Passivity-short-based system-wide stability with L ₂ gain and stabilization of heterogeneous power systems

The problem of decentralized control for overall system stability has received increasing attention due to heterogeneity in power networks. To address this problem, two passivity indices are introduced to characterize the shortage of nonlinear negative imaginary property and L2 stability of the coupling network. In a modular decomposition, novel passivity-short-based conditions in a decentralized manner are investigated to ensure asymptotically stability of the overall system and L2 stability of the network simultaneously, which is so-called system-wide stability with L2 gain. Furthermore, the local subsystems are equipped with a linear matrix inequality-based controller, implementing decentralized stabilization. A numerical simulation with three heterogeneous bus dynamics is illustrated to demonstrate the effectiveness of the proposed controller design considering load change and measurement errors, offering insights into system robustness.