*3.1. Predicting DP When 2FAL Only Is Available*

Figure 1 depicts the modeling configuration that predicts DP when only 2FAL is available. The coaching efficiency graph in Figure 2 clearly shows that the learning ability of the ANN is satisfactory. The average mean square error of the trained ANN was less than the predetermined minimum of 0.0001. The mean square error was 692.943 after the coaching of the ANN. As a result, this model was selected as the definitive option for the specified input and output. The trial set error as well as the verification set error had comparable features, and zero notable overfittings transpired after iteration 14. This was the region where the optimum validation result had been achieved.

**Figure 1.** The ANN classifier for the LOL estimation for model one.

Mineral-based oil units were considered. The condition of the oil was taken as is for analysis as it represents the accurate amounts of furans present. The dataset was utilized to train the ANN. Following ANN training, its efficiency was verified by showing the linear regression graph that correlated the targets to the outputs, as illustrated in Figure 3. The correlation coefficient indicates how effectively the ANN's targets may detect changes in outputs. A correlation of 0 means that there is no correlation at all, whereas a correlation of 1 means that there is a complete correlation. A regression result suggests a close relationship between the outputs and targets. The correlation coefficient in this scenario was observed to be 0.964, indicating a high correlation.

**Figure 2.** Performance of the training process of model one.

**Figure 3.** Model linear fitting in training and testing for model one.

Figure 4 depicts the accuracy of the validation checks using the validation set. When the validation error begins to rise, the ANN terminates the learning session, regardless of whether the target has still not been achieved. Therefore, the ANN has a high degree of generalizability. This will halt the learning session when the abstraction performance has reached its maximum. Figure 5 demonstrate the performance parameters of the proposed FFANN.

**Figure 4.** Validation in the training phase of model one.


**Figure 5.** ANN model training of model one.

*3.2. Predicting LOL Using Predicted DP and Measured 2FAL*

Figure 6 illustrates the model setup for predicting LOL based on the predicted DP and measured 2FAL.

**Figure 6.** The ANN classifier for LOL estimation for model two.

The cumulative mean square deviation of the generated ANN was 0.0006684, and Figure 7 illustrates that the testing and verification curves had comparable properties, indicating efficient training. The trial set error and the verification set error had similar characteristics, and no significant overfitting occurred after iteration 13. The correlation coefficient represents how successfully the ANN's goals can make corrections in outputs, with 0 representing no correlation at all, while 1 represents perfect correlation. The function

of the trained ANN was evaluated in two methods. Initially, the linear regression that ties the goals to the outputs is illustrated in Figure 8. The correlation coefficient in this scenario was observed to be 0.999, indicating a strong correlation.

**Figure 7.** Performance of the training process for model two.

**Figure 8.** Model linear fitting in training and testing model two.

It was observed that the model could be used to predict the DP and LOL of new and existing transformers at the manufacturer's premises and operating in the field, respectively.

In Figure 9, the Gradient, mu (i.e., control parameter for the algorithm used to train the neural network) and validation failure (val fail) results are presented.

**Figure 9.** Validation in the training phase of model two.

The output parameters of the training model for model two are illustrated in Figure 10.

**Figure 10.** ANN model training of model two.

#### **4. Conclusions**

Several publications have suggested that power transformers erected in the 1980s are still in service and that some of these transformers are in an acceptable state based on the data analyses such as DP, furan, CO2, and others. The service durability of these transformers exceeds 21 years, although the conventional technique predicts 21 years. This sustained efficiency is dependent on operational situations. These transformers are most likely to be used within the manufacturers' specified thresholds. Furthermore, the residual lifespan of the insulation is dependent on the transformer overloading cases and may be evaluated utilizing software iterations, considering the variance of overloading and LOL in the past years.

In this work, we proposed an approach for estimating the lifespan reduction and expansion of transformers. To acquire better consistent results, it is preferable to adopt a knowledge-based technique that accommodates all sets of data to accurately estimate the LOL of transformers. The ANN was applied to predict the DP and LOL in oil-submerged transformers by using the solid insulation evaluation. The proposed approach makes it simple to ascertain the extent of lifetime reduction and expansion for transformers, providing for improved accurate prediction of residual serviceability.

In this work, two ANN models were proposed. The first model was based on predicting the DP when only the 2FAL concentration measured from oil samples is available for new and existing transformers. The second ANN model proposed was based on predicting the transformer LOL when the 2FAL and DP are available to the utility owner, typically for the transformer operating at the site where un-tanking the unit will be a daunting and unfeasible task. The training and testing procedures databank was based on the dataset of the 2FAL and DP from a fleet of transformers and measured from laboratory analysis. The correlation coefficient of 0.964 was ascertained when the DP was predicted using the 2FAL measured in oil. On the ANN model, a correlation coefficient of 0.999 was obtained, against the practical data where one can make a reliable prediction of transformer LOL concerning the 2FAL generated and the amount of DP present produced. It was found that this model can be used to predict the DP and LOL of new and existing transformers at the manufacturer's premises and operating in the field, respectively.

This work provides critical knowledge for the electrical energy industry as well as beneficial attributes for future preparation. Operational planning for electrical generation, transmission, and distribution networks can perhaps be designed with greater reliability.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.
