# Methods of computing steady-state voltage stability margins of power systems

## Abstract

In steady-state voltage stability analysis, as load increases toward a maximum, conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned so power flow fails to converge before reaching maximum loading. A method to directly eliminate this singularity reformulates the power flow problem by introducing an AQ bus with specified bus angle and reactive power consumption of a load bus. For steady-state voltage stability analysis, the angle separation between the swing bus and AQ bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation is only made up of a reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point, eliminating a major difficulty in voltage stability analysis for power system operations.

- Inventors:

- Issue Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1429386

- Patent Number(s):
- 9,921,602

- Application Number:
- 14/655,474

- Assignee:
- Rensselaer Polytechnic Institute, Troy, NY

- DOE Contract Number:
- AC02-05CH11231

- Resource Type:
- Patent

- Resource Relation:
- Patent File Date: 2014 Nov 20

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION

### Citation Formats

```
Chow, Joe Hong, and Ghiocel, Scott Gordon.
```*Methods of computing steady-state voltage stability margins of power systems*. United States: N. p., 2018.
Web.

```
Chow, Joe Hong, & Ghiocel, Scott Gordon.
```*Methods of computing steady-state voltage stability margins of power systems*. United States.

```
Chow, Joe Hong, and Ghiocel, Scott Gordon. Tue .
"Methods of computing steady-state voltage stability margins of power systems". United States. https://www.osti.gov/servlets/purl/1429386.
```

```
@article{osti_1429386,
```

title = {Methods of computing steady-state voltage stability margins of power systems},

author = {Chow, Joe Hong and Ghiocel, Scott Gordon},

abstractNote = {In steady-state voltage stability analysis, as load increases toward a maximum, conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned so power flow fails to converge before reaching maximum loading. A method to directly eliminate this singularity reformulates the power flow problem by introducing an AQ bus with specified bus angle and reactive power consumption of a load bus. For steady-state voltage stability analysis, the angle separation between the swing bus and AQ bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation is only made up of a reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point, eliminating a major difficulty in voltage stability analysis for power system operations.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {3}

}

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