Sensitivity analysis of criteria to optimize wind farm localizing: A case study

Abstract

The objective of this study was to perform a sensitivity analysis on the factors affecting wind site localization. A case study is selected based on 13 cities in the province of Fars in Iran which is equally applicable in any other wind sites. Then, the cities are ranked using the dual form of the data envelopment analysis model. Next, six criteria are adopted including wind conditions, population, Available Land condition, distance to distribution networks, rate of natural disasters, and the cost of land. In the sensitivity analysis of each criterion, first, the criterion under analysis is omitted from the model, and then the dual model is applied again to obtain a new ranking. Evaluating the results of the ranking for 13 studied cities indicate that the city of Shiraz is just sensitive to the population criterion and fell 11 places in the ranking by omitting this criterion. But the city is insensitive to any other criteria.

Keywords

Data envelopment analysis localization optimization ranking renewable energy sensitivity analysis

Introduction

The future role of fossil fuels in the modern world is in serious debate. While projections of world’s fossil fuel reserves vary with the technological advances, the fact that this energy source cannot last forever cast concerns. Although the most pressing issue with regard to deprivation of fossil fuels is the environmental impacts on the planet earth, mainly casted in the emerging effects of climate changes and the global warming, these effects have raised public attention to the issue of fossil fuels, therefore motivating many governments, especially those in the developed countries such as European countries, to increase supports to the industry of clean and renewable energy (Bakker and Van den Hurk, 2012). Technologic advances in this industry have made this energy increasingly economic, and growing public awareness about the obvious and latent benefits of renewable power such as reduced pollution and energy security has also contributed to the development and marketability of renewable energies including wind power (Göransson and Johnsson, 2018). Like other renewable energy sources, wind power is geographically dispersed and decentralized and is available almost ubiquitously, but it has a fluctuating and unreliable nature (García-Bustamante et al., 2012; Patlakas et al., 2017) which occasionally makes its utilization problematic. Many countries have heavily invested in wind power industry, but leading countries in this respect are United States, France, China, and Germany, which account for the largest share of world’s wind power generation (Kim and Paik, 2015; Najac et al., 2009; Shi et al., 2017)

Thanks to growing relevance of renewable energies, there has been a steady increase in research on this area to meet the need for careful and expert investigation and scrutiny of all aspects and factors influencing this industry, including type of turbines and layout of installation (Masurowski et al., 2016; Pelletier et al., 2016), project location (Rezaei-Shouroki et al., 2017; Shaheen and Khan, 2016), combination of two or more renewable energies including wind and solar (Khare et al., 2016; Singh et al., 2016), economic yield (Effiom et al., 2016), technical-economic feasibility analysis (Dalabeeh, 2017), hydrogen production (Rezaei et al., 2018a), and the impact of climate change on wind resources (Pryor et al., 2005). One of the important venues of research on renewable energy is the sensitivity analysis of the criteria involved with the location of the site (Martin et al., 2016). This analysis identifies the effective criteria, the absence or presence of which can determine whether a location is suitable for this purpose. Sensitivity analysis of criteria involved with construction of renewable energy facilities can serve multiple purposes, one of which is to understand how these criteria affect such decision (Bossavy et al., 2016). So such analyses are of high practical utility and allow future studies to have a better grasp of behavior of criteria. The aim of sensitivity analysis may be to investigate factors such as economic feasibility, technical feasibility, and the effect of climate change (Azadeh et al. 2014; Martin et al., 2016). In this study, first, the criteria involved with site location are used to prioritize the sites in the order of suitability for installation of wind turbines. Then the primary objective of the study is to perform sensitivity analysis of the effective criteria. For this purpose, researcher should code prioritization programs in Lindo software in numbers equal to the number of criteria (this study investigates six criteria). In each code, one criterion should be omitted and program should be executed and a new ranking should be obtained without that criterion. Any criterion that manages to trigger a change in the ranking should be considered effective, as it may alter the site to be selected for wind turbines. Once the effective criteria are identified, researcher can make a better decision with regard to location of the construction site. The results of this analysis can also contribute to future research on site selection for wind farms and hybrid projects as well as associated criteria.

