With the increasing penetration of new energy sources, one of the main challenges faced by the dispatch analysis of the new power system is how to generate new energy output scenarios that are both temporally and spatially correlated and can meet the coverage requirements for safe dispatch under conditions of high-dimensional uncertain variables and complex spatio-temporal coupling constraints. To address this issue, this paper proposes a method for generating spatio-temporal correlated scenarios in high-dimensional uncertain power systems considering high coverage metric. Firstly, a Markov chain model of prediction errors is established to describe the temporal state transition characteristics of variables. Secondly, a spatial correlation model based on Copula functions is constructed to represent the spatial correlations among multiple variables. Finally, a method for reconstructing the time series of correlated variables is proposed to combine the two, achieving efficient characterization of spatio-temporal correlated scenarios. An evaluation index system for scenario coverage metric is also constructed to assess the number of scenarios required for high-coverage scenario sets. The case study shows that the scenario sets generated by the proposed method can effectively meet the coverage requirements for safe dispatch of the power system while retaining the spatio-temporal correlation characteristics.