  Price responsiveness is a major feature of end use customers (EUCs) that
participate in demand response (DR) programs, and has been conventionally
modeled with static demand functions, which take the electricity price as the
input and the aggregate energy consumption as the output. This, however,
neglects the inherent temporal correlation of the EUC behaviors, and may result
in large errors when predicting the actual responses of EUCs in real-time
pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to
capture the temporal behavior of the EUCs. The states in the proposed dynamical
DR model can be explicitly chosen, in which case the model can be represented
by a linear function or a multi-layer feedforward neural network, or implicitly
chosen, in which case the model can be represented by a recurrent neural
network or a long short-term memory unit network. In both cases, the dynamical
DR model can be learned from historical price and energy consumption data.
Numerical simulation illustrated how the states are chosen and also showed the
proposed dynamical DR model significantly outperforms the static ones.
