A New Method of Making Transmission-Loss Formulas by Means of Eigenvalues and Modal Matrices

Eigenvalues and modal matrices are utilized for the first time in loss formula construction. The new method provides the following advantages: 1. Its biggest advantage is that it greatly reduces the number of B constants required for the loss formula; see Table I. It eliminates all off-diagonal terms. 2. The new method in its complete form gives both power and reactive losses. 3. The new method permits using actual reactive generation as well as actual power generation at each source, if desired and if the reactive information is available. If it is not available, reactive ratios may be taken from the base-case conditions, or any linear type of P/Q relation may be utilized. 4. A new method of taking account of known load ratios has been developed. It uses a simple addition matrix. 5. The new method eliminates the use of unsymmetrical square matrices with their resultant complications. 6. Although some recent computer methods compute "w prime" or "R sub LL," instead of the conventional practice of selecting an arbitrary value for it that will make the base case check perfectly, the new method of load fixation eliminates this alltoo-convenient means of making previous errors and approximations invisible. 7. It is possible to use either an admittance matrix of the transmission system or an impedance matrix. Both have the same eigenvectors, but the eigenvalues are individual reciprocals of each other. (The eigenvectors and eigenvalues are complex quanitities in some of the operations used here.