Abstract: Market power assessment is a key point for electricity market reform. With the integration of large-scale renewable energy into the power system, the uncertainty of the electricity market surges, and the existing deterministic market power assessment model is transformed into a probabilistic model. Because the uncertainty characteristics of renewable energy cannot be considered in the deterministic model, the misjudgment of market power occurs frequently which seriously threatens the safe operation of electricity market. In order to consider the important impact of renewable energy and load uncertainty, a structural market power index, i. e., uncertainty-aware expected minimal generation index（U-EMGI） is proposed. Based on the chance constraint theory, an optimal model of market power assessment considering uncertainty is proposed to minimize the expected output of generators. Then, based on the sensitivity analysis of power flow equations on uncertainties, a second-order cone fast solution method for the proposed chance-constrained optimization model is proposed by introducing relaxation variables to do the second-order cone relaxation for the nonlinear part of the chance constraint. Finally, the PJM 5-bus system and the IEEE 39-bus system are used for the simulation calculation. The simulation results show that the proposed method can effectively reflect the complex relationship between the system overall uncertainty level and the market power of power generation enterprises and provide an effective means for the structural market power assessment of the electricity market in the background of renewable energy.