Hourly Electricity Load Research Articles

Echo state network with wavelet in load forecasting

PurposeThe purpose of this paper is to improve the accuracy of short time load forecasting to ensure the economical and safe operation of power systems. The traditional neural network applied in time series like load forecasting, easily plunges into local optimum and has a complicated learning process, leading to relatively slow calculating speed. On the basis of existing literature, the authors carried out studies in an effort to optimize a new recurrent neural network by wavelet analysis to solve the previous problems.Design/methodology/approachThe main technique the authors applied is referred to as echo state network (ESN). Detailed information has been acquired by the authors using wavelet analysis. After obtaining more information from original time series, different reservoirs can be built for each subsequence. The proposed method is tested by using hourly electricity load data from a southern city in China. In addition, some traditional methods are also applied for the same task, as contrast.FindingsThe experiment has led the authors to believe that the optimized model is encouraging and performs better. Compared with standard ESN, BP network and SVM, the experimental results indicate that WS‐ESN improves the prediction accuracy and has less computing consumption.Originality/valueThe paper develops a new method for short time load forecasting. Wavelet decomposition is employed to pre‐process the original load data. The approximate part associated with low frequencies and several detailed parts associated with high frequencies components give expression to different information from original data. According to this, suitable ESN is chosen for each sub‐sequence, respectively. Therefore, the model combining the advantages of both ESN and wavelet analysis improves the result for short time load forecasting, and can be applied to other time series problem.

Electric Load Forecasting for Western Canada: A Comparison of Two Non-Linear Methods

Seven years of hourly temperature and electric load data for British Columbia in western Canada were used to compare two statistical methods, artificial neural networks (ANN) and gene expression programming (GEP), to produce hour-ahead load forecasts. Two linear control methods (persistence and multiple linear regression) were used for verification purposes. A two-stage (predictor-corrector) approach was used. The first stage used a single regression model that applied weather and calendar data for the previous hour to predict load for any hour of the day, and the second stage applied different corrections every hour, based on a high correlation of today's load with yesterday's load for any given hour. By excluding the day-before variables, the two-stage method reduced the total number of variables in the first-stage regression and gave better results. The first five years of data were used for training (regression finding) and validation (comparative testing of candidate functions to reduce overfitting) and the last two for verification (scoring with independent data). It was found that both non-linear methods worked better than the linear methods for the first stage. All methods worked well for the second stage; hence, persistence is recommended for the second stage because it is easiest to do. After both stages, the load error was less than 0.6% of the load magnitude for hour-ahead forecasts. When used iteratively to create forecasts up to 24 hours ahead, errors grew to about 3.5% of the load magnitude for both GEP and ANNs. We also experimented by training the statistical methods with a shorter period (one year) of past data to examine the over-fitting problem. Overall, ANNs were more useful in fitting the curves to robust data, and GEP was superior for short datasets and was less sensitive to the length of the dataset. We also found that a time-nested electric load forecasting model with different lead times kept maximum load errors to 2.1% of the load magnitude out to a horizon of 24 forecasts. RÉSUMÉ [Traduit par la rédaction] Nous avons utilisé sept années de données de température et de charge électrique pour la Colombie-Britannique dans l'ouest du Canada pour comparer deux méthodes statistiques, les réseaux neuronaux artificiels (ANN) et la programmation génétique (GEP), pour produire des prévisions de charge une heure à l'avance. Nous nous sommes servis de deux méthodes de vérification linéaires (persistance et régression linéaire multiple) à des fins de vérification. Nous avons utilisé une approche en deux étapes (prédicteur–correcteur). Dans la première étape, un modèle de régression simple appliquait des données météorologiques et de calendrier pour l'heure précédente pour prévoir la charge à n'importe quelle heure de la journée et la deuxième étape appliquait à chaque heure différentes corrections basées sur une forte corrélation de la charge d'aujourd'hui avec la charge d'hier pour une heure quelconque. En excluant les variables du jour précédent, la méthode à deux étapes a réduit le nombre total de variables dans la régression de la première étape et a donné de meilleurs résultats. Nous avons utilisé les cinq premières années de données pour l'apprentissage (détermination de la régression) et la validation (essais comparatifs de fonctions candidates pour réduire le surapprentissage) et les deux dernières pour la vérification (établissement d'un score à l'aide de données indépendantes). Il ressort que les deux méthodes non linéaires ont mieux fonctionné que les méthodes linéaires pour la première étape. Toutes les méthodes ont bien fonctionné pour la deuxième étape; la persistance est donc recommandée pour la deuxième étape parce qu'elle est plus facile à appliquer. Après les deux étapes, l'erreur sur la charge était inférieure à 0,6% de la grandeur de la charge pour les prévisions d'une heure à l'avance. Lorsque utilisées de façon itérative pour produire des prévisions de jusqu’à 24 heures, les erreurs ont augmenté jusqu’à environ 3,5% de la grandeur de la charge tant pour la GEP que les ANN. Nous avons aussi expérimenté en entraînant les méthodes statistiques avec une période plus courte (un an) de données passées pour examiner le problème du surapprentissage. Dans l'ensemble, les ANN étaient plus utiles pour ajuster les courbes aux données robustes alors que la GEP était meilleure pour les courts ensembles de données et était moins sensible à la longueur de l'ensemble de données. Nous avons aussi trouvé qu'un modèle de prévision de charge électrique emboîté dans le temps avec différent temps de prévision a limité les erreurs sur la charge à 2,1% de la grandeur de la charge jusqu’à un horizon de 24 prévisions.

