# Dynamics and Stability of Meshed Multiterminal HVDC Networks

## TL;DR

This paper develops a comprehensive dynamic model of multiterminal HVDC grids using hypergraph theory, demonstrating conditions for the existence, uniqueness, and stability of equilibrium points through mathematical analysis and simulation.

## Contribution

It introduces a novel hypergraph-based dynamic model for MT-HVDC systems and provides analytical conditions for equilibrium existence, uniqueness, and stability.

## Key findings

- Existence and uniqueness of equilibrium are confirmed for the tested system.
- A Lyapunov function is derived to analyze stability.
- Simulation results support the theoretical stability conditions.

## Abstract

This paper investigates the existence of an equilibrium point in multiterminal HVDC (MT-HVDC) grids, assesses its uniqueness and defines conditions to ensure its stability. An offshore MT-HVDC system including two wind farms is selected as application test case. At first, a generalized dynamic model of the network is proposed, using hypergraph theory. Such model captures the frequency dependence of transmission lines and cables, it is non-linear due to the constant power behavior of the converter terminals using droop regulation, and presents a suitable degree of simplifications of the MMC converters, under given conditions, to allow system level studies over potentially large networks. Based on this model, the existence and uniqueness of the equilibrium point is demonstrated by returning the analysis to a load-flow problem and using the Banach fixed point theorem. Additionally, the stability of the equilibrium is analyzed by obtaining a Lyapunov function by the Krasovskii's theorem. Computational results obtained for the selected 4 terminals MT-HVDC grid corroborate the requirement for the existence and stability of the equilibrium point.