On the Short-Term Optimisation of a Hydro Basin with Social Constraints

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1 Computatonal Water, Energy, and Envronmental Engneerng, 2013, 2, Publshed Onlne January 2013 ( On the Short-Term Optmsaton of a Hydro Basn wth Socal Constrants Glora Hermda, Edgardo D. Castronuovo Unversty Carlos III de Madrd, Madrd, Span Emal: glorahermda@gmal.com, ecastron@ng.uc3m.es Receved November 19, 2012; revsed December 20, 2012; accepted January 3, 2013 ABSTRACT In ths paper, an optmsaton problem for calculatng the best energy bds of a set of hydro power plants n a basn s proposed. The model s appled to a real Spansh basn for the short-term (24-hour) plannng of the operaton. The algorthm consders the ecologcal flows and socal consumptons requred for the actual operaton. One of the hydro plants s fluent, wthout drect-control abltes. The results show that the fluent plant can be adequately controlled by usng the storage capactes of the other plants. In the smulatons, the costs related to the socal consumptons are more sgnfcant than those due to the ecologcal requrements. An estmate of the cost of provdng water for socal uses s performed n the study. Keywords: Hydro Power Plants; Hydro Generaton; Optmsaton; Short-Term Plannng; Socal Resources 1. Introducton Nowadays, the utlsaton of water for electrcty producton s condtoned by many constrants. In Span, prmarly the Kyoto Agreements and the proposals of the European Commsson to 2020 must be consdered. The European Commsson have specfed a goal of 20% of the fnal energy consumpton delvered from renewable sources by 2020 [1]. In Span, 38.6% of the electrcty generaton comes from renewable resources, manly from hydro (17.4%) and wnd (16.6%) generaton [2]. Because electrcty generaton has to compensate for other nonrenewable energy consumptons, electrcty producton must ncrease ts share of renewable generaton. Hydro producton s a mature renewable technology that can help reach the ambtous objectves proposed by the European Commsson by In addton, the exceptonally varable weather condtons of the past few years, most lkely due to clmate change, complcate the management of water for electrcty producton. The scarcty and the hgh varablty of water resources have recently reduced the profts n several zones [3-6]. Many studes have been performed to calculate the optmal operaton of a hydro basn. In long-term plannng, Soares and Carnero [7] consder the operaton plannng of a hydrothermal power system n Brazl. The paper hghlghts the mportance on the control of the head hydro power plants (HPPs) n the basn. Granvlle et al. [8] consder the stochastc characterstcs of the problem, ncludng a representaton of the market. The soluton algorthm s based on stochastc dual dynamc programmng. Cheng [9] apples partcle swarm optmsaton and dynamc programmng for a large scale hydro system n Chna. Olvera, Bnato and Perera [10] present two technques: the extenson of a bnary dsjunctve technque and screenng strateges for plannng studes n Brazl and Bolva. Fosso et al. [11] gve an overvew of the plannng tool used n Norway for long, medum and short horzons. Kanuda and Loulou [12] propose a stochastc verson of the extended market allocaton model for a hydro system n Québec, Canada. In medum- and short-term plannng, Habbollahzadeh and Bubenko [13] compare dfferent mathematcal methods: Heurstc, Benders and Lagrange methods for hydroelectrc generaton schedulng n the Swss system. Castronuovo and Peças Lopez [14] descrbe economc profts of the coordnaton of wnd and hydro energes. Zhao and Davson [15] analyse the ncluson of storage facltes n a hydro system, demonstratng the senstve dependences between some of the parameters of the hydroelectrc faclty, the expected prces and water nflows. Pousnho, Mendes and Catalão [16] propose a mxednteger quadratc programmng approach for the shortterm hydro schedulng problem, consderng dscontnuous operatng regons and dscharge rampng constrants. Smopoulos, Kavatza and Vournas [17] propose a decouplng method, dvdng the hydrothermal problem nto hydro and thermal sub-problems, whch are solved ndependently. A Greek system s analysed n the study. D- Copyrght 2013 ScRes.

