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Sep 2, 2018 - are uniformly dispersed in CCTO/EPDM composites, and the ... Under DC voltage, a large amount of space charge is accumulated in .... for measuring DC volume conductivity of samples, and the thickness ..... Ye, X.; Han, B.; Huang, Q. Simulation of electrical field distribution of XLPE insulated HVDC cable.
materials Article

Study on Nonlinear Conductivity of CCTO/EPDM Rubber Composites Zhongyuan Li 1 , Hong Zhao 1 and Changhai Zhang 2, * 1

2

*

Key Laboratory of Engineering Dielectric and its Application, Ministry of Education, College of Electrical and Electronics Engineering, Harbin University of Science and Technology, Harbin 150040, China; [email protected] (Z.L.); [email protected] (H.Z.) College of Science, Harbin University of Science and Technology, Harbin 150040, China Correspondence: [email protected]; Tel.: +86-541-8639-1655

Received: 10 August 2018; Accepted: 28 August 2018; Published: 2 September 2018

 

Abstract: Researches of the theories and application of polymer composites with nonlinear conductivity are useful for dealing with the nonuniform electrical fields widely existing in the cable accessory insulation. In the present work, we fabricated CCTO (CaCu3 Ti4 O12 )/EPDM (Ethylene Propylene Diene Monomer) composites and investigated their breakdown strength, dielectric and nonlinear conductivity properties in detail; the microstructures of fillers and composites were characterized by scanning electron microscopy (SEM) and X-ray diffraction. CCTO particles are uniformly dispersed in CCTO/EPDM composites, and the composites showed nonlinear conductivity with electric field changes. When the CCTO particle content is low, the conductivity of CCTO/EPDM composites does not present obvious nonlinearity. However, when CCTO content exceeds 2 vol %, the conductivity experiences a nonlinear change with increasing electric field strength and the threshold field (Eth ) of nonlinear conductivity declines with the increase of CCTO contents. In addition, it can be found from experiment and simulation results that 8 vol % CCTO/EPDM exhibit significant nonlinear conductivity and dielectric properties as expected, and homogenizing the electrical field much more effectively. Therefore, this paper offers a preliminary discussion about the variation trend of nonlinear conductivity CCTO/EDPM composites, providing an effective reference to solve the application of nonlinear conductivity materials for cable accessories. Keywords: copper calcium titanate; nonlinear conduction; electric field simulation; breakdown

1. Introduction High voltage direct current (HVDC) transmission has many advantages such as low loss, large transmission capacity, high operational stability, low environmental effect, cost-effectiveness, and so on. With major breakthroughs in converter technology, its development has received widespread attention [1]. ABB (Asea Brown Boveri) announced the new 525 kV direct current (DC) cable system with a power rating range up to powers above 2 GW that has been developed for both subsea and underground applications [2]. The Prysmian Group declared successful development and testing of its new P-Laser 525 kV cable system for HVDC applications [3]. Cable accessories are an important part of power cable system. Cable accessory faults are the most common among many factors of power cable system faults. The statistics of power cable system faults show that cable accessory fault account for approximately 70% of total cable faults [4]. Therefore, cable accessories need to be carefully designed: as they are a weak link in the cable power system and make the distribution of the internal electric field more reasonable. For cable accessories, there are different types of interface structure, such as interface structure formed by XLPE (Cross-linked polyethylene) and enhanced insulation composites. Under DC voltage, a large amount of space charge is accumulated in the interface structure, and it Materials 2018, 11, 1590; doi:10.3390/ma11091590

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causes serious distortion of the electric field distribution in cable accessories [5,6]. Reasonable design of the structure of and the optimization of their material properties have become prominent requirements for controlling the electric field. Since the 1990s, scientists first proposed the concept of nano-dielectrics, and the exploration and research on nanocomposites has been a hot topic and advanced subject. The dielectric properties of a polymer can be significantly changed by adding nanofillers [7,8]. In order to homogenize the electric field and design reliable cable accessories with stable operation and high universality numerous scholars have concentrated on studying nonlinear dielectrics. The conductivity of nonlinear composites increases nonlinearly as electric field strength increases, which leads to the local area of material present and strong electric field strength, space charge will redistribute and local electrical field strength will reduce [9–12]. L.G. Virsberg et al. proposed a vision that the electric field can be improved using nonlinear dielectrics [13]. ABB researchers studied a technical scheme of cable sleeve that nonlinear composites could be substituted for high conductive composites with constant parameters; the results show that the electric field distribution of the cable sleeve is improved [2]. In a previous study, nonlinear composites were prepared by silicon carbide (SiC) or zinc oxide (ZnO) as nonlinear fillers. Testsushi Okamoto et al. found that SiC and Fe3 O4 were fillers doping in polybutadiene, and the nonlinear characteristics of volt-ampere was determined by SiC; the nonlinear threshold of field strength increases as Fe3 O4 concentration increases [14]. B.R.Varlow researched the DC voltage characteristics of ZnO/LDPE (Low Density Polyethylene) composites. When the concentration of ZnO exceeded 10 wt %, composites had obvious nonlinear volt-ampere characteristics. Moreover, the current density of 10 wt % ZnO/LDPE was lower than pure LDPE [15]. It has been recognized that strongly nonlinear effects in ZnO powders are due to the special structure of fillers: the core of the highly doped ZnO semiconductor is enclosed by a thin complex mixed metal oxide shell (grain boundary in bulk ceramic varistor) that is responsible for the nonlinearity [16,17]. The different crystal forms of SiC are also different nonlinear effects; nonlinearity occurs only when the content of SiC is large enough [18,19]. However, the excessive content may cause the deterioration of mechanical properties and breakdown strength. Therefore, the difficulty of preparing nonlinear composites also increases. In order to adapt the need of higher voltage levels and multiple types of insulation, it is important to research new types of nonlinear composites, which solve the problem of uneven electric field distribution in insulation equipment. Especially for the development of technologies and industries, it has the function of filling a gap in basic theory and applied research, the value and significance of this are even more significant. Copper Calcium Titanate (CCTO) has a perovskite structure and high dielecric constant at room temperature, so CCTO particles are mostly used for the preparation of high-dielectric composites [20,21]. There are few researches about the nonlinear conductivity of CCTO particles. In the present work, EPDM rubber was a matrix of composites; CCTO particles were prepared as fillers. The nonlinear conductance and dielectric properties of CCTO/EPDM composites were investigated in detail. The steady and transient electric field characteristics of CCTO/EPDM composites were investigated by COMSOL Multiphysics theoretical simulation, the feasibility of CCTO/EPDM composites as reinforced insulation was confirmed. 2. Materials and Methods 2.1. Raw Materials CCTO particles were prepared by the sol-gel technique. Firstly, 21.744 g Cu(NO3 )2 ·3H2 O and 7.0845 g Ca(NO3 )2 ·4H2 O were put into a beaker with 160.0 mL C3 H8 O2 , then 41.0 mL Ti(OC4 H9 )4 was slowly poured into the above solution, with stirring, for another 3 h; CCTO sol solutions were obtained. Secondly, the CCTO sol was allowed to stand at room temperature for 24 h to obtain gelatum. Finally, the CCTO gelatum was grinded into a powder, followed by sintering in a muffle furnace with

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a heating rate of 5 ◦ C/min from 0–300 ◦ C, keeping at 300 ◦ C for 2 h, then, with the same heating rate, from 300–1050 ◦ C, keeping at 1050 ◦ C for another 8 h; the crystallized CCTO ceramics were then obtained. Finally, the CCTO ceramics were obtained by Planetary Ball Mill for 12 h with 450 rpm. The above materials are listed in Table 1. Table 1. List of drugs for this experiment. Materials

