Finding the most critical contingencies in a power system is a difficult task as multiple evaluations of load and generation scenarios are needed. This paper presents a mathematical formulation for selecting, ranking, and grouping the most critical N-1 network contingencies, based on the calculation of a Power Constraint Index (PCI) obtained from the Outage Transfer Distribution Factors (OTDF). The results show that the PCI is only affected by the impedance parameter of the transmission network, the topology, and the location of all generators. Other methods, such as the Performance Index (PI) and the Overload Index (OL) are affected by the power generation and demand variations. The proposed mathematical formulation can be useful to accelerate the calculation of other methods that evaluate contingencies in power system planning and operation. Furthermore, the fast calculation of indices makes it suitable for online evaluation and classification of multiple events considering the current topology. The results showed that the proposed al- gorithm easily selected and ranked the expected contingencies, with the highest values of the index corresponding to the most critical events. In the filtering process, the computa- tional calculation time improved without losing the robustness of the results.

Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information from four aspects: approval, objection, abstention and refusal. The partitioned Maclaurin symmetric mean (PMSM) operator is an effective information fusion tool, which can fully capture the interrelationships among any multiple attributes in the same block whereas attributes in different block are unrelated. Therefore, in this paper,we first extendPMSM operator to spherical fuzzy environment and develop spherical fuzzy PMSM (SFPMSM) operator as well as spherical fuzzy weighted PMSM (SFWPMSM) operator. Meanwhile, we discuss some properties and special cases of these two operators. To diminish the impact of extreme evaluation values on decision-making results, then we integrate power average (PA) operator and PMSM operator to further develop spherical fuzzy power PMSM (SFPPMSM) operator and spherical fuzzy weighted power PMSM (SFWPPMSM) operator and also investigate their desirable properties. Subsequently, a new multiple attribute group decision making (MAGDM) method is established based on SFWPPMSM operator under spherical fuzzy environment. Finally, two numerical examples are used to illustrate the proposed method, and comparative analysis with the existing methods to further testy the validity and superiority of the proposed method.