  Low-frequency high voltage ac transmission scheme has recently been proposed
as an alternative approach for bulk power transmission. This paper proposes a
multi-period optimal power flow (OPF) for a multi-frequency HVac transmission
system that interconnects both conventional 50/60-Hz and low-frequency grids
using back-to-back converters with a centralized control scheme. The OPF
objective is to minimize system losses by determining the optimal dispatch for
generators, shunt capacitors, and converters. The OPF constraints include the
operational constraints of all HVac grid and converter stations. The resulting
mixed-integer nonlinear programing problem is solved using a proposed framework
based on the predictor-corrector primal-dual interior-point method. The
proposed OPF formulation and solution approach are verified using a
multi-frequency HVac transmission system that is modified from the IEEE 57-bus
system. The results with the optimal dispatch from the proposed method during a
simulated day show a significant loss reduction and an improved voltage
regulation compared to those when an arbitrary dispatch is chosen.
