The current density in a material is generally given by

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1 1 Sidsel Trætteberg, 1 Erling Ildstad, 2 Rolf Hegerberg 1 Norwegian University of Science and Technology (NTNU), Trondheim, Norway. 2 Sintef Energiforskning AS, Trondheim, Norway The use of extruded polymers for high voltage DC applications has so far been restricted by the problems of predicting and controlling the effect(s) of space charge trapping in the insulation. Space charge originates either from impurities in the material, usually resulting in ionic conduction mechanisms and/or from charge injection at the electrodes. The resulting conduction processes control the field distribution and hence the maximum stress in the insulation. In cable applications, the local current causes a temperature gradient to be set up across the insulation. Since the mobility of the trapped charges as well as the injection mechanisms are temperature dependent, this temperature gradient significantly modifies the DC conduction and the electric field within the insulation. The present paper describes measurements of the DC conductivity of extruded XLPE as a function of field and temperature and the space charge distribution in samples of the same materials resulting from applying both an electric field and a temperature gradient. The current density in a material is generally given by Ex j = σe + ε r ε ( ) (1) dt where E is the electrical field, σ the conductivity, εr the materials permittivity and ε0 is the permittivity in vacuum. When applying a DC-voltage the capacitive current given by the latter term will initially dominate. In steady state the current will be determined by the conductivity, the number of free charges and their mobility. The morphology of polyethylene consist both of amorphous and crystalline parts. This makes it rather complicated to theoretically predict the conduction by physical modelling. Instead it is common to express the conductivity by the empirical equation σ = σ 0 exp( αt + βe) (2) where the coefficients,α and β, denote the temperature and the electric field dependence, respectively. σ 0 is the conductivity at low stress and reference temperature (0 C), and the temperature given in C. When low stress is applied the electric field coefficient, β, is normally much smaller than the temperature coefficient, α. It is therefore usually considered a good approximation to determine the temperature coefficient by using ln( σ) = Const + αt (3) In large insulation systems which likely contain particles and other irregularities space charge may accumulate at their interfaces. This occurs where there is a local change in the ratio between the permittivity, εr, and the conductivity σ. Space charge is thus also generated when there is a temperature gradient in the insulation as the conductivity is

2 much more temperature dependent than the permittivity. The insulation resistance and subsequently the electric field stress will become largest in the cold region. Another process is the formation of homo- and hetero charge at the electrodes. This occurs when there is an imbalance between the ability of the electrodes to supply charge and the ability of the insulation to remove the charge by conduction. If the supply of charge is slower than the conduction process a charge layer of opposite polarity, hetero charge, is formed near the electrode. Homo charges will be formed if the supply of charge from the electrodes are faster than the conduction. Poisson equation εε(x)=ρ(x), together with equation (2) can be used to express the density of space charge ρ( x) = ε 0 ε r αge( x) (4) where g is the temperature gradient dt/dx. [4] The electrical field can then be expressed by the one dimensional solution: Ex ( ) αguexp( αgx) = ( 1 exp( αgd) ) where U is the applied voltage, d is the thickness of the object and x the distance from the electrode. [6] (5) All measurements were done using test objects made of XLPE LE4250, crosslinkable polyethylene. A material used as insulation in commercial HVDC cable production.[2] The pellets received was first extruded and then Rogowski shaped test objects were made. The cups were pressure moulded at 115 C and vulcanized at 175 C. Afterwards they were annealed for 2-3 minutes at 130 C and degassed at 90 C in 3 days, as previously described in [3]. Two types of test objects were made: One type had an insulation thickness of 0.9 mm with semiconducting (LE0500) electrodes of 0.5 mm on both sides. The second objects had an insulation thickness of 0.4 mm equipped with vacuum evaporated aluminium electrodes on both sides. The experimental set up for DC current measurements is schematically shown in figure 1. Spellman SL 150 oven object guard R Keithley 617 electrometer

3 Before the current measurement, the test objects were equipped with a guard electrode, using an aluminium tape at the lower section of the samples. A DC voltage was applied to the test object and the resulting DC current was measured by a Keithly 617 electrometer. The test objects were placed in an oven where the temperature was raised in steps of 10 C from C. The voltage was kept constant and the conductivity as a function of temperature was measured. The stable current values were recorded after 3 to 12 hours of voltage application, depending upon the temperature. The electric field dependence was measured by keeping the temperature constant and raising the voltage in steps of 5 kv, from 5 kv to 20 kv. The experimental set up for space charge measurement are shown in figure 2.. Object The space charge measurements were performed using the Electro Acoustic Pulse Wave method (PEA) [1]. The measurements were performed with a temperature gradient across the object, and with the voltage applied during measurements. Copper coils for heating and cooling were attached to the electrodes.warm oil and cold tap water were circulated through the coils to achive suitable temperatures. Thermoelements were used to measure the temperatures. The gradient was found measuring the temperature of the grounded electrode close to the object, and the temperature of the warm oil flowing into the coils wound around the HV electrode. Separate measurements of the thermal conductivities have shown that the thermal conductivity of the

4 semiconductor is 2.15 times that of the XLPE insulation, thus 68% of the gradient will be across the XLPE insulation. Space charge measurements were done on test objects with kv applied, and a temperature gradient of about 21 C. igure 3 and 4 shows the measured DC-conductivity as a function of temperature and applied DC-stress, respectively. The temperature coefficient, α, was calculated to be 0.07 and 0,1 in case of Al-electrode and SC-electrode respectively. Ã> \ LW W LY X G Q R & Ω P 1.E-13 1.E-14 1.E-15 1.E-16 α=0.10 α= HPSHUDWXUH>&@ obj. with Al-electrode 12.5kV/mm obj. with sc-electrode 19kV/mm. Ã> \ LW W LY X G Q R Ω P 1.E-14 T=70 C T=50 C β= E (OHWULÃ)LHOGÃ>N9PP@ C and 70 C This indicates that the electrodes and their injection properties may strongly affect the resulting conductivity.the different thickness of the test objects may also play an impor-

