ARMA based approaches for forecasting the tuple of wind speed and direction

Short-term forecasting of wind speed and direction is of great importance to wind turbine operation and efficient energy harvesting. In this study, the forecasting of wind speed and direction tuple is performed. Four approaches based on autoregressive moving average (ARMA) method are employed for this purpose. The first approach features the decomposition of the wind speed into lateral and longitudinal components. Each component is represented by an ARMA model, and the results are combined to obtain the wind direction and speed forecasts. The second approach employs two independent ARMA models – a traditional ARMA model for predicting wind speed and a linked ARMA model for wind direction. The third approach features vector autoregression (VAR) models to forecast the tuple of wind attributes. The fourth approach involves employing a restricted version of the VAR approach to predict the same. By employing these four approaches, the hourly mean wind attributes are forecasted 1-h ahead for two wind observation sites in North Dakota, USA. The results are compared using the mean absolute error (MAE) as a measure for forecasting quality. It is found that the component model is better at predicting the wind direction than the traditional-linked ARMA model, whereas the opposite is observed for wind speed forecasting. Utilizing VAR approaches rather than the univariate counterparts brings modest improvement in wind direction prediction but not in wind speed prediction. Between restricted and unrestricted versions of VAR models, there is little difference in terms of forecasting performance.     

Hybrid methodology for hourly global radiation forecasting in Mediterranean area

The renewable energies prediction and particularly global radiation forecasting is a challenge studied by a growing number of research teams. This paper proposes an original technique to model the insolation time series based on combining Artificial Neural Network (ANN) and Auto-Regressive and Moving Average (ARMA) model. While ANN by its non-linear nature is effective to predict cloudy days, ARMA techniques are more dedicated to sunny days without cloud occurrences. Thus, three hybrids models are suggested: the first proposes simply to use ARMA for 6 months in spring and summer and to use an optimized ANN for the other part of the year; the second model is equivalent to the first but with a seasonal learning; the last model depends on the error occurred the previous hour. These models were used to forecast the hourly global radiation for five places in Mediterranean area. The forecasting performance was compared among several models: the 3 above mentioned models, the best ANN and ARMA for each location. In the best configuration, the coupling of ANN and ARMA allows an improvement of more than 1%, with a maximum in autumn (3.4%) and a minimum in winter (0.9%) where ANN alone is the best.     

Prediction of hourly solar radiation using a novel hybrid model of ARMA and TDNN

In this work, a new approach that contains two phases is used to predict the hourly solar radiation series. In the detrending phase, several models are applied to remove the non-stationary trend lying in the solar radiation series. To judge the goodness of different detrending models, the Augmented Dickey-Fuller method is applied to test the stationarity of the residual. The optimal model is used to detrend the solar radiation series. In the prediction phase, the Autoregressive and Moving Average (ARMA) model is used to predict the stationary residual series. Furthermore, the controversial Time Delay Neural Network (TDNN) is applied to do the prediction. Because ARMA and TDNN have their own strength respectively, a novel hybrid model that combines both the ARMA and TDNN, is applied to produce better prediction. The simulation result shows that this hybrid model can take the advantages of both ARMA and TDNN and give excellent result.     

Forecasting weekly electricity consumption : A case study

This paper describes the application of time-series modelling techniques to electricity consumption data for a particular power board. Modelling is performed on total consumption, the data being available on a weekly basis with exact measurements for approximately the past 11 years. Both unforced and forced models are considered. An initial data analysis is performed to ascertain the influence of temperature and rainfall inputs on the model, and later on, a spectral analysis is used to investigate the frequency components present in the time-series data. A significant component of the determination of time-series models is the selection of an appropriate model order. Both low and high order models are evaluated, and their properties compared. For the unforced case, both AR (autoregressive) and ARMA (autoregressive moving average) models are considered. For the forced case, these model structures are extended to include ARX and ARMAX models which have one or more exogenous inputs. Such models are further extended by considering the possibility of predicting the inputs to the models, when a forecasting approach is required. Simulation results are provided for all cases together with a measure of the prediction accuracy. Comparisons are made for the various model structures, as well as models based on short and long data records and models which are driven with an external noise sequence or merely released from appropriate initial conditions.     

