Solar Energy Vol. 62, No. 5, pp. 369–375, 1998 © 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X/98 $19.00+0.00 PII: S0038-092X(98)00018-8 IRRADIANCE CALCULATION ON SHADED SURFACES VOLKER QUASCHNING and ROLF HANITSCH Berlin University of Technology, Institute of Electrical Power Engineering, Renewable Energy Section, Secr. EM 4, Einsteinufer 11, D-10587 Berlin, Germany Received 4 February 1997; revised version accepted 5 August 1997 Communicated by AMOS ZEMEL Abstract—Operating results of recently built photovoltaic systems have shown that shading can cause high losses in performance. We need methods for calculating the reduced irradiance to minimize the shading losses in the planning process. There are well-known models to estimate the irradiance received by a tilted surface. However, these methods normally do not include shading reduction caused by objects in the surroundings. Therefore, methods are proposed to include shading in calculations of direct and diffuse irradiation. Before these methods can be used, the surroundings have to be surveyed. Hence, how to survey objects in an easy way is discussed. Using the proposed methods and calculations it is possible to include shading reduction in the prediction of the irradiance on a tilted surface. Finally, the influence of shading on the irradiance is shown by an example. © 1998 Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION is not possible in most cases. Algorithms that use polygon projection methods are less time Shading of solar systems can reduce their energy consuming than the radiosity method. Powerful gain miserably. Performance losses due to shad- computer equipment, however, is also needed. ing are reported for many recently built photo- In this paper we describe another method for voltaic systems. Operating results from the the calculation of the reduced irradiance due to German’s 1000-Roofs-Programme have shown shading. The surroundings can be surveyed in that more than half of the generators examined a very easy way with this method. Furthermore, are partially shaded and that the annual losses this method allows very rapid calculations. are up to 10% ( Kiefer et al., 1995). At the 40 kWp photovoltaic facade at the University of Northumbria at least 10% of the strings are 2. IRRADIANCE ON UNSHADED SURFACES shaded and up to 30% of the strings can be affected (Pearsall and Wilshaw, 1996). These There are some well-known methods for obtaining the irradiance on an unshaded sur- are some examples that the irradiance reduction due to shading has an important influence on face. The best way, however, is to measure the irradiance on a horizontal or tilted plane. For the operating results of solar systems. We have to take shading into consideration when plan- the additional calculations it is necessary to estimate not only the global irradiance, but also ning or simulating solar systems. However, pho- tovoltaic systems are more sensitive to shading the direct and diffuse irradiance. If only meas- urements of the global irradiance are available, than solar thermal systems. There are some good computer programs for we can split up the global irradiance into direct and diffuse irradiance with statistical correla- analyzing the shading situation at a location. The computer program Radiance from Ward tions (Reindl et al., 1989). We can calculate the position of the sun (1990) can calculate the irradiance situation in complex surroundings. The calculations that with a high accuracy using some well-known algorithms that allow a prediction (Walraven, use the radiosity method are extremely time consuming and the surroundings are difficult to 1978; DIN 5034, 1985; Kambezidis and Papanikolaou, 1990). The different nomencla- describe. Other computer tools, such as Sombrero (Niewienda et al., 1996) or Shading ture in the different algorithms can be a little confusing. (Shaviv and Yezioro, 1997), estimate mutual shading with polygon projections. For these If we know the direct irradiance G b,h and the diffuse irradiance G d,h on a horizontal plane, algorithms the surroundings are also difficult to describe for the computer. An exact description we can use them to calculate the total irradiance G t on a tilted plane that consists of the direct of irregular objects, such as trees or other plants, 369