Inverse Power Model Of Crosslinked Polyethylene Insulation Electrical Life Accounting For Space Charge Effect

Inverse power model（IPM）,namely t=CE^-n,is often used as the phenomenological model to estimate the electrical life of cross-linked polyethylene（XLPE）cable insulation in engineering field to describe the relationship between applied voltage and insulation failure time.The voltage endurance coefficient n in IPM is also used as an important factor to select appropriate AC cable thickness and pre-evaluation test voltage.However,under the influence of DC electric field,space charge accumulation changes the internal electric field strength of XLPE.As a result,the actual electric field strength is quite different from the applied value.The existing IPM does not consider the influence of space charge effect on electrical life and the physical model of electrical life accounting for the space charge effect has complex structure and involves many parameters,which is apparently difficult to be effectively applied in solving engineering problems.In this paper,based on the electric field distortion caused by space charge accumulation,a model of XLPE insulation electrical life accounting for space charge effect is established.Firstly,the effect of space charge accumulation on the short-time breakdown characteristics of XLPE sheet samples under DC voltage is analyzed.Secondly,the effect of space charge characteristics on the E-t characteristic curves of XLPE insulation is studied,and a novel insulation electrical life model is proposed.Then,the functional relationship between the parameters of this model and the field strength distortion rate is examined,and the model parameters are obtained according to the space charge characteristics.Finally,the voltage endurance coefficient n of the real cable is obtained by using the proposed model and parameter calculation method,which proves the effectiveness of the model.The main conclusions are as follows:（1）The influence of space charge accumulation on the breakdown characteristics of XLPE sheet under DC conditions is investigated i.e.,the DC breakdown field strength of XLPE samples increases in the thickness range of 60-100μm,and decreases in the thickness range of 100-170μm.This phenomenon occurs because the trap characteristics of 60-100μm samples have weaker suppression ability to the space charge injection process than those of 100-170μm samples,and their internal electric field distortion is relatively higher.During the breakdown process,the distortion field strength decreases rapidly with the increase of thickness in the range of 60-100μm,and decreases slowly with the increase of thickness in the range of 100-170μm,and the reduction rate in distortion field strength shows the inflection point at the thickness of100μm.This behavior shows that the space charge effect replaces the volume effect and dominates the DC breakdown characteristics.（2）An improved inverse power model incorporting the space charge effect is developed and its rationality is validated.E_a-t curves and E_r-t curves of XLPE sheet samples with three thicknesses of 60,70 and 80μm are obtained by pulsed electro acoustic（PEA）method.The results show that the E_r-t curves of samples with different thicknesses can be linearly characterized by the same straight line in the double logarithmic coordinate system,and there are translational and rotational relationships between the E_r-t curves and the E_a-t curves of samples with different thicknesses.Based on this relationship,the translation factorαand rotation factorβare introduced into the IPM,and an improved IPM,namely t=C_r^αE_r^-βnr,is proposed.In this model,αandβquantitatively represent the influence of space charge effect on the translation and rotation between E_r-t curve and the E_a-t curve.（3）A method to calculate the IPM parameters of the sample is proposed based on the IPM parameters n₀,C₀ and space charge characteristics of the reference sample.Using the E_r-t curve parameters n_r,C_r and the correction coefficientsα_t,β_t,the IPM parameters n_t and C_t of the sample can be calculated by the proposed model.However,n_r and C_r are difficult to obtain in practical application.In order to solve this problem,a method is designed to calculate the factorsαandβof the sample by calculating the relationship between the applied field strength E_a and the field strength distortion rateη,which obtained from the space charge characteristic test results.The factorsα₀,β₀,α_t andβ_t of the reference sample and the sample to be tested are obtained by this method.The IPM parameters n₀ and C₀ of the reference sample are obtained by accelerated life test.According to the above parameters,the IPM parameters n_t and C_t of the sample to be tested are calculated by using the proposed model.This method does not need to calculate n_r and C_r.Compared with the IPM parameters measured by accelerated life test,the deviation of n_t and C_t calculated by the model is 7.11%and 2.67%respectively.（4）Using the proposed model and parameter calculation method,the IPM parameters of the real cable are obtained and its effectiveness is verified.The IPM parameters and space charge characteristics of the reference cable with 2.5 mm insulation thickness are measured.Based on the test results of the reference cable,the IPM parameters of the real cable with the same insulation structure and thickness of 3.5mm are calculated by using this model.The calculated results are compared with the IPM parameters measured by step stress accelerated life test.The deviation of parameter n and C is 8.81%and 5.30%respectively,which proves that the improved IPM is effective in the engineering application of real cables.