Whens The Power Coming back? : Analyzing Power Outages

Project for DSC 80 at UCSD

By Kaushik Agastyaraju

Introduction

Welcome! My name is Kaushik Agastyaraju and I recently completed analyis on a dataset of power outages. The following will be an explanation of my processes and analysis.

This project was meant to investigate a dataset of major power outages in the U.S. that took place from January 2000 to July 2016. These power outages, as defined by the Department of Energy, were included in the dataset if they impacted at least 50,000 customers or caused an unplanned energy demand loss of at least 300 megawatts. The dataset includes many features of data including: geographical, climatic, economic, and land-use data about the states affected. And by conducting open ended analysis I attempted to uncover a very small subset of the trends buried within this dataset.

Uplpading and understanding the data was the first step in this process. I downloaded the data from Purdue University’s Laboratory for Advancing Sustainable Critical Infrastructure, at https://engineering.purdue.edu/LASCI/research-data/outages.

From there I took steps to clean the dataset which would then allow me to perform exploratory data analysis, first through varaible analsysis, then through variable missingness and finally through statistical testing. After loading in the data and observing the features of power outages I decided on my main research question for this analysis:

Research Question

The primary question explored is: What are the key factors influencing outage duration and its severity, and how can we predict the cause of an outage?

Understanding how long power outages last is essential for helping communities recover and build resilience. The length of an outage doesn’t just show how severe the issue was—it also reveals how quickly and efficiently power is restored. Longer outages can have ripple effects, disrupting vital services like healthcare and communication, impacting local economies, and even putting public safety at risk. By examining what causes these delays, energy companies can uncover key challenges, such as aging infrastructure, delays in deploying repair teams, or the sheer size of the incident. This understanding can guide better planning, ensuring resources are in place to respond faster and reduce the impact on everyday life.

Dataset Details

The dataset contains 1534 rows and focuses on the following relevant columns for analysis:

Column	Description	Data Type
`YEAR`	Year when the outage occurred	Integer
`MONTH`	Month when the outage occurred	Integer
`U.S._STATE`	State where the outage occurred	String
`NERC.REGION`	North American Electric Reliability Corporation (NERC) region involved in the outage	String
`CLIMATE.REGION`	U.S. Climate regions as specified by the National Centers for Environmental Information	String
`ANOMALY.LEVEL`	Oceanic El Niño/La Niña (ONI) index for the cold and warm episodes by season	Float
`CLIMATE.CATEGORY`	Classification of the climate episode as “Warm,” “Cold,” or “Normal” based on ONI threshold	String
`OUTAGE.START.DATE`	Day of the year when the outage started	Date
`OUTAGE.START.TIME`	Time of day when the outage started	Time
`OUTAGE.RESTORATION.DATE`	Day of the year when power was restored	Date
`OUTAGE.RESTORATION.TIME`	Time of day when power was restored	Time
`OUTAGE.DURATION`	Duration of the outage (in minutes)	Integer/Float
`CAUSE.CATEGORY`	Broad category of the cause of the outage	String
`CAUSE.CATEGORY.DETAIL`	Detailed description of the specific cause of the outage	String
`HURRICANE.NAMES`	Name of the hurricane (if the outage was hurricane-related)	String (Nullable)
`DEMAND.LOSS.MW`	Amount of peak demand lost during the outage (in megawatts)	Float
`CUSTOMERS.AFFECTED`	Number of customers affected by the outage	Integer
`POPULATION`	Population in the state where the outage occurred	Integer
`POPPCT_URBAN`	Percentage of the state’s population living in urban areas	Float
`POPDEN_URBAN`	Population density of urban areas (persons per square mile)	Float
`POPDEN_RURAL`	Population density of rural areas (persons per square mile)	Float
`TOTAL.PRICE`	Average monthly electricity price in the state (cents/kilowatt-hour)	Float
`RES.PRICE`	Monthly electricity price in the residential sector (cents/kilowatt-hour)	Float
`TOTAL.SALES`	Total electricity consumption in the state (megawatt-hour)	Float
`RES.SALES`	Electricity consumption in the residential sector (megawatt-hour)	Float
`IND.SALES`	Electricity consumption in the industrial sector (megawatt-hour)	Float

This selection of columns ensures focus on essential data for understanding and analyzing power outages, their duration, and their impacts across the U.S.

Data Cleaning and Exploratory Data Analysis

Data Cleaning

The dataset was cleaned using the following steps:

Column Selection: Irrelevant columns were dropped, focusing on features listed above.
Date-Time Conversion: Combined OUTAGE.START.DATE and OUTAGE.START.TIME into a single column. Similarly, combined restoration date and time.
Handling Missing Values: Zero values in OUTAGE.DURATION, CUSTOMERS.AFFECTED, and DEMAND.LOSS.MW were replaced with NaN since these represent missing data.

