Microgrids comprising of diesel generators, storage devices and renewable sources present an effective approach for an economic energy supply to rural areas. This paper presents the development of a stochastic model predictive control (SMPC) with the analytical calculation of chance constraints for the combination of set-based and probabilistic uncertain data. The stochastic uncertainties resulting from changes in load demand and fluctuating power from renewables are directly included in the stochastic optimization problem. To account for these disturbances the presented approach assumes probabilistic constraints on the battery state of charge which can be analytically calculated based on the continuous probability distribution of the uncertainties. The additional set-based uncertainties on the load demand and PV power forecast imply further limitations on the probabilistic constraints. The performance of the SMPC is enhanced by evaluating the probability distribution and probabilistic constraints over several time steps as well as using a relaxation technique to assure feasibility. The presented SMPC approach is used for an efficient optimization of the microgrid operation while reducing the complexity of the operational problem compared to other approaches and satisfying all operation constraints. Simulation studies using a real-world application have been performed to showcase the performance of the proposed method.