A variety of energy management and analytics techniques rely on models of the power usage of a device over time. Unfortunately, the models employed by these techniques are often highly simplistic, such as modeling devices as simply being on with a fixed power usage or off and consuming little power. As we show, even the power usage of relatively simple devices exhibits much more complexity than a simple on and off state. To address the problem, we present a Non-Intrusive Model Derivation (NIMD) algorithm to automate modeling of residential electric loads using concepts from power systems, statistics, and machine learning. NIMD automatically derives a compact representation of the time-varying power usage of any residential electrical load, including both the device's energy usage and its pattern of usage over time. Such models are useful for a variety of analytics techniques, such as Non-Intrusive Load Monitoring, that have relied on simple on-off models in the past. We evaluate the accuracy of our models by comparing them with both actual ground truth data, and against models that have been designed manually by human experts. We show that models derived via NIMD are comparable in accuracy to models built by experts and closely approximate the ground truth data.