Electricity prices rose by 16% in two years

With about 490 kWh electricity consumption I am a rather small customer. Over the year this sums up to about 160 EUR. So I had a look at the costs.

I was suprised to learn that the prices rose quite clearly. My tariff is two-part, a base price and a kilowatt-hour rate. If I look at the total costs and divide them by my consumption, I get


This means, in 2010 I had to pay 4% more than in 2009 and 16% more than in 2008. My energy use per day, on the other side, remained quite stable at 1.35 kWh/day.

What can I do about it? The first impulse was to collect more data, maybe by using a WiFi energy sensor. Would be really fun. However, I can not see many options to reduce my consumption. Maybe I can turn off the internet router while at work.

It seems more sensible to me to switch my energy provider, which I did today. My new energy provider will charge a bit more, but gives me 50 EUR new-customer bonus and claims to deliver certified renewable energy.


How much is a shower?

After looking at my heating expenses, I turned to the costs for water heating. For some time, I looked at my water meter before and after taking a shower or a bath. Quite often, I forgot one or the other measurement, but I collected about 40 observations. Here is what they look like:

The data suggest that for a shower, it takes between 17 and 26.5 liters hot water and between 11 and 16.5 liters cold water. For a bath, it is 60 to 77 liters hot water and 24 to 32.5 liters cold water. (The numbers refer to the 25% and 75% percentiles, respectively.) The larger share of cold water for a shower makes sense, since I use cold water at the end of the shower for its “invigorating effect”.

Multiplied with the average costs, as charged by my landlord the last three years, a bath takes 0.94 to 1.22 EUR and a shower costs 0.29 to 0.45 EUR (again, first and third quartiles). So taking a shower for 0.50 EUR at the fitness club is not optimal, but also not very expensive.

There are water saving shower heads for 30 EUR. It is advertised that such a shower head uses 6.5 liter per minute instead the usual 15 to 16 liters per minute. I believe 15 liters per minute is too much. So let’s assume I save 3.5 liters per minute or (using the median water use of the data) 12 liters per shower. Is it cost-efficient?

Twelve liters less per shower at 10.5 EUR/cbm means a saving of 0.126 EUR per shower. I assume 20 showers a month. This is tentative, since with this assumption the costs sum up to 70 EUR a year for hot water while my bills amount in average to 110 EUR total costs for hot water. So the new shower head saves 20*0.126=2.52 EUR per month.

Let’s calculate the payback period. With an interest rate of 4% p.a. and 5 years expected serviceable life the monthly gain calculates to

2. 52 - 30 * 0. 04 / 12 - 30 / (5 * 12) = 1. 92

so after 30 / 1. 92 = 16 months, the investment is repaid. This seems acceptable. But just to be sure, let’s calculate the internal rate of return, too. In excel, there is a function IRR for this procedure, which is implemented in three lines in R. For convenience, the irr function is stored in the pft package. The result is 8.3% which seems decent.

Just for reference, here comes the R code for the plot and the irr function:


Heating costs

In 2010, my heating costs exceeded my advance payments by about 25%. This motivated me to decompose the costs to see what drove the changes. Here is the result:

The numbers refer to Euros. Read von right to left: 2010 was a cold year (+102EUR), but gas consumption in this house was relatively low (–89EUR). Also, running costs and gas price were below previous year’s value (–49EUR). The main driver (+183EUR) for the increased costs was my share on the total costs. In 2009, I had to pay 1.7% of the total costs, which rose to 2.3% in 2010. This means my landlord assumes I used more energy than the other tennants in 2010. I doubt that, and one aspect to support my doubts is that the values of the two heat meters in my living room were nearly at the same value, while I used only one heater.

Thus I believe it was a measurement error. I am not going to complain about this, but will check next measurements very carefully.

Not a direct result of the decomposition, but also interesting is the (temperature adjusted) enery use per square meter, which was in 2010 by about 110 kWh/m2, which is nearly average.

Here’s the R code to produce the chart:


Semi-transparent colors and EMF -- an open problem

One nice development in visualisation  -- in principle -- is the use of semi-transparent colors. You can use it to plot probability densities, overlapping histograms, surfaces, and maybe other nice things.

