  How to practically maintain the frequency stability of large-scale power
systems by a decentralized way is a simple but non-trivial question. In other
words, is it possible to design any local controller without understanding the
other controlled areas and with less understanding of network structure? With
respect to the special properties of physical interaction between the local
areas, this paper suggests two existing theories for tackling this issue.
Firstly, passivity theory is shown to be a candidate for frequency control
problem using swing equation. Based on the passivity of swing dynamics, it is
possible to guarantee the system stability by designing for each local area a
passive controller. We further extend the passivity approach to the
hierarchically decentralized control system with unknown communication delay.
Secondly, we discuss the application of generalized frequency variable (GFV) to
the frequency control problem using area-control-error. Each local controller
is designed such that each local subsystem follows a nominal model set.
Utilizing GFV theory, we present a triad of conditions that sufficiently
guarantee the system stability. The conditions can be tested conveniently by a
limited set of inequalities established from the GFV and the eigenvalues of the
physical interaction matrix. The effectiveness, limitation, and challenge of
two theories are discussed by design examples with numerical simulations.
