Distributed Optimal Capacity Allocation of Integrated Energy System via Modified ADMM

•Establishment of a power-gas network system model for efficient energy absorption and smart grid load shifting.•Introduction of a novel ADMM-based cooperative regulation scheme, enhancing convergence through dynamic step size adjustment.•Development of an improved cooperative scheme, addressing inequality constraints with privacy guarantees and flexible initial conditions. This paper considers the optimal capacity allocation of integrated energy systems (IESs) with the power-gas systems for clean energy consumption. First, power-gas network models are established with equality and inequality constraints. Second, a novel full distributed cooperative optimal regulation scheme is designed to deal with the optimal capacity allocation problem. Moreover, to deal with the inequality constraints in IESs, a distributed projection operator is developed such that the system states can be guaranteed within the constraint conditions. Then the convergences of those distributed optimization algorithms were proved for strictly convex objective functions. And the initial conditions of systems for the algorithm are free. The simulation is provided to demonstrate the effectiveness of the distributed optimazation approach.