## Inversion Reduction Method for Real and Complex Distribution Feeder Models

## Abstract

We report the proliferation of distributed generation on distribution feeders triggers a large number of integration and planning studies. Further, the complexity of distribution feeder models, short simulation time steps, and long simulation horizons rapidly render studies computational burdensome. To mend this issue, we propose a methodology for reducing the number of nodes, loads, generators, line, and transformers of p-phase distribution feeders with unbalanced loads and generation, non-symmetric wire impedance, mutual coupling, shunt capacitance, and changes in voltage and phase. The methodology is derived on a constant power load assumption and employs a Gaussian elimination inversion technique to design the reduced feeder. Compared to previous work by the authors, the inversion reduction takes half the time and voltage errors after reduction are reduced by an order of magnitude. Using a snapshot simulation the reduction is tested on six additional publicly available feeders with a maximum voltage error 0.0075 p.u. regardless of feeder size or complexity, and typical errors on the order of 1 × 10 ^{-4} p.u. Lastly, for a day long quasi-static time series simulation on the UCSD A feeder, errors are shown to increase with changes in loading when a large number of buses removed, but shows lessmore »

- Authors:

- Bankable Energy, San Diego, CA (United States)
- University of Tennessee, Chattanooga, TN (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- University of California San Diego, La Jolla, CA (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1526221

- Report Number(s):
- SAND-2019-5853J

Journal ID: ISSN 0885-8950; 675796

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Power Systems

- Additional Journal Information:
- Journal Volume: 34; Journal Issue: 2; Journal ID: ISSN 0885-8950

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; Distribution system; network reduction; mutual impedance; quasi static time-series simulations

### Citation Formats

```
Pecenak, Zachary K., Disfani, Vahid R., Reno, Matthew J., and Kleissl, Jan. Inversion Reduction Method for Real and Complex Distribution Feeder Models. United States: N. p., 2018.
Web. doi:10.1109/TPWRS.2018.2872747.
```

```
Pecenak, Zachary K., Disfani, Vahid R., Reno, Matthew J., & Kleissl, Jan. Inversion Reduction Method for Real and Complex Distribution Feeder Models. United States. doi:10.1109/TPWRS.2018.2872747.
```

```
Pecenak, Zachary K., Disfani, Vahid R., Reno, Matthew J., and Kleissl, Jan. Fri .
"Inversion Reduction Method for Real and Complex Distribution Feeder Models". United States. doi:10.1109/TPWRS.2018.2872747. https://www.osti.gov/servlets/purl/1526221.
```

```
@article{osti_1526221,
```

title = {Inversion Reduction Method for Real and Complex Distribution Feeder Models},

author = {Pecenak, Zachary K. and Disfani, Vahid R. and Reno, Matthew J. and Kleissl, Jan},

abstractNote = {We report the proliferation of distributed generation on distribution feeders triggers a large number of integration and planning studies. Further, the complexity of distribution feeder models, short simulation time steps, and long simulation horizons rapidly render studies computational burdensome. To mend this issue, we propose a methodology for reducing the number of nodes, loads, generators, line, and transformers of p-phase distribution feeders with unbalanced loads and generation, non-symmetric wire impedance, mutual coupling, shunt capacitance, and changes in voltage and phase. The methodology is derived on a constant power load assumption and employs a Gaussian elimination inversion technique to design the reduced feeder. Compared to previous work by the authors, the inversion reduction takes half the time and voltage errors after reduction are reduced by an order of magnitude. Using a snapshot simulation the reduction is tested on six additional publicly available feeders with a maximum voltage error 0.0075 p.u. regardless of feeder size or complexity, and typical errors on the order of 1 × 10 -4 p.u. Lastly, for a day long quasi-static time series simulation on the UCSD A feeder, errors are shown to increase with changes in loading when a large number of buses removed, but shows less variation for less than 85% of buses removed.},

doi = {10.1109/TPWRS.2018.2872747},

journal = {IEEE Transactions on Power Systems},

number = 2,

volume = 34,

place = {United States},

year = {2018},

month = {9}

}