Assessing the power grid vulnerability to extreme weather events based on long-term atmospheric reanalysis

Abstract

This study presents a framework for evaluating the vulnerability of the electrical grid to storm outages, based on multi-year atmospheric reanalysis datasets. The underlying methodology encompasses the classification of outage event severity and machine learning-based outage prediction models (OPMs), toward identifying relevant weather events and quantifying the associated outages within the European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5 and ERA5-Land) records. The proposed framework is tested for the Eversource Energy distribution grid over the State of Connecticut, for a period from 1981 to 2020. Within this context, and using as benchmark outage data reported by the utility for the period from 2005 to 2020, the accuracy of the classification for events of high-impact and extreme-severity proved to be high (i.e., 0.84 and 0.95, respectively). Especially for the latter case, the OPMs exhibited acceptable mean absolute percentage errors and high coefficient of determination (R²) values. Further, an analysis based on the annual maxima of the total number of outages, as well as the number of events with outages above various thresholds, indicated an intensification of extreme events over the last decade. Within this context, and given its importance to long-term planning and investment, we ultimately assess the potential impact of climate change on the resilience of the distribution grid, by evaluating the non-exceedance probabilities of six historical hurricanes that impacted the Eversource Energy service territory in Connecticut through a parametric statistical approach.

Appendix

1.1 Variables used in the QWD classification and OPM

See Table

Table 6 Explanatory variables used in the quantile weighted distance (QWD) classification and the outage prediction models (OPMs)

6.

1.2 Evaluation metrics for the storm event classification

For a given class label X (i.e., high or extreme), terms are defined as follows:

• True Positive (TP): Observation is label X and is predicted as label X.

• False Positive (FP): Observation is not label X but is predicted as label X.

• False Negative (FN): Observation is label X but is not predicted as label X.

• True Negative (TN): Observation is not label X and is not predicted as label X.

Precision is expressed as the proportion of events correctly predicted as label X, over all events predicted as label X:

$${\text{Precision = }}\frac{TP}{{TP + FP}}$$

(6)

For a given class label X, Recall is the proportion of events correctly predicted as label X, over the observed events of label X:

$${\text{Recall = }}\frac{TP}{{TP + FN}}$$

(7)

Then, the F₁ score is the harmonic mean of Precision and Recall, given equal weights:

$$F_{{1}} { = 2 } \cdot { }\frac{{{\text{Precision }} \cdot {\text{ Recall }}}}{{\text{Precsion + Recall}}}$$

(8)

1.3 Evaluation metrics for the OPM validation

We use the Absolute Error (AE) to measure the difference between the actual (${\text{o}}_{\text{i}}$) and predicted (${\text{p}}_{\text{i}}$) outage totals for the service territory from each event (i). The first, second, and third quantiles of the sorted Absolute Errors are represented as AE Q25, AE Q50, and AE Q75, respectively. AE can be estimated as follows:

$${\text{AE}} \, = \text{ } \left| {\text{p}}_{\text{i}}-{\text{o}}_{\text{i}}\right|$$

(9)

The first, second, and third quantiles of the sorted Absolute Percentage Errors (APE) are denoted as APE q25, APE q50, and APE q75, respectively. APE is estimated as follows:

$$\text{APE = }\frac{\left|{\text{ p}}_{\text{i}}-{\text{o}}_{\text{i}} \, \right|}{{\text{o}}_{\text{i}}}$$

(10)

We, also, employ the Mean Absolute Percentage Error (MAPE), which is estimated as follows:

$$\text{MAPE } = \frac{\text{100\%}}{\text{n}}\sum_{{\text{i}} \, = \text{1} }^{\text{n}}\left|\frac{{\text{o}}_{\text{i}} -{\text{p}}_{\text{i}}}{{\text{o}}_{\text{i}}}\right|$$

(11)

Moreover, we use the Centered Root-Mean-Squared Error (CRMSE) to quantify both systematic and random error components:

$${\text{CRMSE}} \, \text{=} \sqrt{\frac{1}{{\text{n}}}\sum_{{\text{i}} \, = \text{1} }^{\text{n}}{\left({\text{p}}_{\text{i}}-{\text{o}}_{\text{i}}-\text{(}\overline{{\text{p} }_{\text{i}}}- \overline{{\text{o} }_{\text{i}}}\text{)}\right)}^{2}}$$

(12)

Further, we utilize the coefficient of determination (R²) to assess the goodness-of-fit of the acquired model predictions to the actual outages:

$${\text{R}}^{2} \, \text{=} \, \frac{1}{{\text{n}}}\sum_{{\text{i}} \, = \text{1} }^{\text{n}}\frac{\left({\text{o}}_{\text{i}}-\overline{{\text{o} }_{\text{i}}}\right){\left({\text{p}}_{\text{i}}-\overline{{\text{p} }_{\text{i}}}\right)}^{2}}{{\text{o}}_{\text{i}} \, {\text{p}}_{\text{i}}}$$

(13)

Finally, we employ the Nash–Sutcliffe model efficiency coefficient (NSE), which ranges between negative infinite and 1:

$${\text{NSE}} \, \text{=} \, {1}-\frac{\sum_{{\text{i}} \, \text{=} \, {1}}^{\text{n}}{\left({\text{o}}_{\text{i}}-{\text{p}}_{\text{i}}\right)}^{2}}{\sum_{{\text{i}} \, \text{=} \, {1}}^{\text{n}}{\left({\text{o}}_{\text{i}}-\overline{{\text{o} }_{\text{i}}}\right)}^{2}}$$

(14)

1.4 Variable importance for the GBM-based and RF-based OPMs

See Fig. 

Fig. 10

Variable importance for GBM and RF OPMs

10.

1.5 Model performance of the OPMs for the high-impact and and extreme-severity events

See Table

Table 7 Model performance of the OPMs for the high-impact and and extreme-severity events

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