Geographic distribution of the case study

Geographic specifications of Iran provide it with ample opportunities for exploitation of most types of renewable energy. This study however is focused on Fars province, which has shown great wind power exploitation potential. Fars province is located in southern and south-western parts of Iran between 50°36′ and 55°35′ eastern longitudes and 27°03′ and 31°40′ northern latitudes. With an area of about 122,000 km², Fars is Iran’s fourth largest province and constitutes about 12.5% of its total area. Figure 1 shows the position of this province and 13 cities in Iran (Rezaei-Shouroki et al., 2017).

Figure 1.

Position of Fars province in Iran.

In Fars province, climate varies with location. North and northwestern parts of this province have a mountainous terrain and thus cold winters and moderate summers; the central parts have a Mediterranean climate; and south and southwestern parts have moderate winters and very hot summers (Rezaei-Shouroki et al., 2017). This study was carried out on 13 cities of Fars province. Geographical coordinates of the cities are shown in Table 1. These cities were first ranked in terms of suitability as the site of wind farm, then a sensitivity analysis was performed on criteria involved with site selection to determine which site is more sensitive to which criteria. The potential locations of wind farm for each city selected by experts of this field are shown by red spots in the maps presented in Appendix 1. The most significant reason behind choosing these places is that they are flat, without hills and trees, and easy to build essential facilities. Moreover, it can be seen that these suitable places are almost distributed across the city, not clustered.

Table 1.

Geographical coordinates of 13 cities in Fars (www.noojum.com).

City	Latitude	Longitude
Izadkhast	31°08′N	52°40′E
Estahban	29°12′N	54°03′E
Safashahr	30°36′N	53°11′E
Firuzabad	28°81′N	52°55′E
Eghlid	30°53′N	52°41′E
Neyriz	29°15′N	54°19′E
Sepidan	30°20′N	52°5′E
Arsanjan	29°92′N	53°32′E
Bavanat	30°28′N	53°27′E
Abade	31°08′N	52°40′E
Fasa	29°00′N	53°39′E
Kazerun	29°38′N	51°40′E
Shiraz	29°61′N	52°54′E

Methodology

For sensitivity analysis of effective criteria, each criterion should be analyzed separately. For this purpose, the dual form of data envelopment analysis (DEA) model is applied without that criterion and the resulting change in city ranking should be determined. To do this, first all cities must be ranked. This can be done with DEA method, which has proven effective in ranking multiple decision making units (DMUs) with similar tasks by comparing the efficiency scores calculated for these DMUs (Banker et al., 1984). In this study, the initial objective was to obtain relative efficiency of 13 cities (DMUs) of Fars province according to three inputs and three outputs in order to rank these cities in the order of suitability for the construction of wind farm and determine the best location in this respect.

Experience has shown that when there are about as many DMUs as there are inputs and outputs (total number of criteria), the original DEA reports most of the DMUs as efficient, which is an unrealistic result meaning that ranking is utterly unreliable. It has been shown that the number of criteria relative to DMUs should meet either condition 1 or 2 (Fallahi et al., 2011; Yang et al., 2012)

Number of DMUs \times 3 \leq (Number of inputs + Number of outputs)

(1)

Number of DMUs \times 2 \leq (Number of inputs \times Number of outputs)

(2)

Since the number of DMUs (cities) was 13 and the number of criteria was 6 (including three inputs and three outputs), none of the above conditions were satisfied. To remedy this pitfall, we used the dual form of DEA model as shown in equation (3) (Lu and Yanbai, 2012).

As regards the dual model, it should be mentioned that any linear program can be formulated as a dual form using the same data, also the solution to either of them provides the same information about the problem which is modeled. Hence, DEA is no exception to this rule. The dual model is gained by assigning a variable, which is called dual variable, to each constraint in the original model and constructing a new model on these variables. In the original model, the number of constraints equal n + S + K + 1, which denote the number of DMUs, outputs and inputs, respectively, while the dual model has S + K constraints. Since the number of DMUs is by far more than the summation of inputs and outputs, therefore, the original model has many more constraints than the dual model. Generally, in linear programs, the more the constraints, the more difficult a problem is to solve. Thus, it is usual to solve the dual DEA model rather than the original (Mostafaeipour et al., 2017)

