A Perturbation Analysis of Harmonic Generation from Saturated Elements in Power Systems

作者：Kumano Teruhisa^*

来源：Electrical Engineering in Japan, 2010, 170(4): 35-42.

DOI：10.1002/eej.20895

• saturation
• steady state
• harmonics
• perturbation series

Nonlinear phenomena such as saturation of magnetic flux have considerable effects in power systems analysis. It is reported that a failure in a real 500-kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer it-on core. Time simulation is widely used today to analyze phenomena of this type, but it has basically two shortcomings. One is that the time simulation takes too much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedures such as N-R (Newton-Raphson) must be used and such methods tend to be caught in an ill-conditioned numerical hunting. The other is that such simulation methods sometimes do not aid an intuitive understanding of the studied phenomenon because all of the nonlinear equations are treated in matrix form and are not properly divided into understandable parts, as is done in linear systems.
This paper proposes a new computation scheme that is based on the so-called perturbation method. Magnetic saturation of iron cores in a generator and a transformer are taken into account. The proposed method has a special feature to deal with the first shortcoming of the N-R-based time simulation method stated above. The proposed method does not use an iterative process to reduce the equation residue, but uses perturbation series, so that it is free of the ill-conditioning problem. The user need only calculate the perturbation terms one by one until the necessary accuracy is attained.
In a numerical example treated in the present paper, first-order perturbation can achieve reasonably high accuracy, which means very fast computing time. In a numerical study, three nonlinear elements are considered. The calculation results are almost identical to the conventional N-R-based time simulation, which shows the validity of the method. The proposed method can be effectively used in screening where many case studies are needed.

• 出版日期2010-3