**4. Discussion**

It is difficult to determine the direction and intensity of energy prices in the future. For example, the U.S. Energy Information Administration in its "Independent Statistics & Analysis" publication, "The Availability and Price of Petroleum and Petroleum Products Produced in Countries other than Iran" in its May–June 2015 update states the following:

"The uncertainty on both the supply and demand side of the market could result in large future price movements [underlined by the authors]. The possible lifting of sanctions on Iran could move additional supply on to the world market and reduce prices, while an unexpected supply disruption at a time of low surplus production capacity may push prices higher. Meanwhile, if a slowdown in global economic activity from current levels occurred, it would reduce demand and result in higher-than-expected inventory builds, moving prices lower" [42]. This can be seen from the graph from the same source in Figure 2, where the spread between production and consumption has been widening since July 2014.

In addition to the world energy price uncertainty, in Israel, there are at least four other sources for price uncertainty:


**Figure 2.** Global petroleum and other liquids production, consumption and inventory net withdrawals, January 2012–June 2015 [20].

While it is still difficult with all these sources of uncertainty to determine the direction and intensity of the change of energy price, we must consider, thus, the possibility of high volatility in price. To this end, we will consider hereafter the possibility of high volatility taken to be StD = 40% per annum.

Calculating the call value based on the annual StD estimation of 0.4 yields 59.48 million \$US (compared to 57.05 million \$US based on StD of 0.031). It follows that the net profit of the first stage increased to 59.48 − 50 = 9.48 million \$US (see Table 2, a column for the case of StD = 0.40). It would be worth noticing here that the main statistical parameters of the wind speed in the Merom Golan area, the mean and the StD, are observed with a tendency towards stability, without any significant divergence over the period of the last few years, 2009–2014, as it follows from the calculated data in Table 3:


**Table 3.** Wind speed mean and StD at Merom Golan for the last period.

The expectation value of an annual average is the same as the expectation value for one sample, but the standard deviation of the annual average is equal to the standard deviation of one sample divided by the square root of the annual number of samples (see Appendix A for a mathematical justification). Thus, the standard deviation of the annual average of wind speed is between 0.6–1.1%, and can be further reduced by more sampling. A six year average based on 24,327 samples will be 3.72 m/s, with only 0.4% standard deviation. The power curves of available turbines are described in [45], from which three examples are analyzed in this paper and are depicted in Figure 3.

**Figure 3.** Power curves of wind turbines [45]. The dashed thick curve is the power curve of Enercon's model E101/3000 turbine, the thick line is the power curve of AWE's model 54–900 turbine, and the dashed curve is the power curve of EWT's model Directwind 52/750 turbine.

The wind speeds described in Table 3 are for a height of 10 m, for different heights, we apply the velocity to height connection [46]:

$$v(h) = v\_{10} \left(\frac{h}{10}\right)^{\alpha}$$

in which *v*(*h*) is the velocity at height h, *v*<sup>10</sup> is the velocity at a height of 10 m, and a is Hellmann's exponent, which, for a neutral air above human inhabited areas, is about 0.34. Among the turbines analyzed, the largest is Enercon's model E101/3000 turbine with a radius of 50.5 m. Hence, we will assume from now on that the hub of the turbine is 60 m. Table 4 will summarize the area and radii of the turbines under study:

**Table 4.** Wind turbine geometric parameters.


For this height, we obtain a six year speed average of 6.84 m/s. The eleven year average of the power and the standard deviation obtained for each turbine are depicted in Table 5, the total number of samples in this analysis was 31,292 based on the wind data from Merom Golan.


**Table 5.** Wind turbine power for eleven years of data acquisition.

The standard deviation of average power for all turbines investigated is much lower than the standard deviations of energy price appearing in Table 2. Hence, a long-term project can ignore the risks connected with the standard deviation of wind speed. A formal proof for this decisive circumstance is given in Appendix B.

This circumstance determines the fact of non-relevancy of the speed variance over a prolonged period of time for the wind turbine economic value; this should be compared to the significance of the energy prices for the turbine economic value.

Table 5 also contains the annual economic value of the turbine based on the current price of energy for consumers in Israel, which is 0.486 SH for kW hour on 11 September, 2015, the exchange rate for the same date is 3.866 SH for one US\$. We assume that the turbine owner will need to pay for transmission and distribution, hence the more conservative estimate of an annual profit of 0.2 million \$US per turbine quoted in the previous section. In practice, the price is determined by governmental authorities who strike a balance between the interest of other producers, the cost of transmission and distribution, and the public interest in clean energy.

We previously concluded that the advantage of using ROA over DCF is most significant when the market prices are volatile, and less so when the energy prices are stable. However, the change in wind speed is a small fraction of the value of the wind installation volatility, and this alone cannot justify the use of the ROA method. However, the fluctuations of the market energy prices is reason enough.
