Hybrid numerical simulation of the generation and distribution characteristics of SF₆ heavy particles under different DC PD energies Open Access

Direct current (DC) SF₆ gas-insulated switchgear (GIS) has been widely used in power systems and related industries.^1,2 Some insulation defects will occur inevitably inside the entire life cycle of SF₆ GIS. These insulation defects can gradually evolve into insulation faults during operation, thereby leading to severe accidents, such as power outages.³ Complex decomposition components for insulation faults will occur under SF₆ PD. Characteristic decomposition components, such as SO₂, SOF₂, and SO₂F₂, are often used to diagnose fault types and judge the severity of faults.^4,5 They depend on the formation of low-fluorine sulfides. Therefore, studying the behavior of low-fluorine sulfides has a great reference value for explaining the PD law and the decomposition of SF₆.

Due to lack of corresponding experimental methods, numerical simulation is one of the few effective ways to study the process of SF₆ PD at the microscopic level.⁶ Graves and Jensen⁷ used a fluid dynamics model to simulate the DC and RF discharges at low pressure. Passchier and Goedheer⁸ established a one-dimensional fluid model to study the air PD of a parallel-plate. Boeuf and Pitchford⁹ proposed a two-dimensional fluid model in line with the actual air discharge conditions to study the characteristics of RF glow discharge. The motion behavior of electrons and ions in the cathode sheath region in air discharge was simulated. Liu et al.¹⁰ and Wu^11,12 proposed a fluid-chemical kinetic model under air PD. The correctness of the simulation model was verified with Antao’s experimental data.¹³ Chen et al.^14,15 also proposed a fluid-chemical model by considering 61 kinds of collision reactions that involve electrons to study the formation mechanism of Trichel pulses of a air corona cage. Therefore, the numerical simulation studies mainly focus on the discharge of air and inert gas, whereas studies on the SF₆ PD numerical simulation are relatively few. Liu and Raju¹⁶ used the Monte Carlo model to study the stream formation and development in SF₆. The electric field in the discharge region was calculated by the Poisson equation. Babaeva and Naidis¹⁷ simulated the stepped propagation of SF₆ positive streamers considering the influence factors, such as heat and gas expansion. Dhali and Pal¹⁸ and Ilaş et al.¹⁹ proposed a fluid dynamics model of SF₆ streamer discharge. For the established model that did not include a chemical reaction model, the generation law of particles in the SF₆ streamer discharge was not studied. Mao et al.²⁰ constructed a SF₆ hybrid plasma model, including 98 chemical reactions, to study the inductively coupled plasma discharge (ICP). Kokkoris²¹ considered 50 chemical reactions of SF₆ and established an integrated model of SF₆ plasma to study the SF₆ ICP. However, clear difference in the form of discharge exists between ICP and PD. Our team studied the electronic properties in a single PD systematically.⁶ However, cations and anions play an essential role in the development of PD. Heavy particles (e.g., cations, anions, and neutral particles) are also crucial to the formation of SF₆ decomposition characteristic components. The behavior of heavy particles in the micro process of PD remains unclear. The study of the relationship among different discharge energies and SF₆ decomposition characteristics is the basis for establishing online monitoring and the fault diagnosis of electrical insulation equipment based on SF₆ decomposition characteristics under PD. Consequently, carrying out the study on the generation and distribution properties of SF₆ decomposition heavy particles under different negative DC PD energy is necessary.

Given that the simulation can obtain the micro details that cannot be obtained by the experiment, we attempt to simulate the discharge process accurately to study the generation and distribution mechanisms of low fluoride sulfides in the PD process. Based on the construction of an SF₆ PD hybrid numerical model and the SF₆ PD decomposition experimental platform, the influence of discharge energy on SF₆ PD characteristic quantities (e.g., discharge current and single discharge energy) and SF₆ decomposition products are studied with simulation and experiment.

