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In recent years, there has been a significant focus on advancing the next generation of power systems. Despite these efforts, persistent challenges revolve around addressing the operational impact of uncertainty on predicted data, especially concerning economic dispatch and optimal power flow. To tackle these challenges, we introduce a stochastic day-ahead scheduling approach for a community. This method involves iterative improvements in economic dispatch and optimal power flow, aiming to minimize operational costs by incorporating quantile forecasting. Then, we present a real-time market and payment problem to handle optimization in real-time decision-making and payment calculation. We assess the effectiveness of our proposed method against benchmark results and conduct a test using data from 50 real households to demonstrate its practicality. Furthermore, we compare our method with existing studies in the field across two different seasons of the year. In the summer season, our method decreases optimality gap by 60% compared to the baseline, and in the winter season, it reduces optimality gap by 67%. Moreover, our proposed method mitigates the congestion of distribution network by 16.7\% within a day caused by uncertain energy, which is a crucial aspect for implementing energy markets in the real world.