Elsevier

Applied Energy

Volume 172, 15 June 2016, Pages 132-151
Applied Energy

Day-ahead electricity price forecasting via the application of artificial neural network based models

https://doi.org/10.1016/j.apenergy.2016.03.089Get rights and content

Highlights

  • The paper focuses in short-term price load forecasting.

  • Several Day-ahead forecasting models are proposed and tested.

  • The clustering tool is combined with neural network.

  • We focus on no pre-processed data.

Abstract

Traditionally, short-term electricity price forecasting has been essential for utilities and generation companies. However, the deregulation of electricity markets created a competitive environment and the introduction of new market participants, such as the retailers and aggregators, whose economic viability and profitability highly depends on the spot market price patterns. The aim of this study is to examine artificial neural network (ANN) based models for Day-ahead price forecasting. Specifically, the models refer to the sole application of ANNs or to hybrid models, where the ANN is combined with clustering algorithm. The training data are clustered in homogenous groups and for each cluster, a dedicated forecaster is employed. The proposed models are characterized by comprehensive operation and by high level of flexibility; different inputs can be taken under consideration and different ANN topologies can be examined. The models are tested on a data set that consists of atypical price patterns and many outliers. This approach makes the price forecasting problem a more challenging task, providing evidence that the proposed models can be considered as useful and robust forecasting tools to the actual needs of market participants, including the traditional generation companies and self-producers, but also the retailers/suppliers and aggregators.

Introduction

Modern power systems planning includes a variety of resources to cover the increasing demand subject to the various techno-economic and environmental constrains [1]. Load forecasting is of fundamental importance for power systems operation and this fact is reflected by the plethora of related researches. Many methodologies that differ in the data preprocessing, model selection, calibration and testing phases, have been presented [2]. The load forecasting literature is expanded. It includes single models or more sophisticated models that combine various computational intelligence algorithms [3].

On the other hand, the literature on price forecasting is less numerous [4]. This is due to the fact that most markets were structured as monopolies until recently; wholesale competition was absent or limited. While electricity markets become competitive, price forecasting is gathering research momentum. Price forecasting is a relatively more difficult task due to the endogenous characteristics of price time series [5]. Since the determination of the hourly market clearing price (MCP) is held within a dynamic and competitive environment, MCP is characterized by volatility [6]. MCP’s chronological evolution is influenced by a set of diverse parameters like demand, fuel prices such as coal and natural gas, merit order of generation plants, hydropower capacity, market participants strategies, network congestion and others [7]. Thus, special care should be placed on the inputs selection, model’s parameters and calibration, model’s assessment and generally, on the experimental set-up that will result in a robust forecaster.

The electricity price forecasting problem influences various processes expanded on different time frames in modern power systems operation. It is closely related with other contemporary scientific and engineering problems such as the optimal power generation units scheduling, fuel consumption, energy resources exploitation, GHG emissions, power systems simulation and electricity demand modeling. Therefore, it is inter-connected with other problems and tasks. Due to this attribute, it is a research topic targeting multi-disciplinary audiences within the power systems community. Also, while price forecasting is related to the energy market transactions and operations, various market participants (utilities, grid operators, retailers, aggregators and others) are interested in obtaining short-term predictions.

The aim of this work is to explore the potential of ANN based models on price forecasting. We examine models built solely on ANN and hybrid models that combine unsupervised machine learning via the clustering tool and supervised machine learning via the ANN. A reliable forecaster should be easy to implement and characterized by high level of parameterization. The analysis of the study is centered toward these goals.

In the price forecasting literature, many models have been proposed based on computational intelligence. The models refer to sole algorithms or more complex hybrid approaches. The present paper examines a set of single and hybrid models on the case of using no preprocessed data. The single models refer to ANNs and more specifically, to Multi-Layered Perceptrons (MLPs) and the hybrid combine MLPs and clustering. In the literature, many robust models such as Fuzzy Neural Network (FNN), Support Vector Machines (SVMs) and Radial Basis Function (RBF) networks. Our preference on the MLPs over the others is justified by the following reasons:

  • (a)

    Our focus is mainly on the current data. We adapt the most common approach of the literature (i.e., the MLPs) to examine their performance on special data sets. Also, by using single MLPs, it is easy to examine various configurations that differ in the number and type of inputs. The comparison with more complex models such as the FNN is left for future research.

  • (b)

    A basic advantage of the MLPs is their training flexibility. The user can select between a large set of modified back-propagation algorithms in contrast to SVMs and RBFs networks. Different training algorithms apply to various problems, providing the user a flexible and adaptable modeling tool.

