ANALYSIS OF PUMPED HYDROELECTRIC STORAGE FOR A WIND/PV SYSTEM FOR GRID INTEGRATION


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1 ANALYSIS OF PUMPD HYDROLCTRIC STORAG FOR A WIND/PV SYSTM FOR GRID INTGRATION G. Notton, V. Lzro, L. Stoyno Abstrct: This pper dels with the pumping storge system nlysis. The wter reseroir seres for dily nd sesonl energy storge, thus bsiclly soling the problem of energy storge, which is the biggest problem of wider use of renewble energy sources. The electricl energy produced in excess by the renewble energy system is conerted in potentil energy by pumping wter to higher eletion where it cn be stored indefinitely nd then relesed to pss through hydrulic s nd generte electricity. The estimtion of the stored energy, the nominl electricl power of the hydroelectric plnt nd the eportion rte of the wter reseroir is presented. Keywords: solr energy; wind energy; hybrid systems; pumped storge. 1. INTRODUCTION In smll electricl grids with limited or no connectiity to lrge scle power system some difficulties pper s to keep control of oltge nd frequency. In such n isolted system, we note numerous network filures nd limittion of the renewble energy prt due to the rndom nture of the solr nd/or wind source. Thus the inititie to diersify the energy sources is hindered. This is the cse with the Corsic Islnd in the Mediterrnen Se, which is not connected to the French minlnd electricl grid (nd only smll connection with Srdini). The combintion of renewble resources with energy storge cn be solution becuse it cn increse the lue of photooltic (PV) nd windgenerted electricity, mking supply coincident with periods of pek consumer demnd. nergy storge systems he different ppliction s to follow lod, stbilize oltge & frequency, mnge pek lods, improe power qulity, defer upgrde inestments, nd support renewbles. Fig. 1. sho the power nd dischrge time requirements for riety of storge pplictions in the utility industry. Storge time (minutes) Commodity 1 h Storge T&D Fcility Deferrl Customer nergy T. Voltge Mngement Rpid Resere 1 h Regultion Are Control & Frequency Renewble nergy Mngement Responsie Resere 1 mn Power Qulity & Relibility Trnsmission 1 s System Stbility 1 ms Storge power requirements (kw) Fig. 1. Power nd dischrge time requirements for riety of storge pplictions. OVRVIW The pumped storge is system of generting electricity, lso known s hydroelectric storge, which uses wter tht hs been pumped into n eleted reseroir during the hours of low consumption to generte electricity during hours of pek demnd. This type of hydroelectric system is used by some power plnts for lod blncing. The method stores energy in the form of wter (potentil mechnicl energy) from lower eletion reseroir to higher eletion. In conentionl electricl system, the lowcost offpek electricl 64
2 power is used to run the pumps nd the stored wter is relesed during periods of high electricl demnd, generlly with cost benefit. In Renewble energy system, t time of low electricl demnd, excess genertion power produced by the renewble energy system (wind nd/or photooltic system) is used to pump wter into higher reseroir nd then, when there is higher demnd, the wter is relesed bck in the lower reseroir through, generting electricity. There re two possibilities:  two wter wys: one for the pumping, the other for the ;  one unique wter wy : reersible mchinery (usully Frncis Turbine design) (Fig. ) is used for both pumping nd generting; it is designed s motor nd pump in one direction nd s nd genertor in opposite rottion (Fig. 3) Fig.. A Frncis Turbine Fig. 3. Schemtic of conentionl pumpedstorge deelopment with one reersible pump. The sttion is locted underground if the geologicl conditions re fourble, otherwise it is situted on the lower reseroir. Vrious pumped storge plnts exist worldwide with power from bout 1 MW (RH Lepenic, 1985, Croti) to 7 MW (Knngw, 5, Jpn) [1]. Pumped hydro is ilble t lmost ny scle with dischrge times rnging from seerl hours to few dys. The dntges of such systems re []:  More thn 1 yers of experience;  High efficiency: in the 7% to 85% rnge.  