Novel arc suppression method for single-phase grounding fault considering line voltage drop

The existing active-type voltage arc suppression methods do not consider the influence of line voltage drop, which leads to the existence of large fault residual current at the fault point for low-resistance grounding fault occurring in the distribution network and affects the reliable extinguishing of the fault arc. In this paper, an active inverter is used to inject a compensating current to the neutral point of the system before and after the fault, and the distance between the fault point and the bus is calculated, then the reference value of the neutral point voltage which controls the fault point voltage to zero can be obtained. A double closed-loop control strategy of current inner loop and voltage outer loop is used to track the voltage reference value. The simulation results show that the proposed method is independent of the exact zero-sequence admittance value, and not only has a good arc suppression effect under different fault conditions, but also can effectively suppress the harmonic components of the fault current.


Introduction
The operation of modern distribution network is complex and changeable, and single-phase grounding faults occur frequently, of which about 70% are transient arc grounding faults [1].Quickly extinguishing the arc caused by the fault, suppressing the fault current and the fault point voltage can effectively prevent the transient fault from developing into the permanent fault, improve the reliability of the power supply, and protect the safety of the equipment and personnel [2,3].
In order to realize the reliable extinction of the fault arc, many scholars have done a lot of researches.Existing arc suppression methods can be classified into passive arc suppression method and active arc suppression method according to the presence or absence of an external injection device [4,5].Arc suppression coil (ASC) and transfer arc suppression (TAS) are two representatives of passive arc suppression method.The fault capacitive current can be compensated by the inductive reactive current generated by the ASC after the fault, but the ASC has no effect on active and harmonic components of the fault current, and the compensation effect is greatly affected by the measurement accuracy of the zero-sequence admittance parameters of the system.In addition, the ASC also has some disadvantages, such as slow inductance adjustment speed, easy to cause system resonance and so on [6][7][8].The TAS can suppress the voltage at the fault point by directly grounding the fault phase at the bus after the fault.However, this method is greatly affected by the load, when a long-distance, small transition resistance fault occurs on a heavy-load line, the fault current of using the TAS may be larger than that of not using it [9][10][11].At the same time, the TAS is also affected by the fault phase selection, the wrong phase selection cannot restrain the arc, but will make the fault worse [12].
According to the different control objectives, active arc suppression methods can be divided into active current-type arc suppression methods (ACAS) and active voltage-type arc suppression methods (AVAS) [13].The ACAS obtains the injection current according to the distribution network parameters, it has good performance in low-resistance fault and is not affected by line impedance and load current.However, due to the difficulty in getting accurate distribution network parameters, it is difficult to achieve full compensation of the fault current [14,15].The AVAS can prevent the arc from reigniting and extinguish the arc completely by regulating the voltage at the fault point.In [16][17][18][19], the neutral point voltage is adjusted to the negative fault phase supply voltage by the closed-loop control to clamp the fault point voltage.However, these methods only make the voltage at the bus of the fault phase equal to zero and ignore the voltage drop between the fault point and the bus, its arc suppression ability cannot meet the operation requirements such as low-resistance faults.Considering the influence of the line impedance, the variation trend of fault current under different transition resistance is analyzed in [20], it is proved that only controlling the voltage of the fault phase at the bus to 0 cannot achieve 100% arc suppression.In [21], the TAS is put into immediately after the fault occurs, according to the fault information, the values of the transition resistance and the fault distance can be obtained, and then decides whether to consider the influence of the line voltage drop in terms of the value of the transition resistance.However, this method still has the possibility of increasing the fault current after being put into the TAS.In [22], the fault distance is calculated step by step according to the set step length, and then the optimal neutral point voltage target value can be determined.However, this method has the defect of requiring a long time for arc suppression.In [23], the neutral point voltage for full fault current compensation is derived, and the influence of load current on line voltage drop is eliminated by using the current before and after the fault, but the control strategy is not explained.
Aiming at the problems of the above methods, a novel active voltage-type arc suppression method considering line voltage drop (AVAS-CLVD) is proposed.Before and after the fault, an active inverter is used to inject a current from the neutral point of the system, and the fault distance can be estimated by combining with the zero-sequence network of the system in each state, and then the neutral voltage reference value which can control the fault point voltage to zero is determined.The double closed-loop control strategy is used to control the neutral point voltage equal to the target reference value for arc suppression.Simulation results show that the proposed method has high precision in fault distance calculation and has a good suppression effect on both fundamental and harmonic components, which verifies the correctness and effectiveness of the proposed method.The rest of this paper is organized as follows.In Sect.2, the traditional active voltage-type arc suppression regardless of line voltage drop (AVAS-RLVD) is analyzed.The AVAS-CLVD is proposed in Sect.3, and its principle, fault distance error and the whole operation flow are introduced in detail.In Sect.4, the double closed-loop control strategy of the proposed arc suppression method is introduced, and the setting method of control parameters is discussed.Simulation analysis is carried out by using MATLAB/Simulink to verify the arc suppression effect of the proposed arc suppression method in Sect. 5.

