Abstract: The microgrid cluster system, which is composed of multiple microgrids (MGs), exhibits significant potential in enhancing energy utilization and system stability. However, uncertainties in energy supply and demand, exacerbated by the fluctuations in renewable energy and the integration of complex loads, become more prominent in microgrid cluster systems. To address these challenges, an energy trading model for microgrid cluster systems that takes into account supply-demand uncertainties is proposed. First, the uncertainties associated with renewable energy generation and load demand are quantified using information entropy theory. Subsequently, the energy trading between microgrids and the microgrid cluster agent (MGCA) is modeled as a Stackelberg game. A new entropy-based trading cost is defined to comprehensively account for the impact of supply-demand uncertainties on trading costs. Finally, the existence and uniqueness of the game equilibrium are demonstrated. Experimental results indicate that the Stackelberg game attains optimal resource allocation and cost minimization for microgrids. The proposed energy trading strategy effectively enhances the power quality metrics of the microgrids.