Hierarchical Distributed Optimal Scheduling of Integrated Electricity–Gas–Heat Systems: An ATC–ADMM Approach

Integrated electricity–gas–heat systems require coordinated scheduling while limiting data sharing and representing network constraints. This paper develops a day-ahead model incorporating reactive power, voltage magnitudes, network losses, demand response, and CHP/P2G coupling. Piecewise linearization and second-order cone relaxation reformulate the model as a mixed-integer second-order cone program, while a hierarchical ATC–ADMM method coordinates the electricity–heat and natural gas subsystems by exchanging coupling variables. Residual checks verify approximation accuracy and original equation feasibility. In the test system, ATC–ADMM reached consensus within five iterations, with a total-cost deviation of 0.0075% from centralized optimization, whereas ATC did not converge within 500 iterations. Coordinated operation reduced the total cost by 1.13%, and Shapley allocation benefited both subsystems. Increasing demand-side flexibility from 5% to 9% reduced the total cost by 0.88% and wind curtailment from 6.02% to 4.86%; increasing reactive compensation from 40% to 60% reduced the total cost by 0.41% and wind curtailment to 5.70%. The results reveal non-monotonic penalty-update effects and diminishing marginal benefits of flexibility resources, providing guidance for parameter selection and capacity allocation.