Robustly Maximal Utilisation of Energy-Constrained Distributed Resources

We consider the problem of dispatching a fleet of distributed energy reserve devices to collectively meet a sequence of power requests over time. Under the restriction that reserves cannot be replenished, we aim to maximise the survival time of an energy-constrained network; and we discuss realistic scenarios in which this might be the ultimate goal of the grid operator. We present a policy that achieves this optimality, and generalise this into a set-theoretic result that implies there is no better policy available, regardless of the realised energy requirement scenario. NOMENCLATURE Parameters Di device of index i n number of devices available E i (t) energy stored by device Di at time t ηi efficiency of device Di Ei(t) (extractable) energy of device Di at time t xi(t) time-to-go of device Di at time t ui(t) power output of device Di at time t p̄i maximum power of device Di P diagonal matrix of maximum powers P (t) power reference at time t P r [t0,t] reference trajectory truncated to the interval [t0, t] Θp̄,x(P ) time to failure from state x under reference P (x), and with a vector of maximum device powers p̄ P̄ (x) maximum instantaneous power available in state x Sets N set of all devices X state-space of system Up̄ product set of input constraints, for a given vector of maximum device powers Fp̄,x set of feasible power references from state x, for a given vector of maximum device powers P set of all partitions