What Makes Power Outages Last So Long?

Class: DSC80

Name: Calvin Chen

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Introduction

My project looks at major power outages in the United States from January 2000 to July 2016. The dataset has 1534 rows, where each row is one major outage event.

The central question that I'm investigating is: what characteristics are associated with the duration of power outages?

This matters because outage duration directly determines the economic and social impact of a blackout. I believe that understanding what drives longer outages could help utility companies better allocate restoration resources and help policymakers prioritize grid improvements.

The columns most relevant to my analysis are:

Column	Description
OUTAGE.DURATION	Duration of the outage in minutes
CAUSE.CATEGORY	General category of the cause of the outage
CUSTOMERS.AFFECTED	Number of customers affected by the outage
CLIMATE.REGION	U.S. climate region where the outage occurred
U.S._STATE	State where the outage occurred
SEASON	Season the outage started (derived from start month)
POPDEN_URBAN	Population density of urban areas in the state
AREAPCT_URBAN	Percentage of the state's area that is urban

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Data Cleaning and Exploratory Data Analysis

Data Cleaning

I performed the following steps on the raw dataset to clean it:

1. combined OUTAGE.START.DATE and OUTAGE.START.TIME into a single OUTAGE.START timestamp column, and did the same for OUTAGE.RESTORATION.DATE and OUTAGE.RESTORATION.TIME. This made it easier to work with the time data and also let me create a SEASON column.
2. replaced OUTAGE.DURATION values of 0 with NaN since a real outage can't last 0 minutes. These are probably missing data rather than actual instant events.
3. created a SEASON column by mapping the start month to Winter, Spring, Summer, or Fall.
4. dropped the original split date and time columns after combining them.

Here is the head of the cleaned dataset:

	YEAR	MONTH	U.S._STATE	CAUSE.CATEGORY	OUTAGE.DURATION	CUSTOMERS.AFFECTED	CLIMATE.REGION	SEASON
0	2011	7	Minnesota	severe weather	3060	70000	East North Central	Summer
1	2014	5	Minnesota	intentional attack	1	nan	East North Central	Spring
2	2010	10	Minnesota	severe weather	3000	70000	East North Central	Fall
3	2012	6	Minnesota	severe weather	2550	68200	East North Central	Summer
4	2015	7	Minnesota	severe weather	1740	250000	East North Central	Summer

Univariate Analysis

I first look at the distribution of outage duration and common causes for major outages.

<iframe src="assets/outage-duration-dist.html" width="800" height="450" frameborder="0" ></iframe>

The distribution of outage duration is heavily skewed to the right. Most outages lasted around a few thousand minutes, but a few of them lasted over 100 thousand minutes. I used a log y-scale to make the distribution easier to read.

<iframe src="assets/outage-cause-counts.html" width="800" height="450" frameborder="0" ></iframe>

Severe weather is the most common cause of major outages by far, as it made up nearly half of all events in the dataset. Intentional attacks is the second most common cause.

Bivariate Analysis

Next, I move on to bivariate analysis and examine the outage durations by cause category, as well as looking at the relationship between seasons and cause category.

<iframe src="assets/outage-duration-by-cause.html" width="800" height="450" frameborder="0" ></iframe>

Severe weather and fuel supply emergencies tended to produce the longest outages by a pretty wide margin. Intentional attacks were frequent, but they tend to get resolved much faster than events driven by weather conditions.

Interesting Aggregates

This table below shows the mean outage duration (in minutes) broken down by cause category and season.

CAUSE.CATEGORY	Winter	Spring	Summer	Fall
equipment failure	712.8	4959.8	292.8	389.5
fuel supply emergency	18935.9	16503.3	7626.2	793.7
intentional attack	490.8	782.3	331.8	334.8
islanding	385.0	88.4	231.9	69.0
public appeal	2592.6	2152.3	1187.6	244.0
severe weather	3869.3	3287.7	3214.8	5646.1
system operability disruption	592.3	529.9	1152.1	371.5

I found that fuel supply emergencies are much longer in winter and spring, which makes sense since heating demand is much higher in colder months and consequently puts more stress on fuel supply chains. Severe weather outages are worst in fall, which could be because of the hurricane season in the East Coast.

