  To reduce energy demand in households it is useful to know which electrical
appliances are in use at what times. Monitoring individual appliances is costly
and intrusive, whereas data on overall household electricity use is more easily
obtained. In this paper, we consider the energy disaggregation problem where a
household's electricity consumption is disaggregated into the component
appliances. The factorial hidden Markov model (FHMM) is a natural model to fit
this data. We enhance this generic model by introducing two constraints on the
state sequence of the FHMM. The first is to use a non-homogeneous Markov chain,
modelling how appliance usage varies over the day, and the other is to enforce
that at most one chain changes state at each time step. This yields a new model
which we call the interleaved factorial non-homogeneous hidden Markov model
(IFNHMM). We evaluated the ability of this model to perform disaggregation in
an ultra-low frequency setting, over a data set of 251 English households. In
this new setting, the IFNHMM outperforms the FHMM in terms of recovering the
energy used by the component appliances, due to that stronger constraints have
been imposed on the states of the hidden Markov chains. Interestingly, we find
that the variability in model performance across households is significant,
underscoring the importance of using larger scale data in the disaggregation
problem.
