec.org Abstract- Ths work presents the desgn of a sldng-mode based current controller for a Cascade Full Brdge Multlevel Inverter grd connected PV system. The desgn also ncludes a modulaton strategy to share the control acton among the cascade-connected brdges n order to concurrently synthesze a multlevel waveform and to keep each of the PVG at ts maxmum operatng pont. Expermental results are ncluded to valdate the proposed approach. I. INTRODUCTION Photovoltac (PV) electrcal energy generaton provdes several advantages wth respect to other conventonal energy sources (e.g. coal, nuclear): t uses the nexhaustble world-wde avalable sunlght as a source of energy, t does not generate envronmental pollutants (e.g. CO) and the PV panels used requre mnmum mantenance. Photovoltacs has been ntally used n stand-alone applcatons, nevertheless, PV systems that supply energy drectly to the utlty grd (also referred as grdconnected PV systems) are becomng more popular because of the cost reducton due to the lack of a battery subsystem. Moreover, governmental laws and polces recently created that favors grd-connected PV (GPV) systems have proved to be an effectve way to encourage the use of solar energy. The hgh cost per watt of PV energy compared to other energy sources has motvated the current research n ths area, focusng manly on actvtes that ) mproves the effcency of PV cells/panels, ) reduces the manufacturng costs of PV cells/panels, 3) ncreases the effcency of the assocated power stage. The present paper deals only wth the later alternatve for GPV systems. The power condtonng stage s an essental part of the PV system snce t must account for an optmal energy transfer from the energy source to the load []. A PV panel or group of PV panels lnked to a power unt s referred n ths document as photovoltac generator (PVG). Normally, t s not advantageous to have a unque PVG,.e., only one bg group of PV panels connected to a power unt. For nstance, under dfferent operatng condtons the energy extracton can be maxmzed formng PVGs comprse of PV panels wth smlar condtons []. A power converter topology that can lnk several PVGs to the utlty grd s the so-called cascade H-brdge multlevel converter [3-5]. Besdes allowng havng a maxmum power pont tracker (MPPT) for each PVG ths topology allows reducng the njecton of harmoncs to the grd. One of the man antecedents related wth the control of such PV nverter topology can be found n [5], where the followng control blocks can be formally dstngushed: a) On the DC sde a lnear PI contnuous-tme voltage controller s desgned to fx each PVG at ts maxmum power operatng pont. b) On the AC sde, a PI or Proportonal+Resonant (PR) lnear current controller s desgned to track the output voltage snusodal reference ensurng a unty power factor njecton. c) The use of a PSC-PWM (Phase Shfted Carrer PWM) [6] whch generates the DC-AC multlevel converson and assgns a control sgnal to each brdge by means of weghtng the current controller output by a factor proportonal to the avalable power of the correspondng PVG. More recently, an energy balance sampled data model has been establshed to systematcally desgn a dgtal PI voltage loop ensurng the system s stablty n the framework of grdconnected PV systems wth a sngle central nverter [7]. The aforementoned approach was also appled to the cascade-full brdge nverter topology where a lnear P+R current controller and PSC-PWM modulaton have been used [8]. However, snce the lnear current controller s desgned from the lnear model of system s AC sde, ts robustness strongly depends on the model s valdty range. Alternatvely, ths work s devoted to desgn a sldng-mode based current controller accountng for /0/$ IEEE 55

2 the robustness propertes of ths control technque. Ths desgn also entals developng a modulaton strategy to share the control acton among the cascade-connected brdges n order to concurrently synthesze a multlevel waveform and to keep each of the PVG at ts maxmum operatng pont. After descrbng the man goals of the control strategy n secton II, the voltage control based on the energy-balance model s revsted n secton III. Subsequently, the sldng-mode based current controller desgn and the multlevel waveform synthess are presented n secton IV. To valdate the proposed approach, Secton V presents a set of expermental results carred out on two cascaded full brdge nverters lnkng two solar array emulators to the grd as well as some concludng remarks. case,.e., the control sgnals for the H-brdge multlevel PV converter have to be generated such that. the voltage of each PV strng s set to a desred reference value (normally gven by a maxmum power pont trackng (MPPT) algorthm),. a unty power factor and low