Load frequency control (LFC) is widely employed to regulate power plants in modern power generation systems of smart grids. This paper presents a simple and yet powerful type of attacks, referred to as resonance attacks, on LFC power generation systems. Specifically, in a resonance attack, an adversary craftily modifies the input of a power plant according to a resonance source (e.g., rate of change of frequency) to produce a feedback on LFC power generation system, such that the state of the power plant quickly becomes instable. Extensive computer simulations on popular LFC power generation system models which consist of linear, non-linear, and/or high-order items clearly demonstrate the effectiveness of the proposed attacks. As the attack has very low computational cost and communication overhead, it is easy to launch in resource-limited devices such as intelligent electronic devices. In our simulations, the attacker keeps modified input within the normal operating range so as to invade plausibility and consistency based attack detection methods and yet the modifications can quickly drive the system beyond the admissible boundary. Another interesting finding is that by maliciously modifying the input such as power load and tie-line signal over multi-area interconnection channels, a multi-area LFC power generation system could become unreliable more quickly than a single-area system. Finally, we propose countermeasures on the proposed attacks.