In practice, however, semi-transparent colors suck. Unless you are happy with PNG or PDF for monitor use only, stay away from them. That's my advise. Especially if you are stuck to the windows platform, and want to produce an "enhanced" meta file (EMF) for your word document, chances are you will break out in tears if you try semi-transparent colors.

The problem seems to be the EMF format. Here are some of my experiences of what does *not* work in this setting.

Microsoft office inherent problems
One would expect that Microsoft's office programs work flawless with its proprietary vector-graphic format EMF. But they do not.
  • You can not rely that your Powerpoint graphic with semi-transparent colors will print out properly, neither from powerpoint nor if you copy it to word first.
  • You can not save your word doc as PDF if it contains semi-transparent colors and assume the PDF will contain semi-transparent colors, too.

Problems converting PDF to EMF
Since R's emf() device does explicitly not support semi-transparent colors, one option might be to first export the graphic to PDF or SVG, and then convert it to EMF. I did not succeed on this.
  • a software called pdf reader produces something semi-transparent, but of very poor quality
  • Inkscape's and pstoedit's exported EMF displays semi-transparent color as solid colors
  • pdf2picture has not provided an answer
  • I did not find any converter from SVG to EMF

Other options
So, if your end product is not a SVG, PNG or PDF file not intended for printing, it might be better not to use semi-transparent colors. If you are visualising a probability density, try sampling or the hexbin package.


Resources on Visualization

Enrico Bertini and Jorge Camoes presented their favorite resources on information visualisation. Surfing the free courses mentioned in Bertini's article,
I read about some interesting techniques I wish to learn more about (later)
  • edge bundling when visualizing graphs
  • Dorling circular cartograms named after Danny Dorling. The algorithm is described in Dorling, D. (1996) Area Cartograms: Their Use and Creation. Concepts and Techniques in Modern Geography, 59, 69 pages. Norwich: Geobooks
  • determining the optimal aspect ratio of a line graph by the shape of the graph


Regional differences on what drives CO2 emissions

If you are investigating the change of CO2 emissions, then you might ask: Where do the changes occur? Well here is the answer.

The staircase plots show the contributing factors to CO2 emissions for each continent. population refers to population effects, gdp_pcap refers to income per capita, energy_intensity refers to energy used per dollar added value, and carbon intensity refers to CO2 emissions per energy unit. The numbers are Gt CO2 and come, not very carefully curated, from Worldbank.

As you can see, europe’s emissions stay at nearly the same level, mostly because there is no population effect. On the other hand, Asia’s economic rise seems to explain much of the change of CO2 emissions in the time from 1995 to 2007.

Here is how to produce the chart:


Reproducible blogging

As a fact-based blog, the posts here contain very often diagrams and data tables. To enable you to reproduce the results and insights, I include the computations as computer code.

Most blogposts I write are markdown text combined (or weaved) with computer code written in the R language. I created a small package mdtools that puts the tools together and smoothes the workflow.

This post gives an short introduction to the mdtools package: how to install it, the first post, caveats, and future directions.


Index decomposition with R

Few days ago, I finally finished a small package ida. It enables you to analyse contributions of underlying factors to the change in an aggregate, using methods based on index number theory. These methods have become popular by, but are not restricted to, investigating the change of CO2 emissions.

Here is a chart that shows what the change of population, welfare, efficiency and fuel substitution contributed to CO2 emissions:

The numbers refer to Gt CO2. The data comes from Worldbank, however we treated missing values rather uncautious here. So the result may or may not be valid. However, it puts the efforts in perspective: Clearly the reduction of the energy use per GDP has not been capable to compensate the additional emissions from population growth and income per capita growth. The carbon intensity, i.e. the emissions per energy unit, remained nearly unchanged.

Here is how to produce the chart:

Favicon CC-license backlink

The nice favicon of this blog was created by fatcow and found at iconarchive. Changing the favicon in blogger is nicely explained by Chester Alan Tagudin.