Analytical trajectory extrapolation for power systems

Trajectory extrapolation is important for stability analysis and control of modern power systems. Many functions such as security warning and time-delay compensation for wide-area feedback control can be developed through trajectory extrapolation. But as of now, there are no effective methods to extrapolate power system trajectories except for time-consuming numerical integration methods. The difficulties for trajectory extrapolation in power systems lie within the fact that the underlying dynamic equations are nonlinear, and thus analytical solutions are not possible. In this paper, a method is proposed to approximate the analytical solution of power system dynamics, by which trajectories can be extrapolated. First, the dynamic equations of power system are modified to an equivalent set of equations by polynomial projection technique. Based on the modified equations, an approximate analytical solution is obtained using algebraic Picard iteration without integration operation. This solution depends on the initial values and can be used for on-line trajectory extrapolation. Following a disturbance, with values at the instant of disturbance clearance known (i.e. through PMU - measurements), one can easily extrapolate the system trajectory by extending the approximate analytical solution and updating initial values. Finally, some simulation results are presented to show the effectiveness of the method.