Similar to synchronous generators, the grid-forming converter mostly uses power synchronization or inertial synchronization control strategies, which can provide inertia and damping support to the grid. However, the similar external characteristics of the grid-forming converter and synchronous generator result in its susceptibility to sub-synchronous oscillations when connected to the grid through aseries capacitor compensation line. In view of this, this paper carries out a comprehensive research work on the stability analysis and sub-synchronous oscillation suppression strategy for the grid-forming converter connected to the grid via a series capacitor compensation line.

Firstly, the self-impedance and the accompanying impedance models of the grid-forming converter are established by using the complex variable representation method. The self-impedance and the accompanying impedance are verified using the frequency scanning method, and the scanning results were consistent with the analytical model, verifying the correctness of both. The established the self-impedance and the accompanying impedance models can accurately explain and characterize the single-frequency input and dual-frequency output of the grid-forming converter. Afterwards, the equivalent impedance model of the system with single input and single output of the grid-forming converter is derived, taking into account the frequency coupling effect and the influence of the series complementary lines.

Secondly, the stability of the grid-connected system at different series compensation degrees is analysed by using the Nyquist stability criterion based on an equivalent impedance model that accounts for thefrequency coupling effect. It is found that the larger series compensation degree is, the worse the system stability is. In addition, the impedance stability analysis taking into account the frequency coupling effect is more accurate under certain operating conditions.

Then, a current feedback-based impedance reshaping strategy is proposed for the phenomenon of sub-synchronous oscillations generated by the interaction between the grid-forming converter and the series-complementary line. The strategy is that the grid-connected current passes through the notch filter and the feedback coefficient as part of the modulation wave output to achieve system impedance reshaping. The function of the trap filter is to maintain the fundamental frequency output impedance and avoid the working point offset of the converter. And the current feedback coefficient was introduced into the equivalent impedance model, the feedback coefficient-frequency binary equivalent impedance model was established, and the amplitude-phase contour stability criterion was used to parameterize the current feedback coefficients. It is found that the larger the feedback coefficient k is, the larger the phase margin of the system is, and the more stable the system is. In addition, after the system is shaped by impedance, the phase-frequency curve moves down as a whole, especially in the frequency band below 50 Hz, the phase-frequency curve moves down greatly, resulting in the phase difference at the resonance point less than 180°, and the oscillation is suppressed.

Finally, the grid-connected system model of the grid-forming converter via series-complementary line is built through simulation and experiment, and the impedance remodeling control strategy is implemented on the damping controller to verify the correctness of the theoretical analysis as well as the parameter design. This study draws the following conclusions. (1) The interaction between the grid-forming converter and the series compensation line is easy to cause sub-synchronous oscillation, and the greater the series compensation degree, the higher the oscillation risk. In addition, under certain operating conditions, impedance analyses that take into account frequency coupling effect are more accurate and their influence cannot be ignored. (2) The amplitude-phase contour plot can be used to determine intuitively the influence of the feedback coefficient k on the operating characteristics of the system and to derive the range of values of the feedback coefficient k parameter when the system is in a stable or unstable state.