Application of normal forms of vector fields to stressed power systems

Approximations to nonlinear system performance are useful in analysis of power-system dynamic response to small or large disturbances. Linear analysis provides a modal picture that describes the system\u27s natural response to a disturbance (small or large). Applications, such as modal analysis and energy methods, have taken advantage of linear system approximations. This work investigates the significance of including higher-order terms in the series expansion of the power system\u27s differential equations to the modal behavior of a large, stressed system\u27s transient response. Normal forms of vector fields are used to simplify the system dynamics and to derive an approximate solution to the second-order system in closed form. Interactions of the natural modes of oscillation within the system can be quantified in terms of the solutions for the original-system states. Second-order analysis indicates that many more frequencies of oscillation may have significant influence on the system response. These additional frequencies result from second-order interactions of the linear modes and can not be studied using linear analysis. A methodology based on the normal-form method is developed and utilized to describe the stressed, nonlinear system response by extending linear concepts such as modal dominance and mode-state participation. The relationship between system stress and nonlinearity of the system equations is investigated;The results show that second-order information may be essential to understanding the modal behavior in an interarea-type system separation, whereas linear information may be sufficient for disturbances affecting single plants. Data from the 50-generator IEEE test system is used in this investigation. The contribution of this work is that it includes second-order effects on system performance in a form similar to the linear concept of modal oscillations. In addition, this application of normal forms indicates that higher-order applications may yield additional useful information. Thus, in stressed system conditions where system behavior is not explained using linear analysis, the existing linear methods of control design and placement can be adapted to account for second-order effects. In this manner, the range of usefulness of the existing methods has been extended