2 10 G. HERMIDA, E. D. CASTRONUOVO nz and Pñero Macera [18] use a four-dmensonal pecewse lnear model for the generaton of a hydro plant as a functon of storage, turbned and splled outflows. Shawwash, Thomas and Dens Russell [19] dscuss the optmsaton model used n the Brtsh Columba hydro system for hydrothermal coordnaton. Most of the avalable reports about the optmal programmng of hydro generaton have been publshed n countres wth abundant water (Norway [11], Brazl [10], Canada [15], USA [19]). In the algorthms reported by these studes, the restrctons on the socal use of water and the ecologcal mnmum flows are ether mnmally consdered or not consdered at all, amng at mprovng the utlsaton of the abundant resource n a strctly economcal envronment. In Span, the focus of the present study, ecologcal flows and socal uses of water must be consdered for the optmal utlsaton of the resource. Pérez-Díaz and Wlhelm [20] want to assess the economc mpact of envronmental constrants n the operaton of a short-term hydropower plant. For that purpose, a revenue-drven daly optmsaton model based on mxednteger lnear programmng s appled to calculate the optmal operaton of a HPP n the northwest area of Span. In a more recent paper, Pérez-Díaz et al. [21] propose addng a pumpng capablty to mprove the economc feasblty of an HPP project, always fulfllng the envronmental constrants mposed on the operaton of the hydropower plant. Ths paper presents an optmsaton algorthm for calculatng the optmal energy bds of a set of HPPs, ncludng the economc objectves for energy generaton and the regulatons concernng the use of water n the regon. The algorthm s appled to the upper Guadalquvr Basn, an area wth scarce resources and varable flows, over a 24-hour horzon. Four HPPs are consdered n the analyss. Three of them have storage capacty and the other one s run-of-the-rver, wthout drectly controllable alternatves. All of the plants are operated jontly wth a unque owner or dspatcher (as n current practcal operaton). Actual data from real power plants and markets are consdered n ths study, ncludng the travel tmes of the water (TTW) between the HPPs. The results show that the fluent plant can be controlled to acheve optmal operaton by usng the upstream HPPs. Moreover, an estmate of the costs of provdng water for socal uses (as a functon of reductons n profts from sellng the electrcty produced n the market) s made n ths study. 2. Rules Applcable to the Hydro Generaton 2.1. Regulatons Concernng the Use of Water for Electrcty Generaton The Water Framework Drectve [22] establshes a Euro- pean Communty framework for water protecton and management. The objectves of ths regulaton are the preventon and reducton of polluton, promoton of sustanable water use, envronmental protecton, mprovement n aquatc ecosystems and floods and drought mtgaton. Ths norm was adapted to Spansh regulatons by [23]. In ths drectve, the prortes regardng the use of water are fxed. Electrcty generaton s thrd n the order of precedence, after the use of water by the populaton and rrgaton requrements. Addtonally, ths norm specfes the requrement of a Hydrologcal Plan for each basn or hydrologcal zone. In [24], the hydro regulatons for the Andaluca regon (the area consdered n ths study) are specfed. The Guadalquvr Hydrographc Confederaton ( s the organsaton desgned to control the Guadalquvr basn. Ths organsaton s webste features hstorcal data regardng affluences and other hydro nformaton. The mnmum levels of flows (ecologcal flows) are also specfed for several ponts of the rver The Daly Energy Market In Span, the electrcty market has been deregulated snce 1997 (Electrcty Industry Act [25]). Some renewable productons have specal ncentves for ther producton (Royal Decree 661/2007 [26]). However, large or pre-exstng hydro plants must aucton ther producton n the conventonal market wthout renewable bonuses and, practcally, wthout specal market regulaton. Ths s the stuaton faced by the plants addressed n the present study. The Spansh energy market s organsed nto the followng sub-markets: futures market, daly market and several ntra-daly markets. More than 95% of energy transactons and more than 80% of the economc volume are traded n the daly market [27]. There are also other markets that can affect hydroelectrc producton, such as the reserve and restrcton management. For clarty, n ths work, only daly market partcpaton wll be consdered. In the daly market, producers and consumers make ther offers, n terms of energy quantty and prces for each hour of the D + 1 day. The Market Operator oversees the buyng and sellng of bds usng a smple cassaton model [28,29]. The present paper presents a method to calculate the optmal bds for energy over a 24-hour horzon of the hydro plants n the basn, assumng that the expected prces n these hours are known. 3. Mathematcal Formulaton 3.1. Flow Chart In Fgure 1, the flow chart of the algorthm s presented. Copyrght 2013 ScRes.

