This paper presents a theoretical study of damping

synchronizing and inertial control laws

implemented using controllable power injection devices like HVDC

FACTS or renewable-energy/storage systems which have power-electronic grid interfaces. The approach is to use a simplified dynamical model of a power system to arrive at generalized results regarding the effect of the strategies on the electro-mechanical dynamics of the system. These results are not dependent on the size

network topology and operating condition of the power system. This paper presents a differential-algebraic formulation and generalized eigenvalue analysis to facilitate a unified study of the effects of the control laws on the electro-mechanical modes. The damping

synchronizing and inertial control laws can themselves be extended to include the possibility of mutual-damping

synchronizing and inertial effects when multiple devices are present. The control laws are not only simple and intuitive

but also are found to have a predictable and generally beneficial impact on the electro-mechanical dynamics of the grid

even when detailed models are considered.