Error Analysis Of The Dynamic Order Reduction Approach For Specific Mode In Large-Scale Systems

In small signal stability analysis of power system, QR method is one of the effective full-dimensional eigenvalue methods for its good numerical stability and fast convergence. With the growing size of network, system dimension increased dramatically as "disaster of dimensionality."The eigenvalue and eigenvectors has been concerned more in the original order-reduction method, so its accuracy can be ensured. Eigenvalue sensitivity is also an important indicator In application and often used in site selection and parameter adjustment of the damping controller and so on. To extend the application of reduced-order model further, eigenvalue sensitivity should be investigated. Despite the intuitive view that the more the retained number of motor is, the smaller the reduction error is, but a quantitative analysis is still need.In this paper the Plug-in Modeling Technique (PMT) was used to form the network state equations by transforming all components and the network into two basic transmission modules. As the PMT has very good scalability and flexibility, the system state space equation and state matrix can be gained easily and flexibly through small changes when the components and parameters in power system have any change.To further examine the availability of the order reduction for specific model order, error analysis is extended to eigenvalue sensitivity in the large-scale power system dynamic reduction method. PMT and the QR method have been used to calculate all of the eigenvalues before order reduction, while eigenvalue sensitivities to the gain on the part of the PSS are obtained as the foundation for comparison. On the basic of the order-reduced mode, the analytical expression of eigenvalue sensitivities for reduced-order system is determined with eigenvectors. As the order reduction makes the eigenvalue sensitivity expressions complicated, complex equations caused by the complex eigenvalue are transformed to the real form to reduce the computational error. Computation for eigenvalue sensitivities in reduced-order system is achieved by using the derived equations. The computational sensitivity error caused by order reduction is analyzed by comparing with those obtained from the original system. Error introduced by order reduction is indentified as the reference for the selection of the size reduction.In the Visual Fortran 6.5 compiling environment a 23-machine system is checked, two less stable electromechanical modes were analyzed. In this case with 257 classes, six-order model is adopted on all of the generators equipped with EXC and GOV and zero-gain power system stabilizer (PSS) is installed in each generator. Under different degrees of reduced order mode, a certain law is present between the sensitivity, that is, the more the generator retained in the reduction, the smaller the calculation error of eigenvalue sensitivity. The error is about 10-2～10-3. Compared with other reduction methods, since a single oscillation mode is established for one electromechanical mode, the error of models should not be greater than error of others. So the main error of this paper is the cumulative error in calculation.