Electricity wholesale prices, especially spot market prices, have become very volatile since the liberalization and the establishment of electricity trade on en-ergy exchanges, such as the European Enen-ergy Exchange or NordPool in Europe or PJM and CAISO markets in the USA. Thereby electricity is generally traded via hourly or block contracts on day-ahead spot markets12, while on future markets electricity can be bought with monthly and (quarter) yearly contracts (see EEX (2011)). The hourly trade of electricity on spot markets leads to prices which can strongly vary for different hours of the day depending on the main driver, the ac-tual electricity load (demand). The hourly varying prices are caused by the fact that electricity is not or only in small quantities storable. Therefore the prices re-sult from the marginal costs of the most expensive producing unit adjusted by a scarcity premium, which is driven by the supply and demand situation.
12On the main US electricity markets (PJM, CAISO), the intraday electricity price settlements are done every five minutes.
2.2. Electricity price characteristics and uncertainty
Figure 2.3.: a) Average daily price curves b) Weekly price curves for different seasons (based on 2011 EPEX day-ahead prices)
2.2.1. Characteristics and volatility of electricity prices
Electricity prices at the EPEX display the characteristics of the system load, so that price peaks occur at the same time periods as load peaks (see Weron (2006)).
The electrical load is higher in the midday hours on summer days or in the evening hours on winter days. As the demand for electricity and thus the load is low at night, electricity prices usually reach their minimum in this so-called offpeak time (see Figure 2.3).
The EEX spot prices possess also a weekly pattern, which is caused by the lower load at weekends or on holidays. The lower load at weekends is again directly displayed by the lower electricity prices for the same time period13. A further deterministic cycle determined for electricity prices is the annual season-ality, which results from the different demand for electricity during each season of the year. Beside the seasonal cycles, electricity prices are characterized by a long-term trend, which corresponds to an average growth of the annual mean price by 2.80e/MWh between the year 2002 to 201114. However, the price means of the
13The load-price relation is driven by the merit order of the power plant technologies that take part in the EEX spot market (see Genoese (2010)).
14The growth of the annual average prices is determined as the growth rate of the linear regression line fitted to the curve of the annual price means.
Table 2.3.: Some basic statistics of electricity prices (data source: European Energy Exchange (EEX))
[e/MWh] 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
mean 22.55 29.48 28.55 45.93 50.83 37.95 65.76 38.98 44.48 51.07 std 15.94 26.49 10.80 27.25 49.40 30.37 28.73 18.70 13.97 13.68 skewness 7.78 32.03 0.50 4.86 25.08 6.86 1.16 -1.13 -0.07 -0.66
SPE 71% 90% 38% 59% 97% 80% 44% 48% 31% 27%
single years can significantly vary from the regression line. As it can be observed from Table 2.3, some annual means are clearly lower than the total mean (41.66 e/MWh), while others, such as the price mean in 2008, are distinctly above it.
But not only the annual price level is volatile, but also the inner-year distribu-tion of the prices varies strongly. This can be observed from the high standard deviation (std) of the electricity prices for each year. The "normalized" standard deviation, which is called standard percentage error (SPE) in the following, even reaches values over 90%, which is a sign for high inner-year volatility of electric-ity prices. But as the SPEs and standard deviations vary each year, it can be stated that the volatility is not constant over the years and that electricity price series are heteroscedastic.
The high volatility can also be determined by drawing the boxplot of the elec-tricity prices for the last years. The boxplot shows that the medians significantly differ for the last six years. This issue highlights the different price levels before, during and after the economic crisis in 2009 (see Figure 2.4).
Finally, the different quantile distances for each year indicate that the inner-year volatility is not constant over the analysed time period. The quantile distances of the years 2006 and 2008 are twice than the ones of the years 2009 to 2011.
The varying quantile distances are again a sign for heteroscedastic behaviour of electricity prices.
2.2. Electricity price characteristics and uncertainty
2.2.2. Price peaks
As it is visible from Figure 2.4, there are many prices beyond the whiskers of the boxplot, especially beyond the upper whisker. These prices represent price peaks, which occur in times when the difference between available power plant capacity (excluding system reserves) and the system load becomes very small. This can happen e.g. in cases of power plant outages at times of a high system load. There-fore, these prices can be seen as scarcity prices, which are not explainable by the marginal cost of the price setting power plant, as it should be the case in times of non-scarcity due to the merit order pricing theory.
2006 2007 2008 2009 2010 2011
-50 0 50 100 150 200
Electricity price [€/MWh]
Figure 2.4.: Boxplot of the electricity prices between 2006 and 2011 (data source: EEX, EPEX)
The price peaks or price changes into an upper price level are causing the typical left-skewed distribution of electricity prices. The higher the positive values for the skewness (see Table 2.3), the more left-skewed is the distribution. However, the left-skewness does not exist in the last three years. The prices seem to be
equally distributed around the mean. The small negative values for these years even indicate that the prices are slightly right-distributed.
One reason for the change in the distribution is the new design of the EEX day-ahead market, which allows negative prices since September 2008. Negative prices are balancing the positive price peaks, which in turn leads to the more or less non-skewed distribution of electricity prices in the last four years. Another reason is the change in market mechanism, i.e. the introduction of a second auc-tion, which can be initiated by the EPEX Spot, if e.g. equlibrium prices are not found between -150e/MWh and 500 e/MWh for one or a couple of hours (see section 2.1.2). The second auction can result in the reduction of peak prices far beyond 500e/MWh, which in turn reduces the left-skewness of the distribution of electricity prices.
The second auction seems to change also the amount and height of price peaks determined by applying the Grubbs’ test for outliers (see Table 2.4). The test is separately carried out for the electricity prices of each year15. The first analysis of the outliers shows that their number as well as their mean considerably differ for each year. It can be noticed that the number and the mean of outliers are lower for the years 2010 and 2011. In 2011 only two values are determined as outliers and their mean is slightly higher than the 100e/MWh level, while the mean value of the price peaks was close to 400e/MWh in 2006 (see Table 2.4). This can be seen as a result of the secondary auction introduced in 2011 in the day-ahead spot market, but also as a result of better forecast tools for renewable electricity feed-in, which enables more precise offers on the spot market.
The reduction of price peaks does not automatically equal to a reduction of the volatility of the non-peak prices. For example, nearly the same standard deviation can be notified for the years 2010 and 2011 (13.85e/MWh and 13.55 e/MWh respectively). Thus, it can be stated electricity prices will stay volatile and the
15One of the requirements of the Grubbs’ test for outliers is that the analysed series is normally dis-tributed. As the price logs are rather normally distributed than the prices themselves, the test should be applied for the logs. However, the logarithmisation transforms all peak values to values which are closer to the mean of the series, so that almost all positive outliers are eliminated. Therefore, the Grubbs’ test is still applied for the prices itself rouhgly assuming a normal distribution for them.