To enhance the energy efficiency and financial gains of the park integrated energy system (PIES). This paper constructs a bi-level optimization model of PIES-cloud energy storage (CES) based on source-load uncertainty. Firstly, the scheduling framework of PIES with refined power-to-gas (P2G), carbon capture and storage (CCS) and CES coupling is constructed. Moreover, a bi-level optimization model with the upper tier subject being the PIES operator and the lower tier subject being the CES operator is established under the ladder-type carbon price mechanism with reward and punishment (LCPMRP). Then a proposed entropy weight adaptive information gap decision theory method (EAIGDT) is proposed to eliminate the subjectivity factor and retain its non-probabilistic features while dealing with multiple source-load uncertainties, and according to the operator’s risk preference to build risk-averse (RA) and risk-seeking (RS) strategies, respectively. Finally, the measured data in a certain area of Xinjiang verifies the proposed optimal scheduling method. The results show that the method can effectively take into account the interests of various subjects and realise PIES low-carbon economic operation.