# Experimental Research and Numerical Simulation of Single Soil-Arc-Grounding-Fault in Distribution Networks

Authors: Haoran Chen; Xin Lin; Guanhua Li; Jianyuan Xu; Hui Li; Shuai Wang
Journal: Wireless Communications and Mobile Computing
 (2021)

---

## Abstract

Among the distribution network faults, single-phase grounding faults have the greatest probability. The faults are often accompanied by arcs in the grounding point soil. This type of fault current has a small amplitude and seldom can obtain field record data. A soil arc grounding fault is tested on a realistic-distribution-network-experimental-platform (RDNEP), and it is concluded that the soil-arc-grounding-fault (SAGF) has three main characteristics: hysteresis, nonlinearity, and asymmetry. By comparing with the characteristics of common arc models, it is pointed out that common arc models cannot accurately fit the characteristics of SAGF. This paper proposes and establishes a double exponential function arc model. Through the comparison of simulation waveforms with experimental data, it is verified that the numerical simulation method proposed in this paper can simulate the development process of SAGF more accurately. Furthermore, the equivalence of RDNEP is verified on the real distribution network system (RDNS). On this basis, analyzed the arc characteristic changes of different SAGF development cycles. Finally, by studying the applicability of the proposed model in simulating ground faults in grass and gravel roads, it is verified that the model proposed in this paper has a strong generalization capability. The research has laid a theoretical foundation for a detection algorithm that is based on the characteristics of SAGF.


---

## Body

## 1. Introduction

Among the line faults in 10 kV distribution networks, single line-to-ground faults (SLGF) account for the majority. At the end of the grounding point, soil often does not have a good dispersion channel like a grounding grid. In the process of ground current dissipating at the grounding point, it is often accompanied with soil arc phenomenon that called this type of fault a SAGF. Compared with arc grounding faults (AGF), SAGF has some unique properties. With the deepening of the research on grounding faults identification in distribution networks, research on fault detection, fault type identification, and fault location based on the characteristics of grounding arc has gradually become a hot research direction. Therefore, the establishment of a mathematical model that accurately describes the characteristics of the SAGF is an important basis for studying related issues [1–3].For the simulation of single-phase arc-ground fault characteristics, the difficulty lies in accurately reproducing the dynamic changes in ground resistance, and this requires an accurate arc model. At present, the arc models used by scholars to study AGF in distribution networks are mainly black-box models that describe the external characteristics of the soil arc [1, 4]. The commonly used black-box models are basically based on the improvements of the Mayr model [5], Cassie Model [6], Schwarz model [7], and Cybernetic model [8], and all the above models are established based on the heat balance equation. Reference [9] established a model based on the Mayr series fixed resistance to simulate the arc high-resistance ground fault, but the method of obtaining the model parameters was not given. The arc model established in Reference [10] is based on the Cybernetic arc model series fixed resistance, but it also does not give how the arc parameters are obtained. Reference [11] is based on solid dielectric breakdown theory to model high-resistance ground fault nonlinear resistance, which is essentially a piecewise resistance model. . The models proposed in the above studies are all transplanted applications of the air arc model in the study of AGF.Shiller et al. has related descriptions of the causes of SAGF and the characteristics of current dynamic changes [12]. One of the characteristics is the nonlinear change of fault current from small to large during the development of the fault; another characteristic is the asymmetry of the positive and negative half-waves of the current. This characteristic description is not comprehensive. The arc experiment simulated the soil arc between the electrodes, not the SAGF caused by the wire falling on the soil surface.In order to describe the dynamic characteristics of the development of SAGF, there are currently two main solutions. One is achieved by using two DC sources connected antiparallel by means of two diodes, then series variable resistor. Two DC power supplies are set with different voltages to describe zero-rest characteristics, and variable impedance is used to describe the nonlinear characteristic of the development process [12–17]. Another solution is to use the arc model in the form of double variable resistance in series, one variable resistor is used to simulate the asymmetry of a single cycle, and the other variable resistor is used to simulate the nonlinear characteristic of the development process [18]. However, the characterization of the soil arc in the above research is not accurate.The SAGF fault current is generally small and difficult to be detected, and it is rarely possible to obtain the fault field recording data. In this paper, for establishing an accurate SAGF model, conducted a SAGF experiment on a RDNEP. Analyzing the characteristics of SAGF and comparing it with the characteristics of common arc models, it is pointed out that common arc models cannot accurately describe the characteristics of SAGF. On this basis, an idea of the diffusion channel of a SAGF is proposed and established a double exponential function soil arc model based on current density considering ionization and nonionization regions. By comparing the simulation waveform with the experimental data, it is verified that the SAGF numerical simulation method proposed in this paper can simulate the characteristics of soil arc more accurately. Furthermore, the equivalence of RDNEP is verified on the RDNS. On this basis, it analyzed the arc characteristic changes of different SAGF development cycles. At last, by studying the applicability of the model proposed in this paper in simulating grassland and stone road grounding faults, it is obtained that the model proposed in this paper has a strong general use ability. It laid a theoretical foundation for subsequent research on detection algorithms based on soil arc characteristics.


