Exploratory Data Analysis of Major Outages

By Diego Silva (d1silva@ucsd.edu). My multiclass classification model on this dataset can be found here.

Introduction

In this project, I cleaned and analyzed a data set containing major outages reported by different states in the United States from January 2000-July 2016. The main question I want to answer in this analysis, is there a significant difference between the outages distributions of the seasons in the SPP Region and the Overall outages distributions of the seasons of the NERC Regions? This data set and analysis provide an understanding of major outage patterns and how in the future they can be avoided to improve our national electrical infrastructure. Moving forward I will reference the data set as Outages.  

Cleaning and EDA

In my data cleaning process, I first looked at the raw data set to assess what steps needed to be done. I looked for any unnecessary rows and columns, checked the column names, and anything else that looked out of the ordinary for a data set. In my specific case, I noticed there were a couple of columns and rows that were unnecessary and the column names were incorrect. So I dropped said columns and rows, set the columns to their proper respective names, and reset the index of the data frame. Lastly, I ensured the data types of the columns were the best possible type that allowed me to properly analyze the data frame.  

YEAR	MONTH	U.S._STATE	POSTAL.CODE	NERC.REGION	CLIMATE.REGION	ANOMALY.LEVEL	CLIMATE.CATEGORY	CAUSE.CATEGORY	CAUSE.CATEGORY.DETAIL	HURRICANE.NAMES	OUTAGE.DURATION	DEMAND.LOSS.MW	CUSTOMERS.AFFECTED	RES.PRICE	COM.PRICE	IND.PRICE	TOTAL.PRICE	RES.SALES	COM.SALES	IND.SALES	TOTAL.SALES	RES.PERCEN	COM.PERCEN	IND.PERCEN	RES.CUSTOMERS	COM.CUSTOMERS	IND.CUSTOMERS	TOTAL.CUSTOMERS	RES.CUST.PCT	COM.CUST.PCT	IND.CUST.PCT	PC.REALGSP.STATE	PC.REALGSP.USA	PC.REALGSP.REL	PC.REALGSP.CHANGE	UTIL.REALGSP	TOTAL.REALGSP	UTIL.CONTRI	PI.UTIL.OFUSA	POPULATION	POPPCT_URBAN	POPPCT_UC	POPDEN_URBAN	POPDEN_UC	POPDEN_RURAL	AREAPCT_URBAN	AREAPCT_UC	PCT_LAND	PCT_WATER_TOT	PCT_WATER_INLAND	OUTAGE.START	OUTAGE.RESTORATION
2011	7	Minnesota	MN	MRO	East North Central	-0.3	normal	severe weather	nan	nan	3060	nan	70000	11.6	9.18	6.81	9.28	2.33292e+06	2.11477e+06	2.11329e+06	6.56252e+06	35.5491	32.225	32.2024	2308736	276286	10673	2595696	88.9448	10.644	0.411181	51268	47586	1.07738	1.6	4802	274182	1.75139	2.2	5348119	73.27	15.28	2279	1700.5	18.2	2.14	0.6	91.5927	8.40733	5.47874	2011-07-01 17:00:00	2011-07-03 20:00:00
2014	5	Minnesota	MN	MRO	East North Central	-0.1	normal	intentional attack	vandalism	nan	1	nan	nan	12.12	9.71	6.49	9.28	1.58699e+06	1.80776e+06	1.88793e+06	5.28423e+06	30.0325	34.2104	35.7276	2345860	284978	9898	2640737	88.8335	10.7916	0.37482	53499	49091	1.08979	1.9	5226	291955	1.79	2.2	5457125	73.27	15.28	2279	1700.5	18.2	2.14	0.6	91.5927	8.40733	5.47874	2014-05-11 18:38:00	2014-05-11 18:39:00
2010	10	Minnesota	MN	MRO	East North Central	-1.5	cold	severe weather	heavy wind	nan	3000	nan	70000	10.87	8.19	6.07	8.15	1.46729e+06	1.80168e+06	1.9513e+06	5.22212e+06	28.0977	34.501	37.366	2300291	276463	10150	2586905	88.9206	10.687	0.392361	50447	47287	1.06683	2.7	4571	267895	1.70627	2.1	5310903	73.27	15.28	2279	1700.5	18.2	2.14	0.6	91.5927	8.40733	5.47874	2010-10-26 20:00:00	2010-10-28 22:00:00
2012	6	Minnesota	MN	MRO	East North Central	-0.1	normal	severe weather	thunderstorm	nan	2550	nan	68200	11.79	9.25	6.71	9.19	1.85152e+06	1.94117e+06	1.99303e+06	5.78706e+06	31.9941	33.5433	34.4393	2317336	278466	11010	2606813	88.8954	10.6822	0.422355	51598	48156	1.07148	0.6	5364	277627	1.93209	2.2	5380443	73.27	15.28	2279	1700.5	18.2	2.14	0.6	91.5927	8.40733	5.47874	2012-06-19 04:30:00	2012-06-20 23:00:00
2015	7	Minnesota	MN	MRO	East North Central	1.2	warm	severe weather	nan	nan	1740	250	250000	13.07	10.16	7.74	10.43	2.02888e+06	2.16161e+06	1.77794e+06	5.97034e+06	33.9826	36.2059	29.7795	2374674	289044	9812	2673531	88.8216	10.8113	0.367005	54431	49844	1.09203	1.7	4873	292023	1.6687	2.2	5489594	73.27	15.28	2279	1700.5	18.2	2.14	0.6	91.5927	8.40733	5.47874	2015-07-18 02:00:00	2015-07-19 07:00:00

