运用Maxwell模型对植物油纸绝缘系统老化状态的研究

Research on Aging State of Vegetable Oil-paper Insulation System Based on Maxwell Model

植物绝缘油被广泛运用于油浸式变压器,研究植物油变压器油纸绝缘系统的老化状态至关重要.本文引入分数微积分的概念,建立了分数阶Maxwell介电模型参数辨识的数学模型,同时根据实验得到的复介电常数实虚部的值求得分数Maxwell模型中的各个参数,根据最小二乘法建立目标函数,采用粒子群算法实现参数辨识,得到了不同老化状态下油纸试品的Maxwell模型参数,并利用混合蛙跳算法对其进行验证.得到模型特征参数后,根据模型重构得到的数据,进而研究了绝缘老化对分数Maxwell介电模型参数影响的规律.研究表明:随着老化程度的加深而增大的介电常数ε与聚合度D_p有着较好的线性关系,弛豫时间τ与D_p间有着较好的指函数关系.提出的分数阶Maxwell模型参数可用于量化评估油纸绝缘的老化状态.

As vegetable insulating oil is widely adopted in the oil-immersed transformers,it is more important to study the aging state of the oil-paper insulation in the vegetable-oil transformers.The concept of fractional calculus is introduced and a mathematical model for the parameter identification of the fractional Maxwell dielectric model is established in this paper.At the same time,according to the value of the real and imaginary parts of the complex permittivity obtained from the experiment,each parameter in the Maxwell model is calculated.Moreover,the objective function is established according to the least square method and the particle swarm optimization(PSO)is employed to realize the parameter identification.The parameters of the Maxwell model for the oil paper samples under the different aging conditions are obtained,and the algorithm of Shufled Frog Leaping is used to verify the performance.After obtaining the characteristic parameters of the model,the influence of insulation aging on the parameters of the fractional Maxwell dielectric model is further studied according to the data obtained from the model reconstruction.The studies show that the dielectric constantεis increased while the aging state is deepened.Meanwhile,it has a better linear relationship with degree of polymerization(D_p),and there is a better relationship of the exponential function between the relaxation time and D_p.The proposed fractional Maxwell model parameters can be applied to quantitatively evaluate the aging state of oil-paper insulation.