Corporation

Ca(NO3 )2 ·4H2 O (≥ 99%) Cu(NO3 )2 ·3H2 O (≥ 99%) Ti(OC4 H9 )4 (≥ 99%) C3 H8 O2 (≥ 99%)

Sinopharm Chemical Reagent Co., Ltd., Shanghai, China

This article uses two-roll milling and hot-pressing to prepare composites. EPDM was matrix, and the CCTO particles were nonlinear fillers; dicumyl peroxide (DCP) was employed as the cross-linking agent. The raw materials were mixed uniformly in a two-roll mill at 363 K for 30 min. Then the mixture was cured in a stainless steel mold at 433 K under a pressure of 15 MPa for 15 min, the samples had a thickness of 0.2 mm. 2.2. Performance Testing of Composites The phase of composites was investigated by X-ray diffraction (XRD, Mpyren), which was purchased from PANalytical B.V, Almelo, Netherlands. The Cu target (wavelength of 1.5418 Å) was applied as the electron emission target. The working current was 30 mA and the operating voltage was 40 kV. Scan angle 2θ range was 10–100◦ , the scan rate was 4◦ /min. The dispersion of CCTO particles was observed by SEM, which were purchased from Hitachi Limited SU8020, Shanghai, China. A three-electrode system (Harbin University of Science and Technology, Harbin, China) was used for measuring DC volume conductivity of samples, and the thickness of samples was approximately 0.2 mm, the size was 10 × 10 cm2 . The system was composed of a high-voltage DC power supply (continuously adjustable output voltage from 0 kV to 20 kV), an Ammeter EST122 (pA Ammeter test range of 20 × 10−3 A–1 × 10−15 A), and an oven (the maximum operating temperature was set to 200 ◦ C), as shown in Figure 1. The sample was put into the oven then connected to the electrode and preheated for 2 h, after that, while increasing the DC power output voltage gradually, each voltage level keeping 30 min, then recording the current and the voltage value. In order to avoid accidental errors, prepared samples for each sample and then averaged the three measured results. Materialswe 2018, 11, x FOR three PEER REVIEW 4 of 14

Figure 1. Three-electrode test system schematic. Figure 1. Three-electrode test system schematic.

3. Results 3.1. Microstructures Characterization The XRD spectra of different samples are shown in Figure 2. CCTO particles have a perovskite structure and no impurity peak. Compared to the results of the XRD spectra, it can be found that there is a certain difference in these spectra. Although, when CCTO particles are dispersed in the EPDM and do not find the phase transition of CCTO, the strength of the CCTO phase increases with increasing of content, this is because the intensity depends on the volume fraction of CCTO in the

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The dielectric properties of composites were measuring by Agilent 4294A Precision Impedance Analyzer (Agilent, Santa Clara, CA, USA), the thickness of samples was about 0.2 mm and the size was 30 × 30 mm2 . The highest frequency resolution was 1 MHz. The upper and lower electrodes were both 20 mm, and the test condition was room temperature. The range of frequency was 100 Hz–106 Hz. Before measuring conductivity, the dielectric spectrum, and breakdown of composites, samples needed Figure 1. Three-electrode test system schematic. to be short-circuited at 80 ◦ C, which prevents the result of experiments from being affected by moisture and residual charge inside the sample [22–24].

3. Results

3. Results

3.1. Microstructures Characterization 3.1. Microstructures Characterization

The XRD spectra of different samples are shown in Figure 2. CCTO particles have a perovskite spectra of different samples are in Figure 2. CCTO a perovskite structureThe andXRD no impurity peak. Compared toshown the results of the XRD particles spectra, have it can be found that structure and no impurity peak. Compared to the results of the XRD spectra, it can be found that there there is a certain difference in these spectra. Although, when CCTO particles are dispersed in the is a certain difference in these spectra. Although, when CCTO particles are dispersed in the EPDM and EPDM and do not find the phase transition of CCTO, the strength of the CCTO phase increases with do not find the phase transition of CCTO, the strength of the CCTO phase increases with increasing of increasing of content, this is because the intensity depends on the volume fraction of CCTO in the content, this is because the intensity depends on the volume fraction of CCTO in the composite and composite and its linearcoefficient. absorptionThe coefficient. Thehave neata EPDM have a broad at 2θ = its linear absorption neat EPDM broad diffraction peakdiffraction at 2θ = 20◦ ,peak but the 20°, but the diffraction peak of the EPDM phase is very weak in the CCTO/EPDM composites, diffraction peak of the EPDM phase is very weak in the CCTO/EPDM composites, and its intensity and its intensity with the of CCTO This isparticles due to dispersed CCTO particles dispersed in decreasesdecreases with the increase of increase CCTO content. This content. is due to CCTO in the composite that may destroy the regular arrangement of the EPDM molecules, the diffraction peak of the composite that may destroy the regular arrangement of theleading EPDMtomolecules, leading to the neat EPDM diffraction peakbecome of neatinsignificant. EPDM become insignificant.

Figure 2. X-ray diffraction of CaCu CaCuTi 3Ti4O12 (CCTO) particles and CaCu3Ti4O12/ Ethylene Figure 2. X-ray diffractionpatterns patterns of 3 4 O12 (CCTO) particles and CaCu3 Ti4 O12 / Ethylene Propylene Diene Monomer (CCTO/EPDM) composites. Propylene Diene Monomer (CCTO/EPDM) composites.

cross-section CCTO/EPDMcomposites composites was observed electron microscopy The The cross-section of of CCTO/EPDM observedbybyscanning scanning electron microscopy (SEM), as shown in Figure 3. It can be seen that the CCTO particles are uniformly dispersed in the (SEM), as shown in Figure 3. It can be seen that the CCTO particles are uniformly dispersed in the EPDM matrix, and the size of most of the CCTO, as shown in Figure 3, is approximately 2–5 µm, a few EPDM matrix, and the size of most of the CCTO, as shown in Figure 3, is approximately 2–5 μm, a particles are approximately 100–300 nm. There is no obvious defect; this indicates that CCTO particles few particles are approximately 100–300 nm. There is no obvious defect; this indicates that CCTO have good contact with the EPDM rubber matrix.

particles have good contact with the EPDM rubber matrix.

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Figure 3. SEM morphology of the fresh surfaces of EPDM and composites with different CCTO Figure 3. SEM morphology of the fresh surfaces of EPDM and composites with different CCTO contents: contents: (a) pure (b) 2 vol % (c) CCTO/EPDM; (c) 4 vol % (d) 8 vol % (a) pure EPDM; (b) 2EPDM; vol % CCTO/EPDM; 4 vol % CCTO/EPDM; (d) CCTO/EPDM; 8 vol % CCTO/EDPM. CCTO/EDPM.

