Voltage stability indices for stressed power systems

The use of static voltage stability indices based on a singular value decomposition of the power flow Jacobian matrix and matrices derived from the Jacobian matrix is discussed. It is shown that such indices, together with the singular vectors, contain substantial and important information about the proximity to voltage instability and also about critical buses and disturbances from a voltage instability point of view. This is done by a theoretical analysis of the linear power flow equations and an analysis from model power systems as well as realistic power systems (1033 nodes). It is argued that indices based on these matrices are useful for the system analyst in planning and operations planning     

Fast calculation of a voltage stability index

The minimum singular value of the power flow Jacobian matrix has been used as a static voltage stability index, indicating the distance between the studied operating point and the steady-state voltage stability limit. A fast method to calculate the minimum singular value and the corresponding (left and right) singular vectors is presented. The main advantages of the algorithm are the small amount of computation time needed, and that it only requires information available from an ordinary program for power flow calculations. The proposed method fully utilizes the sparsity of the power flow Jacobian matrix and the memory requirements for the computation are low. These advantages are preserved when applied to various submatrices of the Jacobian matrix. The algorithm was applied to small test systems and to a large system with over 1000 nodes, with satisfactory results     

Plastics for focusing collectors

The use of plastics in fabrication of reflectors for focusing collectors offers possibilities for reduction of material and fabrication costs. Fiber-glass-rein-forced polyesters, cellulose acetate butyrate, and polystyrene have been considered for reflector shell fabrication, and vacuum-metallized films for reflecting surfaces. Polystyrene shells with aluminized Mylar reflective lining have been the most promising of the materials considered. Flexible laminates of aluminized Mylar to vinyl or vinyl-cloth combinations are considered for flexible reflectors. Application of plastic reflectors to solar cookers is noted.