**6. Results**

In this section, we show that there are many factors which influence the distribution of charge stations. Air quality, transformer conditions, change infrastructure location, and local condition have illustrated that there are very important factors to feed the algorithms mentioned in the Introduction section of the paper. For example, the Gaussian distribution method in Equation (15) can give di fferent results, depending on three factors, rather than two factors. Indeed, the factors change the distribution system variance and reference of their changes:

$$f(\mathbf{x}) = \frac{1}{\sqrt{2\pi\sigma}}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2} - \infty < \mathbf{x} < +\infty. \tag{21}$$

In addition, it is one of the distribution systems between di fferent types. Today, most of the distribution systems work by multi-functional operations, based on the same system. The Genetic Algorithm is the most used algorithms for the same goal. However, they can work by di fferent variables and functions. The control of each algorithm has its own special strategy and their responsibility efficiency depends on valid operational information from the location. Figure 9 has illustrated a hierarchy of input data for algorithms. In addition, operations in each algorithm will change if other priorities are used in their hierarchy.

**Figure 9.** Hierarchy of algorithm input data.

In this case, the result of the "Estimation Algorithm" block depends on Turkish energy policy which involves long-term planning. According to the data mentioned in Table 1, two and location information, the GA is a reasonable method in creating a charging station point. Therefore, there are many drivers, reasons, and information, which can change algorithm targets. The information, which is issued by first data can be changed or improved by the GA algorithm. Figure 10 has mentioned an algorithm that was designed by the hierarchy presented in Figure 9. The algorithm has analyzed and sorted pure data to import on the main estimation algorithm. Firstly, the algorithm achieves location information, however, one of the algorithm targets is the charging station determination near the transportation road to reduce equipment faults during energy transmission. In the next step, the algorithm has been redeterminated in each fail loop or unsuccessful operation. In addition, the algorithm sorts each charging stations in some distance, which depends on grid and customers' needs. In the second step, the condition of the grid infrastructure has played a big role on algorithm output. In first technical command, it selects transformers, which have the highest reservoir capacity, so the transformers can absorb and transfer grid energy, and lacking in quality. The transformer

should be selected by the highest criteria so that the charging stations, especially fast charging stations, behave differently than transformers' norm. In the second step, which contains the analysis of technical condition, the determination of the points have been issued by their previous technical conditions. Transformers' conditions can be calculated by temperature or maintenance information.

According to above-mentioned operations, three points (B, D and C) have been determined to be the locations for building EV fast charging stations in Ankara. There are sufficient reasons to select the mentioned transformer centers, by the time they have some difference between mentioned points. Some local infrastructure and transformer responsibility factors have different factors which can be solved by some location problem using GA.

**Figure 10.** Flow chart of Genetic Algorithm (GA) estimation method.

Using the above-mentioned factors, the designers should give some scores to parameters, in order to determine factors' priorities, then, their data might be ready to input on estimating algorithms. For example, in GA it can be solved by the Genetic Algorithm shown in Figure 10.

According to the above flowchart, the algorithm can adapt in most of the estimating algorithms. For three areas, marked B, C, and D, several sets of locations and electric infrastructure have been arranged as chromosome structures, shown in Table 3. Six chromosome sets are based on the flowchart in Figure 10. The locations are sorted based on distance (a gene), local infrastructure (b gene), parking (c gene), and electric infrastructure (d gene). The generations are derived according to

low loads, ageing, and transformer capacity transformer index of the mentioned areas respectively. A maximum of 30 locations have been considered to satisfy the objective function mentioned as:

$$F\_{abj} = a + 2b + 3c + 4d - 30. \tag{22}$$


**Table 3.** Chromosome structure for aforementioned locations with their corresponding areas (termed as B, C, and D).

Six chromosome have been created by location and infrastructure genes. The calculation of determination of the fittest chromosomes have been illustrated in Table 4.