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Assessment of Missingness

MNAR Analysis

I believe that DEMAND.LOSS.MW is likely MNAR. The reason is that measuring demand loss in megawatts requires specialized grid equipment, so smaller or more rural places may not have those equipment. This means that the missingness is actually tied to the value itself. The outages most likely to have low demand loss are also the ones where it probably won't get measured.

To turn this into MAR, you would need data on whether each utility has that kind of metering infrastructure, since that would explain the missingness on its own without needing to look at the actual demand loss values.

Missingness Dependency

I looked at the missingness of CUSTOMERS.AFFECTED, which is missing for about 29% of rows. I tested whether this missingness is related to CAUSE.CATEGORY and YEAR.

The missingness does depend on CAUSE.CATEGORY (p-value = 0.0): intentional attack outages are much more likely to have missing customer counts than severe weather outages. This makes sense because targeted attacks usually affect very few customers and may not be tracked the same way.

The missingness also depends on YEAR (p-value = 0.0): earlier years are more likely to be missing customer data, which suggest that reporting became more consistent over time.

<iframe src="assets/missingness-tvd.html" width="800" height="450" frameborder="0" ></iframe>

The observed TVD of 0.557 falls way outside the permutation distribution, which confirms that the missingness of CUSTOMERS.AFFECTED is strongly tied to CAUSE.CATEGORY.

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Hypothesis Testing

Question: Do severe weather outages last longer on average than intentional attack outages?

• Null hypothesis: Severe weather and intentional attack outages have the same mean duration, and any difference observed is just due to random chance.
• Alternative hypothesis: Severe weather outages have a longer mean duration than intentional attack outages.
• Test statistic: Difference in group means (severe weather minus intentional attack). I used a one-sided test because I had a directional hypothesis based on what I already knew about the data.
• Significance level: 0.05
• Result: The observed difference was 3,454 minutes, and the p-value was 0.0.

Since the p-value is much less than 0.05, I reject the null hypothesis. The data supports the idea that severe weather outages last significantly longer than intentional attack outages on average. Weather events tend to cause widespread infrastructure damage that takes days to repair, while targeted attacks are more localized and faster to fix.

<iframe src="assets/hypothesis-test.html" width="800" height="450" frameborder="0" ></iframe>

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Framing a Prediction Problem

The prediction problem I'm focusing on is predicting OUTAGE.DURATION (in minutes). This is a regression problem since the response variable is continuous.

I chose outage duration as my response variable because it is one of the most practically important outcomes of a power outage. Longer outages cause more economic damage and affect more people, so being able to predict duration could help utilities better plan their response.

To avoid data leakage, I only use features that would be known at the time the outage starts, before restoration happens. This means I can't use anything that gets recorded after the fact, like OUTAGE.RESTORATION or DEMAND.LOSS.MW. The features I use describe the cause, location, climate, and regional context of the outage.

I use RMSE (Root Mean Squared Error) as my evaluation metric because it is in the same units as the response variable (minutes) and penalizes large errors more heavily. That matters here since very long outages tend to be the most impactful.

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Baseline Model

My baseline model predicts OUTAGE.DURATION using a RandomForestRegressor inside a single sklearn Pipeline. I used two features:

• CAUSE.CATEGORY (nominal): encoded with OneHotEncoder since it has no natural ordering
• CUSTOMERS.AFFECTED (quantitative): left as-is after filling in missing values with the median

I picked these two features because cause category showed a clear relationship with duration in my EDA, and customers affected gives a rough sense of the scale of the outage.

The baseline model achieved a train RMSE of 4,347 minutes and a test RMSE of 7,087 minutes. The big gap between train and test RMSE suggests the model is overfitting. The high test RMSE overall is also partly because of extreme outliers in outage duration. This model isn't good enough yet since it only uses two features without any real transformations and no hyperparameter tuning.

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Final Model

For my final model I added the following five features on top of the two from the baseline:

• CAUSE.CATEGORY (nominal): same as baseline, encoded with OneHotEncoder
• CUSTOMERS.AFFECTED (quantitative): log-transformed since both outage duration and customer counts are heavily right-skewed. Doubling the number of affected customers doesn't double the restoration time, so a log transformation fits the relationship better.
• CLIMATE.REGION (nominal): different regions have very different grid infrastructure and utility response capacity. A Northeast outage and a Southwest outage with the same cause will probably have different restoration times, so this adds useful regional context.
• SEASON (nominal): from my EDA, fall severe weather outages lasted around 5,646 minutes on average compared to around 3,215 in summer. Season clearly affects how bad weather-related damage gets and how quickly crews can respond.
• POPDEN_URBAN (quantitative): more densely populated urban areas tend to have more backup grid infrastructure, so outages there can often be fixed faster. I applied StandardScaler to normalize the range.

