This paper proposes a robust periodic economic model predictive control (MPC) using probabilistic set invariance for discrete-time descriptor systems. The considered systems are affected by additive disturbances that are bounded and follow a zero-mean Gaussian distribution. To guarantee robustness of the proposed robust economic MPC, a probabilistic invariant set with a given probability is used to contract the state and input constraints. An auxiliary input variable is defined to satisfy algebraic equations from descriptor systems in presence of disturbances. Finally, an application of the proposed MPC strategy to a smart micro-grid is provided to illustrate the performance. This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project DEOCS (ref. DPI2016-76493) and SCAV (ref. DPI2017-88403-R), the FPI grant (ref. BES-2014-068319), and by AGAUR of Generalitat de Catalunya through the Advanced Control Systems (SAC) group grant (ref. 2017-SGR-482). Peer reviewed