Electricity Price Forecasting

In this paper an efficient method is proposed for electricity price forecasting. This paper focuses on Locational Marginal Price (LMP) that efficiently maintains power markets by alleviating transmission network congestion. There are complicated behaviors of the time series due to uncertain factors in the power markets. From a standpoint of market players, a sophisticated method is required to forecast LMP effectively. The proposed method makes use of the hybridization of GP (Gaussian Process) of hierarchical Bayesian estimation, EPSO (Evolutionary Particle Swarm Optimization) of evolutionary computation and fuzzy c-means of allowing data to belong to two or more clusters. EPSO is used to improve the accuracy of parameters in MAP (Maximum a Posteriori) estimation for GP. The use of fuzzy c-mean is useful for increasing the number of learning data for GP to deal with spikes. The effectiveness of the proposed method is demonstrated for real LMP data.

ABSTRACT: The Iberian Market for Electricity resulted from a cooperation process developed by the Portuguese and Spanish administrations, aiming to promote the integration of the electrical systems of both countries. This common market consists of organised markets or power exchanges, and non-organised markets where bilateral over-the-counter trading takes place with or without brokers. Within this scenario, electricity price forecasts have become fundamental to the process of decision-making and strategy development by market participants. The unique characteristics of electricity prices such as non-stationarity, non-linearity and high volatility make this task very difficult. For this reason, instead of a simple time forecast, market participants are more interested in a causal forecast that is essential to estimate the uncertainty involved in the price. This work focuses on modelling the impact of various explanatory variables on the electricity price through a multiple linear regression analysis. The quality of the estimated models obtained validates the use of statistical or causal methods, such as the Multiple Linear Regression Model, as a plausible strategy to achieve causal forecasts of electricity prices in medium and long-term electricity price forecasting. From the evaluation of the electricity price forecasting for Portugal and Spain, in the year of 2017, the mean absolute percentage errors (MAPE) were 9.02% and 12.02%, respectively. In 2018, the MAPE, evaluated for 9 months, for Portugal and Spain equals 7.12% and 6.45%, respectively.

Abstract—Electricity price forecasting is considered as an important tool for energy-related utilities and power generation industries. The deregulation of power market, as well as the competitive financial environment, which have introduced new market players in this field, makes the electricity price forecasting problem a demanding mission. The main focus of this paper is to investigate the performance of asymmetric neuro-fuzzy network models for day-ahead electricity price forecasting. The proposed model has been developed from existing Takagi–Sugeno–Kang fuzzy systems by substituting the IF part of fuzzy rules with an asymmetric Gaussian function. In addition, a clustering method is utilised as a pre-processing scheme to identify the initial set and adequate number of clusters and eventually the number of rules in the proposed model. The results corresponding to the minimum and maximum electricity price have indicated that the proposed forecasting scheme could be considered as an improved tool for the forecasting accuracy.

The problem of electricity price forecasting is related yet distinct from that of electricity load (demand) forecasting [2–5]. Although the load and the price are correlated, their relation is non-linear. The load is influenced by various factors such as non-storability of electricity, consumers’ behavioral patterns, and seasonal changes in demand. The price, on the other hand, is affected by those aforesaid factors as well as additional aspects such as financial regulations, competitors’ pricing, dynamic market factors, and various other macro- and micro-economic conditions. As a result, the price of electricity is a lot more volatile than the electricity load. Interestingly, when dynamic pricing strategies are introduced, prices become even more volatile, where the daily average price changes by up to 50% while other commodities generally exhibit only about 5% of change in maximum [6]. A number of research works have been performed on electricity price forecasting [7–10]. However, to our best knowledge, none of them is able to provide adequately accurate results consistently for all the cases for the respective experimental data of their target market. Thus, a more accurate price forecasting system is necessary to facilitate all the stakeholders, where the consumers’ consumption patterns will depend on the future electricity prices, and so are the businesses of the wholesalers, the traders, and the retailers.

