Homoclinic Bifurcation of a Grid-Forming Voltage Source Converter

Under transient disturbance, the grid-forming voltage-source converter may lose its synchronization with the grid, inducing sustained low-frequency oscillation in instantaneous power, current, and phase angle. The physical origin of such oscillations is found to be a homoclinic bifurcation in this article. Before the system runs into a homoclinic bifurcation, a stable equilibrium point (SEP) and a stable periodic orbit coexist. When a large transient disturbance is applied, the system exhibits a periodic orbit, which manifests itself as low-frequency oscillation. Moreover, after the homoclinic bifurcation, the periodic orbit subsides, and only a single attractor, the SEP, exists in the phase space. In this case, the grid-forming converter is able to resynchronize with the grid even under transient disturbances. Bifurcation diagrams are derived as the boundaries of stable operation in the parameter space, which serve as practical design guidelines to avoid sustained oscillations. Cycle-by-cycle simulations and laboratory experiments are performed to verify the analytical findings.