Fast Grid Security Assessment With N − k Contingencies

The challenge of grid security assessment with <inline-formula><tex-math notation="LaTeX">$N- k$</tex-math> </inline-formula> contingencies lies in a huge amount of transmission security constraints and even for the modest values of <italic>N</italic> and <italic>k</italic>, the computational complexity would be very high. A new method for fast grid security assessment is presented in this paper for DC grid. The key idea is to construct a small number of representative constraints to equivalently “represent” the huge number of original security constraints. It is proved that applying the representative constraints is sufficient to assess grid security as the original security constraints do. An important feature of the new method is that the representative constraints need to be constructed only once offline. They are only related to the parameters of transmission network and do not change with power injections. Numerical testing is performed for IEEE-RTS 24-bus system, IEEE 118-bus system, and the Polish 2383-bus system. The number of representative constraints to be assessed is only 1.1%, 0.32%, and 0.27% of that of the original constraints, respectively, and the computational time of security assessment is greatly reduced.