3 G. HERMIDA, E. D. CASTRONUOVO 11 Intal condtons of the basn Prces forecast Expected flows Max. nrnwr T Ct P, t 1 t1 (1) s.t. Scenaro Generaton V V V V V V V AF T C D t, t, 1 t, 1, t t, t, t, 1,, nr (2) Mathematcal soluton Analyss of results and generaton of optmal bds Fgure 1. Flow chart of the proposed algorthm. The ntal condtons of the basn (level of stored water n the reservors, current flows, etc.) are known at the begnnng of the study. Moreover, the expected flows n the analysed perod can be consdered known or estmated. The expected flows are dependng also of the medum term plannng for the operaton of the basn. In the present study, an estmaton of the prces n the market, for all the hours of the next day operaton, s requred. Ths predcton can be obtaned from forecastng tools, outsde the scope of the present study. Wth the knowledge of the ntal condton, the prce forecast and the expected flows, a scenaro can be developed. In the present analyss, a determnst approach s used. However, the present method can be easly extended for consderng uncertantes n the prces and/or n the expected flows, by solvng many probable scenaros. When the probable scenaro s determned, the optmal soluton for the operaton n the hydro plants n the basn must be calculated. In the present case, ecologcal and socal constrants are also ncluded n the analyss. In the next secton, a fully representaton of the optmzaton problem s provded. After the calculaton, the optmal flows of waters and the power and energy optmal bds are obtaned. For achevng the profts presented n the analyss, t s consdered that all the presented bds are accepted n the market, by offerng the hydro producton at low prces Mathematcal Representaton The best operaton of hydro plants n a basn can be calculated from the soluton of an optmsaton problem. In ths problem, the restrctons to the operaton are represented as mathematcal constrants. The formulaton of the problem s descrbed by Equatons (1)-(15). V V V V V 1,, nwr AF T C D t, 1, t t, t, t, 0 V V V T D 1, t 1, ttv 1, ttv 1,, nrnwr (3) (4) SP V 1,,,1 V,1 nr (5) SP VT, VT, 1,, nr (6) T Pt, Vt, ght, 0 1,,( nrnwr) (7) U 0 U h k k V V t, 0, 1, U 2, 3, k V V k V V 1,, nrnwr r max 0 V V 1,, nr (12) T T max 0 V V 1,, nr (13) D 0V 99 1,,nr (14) max 0 h h 1,, nr (15) (8) T C CT mn Vt, V 1,, nrnwr (9) t 1 Cmn C Cmax V V, t V 1,, nrnw (10) V V V nrnwr (11) T D ECmn t, t, 1,, t, t, t, t, t 1,, T where the varables ndcate the followng: P,t, the actve power njecton to the grd of hydro plant at hour t; V,t, the useful volume stored n the reservor of the hydro plant n the perod t; V -1,t, the affluence nto reservor at perod t, comng through the rver from upstream plant T (or plants); V t,, the turbned volume at hour t by plant ; D, the devated (splled) volume at hour t by plant ; V t, C V t,, the output water consumpton for socal uses delvered by plant at hour t; and h,t, the heght of reservor at hour t. The followng are the parameters n the optmsaton formulaton: c t, the expected market prce of AF hour t; V t,, the ndvdual affluence nto reservor at perod t, not consderng the flows comng through the Copyrght 2013 ScRes.

4 12 G. HERMIDA, E. D. CASTRONUOVO rver from the prevous plant; t V, the TTW between the SP consdered HPPs; V,1 and V ȘP T, the specfed volumes at the begnnng and at the end of the horzon (respectvely) by plant ; η, the average effcency of the hydro plant ; g, the acceleraton of gravty; k 0,, k 1,, k 2, and k 3,, the coeffcents relatng volume and heght at reservor ; U V, the unused volume for electrcty generaton of res- CT mn ervor ; V, the mnmum daly requrements of wa- C mn C max ter for socal uses n hydro plant ; V and V, the mnmum and maxmum (respectvely) hourly re- EC max qurements of water for socal uses, n plant ; V, the mnmum (ecologcal) volume to be mantaned n the max T max rver downstream of reservor ; V and V, the maxmum useful reserve and capacty of prod ucton (remax spectvely) of hydro plant ; and h, the maxmum heght at plant. In the equatons, nr s the number of hydro plants wth reservors, nwr s the number of fluent hydro plants (wthout reservor), α s the set of hydro plants upstream from the reservor and T s the number of dscretsaton steps. The goal of the optmsaton p roblem (1)-(15) s to calby us- culate the optmal producton of coordnated hydro plants n a basn n T perods and consderng the expected prces n the market (1). Equalty constrants (2) and (3) express the energy balances n the hydro plants wth and wthout a reservor, respectvely. When the hydro plant has storage capacty (2), the useful volume n the reservor can be ncreased by the