3.2. The Conductivity of Composites 3.2. The Conductivity of Composites 3.2.1. The Characteristic of Conductivity (Γ)—Electric Field (E) 3.2.1. The Characteristic of Conductivity (Γ)—Electric Field (E) The empirical formula for the relationship between electric field and conductivity is: The empirical formula for the relationship between electric field and conductivity is: γ = αEβ γ = αEβ

(1) (1)

In By In the the Equation Equation (1), (1), β β is is the the nonlinear nonlinear conductivity conductivity coefficient coefficient of of material, material, α α is is aa constant. constant. By logarithm Equation (1), Equation (1) is converted to linear form: logarithm Equation (1), Equation (1) is converted to linear form: lgγ = lgα βlgE lgγ = lgα + +βlgE

(2) (2)

The value of the nonlinear coefficient β can be obtained by Equation (2). The conductivity The value of the nonlinear coefficient β can be obtained by Equation (2). The conductivity mechanism of composites may change with applied electric field or temperature, which determines mechanism of composites may change with applied electric field or temperature, which determines the different relationship between applied electric field (E) and the conductivity (γ) of CCTO/EPDM. the different relationship between applied electric field (E) and the conductivity (γ) of CCTO/EPDM. The γ-E curve of CCTO/EPDM is shown in Figure 4 at 30, 50, and 70 °C. It can be seen that the γ-E The γ-E curve of CCTO/EPDM is shown in Figure 4 at 30, 50, and 70 ◦ C. It can be seen that the γ-E curve of CCTO/EDPM has an inflection point when the electric field increases, this phenomenon can curve of CCTO/EDPM has an inflection point when the electric field increases, this phenomenon can be explained by the SCLC (space-charge-limited-current) theory. Due to the discontinuous energy be explained by the SCLC (space-charge-limited-current) theory. Due to the discontinuous energy level level in polymer, charge carriers are easily trapped by traps to form space charges under a lower in polymer, charge carriers are easily trapped by traps to form space charges under a lower electric electric field, so the conductivity of EPDM increases inconspicuously with the change of the electric field, so the conductivity of EPDM increases inconspicuously with the change of the electric field. field. When the applied electric field exceeds a certain threshold electric field (E th), the trapped When the applied electric field exceeds a certain threshold electric field (Eth ), the trapped carriers can carriers can obtain enough energy to become detrapped and participate in the conduction process, obtain enough energy to become detrapped and participate in the conduction process, leading to a leading to a significant increase in conductivity. significant increase in conductivity. Dispersing CCTO particles will make the conductance mechanism more complex. Firstly, the Dispersing CCTO particles will make the conductance mechanism more complex. Firstly, the conductivity characteristics of 2 vol. % CCTO/EPDM display a similar trend to that of EPDM. conductivity characteristics of 2 vol % CCTO/EPDM display a similar trend to that of EPDM. According According to the percolation theory [25], the average distance is enough large between particles to the percolation theory [25], the average distance is enough large between particles under doping under doping slight content of conductive or semiconductive particles, leading to charge carriers slight content of conductive or semiconductive particles, leading to charge carriers migrate difficultly migrate difficultly between particles. Thus, doping low content of CCTO particles does not change between particles. Thus, doping low content of CCTO particles does not change the conduction the conduction mechanism of composites. Besides, it can be found that the conductivity of 2 vol. % mechanism of composites. Besides, it can be found that the conductivity of 2 vol % CCTO/EPDM CCTO/EPDM is slightly higher than that of EPDM, the improvement in conductivity is shown to be is slightly higher than that of EPDM, the improvement in conductivity is shown to be due to the due to the doping CCTO particles that make the change in chain structure in the polymer, where the doping CCTO particles that make the change in chain structure in the polymer, where the stretched stretched conformation of polymer chains changes [26–28]. Secondly, with the increase of doping conformation of polymer chains changes [26–28]. Secondly, with the increase of doping content, when content, when the applied electric field E < Eth, carriers cannot go through the barrier between the the applied electric field E < Eth , carriers cannot go through the barrier between the CCTO and EPDM CCTO and EPDM matrix. However, when E > Eth, the tunneling effect occurs [29]. A large number of matrix. However, when E > Eth , the tunneling effect occurs [29]. A large number of carriers can directly carriers can directly transport through trap barriers by tunneling in the high electric field area, and transport through trap barriers by tunneling in the high electric field area, and can participate in the can participate in the conduction process, which grows nonlinearly with the electric field. conduction process, which grows nonlinearly with the electric field.

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Figure 4. Conductive characteristics of composites filled with CCTO at different temperatures. Figure 4. Conductive characteristics of composites filled with CCTO at different temperatures.

According the above above analysis, analysis, the the nonlinear nonlinear conductance conductance characteristics characteristics of of CCTO/EDPM CCTO/EDPM are According to to the are related the tunneling tunneling effect in high high electric electric field. field. In related to to the effect in In aa high high electric electric field field region, region, the the relationship relationship between between the the current current density density (J) (J) and and the the applied applied electric electric field field strength strength (E) (E) should should be be satisfied satisfied by by the the following Equation (3): following Equation (3): (−B/E) J =JAe = Ae(−B/E)

(3) (3)

In Equation Equation (3), and B In (3), the the current current density density(J) (J)isisthe theratio ratioofofmeasured measuredcurrent currenttotomeasured measuredarea. area.AA and are constants, B are constants,which whichrelate relatetotothe thework workfunction functionbetween betweenthe theelectrode electrodeand and medium, medium, and show little relationship with temperature. In In the the high high electric electric field field area, area, lgJ lgJ and and lgE lgE should should be be linear linear in in Equation Equation relationship with temperature. at different different temperatures, temperatures, it can (3). Figure 5 shows the tunneling fit curves of 4 vol % CCTO/EDPM CCTO/EDPM at be seen that there is good linear relation between lgJ and lgE in high electric field area. This verifies the conductance conductancemechanisms mechanismsof ofCCTO/EDPM CCTO/EDPM composites affected tunneling effect that the composites areare affected byby thethe tunneling effect in in areas high electric field. With exception another important parameter areas of of high electric field. With thethe exception of of thethe EthEparameter, another important parameter to th parameter, to reflect nonlinear characteristic thenonlinear nonlinearcoefficient coefficientββ , definedasasthe theratio ratioof of lgγ lgγ to to lgE reflect thethe nonlinear characteristic is is the 0, 0defined theEE>>EthE,ththe , the nonlinear coefficient β0 changes the increase of contents, as shown in under the nonlinear coefficient β0 changes withwith the increase of contents, as shown in Figure Figure can be the Eth decreases and β0 increases with increasing quantity of CCTO 6. It can6.beItseen thatseen the that Eth decreases and β0 increases with increasing quantity of CCTO particles. particles. Moreover, 8 vol % CCTO/EPDM sample exhibits best nonlinear conductivity the Moreover, the 8 vol.the % CCTO/EPDM sample exhibits the bestthe nonlinear conductivity and theand lower lower threshold electric (approximately 10 kV/mm). is mainly becausethe theaverage average distance distance threshold electric field field (approximately 10 kV/mm). ThisThis is mainly because between particles decreases with increasing CCTO particle content in Figure 2, leading to the tunneling particles decreases with increasing CCTO particle content in Figure 2, leading to the effect occurring low electric field. In addition, on the percolation theory [25],theory the higher tunneling effect at occurring at low electric field. Inbased addition, based on the percolation [25], the doping the content, the easier thethe formation conductive leading to carriers transporting easily higher doping content, easier of thethe formation of path, the conductive path, leading to carriers from cathode to anode, thus the nonlinear characteristics of CCTO/EPDM are more obvious. transporting easily from cathode to anode, thus the nonlinear characteristics of CCTO/EPDM are more obvious.

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Figure 5. Fitted curves of tunneling effect in CCTO/EPDM composites at different temperatures. Figure 5. Fitted curves of tunneling effect in CCTO/EPDM composites at different temperatures. Figure 5. Fitted curves of tunneling effect in CCTO/EPDM composites at different temperatures.

Figure 6. The nonlinear parameters of neat EPDM and CCTO/EDPM composites changes with Figure 6. The(a)nonlinear parameters of neat E EPDM and CCTO/EDPM composites changes with temperature: The threshold electric th; (b) The coefficient β0. Figure 6. The nonlinear parameters of field neat EPDM and nonlinear CCTO/EDPM composites changes with temperature: (a) The threshold electric field Eth; (b) The nonlinear coefficient β0. temperature: (a) The threshold electric field Eth ; (b) The nonlinear coefficient β0.

