Short term solar irradiance forecasting using a mixed wavelet neural network

In modern smart grids and deregulated electricity markets, accurate forecasting of solar irradiance is critical for determining the total energy generated by PV systems. We propose a mixed wavelet neural network (WNN) in this paper for short-term solar irradiance forecasting, with initial application in tropical Singapore. The key advantage of using wavelet transform (WT) based methods is the high signal compression ability of wavelets, making them suitable for modeling of nonstationary environmental parameters with high information content, such as short timescale solar irradiance. In this WNN, a combination of the commonly known Morlet and Mexican hat wavelets is used as the activation function for hidden-layer neurons of a feed forward artificial neural network (ANN). To demonstrate the effectiveness of the proposed approach, hourly predictions of solar irradiance, which is an aggregate sum of irradiance value observed using 25 sensors across Singapore, are considered. The forecasted results show that WNN delivers better prediction skill when compared with other forecasting techniques.     

Hourly solar radiation forecasting using optimal coefficient 2-D linear filters and feed-forward neural networks

In this work, the hourly solar radiation data collected during the period August 1, 2005–July 30, 2006 from the solar observation station in Iki Eylul campus area of Eskisehir region are studied. A two-dimensional (2-D) representation model of the hourly solar radiation data is proposed. The model provides a unique and compact visualization of the data for inspection, and enables accurate forecasting using image processing methods. Using the hourly solar radiation data mentioned above, the image model is formed in raster scan form with rows and columns corresponding to days and hours, respectively. Logically, the between-day correlations along the same hour segment provide the vertical correlations of the image, which is not available in the regular 1-D representation. To test the forecasting efficiency of the model, nine different linear filters with various filter-tap configurations are optimized and tested. The results provide the necessary correlation model and prediction directions for obtaining the optimum prediction template for forecasting. Next, the 2-D forecasting performance is tested through feed-forward neural networks (NN) using the same data. The optimal linear filters and NN models are compared in the sense of root mean square error (RMSE). It is observed that the 2-D model has pronounced advantages over the 1-D representation for both linear and NN prediction methods. Due to the capability of depicting the nonlinear behavior of the input data, the NN models are found to achieve better forecasting results than linear prediction filters in both 1-D and 2-D.     

Study of forecasting solar irradiance using neural networks with preprocessing sample data by wavelet analysis

Artificial neural network is a powerful tool in the forecast of solar irradiance. In order to gain higher forecasting accuracy, artificial neural network and wavelet analysis have been combined to develop a new method of the forecast of solar irradiance. In this paper, the data sequence of solar irradiance as samples is mapped into several time-frequency domains using wavelet transformation, and a recurrent back-propagation (BP) network is established for each domain. The solar irradiance forecasted equals the algebraic sum of the components, which were predicted correspondingly by the established networks, of all the time-frequency domains. A discount coefficient method is adopted in updating the weights and biases of the networks so that the late forecasts play more important roles. On the basis of the principle of combination of artificial neural networks and wavelet analysis, a model is completed for fore-casting solar irradiance. Based on the historical day-by-day records of solar irradiance in Shanghai an example of forecasting total irradiance is presented. The results of the example indicate that the method makes the forecasts much more accurate than the forecasts using the artificial neural networks without combination with wavelet analysis.     

A regime-dependent artificial neural network technique for short-range solar irradiance forecasting

Solar power can provide substantial power supply to the grid; however, it is also a highly variable energy source due to changes in weather conditions, i.e. clouds, that can cause rapid changes in solar power output. Independent systems operators (ISOs) and regional transmission organizations (RTOs) monitor the demand load and direct power generation from utilities, define operating limits and create contingency plans to balance the load with the available power generation resources. ISOs, RTOs, and utilities will require solar irradiance forecasts to effectively and efficiently balance the energy grid as the penetration of solar power increases. This study presents a cloud regime-dependent short-range solar irradiance forecasting system to provide 15-min average clearness index forecasts for 15-min, 60-min, 120-min and 180-min lead-times. A k-means algorithm identifies the cloud regime based on surface weather observations and irradiance observations. Then, Artificial Neural Networks (ANNs) are trained to predict the clearness index. This regime-dependent system makes a more accurate deterministic forecast than a global ANN or clearness index persistence and produces more accurate predictions of expected irradiance variability than assuming climatological average variability.     

