In many countries domestic electric hot water storage cylinders have high penetration and account for a large proportion of electricity demand. Their ability to store energy makes them a significant opportunity for emerging smart home energy management systems. One approach to evaluating the potential of hot water cylinders under smart control is to simulate electricity demand via a physical model of a cylinder together with assumed hot water usage patterns. Determining the accuracy of these simulations is made difficult by the lack of detailed data on cylinder variables and household hot water usage. This results in simulation methods that potentially miss essential features or are overly complex. To address this issue, we first propose a statistical fidelity measure that can be used to compare simulated with monitored electricity demand time series from an individual cylinder. We then present a minimal simulation method that achieves reasonable fidelity with monitored demand. The proposed method is particularly useful for simulating individual households using only electricity time-series data for the purpose of evaluating smart home management scenarios.