  • (c)

    The MLPs require less training time contrary to SVMs and RBFs. For example, in the case of the RBFs networks, the number of RBF units equals to the number of patterns. This fact may increase the problem’s complexity when dealing with large data sets.

Prior to entering the data into the forecasting models, some researches utilize the wavelet transform to decompose the original signal into low and high-frequency subseries (wavelet domain) [8]. This approach leads to better predictions in some cases. In the present paper, our main focus is to test the accuracy of some models on the raw data coming directly from the metering system. The wavelet analysis appears to be prominent and will be the regarded into a future study by the authors.

Due to their potential of simulating data with complex and non-linear relationships, ANNs are preferable in cases where a model that describes the data is absent [9]. ANNs are data driven models that are trained with a limited number of data and are to provide a generalization of their operation. A forecaster built on ANN receives as inputs the parameters that influence the quantity under examination, i.e. the MCP. For instance, the inputs include past MCP values, exogenous variables like temperature, fuel prices, day type identification codes and others. The majority of the price forecasting related literature focuses in specific electricity markets with relatively smooth data. Our approach differs from the related literature on the attributes of the data set. The models are tested on a raw data sample that contain null values and have missing entries. At least theoretically, this approach increases the difficulties that will prevent an analysis to formulate a robust forecasting model. To further analyze the problem of working with raw data, we explore the potential of utilizing the clustering tool for the purpose of increasing the forecasting accuracy of a feed-forward neural network trained by the Levenberg–Marquard algorithm [10].

The developed models are applied on the Southern (SUD) Italy electricity market [11], [12], [13]. The available data set covers the period between 01/02/2012 and 30/04/2015. Among them, the period between 01/02/2012 and 31/12/2014 is used as the training set and the rest is used as test set. The role of the training set is the determination of the optimal ANN configuration, i.e. the optimal selection of the type of neurons activation function, number of hidden layers, number of neurons in the hidden layer(s) and maximum number of training epochs. One training epoch corresponds to one forward pass and one backward pass of all the training examples. The test set is used for the models comparison.

From a market’s participant perspective, the estimation of the MCP in short-term horizon aids on the adoption of a proper strategy in wholesale market exchanges, i.e. the establishment of bilateral contracts or the generation units scheduling. The importance of the estimation of MCP is evident in profit maximization problems [14], [15]. The MCP is treated as a stochastic variable and a set of scenarios are constructed to estimate its future variation.

Reviews of the state-of-the-art on the existing techniques on price forecasting can be found in [4], [16]. A literature review including the amount of the recently published papers can be found in [17]. These studies attempt to reveal both the similarities and the differences between current techniques. According to [4] the existing approaches can be distinguished in three major categories: Game theory models, simulation models and time series models. The latter can be further categorized to stochastic models, artificial intelligence models and regression models. Time series models, such as ARIMA and GARCH, are a popular approach; they can serve as benchmark models for further model comparison and can be combined with other models leading to the formation of hybrid models. Their widespread usage is due to the fact that the mathematical formulation that refers to is comprehensive. Time series models require historical values of the quantity under prediction and they assume that the quantity evolution follows a specific pattern. The prediction is accomplished through the pattern’s extension to a pre-defined future time period [18], [19]. A comparison of various time series models like AR, ARMA and ARIMA can be found in [20]. Various sub-models are built (i.e. AR(1) with jumps, AR(1) in logs with jumps, AR(1) with time variant mean and others) and tested on the LPX market. Another comparative simulation study is conducted in [21] between a k-factor GIGARCH process and a SARIMA-GARCH model. The test study is applied on one month data of EEX market and the models include only lagged price values.

The time series models category includes the ANN based models. Representative bibliography is registered in Table 1. The ANNs that have been proposed in the literature are the following: Feed-Forward Neural Networks (FFNNs) and specifically Multi-Layered Perceptrons (MLPs) and Radial Basis Function Networks (RBFNs), Support Vector Machines (SVMs), Fuzzy Neural Networks (FNNs), Recurrent Neural Networks (RNNs), Probabilistic Neural Networks (PNN) and Self-Organizing Maps (SOMs). MLPs are the most commonly used networks due to their simplicity, training speed and reported effectiveness. MLPs are implemented as the sole forecaster in [9], [10], [19], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67] or in combined models utilizing another time series models [68], [69], [70], [71]. Other approaches propose of using the same ANN for both load and price forecasting or combining the ANN with a data mining technique to select appropriate days for training [72], [73], [74], [75]. While the majority of the studies refer to Day-ahead predictions, the MLPis also utilized in hour-ahead time framework [75], [76]. The role of the MLP in a combined model is to enhance the prediction produced by the conventional time series model (for example an ARIMA). Apart from price values, the ARIMA can be used to predict other variables like stored energy in reservoirs, inflow energy in reservoirs, total hydro generation and system load [77]. The predictions are used as inputs in the ANN system. Also, time series approaches combining ARIMA and GARCH have been proposed in the literature [78]. The ANN is compared with different AR and ARIMA models in [79].

