DEVELOPMENT TECHNOLOGY UNIT Working Paper No. 46 Operating Strategies for Hydropower Systems Using Unregulated ‘lurbines January 1996 C.Alstocce Frenis & T.H. Thoroas Developmert Technology Unit Departmeat ot ngmeering University of Warwick Coventry CV4 TAL UK ‘Pek 444 (0) 203 523122 Fax: (0203 41R902 cenall: dni @eng. warwick. wo.ck Operating Strategies for Hydropower Systems Using Unregulated Turbines Ur, Claueto Atatorre Freak’ and Ur. feny Thomas” ‘.introduetion For micro hydropower systems, say uncer 100 kW, there haw heen a growing snferest in using turbines having no hydraulic controls. The financial savings from omitting controt yea i sbstaial and farcher savings aro possible if pumps". mass-produced in country. are used instead of individually designed turbines, often imported. Taere is now e considerable literature on tae use an¢ selection of pemps-as-turbines. A commun configuiatiin of wicro-tydra plant is far thee to be vay “llle water sto.age and therefore for the system gross head to be nearly constant. The speed of tae turbine-peneratos set fg held constant by electrical means Tus the Heed geometry turbines run al constant flow, ofortuaately the river fw is never constant, When it exceeds the total turbine flow there is 02 problem, bat when i is fxs than rated turbine flow ahere is a mismatch, The absence of svorage {which ie tap costly) remaves the pessbility of Sitecing gut river low flacnearions, ‘There ave three systemfoperation designs we might use in this context. The simplest way of ‘operating (SO) is +0 employ a single turbine that runs only when sver flow exceeds turbine rated flow. A second option is lo employ several small turbines operating in peratel PO): the suber in uses varied to watch the vacation in siver fow. A shied option isto intermittently operate (10) 4 Siagle tsbine fed trom a small reservoir (e.g. holding only 15 mines flow). I is the purpose of tis papér to compere thesc three altematives and to show that the third (10) has apparert rscanmic advantages qver the others. All three alternatives son give higher exanomie.retims ia many seni industrialised countries where, power for power, turbines cost over four Hines tore than pumps. Jn making economic compatisons there are 2 great many system variables and cost factors we might accommodate. To reduce the complenty of the analysis we will rewrict ourselves t0 odeticg bydhe systems eouetel 10 a ‘large’ elecrival yrid. This allows uy wo reasonably asgume “at alle electrical energy produced wil be petchased and that ech unit wit command te same (daity average) price. Even with this sinplifcation, however, it bas beer. necessary to develop a mere Bexible economic methodology “hen s normally used for evaluating hydropower. “This methodology. described in section 5, i= we hope of value in ts own righ independent ofits speciic epplication here. ‘The ensuing analysis is a simplified form of tat developed in a PHD thesis fiom Warwick University, UK Ref. 1), pstantenglcor. Ap. Fost 280, 9160] Xalapa, Ver, MEXICO. Fae. (31 28) 125134 ral cafspedy.coaade.w. ane Disco, Developteat Tedusloss oil, Ua e-siy of Waawah, Cunceey CVA TAL, UK: Fated 1208) 418922, Eval ciecsaghe mnie wk 2 Option SO: Simple Operation of a Single Turbine [As observed above, 2¢ xed brad and speed an unregulated tuibine will draw a conseent cated Slow, Qj, Should thin fave not be svailebls (2, <Q), there ae two operating eternatives, One is tu at dose the turbine. Tle ther is 1 les the wales level ithe penstock draw down unt flaw equltrium is reached (Q, =p, 0.“ Q,): Yeducing the effective gross head in chis way sal seduce the turbine low. Although the second atterative is inecicien, since some head is being ‘wasied and the turbine is being operated away ftom its best eflciency point (BEP), some awer x better than none. Figure 1 shows the advantage of leaving the tarbine runing at low flow: typically an extra 108 energy van be obtained per yearby doing so. a the subsequent analysis we assume alternative (i) is followed. in practice, to avoid cerain operational problems it is sometimes desirable to tum off the tursire flow when, falls below say 60% of (2, (which corresponds to ver litle powes) ANommatized eutpur power: PP, iterative th fur of turbine wien Ce = Oe Patton turbine {tac comparison) ehernave i leave turing ating Es ‘co > Nocmatised availhte fw QxiQr ‘sonia dita Sica 2 PRT Wak parC Fal PENOGELY Jn tae design of this eption the key variable iy the size ofthe turbine and hence its rated dow 2, Increasing Q, wil iocranse the capital st ofthe aystem Up to some Finit it wil also incease the energy ostput. Using the econamis model daserited later, by tial and error an aptimam (2p can be dertiied. It is soch an optimised SO system we wi. Inter compare wilh uptiaivel PO nd TO systems, 3. Option PO: Several Turbines Operated in Parallet If lwo or mae PATS ace operated in sarlll, they can be switched or aad off according to the available flow. Parallel operation (PO) of up to 7 