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


 Maximilian Jason Bruce
 11 months ago
 Views:
Transcription
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
The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O
IAPWS R7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More informationSimulations of the irradiation and temperature dependence of the efficiency of tandem photoelectrochemical watersplitting systems
SUPPORTING INFORMATION FOR Simultions of the irrdition nd temperture dependence of the efficiency of tndem photoelectrochemicl wtersplitting systems Sophi Hussener, Shu Hu, Chengxing Xing, Adm Z. Weber,
More informationNUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.
NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with
More informationFactors affecting the phonation threshold pressure and frequency
3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch
More informationA027 Uncertainties in Local Anisotropy Estimation from Multioffset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multioffset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationWindinduced vibration: a serviceability study
Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN 214 Porto, Portugl, 3 June  2 July 214 A. Cunh, E. Cetno, P. Ribeiro, G. Müller (eds.) ISSN: 231192; ISBN: 9789727521654
More informationFBR Neutronics: Breeding potential, Breeding Ratio, Breeding Gain and Doubling time
FBR eutronics: Breeding potentil, Breeding Rtio, Breeding Gin nd Doubling time K.S. Rjn Proessor, School o Chemicl & Biotechnology SASTRA University Joint Inititive o IITs nd IISc Funded by MHRD Pge 1
More informationFundamentals of Analytical Chemistry
Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electronpir cceptor (Lewis) hrcteristic
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationFreely propagating jet
Freely propgting jet Introduction Gseous rectnts re frequently introduced into combustion chmbers s jets. Chemicl, therml nd flow processes tht re tking plce in the jets re so complex tht nlyticl description
More informationSynoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?
Synoptic Meteorology I: Finite Differences 1618 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n1)/ E/[ n(n1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More informationDepartment of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Lecture 33. Psychrometric Properties of Moist Air
Deprtment of Mechnicl Engineering ME 3 Mechnicl Engineering hermodynmics Lecture 33 sychrometric roperties of Moist Air AirWter Vpor Mixtures Atmospheric ir A binry mixture of dry ir () + ter vpor ()
More informationTests for the Ratio of Two Poisson Rates
Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationCML: Series Low Resistance Chip Resistor Specification
CML: Series Low Resistnce Chip Resistor Specifiction 1. Scope This specifiction pplies to CML**** Series Low Resistnce Chip Resistor for use in electric equipment. *****METAL FOIL***** 2. Prt number CML
More informationThe Thermodynamics of Aqueous Electrolyte Solutions
18 The Thermodynmics of Aqueous Electrolyte Solutions As discussed in Chpter 10, when slt is dissolved in wter or in other pproprite solvent, the molecules dissocite into ions. In queous solutions, strong
More informationAPPLICATION OF WATER EQUIVALENTS METHOD TO CALCULATION OF CERAMIC HEAT EXCHANGERS
METALLURGY AND FOUNDRY ENGINEERING Vol. 35, 2009, No. 2 Krzysztof Krczewski* APPLICATION OF WATER EQUIVALENTS METHOD TO CALCULATION OF CERAMIC HEAT EXCHANGERS Nottion: c het cpcity of ir, kj/(m 3 K), c
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
More informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More informationDIFA, University of Basilicata, Italy
Guido Msiello nd Crmine Serio DIFA, Uniersity of Bsilict, Itly 1 Bsic methodologicl steps to retriee surfce emissiity Step 1: Represent emissiity with Fourier cosine truncted series to lower it dimensionlity
More informationPOLYPHASE CIRCUITS. Introduction:
POLYPHASE CIRCUITS Introduction: Threephse systems re commonly used in genertion, trnsmission nd distribution of electric power. Power in threephse system is constnt rther thn pulsting nd threephse
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More informationSimulation of Eclipsing Binary Star Systems. Abstract
Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.
More informationDetermination of the activation energy of silicone rubbers using different kinetic analysis methods
Determintion of the ctivtion energy of silicone rubbers using different kinetic nlysis methods OU Huibin SAHLI ohmed BAIEE Thierry nd GELIN JenClude FETOST Institute / Applied echnics Deprtment, 2 rue
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationOverview. Before beginning this module, you should be able to: After completing this module, you should be able to:
Module.: Differentil Equtions for First Order Electricl Circuits evision: My 26, 2007 Produced in coopertion with www.digilentinc.com Overview This module provides brief review of time domin nlysis of
More informationMinimum Energy State of Plasmas with an Internal Transport Barrier
Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University
More informationNUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL
NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL V. Bkhnov, O. Kryvook, B. Dormn Ukrinin Hydrometeorologicl Reserch Institute, Avenue of Science 37,
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More informationHT Module 2 Paper solution. Module 2. Q6.Discuss Electrical analogy of combined heat conduction and convection in a composite wall.
