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Accurate forecasting tools are essential in the operation of electric power systems, especially in deregulated electricity markets. Electricity price forecasting is necessary for all market participants to optimize their portfolios. In this paper we propose a hybrid method approach for short-term hourly electricity price forecasting. The paper combines statistical techniques for pre-processing of data and a multi-layer (MLP) neural network for forecasting electricity price and price spike detection. Based on statistical analysis, days are arranged into several categories. Similar days are examined by correlation significance of the historical data. Factors impacting the electricity price forecasting, including historical price factors, load factors and wind production factors are discussed. A price spike index (CWI) is defined for spike detection and forecasting. Using proposed approach we created several forecasting models of diverse model complexity. The method is validated using the European Energy Exchange (EEX) electricity price data records. Finally, results are discussed with respect to price volatility, with emphasis on the price forecasting accuracy.

During the last twenty years, the traditional vertically integrated electric utility structure has been deregulated and replaced by a competitive market. The deregulated power market is an auction market with market clearing prices. Companies that trade in the electricity market today make extensive use of price prediction techniques to stay competitive. Along with forecasting electricity prices, producers and traders can develop bidding strategies to maximize profits and minimize risks and allocate purchases between long term bilateral contracts and spot prices.

Electricity today is not storable in economically significant quantities and as a result electricity prices are volatile. Aside from volatility (elaborated in detail in Section 4), liquidity is another major market parameter. Market liquidity is an asset's ability to be sold without causing a significant change in the price and with minimum loss of value [

The European Energy Exchange (EEX) is the most important energy exchange in central Europe which provides a spot market for power derivatives and emission trading in Germany, France, Austria and Switzerland. EEX is a highly liquid market affected by domestic and regional power system factors. Due to the importance and regional influence of the price of the EEX, it is important to find a suitable model for electricity spot market price forecasting [

Accuracy of a certain method can be evaluated by mean absolute percentage error (MAPE). Although the concept of MAPE sounds very simple and convincing, it has two major drawbacks in practical applications. If there are zero values (which can happen as EEX allows prices in the range from −500 € to 3,500 €), a division by zero will occur. On a perfect fit, however, MAPE will be zero. With regard to its upper level, MAPE has no restriction. When calculating an average MAPE for multiple time series, a few numbers in the series that have a very high MAPE might distort a comparison between averages MAPE of time series fitted with different methods [

Our goal is to reuse existing methods for price forecasting to create a hybrid price forecasting model which combines advantages of existing techniques to cover specificity of electricity price movements. Initially data is processed and filtered using statistical methods resulting with a data model of similar days. This model is then improved by using a multi-layer (MLP) neural network or price spike detection and forecasting. We validated our approach using the EEX electricity price history data, and evaluated our results by applying several measures of accuracy (MAPE, MAE and RMSE). In addition we emphasized the problem of price volatility by showing how price volatility affects the accuracy of each forecasting method.

The rest of the paper is organized as follows. Section 2 describes price forecasting framework. Section 3 is devoted to the proposed forecasting methodology while Section 4 describes price volatility. Section 5 provides our simulation results. Finally, Section 6 concludes the paper.

Most of the existing studies of electricity price forecasting use only historical price and consumption data to forecast electricity prices over various time spans [

The proposed hybrid price forecasting model has both linear (similar day-SN) in Case 1 and nonlinear (ANN) forecasting capabilities in Case 2. In addition in Case 2 if possibility of price spikes (PS) are detected price is forecasted as price spike. Time horizon is day-ahead and the price is forecasted for every hour.

The price forecasting framework and methodology are presented in

Daily price history data is processed with data mining technique which defines:

Similar day types.

Relevant history horizon for similar days—

Hourly correlation time horizon—_{h}

Day type can be divided in three categories: working days (Monday-Friday), Saturdays and Sundays/Holidays. Days before or after holidays also reveal distinct behavior, but due to the negligible influence on forecasting performance, these cases are ignored and not performed.

To define the relevant history horizon for similar days—

Prior to performing the forecast, an hourly horizon is defined by applying ^{+} and ^{−} (“significant neighbors” shown in green in _{h}

Our approach of using hybrid forecasting model, based on similar-day analysis, improved by neural network and price spikes detection and forecasting is shown in _{h}

_{h}

_{h}

_{h}

The hybrid forecasting model consists of:

Electricity price forecasting methods based on similar day's methodology were presented by Paras Mandal

_{t}

_{t}

_{pt}

_{pt}

_{t}

_{t}

ω—weighted factor is determined using least square method based on regression model constructed by using historical load and price data.

Input data for the proposed method includes consumption and wind forecast data taken from the Point Carbon web service [

δ—average hourly difference between forecasted hours.

The linear price component can be observed as independent because it represents a starting point for the forecasting model which can be improved by neural network and price spikes component.

Neural networks are applied widely for solving different problems which in general are difficult to solve by humans or conventional computational algorithms. In power systems the ANN's have been used to solve problems such as load forecasting, unit commitment, power system topology recognition, and safety analysis, price forecasting

For hourly neural network component used in our approach, a multi-layer feed-forward neural network is proposed as shown in

^{−}, ^{+}〉—number of similar hour before (^{−}) and after (^{+}) forecasted hour

The neural network is trained on 70% randomly chosen cases from the data set and tested on the remaining 30%.