The electron density control equation is described as²² 

where n_e is the electron number density. S_α, S_η, and S₀ are the impact ionization term, the adsorption reaction term, and the initial term of electrons, respectively. $E⃗$ is the electric field; μ_e and D_e are the electron mobility and diffusion coefficient, respectively.

The electron energy conservation equation is

where S_ε is the energy source term and n_ɛ is the density of the electron energy. D_ε and μ_ε are the diffusion coefficient and mobility of electron energy, respectively.

The continuity equation of heavy particles can be expressed as²³ 

where $Γk⃗$ is the heavy particles flux. R_k is the rate of change in species k. D_k and μ_k are the diffusion coefficient and ion mobility of heavy particle, respectively. n_k is the number density of species k.

The potential distribution equation that describes the discharge process is

where ɛ_r and ɛ₀ are the relative dielectric constant and the vacuum dielectric constant, respectively; φ is the electric potential; and n_p, n_n, and n_e are number density of the cation, anion, and electron, respectively.

Previous research of our team^6,24,25 found that the generation of SF and S in PD of metal protrusion defect need not be studied. The number of final produced SFx mainly depends on the first ionization of SF₆ under PD.²⁶ Therefore, 14 particle species (e.g., e, SF₆, SF₅, SF₄, SF₃, SF₂, $SF6+$⁠, $SF5+$⁠, $SF3+$⁠, $SF4+$⁠, $SF2+$⁠, F, F⁻, and $SF6−$⁠) are considered, and 24 chemical reactions are involved in the plasma chemical reaction model.^20,25,27,28 

Elastic collision:

Collision ionization:

Attachment reaction:

Recombination:

The reaction rate k(ɛ) of R1–R8 is calculated by using the following equation:

where σ is the cross section of reaction. f(ɛ) is the electron energy distribution function.²⁹ 

The adopted metal protrusion model is presented in Fig. 1. Considering that the calculation of the three-dimensional (3D) model is complicated and the metal protrusion model is a two-dimensional (2D) axisymmetric structure, the 3D model is simplified into a 2D-axisymmetric model in this paper, which not only facilitates the calculation amount but also ensures that the simulation information is consistent with the 3D model. The critical boundary conditions are expressed as follows:

The flux boundary conditions for the electron and ion at the electrodes are given by^10,14 

where $Γe⃗$⁠, $Γ⃗i$⁠, and $Γ⃗s$ are the electron flux, ion, and neutral species flux, respectively. M_e, m_i, and m_s are the mass of electrons, ions, and neutral species, respectively. γ_p is the secondary electron emission coefficient. T_e is the electron temperature. T_k is the temperature of heavy particles,³⁰ which can be simplified into T_k = 300 K. n_i and n_s are the number density of ion and neutral species, respectively. μ_i are the mobility of ions. When the electric field is directed away from the electrode, a = 0. Otherwise, a = 1.

The boundary condition of electron energy is listed as

where $Γ⃗ε$ is the electron energy flux.

Given that obtaining the microscopic features of DC discharge through experiment is difficult, the PD current pulse waveform and the curves of applied voltage–current (V–I) obtained by experiment are used to verify the correctness of the DC PC hybrid numerical model.⁶ 

The test wiring diagram of SF₆ PD current pulse measurement under negative DC is shown in Fig. 2. An adjustable transformer provides the AC high voltage. The AC high voltage is converted by a half-wave rectifier circuit composed of a high-voltage silicon stack D (100 kV/5 A) and filter capacitor C₁ (0.2 µF). R₁ (10 kΩ) and R₂ (20 kΩ) are the protection resistors. The capacitive voltage divider C_d and the resistance voltage divider R_d are used to measure the voltage values of AC and DC, respectively. A non-inductive detection impedance R (50 Ω) converts the PD current signal into a voltage signal, which is displayed and stored by the digital storage oscilloscope (DSO). The SF₆ PD gas chamber is a 60 L stainless steel tank that can withstand a pressure of up to 1 MPa.