harmonc dstorton current s njected to the utlty grd, and, 3. a multlevel step-lke AC wave voltage s syntheszed at the output of the converters. II. DESCRIPTION OF THE CONTROL STRATEGY Fg. shows the generalzed power converter structure used to nterface the photovoltac array wth the power grd. It conssts of n full-brdges wth ther AC outputs connected n seres. Ths converter structure syntheszed an output voltage VHT wth +n levels, reducng common-mode dsturbances and voltage harmoncs ampltudes. I PV v c I PV v c PVn In v cn Fgure. Power condtonng system s crcut. Defnng u {,} as the control sgnal that manages swtches S, S, S 3 and S 4 the system can be represented by the followng set of dfferental equatons: dvc ( PV gu) dt = C () d g n = vc u vg () dt L = for = to n, where n s the total number of H-brdge converters connected n seres. The control strategy for the cascade H-brdge multlevel PV converter s based on the control scheme descrbed n [7] and extended n order to fulfll the requrements for ths specfc Fgure. Control scheme. In order to accomplsh the aforementoned objectves a control scheme, shown n Fg., s desgned based on the energy sampled data model descrbed n [8]. Ths model relates the energy stored ( E sto ) n the capactors ( C ) wth the energy generated by the PV arrays and the energy transferred to the grd. Furthermore, the model states that when the system njects a snusodal current to the grd t s possble to set a desred PV voltage by controllng the energy stored n each capactor. That s why n the scheme of Fg. every H-brdge converter has ts own controller n charge of regulatng the energy stored n the capactor to a desred value that can be gven by a MPPT. Note that n the dagram of Fg. and n the present artcle no specfc MPPT s consdered, t s assumed that one of the wdely known MPPT algorthms are used, e.g. [9], to obtan the desred PV voltages ( vpv = v c ) and consequently E sto, see (3). The energy-balance controllers output ther correspondent A I of the njected current ampltude whch sum fracton ( ) 56

3 A I. A sldng mode current controller makes the output current track ts reference value. results n the reference value of the output current ( ) The lnear model of (8) enables to regulate the storage energy E sto to a desred value E sto by desgnng a lnear controller depcted n Fg. 3. G C III. ENERGY BALANCE VOLTAGE CONTROL REVISITED Defne P PV as the power extracted from the -th PVG, P out as the output power njected to the utlty grd, E PE as the energy stored n the nductor and E sto as the energy stored capactor assocated to the -th PVG,.e., Cv c E sto = (3) Consder the nstantaneous power equaton of the system d n n d Esto = PPV Pout EPE dt = = dt where n s the total number of PVG. Assumng a T-perodc output current and followng the procedure descrbed n [7] t s possble to obtan a T-Sampled-Data Model of the system, where T s the utlty grd perod, yeldng, n n n Esto ( kt ) = Esto ( ( k ) T ) + EPV ( ( k ) T ) = = = (5) 0.5AI (( k ) T) AT where k=0,,,3, represents subsequent grd perods, A s the ampltude of the utlty grd perod, A I s the ampltude of the output current, and E PV s the energy extracted from the -th PVG durng one grd perod. Notce that f, durng one grd perod, E sto s kept constant, all the power generated by the PVGs wll be delvered to the grd, ths resultng n a proportonal relatonshp between the PV power and the ampltude of the njected current,.e: n AI (( k ) T) AT E ( kt) = (6) PV = Notce that f E PV corresponds to the maxmum avalable power of each PVGs the maxmum power transfer s ensured. Therefore, by controllng the energy stored n the capactors t s possble to regulate each PVGs voltage to a desred value. The control of the storage energy E sto can be desgned from the Sampled-Data Model of the system gven by the Z- transform of the lnearzed verson of (5),.e: ( ( )) n n A ( ) ( ) ( z ) AT E I sto z = E m E z E PV + z sto sto + = = where each non-lnear functon E PV as descrbed n [7] and around E sto de PV m =. de sto E E sto = sto (4) (7) has been lnearzed If the ampltude s decomposed n components assocated to each mult-nverter stages,.e., AI = AI, (7) can be rewrtten as a system of n equatons, as shown next, ( ) n n A ( ) ( ) ( ) I z AT Esto z = EPV m Esto z Esto z + + = = (8) Fgure 3. Block dagram of the energy-balance control. A smple set of lnear controllers such as z α G ( z) C = γ (9) z where α and γ are parameters of the controllers, allows to successfully regulate the energy stored n the capactors. The procedure to choose these parameters s taken from [7],.e., α s located close to n order to mnmze the unstablzng effect ntroduced by the ntegral element and the value of γ s selected such that the closed-loop system s