3.2.2. The Characteristic of Conductivity (γ)—Temperature (T) 3.2.2. The The Characteristic CharacteristicofofConductivity Conductivity (γ)—Temperature 3.2.2. (γ)—Temperature (T) (T) Due to the structure and operation characteristics of the cable, there are both electric field Due to to thestructure structure operation cable, there electric field gradients and temperature gradients in characteristics the insulation, sothe it there is important to both investigative the Due the andand operation characteristics of theofcable, are bothare electric field gradients gradients and temperature gradients in the insulation, so it is important to investigative the conductivity of CCTO/EPDM at different temperatures. According to the empirical formula, the and temperature gradients in the insulation, so it is important to investigative the conductivity of conductivitybetween ofat CCTO/EPDM at different temperatures. According to the empirical formula, the relationship the conductivity and temperature be expressed as the following: CCTO/EPDM different temperatures. According to thecan empirical formula, relationship between relationship between the conductivity and temperature can be expressed as the following: the conductivity and temperature can be expressed as the following: γ = γ0eαT (4) γ = γαT 0eαT (4) = γ0 e (4) In the Equation (4), α is the temperature γcoefficient and γ0 is a constant. Figure 7 shows the γ-T the Equation (4), is the temperature coefficient and γ(20 0 is a constant.ItFigure the γ-T curveIncharacteristics of α CCTO/EPDM at high electric field kV/mm). can be7 shows seen that the curve characteristics of CCTO/EPDM at high electric field (20 kV/mm). It can be seen that the In the Equation (4), α is the temperature coefficient and γ is a constant. Figure 7 shows temperature coefficient α of CCTO/EPDM is higher than that of neat0 EPDM, and that the conductivity temperature coefficient α of CCTO/EPDM is higher than that of neat EPDM, and that the conductivity the γ-T curve characteristics of CCTO/EPDM at high electric field (20 kV/mm). It can be seen of 8 vol. % CCTO/EDPM composites increases by 2 orders of magnitude with the increase of of 8 the vol.temperature % CCTO/EDPM increases by 2is orders magnitude with the increase of that coefficient α of CCTO/EPDM higherisof than that of neat and that temperature. It indicates thatcomposites the conductivity of CCTO/EDPM greatly affected byEPDM, temperature, the temperature. It indicates that the conductivity of CCTO/EDPM is greatly affected by temperature, the the conductivity of 8 vol % CCTO/EDPM composites increases by 2 orders of magnitude with conductivity of CCTO/EPDM increases significantly, it benefits reducing the difference in conductivity oftemperature. CCTO/EPDM increases significantly, it caused benefits reducing the difference in the increase of It indicates theinsulation, conductivity of CCTO/EDPM ischanges, greatly affected conductivity between cable accessories andthat XLPE by temperature thereby conductivity between cable accessories and XLPE insulation, caused by temperature changes, thereby by temperature, the conductivity of CCTO/EPDM increases significantly, it benefits reducing the improving the uneven electric field distribution. The conductivity of composites is related to nqμ (n improving theconductivity uneven electric field distribution. of composites isthe related toamount nqμ (n difference in between cable and caused by temperature is carrier density, q is charge amount of theaccessories carrier,The andconductivity μ is XLPE carrierinsulation, mobility), since charge is carrier density, q is charge the amount of the carrier, and μ of is carrier mobility), since theofcharge changes, thereby improving uneven electric field distribution. Themainly conductivity composites is of the carrier is substantially constant, the conductivity materials depends on theamount carrier of the carrier is substantially constant, the conductivity of materials mainly depends on the carrier related to nqµ (n is carrier density, q is charge amount of the carrier, and µ is carrier mobility), since the density and mobility. According to semiconductor physics, carrier mobility decreases with increasing densityamount and mobility. According to semiconductor physics, carrier mobility decreases withincrease increasing charge of the carrier is substantially the Therefore, conductivity of materials mainly depends on temperature because of acoustic phonon constant, scattering. the reason for the of temperature because of acoustic phonon scattering. Therefore, the reason for the increase of the carrier density and mobility. According to semiconductor physics, carrier mobility decreases with conductivity is not carrier mobility. Carrier density generally increase with increasing temperature conductivity is not carrier mobility. Carrier density generally increase with increasing temperature increasing temperature because of acoustic phonon scattering. Therefore, the reason for the increase of due to thermal excitation, therefore the conductivity of composites increases with increasing due to thermal therefore thedensity conductivity ofincrease composites increases withfield, increasing conductivity isleading notexcitation, carrier mobility. Carrier generally with temperature temperature, to nonlinear conductivity that can be induced in a increasing lower electric so due the temperature, leading to nonlinear conductivity that can be induced in a lower electric field, so the to thermal excitation, therefore the conductivity of composites increases with increasing temperature, value of Eth reduces while temperature increases in Figure 6. Besides, the nonlinear conduction value of E th reduces while temperature increases in Figure 6. Besides, the nonlinear conduction current density is related to eRE/kT (e is electron charge, R is average distance between local states, current density is krelated to eRE/kT (e is electron R is average distance between states, E is electric field, is Boltzmann constant, and Tcharge, is temperature), it can be seen that thelocal nonlinear E is electric field, k is Boltzmann constant, and T is temperature), it can be seen that the nonlinear

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leading to nonlinear conductivity that can be induced in a lower electric field, so the value of Eth reduces while temperature increases in Figure 6. Besides, the nonlinear conduction current density is Materials 2018, 11, x FOR PEER REVIEW 8 of 14 related to eRE/kT (e is electron charge, R is average distance between local states, E is electric field, k is Boltzmann and T is temperature), it can be seen that the nonlinear coefficient β decreases coefficient βconstant, 0 decreases while temperature increases in Figure 6b, moreover it is related to 0the electric while temperature increases in Figure 6b, moreover it is related to the electric field. field.

Figure 7. Relationship between conductivity and temperature characteristics of CCTO/EEPDM at 20 kV/mm.

3.3 The Dielectric Properties of Composites Figure 8a shows the relationship between the frequency and relative permittivity of CCTO/EPDM composites. The results show that the permittivity of CCTO/EPDM composites increases with the increase CCTO particles content, which depends the dielectric polarization Figure 7. Relationship betweenof conductivity and temperature characteristics of on CCTO/EEPDM at 20 kV/mm. Figure 7. Relationship between conductivity and temperature characteristics of CCTO/EEPDM at mechanism. The polarization effect is more obvious with CCTO particles with a higher relative 20 kV/mm. permittivity [21,22]. Nelson al. suggested that the doping of microsized fillers could decrease the 3.3 The Dielectric Properties of et Composites free volume of composites, leading to relative permittivity increases [30]. The above complex 3.3. The Dielectric Properties Figure 8a shows theof Composites relationship between the frequency and relative permittivity of mechanisms increase the relative permittivity. The permittivity of EPDM is 2.16, and the permittivity CCTO/EPDM composites. The results showthethat the permittivity CCTO/EPDM composites Figure 8a shows the relationship frequency and relativeof permittivity of CCTO/EPDM of 8 vol. % CCTO/EPDM compositesbetween is 2.62. increases withThe the results increaseshow of CCTO content, of which depends oncomposites the dielectric polarization composites. that particles the permittivity CCTO/EPDM increases Figure 8b shows the relationship between loss factor and frequency. The loss factor droppedwith first mechanism. The polarization effect is more obvious with CCTO particles with a higher relative the increase of CCTO particles content, which depends on the dielectric polarization mechanism. and then increased with frequency. Various polarizations have been established in low frequency, so permittivity [21,22]. Nelson et obvious al. suggested that the dopingwith of microsized fillers permittivity could decrease the The effect is more with CCTO particles a higher relative [21,22]. the polarization factor loss decreases while frequency increases. In the high frequency area, the relaxation free volume composites, to relative permittivity increases [30]. The complex Nelson et al.isofsuggested thatleading the doping of increases, microsized fillers could decrease the above free volume of polarization too late to establish frequency and the polarization of composites is mainly mechanisms increase the relative permittivity. The permittivity of EPDM is 2.16, and the permittivity composites, leading to relative permittivity increases [30]. The above complex mechanisms increase the the displacement polarization, resulting in increased losses [30]. The loss factor increases with doping of 8 vol.permittivity. % CCTO/EPDM composites isof2.62. relative The permittivity EPDM is 2.16, andloss, the permittivity of 8 the vol conductance % CCTO/EPDM content of CCTO particles, which depends on conduction mainly because loss Figure 8b shows the relationship between loss factor and frequency. The loss factor dropped first composites is 2.62. play a major role ar this frequency range; the conductivity of CCTO/EPDM is higher than EPDM. and then increased with frequency. Various polarizations have been established in low frequency, so the factor loss decreases while frequency increases. In the high frequency area, the relaxation polarization is too late to establish frequency increases, and the polarization of composites is mainly the displacement polarization, resulting in increased losses [30]. The loss factor increases with doping content of CCTO particles, which depends on conduction loss, mainly because the conductance loss play a major role ar this frequency range; the conductivity of CCTO/EPDM is higher than EPDM.

