In order to develop a new type of power system scheduling model and method under the dual-carbon background, a multi-energy complementary scheduling model with Watershed-type integration of hydro-wind-photovoltaic (WHWP) is constructed by considering stepped carbon trading. In order to improve the solution efficiency and adaptability of such high-dimensional non-convex optimization problems of the WHWP-containing multi-energy complementary scheduling model, this paper proposes an enhanced golden jackal optimization algorithm (EGJO) based on Logistic chaotic mapping, quasi-reflective learning strategy, Gaussian random wandering strategy, and Optimal Individual local search mechanism combined with differential variational perturbation strategy. First, the initialized population is generated using Logistic chaos mapping, which enhances the spatial diversity of the algorithm. Second, by introducing quasi-reflective learning strategy and Gaussian random wandering strategy to update the jackal pair positions in the search, encircle-and-attack phases of the golden jackal algorithm, respectively, the algorithm′s global optimization capability as well as convergence speed are strengthened. Finally, the optimal Individual local search mechanism combined with the differential variational perturbation strategy is introduced after merging the updated positions to improve the solution accuracy. The analysis of the algorithm is carried out in the extended IEEE3 machine 9 node and a simplified power system in a provincial area. The results show that the comprehensive operating costs of the WHWP-containing multi-energy complementary dispatch model considering stepwise carbon trading are reduced by 8.55% and 10.78%, and the carbon emissions are reduced by 178.26 t and 17 841.68 t, respectively; compared with the mainstream seven optimization algorithms, the cost of the EGJO solution is reduced by at least 11 080 yuan and 14.01 million yuan, and the standard deviation of the cost is reduced by 1.598 and 0.004, respectively; fully verifying the effectiveness and superiority of the model and method proposed in this paper. 1.598 and 0.004, respectively; fully verified the effectiveness and superiority of the model and method proposed in this paper.