The coordinated dispatch of interconnected grids characterized by maldistributed sustainable energy encounters challenges with regional privacy. Thus, this study proposes a non-iterative robust economic dispatch method for interconnected grids based on tie-line power transfer regulation. The economic dispatch model with uncertainties is transformed into a two-layer robust model and further treated as a single-layer linear model by strong duality theorem. Then, the intra-regional submodules are established by temporal and spatial decomposition to enable parallel execution. The inter-regional power transfer feasible region (PTFR) and intra-regional operation cost feasible region (OCFR) are evaluated using multi-parameter programming theory to protect the private and sensitive information of each region and to ensure cost efficiency of dispatch results. Additionally, the boundaries of feasible regions are adjusted by the conservatism budget to address multiple fluctuation intervals of stochastic factors. Finally, the information of feasible regions is shared between each intra-regional operator along with central coordination layer, generating feasible regions of joint economic dispatch along with inter-regional power transfer constraints. The intra-regional dispatch strategy could be rapidly obtained following the decision-making of inter-regional dispatch by mapping relations. Case studies by three modified IEEE test systems demonstrate the preciseness and effectiveness of the proposed method.