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Stability may be defined as the capacity of a power system to remain in equilibrium under steady load conditions, and its ability to regain a state of equilibrium after a disturbance has taken place. The lack of stability first manifested itself in the cases of overloaded machines and high impedance tie lines. The transmission of large blocks of power over long distances has presented the problem in a new form. Attention was directed to this problem in a group of papers before the Institute at the Midwinter Convention of 1924. These papers gave a general discussion of the stability problem and pointed out the necessity of considering the limitations imposed not only by the line alone but by the transformers, rotating machines and load. Extensive and pertinent discussions followed which emphasized the importance of the limitations imposed on power transmission by stability conditions. The papers and discussions at the 1924 Midwinter Convention established a method for the determination of power limits under steady load conditions assuming fixed excitation. The limit so determined is due to the inherent characteristics of machines and does not take into account the possibility of changes in excitation due to the action of voltage regulators. The possibility of exceeding the “inherent stability limits” by the operation of the voltage regulators and exciters was pointed out. This condition of “artificial stability” was not at that time believed to be attainable. It was recognized that under the actual operating conditions on a transmission system instability would occur because of short circuits or other disturbances at a point considerably below the maximum static limit. Subsequently extensive studies of stability conditions were made to determine the feasibility and economics of a number of large transmission projects. These studies emphasized the necessity of determining the maximum permissible load under the most severe operating con- itions which obviously arise at the time of system disturbances, such as switching operations or flashovers with the attendant switching. Transmission stability has been the subject of a number of articles in the technical press and of papers before the Institute, the principal ones of which are listed in the bibliography. C. L. Fortescue's paper before the Seattle Convention in September 1925 serves as an introduction to the present paper, presenting in a qualitative manner results of recent investigations whereas this paper presents methods for the quantitative determination of system oscillations. During the early part of 1925 extensive stability tests including switching operations and single phase faults to ground were conducted on the system of the Pacific Gas and Electric Company. These tests will be described in a companion paper by Roy Wilkins. The present paper first deals with the principal elements entering into the stability problem, such as the action of generators and exciters during disturbances, effect of dissymmetry produced by single-phase short circuits, simplification of the load end network and methods for combining these various factors in the determination of the electromechanical oscillations of the system following major disturbances. Results of calculations by these methods are compared with the results of tests on the system of the Pacific Gas and Electric Company. The paper concludes with a discussion of various methods of improving stability.