Short-term Traffic Flow and Hourly Electric Load Forecasting Algorithm based on Echo State Neural Networks

Short-term Traffic Flow and Hourly Electric Load Forecasting Algorithm based on Echo State Neural Networks

Hourly Electricity Load Forecasting: An Empirical Application to the Italian Railways

Hourly Electricity Load Forecasting: An Empirical Application to the Italian Railways

Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling

A dynamic multivariate periodic regression model for hourly data is considered. The dependent hourly univariate time series is represented as a daily multivariate time series model with 24 regression equations. The regression coefficients differ across equations (or hours) and vary stochastically over days. Since an unrestricted model contains many unknown parameters, an effective methodology is developed within the state–space framework that imposes common dynamic factors for the parameters that drive the dynamics across different equations. The factor model approach leads to more precise estimates of the coefficients. A simulation study for a basic version of the model illustrates the increased precision against a set of univariate benchmark models. The empirical study is for a long time series of French national hourly electricity loads with weather variables and calendar variables as regressors. The empirical results are discussed from both a signal extraction and a forecasting standpoint.

H2RES, Energy planning tool for island energy systems – The case of the Island of Mljet☆

When it comes to the energy planning, computer programs like H2RES are becoming valuable tools. H2RES has been designed as support for simulation of different scenarios devised by RenewIsland methodology with specific purpose to increase integration of renewable sources and hydrogen into island energy systems. The model can use wind, solar, hydro, biomass, geothermal as renewable energy sources and fossil fuel blocks and grid connection with mainland as back up. The load in the model can be represented by hourly and deferrable electricity loads of the power system, by hourly heat load, by hydrogen load for transport and by water load depending on water consumption. The H2RES model also has ability to integrate different storages into island energy system in order to increase the penetration of intermittent renewable energy sources or to achieve a 100% renewable island. Energy storages could vary from hydrogen loop (fuel cell, electrolyser and hydrogen storage) to reversible hydro or batteries for smaller energy systems. The H2RES model was tested on the power system of the Island of Porto Santo – Madeira, the islands of Corvo, Graciosa, and Terrciera – Azores, Sal Island – Cape Verde, Portugal, the Island of Mljet, Croatia and on the energy system of the Malta. Beside energy planning of the islands, H2RES model could be successfully applied for simulation of other energy systems like villages in mountain regions or for simulation of different individual energy producers or consumers.

