Short-cut design of small hydroelectric plants

Renewable Energy 19 (2000) 545±563 www.elsevier.com/locate/renene Short-cut design of small hydroelectric plants N.G. Voros*, C.T. Kiranoudis, Z.B. Maroulis Department of Chemical Engineering, National Technical University of Athens, Polytechnioupoli, Zografou, Athens, 15780, Greece Received 20 September 1997; accepted 5 May 1999 Abstract The problem of designing small hydroelectric plants has been properly analysed and addressed in terms of maximizing the economic bene ts of the investment. An appropriate empirical model describing hydroturbine e ciency was developed. An overall plant model was introduced by taking into account their construction characteristics and operational performance. The hydrogeographical characteristics for a wide range of sites have been appropriately analyzed and a model that involves signi cant physical parameters has been developed. The design problem was formulated as a mathematical programming problem, and solved using appropriate programming techniques. The optimization covered a wide range of site characteristics and three types of commercially available hydroturbines. The methodology introduced an empirical short-cut design equation for the determination of the optimum nominal owrate of the hydroturbines and the estimation of the expected unit cost of electricity produced, as well as of the potential amount of annually recovered energy. # 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction The term hydropower refers to generation of shaft power from falling water. The power could then be used for direct mechanical purposes or, more frequently, for generating electricity. Hydropower is the most established renewable resource for electricity generation in commercial investments. Although, hydroelectric generation is regarded as a mature technology, there are still possibilities for * Corresponding author. 0960-1481/00/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0960-1481(99)00083-X

546 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 Nomenclature a, b, c turbine e ciency model coe cients de ned in Eq. (2) c 0, c 1, c 2 capital cost coe cients de ned in Eq. (15) c E unit cost of electricity produced ($/kwh) c EL conventional unit cost of electricity ($/kwh) c OP operational cost coe cient de ned in Eq. (16) ($/kw) C CP capital cost ($) C OP operational cost ($/h) C T total annual cost ($) e percentage of the capital cost on an annual rate E electrical energy annually recovered (W) g gravity constant (m/s 2 ) H available hydraulic head (m) H 0 available vertical fall of water (m) H r nominal vertical fall of water de ned in Eq. (9) (m) k ow duration curve parameter de ned in Eq. (11) P electrical power (W) PI investment e ciency P r nominal hydroturbine power (W) q 50 owrate duration curve parameter de ned in Eq. (13) q min owrate duration curve parameter de ned in Eq. (12) q max hydroturbine maximum working owrate fraction de ned in Eq. (5) q min hydroturbine minimum working owrate fraction de ned in Eq. (4) Q hydroturbine owrate (m 3 /s) Q available water owrate (m 3 /s) Q 50 mid-year stream owrate (m 3 /s) Q max annual highest stream owrate (m 3 /s) Q min annual lowest stream owrate (m 3 /s) S total annual pro ts expected from the investment ($) t time (s) t OP operating time of the plant (s) time of the calendar year (s) t Y Greek letters g short-cut model parameter de ned in Eq. (21) Z turbine e ciency turbine nominal e ciency Z r

