J. Electrical Systems 6-3 (2010): A COMPARATIVE STUDY ON PERFORMANCE IMPROVEMENT OF A PHOTOVOLTAIC PUMPING SYSTEM

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1 A. Betka A.Moui J. Electrical Sytem 6- (00): 6-5 A COMPARATIE STUDY ON PERFORMANCE IMPROEMENT OF A PHOTOOLTAIC PUMPING SYSTEM Thi paper ugget how an optimal operation of a photovoltaic pumping ytem baed on an induction motor driving a centrifugal pump can be realized. The optimiation problem conit in maximiing the daily pumped water quantity via the optimiation of the motor efficiency for any operating point, thi ha led to an optimum v-f relationhip ueful in controlling the motor. The voltage ource PWM inverter feeding the motor i controlled via the Harmonic Elimination or the Harmonic Minimiation trategie. The effectivene of the propoed algorithm i decribed by imulation where the obtained reult how that the Harmonic Minimiation technic allow at the ame time a notable improvement of the plant and an optimum matching of the ytem to the P generator. Thi lead to a implicity of impementation, bearing in mind that the MPPT circuit i omited. Keyword: Photovoltaic array, Pumping, Induction machine, PWM trategie, Optimization.. Nomenclature I Ic th Io R Iop op oc PM E tr t m r r rm x x xm x x l output generator voltage (v). generator current (A). generator hort-circuit current (A). thermic voltage (v). revere aturation current (A) erie generator reitance (Ω). optimum generator current (A). optimum generator voltage (v). open circuit voltage (v). maximum (optimum) generator power (w). inolation (w/m²). unrie time (h). unet time (h). rm motor voltage (v). tator reitance per phae (Ω). equivalent rotor reitance per phae (Ω). core lo reitance (Ω). tator leakage reactance (Ω). equivalent rotor leakage reactance (Ω). magnetizing reactance (Ω). tator cyclic reactance (Ω). rotor cyclic reactance (Ω). angular frequency of the upply (rd/). lip peed (rd/) motor peed (rd/). Correponding author : A. Betka Electrical Engineering Department, Bikra Univerity, Algeria betkaachour@gmail.com, Copyright JES 00 on-line : journal.ergroup.org/je

2 J. Electrical Sytem 6- (00):6-5 f p H H g Q motor frequency (Hz). pair pole number. total head (m). geodetic head (m). flow rate (m /h).. Introduction The upply of drinking water in remote area of unny region i one of the mot attractive application of the photovoltaic energy converion. Field experience with uch ytem in lat year have hown that depending on the ditance to exiting electricity grid, and on the power capacity level, photovoltaic pumping ytem have already etablihed itelf, technically and economically, a a real alternative to conventional ytem. ariou tudie were carried out uing conventional DC motor, Bruhle DC motor or induction motor. The objectif deal with izing, matching and optimiing the ytem performance. Different optimiation trategie have been propoed to improve the overall ytem efficiency, the array efficiency and flow-rate maximiation. The propoed cheme i a mall cale ytem in which the photovoltaic array i directly coupled to an induction motor driving a monocellular centrifugal pump. A comparative tudy on ytem performance i carried out, when the voltage ource inverter feeding the motor i controlled either by the called 'Optimal PWM technique', in which elected number of undeirable harmonic are permanently eliminated; or the called 'Harmonic Minimiation trategy'. The maximiation of the daily pumped amount of water i et to be the comparion bai. Thi i obtained by the minimiation of a non-linear criterion (optimiation of the motor efficiency) and via a proper adjutment of two liberty degree: the inverter frequency and the witching angle. Furthermore, the extracted electric power i controlled via the inverter frequency intead of the MPPT circuit. In order to invetigate the ytem performance, the paper will model each component prior to numerical imulation. While deriving the ytem model, ome aymption were made : the motor i uppoed to be unaturated. The loe in the inverter are uppoed negligible and the ytem i aumed to run in teady-tate. The paper i organized a follow : In ection variou part of the ytem are modelled. The propoed optimiation criterion for the two technique i preented in ection. Simulation reult and dicuion are decribed in ection.. Sytem Modelling: Figure. how a chematic circuit of the propoed ytem. It conit of a photovoltaic array, a voltage ource PWM inverter and a three-phae quirrel cage induction motor driving a monocellular centrifugal pump. The pecification of different component i illutrated in appendice. P Array model : The P generator conidered in thi tudy i a 6 erie connected module type AEG-0. The I- characteritic i expreed by [] : I I c RS.I -I0. exp - + th () 7

