Development of an appropriate solar radiation model for Uganda

Abstract

Sizing of solar energy systems is necessary in order to optimize their output. This requires a database of solar radiation for locations for which the systems are being assessed. Solar radiation data is also required in modeling a building’s thermal performance, as input into ecological and crop models and evaluation of long-term effects of climatological changes.

Solar radiation data can be provided through measurements. In Uganda, measurements of total solar radiation and its two components (diffuse and direct) have been carried out for a few locations, such as in Kampala, Entebbe and Gulu. It is difficult to have measurements from all locations of interest because the measuring instruments are expensive to purchase and install. An alternative to obtaining solar radiation data is to estimate it either by use of an appropriate solar radiation model or interpolation of the few existing records. Interpolation results into solar radiation maps.

This study had an overall objective of developing an appropriate solar radiation model for Uganda. This was achieved through measurement of diffuse and direct solar irradiation and subsequent computation of total solar irradiation at four selected locations in Uganda; investigation of relationship between total, diffuse, direct solar irradiation and a selection of meteorological and geographical parameters, which lead to an appropriate solar radiation model for Uganda; prediction of total, diffuse and direct solar irradiation using this model; interpolation of measured and predicted total, diffuse and direct solar irradiation and subsequent drawing of solar radiation maps for Uganda.

The uncertain nature of solar radiation and the modeling abilities of Artificial Neural Networks (ANN) have inspired the application of ANN techniques to predict solar radiation. ANN are intelligent systems that have the capacity to learn, memorize and create relationships among data. They are ideal for modeling non-linear, dynamic, noise-ridden and complex systems. A survey on existing literature shows limited usage of the ANN method to predict total, diffuse and direct solar radiation. Much of the work on the prediction of solar radiation has been done using the empirical method. Estimation of total solar radiation using ANN has been done for locations in North and South America, Europe, Asia, Middle East and some parts of northern and southern Africa. Solar radiation predictions using ANN in eastern and central Africa are non-existent. Therefore the study utilized the ANN method to predict total solar irradiation and its two components.

The data from the four measurement sites in Uganda were split into two such that the dataset from three stations, that is, Mbarara, Lira and Tororo, was used for training Neural Networks and formulating empirical models. The dataset from the Kampala station was reserved for validating both the ANN and empirical models.

A typical neural network is made up of input, hidden and output layers. The present study utilized meteorological parameters as inputs and solar radiation as output from the neural network. A feedforward back-propagation neural network was used in this study with six input variables for the prediction of total solar irradiation, which included: sunshine hours, cloud cover and maximum temperature, together with latitude, longitude and altitude. The diffuse component had as input the following variables: latitude, longitude, altitude, total solar irradiation, sunshine hours, average temperature, relative humidity and cloud cover; whereas the direct component had: latitude, longitude, altitude, total solar irradiation, sunshine hours and maximum temperature. There was a challenge in determining which transfer function and training algorithm to use in training the neural networks, and also determining the number of hidden layers and number of neurons in the ANN structure.

Total, diffuse and direct solar irradiation values were estimated for eight other stations in Uganda where measurements of solar radiation were not made. This was done using the appropriate ANN models. Consequently, a pool of measured and estimated values of solar irradiation was created and used for the interpolation task. Moving Average interpolation method was used for interpolating total solar irradiation and its two components.

The ANN architecture designed was a feedforward back-propagation with one hidden layer and tangent sigmoid, as the transfer function. The output layer utilized a linear transfer function and Levenverg-Marquardt as the training algorithm. The number of neurons in the hidden layer was fifteen for total solar irradiation, eighteen for diffuse solar irradiation and six for direct solar irradiation. The ultimate part of the design process of the ANN model was the variation of the inputs to the network and evaluation of the corresponding ANN model in pursuit of the most appropriate prediction model. The evaluation involved correlation and error analysis using mean bias error (MBE) and root mean square error (RMSE).

The appropriate ANN model for prediction of total solar irradiation was one which had the following input variables: latitude, longitude, altitude, sunshine hours, maximum temperature and cloud cover. The model yields predictions with MBE=0.069MJm-2 and RMSE=0.504MJm-2. The appropriate ANN model for prediction of diffuse solar irradiation was one which had the following input variables: latitude, longitude, altitude, total solar irradiation, sunshine hours, average temperature, cloud cover and relative humidity. The model yields predictions with MBE=0.018MJm-2 and RMSE=0.268MJm-2. The appropriate ANN model for prediction of direct solar irradiation was one which had the following input variables: latitude, longitude, altitude, total solar irradiation, sunshine hours and maximum temperature. The model yields predictions with MBE=0.005MJm-2 and RMSE=0.197MJm-2.

A pool of measured and estimated values of total solar radiation and its two main components have been interpolated, successfully. The results are three sets of solar radiation maps for Uganda, with normalized percentage root mean square errors of 2.5%, 3.0% and 1.8% for the interpolation of total, diffuse and direct solar irradiation, respectively.