An hourly periodic state space model for modelling French national electricity load

We present a model for hourly electricity load forecasting based on stochastically time-varying processes that are designed to account for changes in customer behaviour and in utility production efficiencies. The model is periodic: it consists of different equations and different parameters for each hour of the day. Dependence between the equations is introduced by covariances between disturbances that drive the time-varying processes. The equations are estimated simultaneously. Our model consists of components that represent trends, seasons at different levels (yearly, weekly, daily, special days and holidays), short-term dynamics and weather regression effects, including nonlinear functions for heating effects. The implementation of our forecasting procedure relies on the multivariate linear Gaussian state space framework, and is applied to the national French hourly electricity load. The analysis focuses on two hours, 9 AM and 12 PM, but forecasting results are presented for all twenty-four hours. Given the time series length of nine years of hourly observations, many features of our model can be estimated readily, including yearly patterns and their time-varying nature. The empirical analysis involves an out-of-sample forecasting assessment up to seven days ahead. The one-day ahead forecasts from forty-eight bivariate models are compared with twenty-four univariate models, one for each hour of the day. We find that the implied forecasting function depends strongly on the hour of the day.

Modeling and forecasting short-term electricity load: A comparison of methods with an application to Brazilian data

The goal of this paper is to describe a forecasting model for the hourly electricity load in the area covered by an electric utility located in the southeast of Brazil. A different model is constructed for each hour of the day. Each model is based on a decomposition of the daily series of each hour in two components. The first component is purely deterministic and is related to trends, seasonality, and the special days effect. The second is stochastic, and follows a linear autoregressive model. Nonlinear alternatives are also considered in the second step. The multi-step forecasting performance of the proposed methodology is compared with that of a benchmark model, and the results indicate that our proposal is useful for electricity load forecasting in tropical environments.

An Hourly Periodic State Space Model for Modelling French National Electricity Load

We present a model for hourly electricity load forecasting based on stochastically time-varying processes that are designed to account for changes in customer behaviour and in utility production efficiencies. The model is periodic: it consists of different equations and different parameters for each hour of the day. Dependence between the equations is introduced by covariances between disturbances that drive the time-varying processes. The equations are estimated simultaneously. Our model consists of components that represent trends, seasons at different levels (yearly, weekly, daily, special days and holidays), short-term dynamics and weather regression effects including nonlinear functions for heating effects. The implementation of our forecasting procedure relies on the multivariate linear Gaussian state space framework and is applied to national French hourly electricity load. The analysis focuses on two hours, 9 AM and 12 AM, but forecasting results are presented for all twenty-four hours. Given the time series length of nine years of hourly observations, many features of our model can be readily estimated including yearly patterns and their time-varying nature. The empirical analysis involves an out-of sample forecasting assessment up to seven days ahead. The one-day ahead forecasts from forty-eight bivariate models are compared with twenty-four univariate models for all hours of the day. We find that the implied forecasting function strongly depends on the hour of the day.

Short-Term Load Forecasting Based on an Adaptive Hybrid Method

This paper aims to develop a load forecasting method for short-term load forecasting, based on an adaptive two-stage hybrid network with self-organized map (SOM) and support vector machine (SVM). In the first stage, a SOM network is applied to cluster the input data set into several subsets in an unsupervised manner. Then, groups of 24 SVMs for the next day's load profile are used to fit the training data of each subset in the second stage in a supervised way. The proposed structure is robust with different data types and can deal well with the nonstationarity of load series. In particular, our method has the ability to adapt to different models automatically for the regular days and anomalous days at the same time. With the trained network, we can straightforwardly predict the next-day hourly electricity load. To confirm the effectiveness, the proposed model has been trained and tested on the data of the historical energy load from New York Independent System Operator.