Exploratory Data Analysis

Exploratory data analysis of the outages dataset allowed me to better understand the data I was working with: Understand the features and thier relations. These steps would allow me to stage more complex missingness and modeling questions later in the project

Univariate Analysis - Exploring single Variables

My univariatne analysis began with looking at the distribution of outages durations to understand the frequency of outage durations in the dataset

Outage Duration: A majority of outages lasted under 5000 minutes, less than 250 happened between 5000 and 20000, but a few extreme cases exceeded 3000 minutes.

From there I looked at the distribution of customers affected. This was to understand the frequency of customers affected for each otuages across the dataset

Customers Affected: The distribution of customers affected is heavily skewed right, meaning the majority outages affected less than 1 million people, with a few cases affecting more

Bivariate Analysis

Outage Duration vs. Customers Affected:
- Positive correlation, though some short outages affected many customers.`

Outage Duration vs. Cause Category:
- Severe weather caused longer outages than intentional attacks.

Grouping and Aggregates

By NERC Region: Grouping the data by climate regeion allowed me to look at the sum and average of customers affect by each region.

By Climate Region and Cause: Creating a pivot table and grouping by cause category and climate region further grouped the data allowing me to look at primary causes of outages based on region which can reveal issues within any specific region.

Assessment of Missingness

NMAR Analysis

I believe the ‘CAUSE.CATEGORY.DETAIL’ column might be NMAR (Not Missing At Random). The missingness in this column could be due to utility companies not fully investigating or reporting detailed causes for certain outages. For instance, an outage categorized as “equipment failure” might not have the specific specific details if the issue had many overlapping problems or if the investigation was left incomplete. The resources to investigate power outages may not be worth it when this is a continous occurence.

To potentially make this missingness MAR (Missing At Random), additional data about the reporting protocols used by utilities or the resources allocated to post-outage investigations would be useful.

Dependency Analysis

Analyzing the dependency of missing values in the duration column provides valuable insights for better data imputation strategies. These dependencies can help identify patterns or relationships that contribute to missing data, enabling more informed and accurate imputation methods.

To better understand the missingness dependecy of the duration column I will test with cause category and customers affected.

Cause Category:

The first step in missingness dependecy is to look at the distribution of cause category given the missingness of duration. similiarites in these bars may indiicate a dependency.

Null Hypothesis: The distribution of cause category is the same when Duration is missing vs not missing

Alternate Hypothesis: The distribution of cause category is the different when Duration is missing vs not missing

Observed Total Variation Distance (TVD): 0.469
P-value: 0.0
Conclusion: This p-value indicates rejection of the null hypothesis in favor of the alterhante meaning Missingness in OUTAGE.DURATION liekley depends on CAUSE.CATEGORY.

Customers Affected

Here we look at a violin plot showing the distribution of Customers Affected given the missingness of duration.

Null Hypothesis: The distribution of customers affected is the same when Duration is missing vs not missing

Alternate Hypothesis: The distribution of customers affected is different when Duration is missing vs not missing

Observed Difference in Means: -7685.716
P-value: 0.8980
Conclusion: At This p-value we fail to reject the null hypothesis in favor of the alterhante meaning the distribtuion is not very different wehn duration is missing, meaning there is likely no dependency between the missingness of Duration and the Customers Affected

Hypothesis Test: Outage Duration and Residential Electricity Prices

For this section I will be testing whetere outage duration differs between low and high residiantial price areas.

Hypotheses:

Null: The mean outage duration is the same for low and high residential electricity price areas.
Alternative: The mean outage duration differs between low and high residential electricity price areas.

Test Statistic and Significance Level:

Test Statistic: I chose the difference in means because it directly compares the groups of interest.
Significance Level: I used a standard significance level of 0.05.

Results:

Observed Difference: ( 397.914 ) minutes.
P-value: ( 0.1970 ).

Conclusion:

Since the p-value 0.1970 is greater than 0.05, I fail to reject the null hypothesis. There isn’t enough evidence to conclude that outage durations differ significantly between low and high residential electricity price areas. The observed difference could simply be due to random chance.

Visualization:

Below is a histogram showing the empirical distribution of permutation differences. The dashed red line represents the observed difference.

Framing a Prediction Problem

Problem Statement

For this project, I am creating a regression model where the goal is to predict the duration of power outages (OUTAGE.DURATION). I chose outage duration as the response variable because it is critical for understanding the severity of outages, improving preparedness, and allowing improved resource allocation for restoration efforts.

At the time of prediction, I assume we would know features like the number of customers affected (CUSTOMERS.AFFECTED) and the cause of the outage (CAUSE.CATEGORY). These are reasonable inputs because they are typically available shortly after an outage begins or is reported.

