Research On The Fractional Order Model Of The Winding Of The Oil Immersed Transformer Equipment

With the rapid development of our country's power industry, Gas insulated substation(GIS) has been widely used because of its small size, compact structure, convenient operation and maintenance. But the opening or closing operation in the substation lightning invasion may cause Very Fast Transient Overvoltage(VFTO) which wave front is very steep, very high frequency on the transformer winding. This may cause insulation aging and even breakdown of the transformer windings.Therefore, it is very important to establish the wide frequency model of transformer winding to analyze the influence of extra fast transient overvoltage on transformer.In this paper, author do the research of black box broadband modeling method based on the theory of fractional calculus.Firstly, Tmultiple fractional order transfer function expression is derived from the multiple fractional order state equation, the fitting method of fractional order rational fraction is proposed by using the basic principle of vector matching method and the validity of the proposed method is verified by numerical examples. Secondly, In order to realize the network synthesis of fractional order transfer function, some theorems and methods about the transformation of fractional order transfer function to the minimum state space are summarized, and a general method for the transformation of the multiple fractional transfer function into the state space equations is derived. The circuit model is realized based on the fractional order state space equations. Finally, as a practical application, the scattering parameters of oil immersed transformer winding model were experimented and thus calculate the cake voltage transfer function. And then fit the experimental data obtained using the fitting method of fractional transfer function to get the voltage transfer function of oil immersed transformer winding cake. By comparing with the integer order, it is found that the fractional order transfer function is more accurate than the integer order. The transfer function is transformed into state space form and integrated circuit model is introduced and the correctness of the model is verified by solving state space equations. This paper takes the transformer winding as an example to study, but the proposed method is also applicable to other types of transformer equipment.