Since the liberalization of the electricity markets, electricity price forecasting has become an essential task for all the players of the electricity markets due to several reasons. Energy supply companies, especially dam-type hydroelectric, natural gas, and fuel oil power plants could optimize their procurement strategies according to the electricity price forecasts. As the share of the regulated electricity markets, such as day-ahead and balancing markets, increase day by day; bilateral contracts also take the regulated-market prices as a benchmark [1]. Moreover, prices of the energy derivatives are also based on electricity price forecasts [2]. From the demand side, some of the companies can schedule their operations according to the low-price zones and operate in these hours or months. Zareipour et al. [3] stress the importance of the short-term electricity forecasting accuracy. A 1% improvement in the mean absolute percentage error (MAPE) would result in about 0.1% - 0.35% cost reductions from short term electricity price forecasting, which results to circa $1.5 million per year for a medium-size utility with a 5-GW peak load [4], [5].

The BFOA was found to search food quicker than other optimization methods (Prabaakaran, Jaisiva, Selvakumar, & Kumar, 2013) and shows a great performance rather than other meta-heuristic optimization approaches like GA (A.V.S.Sreedhar Kumar, V.Veeranna, 2013; Hoo & Han, 2012; Jhankal & Adhyaru, 2011; Majhi, Panda, Majhi, & Sahoo, 2009; Sakthivel, Bhuvaneswari, & Subramanian, 2010), PSO (Hoo & Han, 2012; Karnan & Krishnaraj, 2012; Majhi et al. 2009; Sakthivel et al. 2010), ACO (Karnan & Krishnaraj, 2012), and SA (Hoo & Han, 2012) in many fields. In fact, the application of BFOA in electricity price forecasting is not reported yet. Thus, the hybrid method of LSSVM and BFOA is proposed in this paper to improve forecasting performance for short term electricity price forecasting. The inclusion of BFOA as feature selection and LSSVM’s parameter selection gives more efficient and accurate result with lesser complexity than other optimization methods. The developed models are also applicable for Malaysia when the deregulated electricity market exists in future..

Many electricity price forecasting methods have been proposed, and they generally can be divided into market simulation and the method centred on history data. Market simulation predicts the market clearing prices by simulating the competition operation. The second kind of method based on time series analysis of history data to build ma- thematical model and make the prices forecasting [4]. Box-Jenkins method belongs to the time-series model. Box-Jenkins Analysis refers to a systematic method of identify- ing, fitting, checking, and using autoregressive integrated moving average (ARIMA) time series models.

Electricity price forecasting has become an important aspect of promoting competi- tion and safeguarding the interests of participants in electricity market. As market participants, both producers and consumers intent to contribute more efforts on de- veloping appropriate price forecasting scheme to maximize their profits. This paper introduces a time series method developed by Box-Jenkins that applies autoregres- sive integrated moving average (ARIMA) model to address a best-fitted time-domain model based on a time series of historical price data. Using the model’s parameters determined from the stationarized time series of prices, the price forecasts in UK electricity market for 1 step ahead are estimated in the next day and the next week. The most suitable models are selected for them separately after comparing their pre- diction outcomes. The data of historical prices are obtained from UK three-month Reference Price Data from April 1 st to July7 th 2010.

16- Razak, A.W.A., Abidin, I. Z., Yap, K. S., Abidin, A. A. Z., Rahman, T. K. A., & Nasir, M. N. M. (2016). A novel hybrid method of LSSVM-GA with multiple stage optimization for electricity price forecasting. IEEE International Conference on Power and Energy (PECon), Melaka (2016), 390–395.

16- Razak, A.W.A., Abidin, I. Z., Yap, K. S., Abidin, A. A. Z., Rahman, T. K. A., & Nasir, M. N. M. (2016). A novel hybrid method of LSSVM-GA with multiple stage optimization for electricity price forecasting. IEEE International Conference on Power and Energy (PECon), Melaka (2016), 390 – 395.

POKORA JINDŘICH. 2017. Hybrid ARIMA and Support Vector Regression in Short‑term Electricity Price Forecasting. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 65(2): 699–708. The literature suggests that, in short‑term electricity‑price forecasting, a combination of ARIMA and support vector regression (SVR) yields performance improvement over separate use of each method. The objective of the research is to investigate the circumstances under which these hybrid models are superior for day‑ahead hourly price forecasting. Analysis of the Nord Pool market with 16 interconnected areas and 6 investigated monthly periods allows not only for a considerable level of generalizability but also for assessment of the effect of transmission congestion since this causes differences in prices between the Nord Pool areas. The paper finds that SVR, SVRARIMA and ARIMASVR provide similar performance, at the same time, hybrid methods outperform single models in terms of RMSE in 98 % of investigated time series. Furthermore, it seems that higher flexibility of hybrid models improves modeling of price spikes at a slight cost of imprecision during steady periods. Lastly, superiority of hybrid models is pronounced under transmission congestions, measured as first and second moments of the electricity price.

