Future nearly-zero energy buildings (nZEBs) will be involved with the twofold problem of on-site matching and hybrid-grid interactions. Theoretically, the hybrid grids' information is dynamic, such as primary energy factors, equivalent CO2 emission factors, and grid tariffs. Regarding primary energy consumption, equivalent CO2 emissions or the grid cost of the nZEB, the significance of specific aspects of the matching capability, such as on-site energy faction (OEF) and on-site energy matching (OEM), will also become dynamic and variable with respect to the evolution of the grid information. Therefore, the primary goal is to develop a methodology as a multi-objective control criterion for the nZEB energy system, which can reflect both the on-site matching capability and dynamic grid information of environmental or economic impacts. The developed methodology is to quantitatively link the dynamic grid information with the weighting factors of the weighted matching index (WMI), following the monotone relationships between the extended matching indices and grid information. The methodology is implemented in this study to control an nZEB energy system with hybrid grid connections. The results show that the developed methodology can seek an optimised balance between the objectives of maximising the matching capability and minimising the environmental/economic load. (C) 2015 Elsevier Ltd. All rights reserved.