## 5 Conclusions  
A proactive microgrid-management strategy was proposed based on nested MILP problems with chance constraints to enhance resilience during the event periods. In the proposed method, the MG operates in preparation mode when an external grid outage warning is issued. We formulated the preparation-mode problem as a nested chance-constrained problem reflecting normal and emergency-mode operation conditions. The pre-scheduling problem under normal-mode operation conditions includes the on-event phase operation problem under emergency-mode operation conditions as a subproblem. In the proposed method, proactive actions of the MG are realized by rescheduling the generator and maintaining the high SoC of the battery.  
The value of load shedding during event periods was reflected as ECLS in the proposed method. Further, we reflected the critical load shedding value in chance constraints of the preparation-mode problem. These induce MG to operate conservatively to ensure survivability.  
It was confirmed that the proposed method efficiently and proactively determined the operation of the battery and generator during the normal mode to improve resilience during the event periods when compared to the MG operation without preparation. A comparison of the operation with and without preparation indicated that the proposed method slightly increased the operating cost in the normal mode but was effective in increasing the load survivability and reducing the operating cost during the event periods. Further, we find that the resilience improvement effect of the proposed method may vary depending on the predicted start time of outages. When the predicted start times of outage are high-load time periods, the survivability of critical loads during the event periods is guaranteed above 95% in the proposed method but only guaranteed some time in MG operation without preparation mode. Since all loads are high during the event periods, the survivability of normal loads is low with and without preparation. When predicted start times of outages are low-load time periods, since all loads are low during the event periods, the survivability of critical loads is guaranteed to be above 95% regardless of preparation. However, depending on the preparation, the survivability and ECLS of the normal load are different during the event periods, and the proposed method shows resilience enhancement.  
In the proposed method, we assumed the predicted the start time of outages and event duration. Therefore to maximize the efficiency of the proposed method, the event-prediction information should be delivered to the centralized MG operator a few hours before the actual event occurs. On the other hand, the proposed method may be less effective for events with predictable characteristics seconds or minutes before the event occurs. Furthermore, the characteristics based on the load type and voltage were not considered in the proposed method. In future studies, we plan to reflect on the characteristics of critical loads in the proposed method and extend the proposed method for considering the voltage by applying network constraints.  
Methodology, S.P.; Validation, S.P.; Investigation, H.S.; Writing--original draft, S.P.; Writing--review & editing, H.S.; Visualization, S.P.; Supervision, H.S.; Funding acquisition, H.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022M3C1A3090837).  
Not applicable.  
The authors declare no conflict of interest.