Investigation of the performance of CF3I/c-C4F8/N2 and CF3I/c-C4F8/CO2 gas mixtures from electron transport parameters

Ruishuang ZHONG(钟蕊霜),Su ZHAO(赵谡),Dengming XIAO(肖登明),4,Hui WANG (王辉),4,Xiuchen JIANG (江秀臣),Zhongmin YU (余钟民) and Yunkun DENG (邓云坤)

1 Department of Electrical Engineering,Shanghai Jiao Tong University,Shanghai 200030,People’s Republic of China

2 State Grid Shanghai Electric Power Company,Shanghai 200122,People’s Republic of China

3 Yunnan Power Grid Corporation,Kunming 650217,People’s Republic of China

4 Authors to whom any correspondence should be addressed.

Abstract

Keywords:CF3I/c-C4F8/N2 gas mixtures,CF3I/c-C4F8/CO2 gas mixtures,Boltzmann method,electron transport parameters,synergistic effect

1.Introduction

Sulfur hexafluoride (SF6) is a colorless,odorless,non-toxic,non-flammable gas with stable chemical properties and excellent insulation properties.It is widely used in power systems[1].However,SF6is also a strong greenhouse gas;its global warming potential (GWP) is approximately 23 900.To maintain sustainable development of the environment and resources,SF6was classified as a greenhouse gas under the Kyoto Protocol in 1997,which required a gradual reduction of its use [2].In recent years,researchers have found a number of alternatives to SF6.

Figure 1.The molecular structure of gases:(a) CF3I;(b) c-C4F8.

Trifluoroiodomethane (CF3I) has been proposed as a potential replacement for SF6owing to its excellent physicochemical properties and outstanding dielectric strength.The insulation strength of CF3I is approximately 1.2 times that of SF6in a slightly non-uniform electrical field.It has good oil solubility and material compatibility.Its GWP is approximately 5 and its ozone destruction potential (ODP) is approximately 0.008,which is negligible [3,4].Its molecular structure is shown in figure 1(a).The carbon–iodine chemical bond in the molecular structure of CF3I is relatively active,and easily broken under solar radiation,leading to the decomposition of CF3I.This property limits its diffusion to the stratosphere and reduces its greenhouse effect.However,the liquefaction temperature of CF3I is approximately -22.5°C under normal temperature and pressure.A buffer gas is needed to reduce its liquefaction temperature,and then CF3I gas mixtures can be suitable for applications in electrical equipment [5].

Perfluorocyclobutane (c-C4F8) is another kind of potential electronegative replacement gas for SF6.Its electric insulation performance is better than that of SF6.It has a GWP of 8 700,which is only 36% of that of SF6,and its ODP is zero [6].The molecular structure of c-C4F8is shown in figure 1(b).Owing to its symmetrical structure,and having two more fluorine atoms than SF6,its electronegativity is stronger than that of SF6and it is chemically stable.However,similar to CF3I,c-C4F8also has a high liquefaction temperature.The materials must be mixed with buffer gases to reduce the liquefaction temperature [7,8].

In research into electronegative gas mixtures,N2and CO2are the most commonly used buffer gases.They have stable physico-chemical properties and their liquefaction temperatures are -195.8 °C and -78.5 °C [9].They can greatly improve the liquefaction temperature performance of electronegative gases.

In previous research,De Urquijo et al used a pulsed Townsend (PT) method to measure the microscopic parameters of CF3I and CF3I-N2[10].Katagiri et al found that the dielectric strength of CF3I-CO2(30%–70%)is approximately 0.75 to 0.8 times of that of SF6[5].Li et al analyzed the insulation characteristics of CF3I mixtures with CF4,CO2,N2,O2,and air,and found that CF3I/N2and CF3I/air have better insulation performance than the other three mixtures [2].Zhao et al studied CF3I gas mixtures and found that the synergistic effect coefficient of CF3I/CO2gas mixtures was higher than that of CF3I/N2[11].For c-C4F8,Xiao et al analyzed the insulation characteristics of c-C4F8gas mixtures by Monte Carlo and Boltzmann methods [7,12].Man et al studied the insulating properties of c-C4F8/N2and c-C4F8/CO2under an alternating current and found that 30 % c-C4F8/70% N2and 30 % c-C4F8/70% CO2mixed gases had 75% and 79% respectively of the capacity of pure SF6at 0.1 MPa [13].For ternary gas mixtures,Xu et al studied the CF3I binary and ternary gas mixtures with SF6,CO2,N2,and CF4,and found synergetic effects in CF3I with N2and CO2,whereas the CF3I/SF6system had a slight negative synergetic effect [14].Cheng et al studied the breakdown characteristics of binary and ternary gas mixtures of CF3I/SF6/N2and CF3I/SF6/CO2under DC voltage[15].At present,there has been little research on ternary mixed gases of CF3I and c-C4F8.Therefore,studies of the electron transport parameters of ternary gas mixtures of CF3I and c-C4F8might provide basic data to support the application of these gases as alternatives to SF6.

