| The linearized model of a synchronous generator, known in the literature as the "Heffron-Phillips" model, is extended to apply to a general power system with an arbitrary number of generators, and which takes into account network resistances. In this model a group of constants, called the "M" coefficients are developed which relate the torque, E(,q)(''), and terminal voltage of each machine to the rotor angles and E(,q)('')'s of the various machines. In this investigation these constants are used to determine and analyze the coherency of synchronous generators.;The "Ml" coefficients, a subset of the "M" coefficients, are contained in the inertial matrix. These coefficients are used to develop a technique for establishing inertial coherency that does not require time solutions or eigenvectors. It determines the tendency of coherent machines to "swing together" with a minimum amount of computation.;Dynamic equivalents, formed when two generators are inertially coherent but with exciter modes and mode shapes that show no indication of coherency, are dealt with. A method of eliminating the proper exciter mode for the formation of an exciter equivalent is developed using the constraints of coherency. This provided a criterion by which other methods of exciter reduction can be judged. This modal reduction technique is advantageously incorporated into the more conventional exciter reduction method.;The techniques developed in this research are applied to a 4-machine test system. The "M" coefficients and "A" matrices are calculated for a number of different cases. Inertial coherency is established and the improved method of exciter reduction is shown to be effective.;Using the "M" coefficients and generator parameters the system "A" matrix is formed. The coupling between the system inertial frequencies and the exciter frequencies is investigated using modal analysis. By partitioning the "A" matrix, two subsets, called the inertial matrix and the exciter matrix, are formed. The modal frequencies obtained from the partitioned matrices compare quite favorably with those obtained from the complete "A" matrix. This suggests decoupling the system's inertial and exciter frequencies into independent groups. |
