Dispatch of virtual inertia and damping: Numerical method with SDP and ADMM

• Dynamic performance under various forms of disturbances. Nonlinear programming formulation for dispatch virtual inertia and damping. Semi-definite relaxation to address non-convexity. Clique decomposition approach exploit sparsity. Distributed solution based on the alternating direction method multipliers. Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual damping provided inverters essential synchronism frequency stability future power grids. This paper numerically addresses problem (DID) among in transmission network. The DID is first formulated as a nonlinear program (NLP) Radua collocation which flexible handle types disturbances bounds constraints. Since NLP highly non-convex, semi-definite (SDP) further derived tackle non-convexity, followed its sparsity being exploited hierarchically chordality graphs seek enhancement computational efficiency. Considering high dimension inexactness SDP relaxation, feasibility-embedded distributed finally proposed framework multipliers (ADMM), achieves parallel computing feasibility regarding original NLP. Numerical simulations carried out five test systems demonstrate necessity DID.