Multipurpose fcilities;  nironmentl friendly;  CO  oiding;  Highest ilbility compred to other technologies;  Quick response to lod rition (some seconds) nd resere cpcity. Tking into ccount eportion losses from the exposed wter surfce nd conersion losses, pproximtely 7% to 85% of the electricl energy used to pump the wter into the eleted reseroir cn be regined. A comprison of rious storge mens is shown in Fig. 4 [3, 4] in term of rtings. We note tht hydropumped system (PSH) is dpted for high rted power (4 to 4 MW) with high dischrge time between 1 nd 1 hours. 65
3 P S H Екологично инженерство и опазване на околната среда, No 1, 11, с The cpitl cost is n importnt economic prmeter, so the totl ownership cost (including the impct of equipment life nd O&M (Opertion & Mintennce) costs) is n interesting index for complete economic nlysis. A comprison from n economic point of iew of the energy storges is shown in Fig. 5 [3]. The cost of PSH system is between 1 nd $/kw. 1 CAS Compressed ir NS Sodiumsulfur L/A Led cid NiCd Nickelcdmium VR Vndium redox LiIon Lithium Ion ZnBr Zincbromine NiMH Nickelmetl hybride FW Flywheels DLC Dbllyer cpcitors NS Sodiumsulfur PSH Pumped hydro 1 VR NS CAS Dischrge Time (hr) Dischrge Time (hr) NiMH LiIon ZnBr FW NS NiCd L/A.1 DLC Rted Power (MW) Rted Power (MW) Fig. 4. Storge systems rtings [3] Cpitl cost per unit energy ($/kwh) High power C Cpcitor High power FW Liion Long durtion NiCd FW btteries Zincir Ledcid NS btteries btteries btteries Long durtion Flow btteries C cpcitor PSH CAS Metlir btteries Cpitl cost per unit power ($/kw) Fig. 5. Storge systems costs [3]. fficiency nd cycle life re two importnt prmeters to consider long with other prmeters. Both of these prmeters ffect the oerll storge cost. Low efficiency increses the effectie energy cost s only frction of the stored energy could be utilized. Low cycle life lso increses the totl cost s the storge deice needs to be replced more often. The present lues of these expenses need to be considered long with the cpitl cost nd operting expenses to obtin better picture of the totl ownership cost for storge technology. Fig. 6. illustrtes this influence for rious storge technologies. The lifetime (for depth of dischrge (DOD) 8%) for such pumped hydro system is one of the highest ilble with storge mens. Percycle cost cn be the best wy to elute the cost of storing energy in frequent chrge/dischrge ppliction, such s lod leelling. 66
4 Fig. 7 sho the cpitl component of this cost, tking into ccount the impct of cycle life nd efficiency. For more complete percycle cost, one needs to lso consider O&M, disposl, replcement nd other ownership expenses, which my not be known for the emerging technologies. We note tht the cpitl cost per cycle is lrgely lower thn for other existing storge systems. There is oer 1 GW of pumped storge in opertion world wide, which is bout 3 % of globl genertion cpcity (3 GW in urope, 1 GW in Jpn, 19.5 GW in USA, nd others in Asi nd Ltin Americ) [57]. Pumped storge plnts re chrcterized by long construction times nd high cpitl expenditure. 1% 9% Liion NS.C cpcitor Fly Wheels fficiency 8% 7% 6% LedAcid Flow Bt NiCd PSH CAS 5% Metl ir 4% Lifetime Lifetime t 8% t 8% DOD  Cycles Fig. 6. Life efficiency of rious storge systems [3]. Fig. 7. Percycle cost for rious storge systems [3]. Pumped storge is the most widespred energy storge system in use on power networks. Its min ppliction is for energy mngement, frequency control nd proision of resere. 67