HT Module 2 Pper solution Qulity Solutions wwwqulitytutorilin Module 2 Q6Discuss Electricl nlogy of combined het conduction nd convection in composite wll M16Q1(c)5m Ans: It is frequently convient to
More informationCOMMISSIONING THE NEW PITCH DAMPING RIG AT THE CSIR WIND TUNNEL FACILITIES
3 RD INTERNATIONAL SYMPOSIUM ON BALLISTICS TARRAGONA, SPAIN 60 APRIL 007 COMMISSIONING THE NEW PITCH DAMPING RIG AT THE CSIR WIND TUNNEL FACILITIES F. Dionisio, L. Vn Zyl nd A. Stockenström 3 CSIR DPSS,
More informationContinuous Random Variables
STAT/MATH 395 A  PROBABILITY II UW Winter Qurter 217 Néhémy Lim Continuous Rndom Vribles Nottion. The indictor function of set S is relvlued function defined by : { 1 if x S 1 S (x) if x S Suppose tht
More informationFlow in porous media
Red: Ch 2. nd 2.2 PART 4 Flow in porous medi Drcy s lw Imgine point (A) in column of wter (figure below); the point hs following chrcteristics: () elevtion z (2) pressure p (3) velocity v (4) density ρ
More informationMACsolutions of the nonexistent solutions of mathematical physics
Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences  Finite Elements  Finite Volumes  Boundry Elements MACsolutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE
More informationLine Integrals. Partitioning the Curve. Estimating the Mass
Line Integrls Suppose we hve curve in the xy plne nd ssocite density δ(p ) = δ(x, y) t ech point on the curve. urves, of course, do not hve density or mss, but it my sometimes be convenient or useful to
More informationDesign Data 1M. Highway Live Loads on Concrete Pipe
Design Dt 1M Highwy Live Lods on Concrete Pipe Foreword Thick, highstrength pvements designed for hevy truck trffic substntilly reduce the pressure trnsmitted through wheel to the subgrde nd consequently,
More informationDesign and Testing of Coils for Pulsed Electromagnetic Forming
Design nd Testing of Coils for Pulsed Electromgnetic Forming. Golovshchenko, N. Bessonov, R. Dvies Ford Reserch & Advnced Engineering, Derborn, UA University of MichignDerborn, Derborn, UA Pcific Northwest
More informationSeasonal Variation of Internal Parameters of an Amorphous Silicon (asi) Thin Film Photovoltaic Module
NTENATONAL JOUNAL of ENEWABLE ENEGY EEACH ustu Eke et l., ol., No.4, 0 esonl rition of nternl Prmeters of n Amorphous ilicon (i) Thin Film Photovoltic Module ustu Eke*, **, ener Oktik*** * Mugl ıtkı Kocmn
More informationStrategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?
University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the threephse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the
More informationChapter H1: Introduction, Heat Equation
Nme Due Dte: Problems re collected on Wednesdy. Mth 3150 Problems Hbermn Chpter H1 Submitted work. Plese submit one stpled pckge per problem set. Lbel ech problem with its corresponding problem number,
More informationThe Basic Functional 2 1
2 The Bsic Functionl 2 1 Chpter 2: THE BASIC FUNCTIONAL TABLE OF CONTENTS Pge 2.1 Introduction..................... 2 3 2.2 The First Vrition.................. 2 3 2.3 The Euler Eqution..................
