Research and Analysis of Insulating Gas in Unified Test Conditions.

In order to study the insulation mechanism of SF6 substitute gas, it is suggested to calculate the dielectric strength of insulating gas from the molecular structure. The dielectric strength of a typical gas is modeled by a power frequency breakdown test under a uniform electric field. The molecular parameters of insulating gases are calculated by the density functional theory method, and the effect of molecular structure parameters on the breakdown voltage of power frequency is studied. Based on the molecular structure parameters, which are closely related to the breakdown voltage of power frequency, a model of pressure and distance variation of AC breakdown voltage of insulating gas is established. The breakdown voltages of insulating gases (CF3SO2F) are also derived from the proposed model. The calculated breakdown voltage of power frequency of two gases is compared with the experimental value. The average error is just 2.6%. This model provides a basis for the future search for potential alternative insulating gases.

Introduction

Sulfur hexafluoride (SF6) gas has been widely used in power equipment such as gas-insulated switchgear and gas-insulated transmission lines. It is an excellent insulator, with good arc extinguishing ability, stable chemical properties, nontoxicity, and noncorrosiveness.[1] However, due to the strong greenhouse effect of SF6, it is necessary to study alternative gases for SF6 because it is severely restricted under the “Paris Agreement”.[2,3] Typical alternative gases such as c-C4F8, CF3I, C4F7N, C5F10O, and C6F12O[4] and their mixed gases[5] all have the disadvantage of high liquefaction temperature. It is necessary to have a new method that would form the theoretical basis for experimental screening of alternative gases with better performance.[6]

Compared with SF6 gas, an alternative gas needs to meet basic requirements such as having a breakdown voltage higher than that of SF6 gas, a liquefaction temperature lower than that of SF6 gas, and GWP (global warming potential) lower than 5% of SF6 gas under the same conditions. AC breakdown voltage has the advantages of being intuitive and reliable and is an important indicator of the performance of gas insulation in the field of high voltage. Due to the variety of gases available, it is difficult to carry out exhaustive tests. Therefore, it would be useful to establish a simulation model of power frequency breakdown voltage based on the characteristic parameters of gas molecules, which can theoretically predict the power frequency breakdown voltage of insulating gases.

Meurice’s team[7] used density functional theory (DFT) to obtain a gaseous medium, the integrator optical spectra (IOA), in conjunction with electron energy loss spectroscopy. They analyzed the relationship between the dielectric strength of the insulating gas IOA. Olivet’s team[8] used the Austin model and parametric model to study the ionization process and adsorption process of nine insulating gases occurring in different energy bands and studied the electron energy affinity and ionization power of the gas medium’s quantitative relationship with dielectric strength. Franck of ETH Zurich[9−11] used a new procedure to systematically identify and quantify novel molecular gases with low global warming potential for application in high-voltage insulation. However, the prediction error of insulation strength of polar molecules was large. Rong et al.[12] used neural networks and random forests to predict the electrical strength and boiling temperature of the substitutes for greenhouse gases. However, they were unable to describe the breakdown voltage of environmentally friendly gas with the change of gas pressure and spacing. Based on the analysis of carrier collision process, Chen[13] selected five insulating gases with high replacement potential from 137 alternative gases. The effect of gas pressure on insulation strength was not considered.

Wang[14] used the molecular characteristics of the insulating gas as parameters based on density functional theory and regressed to obtain a structure–activity relationship model to determine the insulation strength of SF6 gas. Since the AC breakdown voltage of different insulating gases has a saturation point which increases with pressure, the breakdown voltage does not increase linearly with the increase of pressure. So the relative SF6 insulation strength is used to characterize the insulating ability of the gas, and AC breakdown voltage needs to be limited so that the saturation state is not reached when subject to change in a smaller gas pressure range.

This paper will carry out the power frequency discharge test of a typical insulating gas under a uniform electric field, which will be combined with the characteristics of the AC breakdown voltage of different insulating gases.[15] Then a power frequency based on molecular characteristic parameters considering the influence of pressure and distance (pd) will be established. The breakdown voltage calculation model analyzes the influencing mechanism of molecular characteristic parameters on the power frequency breakdown voltage. The reliability of the model is verified through experiments.