A simple approach to the synthetic generation of solar irradiance time series with high temporal resolution

Modeling the performance of some concentrating solar systems for thermal power plants may require high temporal resolution irradiance as input, in order to account for the impact of the cloud transient effects. This work proposes a simple method of generating synthetic irradiance of 10-min intervals from the hourly mean values. Boundary conditions are imposed to preserve the expected behavior under clear sky situations. The procedure consists basically on adding a random fluctuation, which characteristic amplitude depends on the sky conditions, to the hourly interpolated values. The assessment of the method with ground data have shown to main aspects to remark: daily and monthly means from the synthetic data are below 5% of root mean squared deviation compared to the original time series; despite the noticeable uncertainty in the 10-min synthetic irradiance values, the dynamic behavior of the fluctuations is comparable to the original data.     

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.     

Computation of solar radiation from observations of cloud cover

Techniques of computation of global and diffuse solar radiation from the daily duration of bright sunshine and cloud cover are well-known. However, since radiation computations from cloud cover data provide rather imprecise results, this method is resorted to only when sunshine data are not available. To obtain a better idea of the inverse relationship between the long-term averages of sunshine duration and total cloud cover, an analysis of the monthly mean values of the fraction of the sky C, covered by clouds of all types and the duration of bright sunshine, n, was carried out. The relationship between C and (1−n/N′), where N′ is the maximum possible hours of sunshine, was found to be non-linear. The shape of the regression line connecting the two parameters also shows that ground observations of cloud cover always tend to be overestimates. The differences between such estimates and cloud cover values derived from sunshine duration tend to become zero when skies are either clear or overcast and are a maximum for cloud cover values in the range 0.4–0.7. A cubic regression equation was derived relating C and (1−n/N′) and using this relationship, it has been possible to compute sunshine duration from cloud cover data to an accuracy of about 4–7 per cent and from the cloud derived sunshine data, to compute monthly mean values of global solar radiation to an accuracy of about 6–10 per cent and diffuse solar radiation within an accuracy of about 10–15 per cent.     

PV system sizing using observed time series of solar radiation

Sizing represents an important part of photovoltaic system design. This paper describes a sizing procedure based on the observed time series of solar radiation. Using a simple geometrical construction, the sizing curve is determined as a superposition of contributions from individual climatic cycles of low daily solar radiation. Unlike the traditional methods based on loss-of-load probability, the reliability of supply enters in this method through the length of the time series of data used in the analysis. The method thus resembles techniques used in other branches of engineering where extreme values are considered as functions of certain recurrence intervals.     

Forecasting of preprocessed daily solar radiation time series using neural networks

In this paper, we present an application of Artificial Neural Networks (ANNs) in the renewable energy domain. We particularly look at the Multi-Layer Perceptron (MLP) network which has been the most used of ANNs architectures both in the renewable energy domain and in the time series forecasting. We have used a MLP and an ad hoc time series pre-processing to develop a methodology for the daily prediction of global solar radiation on a horizontal surface. First results are promising with nRMSE ～ 21% and RMSE ～ 3.59 MJ/m². The optimized MLP presents predictions similar to or even better than conventional and reference methods such as ARIMA techniques, Bayesian inference, Markov chains and k-Nearest-Neighbors. Moreover we found that the data pre-processing approach proposed can reduce significantly forecasting errors of about 6% compared to conventional prediction methods such as Markov chains or Bayesian inference. The simulator proposed has been obtained using 19 years of available data from the meteorological station of Ajaccio (Corsica Island, France, 41°55′N, 8°44′E, 4 m above mean sea level). The predicted whole methodology has been validated on a 1.175 kWc mono-Si PV power grid. Six prediction methods (ANN, clear sky model, combination…) allow to predict the best daily DC PV power production at horizon d + 1. The cumulated DC PV energy on a 6-months period shows a great agreement between simulated and measured data (R² > 0.99 and nRMSE < 2%).     

