The additional carbon emission generated during the operation of the power system due to damage or functional failure of power plants and power grids caused by natural disasters is defined as the carbon emission increase of power system operation due to natural disaster (CEI-OD). Neglecting the cumulative effects of CEI-OD from frequent natural disasters will overestimate the carbon reduction effectiveness of new power systems and affect global decarbonization process. Therefore, calculating CEI-OD and determining its obligation allocation has become an important issue. First, the carbon emission equivalent factor (CEEF) for power system operation modes is proposed, and CEI-OD is calculated based on CEEF when the power system operation mode changes. Secondly, a disaster prevention and recovery measure effect model is constructed using two indicators: the intensity of designed disaster prevention and the corresponding maximum allowable repair time. Simultaneously, the criteria for component disaster prevention negligence and repair negligence are proposed, and based on these, a theory and calculation method for decomposing CEI-OD into accountability allocation and no-fault sharing are introduced. Then, for the collective sharing of the no-fault portion, an improved Aumann-Shapley method is proposed, which effectively addresses the unfair allocation of carbon emission increase resulting from high-carbon power generation forcibly replacing disaster-affected low-carbon power generation. Finally, the feasibility of the proposed method is validated through relevant cases.