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The rapid development of low-carbon energy technologies and energy storage technologies has provided an important and feasible path to decarbonizing the power system. In this context, there is an increasing number of studies on renewable energy, carbon capture, utilization and storage (CCUS) and energy storage expansion planning. However, most of the existing studies attribute the carbon responsibilities to the source side and a small number to the load side. Expansion planning studies that consider the overall carbon emissions of the system to be shared between the source and the load side are still relatively few. Therefore, it is necessary for the source and the load side to share the responsibility for the total system carbon emissions. To fill this research gap, this paper proposes a source-load bilateral carbon incentive mechanism for wind-CCUS-battery power systems based on the carbon emission flow theory. Besides, a bi-layer wind-CCUS-battery expansion stochastic planning framework considering wind and load uncertainties is constructed. The first layer takes the minimum expectation of power generation costs, fixed investment costs of wind turbines and CCUS units and carbon incentive costs as the objective function from a source-side perspective. The second layer takes the minimum battery investment cost and the expectation of electricity purchasing costs and load-side carbon incentive costs as the objective function from a load-side perspective. Finally, the proposed model is tested on the IEEE 24 bus power system for validity and advantage. The results show that the current high investment cost is not favorable to CCUS construction. At this time, the bilateral carbon incentive mechanism is more conducive to promoting system carbon reduction than the unilateral carbon incentive mechanism. In the future, as the cost of CCUS decreases, the source-side carbon incentive mechanism is more conducive to system carbon reduction than the bilateral carbon incentive mechanism. Due to the consideration of the stochastic uncertainty of wind turbines and loads, the research in this paper is closer to the reality, which can provide a reference for the future carbon emission reduction path of the power system, especially for the quantitative analysis of carbon emission reduction of CCUS, which is an important guiding significance for the promotion of the engineering practice of CCUS. [ABSTRACT FROM AUTHOR]