## Renewable Energy Integration

The increasing penetration of variable-energy sustainable generators (e.g., solar and wind) has raised the question of how best to manage them as replacements for the coal and fuel energy sources. One of the significant barriers for complete replacement is the burstiness of the short-term and long-term variations of sustainable generators. In particular, for solar energy, the long-term variation due to the variations induced by the position of the sun in the sky quite predictable but short-term variation is due to clouds may attenuate or even enhance (counter-intuitively) ground level solar irradiation. This short-term variation can be modeled as a stochastic process that can be studied using techniques from stochastic network calculus (see Y. Ghiassi-Farrokhfal, S. Keshav, C. Rosenberg, and F. Ciucu. Solar Power Shaping: An Analytical Approach, IEEE Transactions on Sustainable Energy, Vol 6, No. 1, Jan. 2015.).

We use this approach to study problems such as

**Day-ahead revenue maximization:**Most large-scale generators of electrical power enter into daily or hourly contracts with market makers such as Regional Transmission Organizations, where they pre-commit to a certain constant level of power generation. The payment is proportional to the power level and suppliers must pay a penalty if the commitment is not met. The high variability of solar power, due to intrinsic diurnal variability as well as additional stochastic variations due to cloud cover, have made it difficult for solar farms to enter these markets. We therefore study the use of battery storage to ‘firm’ solar power, that is, to remove variability so that such pre-commitments can be made. Due to the high cost of storage, it is necessary to size the battery parsimoniously, choosing the minimum size to meet a certain reliability guarantee.

# Past Projects:

- Y. Ghiassi-Farrokhfal, F. Kazhamiaka, C. Rosenberg, and S. Keshav, Optimal Design of Solar PV Farms with Storage, IEEE Transactions on Sustainable Energy, October 2015. We consider the problem of allocating a capital budget to solar panels and storage to maximize the expected revenue in the context of a large-scale solar farm participating in an energy market. This problem is complex due to many factors. To begin with, solar energy production is stochastic, with a high peak-to-average ratio, thus the access link is typically provisioned at less than peak capacity, leading to the potential waste of energy due to curtailment. The use of storage prevents power curtailment, but the allocation of capital to storage reduces the amount of energy produced. Moreover, energy storage devices are imperfect. A solar farm owner is thus faced with two problems: 1)deciding the level of power commitment and 2) the operation of storage to meet this commitment. We formulate two problems corresponding to two different power commitment approaches, an optimal one and a practical one, and show that the two problems are convex, allowing efficient solutions. Numerical examples show that our practical power commitment approach is close to optimal and also provide several other engineering insights.