In a distributed optimization framework for the economic dispatch problem of integrated energy systems (IESs)

the topological design of the node collaboration mechanism is necessarily constrained by information interaction. Existing studies are mainly classified into two types of communication protocols

synchronous and asynchronous communication. However

synchronous communication requires timing consistency and waits for a synchronized response or acknowledgement to be received among the communicators before subsequent operations can be executed

which is challenging to achieve in large-scale network environments. In this paper

we propose a distributed economic scheduling algorithm for asynchronous communication

based on the Gossip algorithm

which leverages its asynchronous characteristics. The convergence of the algorithm is rigorously proved using matrix perturbation theory and the eigenvalue theorem. Further

two typical network attack models

Denial of Service (DoS) and False Data Injection (FDI)

are considered

and a resilient security policy is designed to mitigate the impact of network attacks on optimal economic scheduling. Finally

an arithmetic case analysis is performed based on the IES of IEEE39-32 nodes

which verifies the effectiveness and superiority of the proposed strategy in terms of communication methods and network security from multiple perspectives by combining different scheduling scenarios

the performance of the attackers

and the comparison of synchronous communication methods.