 

The bar plot below presents the count of outages that occurred in each U.S. state. One interesting note is that California seems to have a significantly higher count of outages compared to the rest of the states, even though it is not the biggest state by land area.

The scatter plot below presents the relationship between the OUTAGE DURATION and DEMAND LOSS MW columns of Outages. The plot suggests that short Outage Duration times results in a higher Demand Loss (MW) and longer Outage Duration times results in a lower Demand Loss (MW).

 

This table shows gives a break down of Outage CATEGORY CAUSE for each state, showing which Outage ‘CATEGORY.CAUSE’ value is the most and least common among each state. Also gives a general idea of how severe the problem of outages is in each state.  

U.S._STATE	equipment failure	fuel supply emergency	intentional attack	islanding	public appeal	severe weather	system operability disruption
Alabama	0	0	1	0	0	5	0
Alaska	1	0	0	0	0	0	0
Arizona	4	0	18	0	0	4	2
Arkansas	1	0	6	1	7	10	0
California	21	17	24	28	9	70	41
Colorado	0	1	5	1	0	4	4
Connecticut	0	0	8	0	0	10	0
Delaware	1	0	37	0	0	2	1
District of Columbia	1	0	0	0	0	9	0
Florida	4	0	2	0	3	26	10

 

Assessment of Missingness

NMAR Analysis:

In the Outages data frame, the ‘CAUTEGORY.CAUSE.DETAIL’ column is supposed to give a specific reason for the ‘CATEGORY.CAUSE’ of the outage. This column could be NMAR because the reason why a value would be missing can be due to negligence of the person logging the data because they may have felt the specific reason may not be significant enough or if an investigation was not done. This column would be MAR if another column provided information on whether an investigation was done to figure out the specific cause of the outage.

Missingness Dependency:

I wanted to find out a column in which the missingness of ‘CUSTOMERS.AFFECTED’ was dependent and a column in which its missingness was not dependent. For this investigation, I chose the ‘YEAR’ and ‘PC.REALGSP.CHANGE’ columns to test the missingness dependency of these columns.  

Missingness dependency on the ‘YEAR’ column

For my test of the missingness dependency on the ‘YEAR’ column, I first created a distribution plot as seen below. This plot shows the distribution of ‘YEAR’ by missingness of ‘CUSTOMERS.AFFECTED’. To investigate whether the differences in the distributions were significant, I decided to perform a permutation test.  

 

Null Hypothesis: The distribution of ‘YEAR’ when ‘CUSTOMERS’ is missing is the same as the distribution of ‘YEAR’ when ‘CUSTOMERS.AFFECTED’ is not missing.

Alternative Hypothesis: The distribution of ‘YEAR’ when ‘CUSTOMERS’ is missing is not the same as the distribution of ‘YEAR’ when ‘CUSTOMERS.AFFECTED’ is not missing.

I decided to use the total variation distance (TVD) as my test statistic, the observed TVD value I saw was 0.306. Additionally, I chose a significance level of 0.05 as a cut-off for my p-value, since a p-value smaller than 0.05 indicates strong evidence against my null hypothesis. The plot below shows the results of my permutation test. It displays the empirical distribution of the generated TVDs under the null. The green line shows the observed value. The p-value I calculated was essentially 0.  

In conclusion, we reject the null, since my p-value, 0, is smaller than the 0.05 significance level. There is strong enough evidence to suggest the distribution of ‘YEAR’ when ‘CUSTOMERS.AFFECTED’ is missing is not the same as the distribution of ‘YEAR’ when ‘CUSTOMERS.AFFECTED’ is not missing. As a result, the evidence suggests that the ‘CUSTOMERS.AFFECTED’ column may be dependent on the ‘YEAR’ column.  