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 547 improvement. While some elements of hydropower, such as turbine e ciency and cost, have reached an extreme, the same cannot be said for the system itself. New turbine designs and transmission technology (which is of great importance to hydropower development) with respect to regional characteristics, continue to advance. Moreover, environmental concerns are driving changes in the design, construction, operation and optimization of hydroelectric plants [1,2]. Taking into consideration the aforementioned technological advances, as well as the economic bene ts of this technology, the generation of electricity derived from hydroturbines has now a growing capacity of total world-wide installations of about 5% per year, doubling about every 15 years. More speci cally, hydro installations and plants are long lasting (due to continuous steady-state operation without high temperatures and mechanical stresses), thus producing electricity at low cost with consequent economic bene ts [3]. No consensus has been reached on the de nition of small, mini, and micro hydropower plants. Micro hydropower schemes are usually described as those having capacities below 100 kw, mini hydropower plants as those ranging from 100 kw to 1 MW while small hydroelectric plants as those that produce electric power ranging from 1 to 30 MW. Recent international surveys on small hydropower facilities (with capacities below 10 MW) reveal that small hydropower plants are under construction or have been already constructed in more than 100 countries [4±6]. The design of reliable and cost e ective small hydropower plants capable of large-scale electrical energy production is a prerequisite for the e ective use of hydropower as an alternative resource. In this sense, the design of a small hydroelectric plant or equivalently the determination of type and energy load of the particular hydroturbines, should maximize the energy output together with the life-time of the machines. In all cases, the design objective is closely related to the total annual output of the overall hydroturbine operation in power terms. Obviously, given the power curve of the hydroturbine to be used and regional ow duration statistical data as well as the topology of the site, we can estimate the total annual energy output of a small hydroelectric plant to be installed. In this case, both the type and size of the hydroturbine, expressed in terms of its nominal owrate have to be determined under a certain economic environment. The determination of the optimal plant characteristics must be based on speci c design objectives. In this case, the design problem may be formulated as a mathematical programming problem, involving an objective function representing the investment e ciency which is expressed by the pro ts expected per unit of capital invested. The construction and operation of various types of hydroturbines to be used has been investigated to an extent that several operating experimental data are currently available in the literature. Furthermore, hydrogeographical statistical data and hydropower potential have been thoroughly investigated for a wide range of regions where hydropower seems promising for exploitation. In addition, suitable mathematical models describing the operation of hydroturbines have been developed and used for the simulation of hydroelectric plants. Fasol and Pohl [7]

548 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 developed suitable mathematical models for the simulation of the operation of a hydroelectric plant and its advanced control schemes. However, design e orts in this eld is limited with respect to the general objectives described previously. Charles et al. [8] used advanced computational uid dynamics for the design of hydroelectric plants and calculated in detail ow quantities, including energy loss and plant e ciency. Short-cut design is a technical procedure for expressing in a straightforward way the optimal results of a detailed design problem through empirical equations involving the corresponding design variables. In this way, all other model variables are directly computed through the model equations. The parameters of the empirical equations are evaluated by tting the short-cut model equations to the corresponding design problem optimal results computed using the full process model. Short-cut design is extremely important for preliminary selection of alternative design scenaria for diversi ed policies of investment at a regional level. In this way, short-cut evaluations of optimal designs for certain sites is an indispensable tool for assessing regional planning strategies at a national or international level. Moreover, it is extremely important for determining the way that alternative energy sources could possibly penetrate the energy market by an appropriate subsidy policy. This work addresses the problem of small hydroelectric plant short-cut design in terms of maximizing the economic bene ts of the investment. The mathematical model of hydroturbines was developed taking into consideration their performance with respect to construction and operation. An empirical model was used for estimating the overall turbine e ciency. The objective function to be maximized was the investment e ciency. The hydrogeographical characteristics of a site have been analyzed in terms of signi cant physical parameters and modeled appropriately. Optimization was carried out for a wide range of site characteristics expressed by the corresponding model parameters and for three di erent types of commercial hydroturbines. An empirical short-cut model equation was introduced for determining the optimum nominal owrate of the hydroturbines. The regions of applicability for all turbines involved, was determined as a function of model parameters. From the engineering point of view, such an analysis will directly serve as an evaluation tool for explicitly determining the pro tability of exploiting hydropower at a certain region. 2. Mathematical modeling of hydroturbines The power obtained by a hydroturbine operated in a small hydroelectric plant is proportional to the potential energy lost by the falling uid and is given by the following equation [9]: P ˆ ZgQH 1 The turbine e ciency, Z, involved in the calculation of water potential converted

