On more electric aircraft (MEA), reducing fuel consumption and guaranteeing flight safety are pursued by efficient operational management of the electrical power system (EPS). Considering the growing number of onboard electric loads and the increasing complexity of EPS architecture due to the integration of multiple power converters and energy storage systems (ESSs), system-level operation control is required to manage power distribution, load scheduling, and ESSs. In this paper, a chance-constrained stochastic model predictive control (CC-SMPC) method is proposed to improve both the system operation in terms of the system's cost and reconfiguration activities as well as the ability to cope with uncertainties due to fluctuating load demands. Both normal and faulty operating conditions are investigated with multi-failure cases, resulting in different uncertainty propagation paths. The system's operational and technical requirements are formulated as a set of deterministic and probabilistic constraints in the CC-SMPC model. To verify the effectiveness of the proposed strategy, a comprehensive comparison study is conducted. Two uncertainty/failure cases are taken into account and simulations are performed for both offline and online control strategies while the Monte-Carlo algorithm is used for scenario generation. The results are evaluated using the proposed evaluation framework, showing that the CC-SMPC achieves better performance compared to deterministic MPC (DMPC) in both cases. In an offline testing framework, comparing the performance of DMPC and CC-SMPC strategies shows that CC-SMPC reduces the power constraint violations for batteries and generators in all cases following the selected confidence level. In addition, in an online testing framework with 1 % violation probability, the following results are observed in the two cases: In the EPS normal condition, CC-SMPC reduces the total cost by 31.4 % and the overall constraint violation cost by 93 %; while in the EPS faulty condition, CC-SMPC reduces the total cost by 4.37 %, and the overall constraint violation cost by 96 %.