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More information200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes
PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write
More informationMath 0230 Calculus 2 Lectures
Mth Clculus Lectures Chpter 7 Applictions of Integrtion Numertion of sections corresponds to the text Jmes Stewrt, Essentil Clculus, Erly Trnscendentls, Second edition. Section 7. Ares Between Curves Two
More informationAn Application of Phase Change Technology in a Greenhouse 1
An Appliction of Phse Chnge Technology in Greenhouse 1 Yuning Liu Cho Chen Hifeng Guo Hilin Yue grdute student professor grdute student grdute student Deprtment of Building Environment nd Fcilities Engineering,
More informationComputation and Modeling of the AirSea Heat and Momentum Fluxes. By Dr. Nasser H. Zaker
Computtion nd Modeling of the Aire et nd Momentum Fluxes By Dr. Nsser. Zker ICTP June 00 1 Introduction The ocen receives energy through the irse interfce by exchnge of momentum nd het. The turbulent
More informationLecture 10: PN Junction & MOS Capacitors
Lecture 10: P Junction & MOS Cpcitors Prof. iknej eprtment of EECS Lecture Outline Review: P Junctions Therml Equilibrium P Junctions with Reverse Bis (3.33.6 MOS Cpcitors (3.73.9: Accumultion, epletion,
More informationData Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading
Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3dVritionl Method
More information7.6 The Use of Definite Integrals in Physics and Engineering
Arknss Tech University MATH 94: Clculus II Dr. Mrcel B. Finn 7.6 The Use of Definite Integrls in Physics nd Engineering It hs been shown how clculus cn be pplied to find solutions to geometric problems
More informationNumerical Integration
Chpter 1 Numericl Integrtion Numericl differentition methods compute pproximtions to the derivtive of function from known vlues of the function. Numericl integrtion uses the sme informtion to compute numericl
More informationENERGYBASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION
28 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES ENERGYBASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION Anton N. Servetnik Centrl Institute of Avition Motors, Moscow, Russi servetnik@cim.ru
More informationFIRE PROTECTION HYDRAULICS
GAP.1.0.1 A Puliction of Glol Asset Protection Services LLC FIRE PROTECTION HYDRAULICS INTRODUCTION Fluid mechnics is concerned with the forces nd motions ssocited with gses nd liquids. Hydrulics, distinct
More informationOptimum Design of a Horizontal Condenser
Fourth Interntionl Wter echnology Conference IWC 99, Alexndri, Egypt 9 Abstrct Optimum esign of Horizontl Condenser A.M. Abdllh nd Aly Krmeldin Atomic Energy AuthorityNucler eserch Center ectors eprtment
More information63. Representation of functions as power series Consider a power series. ( 1) n x 2n for all 1 < x < 1
3 9. SEQUENCES AND SERIES 63. Representtion of functions s power series Consider power series x 2 + x 4 x 6 + x 8 + = ( ) n x 2n It is geometric series with q = x 2 nd therefore it converges for ll q =
More informationIntroduction to Mechanics Practice using the Kinematics Equations
Introduction to Mechnics Prctice using the Kinemtics Equtions Ln Sheridn De Anz College Jn 24, 2018 Lst time finished deriing the kinemtics equtions some problem soling prctice Oeriew using kinemtics equtions
More informationl 2 p2 n 4n 2, the total surface area of the
Week 6 Lectures Sections 7.5, 7.6 Section 7.5: Surfce re of Revolution Surfce re of Cone: Let C be circle of rdius r. Let P n be n nsided regulr polygon of perimeter p n with vertices on C. Form cone
More informationESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability
ESCI 343 Atmospheric Dynmics II Lesson 14 Inertil/slntwise Instbility Reference: An Introduction to Dynmic Meteorology (3 rd edition), J.R. Holton AtmosphereOcen Dynmics, A.E. Gill Mesoscle Meteorology
More informationMATHEMATICAL SIMULATION OF GEOTHERMAL HEAT TRANSFER IN HOT DRY ROCK UNDERGROUND HEAT EXCHANGERS
SCIENIFIC PROCEEDINGS 009, Fculty of Mechnicl Engineering, SU in Brtislv MAHEMAICAL SIMULAION OF GEOHERMAL HEA RANSFER IN HO DRY ROCK UNDERGROUND HEA EXCHANGERS Kristín KÁZMÉROVÁ, Michl MASARYK Slovk University
More informationA Convergence Theorem for the Improper Riemann Integral of Banach Spacevalued Functions
Interntionl Journl of Mthemticl Anlysis Vol. 8, 2014, no. 50, 24512460 HIKARI Ltd, www.mhikri.com http://dx.doi.org/10.12988/ijm.2014.49294 A Convergence Theorem for the Improper Riemnn Integrl of Bnch
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More informationMapping the delta function and other Radon measures
Mpping the delt function nd other Rdon mesures Notes for Mth583A, Fll 2008 November 25, 2008 Rdon mesures Consider continuous function f on the rel line with sclr vlues. It is sid to hve bounded support
More informationA. Limits  L Hopital s Rule ( ) How to find it: Try and find limits by traditional methods (plugging in). If you get 0 0 or!!, apply C.! 1 6 C.