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 549 energy through expression (1), represents the actual utilization of the available potential energy of the system. Normally, a hydroturbine is designed so that it can be operated for a wide range of working uid owrates around a nominal operating point. The performance of the turbine is characterised by its nominal owrate, Q r, that is an explicit indication of its size. For a speci c type of turbine (con guration of equipment), its size and capacity that are directly analogous to its diameter are proportionally related to its nominal owrate. Therefore, the turbine nominal owrate is a suitable variable for sizing the turbine and all relevant equipment of the plant. The turbine e ciency depends on the working uid owrate and actual turbine characteristics. Experimental data for the turbine e ciency, in the case of three commercial hydroturbines studied in this work (i.e. FRANCIS, PELTON and AXIAL), are given in Fig. 1, as a function of the ratio of working owrate to its corresponding nominal owrate and the turbine e ciency at the nominal owrate, Z r [10]. All curves exhibit a maximum at a owrate representing the nominal performance of the hydroturbine. An empirical expression for representing the turbine e ciency characteristic curve is proposed: Z Q 2 Q ˆ a b c 2 Z r Q r Q r In this expression, the turbine characteristics are the nominal turbine e ciency, Z r, the nominal turbine owrate, Q r, and three parameters expressing the shape of the curves. It must be noted that the nominal power of the turbine is given by the following expression: P r ˆ Z r gq r H 3 Excellent ts to actual experimental data were detected when expression (2) was used as real turbine data. The predictions of the empirical equation proposed for the case of turbine e ciency experimental values are also given in Fig. 1, indicating the excellence of the t and suggesting the practical signi cance of Eq. (2). The estimated turbine parameters of Eq. (2) for all commercial hydroturbines studied, are given in Table 1. The nominal turbine e ciency is independent of the nominal owrate for all turbines examined, and its corresponding values are also given in Table 1. Each hydroturbine is constructed to operate between two extremes, a minimum and a maximum working owrate. We introduce two turbine characteristic parameters q min and q max, representing the fraction of its nominal owrate corresponding the lower and upper extreme working owrates, respectively. These values are also included in Table 1 for each one of the commercial turbines studied. The minimum and maximum working owrates for the turbine are accordingly given by the following equations: Q min ˆ q min Q r 4 Q max ˆ q max Q r 5

550 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 Fig. 1. Hydroturbine e ciency curves (points are experimental data and lines are model predictions). (a) FRANCIS, (b) PELTON, (c) AXIAL.

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 551 Table 1 Hydroturbine e ciency and operational parameters Turbine FRANCIS PELTON AXIAL a 0.537 0.224 0.219 b 1.047 0.483 0.476 c 0.490 0.741 0.743 Z r 0.9 0.9 0.9 q min 0.55 0.35 0.35 q max 1.1 1.5 1.6 The water owrate through the turbine, Q, is determined by the following relationship as a function of the available water owrate, Q [9±11]: 8 < 0, Q < Q min Q ˆ Q, Q : min < Q < Q max 6 Q max, Q max < Q The available hydraulic head involved in Eq. (1) can be estimated by subtracting the friction losses through the penstock from the available vertical fall of water [11]: # Q 2 H ˆ H 0 "1 l 7 Q r The friction coe cient, l, involved in Eq. (7) depends on the penstock size, con guration and topology of the region in the sense that the e ect of piping network and the dam layout is embodied in this parameter. Eqs. (1), (2) and (7) can now be combined to express the actual power converted as a function of turbine working owrate and available vertical fall of water. The nominal power of the plant is given by: P r ˆ Z r gq r H r 8 where: H r ˆ H 0 1 l 9 The potential of a stream is characterized by the available vertical fall (H 0 ) and its owrate that is usually expressed by the owrate duration curve. The ow duration curve provides the time period during which the ow rate of the stream is greater than a speci c value (cumulative distribution of stream owrate on an annual basis). Natural river ow is highly variable, a characteristic that has important implications for the design of hydroelectric plants and their incorporation into the electrical generation system. Most rivers exhibit pronounced seasonal variation in their ow. In some cases, the average three-

552 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 month high ow may be more than ten times greater than the average threemonth low ow, while in others, it is less than double. In order to provide a generalized model for predicting a stream owrate duration curve the following expression is suggested: Q ˆ Q max Q min k Q max t 1 k 1 t 10 where: k ˆ Q max Q 50 Q 50 Q min 11 Eq. (10) describes the owrate duration curve of a stream by utilizing only three parameters; the annual highest stream owrate, Q max, the annual lowest stream owrate, Q min, and the stream owrate corresponding to the mid-year point of the ow duration curve, Q 50. All these characteristic parameters of the stream duration curve along with the stream duration curve itself are presented in Fig. 2. The rst two parameters indicate the poles of the ow duration curve, while the third one, its shape (curvature). Obviously this parameter describes the sharpness Fig. 2. Placement of a hydroturbine on a site stream duration curve.