5 3. APPLICATION WITH RNWABL NRGY SYSTM Using hydropumped storge llo to improe the qulity of the proided electricity nd to reduce the pek power of the other energy generting systems. This system flttens out the lod rition on the power grid, nd permits therml power sttions tht proide bselod electricity to continue operting t pek efficiency while reducing the need for peking power plnts tht use costly nd polluting fuels. Moreoer, pumped storge system helps control electricl network frequency nd proides resere genertion. Therml plnts re much less ble to respond to sudden chnges in electricl demnd, potentilly cusing frequency nd oltge instbility. The hydropumped system cn respond to lod chnges within seconds. These mchines generte in synchroniztion with the network frequency, but operte synchronously (independent of the network frequency) s motorpumps. A new use for pumped storge is to leel the fluctuting output of intermittent power sources. The pumped storge bsorbs lod t times of high output nd low demnd, while proiding dditionl pek cpcity. In certin jurisdictions, electricity prices my be close to zero or occsionlly negtie (Ontrio in erly September, 6), indicting there is more genertion thn lod ilble to bsorb it; lthough t present this is rrely due to wind lone, incresed wind genertion my increse the likelihood of such occurrences. It is prticulrly likely tht pumped storge will become especilly importnt s blnce for ery lrge scle photooltic genertion. The principle is illustrted in Fig. 8. Fig. 8. Principle of coupling between renewble energy sources nd hydropumped system. The typicl oerll efficiency of hydrostorge systems is between 65% nd 77% [4, 8] with mximum depth of dischrge up to 95%. Kldellis et l [4] showed tht this type of system for islnd utonomous electricl networks is the optiml solution for big size islnds nd for smll nd medium sized islnds; it ppers to be the best solution for utonomy of 4 hours. 4. STORD NRGY AND MACHINS POWR STIMATION The reltie low energy density of pumped storge system requires either lrge body of wter or lrge rition in height. For exmple, 1 kg of wter (1 m 3 ) t the top of 1 m tower hs potentil energy of bout.7 kwh. The only wy to store significnt mount of energy is by hing lrge body of wter. We consider the system presented in Fig. 9. The deeloped excel softwre estimtes the stored energy nd the nd pump pek powers for gien cse study. The input dt re:  upper tnk ltitude: h upper  lower tnk ltitude: h lower ;  pump or ltitude h pump or h ;  the wter tnks olume V;  the length nd dimeter of upstrem nd downstrem tubes: L 1, L, D 1, D ;  the mximum wter flow rte into the nd the pump (or the reersible pump) Q pump, Q ;  the roughness height of the tube ε (equl to.1 mm) 68
6 h upper pump,1 L 1, D 1 V turb,1 Pump h pump Turbine pump, h turb V turb, L, D h lower Fig. 9. Schemtic presenttion of the studied system. We clculte:  the mximum wter speed in ech tube: pump,1,,1 : pump ( π ) ( π ), 1 = 4Q pump D 1 nd, 1 = 4Q D 1 (1)  the Reynold number nd the flow regime with υ is the kinemtic iscosity tken equl to m/s²: R e.d ν nd pump = pump R e.d ν () =  the Drcy friction fctor λ clculted using the SwmeeJin eqution [9] which estimtes Colebrook eqution with 5% error nd gien by : ε λ =. 5 Log (3).. D Re  the DrcyWeisbch coefficients J 1 nd J (m) gien by : L1 1 L J1 = λ 1 nd J = λ (4) D1 g D g  the mnometric height t ech tnk H upper nd H lower : ptm H upper = hupper + nd ρg ptm H lower = hlower + (5) ρg where p tm is the tmospheric pressure ( P) nd ρ the wter density (1 kg.m 3 )  the mnometric heights upstrem nd downstrem of the pump nd the re gien by : H down, up, = H J (6) lower upper 1, H = H + J (7), H down,pump up,pump = H J (8) upper lower pump, H = H + J (9) pump,1  the hydrulic power of the pump nd the re gien by : P,hydrulic P P pump,hydrulic ( H down, H up, ) Q ( H up,pump H down,pump ) Q pump = ρ g (1) = ρ g (11)  the electricl powers re gien by :,elec P pump,elec = P η η (1),hydrulic pump,hydrulic ( η η ) pump motor lterntor = P (13)  the gross stored energy, generted by the reseroir, is [1]: gross ( H H ) = ρ g (14) upper lower  the totl dily hydrulic energy (kwh) which the renewble system cn produce t the outlet of the pumping system is obtined by [1]: H, dily ( H down, H up, ) 1 g = ρ (15) 3 Q ( m / dy) 5. WATR TANK VAPORATION RAT STIMATION Fig. 1 sho the principle digrm of the renewble plnt with chrcteristic elements. For clculting the hydrulic blnce of the pump/ system, seerl physicl dt re needed or must be clculted s:  eportion rte  wtershed flow rte  infiltrtion To determine the eportion rte, which cn be importnt prticulrly in rid or sunny res, the min prmeters to clculte re: 69
