A Study On The Impact Of Parameter Uncertainties And Saturation Nonlinearities On Power System Stability

The insecurity and instability problems will certainly cause enormous losses and catastrophic results for modern power systems featured with extra high voltage and long-distance transmission lines, large capacity generators, cross-regional inter-connections and huge inter-area power exchanges. Therefore, studies on the power system security and stability have been paid much attention for a long time. Since the angle stability of power systems is the basic problem in the analysis of the power system security and stability, studies on angle stability have become more and more essential and important. Although much research work on angle stability has been done, there are still many important issues to be solved, such as the impact of parameter uncertainties on the transient stability, and the impact of the saturation nonlinearities on the small-signal stability. This dissertation focuses these problems concerning the angle stability, and some theoretical contributions to nonlinear systems are provided.In the first part of this dissertation, some research work is done, including the stability region estimation of a large class of general autonomous systems, the topological properties of the parameter feasible regions, the impact of parameter uncertainties on the transient stability, the existence of an optimal solution and the equivalent condition about the transient stability constraint. Details are as follows,1. Based on the Taylor Series Expansion and the LaSalle Invariance Principle, a class of methods for estimating the stability region of nonlinear autonomous systems is suggested, and they are used to analyze the transient stability of a power system. Compared to other methods based on the energy function, the methods provided in this dissertation need fewer assumptions and can avoid calculating the unstable equilibrium points. The estimated stability region can be expressed analytically, and the complex calculation is avoided as well.2. The concept of the parameter feasible regions is provided based on the differential-Algeria equations, and some topological properties about the region are obtained as well. Further more, a class of optimization problems consisting of the constraint of transient stability are analyzed with emphasis on the feasible region. Some theoretical conclusions are derived, i.e., the optimal solution may not exist; under certain conditions, the constraints of transient stability can be replaced by an engineering criterion. These results are useful for analyzing and solving the optimized problem.3. An analytical method is suggested to deal with the impact of parameter uncertainties on the transient stability. This method is based on the idea of"Uniformly Ultimately Bound", and a sufficient condition that judges whether the stability characteristics will be changed or not is derived by comparing the limit index and the calculated index in some operating point. The methods suggested are analytically sound, thus the advantage lies in the few calculation and reliability, although they are conservative to some extent.In the second part of this dissertation, some research work is done, including a method for estimating the stability region of a linear system with saturation nonlinearities, a reduced-order method for estimating the stability region of singular linear system with saturation nonlinearities. Further more, these methods are applied to analyze the impact of saturation nonlinearities on power system small-signal stability with the saturated PSS controller. Details are as follows,1. When the disturbance rejection is not considered, a method is suggested to estimate the stability region of linear system with saturation nonlinearities. To reduce the conservativeness in the estimation, a simple convex optimization with linear matrix inequality(LMI) constraints is presented, and it is proved that the optimal solution lies on the boundary of the feasible region, and the optimal solution is in proportion to the upper-bound of the saturation function. Furthermore, an analytical method is suggested to evaluate the performance of saturated PSS controller.2. When both the disturbance rejection and saturation nonlinearities are considered, a multi-objective optimization model is presented to estimate the practical stability region and maximum tolerable disturbance rejection. This optimization problem is solved by an iterative method, which converges to the Pareto Optimal Solution(POS) of the optimization problem in theory. Moreover, as an application of this approach to power systems, an analytical method, based on the POS, to analyze the performance of a controller with saturation nonlinearities and disturbance rejection is introduced to deal with the saturated PSS. Numerical results of a test power system are described, indicating the reliability and simplicity of the approach.3. In the PSS control system mentioned above, there is large difference in the decay speeds of the transient, so the dynamical system is fundamentally singular. To overcome the singularity, a reduced-order method is suggested to estimate the stability region of the singular system with saturation nonlinearities based on the singular perturbation theory. In the reduced-order method, a low system model is constructed to estimate the stability region of the primary high order system, so that the singularity is eliminated, and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proved in theory, and it is validated by some numerical examples.