mactunes has proven to be mare cost-effective (tan a single conventional hydraulic turbine of eomparcble capacity, according up the Witesaure Ref. 2, 3 ‘The mackines can ke dil¥erent oc identiat to each other (Hoc example, in a two-PAT schome, he tucbines can handle ether “4 and ‘A of the ful flow, or one half each). The firs eption increases the energy generation, as ic enables more combmatins (in this case "4, %4 and ¥A); tke latter restricts the combinations (i and “4, hat makes maintenance easier, 26 ibe sume set of spares can be used in al machines, Figure 2 shows che power auton of a S-turhine system, The sold line indicates some af the available ovis being spilled, the dashed fine edicates where the penstack is nor ful, che eumbers show how miny machines aro actively coanected to the penstoc. The shared penstock and equality of turbine sizes are common features of PO. The optimum oumber of machines is not however always 5 but depen, inter ala, on the variability of the river flow. 1a optimising & PO system we therefore need to find best values for two paramalens turbine cumber (7) and toma rated flow 0. 4 Normabised ourpet power 2: s0as pos or > Normalised available flaw. (24 ‘(y "Tie Fal opi STOLE Sl ans WH Sor” ee 4, Option 10: intermittent Operation of One Turbine ‘Whoo the dver flow D; ia fess thao the flow Q, drawn by the tuyine ia operation, we might ‘operate the turbine interttendy foc a fraction Q,/Q2, of the time. We will need a reservir Gn acti en enlarged foray tank) whase level [abs wile the turbine is cumsing 2né rises when the tucbine is stut off Figure 7 shows the eyeic operation, Although in theory tke peastack eocld be opened and closed using a vale, in practice x quiek-priming double siphon (ee Fig. 4) would be ‘ted. Such siphons have no moving para and can operate very swihy Technically therefore intermittent operation cequires us to design an appropr.ate sipon and a penstock that wil tolerate the sudden and flequent changes in low. Liting economic models we feeg 10 optimise chren vnribles, namely the turbine size (Q2y) the drawdown (d) at the forebay ‘anlk and its effective surface aren (4) ‘There are three regimes under which the svstem ean operate Where, is greater then Q, (regime ©) the nrbine vil rn condmtonsty 3t Gall prover Py and the tank wil Be ots fll ee cverflowing Where Q, is amb fess than Q, (regime @) tha riphon will operate cyclically, the power outpat wil be:aermttent and ve water level in the rank wal fcuate belieen leigh 298 (Gated gross bead plus the small surcharge height 6) and height z-d (see Fig 3) however (is only sgl les than (2, we may observe regime it. which the turbine nuns cootinaously bot at a reduced haad apd flow: the wate: level wil be steady somenttee seven heights zand sat “This third regime it unfoctunnte as f may wive less outpat power than when tne How is slightly tower (regime @) Fortunately, wit typical small valoex for drawdown (d= OS), the systea" spends vary fale time operating in regime @ and xo simplify the discassion we can neglect it Figure 5 shows the power output of a typica: syste 4 Nemalived output power: PF, a ‘80 tor comparison 0% > Normalised svailahle Faw" 0/0, Figure 5: Power versus flow for datermitient operation. “The drawdown height (d) and the co-responding drewdown volume (1) affect the power eutpu: uring regime @. A full analysis is given in Re? 1 aad is complex. Portenately the optimum valve Cf dis such a small fraction of gross head that we can use an approximate analysis in which * Cis assumed to remain corstant at Qya¢ the tank level draws down + the mean gross head during turbine overator isnot 2 but z-d/2-= x(1-d/22) the ideas cfete Hime 4. tartan: is extended an extea period &* during which the tank overils by volume 7* which is effectively lest each cycle. As en approximation we can equate /* ta the penstack vohume. 6 “The sffbet of the tas. axsurption iy that tae eyele Ke fg is increased by factor and the mean power correspondingly decreased, it So maan power is Q] ‘We may dacids a» choore d to simply maximise power regardless ofits influence on cust. If 83, differntiating the function of Zin Eq [2] ané acting te zero gives then, since af 1 typicaly, 6) This power maximising ewdowa varies with Hew fiom 0 at QQ) 16 | 72. at wo tow Although a variable drawdawn siphon i feasible, it will apomally suffice to use a Gxed drawdown for all flows, choosing a flow of eg. 2, =0.8-Q, to get close (o the flowaveraged optisoam, Alometively we cin omploy a ‘hlkcimbing’ search, usiog a spreadsheet version of the fit economic model, co optimise al three variables 4 and Q,, 5, Economic Modelling ‘There are muny economic measares we mighl use for compacing altesative hydro aystem designs for a panioula site. They all cubive the iaiial cust, iy waning costs aud he icvome eased through the life ofthe system into a single measure. The most usval measures are imemal rae of return (IRR), benefit-cost rai (BCR), payback time (PB) and net present valve (NPV). IRR, BOR and PB ceflect the financial return per unit of money invested, whereas NPV reflects the reluro "per site”; a system sized to nuaczhse the latter willbe larger than anc sized te maximise the former three, Ax hydropower wstems are capital intensive and microhydro schomes are paniculacly vulnerable to ciphal shortage, we choose the cetum-por-unit-afmoney-invested approact, te. tie former thiee measures. Moreaver, as we are desting wih systems whose expected iccomes pe: year remain constant aver ther lives, and whose lives are leng, it can be ssanwn that the esamomic ranking af altemative designs will be the same whichever of the three ricssures (TRR, BCR or PB) we choose, As the calculation of BCR and PY (ané NPV) requtes the prior choice of # discount rate, we prefer the TRR as our measure and the ratio of their respective IRR as ocr criterion for comparing two aterratives. TRR is the solution of, fexiiTeRy! way TR” i ‘where Mis project life, NAI is anrual income ret of eomning costs and CAP is capital invested, As \we are nonmally interested ie ERR values greater than 15% and system lives of over 25 years, we ‘can approximate Eq, [4 within 3% ervar to: NA) CaP ‘The net annual income ix equil to gross anal income mirus tte annual operating and naircenence costs. These O&M costs are usualy a fonction of capital costs. owever, for the saks of simplicity, we wil assume that they are a fixed multiple 0° the gross anmual income. The crrorinvurred will be negligible since OM costs in microliydro ace minor This leaves the task of estimating goss annual income (GAL) whichis affected by river flow. The fow can be described ty a hydrological grababilty function UF a, = ProW?<0,) (6 ‘The relationship between output power axd flow varies from desig to design and is exprested by the technical function af each PT) ii) is 1. 2and S as examples } Ata given output power, an economic Function determines the ‘earning mones Gee rate REE) = ypicaly KP 1 ‘The parameter € can be taken as 1 for gerd connected systems so A, becomes the economic value of {Foul and grass anmusl inegrme is a= [xp 710,)€%, vl 8 (Where K', = K,23.16x10" s) The following hydrologieat probability fiction (qaposed ic Ref. 1} fits very ell the typical How-dvation curves 19 the range of muetest tor micre-hydro (se, the range of Hows smaller than the average annua! Hose) hwo no The numencal tegration of Hq. [93 usmg a distnbution such as [10] gives us income. We now eed a flexitle expression for capital zost Let CAP GC CIC fits where the cost components represent respectively huchomackines, pencinek, storage and the rest of the gysiem ‘Noting the economies of wale in machinery manufacture, we get Chie Kahl fo. a machines ne (Note the need f@ change to x aommalised how 4, =O,/D, to keep the couticiont dimensionally simpie.) The elusticky @is typically 0.55 10.0.7, Penstock size will depend upon Hew and the penstack eflicency’ 1, we choose, Penistock east car be shown to have the form, (nat 13; Storage costs only aise i the ease of intermittent operation. Assuming thet storage volume (dd) 5s chosen as alasge fixed mip of peastock voluote we can ase EL 1 Finely we have civil and cleoical costs depcndert respectively on flow Qy and power Py, AS ‘ower is proportional to flow and treating all equipment as having the same cost-scle elasticity Cu ~ att us] We have in equations {11]-{15] tke means of evaliasing the changing ost of a system as parameters soo as Q, ae varied 6. Comparison of Options $0, PO and 10 Having opdmised the IRR of each of the options by Ending the best values for Oy and otner parameters, the three options cat be fairly compared, A efteuey scenaia was detined as fellows Figure 6 shows the rated flow Q, the prose annul income Gl, the capital invested CAP and the selave IRR for PO and 10, taking SO as reference {ean be seen thal oft PO and TO Teal v0 ‘urge schemes whose internal satay of ream are higher than fer SO. Tn the case of interes operation 10, the economic advantage ix suPicient (109) co justify considering this aermnive Simi: advantage was observed across a reresenatve cange of scenarios, vam ° rot] von, LUBE ‘RelIRE » Gar CAP eile QR gulils. Conipacison bee Obnd Say le Finally, the effect af varying the different economic nd bydroiogic parameters is analysed in Ref. 1. One example, relating to the bydroloyical parameter, iv shown in Figure 7, confirming that 10 and PO are especially attractive Eor sal systems 2p Relative IRR vee 10 po —] 120% (emattaveg dog veg of . 7 25 ? ‘Bxceedence curve shape parameter * Pepi’? Rekatve IRR SRO REC eRe Ot Ak ae Ra eT References 3 ‘ALATORRE-FRENK, CLaiDi0 Cast Minimisation in Micro-tydro Sysiems Oving Pumps-as: tarbines, PRD thesis. University of Waewick, (XG, 1954 ‘Micwo.as, WULIAM G. “Using Pumps as Turbines. Selection and Application”, Hydro 38. Third bucmerional Conference on Small Hydro, Canin, Mexico, 1988, WILLIAMS, H.C, "Giaborae Waterworks Intake”. New Zealand Engincermng, Vol 22, No. 12, 1967, pp. 502-5