## 1 Introduction
### Research Literature Review  
A significant body of research has been dedicated to improving the performance of differential protection schemes, with the goal of enhancing the accuracy of internal fault detection amid various operating conditions of transformers. Various methods have been proposed where internal fault detection is performed based on features extracted from the differential current in the time domain [3]. Advanced intelligent techniques have also been developed for internal fault detection, relying on pattern recognition methodologies. These techniques incorporate various classifiers, such as artificial neural networks [4; 5; 6], probabilistic neural networks [7; 8], support vector machines [9], and neuro-fuzzy systems [10], as the primary detection mechanisms. These intelligent systems necessitate extensive training datasets. Furthermore, determining the optimal parameters for neural networks lacks a standardized approach, which necessitates the employment of optimization algorithms [11]. Several proposed methods utilize signal analysis tools to extract features from the differential current waveform. This approach significantly reduces the volume of input data and enhances the generalization ability of the intelligent algorithms. Among the prevalent signal analysis techniques is the wavelet transform [12; 13; 14; 15], which is widely used in the analysis of differential currents. In wavelet-based methods, selecting the appropriate number of decomposition levels and the mother wavelet typically involves trial and error. The features extracted, particularly from the detail levels, are highly susceptible to noise interference. Similarly, the S-transform method relies on a variable parameter associated with the Gaussian window, influencing the decomposed signals [16; 17]. These innovative approaches, which blend advanced signal processing techniques with machine learning algorithms, represent a significant step forward in the field of transformer protection. They offer improved accuracy and reliability in fault detection, thereby contributing to the overall stability and efficiency of power systems. On the other hand, harmonic blocking and harmonic restraint are well-established methods for preventing false tripping caused by inrush currents [18] and are extensively used in commercial relay systems [19; 20]. Although harmonic restraint generally offers high reliability, it often lacks security when dealing with inrush currents that have low harmonic content [21]. Furthermore, harmonic restraint can unexpectedly block the relay when energizing a transformer that has a fault, especially if the healthy phases exhibit high harmonic levels [21]. While harmonic cross-blocking enhances security, it suffers from low reliability during the energization of a faulty transformer [21]. For example, during the energization of a faulty transformer, the differential relay may remain blocked for several cycles [22]. Additionally, modern power transformers may exhibit very low second harmonic ratios during energization, posing challenges for harmonic-based protection methods [21]. Therefore, it is imperative to integrate new functionalities into differential protection systems to improve both the security during energization and the reliability of detecting internal faults. Recent advancements have focused on developing new techniques that leverage artificial intelligence and advanced signal processing to address the limitations of traditional differential protection methods [23; 24; 25]. These innovative approaches aim to enhance the safety and reliability of differential relays during inrush conditions [26; 27]. However, many of these methods face challenges, including the need for large training datasets, high computational demands, and a reliance on specific transformer parameters. To overcome these challenges, researchers have proposed various solutions.