A semi-parametric time series approach in modeling hourly electricity loads

In this paper we develop a semi-parametric approach to model nonlinear relationships in serially correlated data. To illustrate the usefulness of this approach, we apply it to a set of hourly electricity load data. This approach takes into consideration the effect of temperature combined with those of time-of-day and type-of-day via nonparametric estimation. In addition, an ARIMA model is used to model the serial correlation in the data. An iterative backfitting algorithm is used to estimate the model. Post-sample forecasting performance is evaluated and comparative results are presented. Copyright © 2006 John Wiley & Sons, Ltd.

Modulated cycles, an approach to modelling periodic components from rapidly sampled data

Unobserved components models provide a natural framework for the estimation and forecasting of periodic components embedded in the time series, such as business cycles or seasonality. However, periodic behaviour can be complicated to analyse when dealing with rapidly sampled data of the kind encountered in electricity demand forecast problems. Data of this nature tend to show a multiplicity of superimposed periodic patterns, including annual, weekly and daily cycles. In this paper, we present a new seasonal component model based on modulated periodic components, which is capable of replicating multiplicative periodic components in an efficient manner, in the sense that the number of parameters in the model is much lower than in a standard unobserved components model without modulation. The model performance compares favourably with respect to standard techniques on a rolling forecasting exercise based on actual hourly electricity load demand data at a certain transformer in the UK.

Time Series Approach to Hourly Electric Load Forecasting for the Western Province of Saudi Arabia

The hourly electric load in the Western Province of Saudi Arabia has four distinct patterns, namely that of summer season, spring season, fall season, and winter season. This paper demonstrates fitting of an auto regres- sive integrated moving average model to the summer season data using the Box and Jenkins time series approach. The model is tested for forecasting by using a set of test data. The resulting forecasts, which are checked by different criteria, are found to have a high degree of accuracy. The whole exercise has been carried out by using computer programs, which were partly developed.

Application of artificial neural networks to historical data analysis for short‐term electric load forecasting

AbstractThe paper illustrates two different Artificial Neural Networks (ANN) architectures for electric Short‐Term Load Forecasting (STLF). Two multi‐layer perceptron ANN using the back‐propagation learning algorithm have been implemented which provide different, although complementary, forecasting approaches (static and dynamic). In order to test the potentialities of the architectures implemented, the ANN have been applied to the Short‐Term Forecasting of Italian hourly electric load. The importance of this load (peak demands up to about 38 000 MW) requires tools for STLF which must be as more accurate and precise as possible. This fact has imposed the adoption of some algorithmic enhancements to the basic back‐propagation algorithm formulation. Since an adequate formulation of the influence exerted on hourly electric load by the main meteorological and climatic factors is not known at present, the data set used for ANN training phase has concerned only historical series of electric hourly demand. The paper illustrates the two ANN architectures as well as the computational platforms used for implementation. Finally, some results obtained from the application of the two ANN to the short‐term forecasting of Italian electric load relevant to three different weeks of the year 1993 are comparatively reported.

Performance analyses of combined heating and photovoltaic power systems for residences

The performance of a combined solar photovoltaic and heating system for a single family residence has been analyzed over a full year, using hourly U.S. Weather Bureau data for insolation and environmental temperature for Boston, 1963. The collector analyzed is a flat plate thermal collector with heat transfer to the load via a liquid loop. The collector contains in lieu of the usual absorber surface a silicon solar array. The analysis has been carried out by use of existing detailed programs for hourly computation of the building heat load, of solar heating system performance, and of solar photovoltaic system performance. The optical properties of the photovoltaic array were used for the absorber plate in the thermal collector performance evaluation, and the available energy input to the absorber was reduced by 10% to account for the electrical energy taken out, as a first order approximation. The thus obtained hourly absorber temperatures were used in the computation of photovoltaic array performance. The hourly electrical load has been synthesized. The analysis has shown the combination system to be a viable approach. It will require a means for temperature control while heat energy is available in excess of load and is being dumped into the environment. Several system design parameters were varied for a sensitivity analysis.