# High Frequency Transformers for Solid-State Transformer Applications
## 1 Introduction  
The solid-state transformer (SST) is an emerging technology that can influence power transmission/distribution networks, their integration with renewable energy sources, and traction systems, among others. In recent years, the integration of renewable energy sources has increased significantly, leading to numerous investigations to integrate this principle with electrical distribution networks and their optimization [1, 2]. Some advantages of using SSTs instead of conventional transformers, which operate at a low frequency of 50/60 Hz, include reactive power compensation, voltage regulation, power flow control, and the possibility of easy interconnection with equipment, allowing the improvement of power quality. One of the main advantages of using SSTs instead of traditional transformers is the reduction of volume and weight. For example, accordingto [1], a three-phase STT would accomplish a volume reduction of 80% compared to a conventional 50/60 Hz transformer. This significant difference has a great impact as it facilitates portability, decreases installation costs, and significantly reduces the consumption of raw materials [1]. Some relevant works about the design of HFTs based on a two-level voltage converter include [3], which presents and discusses the effect and influence of HFT parasitic capacitances on the operation and design of an SST with two-level converts. The optimization issues of HFT are addressed in [4], via a physics-based design optimization algorithm combined with multi-objective genetic algorithms. In [5], HFT design in relation to Multi Port SST (MPSST) applications is discussed. Different winding placement and distribution on the same core are suggested, and the inductance and coupling coefficient matrices are calculated using ANSYS Maxwell 3D simulation software. In [6], an optimum design of HFT based on winding spacing, minimum weight, and efficiency constraints is presented. This transformer design takes into account series resonant converter applications. Several other papers with HFT for resonant converters can be found in the literature. In [7], the design of HFT for LLC resonant converters with SiC-based semiconductors and high efficiency is proposed. A similar design solution using a GaN power semiconductor is also proposed in [8]. An extended comparison among different HFTs for resonant power converters can be found in [9]. Several papers about multilevel inverters for SSTs have also been published. In [10], an HFT with a high-voltage insulation structure for SST for medium-voltage multilevel converters is presented. A comparative analysis of a multilevel high frequency link and multilevel DClink DC-DC HFT based on Modular Multilevel Converters (MMC) and a Dual-Active Bridge (DAB) for MVDC application can be found in [11]. Several other studies about HFT and SST discuss different types of transformers. For example, [12], proposes a comparative study of two types of HFT (one made of planar cores and windings in the form of thin copper foil and the other built with E-type cores and Litz wire) in a 20-kW phase-shifted full-bridge converter application. An analysis of the electromagnetic characteristics of HFT based on C-type nanocrystalline magnetic cores is proposed in [13]. Another study presents the design and the main advantages of dry-type high-power HFTs based on triangular closed cores [14]. Considerations about the design, modeling, and analysis of compact planar transformers can be found in [15]. The high-frequency modeling of foil-type transformers for shipboard power-electronic distribution systems is studied and analyzed in [16]. However, to achieve the desired operational objectives of SST, many challenges must still be overcome, especially in the dimensions of the components of the High Frequency Transformer. These include determining the optimal flux density and minimizing power losses to maximize efficiency.