An Incentive-based robust flexibility market for congestion management of an active distribution system to use the free capacity of Microgrids

•Design an incentive-based LFM to integrate the flexibility services of MGs.•Demand side energy management and rescheduling to use the free capacity of MGs.•Use a modified ADMM method for LFM based on a request and response structure.•Provide a RO model to consider the real-time price uncertainty in LFM.•A two-stage model for LEM and LFM for congestion management of distribution system.