In order to maximize the return on equity (ROE) of wind-hydrogen system investors, take full advantage of the wind power as well as smooth the wind power output of a wind farm, an optimal sizing model of a coupled wind-hydrogen system (CWHS) is established considering the requirements of wind power grid-connection technology. The fluctuating cost of wind power is calculated by an "equal-kWh following load" method and the chance-constrained programming is introduced to deal with the uncertainty generated by the wind power. The optimal capacity of each unit for a CWHS, including the wind power transmission project, electrolyser, compressor and so on, is acquired and the economic analysis is evaluated under comprehensive aspects, e.g. wind curtailment decisions, hydrogen prices, the correlations between wind power output and system load, and the fluctuation degrees of wind power generation. The simulation is established by the realistic historical data from a wind farm in Fujian, China. When the confidence level is 92%, the capacity of electrolysers increases with the increase of the hydrogen price when it is larger than the equivalent value 4.34 (sic)/kg. In addition, the smaller the correlation between wind power output and load and the bigger the volatility index of wind power output, the less the smoothing benefit of the CWHS, where the smaller capacity of the transmission project and bigger capacities of electrolysers and compressors are required. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.