3 Betka et al.:performance IMPROEMENT OF A PHOTOOLTAIC PUMPING SYSTEM The I- curve i eentially influenced by the variation of two input: the olar inolation and the array temperature. The adaption of equation () for different level of olar inolation and temperature can be handled by the following equation []: ΔT T T r ( ) ΔI α E E r ΔT + ( E E r ) I c () Δ β Δ T R Δ I () r + Δ (5) Where the uffix r refer to rated condition given by E 000W/m and T 5 o C. k Fig. The P Pumping Structure S PWM Inverter Model : A voltage ource PWM inverter with a half bridge control i ued to drive the induction motor. The inverter witching occur at angle defined a α, α,., α m in a quarter-cycle of the period ince the waveform contain both half-wave and quarter-wave ymetry. A generalied form of the rm value of the k th harmonic voltage i given by []:. m i. +. (-). (n. αi ) k. π i C I Ir + ΔI S Inverter P Array PWM Control Centrifugal Pump where k i the harmonic order and m i the number of witching per quarter cycle. (6) (7) - Harmonic Elimination Method : In thi technique, the undeirable harmonic of a quare wave can be eliminated and the fundamental voltage component can be controlled. The number of the eliminated harmonic i (m-). In thi cae, the fundamental i to be controlled and the uppreed harmonic order are 5, 7 and. So m value are required. Thi yield the following equation : 8

4 J. Electrical Sytem 6- (00):6-5 m π - Harmonic Minimiation method : In thi method the total harmonic ditortion factor i minimied. The minimiation of thi quantity and the control of the fundamental are achieved by the approptiate poition of the four witching angle. The THD performance factor i defined a [] : Induction Motor Model : -.. ( α ) +. ( α ) ( α ) +. ( α ) ( 5. α ) ( ) α ( 5. α ) +. ( 5. α ) ( 7. α ) ( ) α ( 7. α ) +. ( 7. α ) (. α ) ( ) +.. α (. α ) +. (. α ) 0 α α α α The teady tate performance of the induction motor i modelled uing the conventional equivalent circuit hown in Fig.. m THD r n jx K jx m K Fig. Motor Equivalent Circuit k r m E a jx - - π r / (8) (9) ( 0) () () () From Figure., it can be hown that the electrical input power i given by : P. R. m ab eq Zeq Where Z eq i the equivalent input impedance per phae : Z eq R eq + j X eq () (5) The motor mechanical equation i expreed a : 9

5 Betka et al.:performance IMPROEMENT OF A PHOTOOLTAIC PUMPING SYSTEM Te r 0 T + T. where the electromagnetic torque T e i given by []: (6) T e.p.( m ) r - l. r x. r ( x.x - x ) l m m + x + l.r.x.r (7 ) and T r i the centrifugal pump load torque given by an aerodynamic equation in the form : where C i a contant which depend on the pump nominal data and T o i the friction coefficient. Centrifugal pump model : l Tr C - The head-flowrate Q-H characteritic of the ued mono-cellular centrifugal pump i obtained uing the Pfleider-Peterman model []. The multi-peed family of head-capacity curve can be expreed approximately by the following quadratic form: H where the motor peed i expreed a : l -. ( The H-Q characteritic of the pipe network can be expreed by []:. a 0. + a..q + a H H g + ψ.q The pump efficiency i defined a the ratio of the hydraulic power imparted by the pump to the fluid to the haft mechanical power and i given by :.Q (8) (9) 0) () Inolation Model : A implified model wa elaborated according to [], and which will erve a a firt aproximative quantification of the incidental inolation. Thi model quantifie the irradiance for a tandard clear day: 0 η p ρg HQ l C- E E M in (5.( t - t r π )). 80 () ()

