Reducing the energy consumption in buildings and homes can be achieved by predicting how energy-consuming appliances are used, and by discovering their patterns. To mine these patterns, a smart-metering architecture needs to be in place complemented by appropriate data analysis mechanisms. Once the usage patterns are obtained, they can be employed to optimize the way energy from renewable installations, home batteries, and even micro grids is managed. We present an approach and related experiments for mining sequential patterns in appliance usage. In particular, we mine patterns that allow us to perform device usage prediction, energy usage prediction, and device usage prediction with failed sensors. The focus of this work is on the sequential relationships between the state of distinct devices. We use data sets from three existing buildings, of which two are households and one is an office building. The data is used to train our modified Support-Pruned Markov Models which use a relative support threshold. Our experiments show the viability of the approach, as we achieve an overall accuracy of 87% in device usage predictions, and up to 99% accuracy for devices that have the strongest sequential relationships. For these devices, the energy usage predictions have an accuracy of around 90%. Predicting device usage with failed sensors is feasible, assuming there is a strong sequential relationship for the devices.