<p>This study establishes a non-deterministic microgrid bidding strategy methodology participating in a day-ahead energy market. In this regard, a stochastic programming-based model is mathematically constructed, fully considering the uncertainty of day-ahead market prices, electricity demand, and renewable generation by creating several scenarios. The real-time electricity market is also considered, where the real-time price uncertainty is modeled using robust optimization. Even though robust optimization has already been employed to model real-time price uncertainty, the correlation among real-time prices at different hours is neglected. Thus, how real-time price correlation affects the optimal microgrid bidding strategy remains unclear. This study develops a novel mathematical model that captures real-time price correlations by constructing an ellipsoidal uncertainty set. In this context, unlike the current approaches in which the real-time price deviation ranges are modeled as constants at each hour, they are assumed to lie within a prespecified ellipsoidal uncertainty set. In doing so, a mixed-integer second-order cone programming problem is created, which existing solving methods can efficiently handle. The presented scheme is applied to a typical microgrid, and the efficiency and excellence of the presented framework are validated by comparing numerical results with traditional models.</p>