An Assessment of Solar Irradiance Stochastic Model for the UK A.M. Dizqah School of CEIS Northumbria University Newcastle Upon Tyne, UK Arash.moradinegade@northumbria.ac.uk A.MAHERI School of CEIS Northumbria University Newcastle Upon Tyne, UK Alireza.maheri@northumbria.ac.uk K. BUSAWON School of CEIS Northumbria University Newcastle Upon Tyne, UK Krishna.busawon@northumbria.ac.uk Abstract— Hybrid Renewable Energy System (HRES) can effectively supply sustainable electrical energy in standalone remote areas. However, in order to design a reliable site and a robust controller, uncertainties in sustainable energy resources need to be modeled properly. This paper proposed a stochastic model of hourly solar irradiance for four locations across the UK. The goodness-of-fit of the proposed model has been evaluated using the Kolmogorov-Smirnov (K-S) test. The proposed model has been employed to simulate the amount of hourly solar irradiance for a location in the UK. Keywords-Hybrid Renewable Energy System; Solar Irradiation; Stochastic Modeling; Uncertainty; Simulation I. INTRODUCTION The term HRES is used to describe energy systems that consist of generators that work with renewable energy sources. In particular, wind kinetic energy and solar irradiance are assumed as energy resources which have considerable share in near future electricity production [1]. A typical standalone HRES site employs an array of Photovoltaic (PV) modules and a Wind Turbine (WT) to supply load demands. There is also a battery bank to reduce power fluctuations. Despite employing the proper sized components there still may be blackout periods because of the uncertainties in the resources and in order to design a reliable site, these uncertainties need to be considered through proper models. Karaki, Chedid, and Ramadan [2] introduced a stochastic model for hourly global insolation absorbing by a PV array based on the beta distribution. Although, it is a considerable achievement in stochastic modeling of insolation, the goodness-of-fit of the model for the hourly solar irradiance depends on location and month of the year [3], [4]. In particular, the global solar irradiance is not necessarily fitted well for some months depending on the location. In this study, a stochastic model for hourly solar irradiance of four locations across the UK has been extracted and evaluated. While the beta distribution has been considered as the stochastic model, the Maximum Likelihood Estimator (MLE) method has been employed to estimate the model parameters based on meteorological records. The goodness-of-fit of the estimated parameters has been evaluated using the K-S test. II. STOCHASTIC MODELS OF HOURLY SOLAR IRRADIANCE Extraterrestrial solar irradiance can be estimated for any particular location with regard to its altitude and longitude as well as the azimuth angel. However, the absorbed energy on an inclined surface is not equal to the terrestrial radiation and instead is a fraction of it. The difference between the terrestrial and absorbed insolation is mainly because of clouds which is a random phenomenon [5]. With attention to the probabilistic behavior of insolation, the amount of the electrical power generated with a Photovoltaic (PV) array is a stochastic process, i.e., the value of the hourly generated power is a random variable with the distribution related to the distribution of the absorbed insolation. This section summarizes the probabilistic model of solar irradiance. A. Solar irradiance Karaki, Chedid, and Ramadan [2] used a stochastic model for global insolation absorbing by a PV array. They modeled the hourly global solar irradiance as the beta probability distribution function (PDF) as follows: 1 0 1 0 1 ) ( ) ( ) ( ) , ; (                                 I i I i i f x x x I x (1) where: x i The solar irradiance ( W/m 2 ) (.)  The gamma function  and  The shape parameters of the beta distribution 0 I The extraterrestrial solar irradiance ( W/m 2 ) ) ( x I i f x The PDF of the solar irradiance random variable x I Equation (1) introduces an hourly random variable which is the ratio of global to extraterrestrial solar irradiance of that hour. This random variable is defined as the clearness index. Paltridge and Platt [6] proposed (2) to calculate the extraterrestrial radiation for a particular location on the earth. 2 0 ) ( 1367 D D I  (2)