## 2. Experimental Work

An experiment has been performed to measure the characteristics of a SAGF. The experiment was carried out on the RDNEP built by China Electric Power Research Institute (CEPRI).


### 2.1. RDNEP Set Up

The RDNEP uses a 220/10 kV transformer as the platform power supply. The platform is equipped with four feeder lines, two 3.5 km true overhead lines, two 560 m cable lines, and capacitors are connected to each line to simulate a larger-scale distribution network. The end of the line is connected to the RLC adjustable load through a 10/0.4 kV transformer. A total of 80 measurement and control devices realize all-round detection of the distribution network status. All equipment site layout drawings and parameters are indicated in Appendix.


### 2.2. Experimental and Results

Simulate a streamlined distribution network structure on RDNEP, the topological structure is shown in Figure1. The platform consists of 4 feeders, 2 overhead line feeders, and 2 cable feeders. Three capacitors are connected to the end of cable Feeder1, the capacitance values C=0.64uF, respectively. Neutral point of the transformer is not grounded.Figure 1
Topological structure of testing power system.Place the faulty line on the surface of the soil ground through a piece of cable to simulate the state of the overhead line falling on the ground surface due to the fault, as shown in Figure2.Figure 2
Schematic diagram of the experimental.Figure3 shows the fault voltage and current waveforms at the grounding point when the fault occurs.Figure 3
Curve of voltage and current of a SAFG.The arc current has an obvious zero-rest at the zero crossings of each half-cycle; it is a standard arc discharge characteristic. A single cycle is selected for further analysis. The voltage and current curves of this cycle are shown in Figure4. The amplitude of the negative half circle current is obviously greater than the positive half circle, the voltage peak and current peak time are not synchronized, and the current peak phase lags the voltage peak phase.Figure 4
Single circle curve of voltage and current of a SAFG.Compared with air arc, SAFG has three main characteristics.(1)
Fault current phase lags behind voltage phase (hysteresis)(2)
The soil ionization rate is faster than the soil deionization rate (nonlinearity)(3)
The soil resistance of the negative half cycle is less than that of the positive half cycle (asymmetry)


## 2.1. RDNEP Set Up

The RDNEP uses a 220/10 kV transformer as the platform power supply. The platform is equipped with four feeder lines, two 3.5 km true overhead lines, two 560 m cable lines, and capacitors are connected to each line to simulate a larger-scale distribution network. The end of the line is connected to the RLC adjustable load through a 10/0.4 kV transformer. A total of 80 measurement and control devices realize all-round detection of the distribution network status. All equipment site layout drawings and parameters are indicated in Appendix.


