In order to reduce the detrimental effects of inter-area oscillations on system stability, it is possible to use Linear Matrix Inequalities (LMIs) to design a multi-objective state feedback. The LMI optimization finds a control law that stabilizes several contingencies simultaneously using a polytopic model of the system. However, the number of cases to be considered is limited by computational complexity which increases the chances of infeasibility. In order to circumvent this problem, this paper presents a method for solving multiple polytopic problems having a common base case. The proposed algorithm determines the necessary polytopic control for a particular contingency and classifies the data as belonging to that polytopic domain. The technique has been tested on an 8-machine, 13 bus, system and has been found to give satisfactory results. / Master of Science

The traditional approach to damp inter-area oscillations is through the installation of Power System Stabilizers (PSSs) which provide damping control action through excitation control systems of the generating units. However, study of recent blackouts has shown that the control action provided by a PSS alone is not sufficient for damping oscillations in modern power systems which operate under stressed conditions. An integrated form of control using remote measurements to coordinate the different control elements present in the system is the need of the hour. One way of implementing such a coordinated control is through the development of a Linear Matrix Inequality (LMI)-based polytopic model of the system that guarantees pole placement for a variety of operating conditions. The size of the polytopic formulation is an issue for application of LMIs to large systems. The use of Selective Modal Analysis (SMA) alleviates this problem by reducing the size of the system. The previous attempts have used a model containing all the and modes, with SMA being used to eliminate all the other states. In practical applications the resulting system was still found to be too large to use in a polytopic model. This thesis presents an algorithm to reduce the size of the system to the relevant modes of oscillations. A 16 machine, 68 bus equivalent model of the New England-New York interconnected power system is used as the test case with DC lines and SVCs acting as the control. The algorithm is then applied to a 127-bus equivalent model of the WECC System. The use of ESDs as a form of control is also demonstrated. The results indicate that the proposed control successfully damps the relevant modes of oscillations without negatively damping the other modes. The control is then transferred to a more detailed 4000+ bus model of the WECC system to realize its performance on real-world systems. / Master of Science