5 tant role, resulting in larger electrode effects in case of the thinnest objects. rom the result presented in igure 4 the field coefficient, β, was found to be Comparing the results to similar measurements on LDPE results, presented in ref [7], showed higher (α=0.15 and β=0.09,) temperature and field dependencies. This indicate that the examined HVDC modified XLPE has a better conduction characteristic than LDPE. igure 5 shows the measured space charge distribution in two different objects, both energised E=-22,5 kv/mm.the full curve presents measured space charge distribution after 24 hours of voltage application at 25 C. The dotted curve shows similar results from a test at a temperature of T=38 C. No charge in space charge distribution was observed due to longer period of voltage application. The spacial resolution of the PEA equipment is limited to about +/-0.15 mm, which means that only the average space charge concentration will be measured for spacial resolutions smaller than this. The graphs presented clearly show that the effect of increasing the temperature by 13 C was to increase the amount of homo charge injected at the electrodes by a factor of 2.2.., 4 2 T=25 C T=38 C nc/mm anode 0.4 mm 0.8 cathode. igure 6 shows the time development of the measured space charge distribution of a test object exposed to a temperature gradient of 21 C and -25kV/mm across the XLPE insulation. The graphs show that space charge is gradually building up within the insulation. Compared to the results presented in figure 5 it is clearly demonstrated that a temperature gradient strongly affects the distribution of space charge within the insulation. The gradient leads to an increased amount of homo charge close to the warm cathode.

6 2 t=0h t=5h t=26h nc/mm anode cold side cathode warm side mm igure 6 igure 7 shows the electric field calculated from the measured space charge distribution.starting with E=-25 kv/mm the field stress at the cold anode was found to increase while the field at the cathode reduced due to the injected homocharge. This is in accordance with the theoretical predictions. At a distance of 0.2 mm away from the electrodes, the electric field stress was measured to be 3.4 times higher near the cold than the warm electrode T=0 t=0h T=21 t=5h T=21 r=26h kv/mm anode cold side cathode warm side mm igure 8 shows the maximum field of three objects starting with an average applied electric field stress of E=-22,5 kv/mm. The experimental results presented in figure 8a show to distinct features: i) In the examined temperature range from about 20 to 60 C stable electric field distribution were formed relatively quickly. At the highest temperatures 80% saturation was reached within less than 40 minutes. ii) It also shows that the effect of in-

7 creasing the temperature gradient by a factor of 2 was to double the maximum electric stress. Results presented in figure 8 show that the higher temperature also lead to a higher electric field under isothermal conditions, an effect which can be explained by homocharge formation at the electrodes, causing increased but homogeneous electric stress within the insulation. 70 P P 60 9 >N OG 50 LH Ã) L 40 WU OH 30 ( WLPHÃ>K@ DÃ:LWKÃWHPSHUDWXUHÃJUDGLHQW Tmax=47 C Tmax=57 C P70 T=25 C P 960 T=38 C Ã>N OG 50 LH Ã) 40 L WU 30 O H ( WLPHÃ>K@ E,VRWKHUPDOÃRQGLWLRQ Τ=21 Τ=31 0 Electric ield [kv/mm] Thickness [mm] T igure 9 shows a comparison between measured and calculated electric field distribution in case of a temperature gradient of 21 C. The dotted theoretical curve was calculated by inserting measured values of α and g into equation (5). The theoretical and measured values correspond quiet well. The difference could possibly be caused by the homo charge formation at the electrodes which were not included in the theoretical deduction. In addition the theoretical deduction was made using the assumption that the electric field dependence of the conductivity could be neglected. The results presented in figure 4 show that this is not valid. The effect of increasing the electric field stress from 20 to 50 kv/mm

8 is to increase the conductivity by a factor of 2.5. This increased conductivity in high stress regions will reduce the resulting stress near the cold electrode. Thus the theoretical deduction need to be modified. During isothermal condition homocharge will be found at the interface between XLPE and semiconducting electrodes. The amount of charge will increase with increasing temperature. The DC conductivity of the XLPE insulation increase with increasing temperature and electric stress. Thus in case of a temperature gradient space charge will be formed within the bulk of the insulation to establish an electric field distribution according to the variation of the DC resistance of the insulation. [1] Joseph Barry Bernstein,Electrical Characterization of Polymeric Insulation by Electrically Stimulated Acoustic Wave Measurement,Massachusettes Institute of Technology, 1990,l [2] J.O.Bostrom, A.Campus,R.N.Hampton, U.H.Nilsson, Evaluation of the material for polymeric direct current cables, Cigre , 2002 [3] Hallvard aremo,the EI Test Method- Wet Ageing of High Voltage Material, EI TR A4172, 1994 [4].H.Kreuger:Industrial High DC Voltage,Delft University Press, 1995 [5] Y.Li: Space Charge Measurement in lossy solid dielectric materials by pulsed electroacoustic method,ph.d-thesis, Musashi Inst. of Tech., 1994 [6] E.Ildstad,.Mauseth and G.Balog, Space charge and electric field distribution in current loaded polyethylene insulated HVDC cables, ISH-2003 [7] E.Ilstad and.oldervoll, DC current characteristics of polyethylene with and without antioxidant after thermal aging, NORD-IS 01, 2001