stable (e.g., by applyng the Jury test to the characterstc polynomal). Notce that to ensure that for each capactor E E sto = sto t s necessary to perform addtonal control actons n the multlevel s modulator. IV. SLIDING CURRENT CONTROLLER AND MULTILEVEL SYNTHESIS The aforementoned control strategy allows obtanng the current ampltude requred to extract the maxmum amount of energy from the PV panels. Ths strategy assumes that the current s snusodal n phase wth the utlty grd voltage. It s necessary to desgn a robust and fast nner current controller to assure ths snusodal current condton. A sldng mode controller technque has been chosen for the nner current controller gven that t has shown good performances n buckbased nverters n front of voltage and load dsturbances [0]. The nner controller uses the followng swtchng surface: σ : = gref g = 0 beng gref = AI ( kt)sn( ωt) and vg = A sn( ωt ). The multlevel converter operates by swtchng only one H- Brdge whereas the others reman n fxed ON or OFF state dependng on the relatonshp between the capactor voltages and the grd voltage. In fact, the control polcy guarantes that the overall capactor voltage s greater (lower) than the postve (negatve) grd voltage. Consequently, for nstance, f the grd voltage accomplshes vc < vg< vc + vc, the frst H-brdge wll be n ON state whereas the sldng control law wll be appled to the second one. Assumng these premses the control law s gven by: 57

4 ( σ ) ( σ ) u = sgn( ) when vg > 0 u = sgn( ) when vg < 0 In order to regulate the capactor voltage (PV array voltage) to the reference value, the control law s temporally assgned by consderng the outputs of the correspondng energy-balance controllers ( AI ( kt) ). In case of a multlevel converter composed by three H-brdges, the temporal dstrbuton can be schematzed as shows Fg. 4. Fgure 4. Scheme of sequence assgnaton. AI AI AI A = r B r C r A = I A =. I AI where: T T ; T T ; T T 3 Each sequence consders one H-brdges combnaton where the H-brdge assocated to the energy-balance controller output ( AI ( kt) ) s n the lower level. For nstance, B sequence mples the use of the combnaton, 3, (where each number corresponds to one H-brdge) as shown n Fg. 5, whereas C and A sequence are gven by 3,, and,, 3, respectvely. 3 v G v C +v C 3 + v C > v G v C +v C3 > v G v C > v G B sequence Fgure 5. Example of the B-sequence. V. EXPERIMENTAL RESULTS AND CONCLUSIONS Ths secton apples the presented approach to desgn the control loops of a laboratory prototype PVG multlevel nverter for subsequent expermental valdaton purposes. A block dagram of the laboratory prototype s presented n Fg. 6. The expermental setup conssts of a fve level power nverter wth passve elements. Two Solar Array Smulators (SAS) (Aglent E4350B #J0) delverng maxmum output voltages of 80 V were used to program the PV array electrcal characterstcs. Due to the SAS low output voltage level, the GPV multlevel nverter prototype was connected to the grd by means of a stepup power transformer. All the measurements were done n the low-voltage sde of the transformer, whch exhbts a voltage ampltude of 33 V at 50 Hz. A. Control Desgn The control scheme was mplemented n a feld programmable gate array (Xlnx Spartan 3E) and comprses an outer loop controller, such as the one explaned n Secton III, and a sldng mode nner loop controller, as mentoned n Secton IV. Focusng on the outer loop, the parameter α needs to be set to a value close to to mtgate the nstablty effect of the ntegral component of G C. Therefore α has been fxed to On the other hand, the desgn of the controller gan γψ s strongly related wth system stablty. As shown n Secton III- A, the stablty of the closed-loop GPV system s determned by the parameter m and the controller G C. The value of parameter m depends on the nput capactance and the electrcal characterstcs of the PV array. The maxmum value of m (worst case) s requred to choose the gan γ of the outer loop controller G C and to assure the stablty of the closed-loop system n the whole range of operaton, as can be derved from (8) and (9). For the expermental system a value of γ = 0.05 assures the stablty of the system under a suffcently large operatng range. B. Expermental Results A seres of expermental tests have been carred out to valdate the proposed control scheme. ) Expermental Test Irradance Change: The expermental test conssted of an abrupt solar rradance change from 000 to 800 W/m and then back to 000 W/m n only one of the array smulator. The other SAS was mantaned wth fxed -v characterstcs correspondng to and rradance of 000W/m. The PV arrays power curves for both rradances are shown n Fg. 7. The reference voltage values are held at vc = vc = 4 V. Fg. 8 shows the