Figure 8. The relationship between frequencies and dielectric spectrum of EPDM rubber with different CCTO Figure 8. The relationship between frequencies and dielectric spectrum of EPDM rubber with different content: (a) The relative permittivity; (b) The loss factor. CCTO content: (a) The relative permittivity; (b) The loss factor.

3.4. The Breakdown of Composites Figure 8b shows the relationship between loss factor and frequency. The loss factor dropped first and then increased with Various polarizations have been established in low frequency, It is well-known thatfrequency. the breakdown strength is important in nonlinear composites. The twoso the factor loss decreases while frequency increases. In the high frequency area, the relaxation parameter distribution with 95% intervals for CCTO/EDPM at different Figure 8. TheWeibull relationship between frequencies andconfidence dielectric spectrum of EPDM rubber with different CCTO polarization is too late to establish frequency increases, and the polarization of composites is mainly temperature is shown in Figure 9. It can be seen that the breakdown strength of CCTO/EPDM content: (a) The relative permittivity; (b) The loss factor. the displacement polarization, resulting in increased losses [30]. loss factor increases decreases with doping content of CCTO particles, and theThe breakdown strength with of 8 doping vol % 3.4. The Breakdown of Composites It is well-known that the breakdown strength is important in nonlinear composites. The twoparameter Weibull distribution with 95% confidence intervals for CCTO/EDPM at different temperature is shown in Figure 9. It can be seen that the breakdown strength of CCTO/EPDM decreases with doping content of CCTO particles, and the breakdown strength of 8 vol %

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content of CCTO particles, which depends on conduction loss, mainly because the conductance loss play a major role ar this frequency range; the conductivity of CCTO/EPDM is higher than EPDM. 3.4. The Breakdown of Composites It is well-known that the breakdown strength is important in nonlinear composites. The two-parameter Weibull distribution with 95% confidence intervals for CCTO/EDPM at different temperature is shown in Figure 9. It can be seen that the breakdown strength of CCTO/EPDM decreases Materials 2018, 11, x FOR PEER REVIEW 9 of with doping content of CCTO particles, and the breakdown strength of 8 vol % CCTO/EPDM is 14 higher ◦ than 60 kV/mm at 70 C, it still meets the needs of engineering [31]. Because CCTO particles are CCTO/EPDM is higher than 60 kV/mm at 70 °C, it still meets the needs of engineering [31]. Because Materials 2018, 11,doping x FOR PEER REVIEW 9 of 14 semiconductive, CCTO can introduce a large number of carriers, leading to the breakdown CCTO particles are semiconductive, doping CCTO can introduce a large number of carriers, leading of composites [32,33]. Thus, the breakdown strength of CCTO/EPDM decreases with increasing CCTO/EPDM is higher than 60 kV/mm 70 °C,the it still meets thestrength needs ofofengineering [31].decreases Because to the breakdown of composites [32,33].atThus, breakdown CCTO/EPDM CCTO particles content. Besides, thedoping mobility ofthe carriers increases with temperature, resulting in CCTO particles CCTO are semiconductive, CCTO can introduce a large increases number of carriers, leading with increasing particles content. Besides, mobility of carriers with temperature, easierto breakdown. the breakdown of composites [32,33]. Thus, the breakdown strength of CCTO/EPDM decreases resulting in easier breakdown. with increasing CCTO particles content. Besides, the mobility of carriers increases with temperature, resulting in easier breakdown.

Figure 9. The breakdown strength of CCTO/EPDM composites.

Figure 9. The breakdown strength of CCTO/EPDM composites. 4. Simulation ResultsFigure and Analysis of Electrical Field Distributioncomposites. in DC Cable Termination 9. The breakdown strength of CCTO/EPDM

4. Simulation Results and Analysis of Electrical Field Distribution in DC Cable Termination 4.1Simulation DistributionResults Characteristics of Steady in Cable Termination 4. and Analysis ofElectrical ElectricalField Field Distribution in DC Cable Termination

4.1. Distribution Characteristics of Steady Electrical Field in Cable Termination

In order to analyze the ability of nonlinear conductive CCTO/EPDM composites for homogenizing

4.1 Distribution Steady Electrical Field in Cable Termination In order field, to Characteristics analyze the ofMultiphysics ability of nonlinear conductive composites for the electric the COMSOL simulation was employed.CCTO/EPDM The core voltage (U 0) was 200 homogenizing the electric field, the COMSOL Multiphysics simulation was employed. The core kVInand theto core temperature was °C. The conductive schematic ofCCTO/EPDM cable termination can be for seen in Figure 10. order analyze the ability of70 nonlinear composites homogenizing the electric field, simulation was◦ C. employed. The coreof voltage 0) was 200 can Figure shows the simulation results of the electric distribution in cable termination during voltage (U was 200the kVCOMSOL and the Multiphysics core temperature wasfield 70 The schematic cable (U termination 0 )11 kV and the core temperature was 70 °C. schematic of cableoftermination can be seen in Figure 10.cable the in DCFigure steady state. It can11beshows found thatThe 8 vol % CCTO/EPDM can the electrical field evenly be seen 10. Figure the simulation results the make electric field distribution in 7 V/m,during Figure 11 shows the simulation results of the electric field distribution in cable termination distributed in cable termination, and the maximum electrical field of the root is 1.35 × 10 it does termination during the DC steady state. It can be found that 8 vol % CCTO/EPDM can make the the steady state. It can be found that vol % CCTO/EPDM can make the electrical field evenly not DC exceed the DC breakdown strength of8CCTO/EPDM. electrical field evenly distributed in cable termination, and the maximum electrical field of the root is distributed in cable termination, and the maximum electrical field of the root is 1.35 × 107 V/m, it does 7 1.35 × 10 V/m, it does not exceed the DC breakdown strength of CCTO/EPDM. not exceed the DC breakdown strength of CCTO/EPDM.

