Bilateral privacy-preserving energy sharing in network-constrained models via homomorphic encryption-based distributed optimization

The proliferation of distributed energy enables prosumers to participate in local trading, yet privacy concerns and network constraints hinder market implementation. This paper proposes a bilateral privacy-preserving energy sharing mechanism that secures sensitive data while enforcing grid operational limits. We develop a prosumer decision model incorporating utility functions and transfer distance factors. To resolve privacy-coordination conflicts, a distributed optimization framework compatible with nonlinear models is designed by integrating gradient descent and dual ascent. This framework guarantees convergence under problem convexity and Lagrangian gradient existence. Furthermore, a homomorphic encryption scheme is integrated to enable dual-blind computations, which prevents plaintext disclosure to either prosumers or the operator while maintaining network safety. Theoretical analysis confirms the scheme's correctness and computational tractability. Numerical simulations on IEEE 14-bus and 33-bus systems validate the mechanism regarding convergence, bilateral privacy protection, and social welfare enhancement. Finally, the algorithm's scalability is demonstrated through penalty-based acceleration, which meets the practical deployment requirements of modern power system.