**1. Introduction**

Even during prolonged global economic crisis, the worldwide wind power ascent continues. The world's wind power capacity, according to the Global Wind Energy Council (GWEC) report, added 39.1 GW in 2010, growing by 24% during the year, 40.6 GW in 2011, growing by 20.5% per year, and 44.8 GW in 2012 (18.8% growth during the year: 78% growth in the last three years). Thus, the total installations at the end of 2012 provide up to 282.6 GW. A huge part of this power was produced in China—first place globally, with 75.3 GW, or 26.7% of the world product (about 30% of the world year's additions), the and USA—60.0 GW, or 21.2% of the world product, while Germany, Spain, and India (3rd–5th places) produced 25.7% together [1].

**Citation:** Greenberg, D.; Byalsky, M.; Yahalom, A. Valuation of Wind Energy Turbines Using Volatility of Wind and Price. *Electronics* **2021**, *10*, 1098. https://doi.org/10.3390/ electronics10091098

Academic Editors: Detlef Schulz and Flavio Canavero

Received: 5 January 2021 Accepted: 20 April 2021 Published: 7 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Wind energy is now a significant participant in the world's energy market. The 2012 global wind power market grew by more than 10% compared to 2011, representing investments of about 56 billion €. The main markets of wind energy are situated in Asia, North America, and Europe, each of which installs 13–15 GW of new capacity each year. About half a million people are now employed, corresponding to the European Wind Energy Association (EWEA) publication, by the wind industry around the world [2].

Considering the growing Israeli energy market, even nowadays, when plentiful sources of traditional nonrenewable energy such as the vast gas fields that were found in the Mediterranean Sea off the coast of Israel, Tamar (Tamar gas field [3]), and Leviathan (Leviathan gas field [4]), with the estimated quantity of 356 and 450 billion cubic meters, respectively, the possibility of their exhaustion still forces the state, as other numerous political entities, to devote significant efforts towards 'green' energy research and development. This is also important from the point of view of reducing carbon emission and global warming. These efforts are undertaken primarily for developing solar energy, but also recently for wind energy facilities. Yet, the wind power amount produced in Israel is rather small compared to the continuously growing global market; however, the recent steps undertaken by the state are destined to make the situation better.

Israel currently operates a wind farm in Asanyia mountain in the Golan Heights with an installed capacity of 6 MW (10 turbines reaching a height 50 m (blades included), each with a power capacity of 600 kW), this is the typical consumption of about five thousand families. The duty cycle of the wind farm reaches 97%, and electricity production is worth 1 million US\$ a year. Indeed, the wind energy potential of Israel is rather restricted due to moderate or poor wind velocities in most areas and the restricted number of areas with high average wind speed. In many areas worthy of wind energy development, one is encountered by the opposition of green groups on landscape conservation grounds and the influence of the facility on local and migrating birds. Nevertheless, satisfying the Israel Ministry of Environmental Protection (IMEP) directions, the state of Israel continues efforts towards the development of additional farms with a 50 MW capacity [5].

As it is emphasized in a document issued by the Israeli Parliament (Knesset), a better estimate, based on the wind turbines' technical development, gives a value of more than 500 MW for the Israeli potential wind energy potential capacity [6]. One of the prospective areas for the development of efficient wind technology, considering its climatic characteristics, is the region of Ariel city in Samaria [7], the current research, however, is devoted to another region [8].

While the generic discounted cash flow (DCF) approach using the net present value (NPV) criterion is generally adopted to evaluate investments, the DCF method is inappropriate for a rapidly changing investment situation (Dixit and Pindyck [9]; Herath and Park [10]; Lee and Shih [11]) and does not consider managerial flexibility in investment decisions (Hayes and Abernathy [12]; Hayes and Garvin [13]; Trigeorgis and Mason [14]; Trigeorgis [15]). In the current study, we consider a two-stage approach—one turbine at the first stage and a field of 50 at the second stage, along with the possibility to withdraw at the second stage. Hence, the scenario is a one in which managerial flexibility can be practiced.

Currently, the real option analysis method is widely applied in many studies for the valuation of renewable energy investment projects, for example, Lee and Shih [11] and Kumbaro ˘glu, Madlener, and Demirel [16]. See also Boomsma, Meade, and Fleten [17] and Menegaki [18]. We thus apply in this paper the real options analysis method for the evaluation of the economic value of wind energy turbines in a specific location. In particular, we analyze the value of the investment opportunities that add value to the investment due to managerial flexibility (in the case of energy market price drop, one may abandon the investment). It is worth mentioning that the option valuation method has become more sophisticated by using approaches such as the binomial lattice, the mean reverting jump-diffusion method, and stochastic volatility model. It is also used for other types of hazards such as technological risks (Deng [18]; Menegaki [19]; Siddiqui, Marnay, and Wiser [20]), which may include a change in the wind regime, in our case, or

power output reduction of the turbine. See also Davis and Owens [21] and Baringo and Conejo [22].

The reasons for the current study are as follows, we are interested in estimating the profitability of a Merom Golan wind facility. For this:


The main purpose of this paper is to study the effect of energy value fluctuations on the assessment of the profitability of wind turbine facilities using the real option analysis method. The economic output of a wind turbine installation is a function of its electric energy output [23–25] and the value of market energy. The electric energy output is a function of the turbine used and wind speed statistics. The turbine used can be chosen to have an optimal cut-in velocity (the wind speed level at which the turbine starts to generate electricity), and the cut-out velocity (the speed level at which the facility hits its alternator limit and stops producing more power output following increases in wind velocity) [26]. For a more technical discussion, we refer the reader to the results of our previous studies on wind power production, devoted to the technological appropriateness and environmental relevance issues [7,27]. See also [28,29]. While the total annual energy output of the turbine facility can be known to a high certainty, the market prices of energy may vary indeterminately, and thus should be considered as the most serious investment risk. To evaluate the financial risk correctly, we suggest employing the real option analysis method, which is the subject of the current study. In a wider sense, our manuscript contributes to the risk analysis of Grossman, which is the way a "decentralized economy allocates risk and investment resources when information is dispersed" [30] (p. 773).

In this paper, we shall describe the various sources of the uncertainties in determining the economic value of a wind installation. Both in terms of technical parameters, such as wind velocity change, and the effect on the power output of the turbine. Additionally, in terms of the market value of the power generated, which is dependent on the value of competing power generation methods. We then combine the uncertainties to produce the economic value of the installation using the real option analysis evaluation techniques. On comparing the different sources of uncertainty, we show that the uncertainty in the market value of electric power significantly dominates the technical uncertainties.

The structure of the paper is as follows: in the "Materials and Methods" section we describe the methods of this work, which are the Weibull statistics of wind and the Black–Scholes analysis of the real option technique. In the "Results" section we describe the Weibull fit for the site of installation, deriving the relevant parameters; we also introduce the economic model in terms of its parameters and emphasize the difference between the DCF and ROA methods for evaluation. Next, in the "Discussion" section, we estimate the power production and power uncertainty for different turbines and compare this with the economic uncertainty of energy prices, determining that the latter is much larger. Finally, in the "Conclusion" section, we summarize our conclusions underlining the dominance of market price fluctuations over technical fluctuations and the benefit of using the ROA method over the DCF method for a better economic evaluation of the wind energy facility expedience.
