**4. Transformer Selection**

Transformers are the last operational part of the grid, which directly influence the quality of the grid and charge stations. Generally, all ranges of grid transformers are influenced by storages, such as charging stations or grid independent storages. Low- and mid-range transformers in the grid receive high impact from power electronic equipment, but they need support from high voltage transformers. Some transformer parameters depend on their own operational period, which cannot be determined in routine ways. The capacity of distribution in transformers has the potential to determine the necessary variables in the grid, related to financial problems, aging, health, and their priorities. Hence in this algorithm, the capacity and related problems have a higher priority. Low capacity or overload is the first step in system failure. Overload in electric equipment, like transformers, cause severe faults in the grid. In the second step, it causes a nonlinear increase in the transformers' temperature [19]. One of the regular solutions to solve these problems is by decreasing or changing the load pattern according to different grid specifications [20]. Transformers should be sorted according to their capacity. The flow chart of sorting is shown in Figure 3.

The purpose is to determine high priority transformers in the grid. By changing the timeslot in the Grid Valley filling technology [21], grid demand level, load factor, and transformer aging have been changed at a reasonable scales. It can reduce load about 4~5 GW in a scenario and ambient transformers temperature 1.06~1.64% instead 52~100% in 50 kVA transformers and 200 ◦C temperature rate. Consequently, transformer aging is influenced with these statistics, where it has changed 17~18 factors, instead of 17~96. Another study has illustrated that EVs generate overload and shape impulses. Such grid problems have been solved through timetable changes and transformer hierarchy, as shown by MATLAB V9.5 software [22,23]. The solving method can change in each location, depending on related problem conditions, therefore, there (There will be various conditions at hand). The smart grid transmission and distribution costs are very important and have been influential in the other side of the grid. The function of transmission and distribution costs has been given in Equation (1) [24]. Equation (1) has illustrated the importance of grid infrastructure and equipment costs when they have met low/over load. In this equation transformers and lines are the main factors [24].

$$\begin{array}{l} \text{Min } \mathbf{z} = & \sum\_{\begin{subarray}{c} (\mathbf{i}, \mathbf{j}) \in \text{Line} \end{subarray}} \text{a}\_{\mathbf{i}, \mathbf{j}} \big( \mathbf{X}\_{i, \mathbf{j}} \big) + \sum\_{\begin{subarray}{c} (\mathbf{i}, \mathbf{j}) \in \text{OverLine} \end{subarray}} \text{b}\_{\mathbf{i}, \mathbf{j}} \big( \mathbf{X}\_{i, \mathbf{j}} \big) + \\ & \sum\_{\begin{subarray}{c} \mathbf{m} \in \text{OverLine} \end{subarray}} \text{c}\_{\mathbf{m}}(\mathbf{X}\_{\mathbf{m}}) + \sum\_{\begin{subarray}{c} \mathbf{n} \in \text{OutLon} \end{subarray}} \text{d}\_{\mathbf{n}}(\mathbf{X}\_{\mathbf{n}}) + \\ & \sum\_{\begin{subarray}{c} \mathbf{m} \in \text{OutLon} \end{subarray}} \text{e}\_{\mathbf{n}}(\mathbf{X}\_{\mathbf{n}}) + \sum\_{\begin{subarray}{c} \mathbf{m} \in \text{Ment} \text{ Equip} \\ \mathbf{m} \in \text{Ment} \end{subarray}} \text{f}\_{\mathbf{m}}(\mathbf{X}\_{\mathbf{m}}) + \\ & \sum\_{\begin{subarray}{c} \mathbf{m} \in \text{Pover} \end{subarray}} \text{g}\_{\mathbf{k}}(\mathbf{X}\_{\mathbf{k}}) + \sum\_{\begin{subarray}{c} \mathbf{m} \in \text{Pauli} \\ \mathbf{m} \in \text{Pauli} \end{subarray}} \text{h}\_{\mathbf{m}}(\mathbf{X}\_{\mathbf{m}}) \end{array} \tag{1}$$

**Figure 3.** Electric vehicle (EV) charge stations coordination algorithm.

The above equation shows that transmission and distribution costs create a large part of the grid's maintenance cost. The next equations have illustrated aging and the loss of life rate of the transformer for an average penetration rate of EV [25,26], which completely depends on the transformers' temperature. Through various investigations, EV fast charge stations or similar loads were found to generate an impulse load signal type, consequently, it hides hot-spot temperature points in the transformer, which sensors cannot detect.