In this paper,based on a Boltzmann simulation method,CF3I/c-C4F8/N2and CF3I/c-C4F8/CO2gas mixtures are investigated in terms of the electron energy distribution function(EEDF),reduced effective ionization coefficient,critical reduced electrical field strength,electric field sensitivity coefficient,electron drift velocity,and synergistic effect.

2.Theoretic framework

2.1.Boltzmann equation method

The process of solving the Boltzmann equation is to build a self-consistent model reflecting the interaction between an electric field and particles.This complex model takes into account both elastic and inelastic collision processes,and the effects of external electric fields on charged particles[16].By solving the Boltzmann equation,the EEDFs of gas mixtures at different volume ratios are obtained,and the electron group parameters and transport parameters in the discharge process of the gas mixtures are calculated.The critical reduced field strength of the gas mixtures is determined.Next,we analyze the insulation properties of the gas mixtures.

For a particle that exists in a six-dimensional phase space(r,v),we define the distribution functionf(r,v,t).Its physical meaning is:the number of particles in the six-dimensional volume elementr vd d3 3 around the timetand the phase space (r,v).If the particle is an electron in a weakly ionized gas,its distribution can be described by the Boltzmann equation as follows:

where r is the electron space position,v is the electron velocity,eis the electron charge (approximately ×1.6 10-19C),mis the electron mass,E is the strength of the electric field in space,andandC f[ ]are collision terms,defining the rate of change of the function of the electron during various collisions [17].

Figure 2.The electron impact cross-sections of gases:(a) CF3I;(b) c-C4F8.

To obtain the electron transport parameters,it is necessary to solve the Boltzmann equations.In this paper,the Boltzmann equations were solved with the use of BOLSIG + software by a two-term approximation method.This method has high accuracy and a rapid operation speed,which makes it the most common method for solving Boltzmann equations.The two-term approximation method requires the conditions that the electric field is uniformly distributed in space and the collision probability is equal.Electrons in velocity space are symmetric with respect to the direction of the electric field,and the distribution in the position space changes only along the direction of the electric field[18,19].In a spherical coordinate system in velocity space,equation (1) is written as follows:

wherevis the magnitude of velocity,θ is the angle between the velocity and the electric field,andzis the position of the electric field.

We can expand the energy distribution functionfas a Legendre polynomial aboutθcos .In a two-term approximation method,only two terms are expanded.

wheref0represents the isotropic part andf1represents the anisotropic part [20].

2.2.Collision cross-sections

To calculate the Boltzmann equation and solve the electron transport parameters,the gas collision cross-section data are required,including the attachment cross-sectionQa,the ionization cross-sectionQi,the elastic cross-sectionQel,and the electronic excitation cross-sectionQex.Most of the collision cross-section data(CF3I,SF6,CO2,N2)in this paper are taken from the LXcat website [21],which provides a comprehensive and reliable database for such data.The crosssection data of CF3I are taken from the TRINITI database,as shown in figure 2(a).For c-C4F8,the attachment cross-sectionQaand ionization cross-sectionQiare taken from [22],whereas the elastic cross-sectionQeland electronic excitation cross-sectionQexare taken from [7],as shown in figure 2(b).

According to the selected cross-section,and based on Boltzmann calculations,the reduced effective ionization coefficients(α - η)/N of pure CF3I and c-C4F8are shown in figures 3(a) and (b),respectively.Data obtained from experiments and other calculation methods [10,23–27]are listed in table 1 for comparison.According to table 1,for CF3I,the critical reduced electrical field strength (E/N)crof pure CF3I in our work is 432.7 Townsends (Td),approximately 1.22 times that of SF6,and similar to the results from the PT method,time-of-flight(TOF)method,and steady-state Townsend (SST) method.For c-C4F8,the (E/N)crof pure c-C4F8of is 406.2 Td,approximately 1.14 times that of SF6,and similar to the results from Monte Carlo simulation,and SST and PT methods.The calculated results in this paper are consistent with the experimental results.The microscopic discharge parameters in this paper are accurately solved with the use of the two-term Boltzmann equation under the current calculation conditions,and the results can be used for analysis of gas discharge processes with high reliability.