{Min Z}_{p} = θ

S u b j e c t t o : \sum_{j = 1}^{n} l_{j} y_{rj} \geq y_{rp}

θ x_{ip} - \sum_{j = 1}^{n} l_{j} x_{ij} \geq 0

l_{j} \geq 0

r = 1, 2, \dots, S

i = 1, 2, \dots, K

j = 1, 2, \dots, n

(3)

In this model, Z_p denotes the efficiency of the pth DMU, $θ$ is the variable that should be minimized, y_rj is the rth output (r = 1 to S) of the jth DMU (j = 1 to n), x_ij is the ith input (i = 1 to K) of the jth DMU, and l_j denotes the variables that should be calculated so that constraints become satisfied. In this model, a DMU is efficient only if slack variables are zero (Charnes et al., 1978). In an optimization model, a variable that is added to an inequality constraint in order to transform it into an equality is called slack variable, and if its value is zero at a particular candidate solution, the constraint is binding there, as the constraint restricts the possible changes from that point. On the other hand, if a slack variable is positive at a particular candidate solution, the constraint is non-binding there. In general, the slack variables cannot take on negative values (Azizi and Wang, 2013).

In cases where model results include several DMUs with maximum efficiency score (1), these DMUs cannot be ranked under this condition. In such cases, researcher should utilize a method called Andersen-Petersen technique for the ranking of efficient DMUs. This model allows them to have an efficiency score of greater than 1. This is done by omitting pth constraint in the original model or pth variable (weight) from the constraints of dual model in each run of the model (Azadeh et al., 2011). This model is available for both basic and dual form of DEA model. In this study, initial ranking was obtained by the dual model, so the efficient DMUs were also ranked using the dual form of Andersen-Petersen model. Thus, the above described dual model was modified according to Andersen-Petersen technique (Azar and Gholamrezaei, 2007)

{Min Z}_{p} = θ

S u b j e c t t o : \sum_{\frac{j = 1}{j \neq p}}^{n} l_{j} y_{rj} \geq y_{rp}

θ x_{ip} - \sum_{\frac{j = 1}{j \neq p}}^{n} l_{j} x_{ij} \geq 0

l_{j} \geq 0

r = 1, 2, \dots, S

i = 1, 2, \dots, K

j = 1, 2, \dots, n

(4)

The only difference of this model with the previous one is that in each run of the model, pth term of each constraint is removed (Birman et al., 2003).

Ranking of the cities

The ranking analysis was carried out using the long-term data pertaining to the period 2006-2015, which was collected from the database of National Meteorological Organization of Iran, and in some cases the experts in this field were also consulted.

Effective criteria

A location to be selected for the construction of wind farm should not only generate the maximum wind power but do so with minimum cost; thus, an inadequately chosen location can impose heavy financial losses on the investor. Suitability of a given site can be a factor of different economic, technical, and topographical criteria, but here we selected six criteria including wind conditions, population, Available Land condition, distance to distribution networks, rate of natural disasters, and the cost of land because of their importance to local wind farm developers (Feuchtwang and Infield, 2013; Gao et al., 2014).

Wind conditions

The first and the most important condition for an area to be selected as the location of wind farm is to have sufficiently powerful winds with satisfactory consistency. This condition was checked by using a factor called wind power. Wind power is actually a metric showing how much wind energy of an area can be converted into electricity (Arslan, 2010; Sáiz-Marín et al., 2014). Wind power of a given area can be calculated using its long-term meteorological data and some statistical analysis. In this study, wind power and wind power density were calculated from equations (7) and (9), respectively (Rezaei-Shouroki et al., 2017; Shoaib et al., 2017). The latter equation known as Weibull distribution function (WDF) is the most common method for estimating wind power density available in an area and has also been proven accurate for this application (Mirhosseini et al., 2011). For this part of the study, three-hourly data of wind speed, ambient temperature, and air pressure for a period of 10 years (2006–2015) was collected from Iran Meteorological Organization. Because the collected data for wind speed pertains to the height of 10 m and most common wind turbines in Iran, which are being used commercially, have height of 40 m, to obtain accurate results, it is essential to calculate the wind velocity at turbine blades. Thus, the α coefficient must be estimated through equation (5), and then the wind velocity can be gained at turbine tower (height of 40 m) by extrapolation using equation (6) (Rezaei et al., 2018a)

α = \frac{[0.37 - 0.088 \ln (v_{1})]}{[1 - 0.088 \ln (\frac{h_{1}}{10})]}

(5)

v_{2} = v_{1} {(\frac{h_{2}}{h_{1}})}^{α}

(6)

where $v_{2}$ and $v_{1}$ are the wind speed at the height of $h_{2}$ (turbine blades) and $h_{1}$ (the height where wind speed data were recorded which in this study is 10 m), respectively.

