  In this paper, the optimal power flow (OPF) problem is augmented to account
for the costs associated with the load-following control of a power network.
Load-following control costs are expressed through the linear quadratic
regulator (LQR). The power network is described by a set of nonlinear
differential algebraic equations (DAEs). By linearizing the DAEs around a known
equilibrium, a linearized OPF that accounts for steady-state operational
constraints is formulated first. This linearized OPF is then augmented by a set
of linear matrix inequalities that are algebraically equivalent to the
implementation of an LQR controller. The resulting formulation, termed LQR-OPF,
is a semidefinite program which furnishes optimal steady-state setpoints and an
optimal feedback law to steer the system to the new steady state with minimum
load-following control costs. Numerical tests demonstrate that the setpoints
computed by LQR-OPF result in lower overall costs and frequency deviations
compared to the setpoints of a scheme where OPF and load-following control are
considered separately.