2.3.Synergistic effect

The electrical characteristics of insulating gas mixtures are often better than those of a single gas,owing to synergies between the gases.To compare and analyze the synergies of ternary gas mixtures more intuitively,a synergies factorSis introduced in this paper,defined as follows [11]:

whereUmixis the breakdown voltage of gas mixtures,ξiis the proportion of the gas in the gas mixtures,andUiis the breakdown voltage of a single gas in the gas mixtures.

Figure 3.Comparison of reduced effective ionization coefficients of pure gases:(a) CF3I;(b) c-C4F8.

Table 1.Comparison data of (E/N)cr of pure gases.

If ＞S0,the actual breakdown voltage of the gas mixtures is greater than the theoretical breakdown voltage,indicating that the gas mixtures have a synergistic effect or even a positive synergistic effect.A largerSvalue indicates a more pronounced synergistic effect.If=S0,there is no synergistic effect and the breakdown voltage of the gas mixtures varies linearly.If ＜S0,the gas mixtures have a negative synergistic effect(a Penning effect),which is relevant in the field of plasma applications.

3.Results and discussion

In this paper,the interactions between two strongly electronegative gases in ternary gas mixtures are studied,and the effect of the ratio of the strongly electronegative gas on the buffer gas is discussed.Hence,in the following the ratio of buffer gas is fixed.According to the requirements of the liquefaction temperature and insulation strength,the proportion of buffer gas is determined to be 70%,which generally meets the requirements for applications in power systems.A parameter=kiχ( c‐ C4F8) /(χ( c‐ C4F8) +χ(C F3I) +χ(b uffer gas))(i=1,buffer gas is N2;=i2,buffer gas is CO2)is used to represent the ratio of c-C4F8.The temperature is set at 300 K.

3.1.EEDF of gas mixtures

The EEDFs of CF3I/c-C4F8/70% N2and CF3I/c-C4F8/70%CO2gas mixtures at E/N=300 Td are shown in figure 4.Only slight differences between the EEDFs were observed,and when the electron energy was in the range of 0–1 eV,the number of low-energy electrons increased as the c-C4F8content increased and the CF3I content decreased.We attribute this phenomenon to c-C4F8having a stronger adsorption capacity and to many electrons being concentrated in the low energy region owing to absorption.Conversely,in the highenergy region,the curves of 0%and 30%are higher than any other curves.This result might be attributed to synergistic effects in the gas mixtures.Moreover,the curve of SF6is lower than other curves in the low-energy region but higher than other curves in the high-energy region,which indicates that the CF3I/c-C4F8gas mixtures are more electronegative than the SF6gas mixtures.

The EEDF values of CF3I/c-C4F8/70% N2and CF3I/c-C4F8/70% CO2having the same c-C4F8contents(0%,10%,20%,30%) are compared with 30% SF6/70% N2and 30% SF6/70% CO2,as shown in figure 5.The curves of CO2gas mixtures are lower than the curves of N2gas mixtures of the same proportion in the low-energy region.The reason for this is that the N2molecule has a large vibrational excitation cross-section in the low-energy region,and frequent excitation collisions decrease the kinetic energy of free electrons.Thus,CO2is more effective than N2in reducing electron energy in the high-energy region.

3.2.Electron transport parameters of gas mixtures

The reduced effective ionization coefficient (α - η)/N,critical reduced electrical field strength (E/N)cr,electric field sensitivity coefficient c,and electron drift velocity Vecan be determined from the EEDFs of gas mixtures.

Figure 4.The EEDF of CF3I/c-C4F8/70% N2 and CF3I/c-C4F8/70% CO2 gas mixtures at 300 Td.(a) CF3I/c-C4F8/70% N2,(b) CF3I/c-C4F8/70% CO2.

Figure 5.The comparison of EEDF of CF3I/c-C4F8/70% N2 and CF3I/c-C4F8/70% CO2 gas mixtures at 300 Td.

Figure 6.Relationship between effective ionization coefficient and E/N in CF3I/c-C4F8/70% N2 and CF3I/c-C4F8/70% CO2 gas mixtures at different ratio k.(a) CF3I/c-C4F8/70% N2;(b) CF3I/c-C4F8/70% CO2.

