Three-Phase Grid-Connected PV System With Active And Reactive Power Control Using dq0 Transformation

Transcription

1 Three-Phase Grd-Connected PV System Wth Actve And Reactve Power Control Usng dq0 Transformaton Mateus F. Schonarde, Adrano Ruseler, Roberto F. Coelho and Denzar C. Martns Federal Unversty of Santa Catarna, Department of Electrcal Engneerng, Power Electroncs Insttute Abstract- Ths paper presents a three-phase grd-connected photovoltac generaton system wth unty power factor for any stuaton of solar radaton. The modellng of the PWM nverter and a control strategy usng dq0 transformaton are proposed. The system operates as an actve flter capable of compensate harmonc components and reactve power, generated by the loads connected to the system. An nput voltage clampng technque s proposed to control the power between the grd and photovoltac system, where t s ntended to acheve the maxmum power pont operaton. Smulaton and expermental results are presented to valdate the proposed methodology for grd connected photovoltac generaton system. I. INTRODUCTION The works on photovoltac dstrbuted generaton systems, such as photovoltac solar cells connected to the power grd, has ncreased n the last decades due to need of supplyng the world rse demand for electrc power. Several papers have been publshed wth vared topologes and control strateges for three-phase systems [1], [2], [3], [4], [5], [6], [7]. There are some advantages that have been motvatng grd-connected photovoltac system applcatons, whch are: Reducton n the costs of the PV panels [8]. Operaton does not pollute the atmosphere [9]. Capablty to supply AC loads and nject actve power, from the photovoltac system to the grd, relevng the grd demand (dstrbuted generaton system). The researches developed n ths area have shown another great advantage, whch s the possblty to accomplsh a reactve power control orgnated from lnear and non-lnear loads also connected to the system [10]. Ths fact s so attractve, snce a sngle system s able to realze two dfferent functons as energy generaton to supply AC loads and actve power flter. Followng ths research lne, ths work presents a threephase PWM nverter modelng and a control strategy usng dq0 transformaton to be employed n a grd-connected photovoltac generaton system (Fg. 1). The proposed system also operates as an actve power flter capable of compensate harmonc components and reactve power, generated by the other loads. Therefore, the control strategy permts the operaton near unty power factor to any solar radaton, UPS functon for any knd of load and control of the energy flux between the photovoltac panels and the grd. In order to acheve the maxmum power pont (MPP) operaton an nput voltage clampng technque s proposed for the nverter. To valdate the proposed methodology some smulaton and expermental results are presented. Fg. 1. Proposed three-phase power photovoltac system. II. MODELLING CONVERTER A. The three-phase converter The converter proposed n ths work s a three-phase bdrectonal DC-AC converter wth PWM modulaton usng sx power swtches. The smplfed electrcal dagram of the converter s shown n Fg. 2. The b-drectonal characterstc of the converter s very mportant n ths proposed photovoltac system, because t allows the processng of actve and reactve power from the generator to the load and vce versa, dependng on the applcaton. Thus, wth an approprate control of the power swtches t s possble to control the actve and reactve power flow. Fg. 2. B-drectonal DC-AC PWM converter. B. Current control modelng The converter modellng s relatvely smple and s accomplshed through dq0 transformaton. The modellng for the current control s obtaned consderng the AC output.