Figure 10. Cable termination model and simulation results: 1: core; 2: XLPE; 3: reinforced insulation; 4: inner shield; 5: stress cone; 6: outer shield. Figure 10. Cable termination model and simulation results: 1: core; 2: XLPE; 3: reinforced insulation;

Figure 10. Cable termination model andshield. simulation results: 1: core; 2: XLPE; 3: reinforced insulation; 4: 4.2 Distribution Characteristics of6:Transient Electrical Field in Cable Termination 4: inner shield; 5: stress cone; outer inner shield; 5: stress cone; 6: outer shield. There are transient processes, such as polarity reversal, and a lightning impulse process in the 4.2 Distribution Characteristics of Transient Electrical Field in Cable Termination course of HVDC transmission. Transient processes are more easily to aggravate the destruction of the areAiming transientatprocesses, such polarity reversal, and a in lightning process in the cableThere system. the problem ofas electric field distribution HVDC impulse cable insulation, some researchers usedtransmission. simulation software study the field the distribution in of cable course of HVDC Transienttoprocesses aresteady-state more easily electric to aggravate destruction the cable system. Aiming at the problem of electric field distribution HVDC cable insulation, some insulation under a temperature gradient [34]. However, there is noinrelevant research report on the researchers used field simulation software to cable studyinsulation. the steady-state electric field distribution in cable transient electric distribution of DC Thus, this section mainly investigates the insulation under a temperature gradient [34]. However, there is no relevant research report on the

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4.2. Distribution Characteristics of Transient Electrical Field in Cable Termination There are transient processes, such as polarity reversal, and a lightning impulse process in the course of HVDC transmission. Transient processes are more easily to aggravate the destruction of the cable system. Aiming at the problem of electric field distribution in HVDC cable insulation, some researchers used simulation software to study the steady-state electric field distribution in cable insulation under a temperature gradient [34]. However, there is no relevant research report on the Materials 2018, 11, x FOR PEER REVIEW 10 of 14 transient electric field distribution of DC cable insulation. Thus, this section mainly investigates the Materials 2018, 11, x FOR PEER REVIEW 10 of 14 influence of lightning impulse voltage and polarity reversal on the electric field distribution of cable influence of lightning impulse voltage and polarity reversal on the electric field distribution of cable termination, especiallyimpulse at the root of theand stress cone. reversal on the electric field distribution of cable influence of lightning voltage polarity termination, especially at the root of the stress cone. In the process of polarity reversal, external applied voltage amplitude UTP1 = 1.45U0 . termination, especially the rootreversal, of the stress cone. applied In the process of atpolarity external voltage amplitude U TP1 = 1.45U0. The The waveform of the applied voltage is shown in Figure 12a during the polarity is In the process of polarity reversal, external applied voltage U TP1 reversal, =Δt1.45U 0.∆t The waveform of the applied voltage is shown in Figure 12a during the amplitude polarity reversal, is polarity polarity reversal time. When the applied voltage is reversed from the polarity to positive waveform of the applied voltage is shown in Figure 12athe during the negative polarity reversal, Δtthe is polarity, polarity reversal time. When the applied voltage is reversed from negative polarity to the positive polarity, the distribution characteristics of the electrical field are not substantially changed. Therefore, reversal time. When the appliedofvoltage is reversed thesubstantially negative polarity to the positive polarity, the distribution characteristics the electrical fieldfrom are not changed. Therefore, only the only the polaritycharacteristics reversal process of electrical the positive polarity to the negative polarityTherefore, is studied.only Before the distribution of the field are not substantially changed. the polarity reversal process of the positive polarity to the negative polarity is studied. Before the polarity the polarity reversal occurs, thepositive cable termination is anegative steady operation. The waveform of lightning polarity reversal process of the polarity to the polarity is studied. Before the polarity reversal occurs, the cable termination is a steady operation. The waveform of lightning impulse impulse process is shown in Figure 12b. GB/T 3048.13-2007, taking a standard 1.2/50 µs lighting reversal occurs, termination a steady operation. waveform process is shownthe in cable Figure 12b. GB/T is 3048.13-2007, taking a The standard 1.2/50ofμslightning lighting impulse impulse impulse voltage waveform. In the lightning impulse process the applied voltage amplitude UP1 =1050 process is shown in Figure 12b. GB/T 3048.13-2007, taking a standard 1.2/50 μs lighting voltage waveform. In the lightning impulse process the applied voltage amplitude U P1=1050impulse kV [35]. kV [35]. waveform. In this section, 8 vol % CCTO/EPDM replaces reinforced insulation. voltage lightning impulse process thetraditional applied voltage amplitude U P1=1050 kV [35]. In this section, 8 volIn%the CCTO/EPDM replaces traditional reinforced insulation. In this section, 8 vol % CCTO/EPDM replaces traditional reinforced insulation.

(a) (b) (a) (b) Figure 11. Cable termination simulation results: (a) The simulation results of EPDM; (b) the Figure 11. Cable termination simulation results: (a) The simulation results of EPDM; (b) the simulation Figure 11. results Cable of termination simulation results: (a) The simulation results of EPDM; (b) the simulation 8 vol. % CCTO/EPDM. results of 8 vol % CCTO/EPDM. simulation results of 8 vol. % CCTO/EPDM.

(a) (b) (a) (b) Figure 12. Waveform of applied voltage during the transient process: (a) Polarity reversal process Figure 12. Waveform of applied voltage during the transient process: (a) Polarity reversal process applied12. voltage waveform; (b) lightning voltage waveform. Figure Waveform of applied voltage impulse during the transient process: (a) Polarity reversal process applied voltage waveform; (b) lightning impulse voltage waveform. applied voltage waveform; (b) lightning impulse voltage waveform.

4.2.1. The Electric Field Distribution of Cable Termination during Polarity Reversal 4.2.1. The Electric Field Distribution of Cable Termination during Polarity Reversal 8 vol % CCTO/EPDM composites are replaced with traditional reinforced insulation materials. 8 vol % CCTO/EPDM composites replaced traditional reinforced insulation materials. Set the applied external applied voltageare UTP1 = 1.45Uwith 0, Δt = 120 s, the variation of the field strength of Set the applied external applied voltage U TP1 = 1.45U0, Δt = 120 s, the variation of the field strength of XLPE and the root in polarity reversal process is shown in Figure 13a. Firstly, when the applied XLPE and the root polarity reversal process is shown 13a. Firstly, when the which applied 7 V/m, concentrated voltage reaches -UTP1in, the maximum electrical field is 2.37 ×in10Figure in XLPE, is 7 voltage reaches TP1, the maximum electrical field is 2.37 × 10 V/m, concentrated in XLPE, which is higher than the -U root. Secondly, when the polarity reversal process ends, and the electric field reaches

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4.2.1. The Electric Field Distribution of Cable Termination during Polarity Reversal 8 vol % CCTO/EPDM composites are replaced with traditional reinforced insulation materials. Set the applied external applied voltage UTP1 = 1.45U0 , ∆t = 120 s, the variation of the field strength of XLPE and the root in polarity reversal process is shown in Figure 13a. Firstly, when the applied voltage reaches -UTP1 , the maximum electrical field is 2.37 × 107 V/m, concentrated in XLPE, which is higher than the root. Secondly, when the polarity reversal process ends, and the electric field reaches -UTP1 , the electric field strength of XPLE is significantly higher than before the polarity reversal, and the electric field of the root is opposite in Figure 13b. The reason is the presence of a different charge in the insulator after polarity reversal, resulting in the increase of the maximum electric field in XLPE insulation. kind of different Materials 2018, This 11, x FOR PEER REVIEW polarity charge is different from the space charge determined 11 of by 14 the trapping factor under the uniform electric field. It is determined by the slow polarization, which caused byby the nonlinearity ofofthe is caused the nonlinearity thematerial. material.The Thecharge chargeisisthe thesame same polarity polarity charge charge before before polarity reversal, and the charge is the different polarity after polarity reversal. The charge of the root may be opposite to the above condition [34].

(a)

(b)

Figure 13. Electric field distribution inside the cable termination in the polarity reversal process: (a) Figure 13. Electric field distribution inside the cable termination in the polarity reversal process: (a) When When the applied voltage reaches-UTP1; (b) variation of the electric field strength with respect to time. the applied voltage reaches-UTP1 ; (b) variation of the electric field strength with respect to time.