Test Setup and Method

Although many research teams in the world have conducted power frequency breakdown test research on insulating gas, the test results were not in good agreement due to inconsistent test conditions.[16−19]

Breakdown voltage is the main parameter to characterize the performance of gas insulation, but it is affected by various factors during experimental measurement, including electric field uniformity (f), gas pressure (p, Pa), electrode spacing (d, mm), etc. (the product of the p and d).

In relevant national standards[20] and IEC standards,[21] the high voltage test conditions were specified, and the unified test conditions were determined (the unified test conditions are a temperature of 293 K, a 60% relative humidity (RH), a ventilated and cool place with avoidance of direct sunlight).

Therefore, this paper will determine the AC breakdown voltage of the insulating gas through the AC breakdown test under a uniform electric field. This will help provide data for the establishment of the calculation model on AC breakdown voltage based on characteristic molecular parameters.

Test Setup

The schematic diagram of the test setup is shown in Figure . The finite element calculation software COMSOL was used to simulate and analyze the experimental cavity and the test electrode. The test electrode was a plate electrode with a diameter of 15 mm, and the electrode spacing was less than 10 mm. The electric field distribution between the electrodes was uniform. The analysis results show that test electrode and experimental cavity could be used for the power frequency breakdown test under a uniform electric field.

Figure 1

Schematic diagram of the test setup.

Electric field distribution under the plate electrode and schematic diagram of the test electrode.

In Figure , the resistance of the protective resistor was 50 kΩ. The highest output voltage of the transformer was 250 kV. The capacitive divider included two capacitors. The voltage ratio of the capacitor divider was 1015:1. The test chamber denotes the electrode inside the discharge chamber.

In the AC test platform, gas breakdown characteristics were studied. The schematic diagram of the test circuit and the parameters of the test equipment and chamber were detailed previously.[22,23] The laboratory ambient temperature was maintained at 20 °C. The electrode distance d was adjustable with a screw micrometer in the range of 0–10 mm.

According to the streamer theory, a sustained discharge is the result of spatial photoionization, not the ionization of the electrode surface. If the pd is large, the breakdown voltage is basically independent of the electrode material. The W–Cu electrode has good electrical conductivity, high hardness, and ablation resistance, which can be tested many times. Therefore, the W–Cu electrode is used. The test electrodes used in the experiment are shown in Figure .

Figure 3

Illustration of the test chamber.

Experiment Procedure

According to the power frequency breakdown test requirements specified in GB/T 16927.1-2011[20] and IEC60060,[21] the test steps are as follows.

After setting the electrode, close the cavity and evacuate the test cavity and the gas-filled pipe until the air pressure drops below 3 Pa.

Carry out the power frequency breakdown test 10–20 times and “burn-in” the electrode.

In the case of a laboratory temperature of 20 °C, fill the chamber with the gas to be tested, leave it to settle for 15 min, pump to 3 Pa with a vacuum pump, repeat three times, perform “washing”, and finally charge the gas to the test pressure. Let it stand for 15 min.

Increase the voltage to the level for the gas to breakdown according to the power frequency discharge voltage test procedure specified in GB/T 16927.1-2011, and record the test breakdown voltage value.

After completing the test of the pressure to be measured, elevate the test chamber to the next pressure and measure with a vacuum pump; repeat the above steps until the test is completed.

Test Result

With the above procedure, the power frequency breakdown test of SF6 gas was carried out under unified test conditions (temperature of 20 °C, 20–30% RH, plate electrodes, electrode spacing of 5 mm, and gas pressure of 0.1–0.5 MPa). The experimental value was compared for SF6 gas on the AC breakdown voltage with the reference value.[24−28] The comparison result is shown is Figure .

Figure 5

AC breakdown voltages of four typical gases under high saturated vapor pressure.

To verify against the results of the reference, the referenced value and the test value were put into formula to obtain the error between the two.

It can be seen from Figure , that the error between the effective value of the AC breakdown voltage of SF6 gas and the values reported in refs (25) and (26) under uniform test conditions was 3%. The test shows that the platform was reliable and can be used to perform power frequency breakdown of typical gases.

Figure 4

Comparison between SF6 gas test values and literature values.