To evaluate the performance of the regression model, I am using Mean Absolute Error (MAE) as the evaluation metric. I chose MAE because it provides a clear measure of prediction accuracy by quantifying the average difference between predicted and actual durations in minutes. Unlike metrics such as Mean Squared Error, MAE is less sensitive to outliers, making it a practical choice for understanding average model performance.

By focusing on these features and using MAE, I aim to create a model that is both interpretable and effective for predicting outage durations in real-world scenarios.

Baseline Model

For my baseline model, I aimed to predict outage duration (OUTAGE.DURATION) using two features:

Number of Customers Affected (CUSTOMERS.AFFECTED) - Quantitative
Cause Category (CAUSE.CATEGORY) - Nominal

Predicting outage duration is crucial for efficient resource allocation, minimizing disruptions, and helping communities and utilities better prepare for and respond to power outages.

Feature Encoding:

I left CUSTOMERS.AFFECTED as-is since it’s a numeric column.
I used one-hot encoding for CAUSE.CATEGORY to handle its categorical nature.

Model:

I used a Linear Regression model. To preprocess the data:

Numeric features were passed through directly.
Categorical features were one-hot encoded using a pipeline.

I split the dataset into training (80%) and test (20%) sets to evaluate the model.

Performance:

The Mean Absolute Error (MAE) on the test set was X.XX minutes. This metric indicates the average difference between the actual and predicted outage durations.

Reflection:

This baseline model is simple and gives a starting point for further improvements. While the MAE provides some insight into the model’s accuracy, I believe it could be improved by incorporating additional features (e.g., climate data, residential electricity prices) or trying a more sophisticated model.

Final Model

Final Model and Feature Selection

For my final model, I implemented a search algorithm to determine the best combination of features for predicting outage duration (OUTAGE.DURATION). The model evaluated different subsets of features based on their performance, and measured their performance based on Mean Absolute Error (MAE).

The features selected by this process are:

Quantitative Features:
- DEMAND.LOSS.MW
- CUSTOMERS.AFFECTED
- POPDEN_URBAN
- TOTAL.PRICE
Nominal Features:
- U.S._STATE
- CAUSE.CATEGORY

Modeling Algorithm and Hyperparameters

I used Linear Regression as the modeling algorithm, integrated within a preprocessing pipeline:

Numerical Features:
- Scaled using StandardScaler.
- Since the model couldn’t run given missing values I imputed with the median.
Categorical Features:
- Encoded using OneHotEncoder, with support for unknown categories.
- Missing values were imputed with a placeholder value (missing) this would make sure that missing values again wouldn’t affect the model perforamce

The pipeline was tested on various combinations of features, using a loop to evaluate their performance. This approach allowed an unbiased feature selection process based on the data and MAE

Model Performance

Final Model Performance:
- Selected Features: DEMAND.LOSS.MW, CUSTOMERS.AFFECTED, POPDEN_URBAN, TOTAL.PRICE, U.S._STATE, CAUSE.CATEGORY
- Mean Absolute Error (MAE): 1944.39 minutes
Baseline Model Performance:
- Features: CUSTOMERS.AFFECTED, CAUSE.CATEGORY
- Mean Absolute Error (MAE): 2358.12 minutes

The final model improved upon the baseline by reducing the prediction error by approximately 400 minutes.

Conclusion

By automating feature selection, I allowed the data to guide the process of building a better model. The final feature set effectively captures the factors influencing outage duration, leading to a more accurate and actionable prediction model.

Fairness Analysis

Groups for Comparison

For the fairness analysis, I compared two groups: highly affected outages (with customers affected above the median) and lowly affected outages (with customers affected at or below the median). These groups were chosen to investigate if the model performs differently based on the number of customers affected.

Evaluation Metric

I used Mean Absolute Error (MAE) as the evaluation metric because it quantifies the average prediction error in a straightforward and interpretable way. This is ideal for understanding prediction accuracy across the two groups.

Hypotheses

Null Hypothesis: The model is fair. The MAE for highly and lowly affected groups is similar, and any observed difference is due to random chance.
Alternative Hypothesis: The model is unfair. The MAE for highly and lowly affected groups is significantly different.

Test Statistic and Significance Level

The test statistic used was the difference in MAE between the two groups. I set the significance level ((\alpha)) to 0.05.

Results

Observed MAE Difference: 1972.95
P-value: 0.0

Conclusion

Since the p-value is less than the significance level alpha = 0.05, I reject the null hypothesis. This indicates that the model’s performance differs significantly between highly and lowly affected groups, suggesting potential unfairness.

Visualization

The figure below shows the distribution of the MAE differences under the null hypothesis, with the observed difference marked: