  The growing amount of fluctuating renewable infeeds and market liberalization
increases uncertainty in power system operation. To capture the influence of
fluctuations in operational planning, we model the forecast errors of the
uncertain in-feeds as random variables and formulate a security constrained
optimal power flow using chance constraints. The chance constraints limit the
probability of violations of technical constraints, such as generation and
transmission limits, but require a tractable reformulation. In this paper, we
discuss different analytical reformulations of the chance constraints, based on
a given set of assumptions concerning the forecast error distributions. In
particular, we discuss reformulations that do not assume a normal distribution,
and admit an analytical reformulation given only a mean vector and covariance
matrix. We illustrate our method with a case study of the IEEE 118 bus system,
based on real data from the European system. The different reformulations are
compared in terms of both achieved empirical violation probability and
operational cost, which allows us to provide a suggestion for the most
appropriate reformulation in an optimal power flow setting. For a large number
of uncertainty sources, it is observed that the distributions of the line flows
and generator outputs can be close to normal, even though the power injections
are not normally distributed.
