# MATHEMATICAL MODEL OF SENSITIVITY ANALYSIS OF ECONOMIC EFFICIENCY OF WIND POWER PLANT INVESTMENT PROJECT

• B. Tuchynskyi Institute of renewable energy, NAS Ukraine, 02094, 20А, Hnata Khotkevycha St., Kyiv.
• S. Kudria Institute of Renewable Energy of the National Academy of Sciences of Ukraine, 02094, 20А Hnata Khotkevycha St., Kyiv, Ukraine.
• V. Tochenyi Institute of Renewable Energy of the National Academy of Sciences of Ukraine, 02094, 20А Hnata Khotkevycha St., Kyiv, Ukraine.
• I. Ivanchenko Institute of renewable energy, NAS Ukraine, 02094, 20А, Hnata Khotkevycha St., Kyiv.
Keywords: sensitivity analysis, wind farm investment project, net present value, elasticity coefficients, economic efficiency.

### Abstract

Important section of investment calculations is the sensitivity analysis, which allows you to put in order the initial parameters of the project according to the impact of their changes on changes in project effectiveness. A commonly used tool for sensitivity analysis is a spider chart- a set of graphs in a common coordinate system. This method of sensitivity analysis is purely graphical. It provides a clear idea of the approximate qualitative picture of sensitivity, leaving researchers without appropriate quantitative assessments and analytical constructions. In this article, the problem of sensitivity analysis of the wind farm investment project is solved by building and studying an appropriate economic and mathematical model. The model consists of a system of equations that reflects the direct and indirect relationships between the initial parameters and indicators of the wind farm investment project. Next, the system of equations is reduced to the function of all the presented parameters, to which the formulas for calculating the coefficients of elasticity are applied. The article presents the formulas for calculating the parameters of the mathematical model of the coefficients of elasticity of the net present value of the wind farm investment project and presents the results of calculations of the elasticity coefficients of the wind farm investment project. The existence of an explicit solution of the economic-mathematical model allowed to obtain explicit formulas for the coefficients of elasticity and to perform a comprehensive mathematical study of the problem. Analysis of the results of experimental calculations of elasticity coefficients showed that the economic efficiency of the wind farm investment project is most sensitive to changes Capacity factor and electricity tariffs of wind farms, and with increasing cash flow discount rate the sensitivity of the project to changes in initial parameters increases (in absolute terms). The presented results of calculations demonstrated the effectiveness of the application of elasticity coefficients for both classical and non-standard sensitivity analysis of wind farm investment projects. References 6, tables 5, fig. 3.

### Author Biographies

B. Tuchynskyi, Institute of renewable energy, NAS Ukraine, 02094, 20А, Hnata Khotkevycha St., Kyiv. Author information: Senior Researcher at wind energy department at Institute of Renewable Energy of NAS of Ukraine, Senior Researcher, Candidate of Economic Sciences.
Education: Taras Shevchenko National University of Kyiv, Faculty of Mechanics and Mathematics.
Research area: Applied Mathematics, Computational Methods in Mathematics, Mathematical Statistics, Mathematical Models and Methods in Economics, Investment Analysis, Wind Power.
Publications: 117.

S. Kudria, Institute of Renewable Energy of the National Academy of Sciences of Ukraine, 02094, 20А Hnata Khotkevycha St., Kyiv, Ukraine. director of the Institute of Renewable Energy of NAS of Ukraine, corresponding member of NAS of Ukraine, professor, doctor of technical sciences.
Education: Kyiv Polytechnic Institute, engineer-technologist on the specialty "Technologies of electrochemical manufactures".
Research area: renewable energy sources, energy storage, energy efficient technologies, hydrogen energy.

Publications: 376.
Patents: 45.
Monographs: 11.

V. Tochenyi, Institute of Renewable Energy of the National Academy of Sciences of Ukraine, 02094, 20А Hnata Khotkevycha St., Kyiv, Ukraine. Author information: Senior Researcher at wind energy department at Institute of Renewable Energy of NAS of Ukraine, Candidate of Technical Sciences.
Research area: long-term prediction of wind power generation at the wind farm site, mathematical modeling analysis of the costs of the investment project wind farm.
Publications: 26.

I. Ivanchenko, Institute of renewable energy, NAS Ukraine, 02094, 20А, Hnata Khotkevycha St., Kyiv. Author information: chief technologist at wind energy department at Institute of Renewable Energy of NAS of Ukraine.
Education: Kiev National University of Technology and Design, Faculty of Engineering and Economics.
Research area: wind energy, assessment of wind energy potential, economic efficiency of investments in the construction of wind power plants.
Publications: 30.

### References

1. Bernar I., Kolli Zh.-K. Tolkovyj ekonomicheskij i finansovyj slovar. [Thesaurus Economic and Financial Dictionary]. T. 1. M. Mezhdunarodnye otnosheniya. 1997. 639 p. [in Russian].
2. Birman G., Shmidt S. Ekonomicheskij analiz investicionnyh proektov. [Economic analysis of investment projects]. M. Banki i birzhi. Izdatelskoe obedinenie “YuNITI”. 1997. Pp. 149-158. [in Russian].
3. Vilenskij P.L., Livshic V.N., Smolyak S.A. Ocenka effektivnosti investicionnyh proektov. [Evaluation of the effectiveness of investment projects]. M. Delo. 2007. Pp. 139-145. [in Russian].
4. Intriligator M. Matematicheskie metody optimizacii i ekonomicheskaya teoriya. [Optimization Mathematical Methods and Economic Theory]. M. Progress. 1975. 536 p. [in Russian].
5. Fandel H. Teoriia vyrobnytstva i vytrat. [Theory of production and costs]. K. Takson. 2000. 85 p. [in Ukrainian].
6. Tuchinskij B.G., Tochenyj V.A., Ivanchenko I.V., Anton A.A. Analiz i modelirovanie zatrat vetrovoj elektrostancii na proizvodstvo elektroenergii. [Analysis and modeling of wind power costs for power generation]. Mezhdunarodnyj nauchnyj zhurnal «Alternativnaya energetika i ekologiya» (ISJAEE). 2012. No. 7. Pp. 68-76. [in Russian].

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