ReviewCost determination of the electro-mechanical equipment of a small hydro-power plant
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 iswhere 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.
Pelton turbines
Carrying out the linear correlation, we obtain the planewith a quite good fit of R2 = 93.16%.
Once the equation Z is obtained, and according to Eqs. (10), (11), (12) searched constants would value
Cost equation for these constant values would be the following1
The graphic representation of the afore-mentioned surface is shown in Fig 3
Francis turbines
Carrying out linear correlation:
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 be
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).
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