Ground level solar radiation prediction model including cloud cover effects

The model Estimated Solar Radiation (ESR) was developed to predict solar radiation on a horizontal surface for any latitude as a function of total opaque cloud cover. ESR was verified by comparing predicted and observed daily totals of solar radiation on a horizontal surface for Salisbury, Maryland (lat. 38.5°N), and Ely, Nevada (lat. 39.2°N), using hourly values of observed total opaque cloud cover for each location obtained from the National Climatic Center, Asheville, North Carolina. Although the model slightly underpredicts on those days when total opaque cloud cover is high (9–10) and overpredicts on those days when total opaque cloud cover is low (0–1), it provides excellent correlation with observed data (R = 0.87 for Salisbury and 0.94 for Ely).     

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.     

Artificial intelligence techniques applied to hourly global irradiance estimation from satellite-derived cloud index

Artificial intelligence techniques, such as fuzzy logic and neural networks, have been used for estimating hourly global radiation from satellite images. The models have been fitted to measured global irradiance data from 15 Spanish terrestrial stations. Both satellite imaging data and terrestrial information from the years 1994, 1995 and 1996 were used. The results of these artificial intelligence models were compared to a multivariate regression based upon Heliosat I model. A general better behaviour was observed for the artificial intelligence models.     

MEO shadowring method for measuring diffuse solar irradiance: Corrections based on sky cover

The present paper deals with atmospheric corrections factors proposed as a function of the atmospheric transmissivity in order to correct the diffuse solar irradiance measured with the Melo-Escobedo-Oliveira Shadowring Measuring Method (MEO shadowring Method). Global irradiance was measured by an Eppley-PSP pyranometer; direct normal irradiance by an Eppley-NIP pyrheliometer fitted to a ST-3 sun tracking device and diffuse irradiance by an Eppley-PSP pyranometer fitted to a MEO shadowring. The Solar Radiometric Laboratory at Sao Paulo State University provided the measurements during the years 1996–2005. Two correction models for diffuse solar irradiance were proposed: All Sky Correction Model (ASC Model) and Sky Cover Correction Model (SCC Model). The MBE and RMSE statistical indicators performed the validations. The correction models showed results in the same order of magnitude: ASC Model showed 0.81% deviation, while SCC Model showed 0.66% deviation. Therefore, the correction models proposed as a function of the sky covering (atmospheric transmissivity) were efficient to correct the isotropic diffuse irradiance, approaching the measured and reference diffuse irradiance less than 1%. Corrections show dependence on sky coverage and seasonality. The results presented that the sky cover corrections improve the MEO shadowring method, allowing the generation of a reliable global, direct and diffuse radiation database without high financial investments.     

Modeling and forecasting the mean hourly wind speed time series using GMDH-based abductive networks

Wind speed forecasts are important for the operation and maintenance of wind farms and their profitable integration into power grids, as well as many important applications in shipping, aviation, and the environment. Modern machine learning techniques including neural networks have been used for this purpose, but it has proved hard to make significant improvements on the performance of the simple persistence model. As an alternative approach, we propose here the use of abductive networks, which offer the advantages of simplified and more automated model synthesis and transparent analytical input–output models. Various abductive models for predicting the mean hourly wind speed 1 h ahead have been developed using wind speed data at Dhahran, Saudi Arabia during the month of May over the years 1994–2005. The models were evaluated on the data for May 2006. Models described include a single generic model to forecast next-hour speed from the previous 24 hourly measurements and an hour index, which give an overall mean absolute error (MAE) of 0.85 m/s and a correlation coefficient of 0.83 between actual and predicted values. The model achieves an improvement of 8.2% reduction in MAE compared to hourly persistence. The above model was used iteratively to forecast the hourly wind speed 6 h and 24 h ahead at the end of a given day, with MAEs of 1.20 m/s and 1.42 m/s which are lower than forecasting errors based on day-to-day persistence by 14.6% and 13.7%. Relative improvements on persistence exceed those reported for several machine learning approaches reported in the literature.     