## 2.2. Experimental and Results

Simulate a streamlined distribution network structure on RDNEP, the topological structure is shown in Figure1. The platform consists of 4 feeders, 2 overhead line feeders, and 2 cable feeders. Three capacitors are connected to the end of cable Feeder1, the capacitance values C=0.64uF, respectively. Neutral point of the transformer is not grounded.Figure 1
Topological structure of testing power system.Place the faulty line on the surface of the soil ground through a piece of cable to simulate the state of the overhead line falling on the ground surface due to the fault, as shown in Figure2.Figure 2
Schematic diagram of the experimental.Figure3 shows the fault voltage and current waveforms at the grounding point when the fault occurs.Figure 3
Curve of voltage and current of a SAFG.The arc current has an obvious zero-rest at the zero crossings of each half-cycle; it is a standard arc discharge characteristic. A single cycle is selected for further analysis. The voltage and current curves of this cycle are shown in Figure4. The amplitude of the negative half circle current is obviously greater than the positive half circle, the voltage peak and current peak time are not synchronized, and the current peak phase lags the voltage peak phase.Figure 4
Single circle curve of voltage and current of a SAFG.Compared with air arc, SAFG has three main characteristics.(1)
Fault current phase lags behind voltage phase (hysteresis)(2)
The soil ionization rate is faster than the soil deionization rate (nonlinearity)(3)
The soil resistance of the negative half cycle is less than that of the positive half cycle (asymmetry)


## 3. Results Analysis

The commonly used arc models can only partially simulate SAFG characteristics and compare the V/A characteristics of some ground fault models and SAFG, including Cassie arc model [6], Cassie series fixed-resistance model, and high resistance grounding fault nonlinear resistance model based on solid dielectric breakdown theory (SDBHGF) [11]. All parameters are set for simulated test conditions.


### 3.1. Cassie Series Fixed-Resistance Arc Model

The Cassie arc model was proposed in 1939, and it considers the convection heat dissipation effect of the arc model. It is assumed that the energy dissipated from the electrode and the energy diffusion caused by the arc column change process can be ignored, and as the energy changes, the larger the arc column cross-sectional area, the greater the energy diffusion speed. Equation (1) is its mathematical model.
(1)1gdgdt=dlngdt=1τcE2Ec2−1,whereg is the conductance of the arc; t is the time; τc is time constant; E is the electric potential per unit length of the arc, and Ec is the potential gradient constant. As in (1), when the voltage exceeds a certain threshold, the arc ignites, and conductance increases exponentially; when the voltage decreases to reach the electric field strength E=Ec, the arc is in a steady state.Figure5 is the V/A characteristic curve when Cassie is connected in series with resistors. Due to the linear resistance, the voltage and current basically reach the maximum at the same time, and this does not match the hysteresis characteristic of SAFG. Before the current (or voltage) crosses the zero points, the V/A characteristic is mainly affected by the linear resistance, the linearity is basically maintained, and this does not match the nonlinearity characteristic. And obviously, the positive and negative half-waves of this kind of models are symmetrical.Figure 5
V/A characteristics of arc in serial with resistance.


### 3.2. SDBHGF Model

The SDBHGF model is based on the principle of electrical breakdown of solid media. The conductance of a solid medium is mainly divided into ionic conductance and electronic conductance. When the external electric field is low, it is mainly the ionic conductance that plays a role. At this period, the voltage and current are in a linear relationship. When the electric field gradually increases, within a certain range, the ion conductance still plays a major role, but the voltage and current show an exponential relationship. As the electric field continues to increase and exceeds a certain limit, the electronic conductance starts to take effect. At this period, the voltage and current are still in an exponential relationship, but the conductance value is already large, and the equivalent resistance value is small. The model is divided into 3 sections, as in the following equation.(2)g=g1∣u∣<u1,2k1∣u∣+k2u1<∣u∣<u2,g2∣u∣>u2.The voltage and current of the SDBHGF model will reach the maximum at the same time, and it cannot simulate the nonlinearity and asymmetry of SAGF as shown in Figure6.Figure 6
V/A characteristics of SDBHGF.Therefore, none of the abovementioned commonly used arc ground fault models can fully reflect the characteristics of SAGF, and the characteristic quantities of ground fault detection methods proposed based on the above models may fail when identifying a SAGF.


