Within power systems, high-power pulsewidth-modulated ac-dc converters are used in flexible ac transmission systems controllers and for interfacing renewable energy sources to the grid. These converters traditionally employed PI controllers designed in the synchronous dq-frame with decoupling of d and q axes. Recently, stationary -frame proportional-resonant (PR) controllers have been proposed. Though both types of control are suitable for the regulation of three-phase converters, the PR controller displays steady-state and dynamic behavior that differs significantly from that of decoupled dq-frame controllers. This paper derives a stationary frame controller that is the exact equivalent of the commonly used synchronous frame controller with L decoupling. The new stationary frame “PRX2” controller consists of a proportional (P), a resonant (R), and two cross-coupling components. The PRX2 controller offers identical transient and steady-state performance and has the same frequency response as the decoupled synchronous frame PI controller. Unlike other stationary frame controllers containing resonant components, the PRX2 controller is unique because it contains a cross-coupling feedback component, which accounts for the behavior of the L decoupling branches present in synchronous frame controllers. It is shown that ignoring this decoupling component greatly increases the controller's sensitivity to frequency variation. Numerous stationary frame controllers, including the common PR controller, may be derived from the general PRX2 controller.
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