Accurate Identification of Critical Boundary Hyperplanes of Practical Steady-State Security Region in Distribution Grids

The practical steady-state security region (PSSR) in distribution grids describes the region where the power flow can be managed securely. The PSSR is irrelevant to operation states and its boundaries can be approximated by hyperplanes (HPs). Benefit from these, the PSSR can dramatically simplify complicated optimal scheduling problems, such as deliverable energy flexibility scheduling. However, calculating the PSSR boundaries corresponding to all the power flow security constraints indiscriminately will theoretically produce lots of HPs to bound the whole PSSR and thus make solving of the PSSR-based optimal scheduling challenging. In fact, the whole PSSR is the intersection of the regions bounded by all the HPs within practical power injection ranges, and only a few HPs, called the critical boundary hyperplanes (CHPs), can bound it. Therefore, it is necessary to identify the CHPs before applying them to the optimal scheduling as power flow security constraints, so as to accelerate the solution. In this paper, a fast and accurate method is first proposed to identify the CHPs. The identified results are irrelevant to the specific objective and can be applied to different optimal scheduling problems. The proposed method is applied to several case-study networks and the results demonstrate its effectiveness and speed.