Electricity transmission in a grid-connected system provides an effective solution to promoting clean energy accommodation. However, with arbitrary determination in current operation models, the clean energy utilization ratio (CEUR) is not satisfactory largely due to the lack of electricity curtailment (the electricity equivalent of clean energy curtailment) cost-dependent optimization. In this study, a curtailment cost-dependent multi-objective operation (CCMO) model was proposed to complementarily operate a grid-connected hybrid energy system, identify optimal CEUR, and thus maximally reduce electricity curtailment. The CCMO model centers on coupling the punishment cost of electricity curtailment with the multi-objective function defined as the total cost of each grid component. The CCMO model was solved to derive the optimal equilibrium solution determined based on multiple non-dominated solutions. A grid-connected hybrid energy system including the Yunnan, Guangdong, and Guangxi Power Grids was used to test the model performance. The results showed that the CCMO model’s CEUR was up to 100% at hourly scale and 96.9% on daily average, which were both significantly higher than those in the current operation models. Furthermore, the CCMO’s optimal equilibrium solution, i.e., respective minimum total cost of each grid component, can also identify optimal transmission schemes of the daily channel utilization to make the peak utilization hours largest.