Equation (7) was used to calculate the wind power of each area (Rezaei-Shouroki et al., 2017)

\frac{P}{A} = \int_{0}^{\infty} \frac{1}{2} ρ v^{3} f (v) d v = \frac{1}{2} Γ ρ c^{3} (1 + \frac{3}{k})

(7)

where $ρ$ (density of air), $f (v)$ (wind power density), and $Γ$ can be calculated by equations (8) to (10), respectively (Mirhosseini et al., 2011)

ρ = \frac{\bar{P}}{R_{d} \bar{T}}

(8)

f (v) = (\frac{k}{c}) * {(\frac{v}{c})}^{k - 1} * e^{[- {(\frac{v}{c})}^{k}]}

(9)

Γ (x) = \int_{0}^{\infty} e^{- u} u^{x - 1} d u

(10)

where $\bar{P}$ , $\bar{T}$ , and $R_{d}$ are the mean air pressure (Pa), the mean air temperature (K), and the gas constant for dry air (which equals 287 J/kg K), respectively (Rezaei et al., 2018a). Equation (9) contains two constants c and k called, respectively, scale parameter and shape parameter, which should be calculated by equations (11) and (12) (Rezaei et al., 2018b)

c = \frac{v}{Γ * (1 + \frac{1}{k})}

(11)

k = 0.83 v^{0.5}

(12)

Finally, the mean wind power density in each city was calculated through WDF with Excel software. After calculating wind power density for each city, the results were almost consistent with the Iran wind atlas. For instance, Izadkhast which has the largest amount of wind power compared to 12 other cities and enjoy wind power density of 152.32 (W/m²) is located in the brown zone of the atlas showing that these places have high wind power density. On the other hand, Shiraz and Fasa are placed in the green zone showing low wind power density. The final results of this part of study are presented in Figure 2.

Figure 2.

The calculated mean wind power density for DMUs.

Available land condition

Since a wind farm cannot be constructed inside the city, the potential areas suitable for developing a wind power site for each city were assumed to be located inside a specific range almost extended 10 km from each city’s border. Then residential, commercial, and industrial zones and areas with tree cover and hills were omitted from this area and the most suitable places for a wind farm was determined with the aid of experts of the field. The areas calculated for the cities are presented in Figure 3.

Figure 3.

Available land (km²) for constructing wind farm for DMUs.

Distance to electricity distribution networks

Figure 4 shows the mean distance of topographically suitable sites from 20 kW substations (located within the city). This mean distance was calculated using the aerial maps provided by Google.

Figure 4.

Distance to distribution network for DMUs.

Cost of land

Given that areas suitable for wind farm lay outside the residential zones, this criterion was calculated according to the average price of farmlands and barren lands. The values of this criterion are also presented in Figure 5.

Figure 5.

Cost of land for DMUs.

Since economic factor is of significant role in the ranking of DMUs, other criteria should be considered including electricity price and the cost to build (because they may vary by region and by season) in order to gain the most accurate results. However, in Iran, electricity price for all provinces is the same due to its governmental policy, so different seasons and regions have no effect on the ranking in this study. Furthermore, construction price is almost the same, because all cities are in one province (Fars) and it was attempted to choose places with the same conditions (flat, without hills and trees) for each city, as a result, the price of building necessary facilities is equal due to equal circumstances. Wages paid to experts and manpower also do not vary by region in Iran, because it is based on rules of Ministry of Cooperatives, Labor and Social Welfare. Hence, these factors have no impact on our results.

