Abstract: Large-scale virtual power plants (VPPs) are gradually becoming equal to traditional generation resources, and their optimized operation strategies will significantly affect the equilibrium state of the electricity market. Efficiently characterizing the external properties of VPPs under key ports will promote the compatibility of VPPs with the existing market model, which is of great practical significance for their in-depth participation in the electricity market. Based on the theory of multi-parametric linear programming (MPLP), we propose an analytical characterization of the marginal cost function of a VPP, which reflects the overall flexibility, trading feasibility region, and the marginal cost of a VPP through the low latitude parameter of the power traded between the VPP and the primary grid at the point of standard coupling (PCC). The initial parameter space is optimally partitioned into many critical regions (CRs) based on cost minimization, and then the economic properties of the optimal segmentation are revealed and used to portray the segmental mapping relationship between the parameter space and the cost of the VPP. Finally, the effectiveness of the proposed algorithm is verified based on the improved IEEE 33 and IEEE 123 bus systems, which provides a theoretical basis for VPPs to participate in the market clearing in a non-iterative way.