## 3.1. Cassie Series Fixed-Resistance Arc Model

The Cassie arc model was proposed in 1939, and it considers the convection heat dissipation effect of the arc model. It is assumed that the energy dissipated from the electrode and the energy diffusion caused by the arc column change process can be ignored, and as the energy changes, the larger the arc column cross-sectional area, the greater the energy diffusion speed. Equation (1) is its mathematical model.
(1)1gdgdt=dlngdt=1τcE2Ec2−1,whereg is the conductance of the arc; t is the time; τc is time constant; E is the electric potential per unit length of the arc, and Ec is the potential gradient constant. As in (1), when the voltage exceeds a certain threshold, the arc ignites, and conductance increases exponentially; when the voltage decreases to reach the electric field strength E=Ec, the arc is in a steady state.Figure5 is the V/A characteristic curve when Cassie is connected in series with resistors. Due to the linear resistance, the voltage and current basically reach the maximum at the same time, and this does not match the hysteresis characteristic of SAFG. Before the current (or voltage) crosses the zero points, the V/A characteristic is mainly affected by the linear resistance, the linearity is basically maintained, and this does not match the nonlinearity characteristic. And obviously, the positive and negative half-waves of this kind of models are symmetrical.Figure 5
V/A characteristics of arc in serial with resistance.


## 3.2. SDBHGF Model

The SDBHGF model is based on the principle of electrical breakdown of solid media. The conductance of a solid medium is mainly divided into ionic conductance and electronic conductance. When the external electric field is low, it is mainly the ionic conductance that plays a role. At this period, the voltage and current are in a linear relationship. When the electric field gradually increases, within a certain range, the ion conductance still plays a major role, but the voltage and current show an exponential relationship. As the electric field continues to increase and exceeds a certain limit, the electronic conductance starts to take effect. At this period, the voltage and current are still in an exponential relationship, but the conductance value is already large, and the equivalent resistance value is small. The model is divided into 3 sections, as in the following equation.(2)g=g1∣u∣<u1,2k1∣u∣+k2u1<∣u∣<u2,g2∣u∣>u2.The voltage and current of the SDBHGF model will reach the maximum at the same time, and it cannot simulate the nonlinearity and asymmetry of SAGF as shown in Figure6.Figure 6
V/A characteristics of SDBHGF.Therefore, none of the abovementioned commonly used arc ground fault models can fully reflect the characteristics of SAGF, and the characteristic quantities of ground fault detection methods proposed based on the above models may fail when identifying a SAGF.


## 4. SAGF Model

The essence of the SAGF model is a variable grounding resistance, which is used to describe the process of resistance change during the arc from ignition to extinction. Figure7 depicts a schematic diagram of the current and impedance changes for a complete arc development cycle. A ~ B and D ~ E stage for the arc zero rest stage, and B ~ D for the arc from ignition to extinguish the process. The arcing period, from t1−t2, is the most critical, called soil ionization period, and other moments are called the arc extinguishing period.Figure 7
Schematic diagram of SAGF resistance.As observed by the SiO2 crystal after the test in Figure 8, the ionization zone radius is about 0.015 m, and the depth is about 0.15 m when the upper and lower parts are added together.Figure 8
SiO2 crystals after single-phase soil arc test.When the energy density of the injected current exceeds the critical value, soil ionization will occur. As the injected current increases, its resistivity is much lower than the initial resistivity of the soil. After the soil is ionized, a large amount of heat is generated. The soil in the ionization zone will be molten, and SiO2 will be precipitated. After the test, the soil near the grounding point is excavated and sampled. The cooled SiO2 crystal is almost cylindrical and perpendicular to the ground surface. The ionization current dispersion channel is cylindrical, as shown in Figure 9. A cylindrical shape with the grounding point as the center, radius r0, and depth ℓ, at the bottom of the cylinder is a hemisphere with radius r0. Set this area as the ionization area. When the energy density of the injected current exceeds the critical value in this area, soil ionization will occur and soil properties will change. Outside the ionization zone is a nonionization zone. In this area, the soil is affected by the ionization heat effect, and the resistivity changes dynamically during the ground fault process.Figure 9
Schematic diagram of SAGF dispersion channel.Set the basic assumptions for the established soil arc model. Because the SAGF current is small, as observed in Figure9, it is considered that the fault occurs in the shallow surface of the soil. It is assumed that the soil properties are uniform, that is, the resistivity of the soil in all directions and the result of the injection current. The resistivity change curve is consistent.When the current density is greater than the critical value, the soil is ionized, and the soil resistivity decreases rapidly as the degree of ionization increases. This change state changes exponentially with the current density, as shown in (3).
(3)ρ1=ρ0expjτ1,whereρ1 is the soil resistivity in the ionization zone, ρ0 is the soil resistivity in the ionization zone when the current density j=0, τ1 is the current density constant of the ionization process, and the current density is a function of current.
(4)j=iπr2,wherer is the radial distance of the ionization zone, and the resistance of the ionization zone can be expressed as the following equation.
(5)R1=ρ1r+ℓ.The resistivity change in the nonionized zone is mainly affected by the heat released by the ionization of the soil. The soil resistivity gradually increases as the temperature rises. The current density in the ionized zone is used to characterize the temperature change. The changing state also changes exponentially with time, as shown in (6).
(6)ρ2=ρgexpjτ2,whereρ2 is the soil resistivity in the nonionized zone, ρg is the initial soil resistivity in the non-ionized zone, and τ2 is the temperature conductivity.The differential equation of soil resistance in the nonionized zone is shown in the following equation.(7)dR=ρ2dr2πr2+rℓ=ρ2dr2πℓ1r−1r+ℓ.Integrate both sides.(8)R=ρ22πℓlnr+ℓr∞r0.Asr⟶∞,lnr+ℓ/r⟶ln1=0, the resistance of the nonionization zone is as in the following equation.
(9)R2=ρ22πℓlnr0+ℓr0.The actual grounding resistance of the soil in the grounding process is the sum of the resistance of the ionization zone and the resistance of the nonionization zone, as shown in the following equation.(10)R=R1+R2=ρ1r+l+ρ22πℓlnr0+ℓr0,whereR is SAGF resistance during ionization.The above description is the arc mathematical model of the soil ionization stage. The ionization process and the deionization process take the moment of the maximum current density as the dividing point. The soil deionization process is similar to the ionization process, but the parameters are different. The ionization process of the negative half cycle is similar to the deionization process, but the current densityj is negative, and the current density constant τ1 and temperature conductivity τ2 are opposite to the ionization process.When the current densityj is less than the critical value jc, the soil does not undergo ionization and is in the arc extinguishing stage. At this period, the soil as a whole presents the characteristics of high resistance. The resistance R=R0=5000Ω is used to simulate this high resistance state. The SAFG resistance model can be described as the following equation.
(11)R=R0=5000Ωj<jc,R=R1+R2=ρ1r+l+ρ22πℓlnr0+ℓr0j≥jc.