Natural disasters

For this criterion, we assumed three disasters as sub-criterion: flood, earthquake, and dust storm. Statistics obtained for each city are listed in Table 2. For the sub-criterion flood, we used the number of floods recorded during 62 years prior to the end of 2015 (older records are not available) (www.desinventar.net). The probability of at least one flood during 25 years of turbine life was calculated using Poisson distribution which is a discrete probability distribution for the counts of events happening randomly (an event can occur 0, 1, 2, … times) in a fixed interval of time or space. The probability of observing x events in an interval can be estimated by equation (13) (Rezaei et al., 2018b)

P (x) = e^{- λ} (\frac{λ^{x}}{x!})

(13)

where λ (lambda) denotes the average number of events in an interval, called the event rate or the rate parameter. Table 2 shows the flood statistics of the cities and the calculations performed to determine the probability of this event.

Table 2.

Flood statistics (for 62 years), Poisson lambda (for 25 years), and Poisson distribution.

City	Number of floods (for 62 years)	Lambda or λ (for 25 years)	Poisson distribution of floods
Izadkhast	5	2.016	0.816
Estahban	6	2.419	0.911
Safashahr	5	2.016	0.867
Firuzabad	7	2.823	0.941
Eghlid	5	2.016	0.867
Neyriz	6	2.419	0.911
Sepidan	6	2.419	0.911
Arsanjan	3	1.210	0.702
Bavanat	2	0.806	0.554
Abade	5	2.016	0.867
Fasa	4	1.613	0.801
Kazerun	4	1.613	0.801
Shiraz	4	1.613	0.801

For earthquake, we investigated the number of earthquakes recorded in Fars province in the last 100 years (www.desinventar.net) and found no record of any earthquake that could seriously damage a wind turbine (⩾8 on the Richter scale) (Aras et al., 2004); therefore, for all cities, the likelihood of destructive earthquake was calculated to zero.

We also checked the statistics related to dust storms and found that due to high frequency of occurrence, this sub-criterion cannot be explained with Poisson distribution. Therefore, given the large number of tests (the number of considered days), we used binomial distribution with normal approximation for this purpose.

In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent experiments; each has two options as answers, which are yes or no. This distribution was extended from a single success/failure experiment known as Bernoulli trial which in this case n equals 1. Also, normal approximation involves calculating the probability of success (p) and the number of trials (n) for binomial distribution, then calculating the mean (μ) and standard deviation (σ) of normal distribution by equations (14) and (15), and ultimately calculating the probability of at least 1 event by normal distribution by equation (16) (Rezaei et al., 2018b; Roy and Majumdar, 2012)

μ = np

(14)

σ^{2} = np (1 - p)

(15)

P (k; n, p) = (\begin{matrix} n \\ k \end{matrix}) p^{k} {(1 - p)}^{n - k}, k = 1, 2, 3, \dots (at least one dust storm)

(15)

Here, n is the number of considered days, that is, the common lifespan of the turbine (Rezaei-Shouroki et al., 2017), which for 25 years will be (6 + 365 × 25) 9131 days. Finally, the probability of at least one dust storm during 25 years of turbine life was calculated. Table 3 shows the statistics of this event for the cities, the calculations performed for variables p (probability of occurrence of dust storms in 1 day according to binomial distribution) and n (the number of considered days or the number of tests in binomial distribution), normal σ and μ, and finally the probability of at least one occurrence of dust storm.

Table 3.

Parameters required calculating the likelihood of dust storms using binomial distribution with normal approximation.

City	p	n = 9131 (25 × 365 + 6)	μ = np	σ	Probability of at least once dust storm with normal distribution
Izadkhast	0.0822	9131	750.49	26.245	0.86
Estahban	0.1096	9131	1000.66	29.85	0.87
Safashahr	0.0740	9131	675.44	25	0.86
Firuzabad	0.0575	9131	525.35	22.25	0.86
Eghlid	0.1370	9131	1250.82	32.85	0.88
Neyriz	0.1452	9131	1325.87	33.66	0.88
Sepidan	0.0329	9131	300.20	17.04	0.85
Arsanjan	0.0027	9131	25.02	4.99	0.84
Bavanat	0.6850	9131	625.41	24.14	0.86
Abade	0.1096	9131	1000.66	29.85	0.87
Fasa	0.0904	9131	825.54	27.4	0.86
Kazerun	0.0575	9131	525.35	22.25	0.86
Shiraz	0.2137	9131	1951.28	39.17	0.90

The final step was to combine the data of these three natural disasters into one criterion so that they can be incorporated into the model. This aim was achieved by using the weighted sum of probabilities of individual disasters. The final results of calculations performed using the weights 0.25, 0.25, and 0.5 for flood, earthquake, and dust storm, respectively, are presented in Figure 6.

