In this brief paper, we formalise a fault-tolerant control and mitigation strategy for the energy management of renewable microgrids. The scheme is composed by a Model Predictive Control (MPC) algorithm based on a Linear Parameter Varying (LPV) model for the microgrid energy dispatch. The MPC uses fault diagnosis information to correctly schedule the microgrid model, while adapting the process constraints in consonance with the level and location of faults. We show how closed-loop stability is ensured with simple quadratic terminal ingredients, provided through LMI-solvable remedies. Nonlinear simulation results for a real microgrid benchmark are included in order to demonstrate the effectiveness of the approach.