ndvdual affluence (ran, trbutares, etc.) and the flows comng from the mmedately upstream hydro plants. Addtonally, the energy stored n these plants can be reduced by electrcty generaton and socal consumpton. When large nflows enter the reservor, a porton of the water can be devated by usng the spll way to preserve the securty of the plant s operaton. The amounts of useful energy at the reservors at the begnnng and end of the programmng horzon (5), (6) are pre-specfed quanttes. The hydro producton effcency for power producton s expressed by usng a thrd-order polynomal Equatons (7), (8), as a functon of the heght. In hydro reservors wth large nonlnear relatonshps between the heght and the stored water (Equaton (7)), partal approxmatons by usng thrd order polynomal equatons for each level of the reservor can be adopted. In the present formulaton, the socal requrements for water are represented as mnmum daly consumptons (9) and restrctons on hourly water flows (10). The operaton of the hydrologcal system requres mantanng the mnmum ecologcal levels of water flows nto the basn (11). In Equatons (12)-(15), the maxmum capactes of the equpment of the hydro plants are expressed. In the present analyss, the al gorthm s solved ng Matlab [30]. Equatons (1)-(15) consttute a large nonlnear optmsaton problem requrng (T (7nr + 6nwr)) varables, (4T (nr + nwr) + 2nr) equalty restrctons and (T (16nr + 14nwr)) nequalty constrants. 4. The Test Case The proposed optmsaton problem (1)-(15) s appled to water management n the upper basn of the Guadalquvr Rver, Span. Fgure 2 shows a map of the headwaters of the Guadalquvr Rver. Fgure 3 shows a schematc representaton of four hydro power plants (HPPs). Three of them have a reservor (HPP 1, Doña Aldonza; HPP 3, Guadalmena; and HPP 4, Marmolejo), and the other (HPP 2, Pedro Marín) s runof-the-rver. The TTW between the plants s shown n the dagram as T v. Other mportant data related to the plants are presented n Tables 3, 4 of the Appendx. In the present analyss, typcal prces n the Daly Market n March 2011 (a month wth medum hydro producton) n Span are used to smulate the optmal operaton of the hydro system (Fgure 4). The acceleraton of gravty, g, s 9.81 m/s 2. To analyse the effect of the constrants on electrcty producton, several cases are consdered: Case A: base case, n whch socal consumptons and ecologcal flows are not represented. Therefore, the optmsaton problem s solved wthout consderng Equatons (9)-(11). Case B: ecologcal flows are not consdered. The optmsaton problem s solved wthout Equaton (11). In ths case, the socal consumptons are ncluded n the formulaton. Case C: socal consumptons are not appled. The optmsaton problem s solved wthout Equatons (9) and (10). In ths case, the ecologcal flows are ncluded n the formulaton. Case D: soluton of the optmsaton problem (1)-(15), consderng both socal consumptons and ecologcal flows. 3 In all of the cases, the same flow (7.944 Hm /day, the average flow of March 2011) s consdered. The same flow (3.972 Hm 3 /day n each HPP) s njected at the heads of the basn and unformly dstrbuted over 24 hours ( Hm 3 /hour n each HPP). For smplcty n AF the analyss, no ndvdual affluences ( V t, ) n HPPs 2 and 4 are consdered. Fgure 2. Geographcal poston of the Guadalquvr basn and relevant hydro power plants [31]. Copyrght 2013 ScRes.

5 G. HERMIDA, E. D. CASTRONUOVO 13 Fgure 3. Spatal dstrbuton of the reservors n the upper Guadalquvr basn. Prce preco c /kw horaro perodo de programacón hour Fgure 4. Typcal spansh next-day market prces n march For ths sample basn, assumng 24 hours of operaton and hourly dscretsaton, the formulaton descrbed by (1)-(15) mples 648 varables, 390 nequalty constrants and 1488 nequalty restrctons. 5. Results 5.1. Base Case, wthout Socal Consumpton and Ecologcal Flows In Fgure 5, the optmal producton of the four hydro plants s shown. The hydro plants at the head of basn (HPPs 1 and 3) put the resources nto crculaton, f possble, durng the hgh-prce perods n the mornng. However, the behavour of these two plants s qute dfferent due to the TTW between the plants n the basn and the type of plants downstream. The producton of HPP 1 s lmted by the capacty of the run-of-the-rver HPP 2 located downstream. In ths scheme, all of the water enterng HPP 2 s turbned, obtanng the maxmum possble proft n the combned operaton. HPP3, wth a controllable power plant downstream (HPP 4), generates electrcty durng the early hours of the day at the hghest prces and full capacty. The resources comng from HPP 2 and HPP 3 reach HPP 4 n tme to be turbned at full power durng the hours of maxmum daly