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 553 of seasonal variations in stream owrate. To illustrate the way that a hydroturbine could be placed on the ow duration curve, Fig. 2 also includes the characteristic variables of a hydroturbine placed randomly. In order to describe more e ciently the site characteristic parameters, we introduce the following variables, expressing the corresponding owrate duration curve parameters as a fraction of the maximum annual owrate value of the stream: q min ˆ Q min Q max 12 q 50 ˆ Q 50 Q max 13 The annual energy obtained by the operation of the hydroelectric plant is calculated by integrating Eq. (1) for the entire year: E ˆ top 0 P dt 14 The installation cost of the plant is given by the following equation as a function of the turbine nominal power and the vertical free fall of the site [10]: C CP ˆ c 0 P c 1 r H c 2 0 15 The operational cost of the plant is proportional to the installed plant capacity and is given by the following equation [10]: C OP ˆ c OP P r 16 The total annual cost of the plant is therefore calculated by means of the following equation: C T ˆ ec CP t OP C OP 17 As a result the unit cost of energy produced is the ratio of total annual cost and annual energy recovered: c E ˆ CT E 18 The expected pro ts from the operation of the hydroelectric plant is therefore given below: S ˆ E c EL c E 19 The investment e ciency is expressed as the ratio of expected pro ts per invested capital:

554 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 PI ˆ S C CP 20 Eqs. (1)±(20) constitute the mathematical model of the entire hydroelectric plant. In this case, the design objective is to maximize the investment e ciency from the operation of such a plant. Given the type of hydroturbine and site hydrogeographical characteristics and topology, there is only one design variable to be computed by means of maximizing the objective function; the nominal owrate of the hydroturbine. The optimization procedure throughout this paper was carried out by means of the successive quadratic programming algorithm implemented in the form of the subroutine E04UCF/NAG. All runs were performed on a SG Indy workstation under Unix. 3. Short-cut design of small hydroelectric plants On the basis of the above, the design strategy for small hydroelectric plants can now be clearly stated. Given the type of hydroturbine and site hydrogeographical characteristics (i.e. stream duration curve parameters) and topology (i.e. available vertical fall of water) the nominal owrate at which the hydroturbine should operate must be determined by means of optimizing appropriate technoeconomical criteria under speci c operational and environmental constraints. As a consequence of the above, the determination of the optimum plant con guration must be based on speci c design objectives. In practice, the representation of the design problem for small hydroelectric plants should focus to corresponding mathematical gures obtained through an adequate mathematical model as previously formulated. In all cases, the design procedure should involve an objective function representing the economic bene ts from the operation of such a plant or its e ciency in terms of energy availability towards regional demand. Certain alternative objective function types may be taken into consideration regarding the bene ts expected: 1. Maximization of the investment e ciency. This case suits to design problems confronted by individual power producing industries (either private or municipal) that have invested or plan to invest in this eld, in countries where legislation permits so. In other words, this objective refers to the direct economical bene ts expected from such an investment under a speci c competitive economic environment, thus determining the feasibility of exploiting this type of renewable energy source. 2. Maximization of the amount of energy annually produced from the available hydro resources. This case suits to design problems usually confronted for regions where no other sources of energy are technically exploitable, and the objective is to exploit the highest possible energy potential of a region in order to cover the local demand, assuming that the use of hydropower is still

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 555 pro table compared to the unit cost of electricity available in remote national regions due to increased transportation cost. Throughout this paper we choose the rst possibility for our objective function. Characteristic economical gures concerning capital and operational cost components for a typical economic environment were taken into consideration and are listed in Table 2. Between these two cases, the former evaluates an optimum plant size that is completely di erent (smaller) than the latter. However, it can be shown that the optimal results of the rst objective that is an economically driven function coincide with the ones of the second objective that is a purely technical function (independent of economics) when the unit cost of conventional electricity approaches in nity. In this case the plant operates at the point of maximum energy recovery. In order to illustrate the above mentioned situation we examine the case of a real site (Kourtaliotis, Crete) involving a ow duration curve described by a maximum annual stream owrate of 17,640 m 3 /h, minimum annual stream owrate of 17% of the maximum, mid-year stream owrate of 25% and available vertical water fall of 65 m. The hydroturbine type used for this example was FRANCIS. The e ect of hydroturbine nominal owrate on investment e ciency and total energy recovered is presented in Fig. 3. Obviously, each case results in completely di erent plant size and economic gures. For increasing unit cost of conventional electricity, optimum plant size determined by optimizing the investment e ciency increases to the one determined by maximizing the energy recovery. The power performance curve of the optimal plant size using FRANCIS hydroturbine, determined by the maximization of the annual pro ts for the a typical site involving a linear ow duration curve described by maximum annual stream owrate of 10,000 m 3 /h, zero level of minimum annual stream owrate and available vertical water fall of 100 m, is given in Fig. 4. The power curve is characterised by two di erent regions: a constant power region that lasts for 257 days and a decreasing power region that lasts for the remaining 108 days of the year. The rst region corresponds to days where stream owrate is greater or equal to the maximum hydroturbine owrate. The second region corresponds to Table 2 Design and cost data c 0 (k$) 40 c 1 0.7 c 2 0.35 c OP 0.01 e 0.1 l 0.1 t Y (h/y) 8760 c EL (c/kwh) 6.7

