An Investigation on the Performance of Approximate Methods in the Representation of Stressed Power Systems


1 Department of Electrical Engineering,Ferdowsi University of Mashhad

2 Department of Electrical Engineering,Iran University of Science and Technology

3 Biochemical and Bioenvironmental Research Center,Iran University of Science and Technology

4 Department of Electrical Engineering,University of Illinois at Urbana-Champaign


Abstract. Heavily loaded stressed power systems exhibit complex nonlinear dynamic behavior, which
cannot be analyzed and described accurately by conventional linear methods, such as eigen-analysis. A
normal form of the vector elds theory, a well established mathematical method and the Modal Series
technique (a relatively newly established approach) have been used as tools to analyze, characterize and
quantify some of the stressed power system's sophisticated nonlinear behavior such as low frequency interarea
oscillations. The normal form method has been used extensively in recent years for the analysis
of nonlinear modal interaction and the role of this interaction in causing inter-area oscillations after the
occurrence of large disturbances. However, the normal form has some shortcomings, which must be further
highlighted. In this paper, some of these shortcomings are addressed by the use of simple examples. Linear
modal, normal form and Modal Series methods are used to simulate a two-area, 4-machine power system
test case and the results are compared with its accurate nonlinear simulation to asses the performance and
accuracy of these three methods. It is shown that: 1) Normal form techniques cannot simulate stressed
power systems well in some regions of its operating space, 2) In some regions of state space, even a
linear modal method provides more accurate results than a normal form, and 3) Modal Series' results are
consistently the most accurate of the three.