This paper introduces a modal analysis approach termed as the Iterative Matrix Pencil method. It uses the Matrix Pencil Method as the primary tool for mode identification, and adds to it by utilizing the concept of a cost function in order to reduce the number of signals needed to identify the modes for a large system. The method is tested for a variety of large synthetic power grids in this paper, with the cost function being reported to measure accuracy. A sensitivity analysis is also considered, showing how this new method behaves when adjusting the two primary user-based inputs; the number of iterations, and the SVD threshold.

The efficiency of a power system is reduced when voltage drops and losses occur along the distribution lines. While the voltage profile across the system buses can be improved by the injection of reactive power, increased line flows and line losses could result due to uncontrolled injections. Also, the determination of global optimal settings for all power-system components in large power grids is difficult to achieve. This paper presents a novel approach to the application of game theory as a method for the distributed control of reactive power and voltage in a power grid. The concept of non-cooperative, extensive = form games is used to model the interaction among power-system components that have the capacity to control reactive power flows in the system. A centralized method of control is formulated using an IEEE 6-bus test system, which is further translated to a method for distributed control using the New England 39-bus system. The determination of optimal generator settings leads to an improvement in load-voltage compliance. Finally, renewable-energy (reactive power) sources are integrated to further improve the voltage-compliance level.