6 J. Electrical Sytem 6- (00):6-5 where t r i the unrie time (choen a t r 6 h.00) Inolation (w/m²) day time (h) Fig. Daily inolation curve. Optimiation Criterion: In the centrifugal pump theory, it wa concluded that the improvement of the flowrate quantity i obtained by the maximiation of the mechanical power at the pump haft. In thi paper, Thi will be reached by the optimiation of a non-linear criterion repreenting the motor efficiency and by varying the four witching angle and the inverter frequency. Thi optimiation make poible determining the momentary value of the vector : optimiing the criterion: X [ l f I α α α α ] T () J max f (X) (5) - In the Harmonic Elimination Method, f(x) repreent the motor efficincy and i given by : l C.( - ).(.pi.f ).pi.f f (X) Ic - I + Io (th.ln ( ) I.R ). I I o Subject to the equality and inequalirty contraint : (6) g (X) 0 (7) - In the Harmonic Minimiation Method, the optimiing criterion J to be minimied i given by : J - f ( X) K. k + k k (8)

7 Betka et al.:performance IMPROEMENT OF A PHOTOOLTAIC PUMPING SYSTEM K i a weight factor, and the number of harmonic to be minimied i choen a k. In addition, the generator current I i limited a follow : 0 I I (9) c To optimie the extracted electric energy, the P array hould alway be operated cloe to it maximum output power. Thi will be obtained by etting up a linear relationhip between the generator voltage and frequency [] : f (0) The power balance of the ytem lead to the following expreion: I - I I Req + c o.ln I.R.I.. () th m I o Zeq In the cae of the Harmonic Elimination Method, the equality contraint are formed by the equation : (), (9), (0), (), (), (6) and (),and for the Harmonic Minimiation Technique they are formed by the et of the equation (), (), (6) and (0). Optimiation Method: The non-linear nature of the optimiation criterion (5) a well a of the contraint call for application of nonlinear programming method. At each iteration, the contrained problem (5) and (7) i tranformed to an other uncontrained one with linearied contraint. The olution i, then, carried out uing the Quadratic Programming Algorithm. The Heian Matrix updating i made by the formula of Broyden, Fletcher, Goldfarb and Shanno (BFGS) [5]. After performing the optimiation proce, the daily pumped water quantity i defined a : t D t r The unet time i choen a : t 8 h Simulation Reult : Qdt The imulation i carried out on a ytem compriing a uction and a delivery tank, that are eparated by a ingle pipeline. The volume of the two buffer tank are repectively :.88 m and 0.78 m, while the geodetic head of the plant i: H g 7. m. () Fig. through 9 diplay the ytem performance a function of inolation, which i conidered a the imulation input, and for the reference temperature T r 5 o c, uing the two control technique. Fig. depict the motor efficiency a function of olar inolation. It could be een that with the Harmonic Minimiation Method an optimum efficiency η m 70 % i permanently maintained. The control law given by equation (8) mainly govern the reduction of the frequency dependent loe (iron loe). In fact, thi repreent an advantage a far a the ytem working with the Harmonic Elimination Method i concerned, epecially for weak and medium inolation value. Fig. 5 how the pump flow rate obtained by equaliing equation (9) and (). The pump ucceed in overcoming the geodetic head H g and throw water in the delivery tank only when a certain peed i reached ( 00 rd/ in thi cae). The electric power threhold value correponding to thi limit i ome watt le than 00 w; about 0 % of the rated