prce. A small quantty of water s turbned by HPP 3 at the hour of the maxmum prce of the day, hour 21, wthout reachng HPP 4 durng the daly horzon. As shown n Fgure 6, hydro plants HPP 1 and HPP 3 (at the heads of the basn) use the water stored at the begnnng of the day to ncrease producton durng the frst hours. The nflows n the heads n the evenng help recover the specfed fnal values of stored energy at the end of the day. As expected, HPP 2 has no storage capacty. HPP 4 utlses ts storage capabltes to wat for hgher prces to sell ts producton n the market. The reduced storage capacty of HPP 2 dstrbutes the profts throughout the entre programmng perod (Fgure 7). A hgher generaton capacty n the plants would centralse the revenue only at the peaks of the prce curve. The proft of the jont operaton s M Optmal Operaton Consderng only Socal Consumpton In ths case, the effect of socal consumpton s studed. Socal-consumpton values are requred n all of the plants. The daly mnmum consumpton and the hourly lmt at each plant are specfed n Table 3 of the Appendx, ffth and twelfth columns, respectvely. Fgure 8 shows that at the begnnng of the day HPP 1 turbnes more than the maxmum generaton capacty of HPP 2, delverng water for socal consumpton to HPP 2 and HPP 4. Ths perod has the lowest prces of the day. In the other head plant (HPP 3), socal requests are suppled usng water wth less economc effcency, elmnatng HPP 3 generaton at hour 21 (Fgure 5). Fgure 9 shows the delvery of water for socal uses for the four hydro plants. The upstream plants, HPPs 1, 2 and 3, transfer the volumes for socal consumpton at the begnnng of the day, the perod wth lowest prces. HPP 4, wthout ndvdual nflows, must yeld to ths restrcton along the followng mnma of the prce curve (hours 16 and 24). HPP 3, wth the largest socal consumpton, also uses the mnmum prce at hour 24 to fulfl the socal requrements. The profle of ncremental profts s smlar, consderng (Fgure 10) or wthout consderng (Fgure 7) socal consumpton. However, the fnal profts are Fgure 5. Producton n the four hydro plants, Case A. Copyrght 2013 ScRes.

6 14 G. HERMIDA, E. D. CASTRONUOVO Fgure 6. Energy storage n the hydro plants, Case A. Fgure 7. Incremental profts n the basn, Case A. Fgure 8. Producton n the four hydro plants, Case B. Fgure 9. Energy storage n the hydro plants, Case B. dfferent. When consderng socal requrements, the total revenue s M, 17.20% lower than wthout human consumpton n the basn Optmal Operaton wth only Ecologcal Constrants In ths case, the ndvdual mpacts of the envronmental Fgure 10. Incremental profts n the basn, Case B. restrctons (mnmum flows n the rver) on the profts are analysed. In the present smulatons, ths restrcton can only be mposed at the head plants (HPPs 1 and 3). A constant value of 16 m 3 /s for each plant s consdered. Wth ths value, the mnmum ecologcal flows n all of the basns can be mantaned [32], consderng TTW. Fgure 11 shows that the two head plants (HPPs 1 and 3) generate electrcty at all hours of the day. As n Case A, the generaton of HPP 1 s restrcted by the lmted capacty of HPP 2, and HPP 3 manly generates electrcty durng the frst hgh-prce perods of the day. The ecologcal restrctons (mnmum flow at all hours) make the slope of ncome almost constant (Fgure 12). The profle of the volume turbned becomes flatter, and therefore, there are fewer resources for producng at the hours of maxmum prce. The optmal proft n ths case reaches M (1.5% less than that wthout ecologcal restrctons). In the present smulatons, the restrc- tons on mnmum flows n the rver do not sgnfcantly reduce the proft of operaton. It must be stressed that these restrctons are not consumptve; they only change the generaton tmes of head HPPs 1 and 3. However, thencrease n the amount of ecologcal flow can reduce the total profts Optmal Operaton wth Socal Consumpton and Ecologcal Constrants In ths case, the effects of the two types of constrants (socal consumpton and mnmum flows) are analysed. In ths case (Fgure 13), the optmal profles of generaton are smlar to those observed n Case B (Fgure 8). However, some dfferences must be hghlghted. Frst, the ecologcal mnmum flows requre generaton at HPPs 1 and 3 durng all perods. The dstrbuton of socal consumpton s also dssmlar (Fgure 14). In Case B (wth socal consumpton but wthout consderng ecologcal restrctons, Fgure 9), the volumes for socal consumpton are assgned to hours 2 to 5 n HPPs 1 and 2. The ecologcal flow requrement shfts the delvery of HPP 1 to hours 2 and 7 and the release of HPP 2 to the end of the day (hours 19 to 24). In HPP 3, delvery for Copyrght 2013 ScRes.