Due to the fact that there is no efficient way for storing electric energy, all electricity produced has to be consumed forthwith. Imbalances between consumption and production lead to electricity price jumps (

In the proposed forecasting model we categorize prices as either regular (normal) or price spikes. It is important to find how consumption and wind production affect the price spikes. An index was created which unifies consumption and wind production changes to create a signal, which detects possibility of price spikes. Consumption and wind index (

_{h}

_{sd}

_{h}

_{sd}

Applying the

After calculating the _{h}_{h}

Importance of short-term price forecasting on one hand and its complexity on the other hand led researchers to propose various methods. Among these methods, there are three widely used approaches; time series models, artificial neural network (ANN) and hybrid methods.

Volatility refers to unpredictable fluctuations of a process observed over time. In finance, volatility is a measure for variation of a price of a financial instrument over time [

In [_{t}

When returns are small, the arithmetic and logarithmic returns are approximately equal:

Given the return values, the estimated value of past volatility can be calculated as:

_{h,T}

_{0}—the number of _{t,T}

_{hT}

For this study volatility is calculated as a standard deviation of arithmetic return over a time window

It is interesting to observe the volatility fluctuation on EEX over the last eight years in dependence with traded volume.

We tested our approach for electricity price forecasting on the EEX price history data from a time period 20 November 2010–20 July 2011. Data was processed in Microsoft Excel with Palisade Decision Tool and Visual Basic. Three cases were observed:

Forecasting with similar days (SD);

Forecasting with similar days and neural network (SD + NN);

Forecasting with similar days, neural network and price spikes detection (SD + NN + PS).

Our results are presented in

Model performance was evaluated with _{t}_{t}

Price spikes brought outliers in results and that was the reason for including two additional error measures:

Simulation results show that similar day's method with neural network and price spikes detection gives the best results. Price volatility is a dominant factor affecting the forecast model accuracy. In case of low price volatility, such as March 2011, simple models such as similar days gave adequate results with forecasting error similar to advanced models with neural network and price spikes detection. In case of high volatility, such as December 2010, advanced models gave better results. Therefore it is very important not only to evaluate the forecasting model against the forecast error but also to analyze the complexity of the result distribution, in this case defined by price volatility.

The main difference between the proposed model and other existing methods for short-term electricity price forecasting is in its data utilization approach. In the proposed approach, the data is pre-processed by statistical methods prior to each analysis. Forecasting results obtained by a combination of methods: similar days method (SD), neural network forecasting (NN) and price spikes (PS) in the following combinations; SD, SD + NN, SD + NN + PS were presented; each, respectably, proving to be more accurate. Price volatility has a significant influence on the forecasting results. Simple forecasting models produced satisfactory results in cases of low price volatility. Our method proved robust enough, even in cases of high price volatility.

This work has been supported in part by the European Community Seventh Framework Programme under grant No. 285939 (ACROSS). Part of this research was discussed at the 9th International Conference “European Energy Market” held in Florence, Italy on 10–12 May 2012.

The authors declare no conflicts of interest.

Wind power capacity and generation in Germany.

Flow chart of the hybrid electricity price forecasting model.

Daily price correlation for D nearest neighbor.

Correlation matrix of EEX hourly data averages for the period from 20 November 2010 to 20 July 2011.

Proposed ANN model for hourly neural network component forecasting.

Defining the data set for the forecasted hour

Correlation of

Volatility fluctuations and traded volume show that volatility jumps were more severe on lower levels of EEX spot market liquidity.

Performances of the proposed hybrid model for hourly electricity price forecasting.

December-2010 | SD | 12.81% | 7.48 | 9.38 | 18.30 | 100 |

SD + NN | 8.50% | 7.32 | 10.43 | |||

SD + NN + PS | 6.79% | 6.45 | 10.42 | |||

January-2011 | SD | 11.36% | 6.00 | 7.44 | 15.95 | 86 |

SD + NN | 12.20% | 7.33 | 9.53 | |||

SD + NN + PS | 10.39% | 6.89 | 9.08 | |||

Febuary-2011 | SD | 19.12% | 9.38 | 8.91 | 14.22 | 101 |

SD + NN | 7.84% | 5.48 | 7.24 | |||

SD + NN + PS | 5.87% | 4.59 | 6.55 | |||

March-2011 | SD | 4.88% | 4.84 | 6.05 | 9.67 | 59 |

SD + NN | 3.73% | 4.01 | 5.31 | |||

SD + NN + PS | 3.62% | 3.89 | 4.51 | |||

April-2011 | SD | 10.86% | 5.69 | 6.98 | 11.73 | 119 |

SD + NN | 7.52% | 5.29 | 6.91 | |||

SD + NN + PS | 5.03% | 4.58 | 6.31 | |||

May-2011 | SD | 7.51% | 5.85 | 6.55 | 12.01 | 141 |

SD + NN | 6.96% | 5.45 | 6.10 | |||

SD + NN + PS | 6.11% | 5.12 | 5.95 | |||

June-2011 | SD | 13.05% | 5.49 | 6.41 | 13.20 | 74 |

SD + NN | 12.90% | 5.55 | 6.81 | |||

SD + NN + PS | 5.55% | 4.30 | 5.50 | |||

Average | SD | 10.63% | 5.90 | 7.14 | 14.05 | 681 |

SD + NN | 8.49% | 5.75 | 7.08 | |||

SD + NN+PS | 6.20% | 5.26 | 6.92 |