Predicting solar irradiance on inclined surfaces using sky radiance data

The availability of more comprehensive solar irradiance data is invaluable for the reduction of cooling load in buildings and for the evaluation of the performance of photovoltaic plants. In many parts of the world, however, the basic solar irradiance data are not always readily available. This paper presents an approach to calculate the solar irradiance on sloped planes by integrating the sky radiance distribution. Sky radiance data recorded from January 1999 to December 2001 in Hong Kong were used to estimate the solar irradiance for the horizontal and four principal vertical surfaces (N, E, S and W). The performance of this approach was assessed against data measured in the same period. Statistical results showed that using sky radiance distributions to predict solar irradiance can give reasonably good agreement with measured data for both horizontal and vertical planes. The prediction approach was also employed to compute the solar irradiance of a 22.3° (latitude angle of Hong Kong) inclined south oriented surface. The findings indicated that the method can provide an accurate alternative to determine the amount of solar irradiance on inclined surfaces facing various orientations when sky radiance data are available.     

Electric power demand forecasting using interval time series: A comparison between VAR and iMLP

Electric power demand forecasts play an essential role in the electric industry, as they provide the basis for making decisions in power system planning and operation. A great variety of mathematical methods have been used for demand forecasting. The development and improvement of appropriate mathematical tools will lead to more accurate demand forecasting techniques.     

The importance of the sampling frequency in determining short-time-averaged irradiance and illuminance for rapidly changing cloud cover

The sampling interval is an important parameter which must be chosen carefully, if measurements of the direct, global, and diffuse irradiance or illuminance are carried out to determine their averages over a given period. Using measurements from a day with rapidly moving clouds, we investigated the influence of the sampling interval on the uncertainly of the calculated 15-min averages. We conclude, for this averaging period, that the sampling interval should not exceed 60 s and 10 s for measurement of the diffuse and global components respectively, to reduce the influence of the sampling interval below 2%. For the direct component, even a 5 s sampling interval is too long to reach this influence level for days with extremely quickly changing insolation conditions.     

Analysis of residuals in daily solar radiation time series

The Box-Jenkins approach is applied to daily solar radiation data from four different locations in Malaysia. The deterministic annual component is obtained by Fourier analysis. The stochastic component of the time series is fitted to three models, ARMA (1,0), ARMA (2,0) and ARMA (1,1). Random shocks from these models are tested by Box-Pierce statistic and Ljung-Box for whiteness of residuals. Skewness and kurtosis coefficients are tested for normality.     

Generation of bivariate solar radiation and temperature time series

A bivariate periodic time series model for daily sequences of dry bulb air temperature and solar radiation is developed. An autoregressive model is first used to produce a monthly time series. A temporal disaggregation process is then employed to produce the daily series from the monthly series. When applied to an historical time series, the models preserve the first- and second-order moment properties as well as the correlation properties of the monthly and daily historical data. In addition, the skewness coefficient of the observed sequence is reasonably well preserved at both temporal levels. The model can provide multilevel synthetic meteorological data that is important in simulating solar energy systems that consider both short- and long-term performance.     

Capacity estimation of a minihydro plant based on time series forecasting

A procedure to estimate the capacity of minihydro plants based on water flow time series forecasting is presented. First, the classic method used for this purpose is introduced and then a set of methodologies to assess the feasibility of minihydro generation and to determine system capacity based on time series forecast is described. The water flow time series is processed to determine the theoretical power generation and to assess if a minihydro plant can be installed. Finally the characteristics of each of the electro-mechanical components for the proposed minihydro plant are selected.