Impact of financial conditions on optimum multipurpose hydro plant design

Transcription

1 Water Resources Management III 343 Impact of financia conditions on optimum mutipurpose hydro pant design J. Lopes de Ameida Department of Civi Engineering, Coimbra University, Portuga Abstract The design of a mutipurpose hydro pant requires the anaysis of severa subjects reated to the hydroogica, meteoroogica, environmenta, geoogica, topographica, structura, eectrica, mechanica, operationa, socia, economic and financia aspects. Once a feasibe site and a base scheme are identified, the vaues of the most significant design decision variabes must be found. For under pressure schemes they are usuay: dam height; type of turbine; number of units; instaed power of each unit; diameters of tunnes and pipes and pipe thicknesses. Due to the considerabe number of decision variabes and constraints, approaches using mathematica programming optimization techniques have been considered. Yet, from our point of view, these approaches do not fuy incorporate the financia aspects. As we beieve that these aspects are of great importance in the design optimization process, we have deveoped an optimization mode that performs a financia anaysis that takes into account the risk associated with the hydroogic and market variabiity, the promoter s capita, the oan interest rate, the repayment period, and the fisca expenses. Research was done using rea data from a Portuguese hydro pant. From the exampes in this paper, it can be shown that the financia aspects can have a considerabe impact on the optimum mutipurpose hydro pant design. Keywords: mutipurpose hydro pant design and operation optimization, financia conditions, opportunity cost of capita. 1 Introduction Hydro pants are widespread hydrauic structures that can pay an important roe in hydroeectric production, eectrica power accumuation, irrigation, water suppy, food contro, water shortage contro, aeria forest firefighting, navigation

2 344 Water Resources Management III and recreation. Some of these mutipurpose aspects are tangibe and easy to evauate in monetary terms, ike the production of hydroeectric power. Others may require a more compex anaysis, ike for instance the water used for irrigation, since its importance depends on the type of agricutura species and on the growing stage of the species. An even more compex evauation is invoved when aspects ike food contro, water shortage contro, improvement of aeria forest firefighting and the fooding of riparian habitats are considered. In Ameida et a [1] the resuts of a mutidiscipinary anaysis of these aspects can be found. Some mutipurpose uses precude competing uses. In this case the mutipurpose aspects can be incorporated as constraints of the probem. An indicative exampe is the abstraction for the pubic water suppy. Once a conceptua methodoogy for mutipurpose incorporation is estabished, the probem can be formuated. We wi adopt the net present vaue, NPV, criteria as the decisive parameter of choice between excusive projects. In Breaey and Myers [3] extensive arguments can be found that support this decision. It is interesting to stress that an economicay feasibe project may not be financiay feasibe Gwet et a [6]. So, the objective function must be expressed in financia terms in order to ensure reiabe optima soution: subject to NS NE 1 1 maximize NPV = ( R i i, Ei, ) (1) NS = 1 i= 1 (1 + T ) g ( X) = (2) m where NPV = Average net present vaue; = 1,, NS; NS = Number of scenarios; i = 1, NE; NE = Number of years for the expoitation period; T = T (Χ) (3) T = Discount rate; X = {X j }; j = 1, NV; NV = Number of decision variabes; X 1 = Dam height; X 2 = Instaed power; X 3 = Type of power station (chosen from a previousy standardized set of power stations characterized by: type of turbine, number of units, distribution mode of the instaed power by the units); X 4 = Surge tank diameter; X 5 = Surge tank throtting; X 6 = Diameter of the tunne; ; X NV-1 = Diameter of ast pipe; X NV = Thickness of ast pipe; R = W Χ, H, P ) + M ( ) (4) i, i, ( i, k, i, k, i Χ R i, = Revenue in year i of scenario ; W i, = Hydroeectric revenue in year i of scenario, obtained by a mutipurpose operation optimization of the hydro pant with the decision variabes X, using H i,k, and P i,k, ; H i,k, = infow time series vaues in year i of scenario ; P i,k, = tariff price during H i,k, infow; k = 1, NI;

