Probabilistic Eigenvalue Analysis Under Power System Multi-operating Conditions

In power system operation, there are many fluctuations and random factors, such as the variations of load powers and generations, changes in network configuration and system parameters, as well as the measure and forecast errors. In order to improve the stability of power systems in more wide operating condition, the probabilistic technique has been adopted to eigenvalue analysis and power system stabilizer (PSS) design. The initial operating state of generators and the probabilistic attributes of nodal voltages are determined by the probabilistic load flow computation. Based on the present probabilistic analysis methods, some works have been carried out in this thesis, including the computational error comparison and the algorithm improvement for probabilistic load flow; the analysis and improvement for probabilistic eigenvalue; PSS parameters optimization by the nonlinear programming approach.With nodal voltages expressed in the rectangular form, the present second order probabilistic load flow computation provides accurate voltage expectations, but not satisfactory voltage covariances, especially those covariances related to the real part of voltages. The correction of voltage covariances is considered in the computation of power expectations. But the linearized mode is used in the computation of voltage covariances. A better algorithm called as the complete model retaining the second order terms is presented in this thesis, and this approach is compared with several present methods at iterative equation and computational precision. Based on the PV and injection curves, the slack nodal curve is taken into account by using extended Joacbian matrix in the presented algorithm. In order to compare the computational errors of several models, the accurate expectations and covariances are calculated by repeated deterministic computation. Results show that the complete model retaining the second order terms is the most accurate model, and it can provide accurate voltage expectations and covariances.In the aspect of probabilistic eigenvalue analysis, the precisions of several probabilistic eigenvalue models are compared. The expectations and covariances of eigenvalues are computed by the linearized model, the simplified second order model,the second order model and the correction to system matrix A. All analysis are on two testing systems. Results obtained from the simplified second order can be acceptable, though there are still errors in the standard variances of eigenvalues. Results calculated from the second order modal should be more accurate in theory, but the results are not so much accurate and the computation requirement becomes much more. The computational precision of correcting to system matrix varies with the used testing system.In probabilistic PSS design, two probabilistic sensitivity indices are applied for PSS location and initial parameter value determination. The PSS parameters are coordinated by using the nonlinear programming technique. The objective function is composed of the expectations and variances of all the dissatisfactory eigenvalues. The approach is tested on an eight-machine system. Results show that the PSS parameter can be further coordinated by using the nonlinear programming technique.