RBFNs is the other type of FFNNs and are utilized in the works of [80], [81], [82], [83]. An RBF network involves a hidden and an output layer. The RBF holds the role of the activation function of the hidden layer. This type of ANNs is able to simulate complex relationships underlying the data and can adapt fast to possible changes of these relationships.

SVMs provide a non-linear mapping of the original data into high dimensional space [84], [85], [86], [87], [88], [89], [90]. The boundaries of the new space are demarcated using linear function. SVMs provide a global solution to a problem unlike MLPs who can operate within local minima of their objective function. This fact has been also recognized in many researches in the load forecasting area [2]. A comparison between SVM and ANN in NYISO is the focus of [91]. Also, the SVM is used for estimating the prediction intervals which quantify the uncertainty related to forecasts by estimating the ranges of the targeted quantities [92].

Another approach in price forecasting is the synergetic operation of Fuzzy Logic (FL) and ANNs. This part of the literature can be further classified into two categories: Studies that utilize FL and ANN in the same system (i.e. neuro-fuzzy systems like ANFIS) and the studies where FL and ANN are separated forecasters that are combined into a two-part forecaster [83], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105]. In the latter, the forecasting is accomplished via a linguistic description of the relationships between the input data. On the other hand, usually in ANFIS implementations the inputs involve only historical price values that are close to the days of the prices that are to be predicted. In [106], the forecasts of three models, i.e. ANN, ANFIS and ARIMA are fused by a Kalman filter to provide the forecast for the Spanish electricity system. The same models are also combined in [107]. The modified ordered weighted average algorithm is used to fuse the predictions produced by each model and the algorithms are tested on four representative weeks in the system of Spain. In [108], a hybrid system is used to predict prices in the Spanish market. The inputs are selected via the mutual information method and fed into the ANFIS. The optimal parameters of ANIS are determined by the evolutionary particle swarm optimization method.

RNNs rely their operation on the memory of the previous stages of the network, a concept that leads to a dynamic operation [98], [109], [110]. The output layer provides a feedback to the units of the hidden layer that process information from external signals and for a set of context units; the latter have fixed weights and serve as the memory units.

Electricity spike prices are abnormal values within price time series that can cause considerable economical effects on market participants. There are some researches that have focused on this problem proposing a series of techniques [111], [112], [113], [114], [115], [116], [117], [118], [119], [120]. The most common approach is the PNNs implementation. PNNs are rapidly trained feed forward networks with a single output. Through a preliminary analysis, the threshold value of price that is recognized as spike is extracted. The PNN is used for the occurrence prediction (i.e. spike or not spike) or combined with a ANN, apart from the occurrence, the spike value can also be predicted.