The actual needle-plate electrode defect model is made according to the structure size shown in Fig. 1. The specific experimental steps are detailed as follows:

1. The needle-plate electrode defect is installed in the chamber. The vacuuming and injecting of new SF₆ gas are repeated three times to exhaust different kinds of impurity gas as much as possible.

2. Fresh SF₆ gas is injected into the cleaned chamber to 0.3 MPa, and it is stabilized for several hours to diffuse SF₆ evenly.

3. The applied voltage is gradually increasing to the setting value. An oscilloscope is used to record the PD voltage waveform.

The SF₆ PD hybrid numerical model has a high degree of nonlinearity because it consists of many partial differential equations, which makes it possible to obtain only short-term transient results.¹¹ However, the simulation results are sufficient for studying the transient distribution of SF₆ decomposition heavy particles under negative DC PD. A single-current pulse waveform of SF₆ negative DC PD by simulation and experiment when a DC voltage of −13.5 kV is applied under 0.3 MPa is drawn in Fig. 3, which are almost the same in the current pulse width and all shows a rapid rise and slow fall process. Furthermore, the PD discharge current at different voltages under 0.3 MPa is studied by simulation (−11.5, −12, −12.5, −13, and −13.5 kV) and experiments (−12.5, −13, and −13.5 kV). The relationship between applied voltage and the peak value of the PD current is shown in Fig. 4, which shows that the peak value of the PD current increases exponentially with the applied voltage. The simulation data of the applied voltage–current characteristics show good agreement with that of the experiment. Therefore, the validity of the proposed hybrid mathematical model can be confirmed with the above findings.

The relationship between the simulated single discharge energy and the applied voltage is shown in Fig. 5, which illustrated that the single discharge energy also increases exponentially with the applied voltage. The simulation results are basically consistent with the relationship of the current amplitude and discharge energy with applied voltage obtained by Liu³¹ under air PD.

The formulas of the maximum of PD current I_max (A) and single discharge energy W_one (J) with the applied voltage U (kV) are obtained by exponential function fitting, as shown in Eqs. (35) and (36). The fitting degrees R² of the I_max and W_one with U are high, thereby indicating that the derived mathematical formulas can explain their relationship,

When the PD current pulse reaches the maximum value, the variation curves of the electric field intensity and the average electron energy on the symmetry axis with the applied voltage are depicted in Fig. 6.

Figure 6 indicates that the electric field intensity increases as the applied voltage rises at the axial distance of ∼4.97–5 mm because the higher the applied voltage is, the greater the electric field strength will be. The electric field intensity between ∼4.79 and 4.97 mm decreases with the increase in applied voltage. The anion clouds generated by the adsorption reaction gradually moves toward the plate electrode (anode), which will weaken the field strength. With the increase in applied voltage, the amount of anion increases. The electric field intensity will be weaker. The electric field intensity at the axial distance of nearly 0–4.79 mm increases with the applied voltage. On the one hand, the higher the applied voltage is, the more anions are generated, which strengthens the electric field strength between the anion clouds and the plate electrode (anode). On the other hand, the higher the applied voltage is, the greater the electric field strength will be.

Figure 6(b) illustrates that the relationship between the average electron energy and the applied voltage is basically consistent with the relationship between the electric field intensity and the applied voltage. The reason is that the simulation is carried out under the same gas pressure, and the particle number density N in each group is the same. Thus, the reduced electric field E/N is a constant multiple of the electric field intensity E. Furthermore, the reduced electric field is positively correlated with the average electron energy.⁶ In addition, Fig. 6(b) shows that the average electron energy near the tip (4.79–5 mm) of the discharge is in the average energy range (5–10 eV) of the SF₆ PD discharge region indicated by Chu,³² which also confirms the correctness of the simulation.