Figure 6.

Amount of disaster criterion for DMUs.

Population

The last criterion affecting the choice of site of a wind farm is the population. It is clear that this factor should be considered as an output of DEA model, because the larger the population, the more suitable is the area for wind power generation. Population of the investigated cities is given in Figure 7.

Figure 7.

Number of people in each DMUs.

Model execution

Given the large number of problem constraints, this linear problem was solved with Lindo software. For this purpose, the objective function, Min Z_p = θ, was put at the beginning of the model, since the dual form of DEA was utilized in this study so the objective function starts with min. Then, all the constraints which equal the summation of inputs and outputs (6) were added to the software. Finally, after running the program, efficiency score of the DMU was estimated. And also, in order to rank DMUs with full efficiency (1), pth variable from the constraints of dual model in each run of the model was omitted.

The results obtained for the studied cities are presented in Table 4. As can be seen, the efficiency of Izadkhast, Bavanat, Fasa, Kazerun, and Shiraz was calculated to 1, so they could not be ranked at this stage.

Table 4.

Efficiency of studied DMUs and ranking of inefficient DMUs.

City	Efficiency scores of DEA	Rank
Izadkhast	1	?
Estahban	0.839	8
Safashahr	0.790	10
Firuzabad	0.631	13
Eghlid	0.889	7
Neyriz	0.724	12
Sepidan	0.775	11
Arsanjan	0.983	6
Bavanat	1	?
Abade	0.836	9
Fasa	1	?
Kazerun	1	?
Shiraz	1	?

DMU: decision making unit; DEA: data envelopment analysis.

Andersen-Petersen technique was used to resolve the problem of full efficiency of these five cities via omitting the pth variable from the constraints of dual models. The results obtained from this technique are shown in Table 5.

Table 5.

Ranking of efficient DMUs by Andersen-Petersen model.

City	Efficiency scores of AP	Rank
Izadkhast	1.636	2
Bavanat	1.005	5
Fasa	1.05	4
Kazerun	1.139	3
Shiraz	5.758	1

DMU: decision making unit; AP: Andersen-Petersen.

Sensitivity analysis

To determine the effect of each criterion on the results, a sensitivity analysis was performed on each criterion. In this analysis, the criteria were omitted one by one, and model was applied with the remaining criteria to determine a new ranking for the cities. The city that showed the highest change in the rank as the result of omission of a certain criterion was considered to be more sensitive to that criterion, which means that criterion has the greatest impact on that city. Results of sensitivity analysis of all criteria are shown in Table 6.

Table 6.

Sensitivity analysis of criteria and resulting changes in ranking.

City	Rank of cities before sensitivity analysis	Remove wind power criterion		Remove Available Land criterion		Remove distance to distribution network criterion		Remove land cost criterion		Remove natural disaster criterion		Remove population criterion
	Rank of cities before sensitivity analysis		Efficiency	New rank	Efficiency	New rank	Efficiency	New rank	Efficiency	New rank	Efficiency	New rank	Efficiency	New rank
Izadkhast	2	1.49	2	1.400	2	1.636	2	1.308	2	1.636	2	1.636	1
Estahban	8	0.839	6	0.721	7	0.839	8	0.675	12	0.839	7	0.676	11
Safashahr	10	0.770	8	0.790	5	0.790	10	0.790	9	0.773	10	0.776	8
Firuzabad	13	0.631	13	0.423	12	0.618	12	0.631	13	0.617	13	0.627	13
Eghlid	7	0.889	5	0.541	10	0.889	6	0.889	6	0.832	8	0.867	5
Neyriz	12	0.724	12	0.368	13	0.724	11	0.724	11	0.654	12	0.699	10
Sepidan	11	0.747	10	0.590	9	0.566	13	0.775	10	0.775	9	0.775	9
Arsanjan	6	0.726	11	0.983	4	0.846	7	0.982	5	0.983	6	0.978	4
Bavanat	5	0.751	9	1.005	3	0.931	5	1.005	4	1.005	5	0.995	3
Abade	9	0.836	7	0.454	11	0.836	9	0.836	8	0.753	11	0.815	6
Fasa	4	1.05	4	0.679	8	1.050	3	0.850	7	1.050	4	0.795	7
Kazerun	3	1.139	3	0.757	6	0.977	4	1.139	3	1.139	3	1.091	2
Shiraz	1	5.758	1	5.758	1	5.138	1	5.758	1	5.758	1	0.648	12