7  the conectie het trnsfer coefficient h c ;  the mss trnsfer coefficient K  the wter surfce temperture T  nd finlly the eported wter rte. A study mde by Srtori [11] sho tht rious methods re ilble to clculte the eportion flow rte. It hs been shown tht the reltie humidity must be tken into ccount for better ccurcy. A similr more recent work [1] confirms the ribility of the results obtined by the rious models. In this work, the eportion rte estimtion must sty simple becuse its influence on the energy system behiour is not importnt enough to necessitte ery thorough work. Power Sttion Q WSU (i) Q PRU (i) Q VU (i) nergy consumption LOAD (i) PV plnt Φ SUN (i) Wind energy plnt (i) PS (i) PSD (i) PSP (i) T (i) PV (i) Upper reseroir Q INFU (i) Q P (i) Q WSL (i) Turbine/ QPRL (i)q VL (i) lterntor Q T (i) PVD (i) PVP (i) WTD (i) WT (i) WTP (i) Pump P (i) Q INFL (i) Lower reseroir Fig. 1. Principle digrm of the renewble plnt with chrcteristic elements Wtmuss et l [13] suggested to use s conectie het trnsfer coefficient the following expression: h c = (16) with the wind speed. The uthors conerted this eqution tking into ccount tht the wind speed is generlly mesured t 1 m height. Their fitted eqution becme: h c = (17) q. (17) is used in this work. The mss trnsfer coefficient, s expressed by the exct form of Chilton Colburn nlogy my be written s follo [14]: K hc = β with ρc p.67 pt Pr β = (18) P Sc P nd P T re respectiely the prtil pressure of ir nd the totl pressure. The simplified form of ChiltonColburn Anlogy ssumes the rtio of Pr to Sc is equl to one nd ignores the effect of wter pour pressure on the prtil pressure of ir (P =P T ). Under such condition, β will be equl to 1 nd eqution (18) simplifies to: K c ( ρc ) = h (19) p This simplifiction is clled the Lewis hypothesis, only lid for the ir nd used by Belrbi nd Sïghi [15] to estimte the eportion rte of wter surfce. The sturted nd prtil wter pour pressures (in P) re gien by [1]: P, w 177. ( ) ( T ) T = exp ( T ) P ( T ) h P ( T ) s () = (1) r s, w The wter density nd its specific het cpcity depend on the bsolute humidity X nd re gien by: P( T) X =. 61 () P P T [ T ( )] ( T ) p ( T ) pt p ρ = + (3) 87. 5T T C = C + XC (4) p p,w p,dryir 7
8 The eportion from wter body is estimted s the difference between energy inputs nd outputs mesured t site. The energy loss through eportion represents mjor component of the energy blnce in typicl wter body. The temperture of the wter surfce is clculted from n energy blnce [1517]: R = L + H G (5) n w, + A prt of the rdition R n is used to eporte the wter ilble t the wter surfce nd cretes the ltent het flux L w, where is the eportion rte nd L w, the ltent het of wter poriztion. The rest is dissipted in het into the ir by conection (H sensible het) or stored into wter (G conductie het flux). The wter ltent het flux for poriztion is expressed from Hrrison formultion [18]: 3 w L, = T (6) The storge of the het into the wter during one hour period is generlly smll compred with the other het fluxes [1516] nd G cn be neglected. Then q. () becomes: R R = L H (7) n w, + n 4 4 ( α ) R + εσ ( T 6) εσt = (8) 1 g with R g, the globl solr rdition, α the lbedo of the wter surfce (.8) [19], ε the wter surfce emissiity (.98) [] nd σ the StefnBoltzmnn constnt, T sw nd T re the wter surfce nd ir tempertures. c ( T T ) H = h (9) The ltent het flux is clculted by the Stefn method (simplified expression of the Fick theory) bsed on the mss trnsfer or bulk trnsfer theories. L w, L K w, w = [ P ( T ) P ( T )] (3) RT M s,w with M w, the moleculr mss, P s,w sturted wter pour pressure nd P wter pour prtil pressure. Thus, in replcing equtions (8), (9) nd (3) into eqution (7), the energy blnce becomes: 4 4 ( 1 α) R + εσ( T 6) εσt h ( T T ) L w, K RT g M w [ P ( T ) P ( T )] s, w c = (31) Thus, we cn clculte, using method of dichotomy, the wter surfce temperture t ech hour, from the following mesured dt :  wind speed  mbient temperture T  reltie humidity h r  horizontl globl irrdition R g The next step consists in estimting the eportion rte nd rious methods re ilble to rech this gol with more or less precision. Seerl formultions he been compred [111]. We decided to use for our study the Penmn method which is bsed in physicl principles nd gies lues tht should sere for most project studies [1516, 19]. The Penmn formule cn be expressed by: L = R + γ n + h c ( Ps,w ( T ) P ( T )) ( + γ ) (3) where γ is the psychometric constnt gien by [19]: ( 168. P ) L w, γ = 6 (33) is the slope of pour pressure ersus temperture cure gien by [1516]: ( P ( T ) P ( T )) ( T T ) = (34) s,w s,w From hourly meteorologicl dt of Ajccio (wind speed, solr irrdition, mbient temperture nd reltie humidity), we clculted the eportion rte. The results for one yer re presented in Fig. 11. We note tht sometimes during the night the eportion is negtie i.e. the wter surfce temperture is below the dew point temperture nd condenstion occurs. At lst, we estimted the monthly erge lues of the dily eportion rte with the meteorologicl dt for two sttions Ajccio (Frnce) nd m. Bote (Bulgri) with colder climte (Fig. 1). We note tht the eportion phenomenon is not negligible nd influences the energy blnce of the system. 6. CONCLUSION The pumping storge is the most widely implemented lrgescle electricl energy storge. PHS is mture technology with lrge olume, long storge period, high efficiency nd reltiely low cpitl cost per unit of energy. We estimted the stored energy nd the pump nd pek powers ccording to the chrcteristic of the wter storge. Then, the influence of the eportion phenomenon t the wter surfce hs been estimted. This work gies n ide for some procedures in the pumping storge nlysis before its integrtion in electricl power system with renewble energy sources. 71
9 1 1 Hourly solr irridtion, portion rte Wind Speed (m/s) Reltie Humidity (%) Hourly Solr Irrdition (Wh/m²) Ambient Temperture ( C) Reltie humidity, wind speed, Ambient temperture Hour 1,4 1, portion Rte (mm/h) portion rte (mm/hour) 1,8,6,4, , Hour Fig. 11. Meteorologicl prmeters nd estimted eportion rte for Ajccio Dily Solr Irrdition, Dily eportion, Reltie humidity Dily Solr Irrdition (kwh/m²) Wind Speed (m/s) Ambient Temperture ( C) reltie humidity (x1%) 5 Dily portion Rte (mm/dy) Wind speed, Ambient temperture JAN FB MAR APR MAY JUN JUL AUG SP OCT NOV DC Dily Solr Irrdition, Dily eportion, Reltie humidity Dily Solr Irrdition (kwh/m²) 1 Wind Speed (m/s) Ambient Temperture ( C) reltie humidity (x1%) Dily portion Rte (mm/dy) JAN FB MAR APR MAY JUN JUL AUG SP OCT NOV DC Fig. 1. Monthly erge lues of the dily eportion rte for Ajccio nd Bote Wind speed, Ambient temperture 7
10 RFRNCS Pirker, O. (8) Role of storge nd pump storge hydro power plnts for grid regultion. nd urelectric Smll Islnds Seminr, April 8, Ajccio, Frnce. 3. lectricity Storge Assocition. (9) Kldellis, J.K., Zfirkis, D., Kdis, K.. (9). Technoeconomic comprison of energy storge systems for islnd utonomous electricl networks. Renewble nd Sustinble nergy Reie, 13, Chen, H., Ngoc Cong, T., Yng, W., Tn, C., Li, Y., Ding, Y. (9). Progress in electricl energy storge system: criticl reiew. Progress in Nturl Science, 19, Aherne, J. (4). Storge of electricl energy. Report on reserch nd deelopment of energy technologies. Interntionl Union of Pure nd Applied Physics, 4, p ilble t 7. Linden, S. (3). The commercil world of energy storge: reiew of operting fcilities (under construction or plnned). Proceeding of 1 st nnul conference of the energy storge council, Houston, Texs, Mrch, 3, D. Ppntonis. (1995). Hydrodynmic mchines: pumphydro s. nd d., Symeon: Athens. (in Greek). 