4.2.2. during Lightning Lightning Process Process 4.2.2. The The Electric Electric Field Field Distribution Distribution of of Cable Cable Termination Termination during Overhead likely to by lightning, Overhead lines lines are are more more likely to be be affected affected by lightning, resulting resulting in in higher higher possibility possibility of of line line trips and faults. Due to the fact that cables are connected with overhead lines, this will also be affected trips and faults. Due to the fact that cables are connected with overhead lines, this will also be affected by lightning impulse impulse voltage. voltage. This by the the lightning This section section investigates investigates the the characteristics characteristics of of the the electrical electrical field field distribution in the cable terminal when the working voltage of the HVDC cable is superimposed with distribution in the cable terminal when the working voltage of the HVDC cable is superimposed a positive and negative lightning pulse, respectively. TheThe lightning impulse waveform is shown in with a positive and negative lightning pulse, respectively. lightning impulse waveform is shown Figure 12b. in Figure 12b. Figure shows the Figure 14 14 shows the relationship relationship between between the the maximum maximum field field strength strength of of XLPE XLPE and and root root with with time under different polarity lightning pulse. The electric field of the root is always less time under different polarity lightning pulse. The electric field of the root is always less than than the the electric field of XLPE in termination, it does not change with the polarity of the lightning impulse electric field of XLPE in termination, it does not change with the polarity of the lightning impulse voltage, of the the root voltage, and and the the electric electric field field strength strength of root is is much much lower lower than than the the breakdown breakdown strength. strength. This This is is due a dominant role in in thethe distribution of due to to fact fact that thatthe theconductivity conductivityofofcomposites compositesno nolonger longerplays plays a dominant role distribution the electric field in in cable dielectric of the electric field cabletermination terminationduring duringthe thelightning lightningpulse pulseprocess process and and that that the the dielectric constant of composites also participates in determining the electric field distribution. Figure constant of composites also participates in determining the electric field distribution. Figure 15 15 shows shows the the influence influence of of the the dielectric dielectric constant constant on on the the distribution distribution of of the the electric electric field field in in termination termination during during aa positive lightning lightning impulse. impulse.The Thesimulation simulationresults resultsshow show that increase of the dielectric constant positive that thethe increase of the dielectric constant can can significantly reduce the maximum electric field at the root in lightning impulse process. Therefore, significantly reduce the maximum electric field at the root in lightning impulse process. Therefore, the development of composites with both nonlinear conductance and dielectric properties will be the focus of research on DC cable accessories.

voltage, and the electric field strength of the root is much lower than the breakdown strength. This is due to fact that the conductivity of composites no longer plays a dominant role in the distribution of the electric field in cable termination during the lightning pulse process and that the dielectric constant of composites also participates in determining the electric field distribution. Figure 15 shows the influence of the dielectric constant on the distribution of the electric field in termination during a Materials 2018, 11, 1590 12 of 14 positive lightning impulse. The simulation results show that the increase of the dielectric constant can significantly reduce the maximum electric field at the root in lightning impulse process. Therefore, the development of composites with both nonlinear conductance and dielectric properties will be the focus of research research on on DC DC cable cable accessories. accessories.

Figure 14. Variation of the electric field strength with respect to time in the lightning pulse process. Figure 14. Variation of the electric field strength with respect to time in the lightning pulse process.

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Figure 15. Variation of the electric field strength with different dielectric constants in the lightning Figure 15. Variation of the electric field strength with different dielectric constants in the lightning impulse process. impulse process.

5. Conclusions This paper mainly studies the influence of CCTO particle content on the nonlinear conductivity of CCTO/EPDM also analyzes thethe formation reasons of nonlinear conductivity, and CCTO/EPDMcomposites; composites;it it also analyzes formation reasons of nonlinear conductivity, studies the distribution of electric fieldsfields under steady state state and transient conditions, respectively. The and studies the distribution of electric under steady and transient conditions, respectively. conclusion follows: The conclusion follows: (1) The sol-gel method, method, and and dispersed dispersed evenly evenlyin inCCTO/EPDM CCTO/EPDM (1) The CCTO CCTO particles are fabricated by the sol-gel composites. CCTO/EPDM composites have good nonlinear conductance characteristics. When composites. CCTO/EPDM composites have good nonlinear the contentofofCCTO CCTO particles is low, the conductivity of CCTO/EDPM not exhibit the content particles is low, the conductivity of CCTO/EDPM does notdoes exhibit nonlinear nonlinear characteristics; with ofthe of the the doping content, the conductivity of characteristics; with the increase theincrease doping content, conductivity of CCTO/EDPM shows CCTO/EDPM shows a nonlinear increase with the increase of the electric field strength. a nonlinear increase with the increase of the electric field strength. Moreover, the Eth reduces and Moreover, Eththe reduces andofβCCTO increases with content. the increase of CCTO particle content. β increasesthe with increase particle (2) The increase of CCTO particle content, leading to freefree volume decreases; and and due to thetohigh (2) The increase of CCTO particle content, leading the to the volume decreases; due the dielectric constant of CCTO particles, leading to tothe of CCTO/EDPM CCTO/EDPM high dielectric constant of CCTO particles, leading thedielectric dielectric constant constant of composites content. composites increases increases with with the the increase increase of of CCTO CCTO particles particles content. (3) The simulation results of steady and transient electric field distributions show showthat that CCTO/EPDM CCTO/EPDM (3) The simulation results of steady and transient electric field distributions composites composites exhibit exhibit ability ability to to homogenize homogenize the the electric electric field field distribution. distribution. (4) In the lightning impulse process, the maximum electric field is concentrated on XLPE, it (4) In the lightning impulse process, the maximum electric field is concentrated on XLPE, and itand does does not change with the polarity of the lightning pulse process. The dielectric constant increase not change with the polarity of the lightning pulse process. The dielectric constant increase of of reinforced insulation significantly reduce maximum electric field strength root. reinforced insulation cancan significantly reduce thethe maximum electric field strength of of thethe root. Author Contributions: Z.L. and H.Z. conceived and designed the experiments; Z.L. and C.Z. performed the experiments; Z.L. analyzed the data; C.Z. contributed reagents/materials/analysis tools; Z.L. wrote the paper. Funding: This research was funded by the National Science Foundation of China (No. 51337002). Conflicts of Interest: The authors declare no conflict of interest

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Author Contributions: Z.L. and H.Z. conceived and designed the experiments; Z.L. and C.Z. performed the experiments; Z.L. analyzed the data; C.Z. contributed reagents/materials/analysis tools; Z.L. wrote the paper. Funding: This research was funded by the National Science Foundation of China (No. 51337002). Conflicts of Interest: The authors declare no conflict of interest

References 1.

2.

3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13.

14.

15.

16.

17. 18.

