Can you predict power outage duration?

Dylan Babitch

dbabitch@umich.edu

The Dataset

The Dataset used for this analysis was from the Purdue University Laboratory for Advancing Sustainable Critical Infrastructure. It tracked major power outages in the United States from January 2000 to July 2016. Major outages are those with at least 50,000 customers impacted and/or with a load loss greater 300MW. It also tracked various pieces of information about the location the outage occured, information about energy prices and usage, and much more. This dataset provides crucial information for power companies and consumers that can help them predict future outages and their severity. The question that I will be trying to answer using this dataset is can you predict the length of a power outage?

The dataset has a total of 1534 rows, however some were removed throughout analysis due to them lacking crucial information needed to predict outage duration.

The columns of the dataset are as follows1:

Column Name Description
YEAR Year the outage occured
MONTH Month the outage occured
U.S._STATE US State where the outage occured
POSTALCODE The postal code of where the outage occured
NERC.REGION The North American Electric Reliability Corporation’s region that the outage occured
CLIMATE.REGION The type of climate the outage occured, based on classifications from the National Centers for Environmental Information
ANOMALY.LEVEL The oceanic El Niño/La Niña index
CLIMATE.CATEGORY The climate episode corresponding to the year the outage took place
OUTAGE.START.DATE The date the outage began
OUTAGE.START.TIME The time the outage began
OUTAGE.RESTORATION.DATE The date the outage was resolved
OUTAGE.RESTORATION.TIME The time the outage was resolved
CAUSE.CATEGORY The general category of event that caused the outage
CAUSE.CATEGORY.DETAIL The specific category of the event that caused the outage
HURRICANE.NAMES The name of the hurricane that caused the outage, if applicable
OUTAGE.DURATION The length of the outage in minutes
DEMAND.LOSS.MW The amount of peak demand lost during the outage in Megawatts
CUSTOMERS.AFFECTED The number of customers impacted by the outage
POPULATION The population of the state the outage occured in
POPPCT_URBAN The percent of people who live in an urban area in the state the outage occured

Data Cleaning and Exploratory Data Analysis

Data Cleaning

I began cleaning the data by creating two new columns, OUTAGE.START and OUTAGE.RESTORATION, that contained Pandas datetime objects that combined the OUTAGE.START.DATE and OUTAGE.START.TIME column into one (and the same for restoration).

I then removed all the outages that lasted less than 5 minutes in total. This was an arbitrary choice I made, however I felt like it is a good cutout between not removing too many rows and also not looking at outages that have very little impact because they didn’t last long enough. After removing these rows, I then divided the remaining rows in the OUTAGE.DURATION column by 60 to convert them into hours.

Following this I made the CAUSE.CATEGORY.DETAIL all in title case and then removed all the detailed causes with less than 3 occurances because they made the predictions more difficult.

After cleaning, the first 10 columns of the dataframe looked like2::

CAUSE.CATEGORY CAUSE.CATEGORY.DETAIL DEMAND.LOSS.MW CLIMATE.REGION POPPCT_URBAN OUTAGE.DURATION
intentional attack Vandalism nan East North Central 73.27 10.5178
severe weather Heavy Wind nan East North Central 73.27 50
severe weather Thunderstorm nan East North Central 73.27 42.5
severe weather Winter Storm nan East North Central 73.27 31
severe weather Tornadoes nan East North Central 73.27 49.5

Univariate Analysis

This plot shows the distribution of Cause Categories between different outages. From this plot I can see that storms and vandalism are by far the most common cause of major power outages in the dataset.

Bivariate Analysis

This plot shows the mean outage duration by climate region. From the chart, I can tell that areas with more hurricanes like the east coast and south tend to have longer outages while regions in the north and west tend to have shorter outages.

Interesting Aggregates

Heatmap showing Avg. Outage Duration by Climate Region & Cause

This chart shows the average duration of an outage by Climate Region and Cause Category. This shows that certain causes like hurricanes have a big impact in almost all regions and wildefires in dryer regions like the west tend to have greater impacts on outage duration.

Imputation

I used mean value imputation on the columns without an OUTAGE.DURATION. I imputated by the average for the other outages with the same CAUSE.CATEGORY.DETAIL.

The Prediction Problem

The problem I will be trying to predict the duration of a power outage. This problem will involve regression because the duration of an outage is a continuous, numerical value. The variable I will be predicting is outage duration in minutes (the cleaned OUTAGE.DURATION column).

I will be using mean squared error to evaluate the model’s performance because it is a good indicator of how off the predictions the model makes are from the actual duration of the outages. I chose it over other metrics like mean absolute error because I feel as though the impact of a bad predicition increases more quadratically rather than linearly. This is because a very far off prediction can greatly impact how much a consumer or company cares about a specific outage, causing them to over or under estimate how much they should prepare.

