DFT-based sizing of battery storage devices to determine day-ahead minimum variability injection dispatch with renewable energy resources

Renewable energy (RE) resources are non-dispatchable due to their intermittent nature, and battery storage devices (BSDs) play an important role to overcome their inherent variability. Therefore, for optimal operability, BSDs must be appropriately sized. Historical RE generation data can be used for sizing, with the objective to minimize the annualized planning cost. Application of high and low pass filters about a given cut-off frequency on the frequency spectrum of the historical generation data, calculated using discrete Fourier transform (DFT) approach, segregate the fast and slowly varying components. The proposed methodology is based on 3σ principle and will ensure minimum injection of RE-generation variability into the grid for day-ahead scheduling with both fast and slowly varying components. The analysis shows that the batteries with the minimum unit capacity cost to throughput ratio provide minimum annualized planning cost for both slow and fast varying components. Determination of sizing of BSDs is numerically ‘costly’ and to obtain the optimal cut-off frequency, a derivative-free mode-pursuing sampling method is applied. Exponential reduction in the daily injection of variability with increasing statistical significance in sizing is observed. The impact of unit capacity cost to throughput ratio on the sizing of BSDs is also studied.