7 G. HERMIDA, E. D. CASTRONUOVO 15 case (wthout socal restrctons and ecologcal con- strants). Fgure 11. Producton n the hydro plants, Case C. Fgure 12. Incremental profts n the basn, Case C. Fgure 13. Producton n the hydro plants, Case D. Fgure 14. Socal consumptons, Case D. socal consumpton s ncreased at hour 19 and elmnated at hour 24. HPP 4 contnues to provde for socal consumpton at the end of the day (hour 24) but shfts to small delvery from hour 16 to 15. These changes optmse the utlsaton resources, ncreasng the combned proft of the operaton. However, the optmal ncome n ths case s M, 21.54% less than that of the base 5.5. Comparson of the Analysed Cases As prevously dscussed, the economc results of the prevous secton depend on the type of restrctons added to the base case. Mnmum flows n the rver can be mantaned wthout a loss of resources, only changng the tme of generaton. However, the socal uses of water are consumptve constrants, extractng resources from the basn. Moreover, the economc results are a functon of the amount of avalable resources. Therefore, three dfferent scenaros are compared here: dry, medum and wet scenaros, for the two types of restrctons. The medum value concdes wth the prevous affluence (7.94 Hm 3 /day). For comparson purposes, all of the results are obtaned by mantanng the data prevously used, n partcular, the prce profle shown n Fgure Results Consderng Only Ecologcal Constrants In the present smulatons, the ecologcal requrements of Table 1 (1.6 m 3 /s n HPPs 1 and 3) are mantaned. However, the effect of the ecologcal constrants s evaluated n three dfferent stuatons of affluence. In Table 1, the frst column shows the total nflow n the basn njected n head HPPs 1 and 3. The second and thrd columns show the optmal ncomes obtaned wthout consderng or ncludng the ecologcal constrants (Equatons (9)-(11)), respectvely. The economc dfference between the two prevous cases s represented n the fourth column. In the ffth column of the table, the relatve cost of the ecologcal constrants, for each Hm 3 of nflow n the head HPPs, s calculated. Fnally, the sxth column shows the relatve cost of the ecologcal constrants, for each Hm 3 of mnmum flow requested at the head HPPs of the basn. In ths table, t can be seen that the cost of mantanng the ecologcal constrants depends on the amount of resources njected to the basn. In Fgure 15, the curve of varaton n the ecologcal cost (EC) as a functon of the affluence s presented. As shown n Table 2 and Fgure 15, the cost of mantanng the ecologcal requrements s far more mportant n dry scenaros. In fact, mantanng the same ecologcal flow of 3.42 Hm 3 /day s relatvely ten tmes more expensve than mantanng a flow of Hm 3 /day Results Consderng only Socal Consumptons In the present secton, the effect of socal consumpton (as specfed n Table 3, Appendx) n the three prevous scenaros of affluence s consdered. Table 2 has the same structure as Table 1 but consders the costs of water delvered for socal consumpton. Copyrght 2013 ScRes.

8 16 G. HERMIDA, E. D. CASTRONUOVO Flow n HPPs 1 and 3 (Hm 3 /da) Table 1. Costs of ecologcal requrements for dfferent nflows. Income, Case A. (M ) Income, Case C. (M ) Income Gap. Relatve Ecologcal Costs, Relatve Ecologcal Cost, ( M ) ( /Hm 3 ) ( /Hm 3 ) , , , , ,801,169 4,947,837 Table 2. Socal consumpton costs for dfferent nflows. Flow n HPPs 1 and 3 Income, Case Income, Case Income Gap. Relatve Socal Consumpton Relatve Socal Consumpton (Hm 3 /da) A. (M ) B. (M ) (M ) Costs, (M /Hm 3 ) Cost, (M /Hm 3 ) Accordng to the two tables, the costs of water allo- for socal uses are larger than those of mantanng cated the ecologcal constrants. In fact, for the medum sce- s 967% greater than the decrease n revenue due to naro, the reducton n proft due to the socal uses of water the ecologcal constrants. Socal uses extract resources from the basn; the ecologcal constrant s only request a mod- fcaton n the profle of generaton, but the re- source re- mans n the rver. In Fgure 16, the relatve socal consumpton costs for the three scenaros of affluence are shown. The curve SC, Socal Consum., shows the cost of delverng 1 Hm 3 of water from the basn for socal uses n the smulated scenaros. The values of ths curve can be used to calculate the prce of water allocated for human use n the basn as a functon of the profts lost n electrcty generaton. 6. Conclusons Ths paper presents an optmsaton method to calculate the optmal operaton of a basn wth both controllable and non-controllable hydro power plants. Ths program consders both socal and ecologcal restrctons, assessng the economc weght of each of them n the management of resources. Fgure 16. Socal consumpton (sc) costs for dfferent nflows. The algorthm allows for control over the actons of fluent HPPs, modfyng the operaton of controllable HPPs. The method calculates the maxmum proft electrcty generaton n the daly power market, consderng ecologcal constrants and the socal use of water. The study of dfferent nflow states shows that n ths case the relatve value of the socal consumpton of water s larger than that of mantanng ecologcal flows n the basn. Moreover, ntal evaluatons of the costs of provdng water for socal uses are performed. The proposed algorthm can be easly extended to consder other operatonal restrctons on the hydro systems. 7. Acknowledgements The authors would lke to acknowledge the Mnstry of Scence and Technology of Span (Projects IT , ENE and CENIT-CONSOLIDA) for supportng ths work. Fgure 15. Cost of ecologcal requrements (EC) for dfferent nflows. REFERENCES [1] Concernng Common Rules for the Internal Market n Copyrght 2013 ScRes.