SOMs are unsupervised machine learning neural networks that have found applications in various clustering problems. In load forecasting applications, SOMs are combined with ANN (MLPs or SVMs) or another time series model to form hybrid systems [121], [122]. The SOM is occupied for the clustering of the training set in homogenous clusters. The training patterns within the same cluster display higher similarity compared with the rest. Then a number of forecasting models equals to the number of clusters is employed. This type of hybrid systems is not very common in price forecasting [60], [99], [123], [124], [125]. In [123] the SOM is combined with a SVM for the sort-term price forecasting in New England market. Again the hybrid system in [99] is composed by SOM and SVM examining the PJM market. The particle swarm optimization (PSO) algorithm is used for the optimal selection of SVM parameters via trial and error. To predict the next hour price h, the SVM receives as inputs the loads of hours h, h-1, h-2, h-3, the price of same hour one day before, the minimal and the maximum price of one day before. Also there is a distinction between weekends (entering “0” as input) and working days (entering “1” as input). In [124], [125] the SOM is combined with ANN for load and price forecasting in NYISO, Australia and Spain markets. For each quantity, no exogenous parameters are used for both clustering and forecasting. The SOM is applied to cluster the training data and extract the cluster labels. The ANN is used to predict next day’s cluster label. The predicted cluster label is associated with the topological coordinates of the map and the time series of load and price are obtained. Authors of [126] involve a pattern sequence similarity approach. The clustering is used both for grouping the data and forecasting. No neural network is considered. The K-means algorithm is employed for the purpose of grouping and labeling the samples from the dataset. Next, the pattern sequence prior to the day to be predicted is extracted. This sequence is searched in the historical data and the forecasted values are calculated by averaging all the samples immediately after the matched sequence. In [60] the Fuzzy C-Means (FCM) algorithm is used to cluster the day period into three zones (peak, normal and off-peak hours). There also a distinction of these zones between working days, Saturdays and Sundays. The clustering is combined with a time series model in [127], i.e. the clustering is not combined with ANN. In [128] the FCM clusters into three clusters and for each one a RNN is trained and tested in PJM market. Finally, other ANNs that have been proposed in the literature are the fuzzy Adaptive Resonance Theory (ART), Bayesian and Extreme Learning Machine (ELM) [104], [129], [130]. The ELM is combined with the maximum likelihood method for predicting the prices of ANEM [131]. A comparison takes place between the proposed model and three other models, i.e. the persistence approach, bootstrap ANN and ELM-Bootstrap approach. Also, another type of ANN used in price forecasting is the ELMAN neural network. According to [132], it outperforms the FFNN and the RBN when tested on NSW, Australia. The authors test various configurations differ in terms of number of inputs and number of neurons in the hidden layer.

The ANNs are suitable in problems that a general model or function expressing the relationship between the data and the parameters affecting them is absent or not straight-forward. Since the selection of input data is crucial to the model’ s successful operation, various input selection techniques has been presented, for example the mutual information and correlation coefficient [43], [111]. Historical price and load values are sorted based on the highest similarity in a list with the current hour’s MCP and the top listed values are fed into the ANN. Another aspect in ANN based price forecasting is the importance of network training. Some researches propose nature inspired algorithms like genetic algorithms, invasive weed optimization, cuckoo search and particle swarm optimization as helping techniques for better neural network training [26], [94], [111], [133], [134], [135]. A popular approach is the wavelet decomposition of the MCP series. For each wavelet-domain indicator a dedicated ANN is applied. The predictions on the wavelet domain of each forecaster are synthesized to obtain the MCP time series [8], [26], [36], [37], [82], [87], [89], [90], [94], [100], [114].

The majority of the papers focus on PJM and Spain markets. The test sets correspond to 4 representative weeks, 1 per season. These sets are used as unofficial benchmarks for the models comparison by many researchers. No universal competition in MCP forecasting providing test sets, guidelines and evaluation framework have been taken place, contrary to load forecasting [122]. This fact has been also discussed in [16].

Based on the above brief literature survey, it is obvious that the price forecasting problem has been tackled by many approaches involving sole and hybrid forecasting systems, various input selection techniques and algorithms for advancements in neural network training. The objectives of the present study, aiming at filling gaps and supplementing research in the literature, can be summarized in the following:

  • (a)

    This study is structured around the problem of working with no pre-processed data. The aim is to test the robustness of various MLP topologies in the case of data sample with missing entries and null values. According to the brief literature survey conducted on the previous, it is evident that most studies assess their respective models on four representative weeks of the year. To fully examine the performance of the proposed models, our test set involves a four month period covering working days, weekends and holidays. To limit the effect of null and abnormal values, authors of [130] discuss some modified version of Mean Absolute Percentage Error (MAPE). This scheme leads to smooth MAPE values. Contrary to this paper, in this study the evaluation framework involves the conventional definition of the MAPE, which is the most common indicator in load and price forecasting applications.

  • (b)

    Various types of inputs are investigated. Proportionally to other studies, we are also concerned of using only historical load and price values. The influence of MCP of other countries’ markets that are interconnected with Italy is checked.

  • (c)

    According to [7] another classification of the literature can be held considering the type of the output of the ANN. The output can refer to next hour’s price, the price of several hours ahead, the next day’s peak price (spike), the next day’s average on-peak price and next day’s average price. For example, in next hour’s (denoted with h) price forecasting, the ANN can receive as inputs the prices of previous hour and two hour before, h-1 and h-2, respectively. This is followed in the majority of the studies. Authors of [7] states that the next day’s complete price profile is the less popular group of studies. Our study belongs to this category. The forecasting is focused in the next day’s prices; this means that the prices of h-1 and h-2 cannot be used since they are unknown.