Also, outages like the 108,000-minute event in the data are basically impossible to predict from the available features and were inflating RMSE in a way that wasn't useful. So I decided to cap extreme outliers at the 99th percentile of duration before modeling.

Furthermore, I used a RandomForestRegressor and tuned max_depth, n_estimators, and min_samples_split using GridSearchCV with 5-fold cross validation. The best hyperparameters I got were max_depth=10, min_samples_split=10, and n_estimators=100.

The final model achieved a train RMSE of 2,305 minutes and a test RMSE of 2,548 minutes! In comparision, the baseline test RMSE was 7,087 minutes. That is roughly a 64% drop in test RMSE. The train/test gap also got much smaller, which means the model is overfitting a lot less.

<iframe src="assets/feature-importance.html" width="800" height="450" frameborder="0" ></iframe>

This feature importance chart shows which variables the random forest relied on most. As you can see, log-transformed customer count is the top predictor, which makes sense since larger outages generally take longer to restore. Cause category features also rank highly, which lines up with the earlier finding that severe weather and fuel supply emergencies cause the longest outages.

<iframe src="assets/residual-plot.html" width="800" height="450" frameborder="0" ></iframe>

This residual plot compares prediction errors for the baseline and final model on the same test set. The points closer to the horizontal zero line mean that they are more accurate predictions. The final model's errors are more tightly clustered around zero across the range of predicted values, while the baseline model has larger and more spread out errors, especially for longer outages. Both models tend to underpredict very long outages, which is expected since those events are rare and hard to predict.

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Fairness Analysis

I tested whether my final model performs fairly across outages in highly urbanized vs. rural states, split by the median of AREAPCT_URBAN.

• Group X (high urbanization): outages where AREAPCT_URBAN is above the median
• Group Y (low urbanization): outages where AREAPCT_URBAN is at or below the median
• Evaluation metric: RMSE
• Null hypothesis: the model is fair. Its RMSE for high urbanization and low urbanization outages are roughly the same, and any difference is just due to random chance.
• Alternative hypothesis: the model is unfair. Its RMSE is higher for low urbanization outages than high urbanization outages.
• Test statistic: difference in RMSE (low urbanization RMSE minus high urbanization RMSE)
• Significance level: 0.05
• Result: observed difference = 628.28 minutes, p-value = 0.196

Since the p-value is above 0.05, I fail to reject the null hypothesis. The difference in performance between the two groups is not statistically significant and could reasonably be due to random chance.

<iframe src="assets/fairness-permutation.html" width="800" height="450" frameborder="0" ></iframe>

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Conclusion

The main takeaway from my project is that outage duration is driven heavily by cause category, though climate region and season also matter.

For cause categories, severe weather and fuel supply emergencies produce much longer outages than other causes, and this is true across different seasons and regions. The hypothesis test confirmed that severe weather outages last significantly longer than intentional attack outages on average. Season also mattered. Fall outages tend to be the worst for severe weather, likely because of hurricane season, while winter fuel supply emergencies can last roughly two weeks.

The final model improved on the baseline by a lot, cutting test RMSE from about 7,087 minutes down to 2,548 minutes. I improved the model by 1. adding CLIMATE.REGION and SEASON as features, 2. log-transforming customer counts, 3. capping extreme outliers, and 4. tuning hyperparameters. The fairness analysis found no significant difference in model performance between high and low urbanization areas.

However, there is still a lot of room to improve on. The model still struggles with very long outages since those are rare and hard to predict from the available features. I think it would also be helpful to include data that has information on 1. the age and size of local grid infrastructure, 2. the number of repair crews available at the time of the outage, and 3. storm severity for weather-related events. Another limitation is that the dataset only goes through 2016, so it may not reflect trends for more recent power outages.

Nevertheless, my project shows that it's possible to build a model that meaningfully predicts outage duration using a relatively simple set of features. And I also learned a lot about what makes power outages last as long as they do.