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The characteristics of isolated grids lead island power systems to rely on stable conventional generation, which is not environmentally friendly and has high carbon emissions. This paper proposes a low-carbon transition model for island power systems considering large-scale offshore wind resources and the long-term uncertainty of carbon prices. First, a detailed model for offshore wind power systems is proposed considering the interaction of multiple wind farms and three transmission technologies. Second, a multi-stage power system planning model is established including the upgrading and decommissioning of thermal units. Meanwhile, an improved long-term carbon price uncertainty modeling method based on the binomial tree is proposed. Then, focusing on the uncertainty of carbon prices, a multi-stage stochastic optimization model is established, and the stochastic nested decomposition algorithm is used to solve the problem. Finally, numerical results show that the low-carbon transition develops plenty of offshore wind power as the primary power source and usually adopts a fractional frequency transmission system for offshore wind integration. The uncertainty of carbon prices has a significant impact on the transition: in the high carbon price realization, the annual carbon emissions are only 0.088 Mt, while in the low carbon price realization, the annual emissions are 0.255 Mt. • Low-carbon transition is modeled via multi-stage programming and solved by SND. • Improved binomial tree model for long-term carbon price uncertainty is proposed. • Detailed planning model of offshore wind systems is established. • Wake effect between wind farms are considered and linearized by wake factors. • Fractional frequency transmission system is adopted and analyzed. [ABSTRACT FROM AUTHOR]