In this paper we provide a complete theoretical analysis of a two-dimensional

degenerate non convex singular stochastic control problem. The optimisation is motivated by a

storage-consumption model in an electricity market, and features a stochastic real-valued spot

price modelled by Brownian motion. We find analytical expressions for the value function, the

optimal control and the boundaries of the action and inaction regions. The optimal policy is

characterised in terms of two monotone and discontinuous repelling free boundaries, although

part of one boundary is constant and and the smooth fit condition holds there.