## 1 Introduction
In the modified problem, a distributed service operator can simultaneously achieve compatibility incentives and optimality for the max-min fairness objective. [PERSON] et al. proposed a collaborative framework for power exchanges inside a low-voltage community to minimize the total costs [23]. To share community costs in a fair manner, a cost compensation process was conducted after all power exchanges had been performed. [PERSON] et al. presented a two-stage cost-sharing strategy to minimize all community members [24]. However, the cost was settled only after the operation process was completed. [PERSON] introduced a community solar service strategy for commercial buildings, considering profit balancing between the service provider and participants [25]. Cost fairness is considered an aspect of proportional fairness. However, these studies suffer from two issues. First, the problems formulated in the studies considered the overall benefit as the objective because they were centrally operated. This simplifies the problem but requires additional processes such as settlement or weak fairness, as in the worst case only. Second, to optimally solve the problems formulated in the studies, perfect information that includes information on future time is required. This study focuses on a community solar operation strategy for an SEC that considers resource fairness. The main objective is to solve the existing problems in conventional studies including centralized control for the overall benefit and perfect information usage such as including future time information. The main contributions of this study are summarized as follows. * Distributed operation: The baseline problem is formulated as a mixed-integer linear programming problem that considers the minimization of the overall electricity bill and resource fairness. To design the distributed operation, the problem is decomposed into two problems using the slack variable, for the community smart energy service provider (SESP) and community members. Each member solves the community solar operation problem by minimizing their own electricity bill using resource constraints. The SESP manages the required operational results, as shown in Figure 1. It is converged in an iterative manner based on information exchange between the SESP and the members. Partial information usage: To select the correct operation while considering resource fairness, information on the future time is required. This is because the priority of all decision times must be measured to determine the optimal solution. In this study, the forecasted values of the demand and generation were obtained using forecasting techniques. Due to forecast errors, a mismatch occurs between the resource allocation constraint and actual allocation. It is defined as the residual allocation factor. This factor is used as a priority factor to determine the operation at each decision time. Therefore, community solar operations are decided at each decision time and not for all decision times. * Experimental results and discussions on a real data set: The proposed community solar operation was performed using a real data set obtained in Korea. To verify its performance, the overall electricity bill savings, distribution of electricity bill savings, performance gap with respect to the baseline problem, and fairness indices were measured by varying the community solar capacity. The experimental results show that by using the proposed operation, members in the SEC can achieve fairly distributed electricity bill savings, and the benefit reduction of the overall electricity bill saving is marginally less than 10% compared to the baseline operation that requires a centralized controller and perfect information, including the future time. Moreover, the effects of fairness and future research prospects of community solar operations are also discussed.