In this paper, we present the Home Electricity Data Generator (HEDGE), an open-access tool for the random generation of realistic residential energy data. HEDGE generates realistic daily profiles of residential PV generation, household electric loads, and electric vehicle consumption and at-home availability, based on real-life UK datasets. The lack of usable data is a major hurdle for research on residential distributed energy resources characterisation and coordination, especially when using data-driven methods such as machine learning-based forecasting and reinforcement learning-based control. A key issue is that while large data banks are available, they are not in a usable format, and numerous subsequent days of data for a given single home are unavailable. We fill these gaps with the open-access HEDGE tool which generates data sequences of energy data for several days in a way that is consistent for single homes, both in terms of profile magnitude and behavioural clusters. From raw datasets, pre-processing steps are conducted, including filling in incomplete data sequences and clustering profiles into behaviour clusters. Generative adversarial networks (GANs) are then trained to generate realistic synthetic data representative of each behaviour groups consistent with real-life behavioural and physical patterns.