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    REMAINING LIFE ESTIMATION ON 6.6 kV RATED XLPE CABLES Sheng Haifang and S.Birlasekaran School of Electrical & Electronic Engineering  Nanyang Technological University, Singapore 639798 Abstract Aging model of service aged XLPE cables is built by accelerated aging test. Part of XLPE cable laid in 1993 was removed from distribution network in 2000. They were further aged in the laboratory for about 8000 hours at an elevated temperature. Four identical samples were taken and they were aged separately at 60 ° C, 80 ° C, 100 ° C and 120 ° C respectively in separate ovens. Periodic depolarization,  polarization and harmonic current analysis and dielectrometry studies were carried out to extract aging indicators. In this paper, we present the analysis on depolarization current measurement using the  parameters derived with extended Debye model. Variation of parameters as aging indicators is estimated and a life model is built. Thermal endurance graph, temperature index, thermal endurance  profile and halving interval as described in IEC 216 are determined by the relevant aging markers. The model is verified for prediction by taking the readings on similar cable samples removed from service in 2000 but laid in 1997 and 1999 respectively. Key words: Aging test, XLPE cable, Debye theory, Temperature index  1. INTRODUTION The aging problems on cable like water and electrical tree formation and thermal oxidation processes leading to cavities etc. are influenced by electrical, thermal, mechanical and morphological properties. Aging tendency should be diagnosed to determine the remaining service life of a power cable using the Non-destructive methods. Many studies were done to understand the degradation mechanism and a summary is given in Table 1 of reference [1]. We identified aging factors and developed life models to predict the remaining life. This paper presents the results of identified aging markers based on measurements on 3.3kV/6.6kV rated XLPE cables used by Power Grid, Singapore. 2. THERMAL ENDURANCE PROPERTIES IEC methods [2-4] to determine and express the thermal endurance of electrical insulating materials reveal a clear trend of degradation related to operating temperature. Destructive Test methods [4] have been developed which enable the validity of the underlying physical model to be verified. A complete test program for materials produces the temperature index (TI)  which is one-point characteristic. TI is the operating temperature in degree Celsius to get a certain (normally 20,000) hours of thermal endurance period. The one-point evaluation does not permit a complete description of a material’s thermal endurance behaviour. A composite index called the thermal endurance profile (TEP)  is defined. It is known as the thermal endurance graph (Arrhenius graph) shown in Figure 1 in which the logarithm of time (t) needed to reach a specified end- point in a thermal endurance test is plotted versus the reciprocal of operating absolute temperature (T). The slope of the thermal endurance graph is now explicitly given by means of the easily comprehensible halving interval (  HIC  ).  HIC   is defined as the number corresponding to the temperature interval in degrees Celsius which expressed the halving of the time to end- point taken at the temperature of the TI. Figure 1. Thermal Endurance Graph  3. MEASUREMENT SYSTEM FOR AGING STUDIES A computer controlled on-line measurement system was developed with GPIB-controlled instruments and Labview software [5,6]. For the reported study on depolarization current measurement, the initial charging voltage was kept at 500 Vdc to get good signal to noise ratio. 3.1 Cable Samples The cross section of the tested distribution cable samples supplied by Power Grid, Singapore is shown in Figure 2. The year of manufacturing was 1993 and it was removed from continuous service from the 6.6 kV distribution in March 2000. The cable sample was cut into four pieces of 65mm in length to study the aging behavior at different thermal loading. Figure 2. The cross section of the cable specimen 3.2 Aging Studies For the accelerated thermal aging, four laboratory ovens of cubical size with length of 0.6m were used to heat the four cable samples. They were heated at constant 60 ° C, 80 ° C, 100 ° C and 120 ° C continuously to study the aging  behavior of cables with thermal loading. It was planned to study the behavior up to 8000 hours continuously. All the four aging cable samples were tested periodically using the depolarization current measurement and other condition monitoring methods. The response was  processed by signal processing techniques to extract characterizing parameters. 4. EXPERIMENTAL RESULTS 3D plots of the depolarization current variation of cables aged at 60 ° C, 80 ° C and 120 ° C from 0 hours to 5000 hours of aging time are shown in Figures 3 to 5 respectively with the characteristics of “ Year 97” and “Year 99” cables. “Year 97” cable was in service (field aged) for 3 years. It was removed from service in 2000 and was kept in the laboratory at 25 ° C until tested. “Year 99” cable was manufactured in 1999 and it was in service for one year only. Figure 3. Variation of depolarization current with measurement time and aging time at 60 ° C Figure 4. Variation of depolarization current with measurement time and aging time at 80 ° C Figure 5. Variation of depolarization current with measurement time and aging time at 120 ° C  Before aging the cables in oven, the measured depolarization current was 25nA at t m =0 and 0.1nA at t m =1800 s as shown in Figure 3 to Figure 5. The slope of its characteristics was 0.014 nA/s at t m =0. After aging the cables for 8000 hours, the measured depolarization current decreased to 4.2 nA at 60 ° C of aging with the rate of change of its characteristics as 0.0023 nA/s when t m =0. While at 120 ° C of aging, the measured current was 3.4 nA with a slope of 0.0019 nA/s. The initial depolarization current and the rate of current change with measuring time were decreasing with aging for all the cases. 