Voltage Control in the Presence of Photovoltaic Systems
  In the past decade, the landscape of energy production has had to shift to accommodate renewables. Which, unlike fossil fuels, are subject to frequent fluctuations; potentially destabilizing grid operators. With the continued demand for solar PV system installation, there is a pressing need for utilities to regulate the voltages at the low voltage distribution grids. We develop a stochastic model for voltage rise as a function of injected power into the grid. This model is formed as a linear combination of gamma random variables. This is achieved by finding sparse bases and clustering the data into subsets by its correlation with those bases, and fitting a gamma distribution within each subset. We are concerned with modeling voltage rise, while taking into account sparse events in the voltage. We use sparse singular value decomposition (SVD) with $\ell_1$ penalty to model sparse voltage rise. More randomness and disorder in voltage rises was observed at the point of common coupling (PCC) of the PV systems with greater line impedance. A controller to regulate the voltage at the PCC of a single phase solar PV system is presented. This controller uses the stochastic model to minimize the risk of voltage rise. Simulation results confirm that this voltage controller can lower the voltage more effectively than conventional voltage regulators during periods of high solar PV output. 
Ashkan Zeinalzadeh, Reza Ghorbani, James Yee
math.OC