  • (d)

    Another objective is to analyze the potential of the clustering tool in the data sample under study. The clustering algorithm and the conventional forecaster are hybridized to combined models. Through the clustering algorithm, the historical MCP data are separated into well-separated and homogenous groups. Next, for each group a dedicated ANN is trained and applied. It should be noted that since the ANN is trained with a different sub-set of the historical data, the optimal parameters of each network obtained by the training phase may differ. While hybrid models have been successfully applied in load forecasting problems, so far their utilization in MCP is relatively limited; it is represented by only six studies [60], [99], [123], [124], [125], [127].

To sum up, the paper proposes ANN and hybrid ANN models for the Day-ahead Market price forecasting, working with no pre-processed data, elaborating historical load and price data and analyzing the potential of the clustering algorithm, which separates historical data in well-separated and homogeneous groups. The proposed ANN models aim at providing evidence so as to be considered as useful and robust forecasting tools to the actual needs of market participants, including the traditional generation companies and self-producers, but also the retailers/suppliers and aggregators.

The rest of this paper is organized as follows: The general price forecasting framework is presented in Section 2. The models description as included in this section. In Section 3 the models are compared using various indicators. The purpose is to examine the models within a general evaluation background in order to reach into safe conclusions regarding the potential and drawbacks of each model. The main findings of the present work are presented in Section 4.

Section snippets

Data collection

The general framework followed in the study is graphically presented in Fig. 1. It is based on a feature selection stage, models training and test stages. Due to the absence of previous works on price forecasting in the SUD Italy, an investigation on the selection of the number and type of inputs of the ANN takes place. Each developed model refers to different types of inputs. It should be noted that the current data set present many spikes, null values and missing entries.

The price time series

General aspects

FFNNs have adjustable parameters providing a framework for experimentation on trial and error. A series of experiments are required to define the optimal ANN configuration of each model. The parameters that need to be properly determined are the number of hidden layers, the number of neurons of the hidden layer(s) and the type of transfer functions of the neurons of the hidden and the output layers. Also, the maximum number of training epochs of the Levenberg–Marquardt algorithm is a parameter

Discussion and concluding remarks

Generation electricity trends are largely affected by the market clearing price patterns. The importance of accurate predictions of market prices is manyfold. For instance, the Day-ahead strategy of a producer can be built and carried on reliable forecasts, leading to increased profits, economic viability, limited risks and competiveness. While load forecasting counts many years of research efforts and application, the price forecasting literature is relatively more limited. Many markets were

References (140)

  • A.K. Diongue et al.

    Forecasting electricity spot market prices with a k-factor GIGARCH process

    Appl Energy

    (2009)
  • O. Abedinia et al.

    Electricity price forecast using Combinatorial Neural Network trained by a new stochastic search method

    Energy Convers Manage

    (2015)
  • N. Amjady et al.

    Mixed price and load forecasting of electricity markets by a new iterative prediction method

    Electr Power Syst Res

    (2009)
  • N. Amjady et al.

    Design of input vector for day-ahead price forecasting of electricity markets

    Expert Syst Appl

    (2009)
  • N. Amjady et al.

    Day ahead price forecasting of electricity markets by a mixed data model and hybrid forecast method

    Int J Electr Power Energy Syst

    (2008)
  • N. Amjady et al.

    Day-ahead price forecasting of electricity markets by a new feature selection algorithm and cascaded neural network technique

    Energy Convers Manage

    (2009)
  • S. Anbazhagan et al.

    Day-ahead deregulated electricity market price classification using neural network input featured by DCT

    Int J Electr Power Energy Syst

    (2012)
  • S. Anbazhagan et al.

    Day-ahead deregulated electricity market price forecasting using neural network input featured by DCT

    Energy Convers Manage

    (2014)
  • N. Bigdeli et al.

    Market data analysis and short-term price forecasting in the Iran electricity market with pay-as-bid payment mechanism

    Electr Power Syst Res

    (2009)
  • J.P.S. Cataláo et al.

    Short-term electricity prices forecasting in a competitive market: a neural network approach

    Energy Convers Manage

    (2007)
  • S. Chakravarty et al.

    Dynamic filter weights neural network model integrated with differential evolution for day-ahead price forecasting in energy market

    Expert Syst Appl

    (2011)
  • P. Dev et al.