556 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 Fig. 3. E ect of hydroturbine nominal owrate on certain process variables. (1) Investment e ciency, (2) energy recovered. (a) c EL =4 c/kwh, (b) c EL =8 c/kwh, (c) c EL =20 c/kwh. days where the stream owrate is less than the maximum hydroturbine owrate. In this case, the turbine operates for only 55 days where the stream owrate is greater or equal to the minimum hydroturbine owrate. Obviously, for the remaining 53 days the plant is out of operation since the stream owrate is less than the minimum hydroturbine owrate. Therefore, the total annual energy

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 557 Fig. 4. Power performance curve. recovered corresponds to the area below the hydroturbine power curve that extends up to the 312th day. The optimization procedure for the determination of the optimal turbine size described earlier, was concentrated on the solution of a speci c design problem involving a prede ned turbine type and site hydrogeographical characteristics. This procedure can be extended to include a wide range of turbine types and stream particularities described by di erent values for the parameters of its ow duration curve as well as for di erent vertical water fall values. When the results of the optimization for each turbine and site combination are systematically compiled and presented, an empirical short-cut design equation can be evaluated so that the design engineer can automatically determine the optimal size of each plant and subsequently evaluate its performance in terms of the recovered amount of energy and the unit cost of power produced. A short-cut design empirical equation of the following form is proposed: Q r ˆ " gq 50 1 g 1 q 50 1 q min q min q max q max # Q max 21 It involves only one parameter, g, and expresses the optimal hydroturbine nominal

558 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 Table 3 Short-cut model parameters Turbine g FRANCIS 0.422 PELTON 0.369 AXIAL 0.364 owrate in terms of investment e ciency maximization. The determination of this short cut model parameter was carried out by tting Eq. (21) to the optimal results of the full design problem for all turbines studied. The values of g for all turbines are given in Table 3. The tting of the short-cut empirical model to the optimal plant nominal owrate for all turbines studied are given in Figs. 5±7. Obviously, all ts were extremely satisfactory and Eq. (21) can be safely used for short-cut design purposes in the case of small hydroelectric plant design. Eq. (21) Fig. 5. Fitting of the short-cut empirical equation (lines) on optimal plant nominal owrate for FRANCIS hydroturbine (points) (1) q 50 =20%, (2) q 50 =40%, (3) q 50 =60%, (4) q 50 =80%. (a) q min =0%, (b) q min =30%, (c) q min =60%.

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 559 Fig. 6. Fitting of the short-cut empirical equation (lines) on optimal plant nominal owrate for PELTON hydroturbine (points) (symbols as in Fig. 5). does not include any dependence of the optimum plant size on the available vertical fall. For the entire range of sites studied, PELTON and AXIAL hydroturbines involve smaller optimum installation than the one evaluated for FRANCIS. All hydrogeographical model parameters (Q max, Q min and Q 50) have positive e ect on the optimum value of the plant nominal owrate (Q r ). Between the site hydrogeographical parameters, the maximum annual stream owrate has the greatest impact on the plant nominal owrate, while the mid-year annual stream owrate has the smallest one. Clearly, for sites with high hydropotential, larger hydroturbines should be utilised to fully exploit hydropower in this case. Figs. 5±7 expressing Eq. (21) are the essence of design of small hydroelectric plants with capacities up to 100 MW. Given the type of hydroturbine used and the regional hydrogeographical and topological characteristics (expressed by appropriate model parameters), the engineer can automatically evaluate the plant optimum nominal size, the corresponding total amount of energy recovered and a reasonable estimation of the total plant cost and pro ts expected at a preliminary design level. At this stage of design, the short-cut design equation for small

