# Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters

## Abstract

Power-electronics inverters are expected to satisfy a significant fraction of system load in next-generation power networks with the growing integration of renewable resources and flexible loads. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. In our previous work, we have shown that a system of parallel-connected grid-tied three-phase inverters can be modeled as one aggregated inverter unit with the same structure and state-space dimension as any individual inverter in the system. Here, we extend this result to networks with arbitrary topologies by leveraging a classical aggregation method for coherent synchronous generators in transmission networks, and a linear approximation of the AC power-flow equations to ease computational burden. Numerical simulation results for a prototypical distribution feeder demonstrate the accuracy and computational benefits of the approach.

- Authors:

- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
- University of Minnesota
- University of California at Santa Barbara

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), Solar Energy Technologies Office (EE-4S)

- OSTI Identifier:
- 1457655

- Report Number(s):
- NREL/CP-5D00-70310

- DOE Contract Number:
- AC36-08GO28308

- Resource Type:
- Conference

- Resource Relation:
- Conference: Presented at the 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 3-6 October 2017, Monticello, Illinois

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; inverters; phase locked loops; reduced order systems; mathematical model; aggregates; electronic mail; load modeling

### Citation Formats

```
Johnson, Brian B, Purba, Victor, Dhople, Sairaj V., Jafarpour, Saber, and Bullo, Francesco.
```*Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters*. United States: N. p., 2018.
Web. doi:10.1109/ALLERTON.2017.8262732.

```
Johnson, Brian B, Purba, Victor, Dhople, Sairaj V., Jafarpour, Saber, & Bullo, Francesco.
```*Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters*. United States. doi:10.1109/ALLERTON.2017.8262732.

```
Johnson, Brian B, Purba, Victor, Dhople, Sairaj V., Jafarpour, Saber, and Bullo, Francesco. Thu .
"Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters". United States.
doi:10.1109/ALLERTON.2017.8262732.
```

```
@article{osti_1457655,
```

title = {Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters},

author = {Johnson, Brian B and Purba, Victor and Dhople, Sairaj V. and Jafarpour, Saber and Bullo, Francesco},

abstractNote = {Power-electronics inverters are expected to satisfy a significant fraction of system load in next-generation power networks with the growing integration of renewable resources and flexible loads. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. In our previous work, we have shown that a system of parallel-connected grid-tied three-phase inverters can be modeled as one aggregated inverter unit with the same structure and state-space dimension as any individual inverter in the system. Here, we extend this result to networks with arbitrary topologies by leveraging a classical aggregation method for coherent synchronous generators in transmission networks, and a linear approximation of the AC power-flow equations to ease computational burden. Numerical simulation results for a prototypical distribution feeder demonstrate the accuracy and computational benefits of the approach.},

doi = {10.1109/ALLERTON.2017.8262732},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Jan 18 00:00:00 EST 2018},

month = {Thu Jan 18 00:00:00 EST 2018}

}