A power flow controller with a fractionally rated back-to-back (BTB) converter is provided. The power flow controller provide dynamic control of both active and reactive power of a power system. The power flow controller inserts a voltage with controllable magnitude and phase between two AC sources at the same frequency; thereby effecting control of active and reactive power flows between the two AC sources. A transformer may be augmented with a fractionally rated bi-directional Back to Back (B TB) converter. The fractionally rated BTB converter comprises a transformer side converter (TSC), a direct-current (DC) link, and a line side converter (LSC). By controlling the switches of the BTB converter, the effective phase angle between the two AC source voltages may be regulated, and the amplitude of the voltage inserted by the power flow controller may be adjusted with respect to the AC source voltages.
STATEMENT OF RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSORED RESEARCH
 This invention was made with Government support under DE-AR0000108 awarded by the United States Department of Energy. The Government has certain rights in the invention.