## 5. SAGF Numerical Simulation

In the model, seven parameters need to be determined, the radius of the ionization zoner0, the depth of the ionization zone ℓ, the soil resistivity ρ0 at the current density j=0 of the ionization zone, the current density constant of the ionization process τ1, the initial soil resistivity of the non-ionization zone ρg, the temperature conductivity coefficient τ2, and the ionization criticality current density jc.In this test, a lot of heat is generated after the soil is ionized, the soil will be in a molten state, and SiO2 will be precipitated. After the test, the soil near the grounding point is excavated and sampled. The ionization zone radius is about 0.015 m, and the depth is about 0.15 m. Set the ionization zone parameters r0=0.015m, ℓ=0.15m.The positive half-cycle grounding resistance of the soil ionization stage is fitted with the model proposed in this paper, the characteristic curve of the fault resistance is corresponding to the current density, and the resistance change curve of the ionization zone and the resistance change curve of the nonionization zone of the model are obtained, as shown in Figures10 and 11.Figure 10
SAGF positive half-circle ionization process.Figure 11
SAGF positive half-circle deionization process.In Figure10, the grounding resistance curve functions as the following equation.
(12)R=2112⋅e−j/1822+951⋅e−j/18885.The parameters of the positive half-wave ionization process are thus obtained.ρ0=348Ω⋅m, ρg=373Ω⋅m, τ1=−1822A/m2, and τ2=−18885A/m2.The deionization process is shown in Figure12, and the grounding resistance curve functions as follows.
(13)R=1297⋅e−j/2792+557⋅e−j/54704.Figure 12
SAGF negative half-circle ionization process.Therefore,ρ0=214Ω⋅m, ρg=219Ω⋅m, τ1=−2792A/m2, and τ2=−54704A/m2.Similar to the positive half cycle, the negative half cycle resistance characteristic of the soil ionization stage is shown in Figures12 and 13.Figure 13
SAGF negative half-circle deionization process.In the same way, the comparison table of positive and negative half-wave model parameters is shown in Table1.Table 1
Samples of times roman type sizes and styles.
ParameterPositive half-wave ionization processPositive half-wave deionization processNegative half-wave ionization processNegative half-wave deionization processInitial soil resistivity in ionization zoneρ0/Ωm348214773183Initial soil resistivity in nonionized zoneρg/Ωm373219398100Current density constant of ionization processτ1/A/m2-1822-279266003747Temperature conductivityτ2/A/m2-18885-547041868149652Due to the minimum precision voltage and current measurement problem in this experiment, the measured voltage and current data are reliable only when the ground currenti>1A. Set the critical current density jc=1/πr02=1415A/m2.Using the above parameters, the arc model proposed in this paper is simulated using PSCAD, and the simulated waveform is compared with the voltage/current obtained in the experiment, as shown in Figures14 and 15.Figure 14
SAGF voltage and current comparison.Figure 15
SAGF V/A characteristic comparison.The comparison between the simulated waveform and the experimental waveform verifies that the SAGF model proposed in this paper can simulate the development process of the soil arc more accurately, reflecting the characteristics of hysteresis, nonlinearity, and asymmetry of the soil arc. Therefore, the SAGF model is more suitable for describing the SAGF than the commonly used arc models.