Missingness Dependency on the ‘PC.REALGSP.CHANGE’ Column

For my test of the missingness dependency on the ‘PC.REALGSP.CHANGE’ column, I first created a kernel density plot as seen below. This plot shows the kernel density of ‘PC.REALGSP.CHANGE’ by missingness of ‘CUSTOMERS.AFFECTED’. Since the difference of means of the plots was 0.0577, which tells us the means of the two distributions are similar. But as seen in the plot the shapes look different. As a result, I decided to test whether the differences in shape were significant or not by using the Kolmogorov-Smirnov (ks) test statistic as my test statistic for this permutation test.

Null Hypothesis: The shape of the distribution of ‘PC.REALGSP.CHANGE’ when ‘CUSTOMERS.AFFECTED’ is missing is the same as the shape of the distribution of ‘PC.REALGSP.CHANGE’ when ‘CUSTOMERS.AFFECTED’ is not missing.

Alternative hypothesis: The shape of the distribution of ‘PC.REALGSP.CHANGE’ when ‘CUSTOMERS.AFFECTED’ is missing is not the same as the shape of the distribution of ‘PC.REALGSP.CHANGE’ when ‘CUSTOMERS.AFFECTED’ is not missing.

Additionally, I chose a significance level of 0.05 as a cut-off for my p-value, since a p-value smaller than 0.05 indicates strong evidence against my null hypothesis.

After performing the permutation test with the ks as my test statistic, I got a p-value of 0.279.

Since the p-value is greater than the 0.05 significance level, we fail to reject the null. There is not enough evidence to suggest that the shape of the distribution of ‘PC.REALGSP.CHANGE’ when ‘CUSTOMERS.AFFECTED’ is missing is not the same as the shape of the distribution of ‘PC.REALGSP.CHANGE’ when ‘CUSTOMERS.AFFECTED’ is not missing. Which suggests the missingness of ‘CUSTOMERS.AFFECTED’ may not be dependent on ‘PC.REALGSP.CHANGE’.

Overall Conclusion For Missingness Dependency Investigation:

In my missingness dependency investigation, I concluded that there is strong enough evidence to suggest that the missingness of the ‘CUSTOMERS.AFFECTED’ column may be dependent on the ‘YEAR’ but the same can not be said for the ‘PC.REALGSP.CHANGE’. Since my investigation shows that there is not enough evidence to suggest that the missingness of ‘CUSTOMERS.AFFECTED’ may not be dependent on ‘PC.REALGSP.CHANGE’.  

Hypothesis Testing

Is there significant difference between the distribution of outages of the seasons in the SPP NERC Region compared to the Overall distribution of outages in the NERC Regions?

To answer my main question I decided to compare the distributions of the outages in each season of the SPP Region and the Overall NERC Region distribution of outages in each season. To create these distributions, I first created a new column called ‘Season’, which stated the season in which the outage occurred. Once I did that I then created a table that displays the distributions, the table below displays a couple of the NERC Regions.  

NERC.REGION	Fall	Spring	Summer	Winter
ECAR	0.235294	0.264706	0.411765	0.0882353
FRCC	0.325581	0.186047	0.325581	0.162791
FRCC, SERC	0	0	0	1
HECO	0.666667	0	0.333333	0
HI	1	0	0	0

 

The plot below displays the distributions of the outages in each season in the SPP Region and the Overall NERC Region distribution of outages in each season. I noticed that there does seem to be a difference between the distributions but to test whether the differences are significant or not I decided to perform a hypothesis test. Like my previous tests, I chose a significance level of 0.05 as a cut-off for my p-value, since a p-value smaller than 0.05 indicates strong evidence against my null hypothesis.  

 

Null Hypothesis: There is not a difference between the outages distributions of the seasons in the SPP Region and the Overall outages distributions of the seasons of the NERC Regions

Alternative Hypothesis: There is a difference between the outages distributions of the seasons in the SPP Region and the Overall outages distributions of the seasons of the NERC Regions

For my hypothesis test, I will use total variation distance (TVD) as my test statistic, since I am comparing the distributions of outages in each season which are categorical distributions. My observed TVD was 0.123.

After performing my hypothesis, I plotted my results in the plot below. The plot displays the empirical distributions of the generated TVDs under the null. The green line in the plot represents my observed TVD. Additionally, my calculated p-value was 0. Which can be seen in the graph since there are essentially no TVDs generated in the hypothesis test under the null that were equal to or greater than my observed TVD.

In conclusion, the probability that the observed TVD came from the distrubtion of TVDs under that the assumption that null is true is essentially 0. There is strong enough evidence to suggest that there is a difference between the outages distributions of the seasons in the SPP Region and the Overall outages distributions of the seasons of the NERC Regions