Modern power grids are critical infrastructures that include interacting networks of physical and computational components. In other words, they are critical smart grids. Therefore, they face serious safety and cyber-security problems. Failures in real power grids and numerous successful attacks on these grids, resulting in large economical losses, put forward the development of protection means against them as the main problems. The difficulty of solving these problems is due to the permanent emergence of new increasingly sophisticated attacks types against power grids. This results in the permanent development of protecting the power grid means from new types of attacks. The main aim of the given paper is a short survey of mathematical models for the most dangerous attacks against modern power grids and known protection schemes against these attacks.