$$\mathbf{V} = \mathbf{e}^{\frac{15000}{110+273} - \frac{15000}{6h+273}}\tag{2}$$

$$\mathbf{L} = \int\_{\mathbf{t}\_1}^{\mathbf{t}\_2} \mathbf{V} \mathbf{dt} \text{ Or } \mathbf{L} \approx \sum\_{\mathbf{n}=1}^{N} \mathbf{V}\_{\mathbf{n}} \times \mathbf{t}\_{\mathbf{n}} \tag{3}$$

$$\mathbf{D}\_{\text{TR\\_PHEV\\_X}} = \mathbf{A} \times \mathbf{e}^{(\mathbf{B} \times \mathbf{T}\_{\text{x\\_}} \mathbf{T}\_{\text{r}})} \tag{4}$$

$$\text{V}\_{\text{TR\\_PHEV\\_X}} = \frac{\text{D}\_{\text{TR\\_PHEV\\_WTHOUT}}}{\text{D}\_{\text{TR\\_PHEV\\_X}}} \tag{5}$$

$$\mathbf{V\_{TR\\_PHEV\\_LOW}} = \mathbf{A} \times \mathbf{T\_{x\\_T}} + \mathbf{B} \tag{6}$$

$$\mathbf{V\_{TR\\_PHEV\\_X}} = \mathbf{A} \times \mathbf{e^{\left(B \times T\_{x\\_}T\_{\mathbf{r}}\right)}} + \mathbf{C} \times \mathbf{e^{\left(D \times T\_{x\\_}T\_{\mathbf{r}}\right)}} \tag{7}$$

Figure 4 clearly shows the temperature influence on the loss of life (LOL) rate on transformers, which can be proved by Equations from (2) to (7) [25]. The transformers' overall condition is important when transformer temperature exceeds 110 ◦C, so the LOL rate starts increasing.

**Figure 4.** LOL and θh in different time [25].

One of the most effective ways to solve this type of problem is to monitor transformer temperatures, which are controlled at SCADA or matched on relay settings [25]. Indisputably, sometimes by assigning more EVs in each grid, some transformers might ge<sup>t</sup> overloaded, consequently leading towards faults or interruptions in the grid. The solution to capacity problems depends on the grid communication infrastructure and the grid creation hierarchy. The flow chart of the grid communication infrastructure and the grid creation hierarchy is also represented in Figure 3.

According to the grid condition, there are many factors in the flowchart that can be calculated altogether. For Ankara, we do not have a smart transformer with online monitoring, therefore, we must use tools based on summary data. Table 2 shows information that owner C and D have a high priority to create a charge station on their locations. For example, the data of a grid with air quality sensor results are provided below.


**Table 2.** A grid transformers' center and their environmental condition.

In localizing EV charge stations, the regional condition and some of their priorities were more important than the grid infrastructure on their locations. Therefore, they should develop their own location grid infrastructure. In most of the locations parking and public areas provide benefits from the financial and technical side, to create a battery bank and base for an EV charging station. In addition, all of them are explained in the "Selection of High Efficiency and Operational Locations" section of this paper. In this case, the transformers are not smart and the operations group cannot monitor the transformers status, so they do maintenance operations using technical data and by estimation. The transformers are replaced every 30 years and they reach 55~70% capacity during load peak times. These provide some information about the grid, such as transformers work condition. The ANSI/IEEE C57.96-1989 standards [27] recommend transformers be replaced every 20 years, if they have been run under ideal maintenance conditions. The transformers' life expectancy may be calculated by their insulation life equation, as illustrated below:

$$\log\_e life \left( t \right) = A\_\ell + \frac{B\_\ell}{T} \tag{8}$$

$$
\log\_{10} \operatorname{life} \left( t \right) = A\_{10} + \frac{B\_{10}}{T} \,. \tag{9}
$$

Based on Equations (8) and (9), Figures 5 and 6 illustrates the time expectancy curve, used in Equations (8) and (9). It shows that transforms, which age more than 20 years, have been in the best maintenance condition.

Figures 5 and 6 and the related Equations (Equation number 8 and 9) have shown that the transformers have been maintained and are in good condition (the grid has passed "Calculate Transformers Health by Load Summery, Age," term).

**Figure 5.** Life hours and hottest spot temperature ◦C in transformers by LOG10.

**Figure 6.** Life hours and hottest spot temperature ◦C in transformers by LOG10.
