The ROADEF 2020 challenge presents a maintenance scheduling problem from the French electricity grid company RTE. The modeling of uncertainty makes the problem highly nonconvex and apparently out of the reach of mathematical solvers. We present our approach for the challenge problem. It is based on a new family of cutting planes, coupled with a constraint generation approach. We present mathematical proofs and separation algorithms for the cutting planes. We then study the practical impact of our additions on the challenge instances, showing that our approach significantly reduces the optimality gap obtained by the solver.