Electricity price forecasting for Nord Pool data Rita Beigaitė Vytautas Magnus University, Lithuania Baltic Institute of Advanced Technology, Lithuania e-mail:rita.beigaite@bpti.lt Tomas Krilavičius Vytautas Magnus University, Lithuania Baltic Institute of Advanced Technology, Lithuania e-mail: t.krilavicius@bpti.lt Abstract–Due to worldwide liberalization of differently with distinct countries (markets). power markets, electricity can be purchased and In recent literature many of electricity price sold as any other commodity. The market spot forecasting approaches are hybrid solutions, which price of electricity has features such as high combine two or more different methods. For instance, volatility, seasonality and spikes. In order to the proposed approach in [1] is a combination of minimize risks, maximize profits and make future adaptive-network based fuzzy inference system and plans, it is important for participants of electricity particle swarm optimization. It is applied to forecast market to forecast future prices. The vast number next-week prices in the electricity market of mainland of various methods is applied for solving this Spain. For the sake of simplicity and clear problem. However, the accuracy of forecasts is not comparison, no exogenous variables are considered. sufficient, different approaches work differently The forecasting accuracy is measured by using MAPE with different countries (markets). In this paper error which is 5.28 %. we describe our experiments with electricity spot Another example would be in [2] introduced price data of Lithuania’s price zone in Nord Pool hybrid intelligent algorithm utilizing a data filtering power market. Short-term forecasts are made by technique based on wavelet transform, an using Average, Seasonal Naïve and Exponential optimization technique based on firefly algorithm, and smoothing methods, and results are reported. a soft computing model based on fuzzy ARTMAP network. This method is used to forecast day-ahead Keywords–electricity spot price; forecasting electricity prices in the Ontario market. Prognoses are made for 24 and 168 hour short-term horizons. The accuracy of method is measured by using MAPE, I. INTRODUCTION MAE errors as well as coefficient of determination. MAPE error, which is calculated for 24 hour horizon, Nowadays electricity can be considered as varies from 6.24 % to 7.67 %. any other commodity. It can be purchased, sold, traded A hybrid wavelet-ELM (Extreme Learning under the rules of electricity market. This is the Machine) method is applied in [3]. Short-term outcome of worldwide liberalization of power forecasts are made for Ontario, PJM, Italy and New markets. In order to minimize risks, maximize profits York Electricity markets. MAE, MAPE, MDE errors and make plans, it is important for participants of are chosen for evaluation of accuracy. electricity market to forecast future prices. For In [4] an econometric model for the hourly instance, using accurate short-term price forecasting, electricity price of the European Power Exchange for power suppliers can make bidding strategies, which Germany and Austria is presented. The model, which would lead to higher profits. However, due to can be regarded as a periodic VAR-TARCH, is characteristics of electricity spot price such as high proposed in order to capture the specific price volatility, multiply seasonality and spikes, it is a movements. Wind power, solar power, and load are challenging task to forecast accurately. Despite the considered as factors which have influence on the large number of various methods which are applied for price. prediction of electricity spot prices, the accuracy of Out of literature by Lithuanian authors, there forecasts is not sufficient as various approaches work was only one master thesis on the topic of electricity Copyright © 2017 held by the authors 37 Figure 1. Boxplots of aggregated price data price forecasting. Forecasts in [5] are made groups: for France market using SARIMA-TGARCH and 1) multi-agent (Nash-Cournot framework, supply SARFIMA-TGARCH models. function equilibrium, strategic production-cost In this paper we discuss application of models, agent-based simulation models); short-term forecast using Average, Seasonal Naïve 2) fundamental (parameter-rich fundamental models, and Exponential smoothing methods to electricity spot parsimonious structural models); price data of Lithuania’s price zone in Nord Pool 3) reduced-form (jump-diffusion models, Markov power market. regime-switching models); 4) statistical (similar-day and exponential smoothing II. METHODS methods, regression models, AR-type time series models, ARX-type time series models, threshold Based on [6], models, applied for electricity autoregressive models, heteroskedasticity and price forecasting, can be classified into five broad GARCH-type models); 38 5) computational intelligence (feed-forward neural an influential factor. networks, recurrent neural networks, fuzzy neural Historical electricity prices and demand data networks, support vector machines). are