Online optimization for residential PV-ESS energy system scheduling

Abstract

This paper studies a residential PV-ESS energy system scheduling problem with electricity purchase cost, storage degradation cost and surplus PV generated cost [ 2 ]. This problem can be viewed as an online optimization problem in time \begin{document}$ t \in [1, T] $\end{document} with switching costs between decision at \begin{document}$ t-1 $\end{document} and \begin{document}$ t $\end{document} . We reformulate the problem into a single variable problem with \begin{document}$ {\bf{s}} = (s_1, ..., s_T)^T $\end{document} , which denotes the storage energy content. We then propose a new algorithm, named Average Receding Horizon Control (ARHC) to solve the PV-ESS energy system scheduling problem. ARHC is an online control algorithm exploiting the prediction information with \begin{document}$ W $\end{document} -steps look-ahead. We proved an upper bound on the dynamic regret for ARHC of order \begin{document}$ O(nT/W) $\end{document} , where \begin{document}$ n $\end{document} is the dimension of decision space. This bound can be converted to a competitive ratio of order \begin{document}$ 1+O(1/W) $\end{document} . This result overcomes the drawback of the classical algorithm Receding Horizon Control (RHC), which has been proved [ 11 ] that it may perform bad even with large look ahead \begin{document}$ W $\end{document} . We also provide a lower bound for ARHC of order \begin{document}$ O(nT/W^2) $\end{document} on the dynamic regret. ARHC is then used to study a real world case in residential PV-ESS energy system scheduling.