Modeling of out-of-step conditions in power systems

Out-of-step protective relays are employed for detecting out-of-step conditions in power systems. The relay parameter setting requires simulations of expected out-of-step conditions. Here, the out-of-step conditions are modeled as a periodic motion, and are represented analytically by the Fourier series. The Fourier coefficients are computed using numerical iterations. A two-level iteration process is developed to obtain periodic bus-voltage dynamics. The computed bus voltages are then used to derive and to plot apparent impedance and line power loci needed for the out-of-step relay parameter setting. The proposed techniques are illustrated using an example of the National Power Company of Ukraine.