# The Effect of Transmission-Line Dynamics on a Globally Synchronizing Controller for Power Inverters

## Abstract

In this work, we analyze a dispatchable virtual oscillator control (dVOC) strategy for grid-forming power inverters that ensures almost global synchronization of inverterbased AC power systems when the dynamics of the transmission network are neglected, i.e., if an algebraic model of the transmission lines is used. While this approximation is often justified for conventional power systems, the dynamics of the transmission lines can compromise the stability of an inverterbased power system. Therefore, in this article, we use tools from singular perturbation theory to construct a Lyapunov function candidate and explicit bounds on the controller gains that guarantee global convergence to the set of steady-states for the full power-system with transmission line dynamics. Moreover, we show that the only undesirable steady-state is unstable.

- Authors:

- ETH Zurich
- National Renewable Energy Laboratory (NREL), Golden, CO (United States)

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- OSTI Identifier:
- 1493692

- Report Number(s):
- NREL/CP-5D00-73225

- DOE Contract Number:
- AC36-08GO28308

- Resource Type:
- Conference

- Resource Relation:
- Conference: Presented at the 2018 European Control Conference (ECC), 12-15 June 2018, Limassol, Cyprus

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; inverters; steady-state; power system dynamics; power transmission lines; power system stability; transmission line matrix methods; stability analysis

### Citation Formats

```
Brouillon, Jean-Sebastien, Colombino, Marcello, Gross, Dominic, and Dorfler, Florian.
```*The Effect of Transmission-Line Dynamics on a Globally Synchronizing Controller for Power Inverters*. United States: N. p., 2018.
Web. doi:10.23919/ECC.2018.8550600.

```
Brouillon, Jean-Sebastien, Colombino, Marcello, Gross, Dominic, & Dorfler, Florian.
```*The Effect of Transmission-Line Dynamics on a Globally Synchronizing Controller for Power Inverters*. United States. doi:10.23919/ECC.2018.8550600.

```
Brouillon, Jean-Sebastien, Colombino, Marcello, Gross, Dominic, and Dorfler, Florian. Thu .
"The Effect of Transmission-Line Dynamics on a Globally Synchronizing Controller for Power Inverters". United States. doi:10.23919/ECC.2018.8550600.
```

```
@article{osti_1493692,
```

title = {The Effect of Transmission-Line Dynamics on a Globally Synchronizing Controller for Power Inverters},

author = {Brouillon, Jean-Sebastien and Colombino, Marcello and Gross, Dominic and Dorfler, Florian},

abstractNote = {In this work, we analyze a dispatchable virtual oscillator control (dVOC) strategy for grid-forming power inverters that ensures almost global synchronization of inverterbased AC power systems when the dynamics of the transmission network are neglected, i.e., if an algebraic model of the transmission lines is used. While this approximation is often justified for conventional power systems, the dynamics of the transmission lines can compromise the stability of an inverterbased power system. Therefore, in this article, we use tools from singular perturbation theory to construct a Lyapunov function candidate and explicit bounds on the controller gains that guarantee global convergence to the set of steady-states for the full power-system with transmission line dynamics. Moreover, we show that the only undesirable steady-state is unstable.},

doi = {10.23919/ECC.2018.8550600},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {11}

}