Baseline Model

I first started by creating my own custom Imputer that fills in the NA values of DEMAND.LOSS.MW that takes the mean for the other rows with the same CAUSE.CATEGORY

    from sklearn.base import BaseEstimator, TransformerMixin

    class CategoryMeanImputer(BaseEstimator, TransformerMixin):
        def __init__(self, category_col, value_col):
            self.category_col = category_col
            self.value_col = value_col

        def fit(self, X, y=None):
            self.category_means_ = (
                X
                .groupby(self.category_col)[self.value_col]
                .mean()
                .to_dict()
            )
            self.global_mean_ = X[self.value_col].mean()
            return self

        def transform(self, X):
            X = X.copy()
            X[self.value_col] = X.apply(
                lambda row: (
                    self.category_means_.get(row[self.category_col], self.global_mean_)
                    if pd.isna(row[self.value_col])
                    else row[self.value_col]
                ), axis=1
            )
            return X

Then I created my model:

    from sklearn.pipeline import Pipeline
    from sklearn.compose import  ColumnTransformer
    from sklearn.preprocessing import OneHotEncoder
    from sklearn.linear_model import LinearRegression
    from sklearn.metrics import mean_squared_error


    pipeline = Pipeline([
        ('imputer', CategoryMeanImputer('CAUSE.CATEGORY', 'DEMAND.LOSS.MW')),
        ('features', ColumnTransformer([
            ('detail_ohe', OneHotEncoder(handle_unknown='ignore'), ['CAUSE.CATEGORY.DETAIL']),
            ('mw', 'passthrough', ['DEMAND.LOSS.MW'])
        ], remainder='drop')), 
        ('regressor', LinearRegression())
    ])

    pipeline.fit(X_train,y_train)

In this model I used two features, CAUSE.CATEGORY.DETAIL and DEMAND.LOSS.MW. CAUSE.CATEGORY.DETAIL is a quantitative feature and DEMAND.LOSS.MW is nominal. I chose these two columns because I felt like they would be good predictors of total outage duration. This is because certain causes lead to longer outages and the total amount of demand lost is a good predictor of length of outage.

As described earlier, I had to impute missing values in DEMAND.LOSS.MW with their means from other outages with the same CAUSE.CATEGORY (this is not the same as CAUSE.CATEGORY.DETAIL, CAUSE.CATEGORY is a broader category that I used because it had fewer total categories meaning that imputing using it would likely be more accurate). I also had to one hot encode the CAUSE.CATEGORY.DETAIL column to allow it to be used. After this I preformed a simple linear regression on the columns and then fit the data to it with the training data set.

With this model, I achieved a mean squared error of about 6085 hours or 253 days. Square rooting this, it means my average predicition was a little less than 16 days off on average. I do not feel like this is a good predicition because it meant that the average predicition was over half a month off the true value.

Final Model

After tweaking the columns used and other factors, I arrived at my final model:

    from sklearn.linear_model import Ridge, Lasso, ElasticNet, BayesianRidge
    from sklearn.preprocessing import PowerTransformer, QuantileTransformer
    from sklearn.model_selection import GridSearchCV

    qt = QuantileTransformer(
        n_quantiles=100,
        output_distribution="normal",
        random_state=98
    )

    pipeline = Pipeline([
        ('imputer', CategoryMeanImputer('CAUSE.CATEGORY', 'DEMAND.LOSS.MW')),
        ('features', ColumnTransformer([
            ('detail_ohe', OneHotEncoder(handle_unknown='ignore'), ['CAUSE.CATEGORY.DETAIL', 'CLIMATE.REGION']),
            ("quantile_loss", qt, ["DEMAND.LOSS.MW", 'POPPCT_URBAN'])
        ], remainder='drop')),
        ('regressor', Ridge())
    ])



    gridSearch = GridSearchCV(
        pipeline,
        param_grid = {'regressor__solver': ["auto","lsqr","sparse_cg","sag"], 
                    'regressor__max_iter': [10, 100, 1000, 5000, 10000, 50000], 
                    'regressor__alpha': [0, 0.001, 0.01, 0.1, 1, 1.5, 1.6, 10]},
        scoring='neg_mean_squared_error'
    )

    gridSearch.fit(X_train,y_train)

For the final model I added two new features. Firstly, I added CLIMATE.REGION to the model. I did this because I noticed that certain regions tended to lead to longer outages on average. This could be for many reasons such as why the outage was caused and the ability of the workers and availability of resources in certain regions. I found this caused a drop of mean squared error of about 300 hours. The other feature I added was POPPCT_URBAN which is the percent of people in the state which live in an urban area. I did this because outages in urban areas tend to be solved faster because of less distance between potentional power stations and there typically are more people impacted. I found this feature decreased mean squared error by about 75 hours, so not a massive improvement but still helpful.

Additionally, I switched from linear regression to ridge regression. This was for a few reasons. Firstly, ridge regression can deal with multicolinearity in the data which I noticed in the CLIMATE.REGION and POPPCT_URBAN categories. This is because there tends to only be a handful of states in each climate region meaning it is correlated to the states percentage of urban population. I found that this increased my model’s performance over simple linear regression.

Additionally, I added a quantile transformer function to the DEMAND.LOSS.MW and POPPCT_URBAN columns. This is because it helps create a normal distribution from a skewed dataset. This is because I saw that both datasets had a left skew to them and wanted to ensure that these outliers did not have too much impact on the final model.

I used GridSearchCV to find the optimal hyperparameters for the Ridge Regression functions. The values I found were:

Hyperparameter Optimal Value
Alpha 1.6
Max_iter 10
Solver lsqr

This finalized model achieved a mean squared error of 5573 hours or 232 days. This is an improvement of a little over 500 hours squared over my original model. This means an average of around 4.5 days more accuracy over the original prediction. This is a big improvement and means that that my new predictions are far closer to the true values than the original ones.

  1. There are more columns in the dataset that were ignored because they have little to no relevance to the analysis. ↩

  2. The nan values in DEMAND.LOSS.MW are fixed later using imputation ↩