560 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 Fig. 7. Fitting of the short-cut empirical equation (lines) on optimal plant nominal owrate for AXIAL hydroturbine (points) (symbols as in Fig. 5). hydroelectric plants produced is a tool of great signi cance for feasibility studies on such investments. The e ect of variation of selected model parameters on optimal process variables for the case of FRANCIS hydroturbine and the typical site of Fig. 4 is given in Fig. 8. Optimal nominal owrate is greatly a ected by the shape of the stream owrate duration curve, while as indicated above the available vertical fall of water, has no e ect at all. The unit cost of electricity produced is greatly a ected by the available vertical fall of water, while the shape of the stream owrate duration curve has the smallest e ect. Moreover, the available vertical fall of water has the greatest impact on the total energy recovered while the minimum annual stream owrate has the lowest one. The short-cut design model equation parameter, g, is generally a ected by the economic environment assumed. More speci cally, no impact of capital turbine cost was observed on this parameter. On the contrary, the unit cost of conventional electricity had a strong positive e ect on it, indicating that larger hydroturbines are favored as conventional electricity cost increases. This e ect is

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 561 Fig. 8. E ect of variations of selected model parameters on optimal process variables for the FRANCIS hydroturbine. (1) Q R, (2) c E (3) E (a) H, (b) q 50, (c) q min. Squares: +25%; triangles: 25%. given in Fig. 9 for the FRANCIS hydroturbine. The results are directly related to the ones obtained from the case study of Fig. 3. In order to determine the range of applicability of each hydroturbine, all hydroturbines were directly compared for a wide range of model parameters expressing topology and hydrogeography. Only two parameters could discern between the various types of hydroturbines. The range of application for all hydroturbines are given in Fig. 10. Clearly FRANCIS hydroturbine is inferior to both others while PELTON is chie y preferred for literally most common practical cases. 4. Conclusions The design of small hydroelectric plants can be properly analysed and addressed by means of optimizing the expected bene ts from such an investment in the eld

562 N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 Fig. 9. E ect of conventional unit cost of electricity on short-cut model parameter g. Fig. 10. Regions of applicability of all hydroturbines studied.

N.G. Voros et al. / Renewable Energy 19 (2000) 545±563 563 of renewable energy exploitation. Optimization can be carried out by developing the mathematical model of the hydroturbines, taking into account their construction characteristics and operational performance. The turbine e ciency can be successfully modeled by means of an empirical equation. The plant model must also involve the regional characteristics in terms of hydrogeographical and topological model parameters. The design problem can be formulated as a mathematical programming one, and can be solved using appropriate programming techniques. An empirical short-cut design equation describes optimal size of the plant for a wide range of site characteristics and all commercially available hydroturbines studied. In this case, the optimum nominal owrate, the amount of energy recovered and a reasonable estimation of the plant cost can be automatically determined. References [1] Donald JJ. Hydro power engineering. New York: Ronald Press, 1958. [2] Hammond R. Water power engineering. London: Heywood, 1958. [3] Raabe IJ. HydropowerÐthe design, use and function of hydromechanical, hydraulic and electrical equipment. Duesseldorf: VDI-Verlag, 1985. [4] Biswas AK. In: El-Hinnawi B, Biswas AK, editors. Hydroelectric energy. Renewable sources of energy and the environment. Dublin: Tycooly International Publishing, 1981. [5] Moreira JR, Poole AD. In: Johansson TB, Kelly H, Reddy AKN, Williams RH, editors. Hydropower and its constraints. Renewable energy: sources for fuels and electricity. London: Earthscan Publications, 1993. [6] Havery A. Micro-hydro design manual. A guide to small-scale water power schemes. London: Intermediate Technology Publications, 1993. [7] Fasol KH, Pohl GM. Simulation, controller design and eld tests for a hydropower plantða case study. Automatica 1990;26:475. [8] Charles S, Xiangying C, Fayi Z. Using computational tools for hydraulic design of hydropower plants. Hydro Review 1995;14:104. [9] Twidell JW, Weir AD. Renewable energy resources. Cambridge University Press, 1986. [10] Prefeasibility Study for the Renewable Energy Sources Exploitation in Crete, ALTENER No.1030/93, Final Report, 1996. [11] Warnick CC. Hydropower engineering. Englewood Cli s, NJ: Prentice Hall, 1984.