**Table 4.** Determination of fitness function and probability for the first generator.

If the random values ranging from 0–1 are initiated and if C[1] < R[1] < C[2], then chromosome [2] can be set as the new population for the next generation.

$$R = [0.37, \ 0.08, \ 0.971, \ 0.829, \ 0.735, \ 0.359]]$$

By those random patterns, new chromosomes have listed in below:

> Chromosomes 2: [09; 06; 15; 09] as New Chromosome 1 Chromosomes 1: [27; 24; 27; 12] as New Chromosome 2 Chromosomes 6: [15; 21; 21; 18] as New Chromosome 3 Chromosomes 5: [27; 15; 06; 27] as New Chromosome 4 Chromosomes 5: [27; 15; 06; 27] as New Chromosome 5 Chromosomes 2: [09; 06; 15; 09] as New Chromosome 6

Considering a crossover-rate of 25%, if the corresponding value of *R*[*k*] is less than the rate, the chromosome will be considered as the parent chromosome. For an array of random number:

> *R* = [0.518, 0.224, 0.108, 0.383, 0.071, 0.481]

By the new randomization and chromosomes, the parents can be presented as below:

> Chromosome 2: [27; 24; 27; 12] Chromosome 3: [15; 21; 21; 18] Chromosome 5: [27; 15; 06; 27]

By the random numbers that have given in crossover section, new set of crossovers will be:

> Chromosome [2] × chromosome [3]

> Chromosome [2] × chromosome [5]

> Chromosome [3] × chromosome [5]

Chromosome 2: Chromosome 2 × Chromosome 3 = [27; 24; 27; 12] × [15; 21; 21; 18] = [27; 24; 21; 18] Chromosome 3: Chromosome 3 × Chromosome 5 = [15; 21; 21; 18] × [27; 15; 06; 27] = [15; 21; 06; 27] Chromosome 5: Chromosome 5 × Chromosome 2 = [27; 15; 06; 27] x [27; 24; 27; 12] = [27; 15; 27; 12]

New chromosomes after the crossover process have been illustrated below:

> Chromosome [1]: [09; 06; 15; 09] Chromosome [2]: [27; 24; 21; 18] Chromosome [3]: [15; 21; 06; 27] Chromosome [4]: [27; 15; 06; 27] Chromosome [5]: [27; 15; 27; 12] Chromosome [6]: [09; 06; 15; 09]

For a mutation rate of 10%, as there are 24 genes in total, the number of mutation will be 0.1 × 24 = 2.4, which can be equated to 2. Thus, the mutated genes are marked in bold.

> Chromosome [1]: [09; **06**; 15; 09] Chromosome [2]: [27; 24; 21; 18] Chromosome [3]: [15; 21; **06**; 27] Chromosome [4]: [27; 15; **06**; 27] Chromosome [5]: [27; 15; 27; 12] Chromosome [6]: [09; **06**; 15; 09]

The mutated genes must be replaced by random numbers from 0–30 to obtain the new set of chromosomes to proceed for iterating in the next generation. If the numbers be 10, 15, 20 and 25 respectively, the new chromosomes will be:

> Chromosome [1]: [09; **10**; 15; 09] Chromosome [2]: [27; 24; 21; 18] Chromosome [3]: [15; 21; **15**; 27] Chromosome [4]: [27; 15; **20**; 27] Chromosome [5]: [27; 15; 27; 12] Chromosome[6]:[09;**25**;15;09]

This is the chromosomes of generation one of the algorithm. The process will be iterated until the value of a, b, c, and d meets the optimum value to satisfy the equation. After iterating for 5 generations, the evolution fitness chart will be as represented in Figure 11:

**Figure 11.** Evolution fitness curve showing gradual increase in fitness value corresponding to the generation.

The algorithm considered three areas, and after selecting several locations according to the aforementioned parameters (Figure 9), sorted the data into four segments. However, by creating six chromosomes, the algorithms mentioned in Figure 10 were followed to obtain the first generation of the chromosome. The aim was to attain the best value for the variables in the objective function, so that the optimum location for the charging station can be determined. Fitness value for each corresponding

generation is calculated, and as it can be seen, fitness increased with each generation, indicating the success of the algorithm. The higher the value of fitness, the better the algorithm. Thus, after several iterations, the optimal locations in these areas were determined in Ankara metropolitan, as the locations illustrated in Figure 12.

**Figure 12.** Selected points in Ankara (By Bing map).