The net charge distribution is the reflection of all macroscopic charged particles in the PD region, from which the microscopic process of SF₆ PD and the area distribution of ionization and transfer can be clearly determined. Distributions of net charge density at five typical moments (Fig. 3) are shown in Fig. 7 when a DC voltage of −13.5 kV is applied under 0.3 MPa, which shows that most of the discharge area of SF₆ is neutral, and the cation clouds only exist in the ionosphere. Therefore, concluding that the SF₆ discharge decomposition is mainly concentrated in the range of 4.79–5 mm is not difficult with the distribution of average electron energy and cations. Specifically, we have the following:

1. At the initial discharge stage (t₁), the net charge density in the needle-plate gap is very low. The equivalent resistance of the entire gas chamber is large, and the current pulse at the initial stage of discharge is close to zero.

2. With the PD continuing to develop (t₁–t₃), a strong distortion electric field is observed near the needle electrode (within 0.2 mm from the needle tip), which causes many collision ionization and adsorption reactions. Moreover, many cations and negative particles are rapidly produced in the gap. The cation clouds formed by SF₆ PD will strengthen the electric field between cathodes, whereas the electric field between the cation clouds and anion clouds is weakened and that between the anion clouds and the anode is strengthened. After enhancing the electric field in the ionization zone, the ionization avalanche increases. During this period, the cation clouds gradually reach the surface of the cathode, and charge exchange occurs [Eq. (35)], which causes the PD current pulse to increase rapidly. The charge density of the cation clouds and the current pulse reach the maximum simultaneously at t₃,

   $SFx+→SFx.$

   (37)

   During this period, the anion clouds continued to move toward the anode and became divergent. However, as the collision ionization and adsorption reactions continue, the peak density is still increasing.

   The negatively charged particles in air PD are mainly electrons, and no layering of cation and anion clouds occurs, which makes the duration of a single discharge very short.³³ Given that SF₆ has a strong electronegativity, the negatively charged particles in PD are mainly anions (Table I). The migration speed of anions and cations under the action of an electric field is slower than that of electrons, which can be separated from each other and form a long-lasting ion cloud with obvious stratification. This phenomenon makes the SF₆ discharge pulse width one order of magnitude larger than that of the air PD discharge.

3. From t₃ to t₅, the cations gradually reach the cathode and disappear through Eq. (35), whose density gradually decreases. The increase in the anion clouds makes the electric field of the ionization zone drop below the threshold. The adsorption reaction continues, and the number of anions is not increasing. Thus, the ionization process is stopped quickly. From the perspective of the PD current pulse, a current pulse rises rapidly and then falls quickly.

4. At t₆, the cations have almost disappeared. The negative plasma gradually diverges toward the anode, and its density gradually decreases.

The main reactions at the five typical moments are presented in Table II. R1 is an elastic collision reaction between electrons and SF₆ molecules, which exists in the whole discharge process. R1 does not generate new particles so that it does not contribute to the development of the discharge process. R2, R3, and R8 all exist in the main discharge period (t₂–t₄), which are the most important reactions that affect the SF₆ discharge process. R2 and R3 are the main reactions of electron proliferation, which are related to the formation of $SF6+$ and $SF5+$⁠, respectively. R8 is the primary reaction of electron disappearance related to the formation of $SF6−$⁠. Among the five typical moments, the number of main reactions at t₂ is the largest, indicating that the SF₆ discharges most violently during the rising edge of the discharge pulse. During the falling edge of the discharge pulse (t₃ and t₄), the number of main reactions gradually decreases, indicating that the SF₆ discharge intensity gradually decreases.

The formation of SF₆ characteristic components, such as SOF₂ and SO₂F₂, are generated by the reaction of low fluoride sulfides with impurities, such as trace moisture and trace oxygen in the gas chamber, which mainly depends on the formation of low fluoride sulfides. Thus, studying the generation process and law of low fluoride sulfides under different discharge energies is of great significance.

At the end of the discharge (1 × 10⁻⁶ s), the amount of cations, neutral particles, and anions generated in the simulation area at different discharge energies are shown in Table III. It shows minimal difference in the amount of generated cations among different discharge energies. Although more cations are generated in the discharge process with the increase in discharge energy, most of the cations have gradually disappeared on the surface of the needle electrode (cathode) at the end of a single discharge. Therefore, the amount of cations is very small.