The relationship between the effective ionization coefficient and E/N in CF3I/c-C4F8/70% N2and CF3I/c-C4F8/70% CO2gas mixtures at different k ratios is shown in figure 6.With the increase of E/N,free electrons in the gas mixtures can obtain more energy under acceleration by an electric field.As a result,the probability of collision ionization increases and the effective ionization coefficient of the gas mixtures also increases.Research on binary gas mixtures[2]has shown that as the proportion of the strong electronegative gas in the gas mixtures increases (i.e.,giving stronger electronegativity of the gas mixtures),(α - η)/N decreases under the conditions of the same E/N.We apply this conclusion to analyze the data in the figures,and 30%SF6/70% N2gas mixtures show stronger electronegativity than CF3I/c-C4F8/70% N2gas mixtures,whereas CF3I/c-C4F8/70% CO2gas mixtures show stronger electronegativity than 30%SF6/70%N2when E/N is approximately 300–600 Td.

Figure 7.The relationship between (E/N)cr and the c-C4F8 content.

When the reduced effective ionization coefficient(α - η)/N=0,the reduced electrical field strength E/N is the critical reduced electrical field strength (E/N)cr.Figure 7 shows the relationship between (E/N)crand the content of c-C4F8.The(E/N)crof CF3I/c-C4F8/70%N2gas mixtures is higher than that of CF3I/c-C4F8/70%CO2,and the difference between these two gas mixtures gradually increases as the proportion of c-C4F8gas increases.Moreover,the (E/N)crof CF3I/c-C4F8/70% N2gas mixtures varies little as the proportion of c-C4F8changes,and is approximately 0.88 times that of 30%bSF6/70%bN2.When the c-C4F8content was 17%,the insulation strength of CF3I/c-C4F8/70%N2was the highest.Furthermore,CF3I/c-C4F8/70% CO2had excellent insulation performance.The (E/N)crof CF3I/c-C4F8/70%CO2was higher than that of 30% SF6/70% SF6for c-C4F8contents of less than 17%.

Table 2 lists values of the electric field sensitivity coefficient c of the CF3I/c-C4F8/70% N2and CF3I/c-C4F8/70%CO2gas mixtures.The electric field sensitivity of CF3I/c-C4F8/70% N2gas mixtures is lower than that of CF3I/c-C4F8/70% CO2gas mixtures,indicating that CF3I/c-C4F8/70% N2gas mixtures have excellent performance in terms of electric field sensitivity.Moreover,a higher content of c-C4F8promoted a lower sensitivity of the gas mixtures to an electric field.Compared with SF6gas mixtures,for CF3I/c-C4F8/70% N2gas mixtures at a c-C4F8content greater than 10%,the electric field sensitivity of the CF3I/c-C4F8/70% N2gas mixtures was higher than that of 30%SF6/70% N2gas mixtures (c=20.1 kV-1).For CF3I/c-C4F8/70% CO2gas mixtures,the electric field sensitivity of the CF3I/c-C4F8/70% CO2gas mixtures was higher than that of 30% SF6/70% CO2gas mixtures(c=28.6 kV-1) at all ratios.

The electron drift velocities Vein gas mixtures,as a function of E/N at different c-C4F8gas mixture ratios k,are given in figure 8.As for CF3I/c-C4F8/70% N2,the electron drift velocity of the gas mixtures of all ratios increased almost linearly as E/N increased.Conversely,as the ratio of c-C4F8increased the electron drift velocity rapidly decreased,particularly in areas where E/N was high.The reason for this is that when E/N is high,after intense collisions between electrons and molecules,the electron energy decreases and enters a region with a large adsorption area by CF3I and c-C4F8.This enhances the adsorption capacity of gas mixtures and weakens the drift motion of electrons in the electric field.Moreover,in the range of 300–900 Td,the electron drift velocity of 30% SF6/70% N2overlaps with that of 5%c-C4F8/25%CF3I/70%N2gas mixtures.For CF3I/c-C4F8/70%CO2gas mixtures,the electron drift velocity is discussed based on the three regimes.In the range of 100–250 Td,when the ratio of c-C4F8increases,the electron drift velocity slowly increases.A reversal occurs at approximately 250 Td.In the range of 300–900 Td,the electron drift velocity rapidly decreases as the ratio of c-C4F8increases.The curve of electron drift velocity of 30%SF6/70%CO2is between the electron drift velocity curves of 5% CF3I/25% c-C4F8/70% CO2and 10% CF3I/20%c-C4F8/70% CO2.

