  Virtual oscillator control is the latest control technique for grid-forming
inverters. Virtual Oscillator based Controllers (VOCs) provide all the
steady-state droop functionalities of conventional droop controllers and, in
addition, the time-domain synchronization with a connected electrical network.
However, existing literature does not consider the aspect of dynamic control
over the voltage stiffness of a VOC. Voltage stiffness is a vital parameter for
a grid-forming inverter. If the voltage stiffness is too high, the inverter
picks up all the reactive power demand of the PCC. In contrast, if the
stiffness is too low, the inverter does not participate in voltage regulation
at all. Limiting the reactive power output during a higher voltage sag,
especially when connected to a weak grid, is challenging for a VOC. Entering
into the current control mode is the existing solution, but it severely affects
the effective synchronization between the VOC and the voltages of the PCC. As a
result, the grid-forming mode of operation becomes inefficient. This article
has introduced a Virtual Impedance (VIm) based dynamic voltage stiffness
control technique for VOCs. The systematic design procedure for the proposed
voltage stiffness controller is presented. In addition, a rigorous approach for
stability analysis is presented.
