# Dynamic Modeling of Power Outages Caused by Thunderstorms

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## Abstract

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## 1. Introduction

## 2. Data Sources and Processing

#### 2.1. Weather Data

#### 2.2. Outage Data

#### 2.3. Feature Representation Framework

## 3. Dynamic OPMs

## 4. Results

#### 4.1. An Eventwise OPM for the Northeastern United States

#### 4.2. Comparisons of Performance

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Cross-correlation of wind speed, averaged at each hour across town centroids, and customer-reported outages (

**left**); horizontal dashed lines indicate the threshold for statistical significance, which is the 95 percent confidence interval when the underlying true correlation values are zero. Histogram of outages per hour across the study period (

**right**).

**Figure 2.**Illustration of 3 hrs. of CT thunderstorm weather conditions over three variables, translated into the eventwise OPM framework (

**middle**) and the temporally dynamic framework (

**bottom**). In the eventwise framework, the processed dataset consists, for each storm, of static geospatial features and statistical aggregations of weather features over the course of the storm. This data is indexed by town ID. In the temporally dynamic framework, the dataset consists of direct timeseries samples of the weather features. The index is time, and town IDs are associated with each weather feature. A toy data sample in the temporally dynamic framework is illustrated with a 2-hr. lookback, predicting outages one hour ahead.

**Figure 3.**Mean LOSO cross-validated squared correlation between actual and predicted outages using Poisson regression on feature sets with varying lags (

**left**), KNN at settings of $k\in \{2,4,6,\dots ,300\}$ (

**middle**); random forest at several settings of the number of trees (

**right**). Selected values are marked by vertical dashed lines.

**Figure 4.**Hourly (solid) and cumulative (dashed) outages for 27 CT thunderstorms, each lasting 18 h, with corresponding LOSO cross-validated predictions by dynamic models.

**Figure 5.**HRRR-simulated zero-hour reflectivity and contours of wind speed at three hours, overlaid with outage occurrences accumulated over the 18-h period of a well-predicted storm (“p”; average hourly ${r}^{2}=0.779$) on 17 July 2018 (

**top**), and a poorly predicted storm (“u”; average hourly ${r}^{2}=0.074$) on 8 August 2018 (

**bottom**). The center plot for each storm illustrates the hour of peak outages, with the left two hours before, and the right two hours later.

**Table 1.**The performance of each model across several metrics and averaged across storms. From left to right: mean absolute error (MAE) in ${t}_{m}$, MAE in ${t}_{{\sigma}^{2}}$, the ${r}^{2}$ of SOD predictions, hourly ${r}^{2}$ and NSE, and storm-total ${r}^{2}$, NSE, and MAPE. The MAPE is unavailable for stormwise total outage predictions because there are hours with zero actual outages. Some correlation metrics could not be computed for some models because of constant predictions. The best model for each metric is bolded.

Time Series | Hourly | Storm Totals | ||||||
---|---|---|---|---|---|---|---|---|

Model | ${\mathit{t}}_{\mathit{m}}$ MAE | ${\mathit{t}}_{{\mathit{\sigma}}^{\mathbf{2}}}$ MAE | SOD ${\mathit{r}}^{\mathbf{2}}$ | ${\mathit{r}}^{\mathbf{2}}$ | NSE | ${\mathit{r}}^{\mathbf{2}}$ | NSE | MAPE |

Event-OPM [11] | 0.665 | 9.555 | 0.142 | −0.459 | 0.262 | −0.187 | 0.430 | |

KNN | 0.777 | 5.560 | 0.252 | −0.219 | 0.328 | −0.676 | 0.422 | |

LSTM | 0.726 | 4.763 | 0.007 | 0.363 | -0.100 | 0.244 | −0.334 | 0.396 |

RF | 0.705 | 4.715 | 0.521 | 0.363 | 0.029 | 0.573 | 0.111 | 0.287 |

Poisson reg. | 0.745 | 3.321 | 0.412 | 0.332 | 0.055 | 0.600 | 0.371 | 0.265 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alpay, B.A.; Wanik, D.; Watson, P.; Cerrai, D.; Liang, G.; Anagnostou, E.
Dynamic Modeling of Power Outages Caused by Thunderstorms. *Forecasting* **2020**, *2*, 151-162.
https://doi.org/10.3390/forecast2020008

**AMA Style**

Alpay BA, Wanik D, Watson P, Cerrai D, Liang G, Anagnostou E.
Dynamic Modeling of Power Outages Caused by Thunderstorms. *Forecasting*. 2020; 2(2):151-162.
https://doi.org/10.3390/forecast2020008

**Chicago/Turabian Style**

Alpay, Berk A., David Wanik, Peter Watson, Diego Cerrai, Guannan Liang, and Emmanouil Anagnostou.
2020. "Dynamic Modeling of Power Outages Caused by Thunderstorms" *Forecasting* 2, no. 2: 151-162.
https://doi.org/10.3390/forecast2020008