| With the increase of electricity demand and the development of relevent science and technology, power system has come into the period called modern power system, which is characterized by power grid interconnection, large generation unit, distant ultra-high voltage AC and DC transmission, highly automated control and market operations. Since the 70s of the 20th century, a series of grid collapse accidents have occurred which are characterized by voltage collapse in large power grid of the world, leading to blackouts, which promote the power system voltage stability studies to become a growing concern of the research issue.By summarizing the existing voltage stability on the definition and classification and associating with practical voltage instability incidents, the paper demonstrates that understanding voltage stability from the perspectives of time continuity and disturbance sizes has a more reasonable explanation. Five methods on Static voltage stability used most commonly are listed, including the mathematical model of each method and their applications. Power system elements from generation, transmission network to the power load are mathematical modeled in the thesis, paying more attention to the analysis about load characteristics on power system voltage stability and the theoretical method of load modeling.A detailed analysis on the application of the modal analysis method used in static voltage stability study is made. The paper points out the shortcomings of traditional VQ (reactive power-voltage) modal analysis method and full voltage modal analysis method based on two sorts of Jacobian matrix which are reactive power-voltage Jacobian matrix and active power angle Jacobian matrix.Since the impact of the changes in active to power voltage amplitude instability can not be ignored when the power system operating at the critical point, the improvement to the existing V-Q (reactive power and voltage) mode analysis method is proposed. Basing on The traditional power flow calculation platform and IEEE10-machine 39-bus standard test system as the simulation model, using the V-Q (reactive power and voltage) mode analysis method,the paper calculates system Jacobian matrix eigenvalues, eigenvectors, participation factors, the overall system stability and the local system stability, as power system operating in the static and critical condition. The system eigenvalues are derived separately based on constant power load model and ZIP load model, the conclusion is:the system using the ZIP load model has a higher stability margin than that using constant power load model. Using the improved modal analysis method which take account into the impact of active power changing, through comparing the eigenvalues of modified Jacobian matrix calculated in the static and critical operating conditions, the conclusion derived as follows:the changing of active power has little effect when power system running in the static condition or the margin of the system is large, however, the changing of active power has great effect to that when power system running in the critical instability condition or the margin of the system is small. This has a certain value to power system static security analysis and voltage stability mechanism study, both of which are characterized of determining the power system stability margin.In order to make eigenvalues of the system Jacobian matrix be more intuitive characterization of power system stability, the paper finds a further processing method for the eigenvalues of Jacobian matrix, namely:according to the concepts of expectation and variance in the probability theory and mathematical statistics, the paper designs two system parameters, they are overall system stability degree and system local stability degree. In addition, in vertifying that nodes operating in the critical unstable state, the article uses the e-index-based variable step continuous flow method to draw PV curves. Taking into account that modal analysis can give more complete information on the voltage stability mechanism, the thesis gets a thought that the modal analysis can be a useful adjunct for power system static security analysis.
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