The amount relationship of neutral particles is SF₅ > SF₃ > SF₄ > SF₂. R3, R4, R5, and R6 are electron impact ionization reactions to generate $SF5+$⁠, $SF4+$⁠, $SF3+$⁠, and $SF2+$⁠, respectively. The reaction rate relationship is R3 > R5 > R4 > R6. SF₅, SF₃, SF₄, and SF₂ are generated by $SF5+$⁠, $SF3+$⁠, $SF4+$⁠, and $SF2+$ through surface reactions R28, R30, R29, and R31, respectively. Therefore, the amount of generated neutral particles will show the relationship of SF₅ > SF₃ > SF₄ > SF₂. Furthermore, the generation amount of $SF5+$ and $SF6+$ is an order of magnitude larger than those of other cations.

With the rise of discharge energy, the amount of generated anions also increases rapidly. The amount of generated $SF6−$ is much larger than those of other generated particles, which is different from air PD. In air PD, cations have an absolute advantage in quantity compared with the generated anions. Because it is difficult for O₂ molecules to capture fast electrons and form anions, the concentration of anions is two orders of magnitude lower than that of cations.

Charged cations $SF5+$⁠, $SF4+$⁠, $SF3+$⁠, and $SF2+$ and uncharged neutral particles SF₅, SF₄, SF₃, and SF₂ are all the low fluorine sulfides. The amount of total low fluorine sulfide n[SF_x] is defined as follows:

where $n(SFx+)$ is the amount of cations, and n(SF_x) is the amount of neutral particles.

Given that the ratio method can avoid the influence of volume effect on fault diagnosis, it has been widely used in power equipment fault diagnosis. Three characteristic ratios of c(SO₂F₂)/c(SOF₂+SO₂), c(CF₄+CO₂)/c(SO₂F₂+SOF₂ + SO₂), and c(CF₄)/c(CO₂) are often used to diagnose insulation defects^4,24 in SF₆ gas insulated equipment. c(SO₂F₂)/c(SOF₂ + SO₂) is the characteristic ratio of SF₆ decomposition components. SOF₂ is mainly formed by the reaction of [SF₄] with H₂O. SO₂F₂ can be formed by the reaction of [SF₂] with O₂, which is traditionally considered the main reaction path.³⁴ Moreover, it can also be generated by the hydrolysis of SOF₄, which is formed by [SF₅], [SF₄], and [OH], [O], which is traditionally considered the unimportance path because it is a secondary reaction. SO₂ usually comes from the hydrolysis reaction of SOF₂ and H₂O. The relationship between c(SO₂F₂)/c(SOF₂+SO₂) and discharge energy can be indirectly reflected by simulating the relationship among n([SF₅])/n([SF₄]), n([SF₂])/n([SF₄]), and discharge energy.

The characteristic ratios of low fluorine sulfide obtained by simulation are shown in Fig. 8, which shows that the characteristic ratio n([SF₅])/n([SF₄]) increases with the discharge energy, whereas the characteristic ratio n([SF₂])/n([SF₄]) decreases with the increase in discharge energy. This finding indicates that with the increase in discharge energy, the amount of low fluorine sulfide with higher fluorine content will be greater.

To obtain the relationship between the characteristic ratio c(SO₂F₂)/c(SOF₂ + SO₂) and the discharge energy, the SF₆ PD decomposition experiment is carried out on the basis of the experimental platform and steps in Sec. III under 0.3 MPa. Furthermore, we have the following:

1. To ensure that the trace moisture and oxygen content in the gas chamber meet the requirements of DL/T596-2005 and those in each of experiments are consistent, the GE600 Dew Point Instrument and the GPR-1200 Micro-oxygen Analyzer Instrument are used to detect the trace moisture and trace oxygen.

