A novel damping strategy for off-grid cost-based virtual synchronous generators

Islanded microgrids (IMGs) address low-inertia challenges using virtual synchronous generators (VSGs), but this introduces low-frequency oscillations (LFOs) due to swing equation replication. Unlike conventional proportional power-sharing, this paper optimizes VSG power allocation based on production costs, improving efficiency but weakening damping due to virtual damping constraints. Moreover, economic power-sharing pushes cost-effective VSGs to their limits, reducing inertia and requiring seamless grid-forming to grid-following transitions. Existing damping methods struggle with inadequate damping, steady-state frequency offsets, reduced inertia, compromised stability, or complex implementation. This paper proposes a virtual inductance in the voltage magnitude loop of cost-based VSGs to dampen LFOs while enabling high virtual inertia for rate-of-change-of-frequency (RoCoF) compliance. The proposed virtual inductance, requiring just one parameter for tuning, is optimized via small-signal stability analysis using the teaching-learning-based optimization technique. Moreover, the paper accounts for seamless mode transitions, multi-VSG interactions, and voltage drop constraints. The method’s efficacy is validated through mathematical proofs, simulations, real-time control-in-loop experiments, and eigenvalue analyses under varying conditions. Its superiority is further demonstrated through comparisons with additional damping strategies, namely feedback-based, feedforward-based, and voltage magnitude-based methods. Moreover, its effectiveness under hybrid cost function scenarios is also confirmed. The economic benefits of the proposed cost-based VSG are quantified, highlighting potential savings in power generation costs.