Distributed bi-level optimal power flow calculation for SVSM interval of integrated transmission and distribution networks considering the uncertain renewables

To accurately and efficiently calculate the static voltage stability margin (SVSM) interval of integrated transmission and distribution networks (ITDNs) considering the uncertain fluctuation of renewables, a distributed bilevel optimal power flow (OPF) calculation method based on the alternating direction method of multipliers for the SVSM interval of ITDNs is proposed in this paper. Due to the different structure characteristics of transmission network (TN) and distribution network (DN), a hybrid node-branch OPF method for calculating the SVSM of ITDNs is proposed, which has better convergence than the traditional node OPF method. Different reactive power-voltage control modes of renewable energy stations (RESs) are also considered in the calculation. Considering the uncertain fluctuation of RESs, two distributed bi-level OPF models for calculating the upper and lower bounds of the SVSM interval of ITDNs are established. Based on the alternating direction method of multipliers, the SVSM interval bounds of ITDNs can be obtained by solving the sub-optimization models and transmitting the boundary coupling variables and the load growth parameter between the TN and multiple DNs iteratively until the given convergence criterion is satisfied. Test results on two ITDNs, the modified IEEE 39-33 & 69 bus system and an actual 2285-bus ITDNs, demonstrate the high computation accuracy and efficiency of the proposed distributed bi-level OPF method compared with other calculation methods.