Abstract—This paper proposes a medium-term equilibrium model which aims to explain the variation of electricity price as a function of several explanatory variables. This analysis uses the cointegration methodology to model stationarity rela- tionships while preserving the long-run relationship lost through differencing. We should note that a cointegration relationship expresses a long-run equilibrium, but obviously in the short term can befall imbalances. Using what is known as Error Correction Model (ECM), we can relate short-term behavior of the different variables with their long-term behavior. Fur- thermore, this multivariate model enables both predict and analyze the dynamic relationships between the used variables. The methodology is comprehensively tested in a case study based on the Spanish market. Examination of the model goodness of fit and interpretability is done by means of statistical and graphical tools. This approach can achieve satisfactory results in capturing the dynamics of the price of electricity and could provide companies with valuable information when facing their decision making and risk-management process.

Figure 8 shows an increase in the ( + ) error as k increased, that is, the performance of the forecast for the day D + k worsens as the considered day D + k is farther away from day D. The forecasts provided at day D for day D + k with k = 2 to 5 can be important for a forecast user when no new forecasts are available at the days following day D due to (for example) fails in technology supporting the communications between such forecast user and the forecast provider, or due to any kind of energy storage, which might need to know prices over the next few days to decide operation now. Figure 8 proves that forecast performances up to k = 5 have an acceptable quality and, therefore, the forecasts for k = 2 to 5 (at day D) could be considered for practical strategic decisions, especially when they are the only information available (i.e., due to fails in technology, as specified above). Furthermore, the price forecast for k = 2 to 5 can be useful for some decisions associated with short- term bidding strategies in electricity markets, as for example bidding in week-ahead future electricity derivative products.

Statistical analysis was used to find the dominant fac- tors that decide the present electricity cost. An overview of price and demand variation for a week, shown in Fig- ure 1 below, shows that the price variation is a complex trend that requires detailed analysis to establish the influ- encing factors. The figure also shows that demand varies with some readily observable repetitive pattern yet in the same period the price shows spikes of varying magnitude and duration.

Specifically, in [15], the authors proposed methods including hybrid networks of self-organized map (SOM) and support-vector machine (SVM) to predict short-term electricity price. With the trained network, one can predict the future hourly elec- tricity prices in one day ahead. To confirm its feasibility, the proposed model had been trained and tested on the data of historical energy prices from the New Eng- land electricity market. In addition, in [16], a sensitivity analysis of similar days (SD) parameters to rise the accuracy of ANN model and SD-based short-term price fore- casting model were presented. In order to train the network, a large sum of data were used. The model had been tested in Pennsylvania-New Jersey-Maryland (PJM) elec- tricity market. The results showed that the mean absolute percentage error (MAPE) was around 11%. Furthermore, in [17], the authors introduced a method to predict next-day electricity prices based on the ARIMA methodology which was used to analyze the time series problem. The ARIMA model was tested in California elec- tricity market. More than 30-day historical data samples were required to train the model.

Support vector machine is another technique which has been reported as a better method than time series [20] and neural network [1]–[4], [21]– [31] in terms of model complexity, accuracy and efficiency. In [32], Chaotic Least Squares Support Vector Machine (CLSSVM) was combined with Wavelet Transform (WT) and Exponential Generalized Autoregressive Conditional Heteroskedastic (EGARCH) model to handle high volatility price series with the average error of 2.7% for PJM market and 2.58% for Spanish market. The hybrid method of rolling time series and LSSVM yielded MAPE of 2.26%; outperforming BPNN (4.11%) and ARMAX-AR-GARCH (2.72%) in [3]. Same goes for GA-LSSVM method in [26] method which produced MAPE of 4.2-9.7%; surpassing other techniques for all seasons.

