## 1 Introduction
\begin{table}
\begin{tabular}{c c c c} \hline
**Reference** & **Methodology** & **Objective** & **Main Contribution** \\ \hline
[16] & Case study & Net profit value & Energy storage system (ESS) sharing as business cases \\
[17] & Linear program & Operation cost minimization & Building-based VESS model \\
[18] & Droop control & Frequency response & VESS model consisting of flexible demand and conventional flywheel ESS \\
[19] & Consensus-driven distributed & & Residential demand with air conditioners as the VESS \\
[20] & control & Voltage regulation & VESS based on electric vehicles combined with air conditioning load \\
[21] & Linear program & Operation cost minimization & VESS based on electric vehicles combined with air conditioning load \\
[21] & Two-stage & Profit maximization of aggregator & Price-based virtual capacity allocation \\
[22] & optimization & and users & Price-based virtual capacity allocation \\
[23] & Combinatorial & Time average system cost & Online algorithm without having to predict future uncertain system states \\
[24] & Optimization & Optimization & Combinatorial auction framework for capacity allocation \\
[24] & Modified auction & Cost saving maximization & Application of a non-cooperative Stackelberg game for payment rules \\
[25] & Coalitional game & Energy cost minimization & Benefit enhancement by cooperation between players \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of virtual energy storage system (VESS) research. Most contemporary studies have only focused on profits by the economies of scale using a VESS. However, the usage of a VESS does not always generate benefits for community participants [26]. Therefore, it is necessary to increase the additional gain when using VESSs. In addition to the economics of scale, another benefit of the VESS is that it allows energy sharing based on logical operation. The logical operation means that the logical charging and discharging operations of the participants cancel each other. Using logical-operation-based energy sharing, ESS with a larger capacity can be serviced [21; 27]. From the participants' point of view, energy sharing according to logical operation can increase the degrees of freedom of operation, as they can achieve additional benefits by dynamic VESS operation. This study proposes a dynamic VESS operation strategy for smart energy communities (SECs). SECs are local energy communities [28; 29] which have their own energy service providers (SPs) or energy management systems (EMSs) and can operate the VESS based on SPs or EMSs. To utilize the VESS, the proposed strategy considers the benefit of increasing the number of participants and operation capacity compared with an individual ESS operation to achieve economic benefit. The main contributions of this study are summarized as follows:  
* _Dynamic VESS operation strategy:_ In this study, a dynamic VESS operation strategy is proposed considering the usage-limited constraint. The existing VESS allocates the VESS capacity to each participant and operates as an individual ESS [21; 27]. When the logical charging and discharging operations of the participants occur simultaneously, the operations of VESS cancel each other. However, at the existing capacity-constraint-based VESS operation, the state of allocated VESS for each participant is logically recorded as used, as in the individual ESS operation. In this case, participants receive cost benefit only without the operation benefit by the multi-participant diversity. To achieve the operational benefit, the proposed strategy considers the usage-limited constraint instead of the allocated capacity constraint of the existing VESS allocations. The usage-limited constraint satisfies the requirement of guaranteeing the usage of the VESS resource of each participant during an operation period. Therefore, the proposed strategy can improve the degrees of freedom of the operation at each decision time.