considered to be the two of the main factors [7]. With multi-agent models price process is simulated by matching the demand and supply in the Forecasting Horizons market. These models are considered as extremely flexible tools for the analysis of strategic behaviour in Electricity price forecasting can be electricity markets. However, as they generally focus categorized into three different categories based on on qualitative issues, high accuracy of prediction time horizons. Nonetheless, there is no consensus in cannot be achieved. the literature as to what the thresholds should actually Fundamental techniques are used to be. These categories are [6, 8]: characterize dynamics of electricity price by taking 1) Short-term forecasts can involve forecasts from a into consideration physical and economical factors, few minutes up to a few days or a week. They are which may have impact on the price. There are two mainly used by the market players with the intention main problems while constructing such models. The to maximize profits in the spot markets. first problem is the availability of information and 2) Medium-term horizons can be considered from a data. The second problem concerns incorporation of few days to a few months ahead. They might be stochastic fluctuations of fundamental factors. preferred for balance sheet calculations, risk Reduced-form approaches are used to management and allow the successful negotiations describe statistical properties of electricity prices over of bilateral contracts between suppliers and time. The accuracy of forecasts using these models is consumers. not expected to be high. On the other hand, such 3) Long-term forecasting period can vary from few models provide realistic description of electricity price months up to few years. Such forecasts might dynamics and are commonly used for derivatives 1 influence the decisions on transmission expansion pricing and risk analysis. and enhancement, generation augmentation and Using statistical models the forecast is made distribution planning. by mathematically combining previous prices. The accuracy of these models depends on efficiency of Measures of Accuracy algorithms, quality of the data, ability to incorporate values of important exogenous factors. The main Point forecasts are used in majority of weakness of these methods is poor performance in the electricity price forecasting papers. Therefore, presence of price spikes. accuracy measures, which are based on absolute Computational intelligence methods are errors, are the mostly used. Error is defined as the flexible and can handle complexity as well as difference between the actual value and the forecast non-linearity. However, the ability to adapt to value for the corresponding period. Due to easy non-linear, spiky behaviours may not necessarily interpretation, by far the most popular measure is the result in better point forecasts. mean absolute percentage error (MAPE). Though, MAPE error might be misleading in the presence of Factors close to zero prices [6, 8]. 1) Mean Absolute Percentage Error 𝑛 A number of factors can influence fluctuation 100 𝐴𝑡 − 𝐹𝑡 of electricity prices. Due to the exogenous variables 𝑀𝐴𝑃𝐸 = ∑| | 𝑛 𝐴𝑡 such as technical limitation and oil price, electricity 𝑡=1 generation capacity and cost are changing. Energy 2) Mean Absolute Error or Mean Absolute Deviation 𝑛 demand varies as well, and depends on the time of the 1 day, weekday, season and weather conditions [7], e.g., 𝑀𝐴𝐸 = 𝑀𝐴𝐷 = ∑ |𝐹𝑡 − 𝐴𝑡 |. 𝑛 during the hot summer day due to high usage of 𝑡=1 cooling systems, demand significantly increases. 3) Mean Squared Error 𝑛 Uncertainty in factors such as weather, equipment 1 outages, fuel prices, and transmission bottlenecks can 𝑀𝑆𝐸 = ∑ (𝐹𝑡 − 𝐴𝑡 )2 . 𝑛 cause extreme price volatility or spikes [3]. 𝑡=1 4) Root Mean Square Error The supply of energy from renewable sources, especially solar and wind, rose significantly 𝑛 1 within the past years [4], hence it is also considered as 𝑅𝑀𝑆𝐸 = √𝑀𝑆𝐸 = √ ∑ (𝐹𝑡 − 𝐴𝑡 )2 . 𝑛 𝑡=1 1 Financial contract with a value based on an underlying asset. 39 For identification of the dominant periods Here 𝐴𝑡 is the real value and 𝐹𝑡 – forecast value. (frequencies) of data set, periodogram 2 was used (Figure 2). Seasonality of daily (the highest spike in III. DATA periodogram), annual (second most significant spike), 12-hour (third highest spike) and weekly (fourth Data Set highest spike) frequencies were detected. In this paper data of Lithuania’s price zone in IV. FORECASTING Nord Pool power market is analysed. The data set consists of historical hourly electricity prices Experimental results (Eur/MWh) from January 1, 2014 to December 31, 2016. Forecasting experiments were made for each day of the year 2016. Average, Seasonal Naïve and Data Analysis Seasonal Exponential smoothing methods were used for short-term day-ahead prognosis of total 24 points Data set was analysed using descriptive (description of these methods can be found in [9]). statistics. In Table 1 and Figure 1 summary electricity Daily seasonality was chosen