2 When the crcut s observed from the AC output, t s possble to make some ntal consderatons that result n a smplfed crcut [11], shown n Fg. 3. The lne voltages are presented n (1) consderng L1=L2=L3=L, R1=R2=R3=R and D are the duty cycle. C. Voltage control modelng The purpose of ths model s to accomplsh the actve nput voltage clampng V (t). Ths actve clampng allows controllng the power flow between the grd and the PV system and possblty to realze the Maxmum Power Pont Trackng (MPPT) of the PV panels. The MPP algorthm s based on the constant voltage method that s acheved by keepng the voltage n the PV termnals constant and close to the MPP [12], [13], as per Fg. 4. Fg. 3. Smplfed crcut from AC output. di12 V12 = L + D12 V + R I12 dt di23 V23 = L + D23 V + R I23 dt di31 V31 = L + D31 V + R I31 dt Applyng dq0 transformaton and developng the equatons system (1), t s possble to fnd the dfferental equatons (2), whch descrbe the currents behavor n axs d and q. did 3 Vp V R Id = ω Iq + Dd dt 2 L L L (2) diq V R Iq = ω Id Dq dt L L The drect axs current depends on the quadrature axs current and vce-versa. In order to decouple ths dependence, a new duty cycle was defned and t s presented n (3). ω L D ' d = Dd Iq V ω L D ' q = Dq + Id V If Dd ( t ) and Dq ( t ) were solated n (3), t s possble to rewrte (2) as follow: did 3 Vp V R Id = D' d dt 2 L L L (4) diq V R Iq = D ' q ( t ) dt L L Developng these equatons, t s obtaned the dfferental equatons that show the behavor of the currents n axs d and q as functons of the duty cycles. So, the transfer functons used n the desgn of the current controllers are shown n (5). d V = d ' d s L + R q V = d ' q s L + R (1) (3) (5) Fg. 4. Example of the current and voltage characterstcs of a PV cell. Observng the MPP ponts (MPP Lne), t s possble to notce that the voltage values vary very lttle even when the ntensty of the solar rradaton suffers great alteratons. Concern to the temperature, fortunately, the regon n Brazl, whch ths system s mplemented, the temperature has no mportant varaton durng the day. So, the expermental tests showed that ths MPP technque can be used, n ths case, wthout any problem. Wth the voltage clamped n a value nsde of the MPP Regon, when a varaton of the solar rradaton happens, the ntensty of the PV cell current also change, however the output voltage of the PV cell wll not be altered. Thus, t s necessary to obtan the transfer functon of nput voltage V as functons of axs d and q currents. The control voltage across capactor C s obtaned consderng the DC nput shown n Fg 2. The equvalent crcut n dq0 axs seen by the DC sde s shown n Fg. 5. Fg. 5. Equvalent crcut seen by the DC sde. In ths equvalent crcut, I(t) represent the current suppled by PV panels (7) and I (t) represents the nput nverter current (8). The transfer functon between the voltage v (s) and the nput current of the nverter (s) s shown n (9). I = I + I (7) C I = I D + I D (8) d d q q

3 v 1 = (9) s C C Developng and substtutng approprately the equatons, t s possble to obtan the desred voltage control modellng. The equatons v (s) as functon of currents n axs d and q are shown n (10) and (11), respectvely. Where: v 1 3 Vp = ( K L s) 2 K R + d s C 2 V v 2 Q L s + 2 R = q 3 V Vp s C L, R - Equvalent resstances and nductances C - Input capactor V p - Voltage peak of grd V - Input voltage d, q - Currents n the axs d and q P - Actve power Q - Reactve power III. K = 2 P V V 3 p (10) (11) IMPLEMENTATION OF THE CONTROL METHODOLOGY Fg. 6 shows the dagram of the control methodology and the modulaton of the proposed three-phase grd-connected PV system. The practcal mplementaton of ths control strategy has been mplemented wth DSP (Dgtal Sgnal Processng) and a zero cross detector crcut to make the synchronsm method wth the grd. As can been seen from Fg 6, the nverter output currents (I 1, I 2 and I 3 ) and the load currents (I 1c, I 2c and I 3c ) are acqured through sensors. In the lne currents t s appled dq0 transformaton. A. Current control strategy To control the currents of the axs d, the current I d (t) and the reference currents I dref1 (t) and I dref2 (t) are used, accordng to Fg. 7. The sgn I dref2 (t) represents the current load I dc (t) alternate porton of the drect axs d and t s obtaned through a hgh-pass flter (Fg. 8) [14]. Ths s necessary to compensate possble power unbalances n the system, and t has negatve sgn so that the power flows n opposton to the load. Fg. 7. Block dagram of the current control n the d axs. Fg. 8. I dref2 (t) obtanng. To control the currents of axs q (Fg. 9), a reference sgnal I qc (t) s used to compensate the reactve power caused by the load connected to the system. Fg. 9. Block dagram of the current control n the axs q. In the output of both controls (d and q axs) ts necessary to accomplsh a uncouplng n order to obtan the duty cycles d d (t) as functon of d (t) and d q (t) as functon of q (t). Fg. 6. Dagram of the control system.

