*5.2. Operational Conditions*

### 5.2.1. Transformer's Main Health Index (HI m)

The transformer main health index has always been a useful factor in the transformer operational period. This index has been sensitive to temperature fluctuations, which changes in various ratios in the transformer life, so it depends on system summary. Transformers Main Health Index (*HIm*) is determined by the initial main health index reference point, which is named: *HI*0. *HIm* is defined by Equations (15) and (16) mentioned below:

$$HI\_m = HI\_0 \times \mathcal{e}^{\otimes \times (T\_2 - T\_1)}\tag{15}$$

$$\beta = \frac{\ln 6.5 - \ln 0.5}{T\_2 - T\_1}.\tag{16}$$

### 5.2.2. Transformers' Insulating Paper Health Index (*HIiso*)

Insulation paper in each transformer directly determines the e fficiency and life of a transformer. The transformer condition can be illustrated by identifying this index. Transformers Insulating Paper Health Index (*HIiso*) can be recognized by analyzing some gases, such as carbon monoxide and carbon dioxide, in the transformer which is damaged due to overheating over its lifetime. The Transformers Insulating Paper Health Index (*HIiso*) is presented in Equation (17):

$$
\delta H I\_{\rm iso} = \omega\_1 H I\_{\rm C,O} \times \omega\_2 H I\_{\rm fur} \tag{17}
$$

$$HI\_{fur} = 3.344 \times \left(\mathbb{C}\_{fur}\right)^{0.413}.\tag{18}$$

From [30], where *Cf ur* is content of furfural to determine, *HIf ur* is the index of it, from [28] *Cf ur* = 5 means that the transformer is deteriorated and it can break down, in this condition *HIf ur* = 6.5. On the other hand *Cf ur* = 0.01 when it is newer and *HIf ur* = 0.5. *HIC*,*<sup>O</sup>* is defined by carbon monoxide and carbon dioxide gases analysis.

#### 5.2.3. Transformer's Dissolved Gas Analysis (DGA) Health Index (HICH)

The Transformer's DGA health index (*HICH*) is one of the important and regular tests to determine a power transformer's health. In this health index, the values of hydrogen (H2), methane (CH4), ethane (C2H6), ethylene (C2H4), acetylene (C2H2), carbon monoxide (CO), and carbon dioxide (CO2) are analyzed in the transformer to estimate the power transformer's material condition, and consequently, the transformer's physical condition can be elaborated. The DGA health index (*HICH*) is illustrated in Equation (19):

$$HI\_{\rm CH} = \sum\_{i=1}^{5} \omega\_{i} \cdot F\_{\rm C,H}(i) \tag{19}$$

where, *FC*,*<sup>H</sup>* is the quantity of transformer ageing, hydrocarbon gas factor function, and ω is the weight of presented gases.

### 5.2.4. Transformer's Oil Health Index (*HIoil*)

The Transformer's Oil Health index can have some errors, such as acid value, high fluctuation of voltage, micro water, and dielectric losses. Also, these factors are the result of the transformer's cooling system and the transformer topology, which is met in transformer oil. This index calculation is given in Equation (20):

$$HI\_{oil} = \sum\_{i=1}^{4} w\_i F\_{oil}(i) \tag{20}$$

where, *Foil* is the oil factor function, determined the hydrocarbon gas factor function and ω is the weight of presented gases.
