An analytic distributed multi-objective optimization algorithm, which is named as interchange objective value method, is proposed for distributed multi-objective optimization problems. The interchange objective value method can be implemented with two types of methods, i.e., interchange unilateral objective value method and interchange bilateral objective value method. To verify the feasibility and effectiveness of the proposed analytic interchange objective value method, these two interchange objective value methods are applied in the distributed multi-objective optimal power flow of distributed multi-area interconnected power systems. The global optimal power flow problem of distributed multi-area interconnected power systems is divided to multiple subsidiary distributed multi-objective optimal power flow problems with interchanging objective values and boundary variables in security. The proposed interchange objective value methods are developed in IEEE 118-bus two-area power system, IEEE 300-bus two-area power system, and Xixiangtang district 22-bus power system. The numerical simulation results verify the feasibility and effectiveness of the proposed security analytic interchange objective value method for the distributed multi-objective optimal power flow of distributed multi area interconnected power systems.