The results of sensitivity analysis of the criterion “wind power density” suggest that the city most affected by this output criterion is Arsanjan, as after omitting this criterion from the model, this city fell five places in the ranking (from 6th best place to 11th best place) among all cities, the second most affected city by wind power density is Bavanat falling four places. On the other hand, this criterion has no effect on Izadkhast, Firuzabad, Neyriz, Fasa, Kazerun, and Shiraz. The sensitivity analysis of the criterion “Available Land condition” showed that the cities most affected by this criterion are Safashahr and Fasa that rose and fell in the ranking five and four places, respectively.

Running the DEA model without the criterion “distance to distribution network” revealed that the city most affected by this criterion is Sepidan, as it showed the greatest decrease in rank (from 11th place to 13th place) once this criterion was omitted.

The results of sensitivity analysis of the criterion “cost of land” showed that the city most affected by this input criterion is Estahban, and sensitivity analysis of the criterion “natural disasters” showed that the cities most affected by this criterion are Sepidan and Abade, which showed the greatest change in rank once this criterion was omitted.

Running the dual model for sensitivity analysis of the last criterion, “population,” showed that the city most affected by this criterion is Shiraz, as this city has the greatest population among all investigated cities and this output criterion can be considered as an advantage for this city.

Conclusion

The significant importance of wind site localization highlights the necessity of present sensitivity analysis in this field to prohibit financial losses for wind farm investors. This study analyzed the sensitivity of criteria involved with location of wind farms in 13 cities in Fars province in Iran. It should be noted that the developed methodology in the present work using sensitivity analysis of wind site localization can be equally implemented for any other regions. The following conclusions may be drawn from the present methodology and case study:

The sensitivity analysis of the criterion “wind power density” indicates that the city most affected by this criterion is Arsanjan, which fell five places in the ranking once this criterion was omitted. Meanwhile, the cities least affected by this criterion are Izadkhast, Firuzabad, Neyriz, Fasa, Kazerun, and Shiraz, which showed no change in rank during this part of analysis.

The sensitivity analysis of the criterion “Available Land condition” shows that the cities most affected by this criterion are Safashahr and Fasa. Meanwhile, the cities least affected by this criterion are Izadkhast and Shiraz (no change in rank).

The sensitivity analysis of the criterion “distance to the distribution network” indicates that the city most affected by this criterion is Sepidan (fell to the last place in the ranking), and the cities that have not been affected by this criterion are Izadkhast, Estahban, Safashahr, Bavanat, Abade and Shiraz.

The sensitivity analysis of the criterion “cost of land” shows that the city most affected by this criterion is Estahban, (fell four places in the ranking). Meanwhile, Izadkhast, Firuzabad, Kazerun, and Shiraz have not been affected by this criterion.

The sensitivity analysis of the criterion “natural disasters” shows that the cities most affected by this criterion are Sepidan and Abade, which climbed and fell two places in the ranking, respectively, once this criterion was omitted. Also, the city most affected by the criterion “population” was found to be Shiraz (fell 11 places in the ranking), but this criterion did not show any effect on Firuzabad.

Due to paramount importance of the economics, for future research in countries where electricity price and the cost to build are different by region and/or by season, it is suggested considering these criteria.

Footnotes

Appendix 1

In order to find the most suitable areas for developing wind warm in each city, aerial maps provided by Google were used (Figures 8 to 20), then the experts of the field selected places meeting the best conditions for this purpose. These potential areas are located inside a specific range extended 10 km from each city’s border. In the following maps, yellow spot shows the location of the met station and the red spots illustrate areas appropriate for constructing a wind farm.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Mostafa Rezaei

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