Time series models to simulate and forecast hourly averaged wind speed in Quetta, Pakistan

Stochastic simulation and forecast models of hourly average wind speeds are presented. Time series models take into account several basic features of wind speed data including autocorrelation, non-Gaussian distribution and diurnal nonstationarity. The positive correlation between consecutive wind speed observations is taken into account by flitting an ARMA (p,q) process to wind speed data transformed to make their distribution approximately Gaussian and standardized to remove scattering of transformed data. Diurnal variations have been taken into account to observe forecasts and its dependence on lead times. We find the ARMA (p,q) model suitable for prediction intervals and probability forecasts.     

Multivariable wind modeling in state space

Turbulence of the incoming wind field is of paramount importance to the dynamic response of wind turbines. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross-spectral density function for the along-wind turbulence component over the rotor plane is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modeling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modeling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modeling method.     

Forecast of hourly average wind speed with ARMA models in Navarre (Spain)

In this article we have used the ARMA (autoregressive moving average process) and persistence models to predict the hourly average wind speed up to 10 h in advance. In order to adjust the time series to the ARMA models, it has been necessary to carry out their transformation and standardization, given the non-Gaussian nature of the hourly wind speed distribution and the non-stationary nature of its daily evolution. In order to avoid seasonality problems we have adjusted a different model to each calendar month. The study expands to five locations with different topographic characteristics and to nine years. It has been proven that the transformation and standardization of the original series allow the use of ARMA models and these behave significantly better in the forecast than the persistence model, especially in the longer-term forecasts. When the acceptable RMSE (root mean square error) in the forecast is limited to 1.5 m/s, the models are only valid in the short term.     

Stochastic modeling and generation of synthetic sequences of hourly global solar irradiation at Quetta, Pakistan

Using hourly global radiation data at Quetta, Pakistan for 10 yr, an Autoregressive Moving Average (ARMA) process is fitted. Markov Transition Matrices have also been developed. These models are used for generating synthetic sequences for hourly radiations in MJ/m² and that the generated sequences are compared with the observed data. We found the MTM approach relatively better as a simulator compared to ARMA modeling.     

Uncertainty in wave energy resource assessment. Part 1: Historic data

The uncertainty in estimates of the energy yield from a wave energy converter (WEC) is considered. The study is presented in two articles. This first article deals with the accuracy of the historic data and the second article considers the uncertainty which arises from variability in the wave climate. Estimates of the historic resource for a specific site are usually calculated from wave model data calibrated against in-situ measurements. Both the calibration of model data and estimation of confidence bounds are made difficult by the complex structure of errors in model data. Errors in parameters from wave models exhibit non-linear dependence on multiple factors, seasonal and interannual changes in bias and short-term temporal correlation. An example is given using two hindcasts for the European Marine Energy Centre in Orkney. Before calibration, estimates of the long-term mean WEC power from the two hindcasts differ by around 20%. The difference is reduced to 5% after calibration. The short-term temporal evolution of errors in WEC power is represented using ARMA models. It is shown that this is sufficient to model the long-term uncertainty in estimated WEC yield from one hindcast. However, seasonal and interannual changes in model biases in the other hindcast cause the uncertainty in estimated long-term WEC yield to exceed that predicted by the ARMA model.     

基于ARMAX-GARCH模型的微电网风功率预测

目前风功率预测多为风功率期望的点预测,且以采样间隔较大的功率序列作为建模序列,这样会降低预测模型对风功率时序特征模拟的准确度和可信度。文中基于小采样间隔风功率序列,提出ARMAX-GARCH风功率预测模型。通过构造风功率新息序列,结合小时平均风功率序列,建立ARMAX点预测模型,采用BIC最小信息准则和相关性分析实现模型定阶和外生变量选择;采用GARCH模型模拟残差的波动特性实现区间预测。以海岛微电网实测风功率数据为例,进行提前1 h风功率预测。结果表明,与持续法、ARMA和RBF神经网络相比,该预测模型能显著提高风功率期望的点预测精度并具有较好的区间预测效果。     

Managing volumetric risk of long-term power purchase agreements

A negative dependence between wind power production and electricity spot price exists. This is an important fact to consider for risk management of long-term power purchase agreements (PPAs). In this study we investigate this dependence by constructing a joint model using constant as well as time-varying copulas. We propose to use score-driven models as marginal model for the spot price of electricity as these are more robust to extreme events compared to ARMA–GARCH models. We apply the new model to pricing and risk management of PPAs and benchmark it against the ARMA–GARCH specification. Our comparison shows that the score-driven model results in a statistically significant improvement of predicting the Value-at-Risk (VaR), which is of high importance for risk management of long-term PPAs. Further, comparing constant and time–varying copulas we find that all time-varying copulas are significantly better than their constant counterparts at predicting the VaR, hence time–varying copulas should be used in risk management of PPAs.     

