Modeling and analysis of the role of fast-response energy storage in the smart grid

The large short time-scale variability of renewable energy resources presents significant challenges to the reliable operation of power systems. This variability can be mitigated by deploying fast-ramping generators. However, these generators are costly to operate and produce environmentally harmful emissions. Fast-response energy storage devices, such as batteries and flywheels, provide an environmentally friendly alternative, but are expensive and have limited capacity. To study the environmental benefits of storage, we introduce a slotted-time dynamic residual dc power flow model with the prediction error of the difference between the generation (including renewables) and the load as input and the fast-ramping generation and the storage (charging/discharging) operation as the control variables used to ensure that the demand is satisfied (as much as possible) in each time slot. We assume the input prediction error sequence to be i.i.d. zero-mean random variables. The optimal power flow problem is then formulated as an infinite horizon average-cost dynamic program with the cost function taken as a weighted sum of the average fast-ramping generation and the loss of load probability. We find the optimal policies at the two extremes of the cost function weights and propose a two-threshold policy for the general case. We also obtain refined analytical results under the assumption of Laplace distributed prediction error and corroborate this assumption using simulated wind power generation data from NREL.