# A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow

## Abstract

Realistic representations of contingencies in AC optimal power flow (ACOPF) often challenge traditional bus-branch network models. Derived from nodal analysis, such approaches represent network constraints in terms of the familiar bus admittance matrix, Ybus. A fixed Ybus is unable to represent common circuit breaker actions such as bus splitting. Work-arounds for Ybus-based analysis typically rely on topology processing, switching between different Ybus matrices depending on breaker settings. In this paper, we propose a very general node-breaker approach, employing multi-port element models and using a sparse tableau formulation (STF) for network constraints. Instead of treating breaker action as altering network topology, and hence changing the structure of Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) equations, this approach represents a breaker’s position as impacting only constraints associated with a single component, thereby maintaining fixed structure in the KVL and KCL constraints. While larger numbers of variables are required, STF proves sparser than Ybus formulations. Numerical case studies herein demonstrate that STF provides computational efficiency comparable to a Ybus-based ACOPF at the scale of several hundred buses, and lower computational cost in an example of over one thousand buses.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)

- OSTI Identifier:
- 1497680

- Report Number(s):
- PNNL-SA-141368

Journal ID: ISSN 0885-8950

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Transactions on Power Systems

- Additional Journal Information:
- Journal Volume: 34; Journal Issue: 1; Journal ID: ISSN 0885-8950

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Park, Byungkwon, Holzer, Jesse, and DeMarco, Christopher L.
```*A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow*. United States: N. p., 2019.
Web. doi:10.1109/TPWRS.2018.2869705.

```
Park, Byungkwon, Holzer, Jesse, & DeMarco, Christopher L.
```*A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow*. United States. doi:10.1109/TPWRS.2018.2869705.

```
Park, Byungkwon, Holzer, Jesse, and DeMarco, Christopher L. Tue .
"A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow". United States. doi:10.1109/TPWRS.2018.2869705.
```

```
@article{osti_1497680,
```

title = {A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow},

author = {Park, Byungkwon and Holzer, Jesse and DeMarco, Christopher L.},

abstractNote = {Realistic representations of contingencies in AC optimal power flow (ACOPF) often challenge traditional bus-branch network models. Derived from nodal analysis, such approaches represent network constraints in terms of the familiar bus admittance matrix, Ybus. A fixed Ybus is unable to represent common circuit breaker actions such as bus splitting. Work-arounds for Ybus-based analysis typically rely on topology processing, switching between different Ybus matrices depending on breaker settings. In this paper, we propose a very general node-breaker approach, employing multi-port element models and using a sparse tableau formulation (STF) for network constraints. Instead of treating breaker action as altering network topology, and hence changing the structure of Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) equations, this approach represents a breaker’s position as impacting only constraints associated with a single component, thereby maintaining fixed structure in the KVL and KCL constraints. While larger numbers of variables are required, STF proves sparser than Ybus formulations. Numerical case studies herein demonstrate that STF provides computational efficiency comparable to a Ybus-based ACOPF at the scale of several hundred buses, and lower computational cost in an example of over one thousand buses.},

doi = {10.1109/TPWRS.2018.2869705},

journal = {IEEE Transactions on Power Systems},

issn = {0885-8950},

number = 1,

volume = 34,

place = {United States},

year = {2019},

month = {1}

}