  Primary frequency response is provided by synchronized generators through
their speed-droop governor characteristic in response to instant frequency
deviations that exceed a certain threshold, also known as the governor dead
zone. This dead zone makes the speed-droop governor characteristic nonlinear
and makes affine control policies that are often used for modeling the primary
frequency response inaccurate.
  This paper presents an optimal power flow (OPF) formulation that explicitly
models i) the primary frequency response constraints using a nonlinear
speed-droop governor characteristic and ii) chance constraints on power outputs
of conventional generators and line flows imposed by the uncertainty of
renewable generation resources. The proposed chance constrained OPF (CCOPF)
formulation with primary frequency response constraints is evaluated and
compared to the standard CCOPF formulation on a modification of the 118-bus
IEEE Reliability Test System.
