Due to the continuous increasing of operating frequency in the power system and the transmission speed, under the high frequencies of the transmission line calculation and simulation process, it is necessary to consider the frequency-dependent properties. At present, the frequency-dependent transmission line modeling has a variety of methods, but in the modeling and calculation of frequency variable term, processing is relatively complicated. This article will introduce transmission line equation of fractional calculus, intuitive representation of frequency varying parameters, and by a time-domain fractional solution, simplify the operation, improve the computational efficiency. Application of this algorithm for fractional differential equations can be obtained the voltage and current responses at any point in the transmission line. Thesis also by comparison with actual example, confirmed the validity and feasibility of the algorithm. At the same time, proposed algorithm can be extended to the multiple conductor transmission lines of fractional order model, also has certain applicability.

A simple fractional order nonlinear supercapacitors (SCs) electrical model has been established, taking into account the parameter variation, diffusion control and Faraday process. Frequency responses resulting from impedance spectroscopies around various operating voltages demonstrated that a SC exhibits a nonlinear behaviour in relation to the operating voltage. The model parameters are identified using fractional vector fitting and then a nonlinear model taking voltage dependency into account is obtained. Through building fractional order differential operator module in Simulink, the numerical solution of fractional order nonlinear calculus equation can be obtained directly. The model accuracy is verified through a comparison with the charging and discharing experimental results.

This paper presents a new digital potential transformer (PT) model. Due to the effect of hysteresis and saturation phenomenon, the magnetization curve of iron core has a strong nonlinear. From the perspective of hysteresis effect of iron core, this article presents a PT core model using the theory of fractional calculus, then propose a new PT circuit model. The model simulates the nonlinear part of iron core using the fractional order expressions and can reflect the feature of saturation. Finally it shows the correctness and validity of the model through the theoretical analysis and simulation results.

Very fast transient overvoltage (VFTO) is very dangerous for the transformer which is directly connected to gas insulated substations (GIS). At the same time, due to the continuous increasing of operating frequency in the power system, under the high frequencies of the transmission line calculation and simulation process, it is necessary to consider the frequency-dependent properties of the parameter. In order to study the voltage distribution in transformer windings under VFTO, a new Lumped parameter model which takes into account the fractional characteristics is proposed, named fractional lumped parameter model (FLP). The model divides each turn of transformer windings into proper sections, whose parameters are all lumped parameters. Finally it shows the correctness and validity of the model through the comparation of the experiment datas and simulation results.

Fractional calculus theory has gained more and more applications in numerous fields. In many cases, using fractional reactance element model can describe the properties of objects more accurately and simply. This paper studies the sensitivity of networks with fractional order reactance, puts forward the adjoint network sensitivity formulas and the incremental network models of fractional order capacitor and inductor, which will further develop the adjoint network and Incremental network theory. The simulation verification is also given.