Dispatch of Virtual Inertia and Damping: Numerical Method with SDP and ADMM

TL;DR

This paper introduces a novel numerical method combining SDP relaxation and ADMM to efficiently dispatch virtual inertia and damping in inverter-based power grids, ensuring stability and scalability.

Contribution

It formulates the dispatch problem as a nonlinear program, relaxes it with SDP, and develops a distributed ADMM-based approach for large-scale, inexact solutions.

Findings

Method effectively handles various disturbances and constraints.

Numerical tests confirm the necessity and efficiency of the proposed approach.

Approach achieves parallel computation and feasible solutions for large systems.

Abstract

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