9 G. HERMIDA, E. D. CASTRONUOVO 17 Electrcty and Repealng Drectve 96/92/EC, European Parlament and of the Councl, [2] The Spansh Electrc System 2010, Red Eléctrca de España (REE), Madrd, [3] R. Sternberg, Hydropower: Dmensons of Socal and Envronmental Coexstence, Renewable Sustanable Energy Revews, Vol. 12, No. 6, 2008, pp do: /j.rser [4] M. Markoff and A. Cullen, Impact of Clmate Change on Pacfc Northwest Hydropower, Clmate Change, Vol. 87, No. 3/4, 2008, pp do: /s [5] I. P. Holman, D. Tascone and T. M. Hess, A Compar- son of Stochastc and Determnstc Downscalng Methods for Modelng Potental Groundwater Recharge under Clmate Change n East Angla, UK: Implcatons for Groundwater Resource Management, Hydrogeology Journal, Vol. 17, No. 7, 2009, pp do: /s [6] M. Mare, B. Franços, K. Stéphane and L. Robert, Adaptaton to Clmate Change n the Management of a Canadan Water-Re sources System Exploted for Hydropower, Water Resources Management, Vol. 23, No. 14, 2009, pp [7] S. Soares and A. A. F. M. Carnero, Optmal Operaton of Reservors for Electrc Generaton, IEEE Transactons on Power Delvery, Vol. 6, No. 3, 1991, pp do: / [8] S. Granvlle, G. C. Olvera, L. M. Thome, N. Campodonco, M. L. Latorre, M. V. F. Perera and L. A. Barroso, Stochastc Optmzaton of Transmsson Constraned and Large Scale Hydrothermal Systems n a Compettve Framework, Proceedngs of the Power Engneerng Socety General Meetng, [9] C. Cheng, S. Lao, Z. Tang and M. Zhao, Comparson of Partcle Swarm Optmzaton and Dynamc Programmng for Large Scale Hydro Unt Load Dspatch, Energy Con- verson and Management, Vol. 50, No. 12, 2009, pp do: /j.enconman [10] G. C. Olvera, S. Bnato and M. V. F. Perera, Value- Based Transmsson Expanson Plannng of Hydrothermal Systems under Uncertanty, IEEE Transactons on Power Systems, Vol. 22, No. 4, 2007, pp do: /tpwrs [11] O. B. Fosso, A. Gjelsvk, A. Haugstad, B. Mo and I. Wangensteen, Generaton Schedulng n a Deregulated System. The Norwegan Case, IEEE Transactons on Power Systems, Vol. 14, No. 1, 1999, pp do: / [12] A. Kanuda and R. Loulou, Robust Responses to Clmate Change va Stochastc MARKAL: The Case of Québec, European Journal of Operatonal Research, Vol. 106, No. 1, pp do: /s (98) [13] H. Habbollahzadeh and J. A. Bubenko, Applcaton of Decomposton Technques to Short-Term Operaton Plannng of Hydrothermal Power System, IEEE Transactons on Power Systems, Vol. 1, No. 1, 1986, pp do: /tpwrs [14] E. Castronuovo and J. A. P. Lopes, Optmal Operaton and Hydro Storage Szng of a Wnd-Hydro Power Plant, Internatonal Journal of Electrcal Power Energy Systems, Vol. 26, No. 10, 2004, pp do: /j.jepes [15] G. Zhao and M. Davson, Optmal Control of Hydroelectrc Faclty Incorporatng Pump Storage, Renewable Energy, Vol. 34, No. 4, 2009, pp do: /j.renene [16] H. M. I. Pousnho, V. M. F. Mendes and J. P. S. Catalão, Schedulng of a Hydro Producer Consderng Head-Dependency, Prce Scenaros and Rsk-Averson, Energy Converson and Management, Vol. 56, 2012, pp do: /j.enconman [17] D. N. Smopoulos, S. D. Kavatza and C. D. Vournas, An Enhanced Peak Shavng Method for Short Term Hydrothermal Schedulng, Energy Converson and Management, Vol. 48, No. 11, 2007, pp do: /j.enconman [18] A. L. Dnz and M. E. P. Macera, A Four-Dmensonal Model of Hydro Generaton for the Short-Term Hydrothermal Dspatch Problem Consderng Head and Spllage Effects, IEEE Transactons on Power Systems, Vol. 23, No. 3, 2008, pp do: /tpwrs [19] Z. Shawwash, K. Thomas, K. Su and S. O. D. Russell, The BC Hydro Short Term Hydro Schedulng Optmzaton