## 3 Method
### RL-Based VESS Operation Strategy
The VESS size is the available operation room to manage uncertainty. Therefore, by increasing the size, the MAE is reduced, as shown in Figure 3a. In particular, in Figure 3a the optimal solution and proposed method have a similar slope with increasing VESS size, but the result obtained with the stochastic method shows a less significant decrease. This implies that the optimal solution and the proposed method effectively operate according to the environment, while the stochastic method does not. The stochastic method is designed according to the Markov decision process, similar to the proposed method. However, the stochastic method applying the backward induction approach in [40] predetermines the reserved capacity for the future decision stage according to the probabilistic information of the WPG, so the operational diversity of the stochastic method is lower than those of the optimal solution and proposed method. Figure 3b shows the optimal gap, which represents the difference from the optimal solution. The optimal gap of the proposed method is less than 2%, and is reduced with increasing size. The proposed method can effectively consider environmental characteristics by learning and clustering, and therefore achieves gain by increasing the size. However, the stochastic method cannot reflect this. Therefore, the optimal gap in the stochastic method increases with increasing size. Figure 3: Mean absolute error (MAE) comparison between the optimal solution, proposed method, and stochastic method. (**a**) Mean absolute error; (**b**) Optimal gap. ### Effect of Vess

Figure 4 compares the MAE of the individual ESS operation and the proposed VESS operation. The results for individual ESS operations are the optimal solution reformulated problem (9) for each WPG. Each WPG presents different uncertainties, so the decrease in the slope with increasing size also differs, as shown in Figure 4a. However, the results of the proposed VESS operation demonstrate that it outperforms all individual operation results. The individual ESS operation works by using its own information. However, in the case of the proposed VESS operation, information from multiple units is used. Therefore, the proposed VESS operation achieves multi-user diversity gain [41]. Figure 4b verifies the diversity gain. By increasing the size, the operation availability also increases. The proposed VESS operation is effectively operated to achieve availability with multi-user diversity. Therefore, the VESS operation gain compared to the individual ESS operation is enhanced with increasing operation availability. ### Effect of Clustering

Figure 5 shows the optimal gap of the proposed method with 1, 3, and 5-cluster cases. As shown in Figure 5, the optimal gap is reduced as the number of clusters increases. In particular, with five clusters, an optimal gap enhancement of more than 1.5% can be obtained when the ESS size is 0.6 p.u. This indicates that the clustering method is an effective way to enhance the performance of the proposed method. However, compared to the performance enhancement provided by three clusters or one cluster, the performance increase provided by five clusters is less than that of three clusters. This is because the distance between the centroids is reduced with increasing cluster size. Moreover, by increasing the cluster size, the number of state-action value functions also increases for policy learning. This increases the system complexity in the implementation. Therefore, it is important to set the appropriate cluster size by considering both performance enhancement and system complexity. As an example, in this study operating with five WPG units, three clusters are efficient considering the performance enhancement, as shown in Figure 5.

Figure 4: MAE comparison among individual ESS operation and VESS operation. (**a**) Mean absolute error; (**b**) Optimal gap. ### Usage of the Proposed Strategy

The VESS operation applying the proposed strategy can get a higher forecast error management performance than that of the individual ESS operation.