  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.
