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In the context of the large-scale participation of renewable energy in market trading, this paper designs a cooperation mode of new energy power stations (NEPSs) and shared energy storage (SES) to participate in the power-green certificate market, which divides SES into physical energy storage and virtual energy storage. Secondly, combining the advantages of scenario generation and robust optimization (RO), a two-stage RO model with improved uncertainty interval is proposed to determine the optimal trading strategy. Then, to better align the distribution results of cooperative benefits with the actual contributions of NEPSs and SES, an entropy weight modified Shapley value benefit allocation strategy is constructed. Finally, the new energy base in Qinghai Province, China is chosen for simulation. The results show: (1) Adding energy storage and using two-stage RO are able to effectively improve the ability of NEPSs to resist uncertainty, which increases the revenue of the alliance by 22.8%. (2) The application of SES has better economic benefits than each member equipped with energy storage separately. Compared with the latter, the deviation penalty cost of the former is reduced by 66.4%, and the revenue is increased by 3.4%. (3) The proposed entropy weight modified Shapley value method embodies the important auxiliary role of SES more obviously. Based on this method, the overall satisfaction of the alliance increases by 12.6%. Generally speaking, the optimization model and benefit allocation strategy proposed in this paper can provide guidance for NEPSs and SES participating in power trading, and promote the low-carbon transformation of the power sector. [Display omitted] • Design a cooperation mode of new energy power stations and shared energy storage. • Divid the shared energy storage into physical energy storage and virtual energy storage. • Propose a two-stage robust optimization model with improved uncertainty interval. • Construct an entropy weight modified Shapley value-based benefit allocation strategy. • Select a new energy base as the simulation system for verifying the effectiveness and applicability. [ABSTRACT FROM AUTHOR]