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Electric power transmission systems are a key infrastructure in modern power system, and the relay protection device is one of the most important components of a power system. Analyses of topology and blackout data of real power systems indicate that many real power systems possess complex networks' characteristics like scale-free or small-world and blackouts behave as a complex dynamical system. Moreover, the topology evolution is a significant characteristic of the network. Therefore, we use an ORNL-PSerc-Alaska (OPA) model considering topology evolution to investigate how these complex system dynamics impact on the assessment of measures for improving relay protection. Simulation results show that a decrease in the probability of failure to operate relay protection does not reduce the probability of large blackouts in the growing scale-free small-world power grid, but increases that instead, and unwanted operation of relay protection is more harmful to the system. The mitigation of failures of relay protection in complex systems needs to be approached with care.