Working with the engineering team at Hanford site in Richland, Washington, we developed a simulation based model of the power supply and consumption of a melter intended to vitrify radioactive waste. Due to the power supply being ungrounded, the goal of our simulation was to determine the ability of a untested ground fault detection system to detect ground faults in this isolated system. Modeled in Simulink and MATLAB, we applied different fault conditions into our model and demonstrated the simulated relays response to the detected condition changes. While exactly accurate parameters are difficult to model, our simulation was able to demonstrate proof of concept for a unconventional method of ground fault detection in a ungrounded system.