We consider the problem of grid-forming control of power converters inlow-inertia power systems. Starting from an average-switch three-phase invertermodel, we draw parallels to a synchronous machine (SM) model and propose anovel grid-forming converter control strategy which dwells upon the maincharacteristic of a SM: the presence of an internal rotating magnetic field. Inparticular, we augment the converter system with a virtual oscillator whosefrequency is driven by the DC-side voltage measurement and which sets theconverter pulse-width-modulation signal, thereby achieving exact matchingbetween the converter in closed-loop and the SM dynamics. We then provide asufficient condition assuring existence, uniqueness, and global asymptoticstability of equilibria in a coordinate frame attached to the virtualoscillator angle. By actuating the DC-side input of the converter we are ableto enforce this sufficient condition. In the same setting, we highlight strictincremental passivity, droop, and power-sharing properties of the proposedframework, which are compatible with conventional requirements of power systemoperation. We subsequently adopt disturbance decoupling techniques to designadditional control loops that regulate the DC-side voltage, as well as AC-sidefrequency and amplitude, while in the end validating them with numericalexperiments.
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