Energy disaggregation is a promising solution to access detailed information on energy consumption in a household, by itemizing its total energy consumption. However, in real-world applications, overfitting remains a challenging problem for data-driven disaggregation methods. First, the available real-world datasets are biased towards the most frequently used appliances. Second, both real and synthetic publicly-available datasets are limited in number of appliances, which may not be sufficient for a disaggregation algorithm to learn complex relations among different types of appliances and their states. To address the lack of appliance data, we propose two physics-informed data generators: one for high sampling rate signals (kHz) and another for low sampling rate signals (Hz). These generators rely on prior knowledge of the physics of appliance energy consumption, and are capable of simulating a virtually unlimited number of different appliances and their corresponding signatures for any time period. Both methods involve defining a mathematical model, selecting centroids corresponding to individual appliances, sampling model parameters around each centroid, and finally substituting the obtained parameters into the mathematical model. Additionally, by using Principal Component Analysis and Kullback-Leibler divergence, we demonstrate that our methods significantly outperform the previous approaches.