Determination of transient stability boundary in functional form with applications in optimal power flow and security control

This thesis presents a novel technique to derive an accurate Transient Stability Boundary which can be readily used in multiple applications related to ensuring dynamic security of a power system. The intended applications of the proposed boundary are: (a) using it as a constraint in a dynamic security constrained optimal power flow program, (b) fast transient security assessment and control, and (c) redispatch of generation for preventive control. The proposed method approximates the ideal transient stability boundary with an accuracy specified by the user. As the transient stability boundary is not perfect, some stable operating points may be classified as unstable and some unstable operating points may be classified as stable. For the applications stated above, the misclassification of operating points must be minimized and any misclassified cases must be confined to marginal cases. Further, the estimated Transient Stability Boundary must be expressed in terms of the pre-contingency operating point. For optimal power flow and preventive control applications, the function must be differentiable. For all these applications, both the speed of determination of the function and its accuracy are very important.; An investigation of currently available transient security assessment and control technics revealed that the transient stability boundary with the required features can only be determined combining powerful features of time domain simulations and machine learning techniques.; The hybrid algorithm proposed in this thesis combine time domain simulation and the Kernel Ridge Regression algorithm, a nonlinear extension of the well known Ridge Regression algorithm. Time domain simulations are used to generate transient stability data which are used in the Kernel Ridge Regression algorithm. The heavy computational burden in data generation is paid off-line.; The modified Kernel Ridge Regression algorithm proposed in this thesis can efficiently handle the high dimensionality of the problem. It can also approximate the transient stability boundary with an accurate nonlinear boundary while confining the misclassifications close to the boundary.; The proposed hybrid algorithm is used to estimate transient stability boundaries for small system (New England 39 bus system) and a medium scale real power system with 470 buses. It is shown that transient stability boundaries with over 95% accuracy can be efficiently derived from the transient stability databases generated off-line. Applications of the derived boundary for (a) fast transient security assessment and control, and (b) dynamic security constrained optimal power flow based generation redispatch are demonstrated using the New England 39 bus system.