as the most important in price data is provided. Seasonal Naïve method. Exponential smoothing was Statistical analysis shows that electricity automatically selected using statistical package R. The price is lower on weekends compared to other days of accuracy was measured using RMSE, MAE and the week. The price is also lower in winter and spring MAPE errors. months, as well as on night hours of the day. In See summary of yearly results in Tables 2, 3 comparison to midday hours, there are much less and 4. outliers during the night hours. Moreover, these price Table II spikes are less significant. The highest price peak, SUMMARY OF YEARLY ERRORS. which reached 300 Eur, was on Monday. During EXPONENTIAL SMOOTHING METHOD. summer months, there are much more spikes (which Statistic RMSE MAE MAPE can be seen as outliers in the boxplot) than in other Mean 8.64 6.49 16.03 seasons of the year. Median 5.76 4.53 12.18 Table I Standard deviation 10.46 7.10 11.43 Variance 109.37 50.48 130.68 DESCRIPTIVE STATISTICS Minimum 0.83 0.69 1.76 Statistic Value Maximum 94.02 70.96 95.04 N 26304 Mean 42.86 Median 40.76 Table III Standard deviation 19.68 SUMMARY OF YEARLY ERRORS. SEASONAL Variance 387.22 NAÏVE METHOD. Minimum 4.02 Statistic RMSE MAE MAPE Maximum 300 Mean 9.36 6.70 16.6 Median 5.89 4.43 12.40 Standard deviation 11.83 7.86 13.87 Variance 139.90 61.74 192.28 Minimum 1.02 0.66 1.91 Maximum 100.2 76.48 118.0 Table IV SUMMARY OF YEARLY ERRORS. AVERAGE METHOD. Statistic RMSE MAE MAPE Mean 11.78 9.79 28.32 Median 8.82 7.72 25.19 Standard deviation 10.78 8.07 15.07 Variance 116.23 65.10 227.08 Minimum 2.11 1.79 4.64 Maximum 99.0 79.63 103.1 Figure 2. Periodogram of data set 2 An estimate of the spectral density of a signal. 40 Figure 3. Forecasts for weekday in winter Figure 5. Forecasts for weekday in summer Figure 4. Forecasts for weekend in winter Figure 6. Forecasts for weekend in summer See forecasts for one work day and one The highest accuracy (considering all three weekend day of randomly chosen winter and summer measures of accuracy) was achieved using weeks of 2016 in Figures 3, 4, 5 and 6. In Figure 6 Exponential smoothing method. The lowest MAPE significant difference between predicted prices and error was equal to 1.76%. However, average MAPE real values can be noticed. MAPE error of this day was error of the year was 16.03% with standard deviation equal to 72.67 %. In this case, predicted day was of 11.43%. As there are many outliers in the data, Saturday and there was prices spikes the day before. In median of MAPE (which is equal to 12.18%) might Seasonal Naïve method each forecast is assumed to be better represent the typical error. equal to the last observed value from the same period. 41 Therefore, prognosis was extremely inaccurate. On an electricity market,” pp. 1-6, 2015. [8] N. Singh, S. Mohanty, “A review of price forecasting problem the other hand, performance of Exponential and techniques in deregulated electricity markets,” Journal of smoothing method was quite accurate with MAPE Power and Energy Engineering, vol. 3(9), p. 1, 2015. error equal to 8.54% that day. Figures 3 and 5 show [9] R. J. Hyndman, G. Athanasopoulos, “Forecasting: principles and how all methods are unable to capture sudden price practice.” OTexts, 2014. peaks. Only on winter weekend day (4 Figure), accuracy of Average method was highest according to MAPE error which was equal to 22.13%. However, RMSE and MAE errors of Exponential smoothing method for that day were lower. V. CONCLUSIONS AND FUTURE WORK Electricity price posses features such as high volatility and spikes. Even though there are many methods which can be used in electricity price forecasting, these features make it difficult to achieve high accuracy of forecasts. Therefore, in the recent literature mostly hybrid models are being suggested. Analysis of Lithuania’s price zone data shows that there is daily, weekly and annually seasonality patterns. Furthermore, prices tend to be lower in winter-spring months, at night and on weekends. Forecasting experiments show that simple statistical methods are not performing well when it comes to capturing spikes as well as transition from workday to weekend day and vice versa. The highest accuracy was achieved using Exponential smoothing method. Future work plans are to search for the best approach for Lithuania’s electricity price zone by testing more advanced statistical, machine learning and hybrid models, especially, including external data. REFERENCES [1] H. M. I. Pousinho, V. M. F. Mendes, J. P. D. S. Catalão, “Short-term electricity prices forecasting in a competitive market by a hybrid pso–anfis approach,” International Journal of Electrical Power & Energy Systems, vol. 39(1), pp. 29-35, 2012. [2] P. Mandal, A. U. Haque, J. Meng, A. K. Srivastava, R. Martinez, “A novel hybrid approach using wavelet, firefly algorithm, and fuzzy artmap for day-ahead electricity price forecasting,” IEEE Transactions on Power Systems, vol. 28(2), pp. 1041-1051, 2013. [3] N. A. 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