Elsevier

Renewable Energy

Volume 34, Issue 1, January 2009, Pages 6-13
Renewable Energy

Review
Cost determination of the electro-mechanical equipment of a small hydro-power plant

https://doi.org/10.1016/j.renene.2008.04.039Get rights and content

Abstract

One of the most important elements on the recovery of a small hydro-power plant is the electro-mechanical equipment (turbine–alternator), since the cost of the equipment means a high percentage of the total budget of the plant. The present paper intends to develop a series of equations which determine its cost from basic parameters such as power and net head. These calculations are focused at a level of previous study, so it will be necessary to carry out the engineering project and request a budget to companies specialized on the construction of electro-mechanical equipment to know its cost more accurately. Although there is a great diversity in the typology of turbines and alternators, data from manufacturers which cover all the considered range have been used. The above equations have been developed for the most common of turbines: Pelton, Francis, Kaplan and semiKaplan for a power range below 2 MW.

The obtained equations have been validated with data from real installations which have been subject to analysis by engineering companies working on the assembly and design of small plants.

Introduction

The cost of the electro-mechanical equipment (turbine, alternator and regulator) means a high percentage of a small hydro-power plant budget (around 30% and 40% of the total sum). It stems from this the importance of the determination of that cost, which could directly influence the project feasibility (Fig. 1).

For the determination of the cost of the electro-mechanical equipment, there are graphs which can approximately calculate those costs. But these graphs refer to a distant time period, since they use to be at least 10 years old. Besides, manufacturers of turbines and alternators do not supply any information about cost, since every installation is different and complex.

An example of these graphs are those developed by the Institute for Energy Diversification and Saving [Instituto para la Diversificación y Ahorro de la Energía, IDAE, Spain], with which it is possible to determinate the cost of a turbine depending on its power and net head [7].

From an analytical point of view and analyzing the state of art for the calculation of the cost of electro-mechanical equipment, it has been checked that a great part of authors use an expression depending on the power (P) and net head (H) of the small plant. This expression isCOST=aPb1Hc(/kW)where a, b and c coefficients depend on the geographical, space or time field in which they are used.

Among some bibliographical references, it should be remarked the contribution made by J.L. Gordon and Penman [3] two of the greatest specialists on the design of small plants. They were pioneers in using an equation which generally relates the cost of the equipment with its power and net head.

Subsequently, several authors have developed different cost equations for different countries [1], [11], [12], [15]. One of the most recent by Dr. Kaldellis [8], [9], in 2007, for plants located in Greece was proposed.

Some functions of costs that have been developed in the literature for various regions are shown in Table 1. This table also gathers the year in which that functions were proposed.

Section snippets

Cost analysis methodology

Given that the different existing equations are more than 20 years old, checking large differences between them and having enough current data of costs depending on power and head, we carried out the determination of the constants a, b and c of expression (1).

For the determination of these parameters a best-fit analysis will be carried out for diverse costs. The methodology of this analysis has been included in the Appendix.

The constants a, b, c are obtained through the following expressions.a=

Pelton turbines

Carrying out the linear correlation, we obtain the planeZ=9.78098+0.635275X0.281735Y,with a quite good fit of R2 = 93.16%.

Once the equation Z is obtained, and according to Eqs. (10), (11), (12) searched constants would valuea=9.7809=17.693b=0.635275c=0.281735

Cost equation for these constant values would be the following1COST=17.693P0.3644725H0.281735(/kW).

The graphic representation of the afore-mentioned surface is shown in Fig 3

Francis turbines

Carrying out linear correlation:Z=10.1542+0.439865X0.127243Y(R2=72.26%)a=10.1542=25.698b=0.439865c=0.127243COST=25.698P0.560135H0.127243(/kW).

The cost function of a Francis turbine (18) is graphically shown in Fig 5, Fig 6; a strong cost increase for high power levels and heads lower than 100 m is noticeable.

Incurred errors have ranged between +22.27% and −15.83%. The largest errors appear within the band of power level ranging from 300 to 400 kW (Table 3).

Kaplan–semiKaplan turbines

The different constants for Kaplan and semiKaplan turbines have been obtained carrying out linear correlation in a similar way to that for Pelton and Francis turbines. Those constants are listed in Table 4.

Cost equations would therefore beCOST=19.498P0.58338H0.113901(/kW)COST=33.236P0.58338H0.113901(/kW)

The cost function of a semiKlapan turbine (19) and Kaplan turbine (20) are graphically shown in Fig 7, Fig 8, respectively.

In the same way, errors incurred using cost equations are shown

Summary of results

The Table 6 lists the results obtained, including cost equations per power unit, their R2 related and error range, for each type of machine.

Validation of results

Equations obtained for every type of turbine have been validated among engineering companies working in the design and assembly of small plants. It is noticeably that all of them perfectly fulfil all manufacturing standards and that cost deviation is that expected in every studied case for different types of real installations.

These companies have provided the following actual costs of electro-mechanical equipment plants located in Europe and Northern Africa. We have simulated the various

Conclusions

We have obtained equations which facilitate the determination of the cost of electro-mechanical equipment from easily available parameters in any small hydro-power plant: net head and power. These expressions have been differentiated for the most common types of turbines: Pelton, Francis, Kaplan and semiKaplan, and for a power range below 2 MW. All equations fit the original costs quite well, as R2 exceeds 75% in all cases.

All the reviewed equations do not match real data as well as those

Acknowledgments

We would like to thank all companies and organizations which have verified the validity of the equations obtained in this work, specially Saltos Del Pirineo, Hydroship and the Institute for Energy Diversification and Saving (IDAE).

References (15)

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