9. Swmee, P.K.; Jin, A.K. (1976). "xplicit equtions for pipeflow problems". Journl of the Hydrulics Diision (ASC) 1 (5): Glsnoic, Z., Mrgetr, J. (9). The feture of sustinble solr hydroelectric power plnt. Renewble nergy, 34, Srtori. () A criticl reiew on equtions employed for the clcultion of the eportion rte from free wter surfces, Solr nergy, 681, pp ,. 1. McJnnet D.L., Webster I.T., Stenson M.P., Shermn B.S. (8) stimting open wter eportion for the MurryDrling Bsin : A report to the Austrlin Goernment from the CSIRO MurryDrling Bsin Sustinble Yields Project. CSIRO, Austrli. 5 pp. Noember Wtmuff J.H., Chrters W.W.S., Proctor D. (1977) Solr wind induced externl coefficients for solr collectors. COMPLS,, pp Frid M. () Miscoseptions in the nlysis of het nd mss trnsfer in drying nd frying. Drying Proceedings of the 13 th Interntionl Drying Symposium (IDS ) Beijing, Chin, 73 August, ol. A, pp Belrbi N, Sïghi M. (7). tude des trnsferts de chleur et de msse entre une surfce d eu d un brrge et l tmosphère. Appliction ux régions rides et semi rides en Algérie. 18 ème Congrès Frnçis de Mécnique, Grenoble, Frnce, 731 Août Belrbi N, Sïghi M. (7). tude comprtie des méthodes d élution du tux d éportion à prtir d une surfce d eu libre. Appliction ux régions rides et semi rides en Algérie. 13 ème Journées Interntionles de Thermique, Albi, Frnce, 83 Août Yu T.W. (1977) Prmetriztion of surfce eportion rte for use numericl modelling. J. Applied Meteorology, 16, Duffie, J. A. nd Beckmn, W. A. (1991). Solr engineering of therml processes. nd d., John Wiley nd sons, New York. 994 p. Hrrison, L. P Fundmentls concepts nd definitions relting to humidity. In Wexler, A (ditor) Humidity nd moisture Vol 3, Reinhold Publishing Co., N.Y. 19. Terzi O; Keskin. (5) portion estimtion using gene expression progrmming. J. Applied Sciences, 5(3), Infrred Serices Incorportion. (9). missiity lues for common mterils. Ailble t com/mteril1.htm. 73
11 АНАЛИЗ НА ПОМПЕНО АКУМУЛИРАЩА ВОДНОЕЛЕКТРИЧЕСКА ЦЕНТРАЛА КЪМ СИСТЕМА С ВЕТРОГЕНЕРАТОР И ФОТОВОЛТАИК ЗА ВНЕДРЯВАНЕ В ЕЛЕКТРИЧЕСКАТА МРЕЖА Ж. Нотон, В. Лазаров, Л. Стоянов Резюме: Тази статия има за цел анализ на помпено акумулираща водноелектрическа централа за запазване на енергия. Водният резервоар има за цел съхраняването на енергия за дни или сезони като по този начин се улесни разпространението на възобновяеми източници на енергия. Електричеството произведено в повече от хибридната система с възобновяеми източници на енергия се превръща в потенциална енергия посредством изпомпване на вода в горния резервоар, където тя може да се съхранява безкрайно много и в последствие да премине през хидравличната турбина произвеждайки електроенергия. Оценката на запасената енергия, на номиналните мощности на хидроенергийния възел и на загубите при изпаряване от водния резервоар са представени. Ключови думи: слънчева енергия, вятърна енергия, хибридни системи, запазване на енергия чрез изпомпване доц. Жил Нотон Изследователски център Виньола Корсикански Университет ЮМР ЦНРС 6134 рут де Сангинерс Ф Аячо, Франция Тел: Факс: имайл: доц. Владимир Лазаров Лаборатория по ВЕИ Електротехнически Факултет Технически Университет София бул. Кл. Охридски 8 1 София, България Тел: Факс: имейл: инж. Людмил Стоянов, докторант Лаборатория по ВЕИ Електротехнически Факултет Технически Университет София Изследователски център Виньола Корсикански Университет бул. Кл. Охридски 8 1 София, България Тел: Факс: имейл: Assoc Prof. Gilles Notton Reserch Centre of Vignol Uniersity of Corsic UMR CNRS 6134 route des Snguinires F Ajccio, Frnce Tel: Fx: mil: Assoc Prof. Vldimir Lzro Lbortory on Renewble nergy Sources Fculty of lectricl ngineering Technicl Uniersity of Sofi 8, Kl. Ohridski Bld. 1 Sofi, Bulgri Tel: Fx: mil: ng. Ludmil Stoyno, PhD student Lbortory on Renewble nergy Sources Fculty of lectricl ngineering Technicl Uniersity of Sofi Reserch Centre of Vignol Uniersity of Corsic 8, Kl. Ohridski Bld. 1 Sofi, Bulgri Tel: Fx: mil: 74
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