The power electronics research community is balancing on the edge of a game-changing technological innovation: as traditionally silicon (Si) based power semiconductors approach their material limitations, next-generation wide bandgap (WBG) power semiconductors are poised to overtake them. Promising WBG materials are silicon carbide (SiC), gallium nitride (GaN), diamond (C), gallium oxide (Ga2O3) and aluminum nitride (AlN). They can operate at higher voltages, temperatures, and switching frequencies with greater efficiencies compared to existing Si, in power electronics. These characteristics can reduce energy consumption, which is critical for national economic, health, and security interests. However, increased voltage blocking capability and trend toward more compact packaging technology for high-power density WBG devices can enhance the local electric field that may become large enough to raise partial discharges (PDs) within the module. High activity of PDs damages the insulating silicone gel, lead to electrical insulation failure and reduce the reliability of the module. Among WBG devices, electrical insulation weaknesses in WBG-based Insulated Gate Bipolar Transistor (IGBT) have been more investigated. The chapter deals with (a) current standards for evaluation of the insulation systems of power electronics modules, (b) simulation and modeling of the electric field stress inside modules, (c) diagnostic tests on modules, and (d) PD control methods in modules.