2. A long period of PD needs to be performed for accurately detecting the change trend of SF₆ decomposition. The needle electrode used in the simulation is too sharp and will become dull during the long-term application of high voltage, which will affect the generation of components. To grasp the influence of discharge energy on the ratio of SF₆ decomposition components, it is advisable to adopt a defect model that the curvature radius of the needle electrode tip is about 0.3 mm, and the needle plate spacing is 10 mm.

3. To ensure the accuracy of the experiment, the ambient temperature of the laboratory is controlled at about 25 °C.

4. The PD decomposition test is carried out for 96 h in each experiments. The SF₆ discharge decomposition sample gas is collected and quantitatively detected by GC/MS.

Five applied voltages selected in this paper are 47, 57, 67, 74, and 79 kV to carry out experiments, and the corresponding average single discharge energies are 1.7 × 510⁻⁶, 3.39 × 10⁻⁶, 5.19 × 10⁻⁶, 7.28 × 10⁻⁶, and 9.63 × 10⁻⁶, respectively. The concentrations of SO₂F₂, SOF₂, and SO₂ are obtained through GC/MS under different PD discharge energies. The variation curve of characteristic component ratio c(SO₂F₂)/c(SOF₂ + SO₂) with average single discharge energy is given in Fig. 9.

Figure 9 depicts c(SO₂F₂)/c(SOF₂ + SO₂) increases with the average single discharge energy (Fig. 9),²⁴ which can be used to characterize the severity of fault development and whose change trend is only consistent with the trend of the low fluoride sulfide ratio n([SF₅])/n([SF₄]). Therefore, it is not difficult to conclude that the generation of SO₂F₂ under PD is mainly carried out by the secondary hydrolysis of SOF₄, and the reaction path of [SF₂] direct reaction with O₂ to generate SO₂F₂ is secondary. The main reason why c(SO₂F₂)/c(SOF₂ + SO₂) can be used as the energy characteristic component ratio is that it can represent low-fluorine sulfide ratio n([SF₅])/n([SF₄]).

A hybrid numerical model of SF₆ negative DC PD is presented in this paper, and the correctness of the model is verified through experiment. Based on the hybrid numerical model, the variation of PD characteristic quantity and particles generation with single PD energy is studied. Combined with the SF₆ negative DC PD experiment platform, the correlation characteristics between discharge energy and SF₆ decomposition characteristic components under different discharge energy are studied. Some conclusions are drawn as follows:

1. The single discharge energy and the peak value of PD current all increase exponentially with the applied voltage.

2. With the increase in applied voltage, the electric field intensity of the needle plate gap does not increase completely and even decreases in some areas for the influence of the generated anions.

3. Most of the discharge area of SF₆ is neutral, and the cation clouds only exists in the ionosphere. Combining with the average electron energy and the distribution of the cation cloud, it can be concluded that the SF₆ discharge decomposition is mainly concentrated in the range of 4.79–5 mm.

4. The SF₆ discharge pulse width is one order of magnitude larger than that of the air PD discharge because the negatively charged particles in SF₆ PD are mainly anions, whereas those in air PD are electrons whose migration speed is faster than that of anions.

5. R2 and R3 are the main reactions of electron proliferation, which is related to the formation of $SF6+$ and $SF5+$⁠, respectively. R8 is the primary reaction of electron disappearance, which is related to the formation of $SF6−$⁠. The generation amount of $SF6−$ is an order of magnitude larger than that of other anions, which is different from air PD. In air PD, cations have an absolute advantage in quantity compared with the generated anions. Moreover, SF₆ discharges most violently during the rising edge of the discharge pulse.

6. Different from traditional opinion, the generation of SO₂F₂ under PD is mainly generated by the hydrolysis reaction of SOF₄, which is formed by [SF₅], [SF₄], and [OH], [O], and the reaction path of [SF₂] with O₂ is not important. Thus, c(SO₂F₂)/c(SOF₂ + SO₂) can be used as the energy characteristic component ratio because of its ability to represent the low-fluorine sulfide ratio n([SF₅])/n([SF₄]).

This work was supported by the National Natural Science Foundation of China (Grant No. 51707011).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.