طراحی PSS مقاوم توسط تجزیه و تحلیل حساسیت مقادیر ویژه احتمالاتی

When a wide range of system operation is taken into account for power system dynamic studies, probabilistic eigenvalue analysis efficiently provides the statistical distributions of concerned eigenvalues. Under the assumption of normal distribution, each eigenvalue can be described by its expectation and variance. To enhance system damping under multi-operating conditions by power system stabilizers (PSSs), effects of PSSs on both eigenvalue expectation and variance should be investigated. In this paper, the conventional eigenvalue sensitivity analysis has been extended to probabilistic environment. Eigenvalue sensitivities for both expectation and variance are determined to form two types of probabilistic sensitivity indices (PSIs). Robust PSS locations are selected by one type of PSI, PSS parameters are tuned by the probabilistic sensitivity analysis using another type of PSI.

To improve system dynamic damping by PSSs, many indices and techniques have been proposed for PSS site selection and parameter optimization. A comparative study was presented in [1] and the most popular indices for PSS locations were identified as the residue method [2] and the damping torque analysis. Relationships among different indices were discussed under special conditions and the computation precision was also compared [1]. Modal analysis [3], damping torque approach [4] and the eigenvalue sensitivity analysis [3], [4] and [5] have been commonly employed for PSS design. A coordinated PSS design approach was presented based on the reduced characteristic equation [6], and the PSS parameters can be ‘directly’ calculated from the desired eigenvalue assignments. This kind of ‘direct’ approach was also employed in [7] and [8]. However, these indices or techniques [1], [2], [3], [4], [5], [6], [7] and [8] can be regarded as deterministic approaches with constant system parameters and a particular load level. If different operating conditions are considered, the same procedure has to be executed repeatedly and the computing time rapidly increases. Variations in parameters and system operating conditions can be treated by the probabilistic such that the algorithm complexity and computation requirement are independent of the selected sample number. The probabilistic approach was firstly used for power system dynamic studies in 1978 [9]. The probabilistic property of an eigenvalue was determined from the known statistical attributes of system parameters, such as the rotor angle and mechanical damping. Based on operating curves of nodal injections, multi-operating conditions of a power system were considered in [10]. With nodal voltages determined by stochastic load flow calculation, the probabilistic distribution of each eigenvalue was obtained from the probabilistic attributes of nodal voltages. Under normal distribution, the random property of an eigenvalue is described by its expectation and variance. Considering multi-operating conditions in this paper, the probabilistic approach is applied to robust PSS design. Taking account the statistical nature of eigenvalues, two types of extended probabilistic sensitivity indices are developed for PSS site selection and parameter adjustment respectively. Initial values of PSS gains and time constants are determined by probabilistic eigenvalue sensitivity analysis. All PSS parameters are tuned by using a PSI matrix.

The probabilistic approach has been applied to robust PSS design in this paper. Based on the probabilistic eigenvalue analysis, the distribution properties of eigenvalues are described by their expectations and variances, and conventional eigenvalue sensitivities have been extended to the expectation sensitivities and variance sensitivities. Two types of probabilistic sensitivity indices are developed to estimate the effectiveness of PSSs. PSIs S′α and S′ξ are used for selecting the robust PSS locations, whilst PSIs S*α and S*ξ are employed for PSS parameter adjustment. Initial values of PSS parameters are determined by PSI analysis from which the washout time constant can be fixed at an appropriate value and two lead/lag stages are applied. In the presented technique, both damping constant and damping ratio are considered, and the proposed approach is applied to the robust PSS design on a three-machine testing system.