Nowadays

transmission system operators (TSOs) encounter the challenges of securely operating power grids with high penetration of renewables. In this context

more flexibility is needed than ever to maintain system reliability. With rapid development of coordinated transmission and distribution technology recently

active distribution networks (ADNs) which have abundant flexible resources

have the potential to provide flexibility to the TSO. Hence

an integrated transmission-distribution flexibility market is proposed in this paper. In the proposed framework

the energy market is first cleared to obtain baseline generation schedules. Then the baseline generation schedules are treated as inputs to the flexibility market. Furthermore

the integrated flexibility market is cleared to facilitate flexibility trading between transmission and distribution networks. To preserve the data privacy of different market participants

an alternating direction method of multipliers (ADMM) based method is utilized to clear the markets in a distributed manner. In the energy market and flexibility market-clearing model

transmission network market clearing models are linear programming (LP) models

and distribution network market clearing models are second order cone programming (SOCP) models. Through the proposed method

only limited information is exchanged between TSO and DSOs. Case studies are conducted on a revised IEEE 30-bus transmission network with two 33-node ADNs. Numerical results demonstrate the proposed flexibility market framework can enhance competitiveness of generation companies in the transmission network and distributed generators (DGs) in the ADNs. Moreover

flexibility purchasing cost is reduced by 17.7% compared to traditional flexibility supplied by generators according to the case study results

and ADNs can gain additional flexibility profit by providing flexibility.