Based on Caputo-Fabrizio fractional calculus, the fractional order model of the frequency converter, the long cable and the electric submersible pump system is established. The model does not contain singular nuclei, unifies the physical dimension of the parameters of the fractional order capacitance and inductance and the integer order capacitance and inductance, and defines the comparison platform of the fractional and integer order model. This is more accurate than the traditional model to describe the transmission characteristics of long deep-sea cables. The effects of starting voltage frequency, cable length, cable resistance, cable inductance, cable capacitance parameters, load characteristic impedance and fractional order secondary factors on the starting of electric submersible pumps are studied. An abnormal influence of cable inductance parameters on cable voltage drop was found. The absolute value of the relative error of the calculated results of the fractional order model and the integer order model variation range is 0.10%~30.35%, especially when the cable length and the cable resistance parameters varied, the absolute value of relative error of the models shows a V-shaped piecewise phenomenon of first decreasing and then increasing. The compensation voltage of the step-up transformer should be one third higher than that of traditional designs. Considering the starting voltage drop based on a fractional order model, in practical application, the electric submersible variable frequency drive cable can break through the 40km distance limitation. This provides a theoretical basis for the design and safe and reliable operation of the power supply system of deep sea electric submersible pumps.