  We develop new optimization methodology for planning installation of Flexible
Alternating Current Transmission System (FACTS) devices of the parallel and
shunt types into large power transmission systems, which allows to delay or
avoid installations of generally much more expensive power lines. Methodology
takes as an input projected economic development, expressed through a paced
growth of the system loads, as well as uncertainties, expressed through
multiple scenarios of the growth. We price new devices according to their
capacities. Installation cost contributes to the optimization objective in
combination with the cost of operations integrated over time and averaged over
the scenarios. The multi-stage (-time-frame) optimization aims to achieve a
gradual distribution of new resources in space and time. Constraints on the
investment budget, or equivalently constraint on building capacity, is
introduced at each time frame. Our approach adjusts operationally not only
newly installed FACTS devices but also other already existing flexible degrees
of freedom. This complex optimization problem is stated using the most general
AC Power Flows. Non-linear, non-convex, multiple-scenario and multi-time-frame
optimization is resolved via efficient heuristics, consisting of a sequence of
alternating Linear Programmings or Quadratic Programmings (depending on the
generation cost) and AC-PF solution steps designed to maintain operational
feasibility for all scenarios. Computational scalability and application of the
newly developed approach is illustrated on the example of the 2736-nodes large
Polish system. One most important advantage of the framework is that the
optimal capacity of FACTS is build up gradually at each time frame in a limited
number of locations, thus allowing to prepare the system better for possible
congestion due to future economic and other uncertainties.