4 B. Voltage control strategy The voltage n the capactor C s compared wth the reference voltage V ref and the error sgnal enters n the voltage controller resultng n the sgnal I dref1 (t) (Fg. 10). B. Smulaton Results Several numercal smulatons of the proposed system were accomplshed for dfferent stuatons of load connected n ths system (lnear and non-lnear). The most mportant parameters of the converter are shown n Table 2. Fg. 10. Dagram of the voltage regulator Ths sgnal I dref1 (t) s used as one of the references n the current control loop of the drect axs d, guaranteeng that voltage V (t) keeps clamped at the desred value, as shown n Fg. 11. Parameters P = 12.6 kva V= 700 V Vout= 220 V fr= 60 Hz fs = 20 khz R = 0.57 Ω L = 1.92 mh C= 2.7 mf TABLE II SIMULATION PARAMETERS Descrpton - Converter Power - Input Voltage (DC) - RMS Output Voltage (grd) - Grd Frequency - Commutaton Frequency - Output nverter equvalent resstor - Output nverter equvalent nductance - Input Inverter capactor IV. Fg. 11. Block dagram of the voltage control. SIMULATION AND EXPERIMENTAL RESULTS A. PV array desgn To valdate the proposed methodology for grd-connected PV generaton system, a 12 klowatts PV array was desgn usng Kyocera KC50, connected n a proper seres-parallel confguraton. Table 1 shows the man characterstcs of the PV array, that was desgn to 700 Volts photovoltac output voltage and 18 Amperes of current. The equvalent crcut smulated s shown n Fg. 12. The smulaton wth lnear loads was done and good results were obtaned to several load parameters. However, to show a better performance of the system proposed, only the results consderng non-lnear loads connected to the system are presented. The performance of the reactve power compensaton and harmoncs current elmnaton s better observed when non-lnear load tests are done. The non-lnear load presented n ths work s a three-phase brdge rectfer wth RC output, shown n Fg. 13. Fg. 14 presents the three grd currents and the nput voltage V (t) behavor for several stuaton of abrupt varatons of the current suppled by the PV panels. It s seen that the grd nput currents always has a snusodal shape. TABLE I PV ARRAY SPECIFICATIONS USING KYOCERA KC50 PANELS Total peak power 12.6 kw Number of seres strngs panels - Ns 42 Number of paralel Np 6 Number of PV panels 252 Corrent peak 18 A Voltage n maxmum power V Corrent: short crcut 18.6 A Voltage: open crcut 903 V Fg. 13. Non-lnear load smulated In the proposed photovoltac array modelng, the DC voltage source represents the open crcut voltage of all seres photovoltac modules, whle de dode mposes ts semconductor characterstc. Fg. 12. PV Array smulated crcut. Fg. 14. Three grd currents and the nput voltage. Fg. 15 shows n the phase 1 the grd voltage, grd current,

5 load current, output nverter current and nput voltage V (t) behavor, when a varaton of the current suppled by the PV panels occurs at the nstant t=150ms. Even wth non-lnear load, the grd currents are snusodal and the voltage control mantans the desred level of 700V. The grd nput current waveform s snusodal and s 180 out of phase to the grd voltage. Ths stuaton means that the grd s recevng energy. Fg. 17. Current spectrum harmonc: Grd and load n the phase 1. Fg. 15. Grd voltage and current (phase 1), Load current and output nverter current (phase1); and Input voltage. Fg. 16 shows the behavor of the current and voltage n phase 1 of the grd, when an abrupt varaton of the current suppled by PV panels occurs. In ths case the energy suppled by the PV panels becomes null at the nstant t=300ms and t returns to the nomnal value at nstant t=450ms. In the absence of energy suppled by the PV panel, the converter only acts as an actve power flter. The nverter output current and the PV current are also shown n Fg. 16. Even wth ths abrupt varaton, the power factor n phase 1 s very hgh n both cases;.e., when there s solar rradaton (grd recevng energy) and n the perods when there s no energy suppled by the PV panels. Fg. 16. Current and voltage n the phase 1 PV current and output current nverter of phase 1. To prove the structure operaton as actve power flter, Fg. 17 shows the grd and load current harmonc spectrum n the phase 1. It was verfed that usng the control strategy, the harmonc components of the grd current are elmnate. Fg. 18 shows the actve power flux n the: grd, load, PV array and converter, for verfyng the control strategy performance for several solar condtons. At the same fgure t s possble to observe that the load actve power remans constant and can be suppled by PV array or by the grd. The grd actve power s negatve when the grd s recevng energy. Fg. 18. Actve Power: Grd, load, PV and converter to several solar condtons. C. Expermental Results To demonstrate the feasblty of the dscussed PV system, a prototype was desgned and mplemented followng the specfcatons presented n Tables 1 and 2. The PV array was desgn to 500 Volts photovoltac output voltage.. Fg. 19 depcts n the phase 1 the utlty voltage (V Utlty ), the Non-lnear load current (I L ) and utlty current (I S ) wth the system operatng just n the actve power lne condtonng mode (cloudy day or nght). The THD of I S s 2.8% for a load crest factor of 2.8, and the PF=0.97. Fg. 20 shows the utlty voltage and the utlty current n the phase 1, wth the system only supplyng power to the utlty grd (THD = 2.5% and PF = 0.98). In ths case no load s connected n the PV system. Fg. 21 presents the performance of the utlty voltage and utlty current (THD = 2.8% and PF = 0.978) wth a 50% of non-lnear load connected between the PV system and the commercal electrc grd.

