# American Institute of Mathematical Sciences

February  2019, 2(1): 55-71. doi: 10.3934/mfc.2019005

## Online optimization for residential PV-ESS energy system scheduling

 1 1400 Washington Ave, Mathematics and Statistics Department, Albany, NY 12222, USA 2 251 Fuller Road, Atmospheric Sciences Research Center, Albany, NY 12203, USA

* Corresponding author: Yiming Ying

Published  March 2019

Fund Project: The second author is supported by NSF grant 1816227

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 $t \in [1, T]$ with switching costs between decision at $t-1$ and $t$. We reformulate the problem into a single variable problem with ${\bf{s}} = (s_1, ..., s_T)^T$, 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 $W$-steps look-ahead. We proved an upper bound on the dynamic regret for ARHC of order $O(nT/W)$, where $n$ is the dimension of decision space. This bound can be converted to a competitive ratio of order $1+O(1/W)$. 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 $W$. We also provide a lower bound for ARHC of order $O(nT/W^2)$ on the dynamic regret. ARHC is then used to study a real world case in residential PV-ESS energy system scheduling.

Citation: Zhenhuan Yang, Yiming Ying, Qilong Min. Online optimization for residential PV-ESS energy system scheduling. Mathematical Foundations of Computing, 2019, 2 (1) : 55-71. doi: 10.3934/mfc.2019005
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48 hours experimental setup
Performance of ARHC
48 hours solution comparison of ARHC and offline optimal
Storage size vs cost
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