## 6. Real Distribution Network Verification

Considering that RDNEP is a realistic distribution network system, in order to verify the credibility of the results measured on the RDNEP, a SAGF was also simulated on a RDNS. The grid structure is shown in Figure16. There are two buses. The bus I runs with 6 feeders. The end of one feeder is used as a grounding point to simulate a SAGF. The bus II runs with 5 feeders, and the system capacitance current is 68 A. In the experiment described in this article, the neutral point is grounded through the arc suppression coil to compensate the inductive current of 47 A, and the theoretical residual current capacity is 21 A.Figure 16
Schematic diagram of electrical wiring of test circuit.A 10 kV overhead line ground fault simulation platform is built at the end of the fault simulation feeder, including 10 kV circuit breaker K1, grounding switch T1/T2, low voltage circuit breaker K2 (replaced with 10 kV pole-mounted circuit breaker), 10/0.4 kV transformer (capacity 400kVA), and 10 kV drop-out fuse The specific wiring method is shown in Figure17.Figure 17
Schematic diagram of ground fault simulation platform.Similar to the RDNEP test, the faulty line is placed on the ground surface through a flat copper wire to simulate the state of the overhead line falling on the ground surface due to a fault. Grounding point after a SAGF test is shown in Figure18. After the fault occurs, the fault phase voltage and the current waveform through the grounding point are measured, as shown in Figure 19.Figure 18
Grounding point after a SAGF test.Figure 19
Curve of voltage and current of a SAFG.In Figure20, compare V/A characteristics with the RDNEP test. It can be seen that although the V/A characteristic shapes are slightly different, they all satisfy the three soil arc properties mentioned above.Figure 20
Compare of RDNEP test and RDNS test.Using the arc waveform measured by the RDNS platform, the parameters of the arc model proposed in this paper are fitted and compared with the RDNEP platform, as shown in Table2. In order to express clearly and reduce the description, the initial resistivity of the ionization zone in the positive half-cycle ionization process is abbreviated as ρ0pii, and the initial resistivity of the ionization zone in the positive half-cycle deionization process is abbreviated as ρ0pdi. Other parameters follow such naming rules.Table 2
SAFG model on RDNEP compared with RDNS.
ParameterRDNEPRDNSρ0pii/Ωm348226ρgpin/Ωm373294τ1pii/A/m2-1822-3245τ2pin/A/m2-18885-28918ρ0pdi/Ωm214176ρgpdn/Ωm219153τ1pdi/A/m2-2792-5527τ2pdn/A/m2-54704-57971ρ0nii/Ωm773491ρgnin/Ωm398236τ1nii/A/m266003302τ2nin/A/m21868133367ρ0ndi/Ωm183314ρgndn/Ωm100143τ1ndi/A/m237473747τ2ndn/A/m24965249652Considering that the soil environment of the RDNEP test and the RDNS test are different, and the fault current is also different, the error of its parameters is acceptable. This proves that the constructed RDNEP can approximate a RDNS, and the SAGF carried out on the RDNEP is also credible. Indirectly prove the rationality of the SAGF model proposed in this article.


