  The integration of more renewable energy sources into the power system is
presenting system operators with various challenges. At the distribution system
level, voltage magnitudes that violate operating limits near large photovoltaic
installations have been observed. While these issues can be partially mitigated
with more advanced control, hardware upgrades are required at some point. This
work presents a scalable, optimization-based approach for deciding which lines
in a network to upgrade. Compared to existing approaches, it explicitly takes
the operating policy of the system into account and provides both reasonable
solutions in short computation times as well as globally optimal solutions when
run to completion. Compared to earlier work on the same topic, an extended
computational approach is taken that can simultaneously optimize for many load
scenarios across arbitrary configurations of machines and CPU cores per machine
in a scalable manner by using the Benders decomposition. In addition to the
theory, numerical experiments are presented along with a discussion of the
scaling properties of the Benders-based approach, giving potential users a
better basis to decide whether their problem is big enough for the approach to
make sense.