A. Limits  L Hopitl s Rule Wht you re finding: L Hopitl s Rule is used to find limits of the form f ( x) lim where lim f x x! c g x ( ) = or lim f ( x) = limg( x) = ". ( ) x! c limg( x) = 0 x! c x! c
More informationDeteriorating Inventory Model for Waiting. Time Partial Backlogging
Applied Mthemticl Sciences, Vol. 3, 2009, no. 9, 42428 Deteriorting Inventory Model for Witing Time Prtil Bcklogging Nit H. Shh nd 2 Kunl T. Shukl Deprtment of Mthemtics, Gujrt university, Ahmedbd. 2
More informationNonLinear & Logistic Regression
NonLiner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More informationZ0103/07/09 series. Blocking voltage to 800 V (NA and NN types)
Rev. September Product dt. Product profile. Description Pssivted trics in conventionl nd surfce mounting pckges. Intended for use in pplictions requiring high bidirectionl trnsient nd blocking voltge cpbility.
More informationSection 14.3 Arc Length and Curvature
Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in
More informationThermodynamic analysis of geothermal heat pump during the cold season
IOP onference eries: Mterils cience nd ngineering PAPR OPN A hermodynmic nlysis of geotherml het pump during the cold seson o cite this rticle: G Dumitrcu et l 2016 IOP onf. er.: Mter. ci. ng. 147 012137
More informationConstruction and Selection of Single Sampling Quick Switching Variables System for given Control Limits Involving Minimum Sum of Risks
Construction nd Selection of Single Smpling Quick Switching Vribles System for given Control Limits Involving Minimum Sum of Risks Dr. D. SENHILKUMAR *1 R. GANESAN B. ESHA RAFFIE 1 Associte Professor,
More informationSolution of Tutorial 2 Converter driven DC motor drive
chool of Electricl Engineering & Telecommunictions, UNW olution of Tutoril Converter driven DC motor drive Question 1. T V s D V I L E V 50 V,.5, I 0 A rted rted f 400 Hz, 0 rev/ min s rted (i) 0 6.8 rd
More informationECO 317 Economics of Uncertainty Fall Term 2007 Notes for lectures 4. Stochastic Dominance
Generl structure ECO 37 Economics of Uncertinty Fll Term 007 Notes for lectures 4. Stochstic Dominnce Here we suppose tht the consequences re welth mounts denoted by W, which cn tke on ny vlue between
More information3.4 Numerical integration
3.4. Numericl integrtion 63 3.4 Numericl integrtion In mny economic pplictions it is necessry to compute the definite integrl of relvlued function f with respect to "weight" function w over n intervl [,
More informationKey comparison BIPM.RI(I)K7 of the airkerma standards of the ENEAINMRI, Italy and the BIPM in mammography xrays
Key comprison BIPM.RI(I)K7 of the irkerm stndrds of the ENEAINMRI, Itly nd the BIPM in mmmogrphy xrys C Kessler, D T Burns, P Roger, M P Toni*, M Pinto*, M Bovi*, G Cppdozzi*, C Silvestri* Bureu Interntionl
More informationMATH STUDENT BOOK. 10th Grade Unit 5
MATH STUDENT BOOK 10th Grde Unit 5 Unit 5 Similr Polygons MATH 1005 Similr Polygons INTRODUCTION 3 1. PRINCIPLES OF ALGEBRA 5 RATIOS AND PROPORTIONS 5 PROPERTIES OF PROPORTIONS 11 SELF TEST 1 16 2. SIMILARITY
More informationEMF Notes 9; Electromagnetic Induction ELECTROMAGNETIC INDUCTION
EMF Notes 9; Electromgnetic nduction EECTOMAGNETC NDUCTON (Y&F Chpters 3, 3; Ohnin Chpter 3) These notes cover: Motionl emf nd the electric genertor Electromgnetic nduction nd Frdy s w enz s w nduced electric
More informationUsing QM for Windows. Using QM for Windows. Using QM for Windows LEARNING OBJECTIVES. Solving Flair Furniture s LP Problem
LEARNING OBJECTIVES Vlu%on nd pricing (November 5, 2013) Lecture 11 Liner Progrmming (prt 2) 10/8/16, 2:46 AM Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com Solving Flir Furniture
More informationHigh speed machines using advanced magnetic materials analyzed by appropriate finite element models
High speed mchines using dvnced mgnetic mterils nlyzed y pproprite finite element models G. D. KALOKIRIS, A. G. KLADAS Lortory of Electricl Mchines nd Power Electronics, Electric Power Division Fculty
More informationA SignalLevel Fusion Model for ImageBased Change Detection in DARPA's Dynamic Database System
SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 160, Orlndo FL. (Minor errors in published version corrected.) A SignlLevel Fusion Model for ImgeBsed
More informationImpact of Device Scaling on Deep SubMicron Transistor Reliability  A Study of Reliability Trends Using SRAM
Impct of Device Scling on Deep SubMicron rnsistor Relibility  A Study of Relibility rends Using SRAM Mrk White,, Bing Hung, Jin Qin, Zvi Gur, Michel lmor,, Yun Chen, Json Heidecker, Duc Nguyen, Joseph
More informationOn the Pairs of Orthogonal Ruled Surfaces
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 5 No. 2 2012 205210 ISSN 13075543 www.ejpm.com On the Pirs of Orthogonl Ruled Surfces Filiz KANBAY Deprtment of Mthemtics Fculty of Arts nd Science
More informationSTEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA. 0 if t < 0, 1 if t > 0.
STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA STEPHEN SCHECTER. The unit step function nd piecewise continuous functions The Heviside unit step function u(t) is given by if t
More informationCALCULATED POWDER XRAY DIFFRACTION LINE PROFILES VIA ABSORPTION
16 17 CALCULATED POWDER XRAY DFFRACTON LNE PROFLES VA ABSORPTON Keji Liu nd Heifen Chen School of Mteril Science nd Engineering, Shnghi nstitute of Technology, Shnghi, Chin 2233 ABSTRACT We hve clculted
More informationx = a To determine the volume of the solid, we use a definite integral to sum the volumes of the slices as we let!x " 0 :
Clculus II MAT 146 Integrtion Applictions: Volumes of 3D Solids Our gol is to determine volumes of vrious shpes. Some of the shpes re the result of rotting curve out n xis nd other shpes re simply given
More informationQuestions on Ship and Offshore Hydromechanics
Questions on Ship nd Offshore Hydromechnics (in progress of formtion) JMJ Journée Contents: Question 1 Stnding Wves Question Regulr Wve Observtion Question 3 Axes Systems in Ship Motion Clcultions Question
More information15. Quantisation Noise and Nonuniform Quantisation
5. Quntistion Noise nd Nonuniform Quntistion In PCM, n nlogue signl is smpled, quntised, nd coded into sequence of digits. Once we hve quntised the smpled signls, the exct vlues of the smpled signls cn
More informationLecture 1. Functional series. Pointwise and uniform convergence.
1 Introduction. Lecture 1. Functionl series. Pointwise nd uniform convergence. In this course we study mongst other things Fourier series. The Fourier series for periodic function f(x) with period 2π is
More informationPhysics Honors. Final Exam Review Free Response Problems
Physics Honors inl Exm Review ree Response Problems m t m h 1. A 40 kg mss is pulled cross frictionless tble by string which goes over the pulley nd is connected to 20 kg mss.. Drw free body digrm, indicting
More informationLecture 14: Quadrature
Lecture 14: Qudrture This lecture is concerned with the evlution of integrls fx)dx 1) over finite intervl [, b] The integrnd fx) is ssumed to be relvlues nd smooth The pproximtion of n integrl by numericl
More informationNumerical integration
2 Numericl integrtion This is pge i Printer: Opque this 2. Introduction Numericl integrtion is problem tht is prt of mny problems in the economics nd econometrics literture. The orgniztion of this chpter
More informationExperiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION
Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly.
More information1 Online Learning and Regret Minimization
2.997 DecisionMking in LrgeScle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in
More informationYour Thoughts. Mechanics Lecture 16, Slide 1
Your Thoughts I get dizzy with ll the equtions being shifted, spun nd switched so much in the prelectures. If the prelectures for, 3 nd 4 re like tht, I m pretty worried. Are we going to be rcing spheres,
More informationSolutions to Supplementary Problems
Solutions to Supplementry Problems Chpter 8 Solution 8.1 Step 1: Clculte the line of ction ( x ) of the totl weight ( W ).67 m W = 5 kn W 1 = 16 kn 3.5 m m W 3 = 144 kn Q 4m Figure 8.10 Tking moments bout
More information11.1 Exponential Functions
. Eponentil Functions In this chpter we wnt to look t specific type of function tht hs mny very useful pplictions, the eponentil function. Definition: Eponentil Function An eponentil function is function
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 218, pp 4448): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 218, pp 4448): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationMATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs
MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching
More informationCzechoslovak Mathematical Journal, 55 (130) (2005), , Abbotsford. 1. Introduction
Czechoslovk Mthemticl Journl, 55 (130) (2005), 933 940 ESTIMATES OF THE REMAINDER IN TAYLOR S THEOREM USING THE HENSTOCKKURZWEIL INTEGRAL, Abbotsford (Received Jnury 22, 2003) Abstrct. When relvlued
More informationBasic model for traffic interweave
Journl of Physics: Conference Series PAPER OPEN ACCESS Bsic model for trffic interweve To cite this rticle: Dingwei Hung 25 J. Phys.: Conf. Ser. 633 227 Relted content  Bsic sciences gonize in Turkey!
More information