The AC discharge voltage of nine typical gases under uniform electrical field test conditions was measured using the platform above. The relationship between pd (p is absolute pressure) and AC breakdown voltage was determined by adjusting the gas pressure and electrode spacing. First, the electrode spacing was fixed at 2.5 mm to obtain the AC breakdown voltage under different gas pressures. Then the electrode spacing was changed to 5 and 7.5 mm, and the above steps were repeated. Finally, the AC breakdown voltage corresponding to the Pd was determined, as shown in Figures and 7.

Figure 6

AC breakdown voltages of five typical gases (low saturated vapor pressure).

Figure 7

Correlation degree of influencing factors of gas molecular structure on insulation strength.

In Figures and 6, the gases were studied separately. The gas in Figure was a conventional gas. The saturated vapor pressure of the conventional gas was relatively high. The high-pressure test was performed under a fixed discharge gap (2.5/5/7.5 mm), and the pd value was 0.25–5.25 mm MPa. The gas in Figure had high insulation strength and is currently the gas with the most potential to replace SF6, but its saturated vapor pressure is small (for example, the saturated vapor pressure of C5F10O at 293.15K is 0.1 MPa). It was not possible to obtain a higher pd value in 7.5 mm electrode spacing (0.1 MPa × 7.5 mm = 0.75 mm MPa).

Through the AC breakdown test of the typical gases under uniform test conditions, the breakdown voltage of the typical gases was obtained. The calculation model of the insulating gases was established based on characteristic molecular parameters.

Calculation of AC Breakdown Voltage of Insulating Gas

Combining the power frequency breakdown test results under unified test conditions, and based on ref (14), research on the molecular structure parameters of insulating gases was carried out.

Molecular Feature Parameter Selection

The molecular structure parameters in refs (28−31) were used as a data set. These articles mainly analyzed the following structural parameters: molecular surface electrostatic potential PA, molecular volume Vm, highest occupied orbital energy EHOMO, lowest non-occupied orbital energy ELUMO, polarizability α, dipole moment μ, molecular surface area As, and molecular surface average statistical deviation stot2. Average deviation of the electrostatic potential on the molecular surface is π, with molecular energy Ev.[32]

Relevance analysis was a new factor analysis method in gray theory, which analyzes the degree of correlation between multiple factors by comparing the geometric relationship of the system statistics series. Gray relational analysis (GRA) is a measure of the correlation of two or more factors. The degree of correlation indicates the degree of mutual restraint and influence between the various factors that affect the development of something.[14] Through GRA analysis, the correlation degree γ0 of the influencing factors of the gas molecular structure parameters affecting the insulation strength were sorted and selected.

For the gas molecular parameter data sample, establish the gray incidence matrix.In the formula, x0 represents the reference sequence, x represents the comparison sequence, i = 1, 2, 3...n.

Initial sequence dimensionless processing.In the formula, represents the average value of the k-th point x(k) in each factor; x′(k) represents the dimensionless value of x(k) after initialization.

Find the difference sequence (absolute difference of each point).In the formula, Δ0(k) is the sum of absolute differences of points.

Calculate the weight of the comparison sequence relative to the reference sequence.

In the formula, minmin is the minimum value of the two poles, maxmax is the maximum value of the two poles, and ρ is the resolution coefficient; usually it is taken as 0.5. It is to prevent the absolute error value from being too large and the distortion to the difference between the correlation coefficients.[15] The value of γ0 is the degree of gray correlation, and γ is the weight of each factor.[16]

Through the above-mentioned GRA method, the correlation degree γ0 of the influence factors of the gas molecular structure parameters affecting the insulation strength, boiling point temperature, and GWP was calculated, and they were sorted as shown in Figure .

Figure 8

Procedure for the selection of molecular characteristic parameters and establishment of calculation model of power frequency breakdown voltage.

The four strongly correlated molecular characteristic parameters used to characterize the gas on AC breakdown voltage were obtained through the above correlation analysis. A is the total surface area of gas molecules; vσtot2 is the balance of positive and negative electrostatic potential and electrostatic potential of the product of the standard deviation; Π is the statistical average deviation of the electrostatic potential on the molecular surface, and Ev is the total energy of the molecule.

The relationship between the selection of molecular characteristic parameters and the calculation model of AC breakdown voltage is shown in Figure .

