Dynamical modeling and numerical analysis for fractional-order power capacitor system

An optimized fractional-order electric field model is proposed to deal with non-uniform electric field distribution in integer-order form of power capacitor design. Following fractional derivative theory, the model for chain type fractional-order circuit topology containing a 10 kV parallel power capacitor is established. Then the frequency domain conversion is performed by Adams-Bashford-Moulton (ABM) predictor-corrector algorithm, the model is simplified and the potential distribution characteristics of fractional-order power capacitor is analyzed by adjusting the parameters. The potential internal capacitance in fractional equivalent circuit can be obtained by taking the fractional order within 0.1-0.9 and the maximum error as 2 dB and 3 dB respectively. The simulation result demonstrates that the electric field inside the capacitor tends to distribute uniformly and the voltage phase value at each point gradually increases as the maximum Bode plot error is determined and the fractional order is heightened.