  Due to uncertainties and the complicated intrinsic dynamics of power systems,
it is difficult to predict the cascading failure paths once the cascades occur.
This makes it challenging to achieve the effective power system protection
against cascading blackouts. By incorporating uncertainties and stochastic
factors of the cascades, a Markov chain model is developed in this paper to
predict the cascading failure paths of power systems. The transition matrix of
Markov chain is dependent on the probability of branch outage caused by
overloads or stochastic factors. Moreover, a robust optimization formulation is
proposed to deal with the cascading blackouts by shedding load optimally for
multiple cascading failure paths with relatively high probabilities.
Essentially, it can be converted to the best approximation problem. Thus, an
efficient numerical solver based on Dykstra's algorithm is employed to deal
with the robust optimization problem. In theory, we provide a lower bound for
the probability of preventing the cascading blackouts of power systems.
Finally, the proposed approach for power system protection is verified by a
case study of IEEE 118 bus system.
