Estimating Power Outage Duration With Scikit-Learn and Pandas DataFrames
Introduction
Welcome! On this page I share the results of a project I completed for a data science course at the University of Michigan.
Data Introduction and Question Identification
For this project I chose to work with this spreadsheet from civil engineering researchers at Purdue University. It contains thorough data on major power outages across the United States from January 2000 to July 2016. Each row contains information on a single outage, reporting details like time, location, cause, and impact (which includes how long the outage lasted, how much it cost, and how many people were affected). The whole table has 1534 rows and 55 columns.
The general question I wanted to answer with this data was: based on where you are, how much will you be affected by major power outages? For example, can you predict how long a power outage will last in a warm urban area in the southeast?
The relevant columns of the data are singled out and described below.
- ‘MONTH’: When the outage took place in the year.
- ‘CLIMATE.REGION’: Which National Centers for Environmental Information designated climate region the outage took place in. (Interactive map here, though the regions seem to have been renamed since this data was released.)
- ‘NERC.REGION’: Which North American Electric Reliability Corporation (NERC) region the outage took place in. (Map of these regions) I chose to use this as well as the more geographical ‘CLIMATE.REGION’ column because while they largely overlap, I think allowing for differences between “climate region” and “power region” is worthwhile.
- ‘ANOMALY.LEVEL’ and ‘CLIMATE.CATEGORY’: the effects of El Niño at the time and place of the outage, based on the Oceanic Niño Index.
- ‘AREAPCT_URBAN’ and ‘AREAPCT_UC’: how much of the state’s land is taken up by urban (population >50,000) and urban cluster (population 2,500 - 50,000 people) areas, in percent.
Data Cleaning and Exploratory Data Analysis
Data Cleaning
I started by reading the Excel spreadsheet into a Pandas DataFrame. I read the raw data, set the correct row indeces and column names, and converted numerical columns from strings to integers and floats. I also converted the start and end time and date columns from strings to timestamp objects. The first few rows of this cleaned DataFrame can be seen below, though most of the columns have been cropped for space. Some rows were missing almost all data (effectively only reporting that an outage occured in a state once), which were dropped due to not providing enough detail to meaningfully impute.
| YEAR | MONTH | POSTAL.CODE | NERC.REGION | CLIMATE.REGION | ANOMALY.LEVEL | CLIMATE.CATEGORY |
|---|---|---|---|---|---|---|
| 2011 | 7 | MN | MRO | East North Central | -0.3 | normal |
| 2014 | 5 | MN | MRO | East North Central | -0.1 | normal |
| 2010 | 10 | MN | MRO | East North Central | -1.5 | cold |
| 2012 | 6 | MN | MRO | East North Central | -0.1 | normal |
| 2015 | 7 | MN | MRO | East North Central | 1.2 | warm |
Univariate Analysis
While I didn’t use the state column directly, I started out by plotting the distribution of outages by state. A handful of states were the sources of a significant portion of the outages.
Later, I plotted the average duration of outages by state. This plot looks noticably different from the one above, suggesting outage frequency is unrelated to duration. (I was surprised to see Wisconsin of all states having the highest average; turns out the longest recorded duration for an outage in the data is 75 days, held by one from Wisconsin from 2014. The state had severe storms that year, so this checks out.)
Bivariate Analysis
This plot shows the distribution of outages based on cause. Many of them (‘intentional attack’ and ‘severe weather in particular’) have significant amounts of outliers, which will make prediction difficult.
Interesting Aggregates
The table below shows the average duration of outages by NCEI region and overall climate category. One could try to make takeaways like “outages in the West North Central region are 87 times worse when El Niño makes the climate warmer,” but I think the relationships here are simple enough to allow for statements based on one pivot table.
| CLIMATE.REGION | cold | normal | warm |
|---|---|---|---|
| Central | 2799.86 | 2708.7 | 2413.84 |
| East North Central | 6568.79 | 5271.22 | 3022.12 |
| Northeast | 3657.25 | 2261.33 | 4175.91 |
| Northwest | 874.681 | 733.612 | 3063.54 |
| South | 2012.71 | 3753.06 | 1861.4 |
| Southeast | 1707.07 | 2392.27 | 2528.94 |
| Southwest | 544.591 | 296.136 | 5127.68 |
| West | 1762.71 | 1249.84 | 2044.23 |
| West North Central | 200 | 28.4286 | 2486.5 |
Imputation
To deal with missing duration values, I imputed them with the overall median duration (since no relationship was clear between the rows missing values). I chose to use the median over the mean due to how many outliers can be seen in the data. The effect this had on distribution is visible below; the added values end up filling out the curved shape of the distribution.
Framing a Prediction Problem
The specific problem my model was to solve is this: given information about the time, location, and environmental conditions of a theoretical major power outage, predict the duration of the outage. This is a straightforward regression problem. I will gauge performance using mean squared error, due to its moderate sensitivity toward outliers.
Baseline Model
My baseline model was a basic linear regression model, with the only transformation involved being one-hot encoding all categorical columns (making all features quantitative or nominal). The model’s performance is shown in the table below, showing mean squared error for the data it was trained on, cross-validation data, and the test data.
| Training | Validation | Testing |
|---|---|---|
| 3.12349e+07 | 6.2102e+06 | 4.68994e+07 |
This is servicable, but not great: it’s effectively throwing all the variables together and taking whatever comes out. There’s a lot of room to improve.
Final Model
First, I put all numerical features through a pipeline consisting of a standard scaler and a polynomial feature generator. The polynomial degree was chosen from 1 to 5 via grid search. (I tried separating the different features out into separate pipelines, but I never found a combination that surpassed this naive one). Additionally, I changed the encoding of the climate category column from one-hot to ordinal (so the values [cold, normal, warm] became [0, 1, 2])—this better communicates that the three are on a scale. I tried several different modeling algorithms—specifically linear regression, LASSO, ridge regression, and k nearest neighbors. Ridge’s alpha parameter and KNN’s number of neighbors were also chosen with grid search.
| Algorithm | Training | Validation | Testing |
|---|---|---|---|
| Baseline | 3.12349e+07 | 6.2102e+06 | 4.68994e+07 |
| Linear | 3.033e+07 | 5.58904e+06 | 4.62628e+07 |
| LASSO | 3.03334e+07 | 5.54924e+06 | 4.62721e+07 |
| Ridge | 3.06578e+07 | 5.07339e+06 | 4.68769e+07 |
| KNN | 2.50766e+07 | 9.96246e+06 | 4.42579e+07 |
Comparing each version’s results, I decided to go with the one using ridge regression as my final model. With the lowest validation error by far, I trust it the most to generalize the most to unseen data.
Using this new model I can predict that, in Michigan, during April, while the climate is warmer than usual, the expected duration of a major power outage is… 78 hours! A similar outage at the same time in California would only be 30 hours. Maybe our regional outage response infrastructure needs some work…