Model Building

Ten kinds of gas constituent elements were input into the molecular structure calculation software Gaussian 09W, and the visualization wave function software was Multiwfn. The molecular structure and molecular orbital data were calculated, and the molecular characteristic parameters are shown in Table .

Table 1

Molecular Structure Parameters of Insulating Gas and Effective Value of AC Breakdown Voltage

gas type	As (nm2)	vσtot2 (kJ/mol)2	Ev	Π (eV)	AC breakdown voltage (kV)	test maximum atmospheric pressure (MPa)
N2	0.542	44.973	109.1	0.173	13.9	0.7
SF6	1.034	0.140	995.2	0.733	36.7	0.7
N2O	0.666	182.831	187.9	0.430	16.8	0.7
C5F10O	1.725	300.214	1264	0.222	37.2	0.1
C2F6	1.118	3.519	673.3	0.144	26.6	0.4
CO2	0.545	94.462	184.6	0.261	15.1	0.7
C3F8	1.212	2.744	912.8	0.124	34.0	0.4
c-C4F8	1.472	5.602	915.2	0.241	33.8	0.2
SO2F2	0.922	186.140	764.2	0.383	23.5	0.2
CF4	0.811	4.219	436.2	0.175	16.2	0.7

Based on the molecular structure parameters and breakdown voltage data in Table , the structure–activity relationship model was obtained using a multivariate nonlinear fitting method, which is given in eq below.

Ub is the AC breakdown voltage of an insulating gas; As is the total surface area of gas molecules; vσtot2 is the balance of positive and negative electrostatic potential and electrostatic potential of the product of the standard deviation, Π is the statistical average deviation of the electrostatic potential on the molecular surface; Ev is the total energy of the molecule; p is the gas pressure of the insulating gas; d is the electrode spacing; A is the accelerated ionization capacity of the unit molecular surface area; B is the electron capacity (adsorption coefficient) captured by the molecule due to the imbalance of the electrostatic potential; C is the degree of symmetry due to the molecular structure, or the degree of difficulty of being ionized (ionization coefficient), and D is the coefficient to be determined.

We selected the same 10 kinds of insulating gases under unified test conditions, and the power frequency discharge voltage under pd of 0.5 mm MPa was calculated and is shown in Table .

The calculation flowchart is shown in Figure .

Figure 9

Flowchart of the calculation.

We used four gas characteristic molecular parameters as input into the AC breakdown voltage model (eq ). The undetermined coefficients of the AC breakdown voltage expression was obtained through the nonlinear least-square method. The undetermined coefficients of the power frequency discharge voltage calculation model under the conditions were A = 19.9384, B = 0.0557, C = −40.4732, D = 0.0128, and a = 1.2282.

Therefore, the expression of the AC breakdown voltage calculation model becomes

At pd = 0.5 mm MPa, it was found through curve fitting that the main factor affecting the AC breakdown voltage of the gas was the molecular structure of the gas itself. At 0.5 < pd < 1.5 mm MPa, the AC breakdown voltage of the gas was affected by the mean free stroke of the molecule and the molecular structure. In this case, the AC breakdown voltage of the gas exhibited an exponential increase with the increase of pd. At pd > 1.5 mm MPa, the AC breakdown voltage of gas was affected by the roughness of the electrode and other factors.[33−35] The AC breakdown voltage of gas increases with the increase of pd, but it no longer showed an exponential trend. Formula proposed in this paper is no longer applicable.

Reliability Analysis

Figure shows the comparison between the calculated and tested values of 10 insulating gases on AC breakdown voltage (N2, SF6, N2O, C5F10O, c-C4F8, C4F7N, C3F8, CO2, SO2F2, CF4). It can be observed from Figure that the calculated values of the insulating gas differed from the test values given in Table .

Figure 10

Deviation of calculated values and test values of insulating gas on AC breakdown voltage.

As can be seen from the above figure, R2 of the above model was 0.952 and the rms was 4.7 kV, indicating that the model had high accuracy.

