Application of 2<sup>nd</sup> order matrix perturbation to compute power system inter-area oscillation modes considering uncertainties

Abstract

Inter-area oscillation modes could be changed with the parameters of large scale power system varying. Therefore, complex modal perturbation is proposed to make modal analysis of inter-area oscillations considering uncertainties in this paper. The 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order perturbation is applicable for the case of small modification of the parameter. However, if the parameter modification is fairly large, the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order perturbation should be used to evaluate the oscillation modes to obtain higher computing accuracy. Firstly, the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order and 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order perturbation of eigenvalues and eigenvectors are deduced, respectively. Then, modes analysis with the parameter modification is also investigated using the 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order perturbation and 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order perturbation, respectively. Finally, the simulated results of IEEE 16-machine, 68-bus study system demonstrate that 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order perturbation has much higher accuracy of modes calculation compared with 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order perturbation in the case of large modification of parameters.