The trend towards more and all-electric apparatuses and more electrification will lead to higher electrical demand. Increases in electrical power demand can be provided by either higher currents or higher voltages. Due to "weight" and "voltage" drop, a raise in the current is not preferred; so, "higher voltages" are being considered. Another trend is to reduce the size and weight of apparatuses. Combined, these two trends result in the high voltage, high power density concept. It is expected that by 2030, 80% of all electric power will flow through "power electronics systems". In regards to the high voltage, high power density concept described above, "wide bandgap (WBG) power modules" made from materials such as "SiC and GaN (and, soon, Ga2O3 and diamond)", which can endure "higher voltages" and "currents" rather than "Si-based modules", are considered to be the most promising solution to reducing the size and weight of "power conversion systems". In addition to the trend towards higher "blocking voltage", volume reduction has been targeted for WBG devices. The blocking voltage is the breakdown voltage capability of the device, and volume reduction translates into power density increase. This leads to extremely high electric field stress, E, of extremely nonuniform type within the module, leading to a higher possibility of "partial discharge (PD)" and, in turn, insulation degradation and, eventually, breakdown of the module. Unless the discussed high E issue is satisfactorily addressed and solved, realizing next-generation high power density WBG power modules that can properly operate will not be possible. Contributions and innovations of this Ph.D. work are as follows. i) Novel electric field grading techniques including (a) various geometrical techniques, (b) applying "nonlinear field-dependent conductivity (FDC) materials" to high E regions, and (c) combination of (a) and (b), are developed; ii) A criterion for the electric stress intensity based upon accurate dimensions of a power device package and its "PD measurement" is presented; iii) Guidelines for the electrical insulation design of next-generation high voltage (up to 30 kV), high power density "WBG power modules" as both the "one-minute insulation" and PD tests according to the standard IEC 61287-1 are introduced; iv) Influence of temperature up to 250°C and frequency up to 1 MHz on E distribution and electric field grading methods mentioned in i) is studied; and v) A coupled thermal and electrical (electrothermal) model is developed to obtain thermal distribution within the module precisely. All models and simulations are developed and carried out in COMSOL Multiphysics. / Doctor of Philosophy / In power engineering, power conversion term means converting electric energy from one form to another such as converting between AC and DC, changing the magnitude or frequency of AC or DC voltage or current, or some combination of these. The main components of a power electronic conversion system are power semiconductor devices acted as switches. A power module provides the physical containment and package for several power semiconductor devices. There is a trend towards the manufacturing of electrification apparatuses with higher power density, which means handling higher power per unit volume, leading to less weight and size of apparatuses for a given power. This is the case for power modules as well. Conventional "silicon (Si)-based semiconductor technology" cannot handle the power levels and switching frequencies required by "next-generation" utility applications. In this regard, "wide bandgap (WBG) semiconductor materials", such as "silicon carbide (SiC)"," gallium nitride (GaN)", and, soon, "gallium oxide" and "diamond" are capable of higher switching frequencies and higher voltages, while providing for lower switching losses, better thermal conductivities, and the ability to withstand higher operating temperatures. Regarding the high power density concept mentioned above, the challenge here, now and in the future, is to design compact WBG-based modules. To this end, the extremely nonuniform high electric field stress within the power module caused by the aforementioned trend and emerging WBG semiconductor switches should be graded and mitigated to prevent partial discharges that can eventually lead to breakdown of the module. In this Ph.D. work, new electric field grading methods including various geometrical techniques combined with applying nonlinear field-dependent conductivity (FDC) materials to high field regions are introduced and developed through simulation results obtained from the models developed in this thesis.