Zero-carbon parks are fundamental hubs supporting both the new-type power system and China's dual-carbon goal. These parks can effectively optimize the energy structure, promote energy coupling, and achieve zero-carbon operation of the system. It is key issue on how to provide an optimization planning scheme for capacity allocation of zero-carbon park integrated energy system(ZC-PIES), especially considering comprehensive interaction among operation uncertainty, multi-energy coupling, zero-carbon emission, etc. Firstly, this paper proposes a coupling operation architecture of ZC-PIES with wind, photovoltaic, hydrogen, and storage as core elements and constructs physical characteristic models for each equipment. Secondly, considering the uncertainties of system supply and demand interaction, a bi-level capacity configuration model is established for electricity-carbon-hydrogen coupled zero-carbon park. The two-stage distributionally robust optimization(DRO) method is applied to handle the uncertainties in wind, photovoltaic and load demand. Finally, a case study of a zero-carbon park in Southern China is used to validate the effectiveness of the bi-level planning optimization model. Sensitivity analysis is conducted on key factors such as the uncertainties of wind and solar power, load demand, investment in gas post-combustion carbon capture (GPCC) equipment, and time-of-use pricing. The research findings indicate that the bi-level planning optimization model for ZC-PIES can reduce investment costs by 16.06 % compared to alternative scenarios. Additionally, it achieves a maximum reduction of 97.24 % in the average absolute deviation of the net load. This provides a technical pathway and reference framework for the planning and construction of zero-carbon park.
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