evoluton of the system s varables durng ths expermental test,.e., the capactor voltages (v c and v c ), the prmary transformer voltage and the njected current ( g ). As can be seen n these fgures, after a small transent tme, the voltage across the capactor mantans ts reference value, thus confrmng a proper voltage regulaton n front of rradance changes. In addton, notce that the output current s always n phase wth the grd voltage. ) Expermental Test Capactor Voltage Regulaton: In the present scheme, no MPPT algorthm was mplemented manly because ts tme constants are relatvely slow compared to the tme constants of the dynamcs of the power converter. Nevertheless, the followng expermental test ams to emulate an MPPT algorthm by varyng the reference capactor voltage connected to the frst array smulator every 5 s,.e., v () t 30 V v c ( t+ 5 s ) = 9 V, v ( t 0 s ) 8 V c =, c + =. The second reference voltage s held at vc = 8 V at all tme. The entre expermental test s shown n Fg. 9 and Fg. 0. Fg. 9 presents the measurements of the capactor voltages (v c and v c ), the prmary transformer voltage and the njected current ( g ) and the zoom area of the frst reference change. Fg. 0 shows the capactor voltages (v c and v c ), the output voltage of the multlevel converter (v HT ), the njected current ( g ) and the zoom are of the second reference change. Notce the smooth overdamped dynamcs of both varables related to the fact that the closed-loop poles of the sampled data system are real. Ths test evdences how the voltage of the frst capactor tracks the voltage reference, whereas the voltage of the second one remans unchanged to ts 58

5 reference value. In addton, the expermental results also show the proper multlevel waveform voltage synthess. Both tests confrm the proper operaton of the system and valdate the proposed control desgn. Fgure 6. Expermental setup block dagram (ADC=Analog to Dgtal Converter, PGA=Programmable Gan Amplfer, FPGA=Feld Programmable Gate Array). MPP MPP Power (W) Voltage (V) Fgure 7. Power versus voltage curves of the expermentally tested PV array (X-axs: 5 V/dv, Y-axs:5 W/dv). Fgure 8. Irradance change. Capactor voltages (v c, green, and v c, blue), prmary transformer voltage (blue) and njected current ( g, magenta). 59

6 Fgure 9. Capactor voltage regulaton. Capactor voltages (v c, green, and v c, blue), prmary transformer voltage (blue) and njected current ( g, magenta). [5] O. Alonso, P. Sanchs, E. Gubía, and L. Marroyo, Cascade H-Brdge Multlevel Converter for Grd Connected Photovoltac Generators wth Independent Maxmum Power Pont Trackng of each Solar Array, Power Electroncs Specalsts Conference, 003, pp [6] J. Rodrguez, J. S. La, F. Z. Peng, Multlevel Inverters: A Survey of Topologes, Controls, and Applcatons, IEEE Trans. On Industral Electroncs, Vol. 49, nº 4, pp ,Aug. 00. [7] C. Meza, J.J. Negron, D. Bel, F. Gunjoan, Energy-balance modellng and dscrete control for sngle-phase grd-connected PV central nverters, IEEE Transacton on Industral Electronc, 008. [8] J.J. Negron, F. Gunjoan, C. Meza, D. Bel, P. Sanchs, Energy-sampled data modelng of a cascade H-brdge multlevel converter for grdconnected PV systems, 0 th IEEE Internatonal Power Electroncs Congress, 006. [9] K.H. Hussen, I. Muta, T. Hoshno, M.Osakada. Maxmum photovoltac power trackng: an algorthm for rapdly changng atmospherc condtons, IEE Proceedngs on Generaton, Transmsson and Dstrbuton, Vol 4, No., pp , January 995. [0] D. Bel, G. Gunjoan, E. Fossas, J. Chavarra, Sldng-Mode Control Desgn of a Boost-Buck Swtchng Converter for AC Sgnal Generaton, IEEE Trans. On Crcuts and Systems, Vol. 55, No. 8, pp , 004. Fgure 0. Capactor voltage regulaton. Capactor voltages (v c, green, and v c, blue), output voltage of the multlevel converter (v HT, blue) and njected current ( g, magenta). ACKNOWLEDGMENT Ths work was supported n part by the Mnstero de Cenca e Innovacón, Span, DPI C03-03, DPI by the European Unon (FEDER). REFERENCES [] G. Petrone, G. Spagnuolo, R. Teodorescu, M. Veerachary, and M. Vtell, Relablty ssues n photovoltac power processng systems, IEEE Transacton on Industral Electroncs, vol. 55, pp , 008. [] G. Velasco, J.J. Negron, F. Gunjoan y R. Pqué. Some Consderatons on Grd-Connected PV Systems Under Partal Shadowng Operaton. XI Semnaro Anual de Automátca, Electrónca Industral e Instrumentacón, 004. (SAAEI 04). Toulouse (Franca), Septembre de 004. ISBN: [3] M. Calas, J. Myrzk, T. Spooner, V. G. Agelds, Inverter for Sngle- Phase Grd Connected Photovoltac Systems An Overvew, PESC, Vol. 4, pp , Feb. 00. [4] M. Calas, V. G. Agelds, and M. Menhardt, Multlevel Converter for Sngle-phase Grd-connected Photovoltac Systems: An Overvew, Solar Energy, Vol. 66, No. 5, pp ,