Distributed optimal scheduling of integrated energy system including ADN and DHN with adaptive robust optimization

• A distributed scheduling framework is developed for ADN–DHN integrated energy systems. • ADMM-based transactive coordination preserves privacy between DSO and microgrids. • Adaptive robust optimization handles renewable generation and demand uncertainties. • Dynamic electricity and heat pricing is obtained through a transactive energy market. • Building and pipeline thermal inertia is exploited to enhance operational flexibility. The rapid growth of distributed generation has transformed passive distribution networks to active distribution networks, while district heating networks have emerged as effective solutions to enhance efficiency and flexibility in integrated energy systems. Microgrids, as local control units, can improve resilience and stability; however, uncertainties in demand and renewable generation, along with privacy concerns, pose challenges to optimal operation. The purpose of this study is to present a distributed optimal scheduling for the operation of an integrated energy system that consists of numerous microgrids interacting through a transactive energy market. The objective is to optimize microgrids and distribution system operator cost while satisfying technical constraints, agent privacy, and accounting for uncertainties. To achieve this, the alternating direction method of multipliers and adaptive robust optimization are used in the decision-making processes of the distribution system operator and each microgrid. The resulting three-level problem is efficiently solved using column and constraint generation and nested column and constraint generation. Numerical studies under various scenarios demonstrate the effectiveness of the proposed approach in dynamic electricity and heat pricing, leveraging building thermal inertia to enhance flexibility, and achieving economical and reliable operation of the integrated active distribution network and district heating network.