This thesis presents a thorough analysis of saddle-node bifurcations for power system dynamic models, including a third order representation of high voltage direct current (HVDC) transmission, classic ac generator dynamics with reactive flows, and voltage and frequency dependent load models. Extensions of the Point of Collapse and Continuation methods, initially used in ac system voltage stability studies, are applied to the determination of these bifurcation points. These methods are compared and used for calculating bus voltage profiles (“nose ” curves) and collapse points on ac/dc systems of up to 2158 buses, considering a variety of operational limits and controls, namely, ac/dc regulating transformer tap limits, voltage and reactive power limits, and area interchange control. AC generator reactive power limits, HVDC firing angle limits and voltage dependent current order limits (VDCOL) are shown to affect the stability and loadability of these systems. A vector Lyapunov function approach is employed to define a system wide energy function that can be used for stability analysis. This thesis describes the derivation

This paper examines dynamic behavior in system models that reflect reasonably detailed (third order) HVDC dynamics along with ac system models that include reactive flows, and frequency and voltage dependent load models. A vector Lyapunov function approach is employed to define a system wide energy function that can be used for general security analysis. The paper describes the derivation of individual component Lyapunov functions for simplified models of HVDC links connected to "infinitely strong" ac systems, along with a standard ac only system Lyapunov function. A novel method of obtaining weighting coefficients to sum these components for the overall system energy function is proposed. Use of the new energy function for transient stability and security analysis is illustrated in a test system.

Abstract—Chaotic behavior in power systems has been studied in relatively simple and theoretical system models, where some particular assumptions are made to represent the system as a set of ordinary differential equations (ODE), using “special” nonlinear system analysis tools. In this paper, chaotic behavior on the IEEE 14-bus benchmark system, using a transient stability model and its associated differential-algebraic equations (DAE), is demonstrated and studied based on classical time-domain simulations, without the use of specialized software or simplifying assumptions. The dynamic behavior of the test system is studied for normal operating conditions and for a single contingency case, and the onset of chaos is verified through a Fourier analysis and Lyapunov exponents. The addition of a power system stabilizer (PSS) to the system is shown to remove the observed chaotic behavior. Index Terms—Chaos, crisis, Hopf bifurcations, period doubling, voltage collapse, power system stabilizer.

Abstract: The approach adopted in this paper for the problem of transient stability of multimachine power systems sees the entire network as the (structure-preserving) interconnection of the network components, described by well known models. These structure-preserving models preserve the identity of the network components and allow for a more realistic treatment of the loads. Our main contribution is the explicit computation of a control law which provides transient stabilization, i.e, prevents the system from loss of synchronism after a large perturbation. The theory is illustrated by means of simulation on a 3-machine power system.

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