8 J. Electrical Sytem 6- (00):6-5 motor power. Thi critical value i obtained at a threhold inolation level E th 0 w/m² for the ytem working with the Harmonic Minimiation Method, wherea the ytem with the Harmonic Elimination Method do not contribute to water yield unle the olar inolation exceed E th w/m². The olar radiation utiliability, defined a the ratio of the total inolation level that exceed the threhold value to the total available inolation over the day [5] i therefore improved : μ t i the hourly time when the inolation croe the threhold level. In addition, due to the proportionnality exiting between the mechanical power on the haft of a centrifugal pump and the flowrate [], the motor efficiency maximiation for the Harmonic Minimiation Method, lead to an increae of the flow-rate and conequently to a rie in the daily pumped quantity. By adopting the inolation model given by equation (), and according to numerical integration of equation (), the obtained daily water amount i : - D 6.0 m for the Harmonic Elimination Method. - D 9.5 m with the Harmonic Minimiation Strategy. Fig. Motor efficiency curve t - t t ( E - E ) t t r th E dt dt Fig. 5 Flow-rate curve () Fig. 6 how the improvement brought to the pump efficiency by the Harmonic Minimiation Strategy. A can be een, thi improvement i more notable at medium and weak inolation level. Thi increae inflict the two following parameter: - An increae of the total head H given by equation (9) a a reult of the friction and hock loe reduction inide the pump. - An increae of the flow-rate Q a a reult of the leakage flow-rate decreae []. Conequently, the hydraulic power (ρ.g. H.Q) i increaed. Fig. 7 illutrate the air-gap flux repreented by the quotient ( m /f) obtained with the Harmonic Minimiation Method. One can notice that the improvement of the motor efficiency i obtained by a field weakening, epecially for low inolation value

9 Betka et al.:performance IMPROEMENT OF A PHOTOOLTAIC PUMPING SYSTEM correponding to low motor peed, and hence to weak load torque. Thi reduced flux yield eentially a motor iron loe decreae, ince thi kind of loe i flux-depending. Fig. 6 Pump Efficiency characteritic Fig.7 Air-gap flux curve Fig. 8 diplay the output inverter frequency f for the two ytem. One notice that the frequency decreae once the inolation fall owing to the reduction of the motor loe that are frequency depending (iron loe). In Fig. 9 the generator Power oltage characteritic and maximum power locu are howed together with the conumed power of the two decribed ytem. It i clear that the extracted electric power for both the ytem with Harmonic Minimiation Method and Harmonic Elimination Method i extremely cloe to the maximum one, leading to an optimum matching of the load to the P generator, bearing in mind that in the propoed cae the MPPT block i omitted. Conequently, the implementation will be le expenive. Fig. 8 Inverter frequency curve Fig. 9 Electric Power characteritic In table, ome performance of the two conidered ytem obtained for a peak inolation level E 000 w/m² are ummaried. For an eventual implementation, the witching angle could be tored in look-up table and the correponding pule width are generated in the time domain with the help of down-counter

10 J. Electrical Sytem 6- (00):6-5 Table. Sytem Performance Control Method η m (%) THD (%) μ (%) α (rd) α (rd) α (rd) α (rd) H. E. T H.M. T Concluion: A comparative tudy of a mall cale photovoltaic pumping ytem baed on an induction motor driving a centrifugal pump wa preented in thi paper. The voltage ource inverter feeding the motor wa controlled via either the Harmonic Elimination Technique or the Harmonic Minimiation Technique The obtained imulation reult how that an increae of the daily pumped quantity and the pump efficiency are reached by the econd control technique for all the inolation range. In addition, the extracted electric power i no longer controlled via the MPPT block, but with the inverter frequency, allowing conequently to a le expenive implementation. Reference [] A. Betka, A.Moui Performance Optimization of a photovoltaic pumping ytem baed on an induction motor drive, Renewable Energy journal, ol 9, 00. [] J.M.D. Murphy and F.G. Turnbull, power Electronic control of AC motor, Pergamon Pre 985. [] K.Khouem and L.Khouem, optimum matching of direct-coupled electromechanical load to a photovoltaic generator, IEEE Tran on Energ Conv, ol 8, No., 99. [] R. Duzat, Analytic and Experimental invetigation of a photovoltaic pumping ytem, PhD work 000, Oldenburg Univerity Diertation. [5] R. Fletcher, A new Approach to variable Metric Algorithm, Computer Journal, ol., 970. Appendice : P generator parameter : Type AEG-0, Maximum power 6. w, Optimal current. A Optimal oltage 79. Open circuit voltage 58. Short circuit current. A Induction Motor parammeter: 80 I.5 A PKw x x 5.7 Ω r.5 Ω r 7.87 Ω x m 586 Ω r m.7 K Ω. Centrifugal pump parameter : Hm Q.59 l/ P5w N000 tr/mn. Pipe network : 0.06m H g 7.m 5