The calculated and tested values of the AC breakdown voltage of insulating gases were evenly distributed on both sides of the 45° oblique symmetry axis. Therefore, the proposed calculation model can accurately reflect the AC breakdown voltage of the insulating gas under uniform test conditions. Low molecular weight gases (N2, CO2, N2O) present a high-frequency discharge coincidence between calculated and experimental values of voltage, with the deviation being 3.7%. However, the calculated value of C4F7N, C5F10O, and other gases with larger molecular weight deviated from the test value by 11.3%. The average free stroke of the macromolecular gas in the breakdown process was small, meaning that other factors had a significant impact on the AC breakdown voltage, such as electrode roughness, electrode flatness, etc. The small molecule gas has a large free stroke during the breakdown process, which may accumulate enough kinetic energy, weaken the influence of other factors, and result in smaller error between the test result and the calculation result. It can be seen from the figure that the calculated value of the power frequency discharge voltage of C4F7N gas had the largest deviation from the test value, but it was only 11.3%.

It can be seen from formula that the AC breakdown voltage of insulating gas was positively correlated with the total surface area of the molecule and the balance of positive and negative potentials. The larger the positive and negative potential of the molecular surface, the more work electrons need to overcome in the process of molecular collision, and the higher the gas discharge voltage.

Model Validation

Breakdown Voltage Verification of Elemental Gas

Two synthetic gases were considered to have the potential to replace SF6 (CF3SO2F[26]). According to reports,[26,35] the GWP values of these two gases are both less than 20% of SF6. Therefore, the gas has a stable presence in the atmosphere for less than 40 years, which is much lower than the 3400 years of SF6 gas. The liquefaction temperature of CF3SO2F gas at 0.1 MPa is −22 °C. These characteristics showed that these two gases are environmentally friendly gases.

In order to verify the accuracy of the calculation model, it is necessary to establish a molecular structure model. We used the molecular structure calculation software Gaussian 09W and the molecular visualization software Multiwfn to calculate the molecular characteristic parameters and molecular energy of CF3SO2F gas. The calculation results are shown in Table .

Table 2

Calculation Parameters of CF3SO2F Gas

gas type	As (nm2)	vσtot2 (kJ/mol)2	Π (eV)	Ev (au)
CF3SO2F	1.230	216.863	0.346	983.267

Formula was used to calculate the AC breakdown voltage of CF3SO2F gas, with the comparison diagram of the test value measured by our team,[27] as shown in Figure .

Figure 11

Effective value of AC breakdown voltage.

As can be seen from the above figure, the AC breakdown voltage of CF3SO2F gas shows a linear increase with the increase of pd. However, the AC breakdown voltage of CF3SO2F gas, relative to that of SF6 gas, shows a downward trend with increasing pd (in a uniform electric field, the power frequency voltage of CF3SO2F gas increases at a rate lower than that of SF6 gas with pressure and gap). The sensitivity of the gas to electric fields is slightly lower than that of SF6.

The deviation between the calculated value of the CF3SO2F gas AC discharge voltage and the test value was only 1.7%. At 0.5–0.7 mm MPa, the calculated value and the test value have a consistent upward trend, although there is a certain error between the calculated value and test value. The dispersion of the power frequency breakdown test and the calculated value is more in line with the increasing trend of the test value. At 0.7–1.5 mm MPa, it can be seen that the growth trend of the calculated value and the test value were relatively slow. The proposed method can predict the AC breakdown voltage of insulating gas more accurately.

Results and Discussion

In this paper, based on DFT and a multiple linear regression method, a calculation model of AC breakdown voltage of insulated gas using molecular characteristic parameters was proposed. The AC breakdown voltage test (condition) on the insulating gas was carried out for the purpose of verification. The calculation results were consistent with the test values. In summary, the following conclusions can be obtained.

The five main influencing parameters of As, vσtot2, Π, Ev, and pd were obtained, and the multivariate nonlinear model was used to implement the least-squares fitting. The obtained prediction model also conformed to the theoretical analysis result, and the fitting error was 2.6%.

An AC breakdown test platform was built. The AC breakdown test of CF3SO2F gas under uniform test conditions was consistent with the calculated results. The error was within 1.5 mm MPa, which is small, but it became excessive after 1.5 mm MPa. Therefore, this method was only suitable for pd values in the range of 0.5–1.5 mm MPa.

If parameters (the interaction force between molecules and their calculation methods) could be substituted into the calculation model for fitting, the accuracy of the calculation model will be further improved. Future research will be carried out to improve the prediction model and to search for new environmentally friendly insulating gas molecules.