| With the growth of interconnected power system, the power system is characterized by the conditions such as'heavily loaded, weakly connected, fast excitation, low damping'. Nowadays, the power system becomes a complex nonlinear system, in which the nonlinear interaction phenomenon, such as the interaction of the state variables and the modes, generally happens. These nonlinear interactions have become one of the most significant factors affecting the stability of system.The linear analysis methods, even the full model numerical simulation, are not able to explain the essence of some nonlinear singularity phenomenon, because those methods are difficult to consider the internal nonlinear structural dynamics. Currently, the Normal Form theory and the Modal Series method in vector fields are the basic tools to study the dynamic characteristic of nonlinear power systems. The 2nd-order analytical solutions of the former are widely applied to analyze the 2nd-order nonlinear characteristic of power system, while the later is a little less used. Moreover, the expressions of the 3rd-order analytical solutions based on Modal Series method are so complex that it is not convenient to implement it in programs. It is shown that the further higher order nonlinear analysis of power system and applications should be developed, and methods for convenient and reliable analysis should be found.The thesis studied the algorithms and software tool of power system small-signal analysis, including two aspects:1. Study on the higher-order modal analysis methodsBased on the theory of Normal Forms, the much simpler 3rd-order analytical solutions of power systems dynamical equation were deduced, and modal interaction indices, such as the 3rd-order nonlinear participation factors, the nonlinearity index and the nonlinear interaction index, were also defined. The validity of the solutions was proved through the simulations of three power system cases. The expression of oscillation analysis based on the 3rd-order analytical solutions is deduced, and used to analyze the mechanism of oscillation. The nonlinear interaction of 3-generator 9-bus system was analyzed by the 2nd- and 3rd-order analytical solutions based on Normal Form theory. It is shown that the higher-order modal interaction is so complicated that the effect of terms higher than 2nd-order should be considered in power system modal analysis.2. Development of the power system higher order analysis toolNowadays, the widely used power system simulation tools only give the small-signal stability analysis which is linear modal analysis, lacking the function of nonlinear modal analysis. In this thesis, the"power system higher order analysis tool"and its operation interface are developed using Matlab?. Both the Normal Form method and Modal Series method are implemented in this tool set. The numerical differentiation algorithm is used to obtain the higher order partial derivatives of the system state space equation. In order to compress the memory requirements and lower the dimension of the matrices, sparse technology is used in the development of the program. An interface class, which is programmed with Java, is developed to interchange data with PSASP. The input data supplied by PSASP include the system parameters, the power flow and transient stability data. The tool provides a mechanism to store these data, and present the results either in tables or in figures. This tool provides an interface, on which modal analysis, such as oscillation modes of power system, with the Normal Form method and the Modal Series method, can be conviently performed. |
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