Wide bandgap (WBG) devices and power electronic converters (PEC) that enable the dynamic control of energy and high-power density designs inevitably contain defects including sharp edges, triple points, and cavities, which result in local electric field enhancements. The intensified local electric stresses cause either immediate dielectric breakdown or partial discharge (PD) that erodes electrical insulators and accelerates device aging. With the goal of addressing these dielectric challenges emerging in power-dense applications, this dissertation focuses on 1) modeling the dielectric characteristics of supercritical fluids (SCFs), which is a new dielectric medium with high dielectric strength and high cooling capability; and 2) establishing the optimal fabrication conditions of electrets, which is a new dielectric solution that neutralizes locally enhanced electric fields. In this dissertation, the dielectric breakdown characteristics of SCFs are modeled as a function of pressure based on the electron scattering cross section data of clusters that vary in size as a function of temperature and pressure around the critical point. The modeled breakdown electric field is compared with the experimental breakdown measurements of supercritical fluids, which show close agreement. In addition, electrets are fabricated based on the triode-corona charging method and their PD mitigation performance is evaluated through a series of PD experiments. Electrets are fabricated under various charging conditions, including charging voltage, duration, polarity, and temperature with the goal of identifying the optimal condition that leads to effective PD mitigation. The PD mitigation performance of electrets fabricated based on these charging conditions is further assessed by investigating the impact of various power electronics voltage characteristics, including dv/dt, polarity, switching frequency, and duty cycle. Electret based electric field neutralization approach is further utilized in increasing the critical flashover voltage associated with the surface flashover voltage. Moreover, due to the high mechanical strength of epoxy composites at cryogenic temperatures, in this dissertation, epoxy-based electrets are fabricated as a solution to PD in high temperature superconducting cables. The experimental demonstrations conducted with electret in this dissertation is dedicated for the establishing the electret based electric field neutralization approach as a dielectric solution for the dielectric challenges in power electronics driven systems.