5. EXTENDED DEBYE MODEL Figure 6. Extended Debye model with n relaxation elements By Extended Debye theory [7], any dielectric depolarization current may be viewed as a sum of leakage ionic current (Rg), geometrical capacitive current (Cg) and various absorption currents (Rpn and Cpn). It is well known that Cpn and Rpn determine the aging trend. The relaxation parameters can be identified  by fitting the experimental results to this model. One can select the number of elements (n) from 1 to 11 or more to fit the current measurements using equation (1). Since it is a virtual short-circuited depolarization current measurement, the effects of Cg and Rg can be neglected. UnCp Rpt  Rp I  ni nnn ⋅⋅−=  ∑ = 1 ))exp(1(  (1) Figure 7. Error variation with Debye fitted order, n= 1,3,5,7,9 and 11 Figure 7 shows the variation of sum of error value  between measurement and fitting with n – RC elements. The error decreases monotonically with n. 6. ANALYSIS TO THE EXPERIMENTAL RESULTS From Figure 7, it can be understood that a reasonable fit can be made by taking 3 RC elements or 6 parameters. A typical fitting on   the measured depolarization current after 3000 hours under 80 ° C is shown in Figure 8 with the fitted parameters and the typical 3 peak Q occurrence times (5,6). In all the cases, as the iteration time is increased, the error decreased. Figure 8. Depolarization current response fitted by Debye Model (Aged 3000 hours under 80 ° C) Fitting was done on all the measured responses of four cable specimens aged for 5000 hours under 60 ° C, 80 ° C, 100 ° C and 120 ° C. Table 1 shows the fitted parameters on the sample aged at 80 ° C under different periods. Table 1: Fitted RC- parameters of Debye model from the measured depolarization current response at 80 ° C  Aging time 0 hours 1000 hours 2000 hours 3000 hours 4000 hours 5000 hours Cp1(F) 14e-10 8.1e-10 4.9e-10 3.9e-10 2.5e-10 2.6e-10 Rp1( Ω ) 1.8e9 2.6e9 3.5e9 6.1e9 5.3e9 5.6e9 Cp2(F) 28e-10 20e-10 13e-10 9.0e-10 3.6e-10 3.0e-10 Rp2( Ω ) 0.75e9 1.2e10 1.2e10 4.3e10 2.9e10 4.5e10 Cp3(F) 220e-10 150e-10 100e-10 19e-10 14e-10 8.4e-10 Rp3( Ω ) 1.0e11 1.5e11 2.7e11 5.7e11 5.3e11 5.3e11 It can be seen that the parameters vary with the aging  period and it is planned to evaluate the thermal endurance properties and the remaining life estimation using the trend of variation. In Figure 9, the variation of the fitted parameters with aging time is plotted. Smoothing of the data is done by second order  polynomial curve fitting and the new results are tabulated in Table 2. Rp1, Rp2 and Rp3 increased linearly with aging time. Cp1, Cp2 and Cp3 decreased with aging time to some power law.   Figure 9. Variation of parameters at 80 ° C with and without smoothing Table 2: Evaluated parameters at 80 ° C after smoothing  Aging time 0 hours 1000 hours 2000 hours 3000 hours 4000 hours 5000 hours Cp1(F) 14e10 8.7e-10 5.3e-10 3.2e-10 2.3e-10 2.8e-10 Rp1( Ω ) 1.5e9 3.0e9 4.2e9 5.1e9 5.6e9 5.8e9 Cp2(F) 28e-10 20e-10 13e-10 8.1e-10 4.6e-10 2.6e-10 Rp2( Ω ) 0.56e10 1.3e10 2.1e10 2.8e10 3.6e10 4.4e10 Cp3(F) 230e-10 150e-10 83e-10 39e-10 13e-10 5.0e-10 Rp3( Ω ) 0.63e11 2.0e11 3.1e11 4.1e11 4.9e11 5.5e11 Similar analysis is done at all the temperatures of aging and the smoothed data is plotted in Figure 10. Figure 10. Variation of Debye parameters at 60 ° C, 80 ° C, 100 ° C and 120 ° C The variation of these parameters is fitted to mathematical functions. In Figure 11, the variation of Rp2 at 60 ° C, 80 ° C, 100 ° C and 120 ° C with aging time up to 5000 hours is shown as solid lines. Figure 11. Variation of parameter Rp2 with aging time Variation of Rp2 with respect to aging time (t) and operating temperature (T) can be described by Equation 2. At 60 ° C, 1121 060 _ 2  ct bt a Rp  ++=  At 80 ° C, 2222 080 _ 2  ct bt a Rp  ++=  At 100 ° C, 3323 100 _ 2  ct bt a Rp  ++=  (2) At 120 ° C, 4424 120 _ 2  ct bt a Rp  ++=  In the equation (2), a i  is related with aging temperature (T). )()()()(2 2 T C t T  Bt T  AT  Rp  ++=  (3) )( T  A , )( T  B  and )( T C  are all second order  polynomials which are the function of temperature T. In Figure 11, the dashed lines show the fitted results using equation (3) to fit the variation of Rp2 with aging time at operating temperatures of 60 ° C, 80 ° C, 100 ° C and 120 ° C. Figure 12 shows the variation of all the 6 parameters after such analysis. An error analysis is made to evaluate the fitted result with actual measurements. Table 3 lists the summed error as given by equation (4) at various T. ( %100 ×− ∑ o fit o  I  I  I  ) (4) A maximum deviation of 9.3% is obtained. Hence equation (3) describes the life model of cable insulation deterioration. In Figure 12, it can be seen that the variation of Cp3 is not significant. The variation of Rp1 with aging time at various T’s is not sequential. Hence the remaining 4 parameters are taken into account for analysis.
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