Hybrid power systems (HPSs) are a variant of distributed generation utilising two or more complementary energy sources for power generation, and are thus more efficient, reliable and cost-effective than single-source systems. HPSs can be used in urban, rural and remote areas. HPS research has focused on sizing and optimisation, which requires efficient and effective methodologies to ensure reliable power supply and a cost-effective system. This paper presents a mathematical programming technique for the design of off-grid and grid-connected HPSs, taking into account uncertainties in renewable energy resources and load demands. The basic model formulation is based on a comprehensive superstructure that includes all possible connections for power allocation. Chance-constrained programming is applied to determine the optimal capacities of power generation and energy storage units with a specified minimum system reliability level. Furthermore, fuzzy optimisation is adopted to account for the trade-off between conflicting economic and environmental goals, as well as parametric uncertainties in HPS design. Two case studies are presented to demonstrate the application of the proposed approach. (C) 2019 Elsevier Ltd. All rights reserved.