Constructive Port-Hamiltonian Energy Shaping Design of Dispatchable Virtual Oscillators in Grid-Forming Converters
Port-Hamiltonian (PH) theory offers a passivity-based framework for grid-forming control, yet conventional dispatchable virtual oscillator control (dVOC) does not naturally admit a dissipative PH realization, since its amplitude egulation, synchronization, and power dispatch are inherently coupled without a unified energy interpretation. This paper formulates the outer-loop dynamics as a dissipative PH system, thereby unifying amplitude regulation, synchronization, and power dispatch within one energy structure. The formulation rests on the key property that logistic-type radial regulation, characterized by an inherent saturation-like nonlinearity, permits an exact gradient decomposition compatible with the quadratic energy storage. On this basis, a unified shaped Hamiltonian is constructed, which encapsulates both amplitude restoration and power dispatch. Radial gain matching derived from this Hamiltonian yields explicit closed-form arameter inequalities that guarantee almost-global asymptotic stability and local exponential convergence. Moreover, tuning the power-error weighting coefficient actively shapes the energy landscape, thereby eliminating the undesirable low-voltage power-flow solution from the stationary set and ensuring convergence to the desired high-voltage equilibrium point. The Hessian singularity condition further provides the critical weight threshold that guarantees uniqueness of the high-voltage equilibrium. Numerical simulations validate the proposed method.