Combining solar irradiance measurements,satellite-derived data and a numerical weather prediction model to improve intra-day solar forecasting

Isolated power systems need to generate all the electricity demand with their own renewable resources. Among the latter, solar energy may account for a large share. However, solar energy is a fluctuating source and the island power grid could present an unstable behavior with a high solar penetration. Global Horizontal Solar Irradiance (GHI) forecasting is an important issue to increase solar energy production into electric power system. This study is focused in hourly GHI forecasting from 1 to 6 h ahead. Several statistical models have been successfully tested in GHI forecasting, such us autoregressive (AR), autoregressive moving average (ARMA) and Artificial Neural Networks (ANN). In this paper, ANN models are designed to produce intra-day solar forecasts using ground and exogenous data. Ground data were obtained from two measurement stations in Gran Canaria Island. In order to improve the results obtained with ground data, satellite GHI data (from Helioclim-3) as well as solar radiation and Total Cloud Cover forecasts provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) are used as additional inputs of the ANN model. It is shown that combining exogenous data (satellite and ECMWF forecasts) with ground data further improves the accuracy of the intra-day forecasts.     

Electricity demand loads modeling using AutoRegressive Moving Average (ARMA) models

This study addresses the problem of modeling the electricity demand loads in Greece. The provided actual load data is deseasonilized and an AutoRegressive Moving Average (ARMA) model is fitted on the data off-line, using the Akaike Corrected Information Criterion (AICC). The developed model fits the data in a successful manner. Difficulties occur when the provided data includes noise or errors and also when an on-line/adaptive modeling is required. In both cases and under the assumption that the provided data can be represented by an ARMA model, simultaneous order and parameter estimation of ARMA models under the presence of noise are performed. The produced results indicate that the proposed method, which is based on the multi-model partitioning theory, tackles successfully the studied problem. For validation purposes the produced results are compared with three other established order selection criteria, namely AICC, Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC). The developed model could be useful in the studies that concern electricity consumption and electricity prices forecasts.     

基于集合经验模态分解和自回归滑动平均的某碾压混凝土重力坝变形预测模型及应用

为更精确地预测大坝变形数据,针对大坝变形监测序列的非线性和非平稳性问题,提出了一种结合集合经验模态分解和自回归滑动平均模型的大坝变形预测模型。首先利用集合经验模态分解法将非平稳的大坝变形监测数据分解为具有不同特征尺度的本征模态函数,然后分析各分量特征并分别建立自回归滑动平均模型,选择各自适合的最优模型参数,最后叠加各分量的预测结果作为最终的变形预测结果。分析结果表明,相较单一预测模型,结合集合经验模态分解和自回归滑动平均模型的组合预测模型的预测精度更高。     

A comparison of various forecasting techniques applied to mean hourly wind speed time series

This paper presents a comparison of various forecasting approaches, using time series analysis, on mean hourly wind speed data. In addition to the traditional linear (ARMA) models and the commonly used feed forward and recurrent neural networks, other approaches are also examined including the Adaptive Neuro-Fuzzy Inference Systems (ANFIS) and Neural Logic Networks. The developed models are evaluated for their ability to produce accurate and fast forecasts.     