3.3.Synergistic effect of gas mixtures

The synergistic effect,as described by the factor S,increased in the ternary gas mixtures (E/N)cras the content of c-C4F8was increased.We studied the synergistic effects of ternary gas mixtures;hence,formula (4) is rewritten as:

whereξ1,ξ2,ξ3are the proportions of the three gases in the gas mixtures,andξ1+ξ2+ξ3=1,[(E/N)cr]1,[(E/N)cr]2,[(E/N)cr]3are the critical reduced electrical field strengths of the three single gases under the same conditions.(ξ1[ (E/N)cr]1+ξ2[(E/N)cr]2+ξ3[(E/N)cr]3) represents the theoretical critical reduced electrical field strength of the gas mixtures,calculated according to the weighting of the mixing proportion.The above equation calculates the synergy factor S of ternary gas mixtures.

Figure 9 shows the relationship between the synergy factor S and the c-C4F8content.The synergistic effect of CF3I/c-C4F8/70% CO2was much greater than that of CF3I/c-C4F8/70%N2when the c-C4F8content was less than 25%.Moreover,as the c-C4F8content increases,the gap of the synergy factors of the two gas mixtures decreased.Furthermore,the maximum synergy factor value of the CF3I/c-C4F8/70%N2gas mixtures occurred when the c-C4F8content was approximately 20%.The synergistic effect for CF3I/c-C4F8/70% CO2was most obvious when the c-C4F8content was approximately 10%.

Table 2.Values of electric field sensitivity coefficient c of gas mixtures.

Figure 8.Electron drift velocities Ve in gas mixtures as a function of E/N at different c-C4F8 gas mixture ratio k.(a) CF3I/c-C4F8/70%N2.(b) CF3I/c-C4F8/70% CO2.

3.4.Comparison of electron transport parameters

Table 3 includes a comparison of parameters of the gas mixtures.Taken together,for CF3I/c-C4F8/70% N2gas mixtures,when the content of c-C4F8is the 15%–20%range,the gas mixtures show the best insulation performance.However,for CF3I/c-C4F8/70% CO2,the gas mixtures have excellent performance when the c-C4F8content is 10%–15%.

Figure 9.The relationship between synergistic factor S and the c-C4F8 content.

4.Conclusions

In this paper,the insulating properties and synergistic effects of ternary gas mixtures CF3I/c-C4F8/N2and CF3I/c-C4F8/CO2were analyzed.The gas mixtures of c-C4F8and CF3I with ratios of 0%,5%,10%,15%,20%,25%,and 30%are calculated with the use of two-term approximation Boltzmann equations.

The main conclusions are as follows.

(1) The critical electric field strength(E/N)crof CF3I/c-C4F8/70% N2is 251.8 Td when the proportion of c-C4F8is 17%,which is the highest among the systems studied here.This value is approximately 0.89 times that of 30%SF6/70% N2.When the content of CF3I was higher than 17%,the CF3I/c-C4F8/70% CO2critical electric field strength was higher than that of 30% SF6/70% CO2.

(2) For electric field sensitivity,an increase of the content of c-C4F8decreased the sensitivity of the gas mixtures to the electric field.Moreover,the electric field sensitivities of the gas mixtures with N2buffer gas were lower than those with CO2.In terms of electron drift velocity,when the content of c-C4F8was greater than 5%,the electron velocity of CF3I/c-C4F8/70% N2was lower than that of 30%SF6/70% N2.For CF3I/c-C4F8/70% CO2,when the content of c-C4F8was greater than 10%,the electron drift velocity of CF3I/c-C4F8/70%CO2was lower than that of 30% SF6/70% CO2.

Table 3.Comparison of parameters of the gas mixtures.

(3) The synergistic effect of CF3I/c-C4F8/70% CO2was greater than that of CF3I/c-C4F8/70% N2when the CF3I content was greater than 5%.The synergistic effects for CF3I/c-C4F8/70% N2were most obvious when the c-C4F8content was approximately 20%,and for CF3I/c-C4F8/70% CO2when the c-C4F8content was approximately 10%.

In summary,in our studies of electron transport parameters and synergistic effects,CF3I/c-C4F8/70% N2shows the best insulation performance when the c-C4F8content is in the 15%–20% range.For CF3I/c-C4F8/70% CO2,when the c-C4F8content is 10%–15%,the gas mixtures have excellent performance.These gas systems might be potential alternatives to SF6as new insulating media.

Acknowledgments

This work is supported by National Natural Science Foundation of China (No.51337006).

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