## 7. Time-Based Development of a SAFG

SAGF is an arc behavior that will not self-extinguish. It will develop dynamically over time, and the development process depends on the soil environment around the fault point.Compare the arc current curves of the 8th, 20th, and 50th cycles in the RDNEP test, as shown in Figure21, and the V/A characteristics of different cycles as shown in Figure 22.Figure 21
Different cycles current curve of a SAFG.Figure 22
Different cycles V/A characteristic of a SAFG.As can be seen from the graph, the ionization process of the earth arc becomes faster and faster as time progresses, zero rest time becomes longer, and the deionization speed is basically the same. The waveforms of all cycles conform to the 3 properties of SAGF.For further comparison, the parameter changes of SAGF models of different periods are shown in Table3.Table 3
Comparison of model parameters in different circles.
Parameter8th20th50thρ0pii/Ωm348837495ρgpin/Ωm373574426τ1pii/A/m2-1822-966-1597τ2pin/A/m2-18885-12178-16906ρ0pdi/Ωm214249622ρgpdn/Ωm219221276τ1pdi/A/m2-2792-2691-751τ2pdn/A/m2-54704-60790-31766ρ0nii/Ωm77313504177ρgnin/Ωm398536545τ1nii/A/m26600606371τ2nin/A/m2186811381913466ρ0ndi/Ωm183260219ρgndn/Ωm100242240τ1ndi/A/m2374718002168τ2ndn/A/m2496523614042016Comparing the soil arc parameters of different circles, the following conclusions can be drawn.(1)
The initial soil resistivity in the ionization zone has a large change, while the change of initial soil resistivity in the nonionization zone is little(2)
With the development of time, the current density constant of the ionization zoneτ1 will rapidly decrease, which means that the ionization speed becomes faster(3)
The temperature conductivity in the nonionization zoneτ2 is basically unchanged, which proves that the soil arc and the heat exchange effect of the nonionization zone are dominant, and the soil properties have not changed(4)
One feature that cannot be reflected in the parameters is that the zero rest time of the arc current is longer


## 8. SAGF Model for General Use

SAGF, as an arc model that specifically refers to the soil, has limited application scope. We hope to develop a general model to describe various forms of high impedance arc grounding faults (HIAF). Therefore, it is necessary to assess the general ability of the SAGF model proposed in this article. The grounding fault through grassland and fault through stone roads is simulated on RDNEP. The test site is shown in Figures23 and 24.Figure 23
Grounding fault through grassland.Figure 24
Grounding fault through stone road.Although the above two types of faults are all time-dependent developmental, a typical cycle of each type of faults is selected for analysis in this article. The single circle fault current of the two types is shown in Figure25.Figure 25
Fault current curves of different grounding media.Using the SAGF model proposed in this article, the curve fitting is consistent with the method described above, the fitting of SAGF models for each fault is shown in Figures26 and 27.Figure 26
Fitting of SAGF model for grassland grounding fault.Figure 27
Fitting of SAGF model for stone road grounding fault.The above fitting curve proves that the SAGF model is also suitable for soil-like grounding media. The HIAF with the arc characteristics proposed in this paper can be approximated by SAGF.


## 9. Conclusion

By simulating a SAGF on RDNEP, this paper concludes that the soil arc ground fault has three main characteristics: hysteresis, nonlinearity, and asymmetry. It is pointed out that common arc models are difficult to accurately describe the characteristics of soil arc. On this basis, the idea of dissipating current channels for soil-associated arcs is proposed, and a double exponential function soil arc model based on current density considering ionization and nonionization regions is proposed. Through the comparison of simulation waveforms with experimental data, with the simulation of SAGF on a RDNS, it is jointly verified that the SAGF numerical simulation method proposed in this paper can simulate the characteristics of soil arc more accurately. On this basis, by adjusting the model parameters, the entire development process of a single-phase soil arc ground fault can be simulated. Furthermore, by studying the applicability of the model proposed in this paper in simulating grassland and stone road grounding faults, it is obtained that the model proposed in this paper has a strong general use ability. The work in this paper laid a theoretical foundation for subsequent research on detection algorithms based on soil arc characteristics.



---

*Source: 1875068-2021-11-05.xml*