# Identification of Transformer Parameters Using Dandelion Algorithm
## 1 Introduction  
In recent years, access to reliable electrical power has become a fundamental right for humanity, underpinning both technological and social development. To meet the ever-growing demand at load centers, a complex infrastructure has been established for generating, transforming, transporting, distributing, and selling electricity. Among the most crucial devices in this chain, and in the electrical sector as a whole, are transformers. These versatile devices play a critical role in interconnecting power generation plants with transmission networks. They also serve as the link between transmission and sub-transmission networks, ultimately delivering power to residential, industrial, and commercial end users. This is achieved by adjusting the voltage level (high, medium, or low) at each stage of the transmission and distribution process. Transformers can highly efficiently transmit energy via transmission lines depending on parameters and losses [1]. Several studies have been conducted to determine transformer-equivalent circuit parameters in order to reduce losses, increase performance, and lower operational costs. The frequency dependence of unknown transformer characteristics complicates the accuracy of transformer modeling [2]. Also, the accuracy of transformer parameter estimation can be significantly impacted by factors like harmonics in the voltage waveform, saturation of the transformer core, and transient events on the power grid. Optimal transformerdesign requires accurate parameter estimates to meet standards and specifications. Hence, precise estimation of transformer parameters was achieved by employing either frequency response [3] or time domain analysis through real-time measurements [4]. To account for the saturation of the transformer core, inrush current measurements [5] were utilized during the parameter estimation process. Moreover, short-circuit and open-circuit tests have been the cornerstone methods for determining transformer parameters. However, these are limited to laboratory settings and require disconnecting transformers from the power grid. This disconnection disrupts service to multiple users in distribution systems, negatively impacting reliability indices [6]. Additionally, the sheer number of transformers in a distribution system makes this approach economically impractical. Traditionally, analytical methods based on finite-element analysis have been the primary tools for rapid transformer physical sizing. However, these methods can struggle with increasingly complex transformer geometries and non-linear material properties. To address these limitations, researchers have begun exploring the application of non-conventional techniques, including evolutionary computation algorithms [7; 8]. Optimization algorithms have become a cornerstone of tackling various electrical engineering challenges. From optimizing the design of electric machines, transformers, and transmission lines to enhancing the performance of fuel cells, photovoltaic modules, power system stabilizers, etc., these techniques offer powerful solutions [9; 10; 11; 12]. In the context of parameter estimation, optimization techniques are employed to establish a correspondence between observed data and their predicted counterparts. This correspondence is quantified by a cost function, which the optimization algorithm aims to minimize. The minimization process effectively reduces the discrepancy between the observed and estimated values. As reported in the literature, there are many optimization algorithms employed in the parameter estimation of transformers, such as evolutionary programming [13], the coyote optimization algorithm [14], the jellyfish optimizer algorithm [15], and the chaotic optimization approach [16]. The aforementioned optimization algorithms possess the advantageous characteristic of being implementable using either load data or mapellate data acquired from the transformer while it remains operational.