Some insights about domestic electricity prices in the IEA countires

In this post we will provide three interactive visualizations of the latest data released by the International Energy Agency (IEA) about the domestic electricity prices*.

Prices in 2013

In the first figure below we compare the prices of the domestic electricity among the countries monitored by IEA. The plot also shows which fraction of the price is represented by taxes:

In 2013, average domestic electricity prices, including taxes, in Denmark and Germany were the highest in the IEA. We also note that in Denmark the fraction of taxes paid is higher than the actual electricity price whereas in Germany the actual electricity price and the taxes are almost the same. Interestingly, USA has the lowest price and the lowest taxation.

Relationship between taxes and full prices

In this figure we highlight the correlation between taxes and full prices: Here we can see that there is a positive correlation (correlation=0.82) between the prices with taxes and the prices without taxes. This indicates that according to this data, when the full price increases, the taxes also increase. Hovering the pointer on the points we can discover that Germany and Denmark have the highest taxes, while USA, UK and Japan have the lowest. Also, we note that Ireland has expensive electricity and low taxes, while Norway shows the reverse trend.

Evolution of the prices from 2010 to 2013

Here we try to compare the trend of the prices among the five countries with the higest prices in 2013: From this chart we can observe that only in 2013 the cost of the electricity for the domestic consumers has become very similar in Germany and Denmark and that the Danish prices were substantially higher in the past. We can also see that prices in Italy and Ireland have a very similar increasing trend while prices in Austria dropped in 2012 but raised again in 2013.

*the prices are showed as pence per Kwh.

A weather forecast accuracy study

Can you trust the weather forecast ?

It's a question that can trigger long passionate conversations, especially in this country (UK) where talking about the weather is deeply embedded in the culture. An answer to such a question can therefore be of interest to anybody living in the UK, but also for companies like us who work constantly with weather forecast data in order to produce accurate estimation of renewable energy production. This study will focus on the daily-averaged solar radiation over the Tokyo area from November 2013 to July 2014.

First, we plot in figure 1 the actual solar radiation in kWh over the Tokyo area.

Figure 1: Actual solar radiation over the Tokyo area from November 2013 to June 2014. It's getting hot! The first and third quartile range shows the geographic variability over the area. We observe that the solar radiation is homogeneous over Tokyo.

We can access weather forecasts for the day ahead, the following day or even a week or a month in advance. The number of days separating the date of the prediction and the date the prediction was done for is called the forecast horizon (abbreviated fh in the following). Our dataset consists of 31 different forecasts for every day, from a forecast horizon of 1 to 31. Short term forecasts (0 < fh ≤ 11) are created by weather models. These models take weather data from the past and use it to predict the future of the weather conditions (temperature, pressure, wind, humidity…). Long term forecasts (11 < fh ≤ 31) are determined from considering previous years’ averages. For all these forecasts, we can compute the error by comparing the forecast solar radiation value to the actual value. We represent in figure 2 the error distribution for both long term and short term forecasts.

Figure 2: Error distribution for long and short term forecasts. We notice that the long term distribution is biased towards the negative values (under-estimation) while the short term is slightly biased towards the positive values (over-estimation). The short term distribution shows more of an even distribution around zero, indicating that this forecast is more accurate than the long term one... but not by much!

This figure shows us that the short term forecast performs better than the long term forecast. Now we can question how this error varries with the forecast horizon. We therefore plot in figure 3 the MAPE (measure of the accuracy) and MPE (measure of the bias) as a function of the forecast horizon.

Figure 3: MAPE (measure of the accuracy) and MPE (measure of the bias) as a function of the forecast horizon. The error and the confidence interval decrease as the forecast horizon approaches 0.

We note that the forecast accuracy is improving (the error is decreasing) when the forecast horizon gets closer to 0, for which we have a vanishing error since it corresponds to actual weather values. Not only does the accuracy gets better, but so does the confidence interval (the shaded regions are narrower for short term forecasts). We also confirm that the solar radiation is under-estimated by the long term forecast and slightly over-estimated by the short term one (see right-hand-side plot). This could be due to the fact that the studied period is particularly sunny compared to previous years. However, we also notice that a 10-day weather model forecast is, on average, worse than a prediction based on previous years’ averages... We know since Lorenz that chaotic systems (weather models are good examples of chaotic equations) are very sensitive to initial conditions... Therefore, a middle term forecast based on a weather model has to be considered with caution.

So please, keep chatting about the weather but when it comes to planning a barbecue a week in advance, don't put all your trust in the forecast!