Smart power grids are currently equipped with open communication infrastructures to improve efficiency, reliability and sustainability of supply. Although technologically cost-effective, this makes them vulnerable to cyber attacks with potentially catastrophic consequences. In this paper an overlapping networked control architecture is investigated for addressing the problem of Load Frequency Control (LFC) under possible malicious attacks in multi-area power grids. Besides providing a certain level of redundancy, this architecture can easily be recast into leader-follower configurations with time-varying hierarchy. Here we propose a reachability analysis for such a class of systems that is instrumental to a model predictive control scheme (see Part II of this paper) able to isolate the nodes under attacks.