6 It s mportant to emphasze that for both stuatons the power factor s always hgh and the currents present low harmonc dstorton. Due to a lttle varaton of the temperature n the regon where the PV panels s mplemented, an nput voltage clampng technque s used to assure the maxmum power pont (MPP) of the PV panels. To valdate the structure operaton some smulaton and expermental results were presented and they show the vablty of the proposed model, as well as the control strategy used for the PV systems. Fg. 19. Utlty current (I S), Load current and utlty voltage (V Utlty) (Ch1 and Ch2 20A/dv and Ch2 50V/dv). ACKNOWLEDGMENT The authors would lke to thanks the CNPq and FINEP by the fnancal support. The authors also wsh to thank the engneer Marco Slvera Ortmann for ther support durng the expermental tests. REFERENCES Fg. 20. Utlty current (I S) and utlty voltage (V Utlty) wth no load. (Ch1 10A/dv and Ch2 50V/dv). The effcency curve of the whole system s shown n Fg. 22. Fg. 21. Utlty current (IS) and utlty voltage (VUtlty) wth 50% of nonlnear load. (Ch1 5A/dv and Ch2 50V/dv). Fg. 22. Effcency curve of the whole system. V. CONCLUSION Ths paper has presented n a smple way the modellng and the control strategy usng dq0 transformaton of a three-phase PWM nverter to be employed n a grd-connected photovoltac generaton system. The man focus of ths work s to realze a desgn of a dual functon system that would provde solar generaton and works as an actve power flter, compensatng unbalances of power and the reactve power generated by other loads connected to the system. [1] O. Wasynczuk, N. A. Anwah. Modelng and dynamc performance of a self-commutated photovoltac nverter system. IEEE Transactons on Energy Converson, vol. 4, Issue 3, pp , [2] W. Bohrer, M. Carpta, T. Ghara, L. Pugls. A flexble control strategy to nterface solar system wth prvleged load and utlty lne. Electrotechncal Conference Proceedngs. Integratng Research, Industry and Educaton n Energy and Communcaton Engneerng, MELECON '89, Medterranean 11-13, pp , [3] N. Mohan. A novel approach to mnmze lne-current harmoncs n nterfacng renewable energy sources wth 3-phase utlty systems. In: Appled Power Electroncs Conference and Exposton, APEC '92. Conference Proceedngs, Seventh Annual, pp , [4] S. Nonaka. A novel three-phase snusodal PWM voltage source nverter and ts applcaton for photovoltac power generaton system. In: Power Converson Conference - Nagaoka, Proceedngs of the vol. 2, pp , [5] I. H. Hwang, K. S. Ahn, H. C. Lm, S. S. Km. Desgn, development and performance of a 50kW grd connected PV system wth three phase current-controlled nverter. In: Photovoltac Specalsts Conference, Conference Record of the 28th IEEE, pp , [6] C. Cecat, A. Dell'Aqula, M. Lserre. A novel three-phase sngle-stage dstrbuted power nverter. IEEE Transactons on Power Electroncs, vol. 19, Issue 5, pp , [7] I. S. Km. Robust maxmum power pont tracker usng sldng mode controller for three phase grd connected photovoltac system. Solar Energy 81, pp , [8] Carlett, R.L., Lopes, C.G., Barbosa, P.G., Actve & reactve power control scheme for a grd-connected photovoltac generaton system based on VSI wth selectve harmonc elmnatons. In: 8 th Power Electroncs Brazlan Conference, COBEP, Recfe, pp [9] F. A. Farret, M. G. Smões. Integraton of alternatve sources of energy. A Wley-Interscence publcaton. IEEE, Copyrght 2006 by John Wley & Sons, Inc, [10] M. C. Cavalcant, G. M. S. Azevedo, K. C. Olvera, B. A. Amaral, F. A. S. Neves, Z. D. Lns. A grd connected photovoltac generaton system wth harmonc and reactve power compensaton. In: 8 th Power Electroncs Brazlan Conference, COBEP, Recfe, pp , [11] D. Borgonovo. Modellng and control of the three-phase PWM rectfer usng park transformaton. Master Dssertaton n Electrcal Engneerng, Floranópols, Brazl INEP, UFSC, [12] R. Demont. Photovoltac panels electrc energy management. Ph.D. Thess, Floranópols, Brazl INEP, UFSC, [13] M. J. Case, J. J. Schoeman. A mnmum component photovoltac array maxmum power pont tracker. In: European Space Power Conference, Granz, Austra, pp , [14] A. S. Moras, I. Barb. Power redstrbutor appled to dstrbuton transformers of the electrcal energy. In: XVI Brazlan Automaton Conference, CBA, Salvador, Brazl, pp , 2006.