Model, IEEE Transactons on Power Systems, Vol. 15, No. 3, 2000, pp do: / [20] J. I. Pérez-Díaz and J. R. Wlhelm, Assessment of the Economc Impact of Envronmental Constrants on Short- Term Hydropower Plant Operaton, Energy Polcy, Vol. 38, No. 12, 2010, pp do: /j.enpol [21] J. I. Peréz-Díaz, R. Mllán, D. García, I. Gusández and J. R. Wlhelm, Contrbuton of Regulaton Reservors Consderng Pumpng Capablty to Envronmentally Frendly Hydropower Operaton, Energy, Vol. 48, No. 1, 2011, pp [22] European Parlament and of the Councl, Establshng a Framework for Communty Acton n the Feld of Water Polcy, Drectve 2000/60/EC of the European Parlament and of the Councl, va.cm?id=296 [23] Government of Span, Mnstry of the Presdency, Royal Legslatve Decree 1/2001, Water Act, pdf [24] Consejera de Medo Ambente, Junta de Andaluca, Royal Decree Law 1/2001, [25] CNE, Comsón Naconal de Energía, Royal Decree Law 54/1997, Law of the Electrc System. [26] Government of Span, Mnstry of the Presdency. Royal Decree 661/2007, Establshng the Regulaton of the Ac- Copyrght 2013 ScRes.

10 18 G. HERMIDA, E. D. CASTRONUOVO tvty of the Electrc Power Producton n the Specal Regme. [27] J. M. Y. Loyo, The Electrc Demand, /CONTRATACION-SUMINISTRO-ELECTRICO-Ener o-2011.pdf [28] OMEL-OMIL, Results of the Iberan Market, o-electrcdad/daro-e-ntradaro/mercado-daro [29] J. Martínez-Crespo, J. Usola and J. L. Fernández, Securty-Constraned Optmal Generaton Schedulng n Large- Scale Power Systems, IEEE Transactons on Power Sys- tems, Vol. 21, No. 1, 2006, pp do: /tpwrs [30] MATLAB, The Languages of Techncal Computng, Verson , Math Works, [31] Government of Span, Mnstry of Envronment, Guadalquvr s Descrpton, rcacon/guadalquvr/brevedescrpcon/ [32] Confederacón Hdrográfca del Guadalquvr, Ecologcal Flows, egal/planhdrologcocuenca/ Copyrght 2013 ScRes.

11 G. HERMIDA, E. D. CASTRONUOVO 19 Appendx Table 3. Hydro plants data. HPP Type Prev. HPP Tv [h] CT mn 3 V Hm max h m 1 R F R R 2, 3 6, HPP max 3 T max 3 SP 3 SP 3 V Hm V Hm V Hm,1 V Hm T, U 3 V Hm In Table 3, Prev. HPP s the number of the HPP upstream to the current HPP (.e., upstream HPP 4 there are the HPP s 2 and 3). Table 4. Coeffcents volume-heght of the hydro plants. HPP k 0 [m] k 1 [m 2 ] k 2 [m 5 ] k 3 [m 8 ] E E E E E E E E E E E E HPP V Hm /h C max 3 EC mn 3 V Hm η Copyrght 2013 ScRes.

12 20 G. HERMIDA, E. D. CASTRONUOVO Bographes Glora Hermd a was born n Coruña (1973), receved her B.S degree n Industral Engneerng from Unversty of La Coruña (2007) and her Master degree n Electrcal, Electroncs and Automaton Engneern g (2011) from Unversty Carlos III de Madrd. She s workng as As- sstant Professor n the Department of Electrcal Engneerng of Unversty Carlos III de Madrd. Her research nterests nclude the optm zaton of water resources and operaton plannng. Edgardo D. Castronuovo receved a B.S. degree ( 1995) n Electrcal Engneerng from the Natonal Un- versty of La Plata, Argentna; both M.Sc. (1997) and Ph.D. (2001) degrees from the Federal Unversty of Santa Catarna, Brazl, and performed Post-Doctorate (2005) at INESC-Porto, Portugal. He worked at the Power System areas of CEPEL, Brazl, and INESC-Porto, Portugal. Currently, Dr. Castronuovo s an Assocate Professo r at the Department of Electrcal Engneerng, Unver sty Carlos III of Madrd, Span. Hs nterests are n optmzaton methods appled to power system problems, renewable producto n, storage a nd deregulaton of the electrc al energy systems. Prof. Castronuovo s Sen- or Member of IEEE. Copyrght 2013 ScRes.