Optimally sizing battery storage and renewable energy sources on an off-grid facility

We consider the problem of sizing battery storage and renewable sources such as PV arrays and wind turbines at an off-grid facility. We consider the power reliability criterion of FLNS - the fraction of total load that can not be served. We present a linear program and a more general convex optimization problem to solve for the storage and renewable source sizes. We show that the control policy where the demand is completely served until the battery is empty is optimal for the FLNS criterion. We then show that the required battery size is a decreasing convex function of the renewable source sizes and the power reliability requirement. We show with an example that a different power reliability criterion that has been considered in the literature - LPSP (loss of power supply probability) - does not share the same properties.