深海油田电潜泵长距离变频驱动系统分数阶建模及起动电压降分析

Research on fractional order modeling and starting voltage drop of long distance electric submersible pump frequency drive systems in a deep sea oil field

基于Caputo-Fabrizio分数阶微积分建立了变频器—长电缆—电潜泵系统分数阶模型,该模型不含奇异核,统一了分数阶电容电感参数与整数阶的物理量纲,厘定了分数阶模型与整数阶模型计算对比平台,比传统模型能更加准确地描述深海长电缆电力传输特性。研究了起动电压频率、电缆长度、电缆分布电阻、电缆分布电感、电缆分布电容参数、负载特性阻抗和分数阶阶次等因素对电潜泵起动的影响。发现了电缆分布电感参数对电缆电压降的反常影响。分数阶模型与整数阶模型的计算结果相对偏差绝对值变化范围是0.10%～30.35%。值得注意的是,当电缆长度和电缆分布电阻参数变化时,模型的相对偏差呈先减后增的V形分段。升压变压器补偿电压需要比传统设计的高三分之一。基于分数阶模型计算结果,认为在实际应用时电潜泵变频驱动电缆距离可以超过40 km。

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.