基于ARMA及神经网络的汽轮机振动故障诊断研究

根据Bently实验台所采集的碰摩、松动、不对中、不平衡4种典型的汽轮机转子振动故障水平方向与垂直方向的数据所建立的汽轮机转子振动故障序列自回归滑移平均(ARMA)模型,由ARMA模型参数计算自谱函数值,建立汽轮机转子振动故障时间序列的自谱函数图谱。对不同类故障所建立ARMA模型的自谱函数图谱分析表明:故障征兆信息较明显,有较好的故障区分度。另外由于ARMA模型的特征向量浓缩了原时间序列信号的全部信息,对ARMA模型的特征向量参数利用多节点输入双隐层BP神经网络完成p维欧氏空间到二维欧氏空间的非线性映射,对汽轮机转子振动故障状态进行诊断。诊断结果表明:对应故障类型的ARMA模型样本通过训练后的神经网络在二维欧氏空间中能较好地对故障进行分类,同类故障的检验样本与目标函数值在欧氏空间具有最小距离,表明基于ARMA模型的二维欧氏空间双隐层神经网络故障诊断方法有较高的故障辨识能力。     

A hybrid neural network model for PEM fuel cells

The goal of this paper is to discuss a neural network modeling approach for developing a quantitatively good model for proton exchange membrane (PEM) fuel cells. Various ANN approaches have been tested; the back-propagation feed-forward networks and radial basis function networks show satisfactory performance with regard to cell voltage prediction. The effects of Pt loading on the performance of the PEM fuel cell have been specifically studied. The results show that the ANN model is capable of simulating these effects for which there are currently no valid fundamental models available from the open literature.

Two novel hybrid neural network models (multiplicative and additive), each consisting of an ANN component and a physical component, have been developed and compared with the full-blown ANN model. The results from the hybrid models demonstrate comparable performance (in terms of cell voltage predictions) compared to the ANN model. Additionally, the hybrid models show performance gains over the physical model alone. The additive hybrid model shows better accuracy than that of the multiplicative hybrid model in our tests.     

Prediction of global solar irradiance based on time series analysis: Application to solar thermal power plants energy production planning

Due to strong increase of solar power generation, the predictions of incoming solar energy are acquiring more importance. Photovoltaic and solar thermal are the main sources of electricity generation from solar energy. In the case of solar thermal energy plants with storage energy system, its management and operation need reliable predictions of solar irradiance with the same temporal resolution as the temporal capacity of the back-up system. These plants can work like a conventional power plant and compete in the energy stock market avoiding intermittence in electricity production.This work presents a comparisons of statistical models based on time series applied to predict half daily values of global solar irradiance with a temporal horizon of 3 days. Half daily values consist of accumulated hourly global solar irradiance from solar raise to solar noon and from noon until dawn for each day. The dataset of ground solar radiation used belongs to stations of Spanish National Weather Service (AEMet). The models tested are autoregressive, neural networks and fuzzy logic models. Due to the fact that half daily solar irradiance time series is non-stationary, it has been necessary to transform it to two new stationary variables (clearness index and lost component) which are used as input of the predictive models. Improvement in terms of RMSD of the models essayed is compared against the model based on persistence. The validation process shows that all models essayed improve persistence. The best approach to forecast half daily values of solar irradiance is neural network models with lost component as input, except Lerida station where models based on clearness index have less uncertainty because this magnitude has a linear behaviour and it is easier to simulate by models.     

Generation of synthetic sequences of electricity demand: Application in South Australia

We have developed a model to generate synthetic sequences of half-hourly electricity demand. The generated sequences represent possible realisations of electricity load that could have occurred. Each of the components included in the model has a physical interpretation. These components are yearly and daily seasonality which were modelled using Fourier series, weekly seasonality modelled with dummy variables, and the relationship with current temperature described by polynomial functions of temperature. Finally the stochastic component was modelled with autoregressive moving average (ARMA) processes. These synthetic sequences were developed for two purposes. The first one is to use them as input data in market simulation software. The second one is to build probability distributions of the outputs to calculate probabilistic forecasts. As an application several summers of half-hourly electricity demand were generated and from them the value of demand that is not expected to be exceeded more than once in 10 years was calculated.     

基于自回归滑动平均模型的风力发电容量预测

利用时间序列分析法对富锦风电场风电机组发电容量时间序列进行分析,通过长自回归模型法建立了基于这些数据的自回归模型(AR)和自回归滑动平均模型(ARMA)。在建模过程中,采用3种定阶方法分别建立了不同的ARMA模型,并在对比分析了不同模型的优缺点之后对其进行加权平均综合处理,最终得到较理想的预测模型,使风力发电容量短期预测的归一化平均绝对误差降到7%以内。