Price spike module

Given n = 3 and w = 90 days, the thus defined price spikes are extracted from the original price series, as shown in Figure 4.5.

Table 4.1 shows the basic distribution parameters for prices and spikes. It can be seen from the number of spikes (Nspike) that the spikes constitute less than 1.5% of all the daily prices. However, their magnitude and unexpectedness cause them to have a disproportionate significance in the electricity markets. The statistics show that there is zero probability of an electricity price spike during weekends and holidays.

Table 4.1. Basic statistics for normal prices and price spikes over the period 2006-2009.

Number of observations

Mean Std Skewness Kurtosis Weekday, Nspike

Weekend/

Holiday, Nspike

Normal 1436 41.26 13.28 0.55 2.91 — —

Spikes 25 71.86 41.88 3.26 14.65 25 0

Figure 4.5. a) Original Finnish daily day-ahead electricity prices for the period 1 Jan 2006–31 Dec 2009; b) extracted price spikes.

In an ideal competitive electricity market, price spikes occur only when the demand exceeds supply. Most electricity markets, however, are not ideally competitive.

Therefore, price spikes may take place even when the supply completely covers the demand. The set of attributes selected to determine the probability of price spike occurrence and its magnitude are given below:

SDI. This study uses the composite relationship between electricity price, demand, and supply that was proposed in (Lu et al., 2005) and presented as a supply-demand balance index (SDI). The SDI on a single day D is defined in Eq. 4.1:

( ) ( ( ) ( )) / ( ) 100%

SDI D Supply D Demand D Demand D (4.1)

where Demand(D) is the market demand on day D, and Supply(D) is the electricity supply on day D.

Nonbase electricity demand. The importance of electricity demand for electricity price forecasting was discussed in Section 3.3.2.

Temperature. Atmospheric temperature is chosen as a main indicator of weather extremity in the electricity price spike study. The main electricity consumption areas in Finland are the south and central regions (Statistics Finland, 2012), and the temperature data for the city of Helsinki are used because the geographical location of the city indicates a temperature that is relevant to overall electricity consumption in the country. Temperature data forecasted for the city of Helsinki are available on the Weather Underground web site (Weather Underground, 2012).

Elspot capacity-flow difference. Power transfer constraints for electricity come in the form of a capacity limit on the transmission lines and the transmission losses, which can make it impossible or uneconomical to transfer electricity in certain regions (Lucia and Schwarz, 2000).

Two regimes of the Finnish electricity system are considered. One of the regimes is the regular regime; the other, the nonregular regime, is the capacity-limited regime and exists when the difference between the total Elspot power flow and the total Elspot capacity to Finland is close to zero. Congestion and thus extreme price changes are more likely to occur when the difference between the total Elspot power flow and the total Elspot capacity is small.

The total Elspot power flow and the total Elspot capacity to Finland were calculated as a daily sum of the Elspot net exchange and Elspot capacities from Sweden, Norway, and Estonia to Finland, respectively. The power flow data and the generation and demand data for the Finnish electricity system are provided by Fingrid, the company responsible for the high-voltage electricity transmission in Finland (Fingrid, 2013b). The Elspot power flow and capacity data for day D-1 are published by the TSO and are available on day D-2. Therefore, to forecast the flow

4.2 Hybrid electricity price forecasting model 81 and capacity for day D, the flow and capacity data of day D-1 are considered known. The Elspot power flow data have strong seasonal patterns, which can be captured by SARIMA. The Elspot capacity is rather constant during the whole week.

Temporal effect. In addition to the physical factors given above, the day status of the sample needs to be implemented into the forecasting model (similarly to the model presented in Section 3.7). The whole data set was divided into weekdays, weekends, and holidays of different yearly seasons.

The distribution of the prices versus the chosen driving factors is shown in Figure 4.6.

Note that the factors cannot exactly determine the occurrence of spikes. The Gaussian Mixture model predicts spikes by evaluating their occurrence probability. The inputs of the model are not necessarily the determinants of spikes.

Figure 4.6. Scatter plots of the prices versus potential price spike driving factors.

One modification is implemented within the GMM model. The probability of spike occurrence is calculated for every input vector and then compared with a predetermined threshold denoted as V0. If the probability is larger than the threshold, a spike is predicted to occur, regardless of whether this probability is larger than the probability of nonspike occurrence. This modification is performed because the price spike prediction problem is a serious imbalanced classification problem (i.e., some classes have many more samples than other classes) (Zhao et al., 2007a). In fact, the probability of spikes is less than the probability of nonspikes on most occasions. Many spikes occur when

their occurrence probabilities are smaller than 50%. Without setting a threshold smaller than 50%, many spikes will be misclassified. The threshold can be determined by historical data. A Bayesian-based classifier considering prior information, that is, prior class probability, tends to be less prone to problems regarding sample class imbalance.