Subtitle: A Bit of Gathering Into Groups Gives Good Results
by: Roger Sowell (1)
Background: Much discussion, and much misinformation, is had over the price of electricity in the US, and many other areas of the world. The discussions sometimes end up as diatribes against renewable energy sources such as wind and solar. The article below is an attempt to begin to bring some facts into the discussion, using actual data from the US Energy Information Agency, the EIA. This is from an article from about a year ago on my main blog, SowellsLawBlog. The take-away points are: 1) there is an almost perfect inverse relationship between price and consumption, and 2) the fact that California prices are below the trend line. That is true even though California has substantial renewable energy statewide, a figure that passed 25 percent in 2015.
It is not often that one creates a graph using actual data and discovers an almost perfect linear relationship. It is even more rare to have a software package calculate the least-squares trend line and obtain a correlation coefficient, R-squared, of 0.99 or higher. Yet, that is exactly what occurred for data from calendar year 2014 for US residential annual electricity consumption per customer, and average price per kWh. The graph and simple statistics are shown below, then a discussion. Note the R-squared value of 0.9997, indicating an almost perfect correlation.
|Figure 1. Data from US Energy Information Agency, by state
Shows 39 states, excludes 10 states with lowest prices and Hawaii
This article follows another SLB article that ascribes the relatively higher price for residential electricity in California compared to the US average to mild climate and large population. (see link to “Why California Electricity Costs More than US Average; Mild Climate and Large Population Contribute to Prices”) Conventional wisdom is very wrong in blaming solar power and wind power for the higher California prices.
With the data ready at hand from US Energy Information Agency files from their website, it was a simple matter to sort the data for each state by annual average residential price in cents/kWh. Being previously aware that low residential prices tend to correspond to high electricity consumption, and vice-versa, inspection of the data for 2014 confirmed that relationship. However, when the data is grouped into quintiles, a convenient grouping as there are 50 US states with ten members in each quintile, an almost perfect straight line resulted, as shown in Figure 1 above. However, there are only four data points in Figure 1. This is discussed below.
The R-squared of 0.9997 resulted when only the four quintiles with highest prices are graphed, that is, the quintile with lowest prices was excluded. Also, Hawaii is excluded as a high-priced outlier. More on that in a moment.
The data for each quintile is shown in table form below.
Quint kWh/y Cents/kWh
1 13,528 9.67
2 12,178 10.78
3 11,445 11.89
4 10,550 13.15
5 7,311 17.58
Next is shown in Figure 2 the graph of all five quintiles for 49 states – Hawaii is excluded as being a-typical and an outlier. This graph has only a slightly lower correlation coefficient, R-squared of 0.9931.
|Figure 2. Showing 49 states (excludes Hawaii)|
The conclusion that can be drawn is that there is indeed a correlation, and a very good correlation, between average price for residential electricity and the quantity of electricity consumed on an annual basis by each utility customer. California is in the fifth quintile for high price but low consumption (16.2 cents/kWh and 6,741 kWh/yr/customer). Other states with California in the fifth quintile are almost all in the North East sector, Massachusetts, Vermont, Rhode Island, New York, Maine, New Jersey, and Connecticut. Example states at the other extreme, in the first quintile are Louisiana, Arkansas, and Oklahoma – all hot, humid, and consuming 14,000 kWh/yr/customer on average, more than double that of California.
In fairness, it should be noted that the high correlation coefficient only results when the quintiles are graphed. For all 49 states individually, again excluding Hawaii as an outlier, a much lower correlation coefficient results, of R-squared 0.546.
The graph shown below as Figure 3 is a repeat of Figure 2 above, with the highest (in red) and lowest (in green) states shown, as their average price’s deviation from the national trend line. California, the green circle at top left, is 2 cents below the trend. Other states substantially below the trend include Maine, Colorado, Illinois, Utah and Montana. Those states with the highest deviation above the trend are Alabama, South Carolina, Tennessee, Mississippi, Connecticut, Louisiana, Maryland, and Texas.
|Figure 3 – Showing individual states
with greatest deviation from trend
as colored circles
(1) Roger Sowell is an attorney in Science and Technology Law. Since earning a BS in Chemical Engineering in 1977, he has performed a great many engineering consulting assignments worldwide for independent and major energy companies, chemical companies, and governments. Cumulative benefits to clients from his consulting advice exceeds US$1.3 billion. Increased revenues to clients are at least five times that amount. He regularly makes public speeches to professional engineering groups and lay audiences. He is a regular speaker on a variety of topics to engineering students at University of California campuses – UCLA and UC-Irvine. He is a founding member of Chemical Engineers for Climate Realism, a “red-team” style think-tank for experienced chemical engineers in Southern California. He is also a Council Member with the Gerson Lehrman Group that provides advice to entities on Wall Street. He publishes SowellsLawBlog; which at present has more than 450 articles on technical and legal topics. His widely-heralded Truth About Nuclear Power series of 30 articles has garnered more than 25,000 views to date. Recently (2016), he was requested to defend climate-change skeptics against an action under the United States RICO statutes.