Various applications of forecasting effective global horizontal irradiance play increasingly vital role in grid-connected photovoltaic installations, but suffer from forecasting inaccuracy and prohibitively expensive computational cost. Although Support Vector Machine (SVM) is one of the most powerful forecasting approaches, it does not provide an interpretable model. This motivates penalized variable selection methods to be introduced to SVM to select important variables. However, in some forecasting problems, there are some underlying logic or hierarchical structure such as heredity principle among the variables. Penalized Kernel SVM approaches do not take heredity principles into consideration when enforcing sparsity. This paper investigates structural variable selection in Kernel SVM based approach which pursues heredity principle and sparsity simultaneously. To achieve heredity principle, both optimization and procedure based structural variable selection approaches are studied in the Kernel SVM. Computationally, we derive fast and simple-to-implement algorithms to perform structural variable selection and solar irradiance forecasting. Furthermore, Support Vector Machines Information Criterion is utilized to select the kernel parameters to guarantee the model consistency. Real data experiments directly reveal that our proposed KSVM-SVS based approach following heredity principle delivers superior performances in terms of forecasting accuracy comparing with other competitors. (C) 2017 Elsevier Ltd. All rights reserved.