A neural network approach for forecasting short-term electricity prices. Almost Until the end of last century, electricity supply was considered a public service and any price forecasting which was undertaken tended to be over the longer term, concerning future fuel prices and technical improvements. Short-term forecasts have become increasingly important since the rise of the competitive electricity markets. In this new competitive framework, short-term price forecasting is required by producers and consumers to derive their bidding strategies to the electricity market. Price forecasting in competitive electricity markets is critical for consumers and producers in planning their Operations and managing their price risk and it also plays a key role in the economic optimization of the electric energy industry. Accurate, short-term price forecasting is an essential instrument which provides crucial information for power producers and consumers to develop accurate bidding strategies in order to maximize their profit.

conditional heteroskedastic (GARCH) models  and ARMA has been successfully demonstrated for  predicting the electricity price in ISO New England market [12]. Alternatively, the combination of  ARIMA  models  and  signal  processing  techniques,  such  as  wavelets,  has  been  explored  for  the  Singapore electricity market [13]. Although some promising results have been achieved using these  linear  techniques,  they  cannot  model  adequately  the  non‐linear  characteristics  of  the  electricity  price. In cases where high‐frequency changes of the electricity price occur, the application of these  methods could be considered as problematic [14]. In recent years, alternative methodologies based  on computational intelligent techniques, including neural networks (NN) have been investigated by  researchers for  EPF.  Multilayer perceptrons (MLP) and radial basis function (RBF) NNs have been  successfully used in forecasting the electricity price volatility in PJM market, the United States [15].    Electricity price signal  characteristics,  such  as  non‐stationarity and  time  variance,  have  been  addressed  with  the  aid  of  appropriate  feature  selection  techniques  [16].  Similarly,  MLP‐based  models have been explored to predict next‐week prices  in California as well as Spanish electricity  markets [17]. These NN approaches outperformed the ARIMA as well as the naïve methods used in  all  cases.  This  reveals  the  superiority  of  NN‐based  systems  over  methods  which  have  been  traditionally used in energy forecasting systems. An Elman recurrent NN has been also utilized to  EPF  for  the  mainland  Spain  market,  using  samples  captured  during  winter  and  summer  weeks,  achieving a superior to MLP‐based NNs performance [18]. The further development of NNs has led  to  the  evolution  of  deep  learning  (DL)‐based  systems.  Long‐short  term  memory  (LSTM)  and  convolutional  neural  network  (CNN)  based  models  have  been  applied  and  compared  against  ARIMA  and single hidden‐layer MLP  models for  the  day‐ahead price  market in Belgium. Results  revealed a clear  advantage of DL models over traditional approaches; however their  performance  against MLP networks was rather comparable [19].   

Abstract – In a competitive electricity market, short-term electricity price forecasting are very important for market participants.Electricity price is a very complex signal as a result of its non-linearity, non-stationary and time-variant behavior. This studypresents a new approach to short-term electricity price forecasting. The proposed method is derived by integrating the kernelprincipal component analysis (KPCA) method with the local Gaussian Process (GP), which can be derived bycombining the GP with the local regression method. Local prediction makes use of similar historical data patterns in the reconstructed space to train the regressionalgorithm. In the proposed method, KPCA is used to extract features of the inputs and obtain kernel principal components forconstructing the phase space of the time series of the inputs. Then local GP is employed to solve the price forecastingproblem. The proposed method is evaluated using real-world dataset. The results show that the proposed method can improvethe price forecasting accuracy and provides a much better prediction performance in comparison with other recentlypublished approaches.

electricity demand is met by these type of fast starting generating units and usually cost 10 to 100 times more than the regular electricity MCP. Therefore, the daily price of natural gas also influences the electricity MCP and should be included as a part of the training input data. Although electricity MCP is very volatile, it is still normally distributed along its average value [50-52]. Therefore, previous year’s monthly average electricity MCP is included in the input data to help the price forecasting model to set the initial forecasting point. Month (1 to 12) is a straightforward element that can represent the impact of season change on average electricity demand and price. For instance, the electricity MCP is high during summer and winter due to the higher consumption of electricity for heating and cooling. Hour of the day (1 to 24) is paired up with electricity daily peak demand so the forecasting model could better locate the time of daily peak demand during forecasting. The target datum at hour t is the electricity MCP at hour t. Moreover, based on the previous published works [22-24] regarding the selection of training data for mid-term electricity price forecasting, one year is the most optimized length of historical data to train the forecasting model.