**4. Analytical Hierarchy Process**

MCDM techniques are applied to solve site selection problems [66]. AHP is one of the most widely used methods in MCDM, introduced by Saaty in 1980 [12]. One of the advantages of AHP is the pairwise comparison among the criteria of the problem. Through this method, sensitivity analysis can be carried out on the criteria and sub-criteria by offering several choices. AHP can minimize the impact of taste decisions and orientations in problem-solving, which is another important advantage of this method [38].

In the AHP method, the problem becomes hierarchical, consisting of four levels. These levels are the problem goal, the criteria, the sub-criteria, and the final choices [67,68].

In the AHP method, the criteria are compared two by two. To compare the criteria, they are given points ranging from one to nine, which can be seen in Table 2 [12,69,70].

Thus, the adjustment ratio (*CR*), indicating the degree of coherence of decision makers' opinions, is calculated according to Equation (2). The appropriate value for *CR* is below 0.1, and if it exceeds this value, decision-makers should reconsider their views in pairwise comparison. If the pairwise comparison does not involve inconsistencies, the principal eigenvalue (*λmax*) is at least the same as the number of columns or rows (*λmax* = *n*) [38].


**Table 2.** Pairwise comparison scales in AHP [69].

Consistency index (*CI*) could be calculated from Equation (1) [12]:

$$CI = \frac{\lambda\_{\text{max}} - n}{n - 1} \tag{1}$$

The consistency ratio (*CR*) is calculated from Equation (2):

$$CR = \frac{CI}{RI} \tag{2}$$

Table 3 represents the Random Index (*RI*) values used to calculate *CR*. As mentioned, the *CR* value should be less than 0.1. Otherwise, the decisions made in the pairwise comparison should be reconsidered [71].

**Table 3.** Random index values according to Saaty and Tran [70].


The suggested criteria for this decision-making problem are wind speed, slope, distance from power lines, distance from substations, distance from highways and roads, and urban areas. Figure 5 portrays the decision process hierarchy for the wind farm.

All of the criteria were compared, the weight of each was determined, and incompatibility rate calculations were performed for the criteria. Table 4 shows a pairwise comparison of the criteria for selecting wind farm locations. Some university experts made this pairwise comparison. Appendix A (Table A1) shows the academic information of these experts.

As can be seen in Table 4, wind speed is an essential criterion, and investigating the wind speed of the study area could help to estimate the wind power potential, and larger wind turbines can be installed to generate more power in areas with higher wind energy potential. Lands with lower slopes are usually prioritized. Because increasing the slope can increase the initial cost of construction and the maintenance cost. The distances from power lines and power stations also have a direct impact on the project cost. In remote areas that do not have access to the facilities of the electricity network, the construction of power stations and lines can incur huge initial and maintenance costs to project investors. Moreover, the remoteness of urban areas, roads, and highways could cause higher investment costs, such as constructing new access roads. Remoteness from urban areas, where most of the electricity consumption occurs, can also be technically problematic. Because increasing the distance between power the producer and consumer and lengthening the power transmission lines will cause more voltage drop and power loss, and maintenance of these long power transmission lines can be tedious and costly.

**Figure 5.** Decision process hierarchy for wind farm.



Table 5 represents the pairwise comparison matrix that is calculated using the pairwise comparison of the criteria shown in Table 4. The last row of this matrix shows the sum of each column. Table 6 represents the normalized pairwise matrix calculated by dividing each element of Table 5 by its last row number. The last column of Table 6 shows each criterion weight from the average of each row of the normalized matrix. In the next step, the consistency of the AHP results investigates using the CR value. Table 7 represents the consistency matrix. The last row of this matrix represents the weight of each criterion. The elements of this matrix calculate by multiplying the elements of each column of Table 5 by that column's weight. Furthermore, one of the columns of Table 7 shows the weighted sum value, which shows the sum of each row of consistency matrix elements. The last column of Table 7 shows the ratio of weighted sum value to weights in each row. *λmax* calculates by averaging the numbers of the last column of Table 7, which is equal to 7.29. Finally, CI and CR calculate using Equations (1) and (2) [24].


**Table 5.** Pairwise comparison matrix of the MCDM problem.

**Table 6.** Normalized pairwise comparison matrix of the MCDM problem with the weights of the criteria.


**Table 7.** Consistency matrix of the criteria with the weighted sum value.


After performing the calculations, each criterion's final weights were obtained in the AHP method, as shown in Figure 6. The CR factor for this weighted criterion was 3.58%, implying that the pairwise comparison matrix is suitable and does not require change.

According to Figure 6, the most significant criterion is wind speed, which was predictable. After wind speed, the slope of the terrain, distance from power stations, distance from power lines, distance from urban areas, and distance from highways and roads are respectively important.

After calculating the weights, the buffer areas will be applied considering multiple restrictions. These restrictions include the distance from communication routes and railways, urban areas, and environmentally restricted areas. Moreover, according to the references, high-altitude lands specify as a buffer area due to the high cost of the construction process. These restrictions were taken into account by considering international and national standards and regulated technical, electrical, environmental, and economic principles. Figure 7 exhibits the methodology of the present paper. The various section of this study, including categorizing the study area using AHP weights and finding restricted areas, are shown in this figure. Finally, the final map can be obtained by overlying the categorized and restricted maps of the study area.

**Figure 6.** Final criteria weights according to the AHP method (CR = 3.7%).

**Figure 7.** Methodology of study.

## **5. Materials and Methods**

Selecting appropriate points for wind farm site selection is a complex process. The methodology for selecting suitable areas is determined by the calculated weights and the restrictions specified for ecological, structural, and topological criteria and sub-criteria. A two-step methodology has been used to select the best areas for wind farms:

1. The province has been divided into two areas according to restrictions, suitable

and unsuitable. 2. The best areas have been chosen according to the weighted criteria among suitable regions.

In the first step, some restrictions are applied to divide the province into two suitable and unsuitable parts. The restrictions are set for the amounts and distances of each topological, ecological, and structural features.

A conceptual model will be developed after dividing the province into suitable and unsuitable areas. Figure 7 depicts the conceptual model for this study. Specific criteria and restrictions are defined in this model. The required data, assessments, and the characterizations of the study area are collected. According to the defined criteria and collected data, the map layer will identify, layers will integrate based on the conceptual model, and the final suitable and the unsuitable area will be represented.

Finally, the main weighed criteria with the AHP method will be used to classify the appropriate area and determine the best area for the wind farm.
