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.