3 Water Resources Management III 345 NI = Number of infow time series vaues; M i = Previousy accorded revenue due to mutipurpose use in year i; E i, [ C( X),PC, IR( X),RP], ( X), EL [ C( X),PC, IR( X),RP], = EOi ( X) + ELi, + EF [ R, EO FT ]. i, i, i i, (5) E i, = Tota expense in year i of scenario ; EO i = Provisiona expense for operation, maintenance and insurance in year i; EL i, = Loan expense in year i of scenario ; C = Cost of the hydro pant at the end of the construction period; PC = Promoter s capita at the end of the construction period; IR(X) = Interest rate, which depends on project risk and therefore depends on the configuration of the hydro pant; RP = repayment period; EF i = Fisca expense in year i of scenario ; FT = Income tax; m = 1,, M; M = Number of constraints. The discount rate, T, pays an important roe in the objective function formua. This decisive parameter in the economic and financia anaysis can make the difference between a feasibe project and an unfeasibe one. Foowing the principes of corporate finance this vaue shoud be the opportunity cost of capita,, which represents the rate of return, RR, offered by aternative investments in the capita market with the same risk Breaey and Myers [3]. Besides the usua risks covered by insurance, project faiure can be caused by unexpected changes of the hydroeectric tariff or by ong unfavourabe successions of dry hydroogica years. The hydro pant configuration can infuence this kind of risk. For instance, a arge reservoir hydro pant can ensure more stabe revenues then a run-of-the-river hydro pant. This dependence is expressed in eqn (3). The oan expense EL i is another major financia item of the objective function. Given a certain promoter s capita, the oan expense depends on the tota cost of the hydro pant (that is, on the hydro pant configuration), on the repayment period and on the oan interest rate. The oan interest rate can be conditioned by the project risk [3], thus by the hydro pant configuration, eqn (5). Unfortunatey the dependence of the T and EL i on the decision variabes cannot be described by anaytica functions. So, these vaues must be evauated for each possibe hydro pant configuration. Next we wi briefy describe the mode that was deveoped to impement this approach. 2 Mode used in the research In order to deveop the economic and financia anaysis of each possibe configuration of the hydro pant, we must know the chronoogica structure of the expenses and revenues during the ifetime of the project. The evauation of the expenses and revenues demands the prior definition of both an infrastructure configuration and the operation of this infrastructure. So, we concude that in the optima mutipurpose hydro pant design process, we must consider the three main probems that must be soved in reation to Water Resources, according to Buras [5]: the optima scae of a

4 346 Water Resources Management III project; the optima design of its structures; the optima operation of those structures. The compexity of this approach ed us to divide the probem into five items. For each item a specific computationa modue was deveoped: Dam (modue: BAR); Hydrauic Circuit (modue: CH); Power Station (modue: CEN); Budget Evauation (modue: BUD); Economica and Financia Anaysis (modue: AEF). Figure 1 iustrates the goba structure of the OPAH mode. OPAH Economic and financia data. Hydroogy, meteoroogy topography, tariff, goba cost data for BUD modue, constrains and reservoir data. BUD BUD BUD BAR CH CEN AEF Power station data. Hydrauic circuit data. OPTIMUM CONFIGURATION Figure 1: Schematic ayout of the OPAH mode. The process begins with the generation of a set of possibe hydro pant configurations. In order to fuy evauate the potentia revenue of each hydro pant configuration, the BAR modue computes a mutipurpose reservoir operation optimization. Mutipe approaches and programming techniques have been used in reservoir operation optimization. In Labadie [7], a commented extensive iterature review and can be found. In the BAR modue, a noninear formuation, with noninear objective function and noninear constrains was impemented. The probem is soved using the modeer GAMS [4] with the sover MINOS [8]. The foowing items were considered: fow into the reservoir; precipitation and evaporation in the reservoir; obigatory seasona discharges from the dam to the river bed by-passed by the hydrauic circuit; obigatory seasona discharges downstream of the hydrauic circuit; obigatory seasona abstractions from the reservoir for irrigation or water suppy; maximum and minimum admissibe operating head of the turbines; maximum and minimum admissibe seasona poo eves; curve with water eve versus fow at the end of the hydrauic circuit; time-dependent hydroeectric production tariff. The mutipurpose reservoir operation optimization is too time consuming. It requires a prior simpification of the mathematica representation of the hydro pant. Consequenty, no head osses or efficiency curves are considered

5 Water Resources Management III 347 initiay. The output of the BAR modue, provides to the CH modue the gross heads and the fows of the optimum reservoir operation poicies associated with each hydro pant configuration. Then, the CH modue computes the optimum soution in terms of most economica combination of pipe thickness, pipe profie, surge tank diameter and surge tank throtting, taking into account the water hammer phenomena. Head osses in the hydrauic circuit are evauated and the gross head vaues provided by the BAR modue are corrected. Each unit of the power station presents is own efficiency curve that varies with the type of turbine, fow and net head. The power station can be equipped with singe or mutipe, equa or unequa, units. In order to compute maximum goba efficiency, the distribution of tota fow by the units is optimised. For each hydro pant configuration, the vaues of the net heads and fows, given by the CH modue, are used by the CEN modue to compute the fina corrected revenues. The BUD modue provides tota technica cost of each hydro pant configuration, considering study, design and construction expenses. The AEF modue deveops the economic and financia anaysis, in order to identify the hydro pant configuration with the highest average NPV. It is interesting to note that the identification of the optimum soution requires a prior evauation of the oan expenses EL i and the discount rate T. The AEF modue adopts a standard reation between risk and rate of return, obtained from a historica anaysis of the USA financia market [3]. The discount rate is computed after a previous risk evauation based on the quantity of negative interna rates of return, IRR, obtained from the hydro pant configuration operation in a possibe hydroogic and tariff scenarios. After oan expenses and average NPV can be computed and stored. Fina comparative inspection wi identify the optimum soution. A detaied description of the OPAH mode can be found in [2]. Cote Dam Admission conduit Surge tank Penstock Power station Horizonta distance Figure 2: Simpified profie of Catapereiro hydro pant scheme.

