Stochastic queuing models for distributed PV energy

In the past few years there have been a tremendous growth in distributed PV generation on commercial and residential buildings. Increasing distributed PV generation has raised concerns about the stability of the distribution grid due to the intermittency of solar PV energy. Before smart grid optimization and control algorithms can be formulated we must obtain a better understanding of the behavior of the distributed PV energy contributions to the electrical grid. This paper develops stochastic models to model each distributed energy source using both spatial and temporal processing. A goal is to develop simple stochastic models that accurately model the distributed energy produced from the PV sources with possible storage so that key events (e.g. ramp downs due to cloud cover can be characterized). The production of energy from PV panels is modeled as a queue with inputs being the nonstationary solar irradiation, the energy produced modeled by a deterministic function, and a queue modeled by storage which can be sold to the grid or used by local loads. A second queue models solar irradiation with inputs being weather conditions (sunny, partly cloudy, cloudy).