# Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power

## Abstract

State and parameter estimation of power transmission networks is important for monitoring power grid operating conditions and analyzing transient stability. Wind power generation depends on fluctuating input power levels, which are correlated in time and contribute to uncertainty in turbine dynamical models. The ensemble Kalman filter (EnKF), a standard state estimation technique, uses a deterministic forecast and does not explicitly model time-correlated noise in parameters such as mechanical input power. However, this uncertainty affects the probability of fault-induced transient instability and increased prediction bias. Here a novel approach is to model input power noise with time-correlated stochastic fluctuations, and integrate them with the network dynamics during the forecast. While the EnKF has been used to calibrate constant parameters in turbine dynamical models, the calibration of a statistical model for a time-correlated parameter has not been investigated. In this study, twin experiments on a standard transmission network test case are used to validate our time-correlated noise model framework for state estimation of unsteady operating conditions and transient stability analysis, and a methodology is proposed for the inference of the mechanical input power time-correlation length parameter using time-series data from PMUs monitoring power dynamics at generator buses.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1438238

- Report Number(s):
- [PNNL-SA-123139]

[Journal ID: ISSN 0885-8950]

- Grant/Contract Number:
- [AC05-76RL01830]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Power Systems

- Additional Journal Information:
- [ Journal Volume: 33; Journal Issue: 4]; Journal ID: ISSN 0885-8950

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; Power system estimation; power system dynamics; wind power generation; time-correlation; stochastic processes; stochastic resonance; ensemble Kalman filter; filter divergence; parameter estimation

### Citation Formats

```
Rosenthal, William Steven, Tartakovsky, Alex, and Huang, Zhenyu. Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power. United States: N. p., 2017.
Web. doi:10.1109/TPWRS.2017.2764492.
```

```
Rosenthal, William Steven, Tartakovsky, Alex, & Huang, Zhenyu. Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power. United States. doi:10.1109/TPWRS.2017.2764492.
```

```
Rosenthal, William Steven, Tartakovsky, Alex, and Huang, Zhenyu. Tue .
"Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power". United States. doi:10.1109/TPWRS.2017.2764492. https://www.osti.gov/servlets/purl/1438238.
```

```
@article{osti_1438238,
```

title = {Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power},

author = {Rosenthal, William Steven and Tartakovsky, Alex and Huang, Zhenyu},

abstractNote = {State and parameter estimation of power transmission networks is important for monitoring power grid operating conditions and analyzing transient stability. Wind power generation depends on fluctuating input power levels, which are correlated in time and contribute to uncertainty in turbine dynamical models. The ensemble Kalman filter (EnKF), a standard state estimation technique, uses a deterministic forecast and does not explicitly model time-correlated noise in parameters such as mechanical input power. However, this uncertainty affects the probability of fault-induced transient instability and increased prediction bias. Here a novel approach is to model input power noise with time-correlated stochastic fluctuations, and integrate them with the network dynamics during the forecast. While the EnKF has been used to calibrate constant parameters in turbine dynamical models, the calibration of a statistical model for a time-correlated parameter has not been investigated. In this study, twin experiments on a standard transmission network test case are used to validate our time-correlated noise model framework for state estimation of unsteady operating conditions and transient stability analysis, and a methodology is proposed for the inference of the mechanical input power time-correlation length parameter using time-series data from PMUs monitoring power dynamics at generator buses.},

doi = {10.1109/TPWRS.2017.2764492},

journal = {IEEE Transactions on Power Systems},

number = [4],

volume = [33],

place = {United States},

year = {2017},

month = {10}

}

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#### Figures / Tables:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*