Objective The rapid development of new power system and power market reform, coupled with a high proportion of renewable energy integration, presents significant challenges to power system flexibility. Integrated electricity-gas energy systems have emerged as a vital solution to mitigate the uncertainty of renewable energy output by leveraging the flexible resources of the natural gas system. Currently, the optimization of collaborative operations in integrated electricity-gas energy systems primarily emphasizes economic costs, often overlooking the critical importance of the systems’ flexible regulation capabilities.

Methods A multi-objective operation optimization model was established to comprehensively address the economic cost and flexibility of the system operation scheme. The model satisfies both the constraints of steady-state power flow in the power grid and transient energy flow in the gas grid. The flexibility is assessed using security region theory, and characterized by the fluctuation range of renewable energy output that the integrated electricity-gas energy system can accommodate under the current operation scheme. In solving the operation optimization model, the Gurobi solver was first employed to identify a feasible solution without objective constraints, which served as the initial population for the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Subsequently, the Pareto frontier was derived through iterative optimization using the NSGA-II. To verify the model’s validity, it was tested on an integrated energy system that consists of a six-bus power system and a six-bus natural gas system.

Results Given the dynamic characteristics of the natural gas system, varying initial pressure and flow conditions significantly impact the availability of flexible resources, thereby affecting the integrated electricity-gas energy system’s capability to stabilize fluctuations in renewable energy output. In addition, there is an inherent trade-off between economic cost and system flexibility in operation schemes: prioritizing economic benefits limits system flexibility, reducing its capability to regulate intermittent renewable energy output, while increasing system flexibility leads to higher operation costs.

Conclusion The multi-objective operation optimization model rectifies the oversight of the system’s flexible regulation capabilities in the collaborative operation optimization of integrated electricity-gas energy systems. It improves the systems’ capacity to manage fluctuations and uncertainties in renewable energy output while providing new insights for future research on optimizing these systems.