    Using neural networks and extreme value distributions to model electricity pool prices: Evidence from the Australian National Electricity Market 1998–2013

    Energy Convers Manage

    (2014)
  • A. Karsaz et al.

    Market clearing price and load forecasting using cooperative co-evolutionary approach

    Int J Electr Power Energy Syst

    (2010)
  • F. Keynia

    A new feature selection algorithm and composite neural network for electricity price forecasting

    Eng Appl Artif Intell

    (2012)
  • P. Mandal et al.

    Neural networks approach to forecast several hour ahead electricity prices and loads in deregulated market

    Energy Convers Manage

    (2006)
  • H.T. Pao

    Forecasting electricity market pricing using artificial neural networks

    Energy Convers Manage

    (2007)
  • R. Pino et al.

    Forecasting next-day price of electricity in the Spanish energy market using artificial neural networks

    Eng Appl Artif Intell

    (2008)
  • C. Unsihuay-Vila et al.

    Electricity demand and spot price forecasting using evolutionary computation combined with chaotic nonlinear dynamic model

    Int J Electr Power Energy Syst

    (2010)
  • V. Vahidinasab et al.

    Day-ahead price forecasting in restructured power systems using artificial neural networks

    Electr Power Syst Res

    (2008)
  • A.J. Wang et al.

    A neural network based estimator for electricity spot-pricing with particular reference to weekend and public holidays

    Neurocomputing

    (1998)
  • H.Y. Yamin et al.

    Adaptive short-term electricity price forecasting using artificial neural networks in the restructured power markets

    Int J Electr Power Energy Syst

    (2004)
  • L. Zhang et al.

    Energy clearing price prediction and confidence interval estimation with cascaded neural network

    IEEE Trans Power Syst

    (2003)
  • N. Amjady et al.

    Application of a new hybrid neuro-evolutionary system for day-ahead price forecasting of electricity markets

    Appl Soft Comput

    (2010)
  • A. Khosravi et al.

    A neural network-GARCH-based method for construction of Prediction Intervals

    Electr Power Syst Res

    (2013)
  • Z. Tan et al.

    Day-ahead electricity price forecasting using wavelet transform combined with ARIMA and GARCH models

    Appl Energy

    (2010)
  • D. Keles et al.

    Extended forecast methods for day-ahead electricity spot prices applying artificial neural networks

    Appl Energy

    (2016)
  • L.D.S. Coelho et al.

    A RBF neural network model with GARCH errors: Application to electricity price forecasting

    Electr Power Syst Res

    (2011)
  • W.M. Lin et al.

    An enhanced radial basis function network for short-term electricity price forecasting

    Appl Energy

    (2010)
  • M. Shafie-khah et al.

    Price forecasting of day-ahead electricity markets using a hybrid forecast method

    Energy Convers Manage

    (2011)
  • H. Shayeghi et al.

    Day-ahead electricity prices forecasting by a modified CGSA technique and hybrid WT in LSSVM based scheme

    Energy Convers Manage

    (2013)
  • H. Shayeghi et al.

    Simultaneous day-ahead forecasting of electricity price and load in smart grids

    Energy Convers Manage

    (2015)
  • J. Zhang et al.

    Day-ahead electricity price forecasting by a new hybrid method

    Comput Ind Eng

    (2012)
  • J. Zhang et al.

    Day-ahead electricity price forecasting using WT, CLSSVM and EGARCH model

    Int J Electr Power Energy Syst

    (2013)
  • J.P.S. Cataláo et al.

    Short-term electricity prices forecasting in a competitive market by a hybrid intelligent approach

    Energy Convers Manage

    (2011)
  • Y.Y. Hong et al.

    A neuro-fuzzy price forecasting approach in deregulated electricity markets

    Electr Power Syst Res

    (2005)
  • D. Niu et al.

    A soft computing system for day-ahead electricity price forecasting

    Appl Soft Comput

    (2010)
  • G.J. Osório et al.

    Electricity prices forecasting by a hybrid evolutionary-adaptive methodology

    Energy Convers Manage

    (2014)
  • H. Seifi et al.

    Electric power systems planning: issues, algorithms and solutions

    (2011)
  • S.K. Aggarwal et al.

    Electricity price forecasting in Ontario electricity market using wavelet transform in artificial neural network based model

    Int J Control Autom Syst

    (2008)
  • K.L. Priddy et al.

    Artificial neural networks: an introduction

    (2005)
  • Cited by (266)

    View all citing articles on Scopus
    View full text