Commission of the European Communities. Limiting Global Climate Change to 2 Degrees Celsius the Way ahead for 2020 and beyond; Communication from the Commission to the Council, the European Parliament, the Europe Economy and Social Committee and the Committee of the Regions; Commission of the European Communities: Brussels, Belgium, 2007. Gustafsson, A.; Jeroense, M.; Sunnegårdh, P.; Saltzer, M.; Ghorbani, H.; Rapp, H. New developments within the area of extruded HVDC cables. In Proceedings of the11th IET International Conference on AC and DC Power Transmission, Birmingham, UK, 10–12 February 2015; pp. 1–5. Available online: http://www.prysmiangroup.com/en/corporate/media/news/Breakthrough-HVDCcable-techology-for-power-transmission-grids/ (accessed on 21 January 2018). Tang, G. The exploration of China advanced transmission technology innovation and the development of UHV technology. China Elect. Equip. Ind. 2015, 15, 43–47. (In Chinese) Liangzhong, Y.; Jing, W.; Zhibing, W.; Yan, L.; Zong-Xiang, L. Pattern analysis of future HVDC grid development. Proc. CSEE 2014, 34, 6007–6020. Hanley, T.L.; Burford, R.P.; Fleming, R.J.; Barber, K.W. A general review of polymeric insulation for use in HVDC cables. IEEE Electr. Insul. Mag. 2003, 19, 13–24. [CrossRef] Wu, J.; Yin, Y.; Lan, L.; Wang, Q.; Li, X.; Xiao, D. The influence of nano-filler concentration on space charge behavior in LDPE/Silica nanocompo-site. Proc. CSEE 2012, 32, 177–183. Qi, X.; Zheng, Z.; Boggs, S. Engineering with nonlinear dielectrics. IEEE Electr. Insul. Mag. 2004, 20, 27–34. [CrossRef] Weida, D.; Steinmetz, T.; Clemens, M. Electro-quasistatic high voltage field simulations of large scale insulator structures including 2-D models for nonlinear field-grading material layers. IEEE Trans. Magn. 2009, 45, 980–983. [CrossRef] Wang, Z.; Nelson, J.K.; Hillborg, H.; Zhao, S. Graphene oxide filled nanocomposite with novel electrical and dielectric properties. Adv. Mater. 2012, 24, 3134–3137. [CrossRef] [PubMed] Christen, T.; Donzel, L.; Greuter, F. Nonlinear resistive electric field grading part 1: Theory and simulation. IEEE Electr. Insul. Mag. 2010, 26, 47–59. [CrossRef] Donnelly, K.P.; Varlow, B.R. Nonlinear dc and ac conductivity in electrically insulating composites. IEEE Trans. Dielectr. Electr. Insul. 2003, 10, 610–614. [CrossRef] Virsberg, L.G.; Björklund, A. New type of turn insulation for medium-sized, high-voltage electrical machines. In Proceedings of the Electrical/Electronics Insulation Conference (EIC 13th), Chicago, IL, USA, 26–29 September 1977. Okamoto, T.; Koyama, M.; Inoue, Y.; Tomimura, T.; Nakamura, S. Non-linear electrical property of composite materials with two kinds of filler. In Proceedings of the 20001 IEEE 7th International Conference on Solid Dielectrics, Eindhoven, The Netherlands, 25–29 June 2001; pp. 117–120. Auckland, D.W.; Rashid, A.; Tavernier, K. Stress relief by nonlinear fillers in insulating solids. In Proceedings of the IEEE 1994 Annual Report Conference on Electrical Insulation and Dielectric Phenomena, Arlington, TX, USA, 23–26 October 1994; pp. 310–315. Tavernier, K.; Auckland, D.W.; Varlow, B.R. Improvement in the electrical performance of electrical insulation by nonlinear fillers. In Proceedings of the IEEE 6th International Conference on Conduction and Breakdown in Solid Dielectrics, Vasteras, Sweden, 22–25 June 1998; pp. 533–538. Tavernier, K.; Varlow, B.R.; Auckland, D.W.; Ugur, M. Improvement in electrical insulators by nonlinear fillers. IEE Proc. Sci. Meas. Technol. 1999, 146, 88–94. [CrossRef] Onneby, C.; Martensson, E.; Gafvert, U.; Gustafsson, A.; Palmqvist, L. Electrical Properties of Field Grading Materials Influenced by the Silicon Carbide Grain Size. In Proceedings of the 20001 IEEE 7th International Conference on Solid Dielectrics (Cat. No.01CH37117), Eindhoven, The Netherlands, 25–29 June 2001; pp. 43–45.

Materials 2018, 11, 1590

19.

20. 21.

22.

23. 24. 25.

26.

27. 28.

29. 30.

31. 32. 33. 34. 35.

14 of 14

Donzel, L.; Christen, T.; Kessler, R.; Greuter, F.; Gramespacher, H. Silicone composites for HV applications based on microvaristors. In Proceedings of the 2004 IEEE International Conference on Solid Dielectrics, Toulouse, France, 5–9 July 2004. Subamanian, M.A.; Li, D.; Duan, N.; Reisner, B.A.; Sleight, A.W. High dielectric constant in ACu3 Ti4 O12 phases. J. Solid State Chem. 2000, 151, 323–325. [CrossRef] Li, J.; Subramanian, M.A.; Rosenfeld, H.D.; Jones, C.Y.; Toby, B.H.; Sleight, A.W. Clues to the giant dielectric constant of CaCu3 Ti4 O12 in the defect structure of “SrCu3 Ti4 O12 ”. Chem. Mater. 2004, 16, 5223–5225. [CrossRef] Li, J.; Du, B.; Liu, Y.; Han, T.; Yin, Q.; Hu, W. Interface charge distribution between LDPE and carbon black filled EPDM. In Proceedings of the 2016 IEEE International Conference on Dielectrics, Montpellier, France, 3–7 July 2016; pp. 406–409. Du, B.X.; Li, J. Electrical and mechanical ageing behaviors of used heat-shrinkable insulation tubes. IEEE Trans. Dielectr. Electr. Insul. 2014, 21, 1875–1881. [CrossRef] Chen, Q.G.; Liu, H.Q.; Chi, M.H.; Wang, Y.; Wei, X. Experimental study on influence of trap parameters on dielectric characteristics of nano-modified insulation pressboard. Materials 2017, 10, 90. [CrossRef] [PubMed] Castellon, J.; Nguyen, H.N.; Agnel, S.; Toureille, A.; Frechette, M.; Savoie, S.; Schmidt, L.E. Electrical properties analysis of micro and nano composite epoxy resin materials. IEEE Trans. Dielectr. Electr. Insul. 2011, 18, 651–658. [CrossRef] Eslami, H.; Mohammadzadeh, L.; Mehdipour, N. Anisotropic heat transport in nanoconfined polyamide-6,6 oligomers: Atomistic reverse nonequilibrium molecular dynamics simulation. J. Chem. Phys. 2012, 136, 104901. [CrossRef] [PubMed] Eslami, H.; Mohammadzadeh, L.; Mehdipour, N. Reverse nonequilibrium molecular dynamics simulation of thermal conductivity in nanoconfined polyamide-6,6. J. Chem. Phys. 2011, 135, 064703. [CrossRef] [PubMed] Jing, Z.; Li, C.M.; Zhao, H.; Zhang, G.L.; Han, B.Z. Doping effect of graphene nanoplatelets on electricalinsulation properties of polyethylene: From macroscopic to molecular scale. Materials 2016, 9, 680. [CrossRef] [PubMed] Ieda, M.; Mizutani, T.; Ikeda, S. Electrical Conduction and Chemical Structure of Insulating Polymers. IEEE Trans. Electr. Insul. 1986, 21, 301–306. [CrossRef] Nelson, J.K.; Utracki, L.A.; Maccrone, R.K.; Reed, C.W. Role of the interface in determining the dielectric properties of nanocomposites. In Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, Boulder, CO, USA, 20–20 October 2004; pp. 314–317. Ye, X.; Han, B.; Huang, Q. Simulation of electrical field distribution of XLPE insulated HVDC cable. Electr. Mach. Control 2014, 18, 19–23. (In Chinese) Mizutani, T. Behavior of Charge Carriers in Organic InsulatingMaterials. In Proceedings of the 2006 IEEE Conference on Electrical Insulation and Dielectric Phenomena, Kansas City, MO, USA, 15–18 October 2006. Kao, K.C. Dielectric Phenomena in Solids; Elsevier Academic Press: Cambridge, MA, USA, 2004; pp. 460–462. Zhang, R.; Li, Z.H.; Guo, W.M.; Lu, X. Simulation of response characteristics of nonlinear insulating dielectrics in coaxial electrodes under the step voltage. High Voltage Eng. 2008, 34, 1363–1367. (In Chinese) Recommendations for Testing DC Extruded Cable Systems for Power Transmission at a Rated Voltage up to 500 kV. Available online: http://b1.cigre.org/Members-Area/WG-B1.32-Recommendations-for-testing-DC-extrudedcable-systems-for-power-transmission-at-a-rated-voltage-up-to-500-kV (accessed on 21 January 2018). © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).