This dissertation presents advanced techniques for power systems stability assessment, focusing mainly on the issues concerning steady state stability. Steady state stability analysis aims at determining the effects of small disturbances on the power system that is assumed to be operating at or near a stable equilibrium state. Eigenvalue techniques are investigated for the purpose of increasing the calculation performance of eigen-algorithms for power system small signal stability analysis. A new method based on non-iterative approach to determine voltage stability boundary is explored to fill the gap in the literature. A support vector machine based approach to select load modeling parameters for stability analysis is examined, aiming at improving the generalization ability of load model parameters. In addition, a new idea of using characteristic ellipsoid to monitor dynamic behaviour of power systems is also explored in this dissertation.
A proper system model described as a set of interconnected non-linear differential equations is necessary to be linearized around the operating point for the purpose of steady state stability analysis. A mathematical tool used to study the small signal stability of power systems based on a linearized system model is eigenvalue/eigenvector analysis. One of the key questions of eigenanalysis of power system stability is how to improve the performance of the eigenvalue/eigenvector algorithm for very large power systems. The first study presented in this dissertation involves the eigenvalue calculation algorithm for small signal stability analysis. The BR algorithm is a new efficient eigenvalue algorithm which has never been applied in power system small signal stability analysis. This dissertation proposes use the BR algorithm as an alternative method for tasks involving eigenvalue and eigenvector calculation for power system small signal stability analysis. The performance of the BR algorithm compared with the QR algorithm is analyzed in terms of calculating time and storage complexity. Results suggest that the BR algorithm is faster than the QR algorithm and requires less storage space, therefore, is an efficient alterative to the QR algorithms.
Voltage stability is another important topic in power system stability analysis based on steady state analysis approach. Voltage stability boundary is usually the focus of this class of stability study. Although a great number of methods to determine voltage stability boundary have been proposed in the literature, they are traditionally based on iterative approaches, such as continuation power flow method and direct method. A gap on non-iterative approaches to determine voltage stability boundary still needs to be filled. This dissertation proposes a new non-iterative method to determine static voltage stability boundary. Like other traditional methods that apply the property of the Jacobian becomes singular at the stability boundary points, the proposed new method also utilizes this property of Jacobian. The differences from other methods lie in 1) the rectangular coordinates are used to form Jacobian matrix, and 2) the singularity condition equation is formed in a way different from traditional iterative methods. The method to treat the situations where the reactive power limits are reached is also provided in this dissertation. Numerical examples show the effectiveness of the proposed non-iterative method.
Load modeling plays an important role in power system stability analysis and planning studies. The parameters of load models may experience variations in different application situations. Choosing appropriate parameters is critical for dynamic simulation and stability studies in power systems. This dissertation presents a method to select the parameters with good generalization ability based on a given large number of available parameters that have been identified from dynamic simulation data in different scenarios. Principal component analysis is used to extract the major features of the given parameter sets. Reduced feature vectors are obtained by mapping the given parameter sets into principal component space. Then support vectors are found by implementing a classification problem. Load model parameters based on the obtained support vectors are built to reflect the dynamic property of the load. The parameters obtained by support vector machines have good generalization capability, and can represent the load more accurately in most situations.
A new idea of multi-dimensional characteristic ellipsoid approach to monitor the dynamic behaviour and stability trend of a power system is presented in this dissertation. The multi-dimensional Minimum Volume Enclosing Ellipsoid (MVEE) is formulated based on phasor measurements to extract the feature of dynamic behaviour of power systems. The geometrical properties and theoretical background are explored. Some feature indexes that can be used to determine the disturbance, and the interpretation rules of the characteristic ellipsoid are also provided. The effectiveness of the ellipsoid method is demonstrated by both simulated dynamic data and real PMU measurement data.