1949-3053 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2018.2807845, IEEE Transactions on Smart Grid Abstract—Competitive transactions resulting from recent restructuring of the electricity market, have made achieving a precise and reliable load forecasting, especially probabilistic load forecasting, an important topic. Hence, this paper presents a novel hybrid method of probabilistic electricity load forecasting, including generalized extreme learning machine (GELM) for training an improved wavelet neural network (IWNN), wavelet preprocessing and bootstrapping. In the proposed method, the forecasting model and data noise uncertainties are taken into account while the output of the model is the load probabilistic interval. In order to validate the method, it is implemented on the Ontario and Australian electricity markets data. Also, in order to remove the influence of model parameters and data on performance validation, Friedman and post-hoc tests, which are non-parametric tests, are applied to the proposed method. The results demonstrate the high performance, accuracy and reliability of the proposed method. Index Terms—Probabilistic Forecasting, Improved Wavelet Neural Network, Generalized Extreme Learning Machine, Bootstrapping, Wavelet Processing. I. INTRODUCTION N the last decades, the structure of the electricity market has changed a lot, forming the restructured market. In this market, it is essential to access a reliable and accurate load forecasting considering some other activities such as economic dispatch, bidding strategies and unit commitment. However, demand is becoming significantly active and less predictable due to the various demand response programs, distributed energy sources and emerging technologies [1]. As a result, load forecasting plays a very significant role in decision- making activities for market participants. The majority of the studies in the field of load forecasting focus on the point forecasting techniques. However, the results are not reliable because of the fluctuations’ existence in load and structure of the electricity market. Point forecasting has done some statistical techniques such as exponential smoothing models [2], regression [3] and time series [4]. Also, the forecasting type has implemented some artificial intelligence techniques such as neural networks [5], support vector machines [6] and fuzzy systems [7]. In [8], a multiple time series equation model, based on frequent use of first- order least squares, is represented to forecast the load, and its superiority is compared with non-linear and non-parametric methods. Recurrent extreme learning machine with high accuracy is proposed in [5] as a new method for forecasting the load. This method has been used to train the single-layer recurrent neural network. In [9], a new design based on type II fuzzy logic system is proposed and applied to the active learning theory to forecast the electrical load. Recently, based on the increased market competition, aging infrastructure, renewable integration requirements and the more active and less predictive electricity market, the market participants are interested in using the probabilistic load forecasting, which provides additional information on the variability and uncertainty of electricity load series in comparison with point forecasting technique. Also, the probabilistic load forecasting is needed in some processes such as stochastic unit commitment [10,11], reliability planning [12] and probabilistic load flow [13]. One form of achieving the probabilistic load forecasting is the prediction intervals (PIs). In this method, the forecasting is based on the point forecasting and the error obtained by uncertainties [14]. In [15], semi-parametric regression model, multivariate time series simulation model and resampling strategy are used for point load forecasting, temperature forecasting and building probabilistic forecasting, respectively. In [16], the quantile regression averaging method on a set of forecasted points is presented to predict the probability. The advantage of this method is the ability to use point forecasting. In [17], a diffused heteroscedastic forecasting method based on the Gaussian process in daily load forecasting is proposed. Another method which is defined and used in this area is deep learning, which is presented in [18, 19]. The aim of such researches on deep learning theory is to show its ability in different areas. But, still there are two common issues about the theory, which are overfitting and computation time. Probabilistic Load Forecasting using an Improved Wavelet Neural Network Trained by Generalized Extreme Learning Machine Mehdi Rafiei, Taher Niknam, Member, IEEE, Jamshid Aghaei, Senior Member, IEEE, Miadreza Shafie-khah, Senior Member, IEEE, and João P. S. Catalão, Senior Member, IEEE I J.P.S. Catalão acknowledges the support by FEDER funds through COMPETE 2020 and by Portuguese funds through FCT, under Projects SAICT-PAC/0004/2015 - POCI- 01-0145-FEDER-016434, POCI-01-0145-FEDER-006961, UID/EEA/50014/2013, UID/CEC/50021/2013, UID/EMS/00151/2013, and 02/SAICT/2017 - 029803, and also funding from the EU 7th Framework Programme FP7/2007-2013 under GA no. 309048. M. Rafiei and T. Niknam are with the Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran (e-mails: m_rafiei@ymail.com; niknam@sutech.ac.ir). J. Aghaei is with the Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran, also with the Department of Electric Power Engineering, Norwegian University of Science and Technology (NTNU), Trondheim NO-7491, Norway (e-mail: aghaei@sutech.ac.ir). M. Shafie-khah is with C-MAST, University of Beira Interior, Covilhã 6201-001, Portugal (e-mail: miadreza@gmail.com). J.P.S. Catalão is with INESC TEC and the Faculty of Engineering of the University of Porto, Porto 4200-465, Portugal, also with C-MAST, University of Beira Interior, Covilhã 6201-001, Portugal, and also with INESC-ID, Instituto Superior Técnico, University of Lisbon, Lisbon 1049-001, Portugal (e-mail: catalao@ubi.pt).