To improve the low-carbon and economic performance of interconnected microgrid systems (IMS) while accounting for the time delay and uncertainty of renewable distributed generation (RDG)

a distributed robust and low carbon economic scheduling of IMS considering iterative delay and energy storage sharing is proposed. Firstly

a multi-operator distributed collaborative operation framework for IMS with jointly rented shared energy storage is established. A dynamic allocation strategy for shared energy storage capacity considering the time-varying requirements of each microgrid's energy storage capacity is proposed

which enhances the efficiency of shared storage through time-division sharing of capacity usage rights. Then

considering that the probability distribution of random variables is difficult to accurately obtain

distributed robust chance constraints are utilized to address the uncertainty of RDG of the microgrid. The unimodal distribution characteristics of random variables is also considered in the constraints to reduce the conservatism of the results while ensuring the robustness of the chance constraints. In the meanwhile

the nonlinear global carbon emission constraint is introduced into the scheduling of IMS to precisely limit its carbon emissions. Lastly

considering that the calculation and communication delays can lead to the loss of boundary variables in distributed optimization

an improved relaxed alternating directions method of multipliers (IR-ADMM) is proposed. By forecasting the lost boundary variables in iterations through a momentum-extrapolation- based method

the convergence speed of distributed optimization algorithms under the non-ideal environments can be improved. The effectiveness of the proposed method is verified through simulation examples.