6 348 Water Resources Management III 12 m 3 /day evaporation Via precipitation 3 m 3 /day (reservoir) Turbines infow (seasona monthy minimum outfow from 45 to 75 m 3 ) Figure 3: Tabe 1: Simpified scheme of mutipurpose constraints. Technicay feasibe hydro pant configurations. Config. Number Dam height Hydra. gross power (Mw) Admission pipe diameter diam diam diam diam diam diam diam diam diam Surge tank diam. Penstock diameter 5 11 diam , 7, 11 diam , 7, 11 diam , 7 11 diam diam diam diam diam , 11 diam Possibe power station types Case study In order to research the impact of financia conditions on optimum mutipurpose design we chose a recenty buit Portuguese hydro pant, the Catapereiro hydro pant, ocated in the Teja river, a tributary of the Douro internationa river. This hydropower scheme is characterized by: a concrete gravity dam, a metaic admission conduit 75 m ong, a concrete surge tank, a metaic penstock 8 m ong, which ends in the power station, as described in [2]. Figure 2 shows the simpified schematic profie of this hydro pant. The buit Catapereiro hydro pant was dimensioned without mutipurpose constraints. However in this paper we wi consider two situations: 1) No mutipurpose constrains; 2) Existence of the mutipurpose constrains underined in figure 3. After preiminary processing the technicay feasibe candidate soutions were reduced to the hydro pant configurations presented in tabe 1. Figures 4, 5 and 6, show resuts from the BAR, CH, CEN and AEF modues.

7 Water Resources Management III 34 Revenue (miion ) Wet Aver./Wet Aver. Dry/Aver. Dry 17.5m/1Mw 17.5m/5.5Mw 17.5m/1Mw 27.5m/1Mw 27.5m/5.5Mw 27.5m/1Mw 37.5m/1Mw 37.5m/5.5Mw 37.5m/1Mw 17.5m/1Mw 17.5m/5.5Mw 17.5m/1Mw 27.5m/1Mw 27.5m/5.5Mw 27.5m/1Mw 37.5m/1Mw 37.5m/5.5Mw 37.5m/1Mw Figure 4: Annua gross optimum revenues computed by the BAR modue. Revenue (miion )_ in a dry hydro. year 1,,75,5,25, Configurations Figure 5: Optimum revenues in a dry year after CH and CEN computations. The revenues associated to the ast configurations on the abscissa axis in figure 4, were computed with the mutipurpose constraints in figure 3. A tariff with 6 different energy prices, varying from 3 to cts/kwh, and a monthy power price of 3.7 /Kw were considered. The five types of hydroogica years (dry, dry/average, average, average/wet and wet) were described by houry infow time series. The revenues presented in figure 5 were computed by the CH and CEN modues in a dry hydroogic year without mutipurpose constraints. Figure 6 presents the tota cost of each hydro pant configuration computed by the BUD modue. The buit Catapereiro hydro pant design was estabished after comparative economic anaysis of aternative configurations, considering the hydroeectric production aone, using an average hydroogic year and a constant tariff. In order to test the OPAH mode we simuated equivaent conditions. To consider

8 35 Water Resources Management III residua sources of risk a minimum discount rate of 3% was imposed. The corresponding OPAH optimum soution was cose to the buit Catapereiro hydro pant design: dam height of 37.5 m; admission pipe diameter of 1.45 m; admission thickness of 5.3 mm; surge tank diameter of 7 m; penstock thickness of 11.7 mm and 2 Francis turbines totaizing 8 Mw. The main differences were found in the penstock diameter and thickness, with 1.1m and 1.7 mm in the buit Catapereiro hydro pant, against 1.27 m and 11.7 mm in the OPAH optimum soution. Hydro pant cost (miion )V Configurations Figure 6: Hydro pant costs computed by AEF modue. After this initia test we progressivey introduced aspects connected to the financia conditions. In figure 7 we can see severa possibe tariff evoution patterns aong the ifetime of the project. Tabe 2 shows optima soution sensibiity to these tariff patterns. We can observe variations in penstock diameter and in NPV dispersion. Future tariff/initia tariff (%)_ Year S7 S5 S3 S1 S2 S4 S6 Figure 7: Possibe tariff evoution patterns. Tabe 3 gives the variation of the optimum hydro pant configuration with the promoter s capita, interest rate, repayment period and mutipurpose constraints. Income tax is 4% and a possibe scenarios are considered. A

9 Water Resources Management III 351 detaied description of further data associated with this case study can be found in Ameida [2]. Comparing tabe 3 with tabe 2 we note a reduction of the average NPV due to income tax and oan expenses introduction. Tabe 2: Optimum soution sensibiity to the tariff patterns of figure 7. Scenarios Dam height Admiss. diam. Surge tank diam. Penstock diam. Instaed power (MW) Average NPV (1 6 ) Min. NPV (1 6 ) Max. NPV (1 6 ) S (2F.) S (2F.) S (2F.) A (2F.) Tabe 3: Optimum soution sensibiity to: promoter s capita, interest rate, repayment period and mutipurpose constraints. Capita (1 6 ) Loan interest rate* Dam height Admission diam. S. tank diam. Penst. diam. Instaed power (MW) Average NPV** (1 6 ) Min. NPV (1 6 ) Max. NPV (1 6 ) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (2F.) % (1F.) *repayment period of 12 years for ines 8, and 1, and 25 years in remaining situations **mutipurpose use for ines 14, 15 and 16

10 352 Water Resources Management III Average NPV (miion ) Configuration Optimum soution Figure 8: Optimum soution isted in ine 11 of tabe Average NPV (miion ) Optimum soution Configuration Figure : Optimum soution isted in ine 13 of tabe 3. Tabe 3 shows that the more expensive 37.5 m height dam is ony chosen when the interest rate is ow. When the interest rate increases, this dam is repaced by the smaest one, except when mutipurpose use is considered. We can aso see that when promoter s capita fas, diameter reductions can occur in the admission pipe or in the penstock. In ines 8, and 1 we can observe that the reduction of the repayment period owers oan expenses, thus increasing average NPV. Lines 11 and 14 of tabe 3 show that, given that the interest rate is inferior to the minimum discount rate, the maximum average NPV is achieved and the major penstock diameter of 1.27 m is chosen. In figures 8 and we show the positioning of the optimum soutions associated with ines 11 and 13 of tabe 3. We can verify that the interest rate has a remarkabe impact on the optimum soution. Lines 14, 15 and 16 of tabe 3 present the optimum mutipurpose hydro pant configurations. We can see that the introduction of the mutipurpose constraints caused a sight reduction of the NPV.

11 Water Resources Management III 353 When the interest rate increases, the more expensive 37.5 m height dam is repaced by the 27.5 m dam instead of the 17.5 m dam. This is because the 17.5 m dam cannot ensure the mutipurpose constraints fufiment in a types of hydroogic years, as we can see in figure 4. In ine 16 of tabe 3, we can notice that in order to offset the higher cost of the 27.5 m dam, a ess efficient but cheaper singe Francis unit power station is chosen. 4 Concusions From the research, based on data from the Catapereiro hydro pant project, we concude that the financia conditions can have a considerabe impact on optimum, singe or mutipurpose, hydro pant design. The impact was identified on the foowing decision variabes: dam height, admission pipe diameter, surge tank diameter, penstock diameter and power station type. The instaed power showed remarkabe ack of sensibiity to the financia conditions. References [1] Ameida A.T., Moura P.S., Marques J.A.A.S. & Ameida J.P.P.G.L., Muti-impact evauation of new medium and arge hydropower pants in Portuga centre region. Renewabe and Sustainabe Energy Reviews, (2), pp , 25. [2] Ameida J.P.P.G.L., Déveoppement d'un modèe goba pour 'optimisation économique et financière de a configuration de petits aménagements hydroéectriques à buts mutipes avec circuit hydrauique en pression, Université de Liège : Liège, Ph.D. thesis, 2. [3] Breaey R.A. & Myers S.C., Principes of Corporate Finance 7/E, McGraw-Hi/Irwing: New York, 23. [4] Brooke A., Kendrick D. & Meeraus A., Gams a user's guide, The Scientific Press: South San Francisco, 12. [5] Buras N., Scientific Aocation of Water Resources, American Esevier Pub. Co.: New York, 172. [6] Gwet, G., Lejeune, A., Tea K., Guide de a fiière Hydro-Éectrique, IEPF : Québec, 15. [7] Labadie J.W., Optima Operation of Mutireservoir Systems: State-of-theart Review, Journa of Water Resources Panning and Management, 13(2), pp , March 1, 24. [8] Murtaght B. & Saunders M., Minos 5.1 user s guide, Stanford University, Caifornia, 187.