Performance analysis of traditional active voltage-type arc suppression
The arc suppression schematic diagram of the distribution network is shown in Fig. 1, where Ė A , ĖB , ĖC are the threephase power supply voltages, UN is the neutral voltage.The distribution network model has n lines, Y xy (x = A, B, C, y = 1, 2, 3…n) represents the zero-sequence admittance corresponding to the x phase of line y.A single-phase active inverter is used to inject a controllable current İi into the neutral point for arc suppression, U DC is the voltage at the dc side of the inverter, L 0 and C 0 are the inductor and capacitor connected to the output filters of the inverter, respectively.T 0 is the main transformer, T S is the isolation transformer, and T Z is the grounding transformer.Assuming that the single-phase ground fault occurs in phase A of the line n, in which UmA and İmA are the voltage and current measured at the beginning of the fault line, respectively, İf is the fault current, İLA is the load current of the fault phase of the fault line, Z is the line impedance per unit length of the fault line, which is also a complex quantity, The impedances in the following text are also complex quantities, which are explained here.l is the distance from the bus to the fault point, R f is the grounding transition resistance.The AVAS-RLVD generally ignores the influence of the line impedance and approximately considers the voltage at the beginning of the fault line to be equal to the voltage at  1, the active injection device is equivalent to a current source, and the equivalent circuit diagram can be obtained as shown in Fig. 2.
According to Fig. 2, using the node-voltage method, (1) can be obtained: where Y A , Y B , Y C are the zero-sequence admittance of the three phases of the system, and Assuming that the three-phase power supply is symmetric, that is, ĖA + ĖB + ĖC = 0, and there is UN + ĖA = Uf , then (1) can be abbreviated as: If the neutral point voltage is controlled according to (3): as a result, the voltage of the fault point can be suppressed to zero, then the condition of maintaining the burning arc would be destroyed, and finally the reliable arc suppression can be realized.At this time, the current injected by the inverter is: In actual operation, due to the existence of line impedance, there will be a line voltage drop U from the bus to the fault point.When the system is controlled by (3), the voltage at the fault point is not locked to zero, and residual current will still flow through the fault branch, which is likely to affect the safe and reliable extinguishing of the arc.According to Fig. 1, U can be expressed as: where İmA1 , İmA2 , İmA0 are the positive, negative, and zerosequence components of İmA , respectively.Z + , Z − , Z 0 are the positive, negative, and zero-sequence components of the impedance per unit length of the fault line, respectively, and in general Z + = Z − , then (5) can be written as: If the voltage at the neutral point is still controlled as (3), then the voltage at the fault point is: The residual current İf at the fault point is: For a single-phase grounding fault, the fault boundary condition is İf1 = İf2 = İf0 , İf1 , İf2 , İf0 are the positive, negative, and zero-sequence components of İf , then the fault current can be expressed as: According to the distribution network model, the zerosequence equivalent network is shown in Fig. 3.where Uf0 is the zero-sequence component of the voltage at the fault point,Z 0 S is the comprehensive zero-sequence impedance of the system behind the exit of the fault line, Z 0 n is the comprehensive zero-sequence impedance of the system behind the fault point.In the process of fault arc suppression, Z 0 S and Z 0 n remain basically unchanged, then using the knowledge of electricians, (10) can be obtained. Let ) can be abbreviated as: Combining ( 4), ( 8), ( 9), (11) and the current relationship İmA = İLA + İf , ( 12) can be obtained by eliminating İmA and İmA0 .
According to (12), load, fault distance and transition resistance all affect the residual current of the fault point after the action of the AVAS-RLVD.Changing the above three variables, the fault current change diagram can be obtained, as shown in Fig. 4.
It can be seen from Fig. 4 that the AVAS-RLVD has good arc suppression performance under high-resistance grounding faults and can suppress the fault current to zero, but under low-resistance grounding faults, the fault point will still be a very large residual current, the arc suppression effect is not ideal.At the same time, the farther the fault point is from the bus and the heavier the load, the greater the fault current will be.In severe cases, it may exceed the fault current before the arc suppression equipment is put into use.

Principle analysis of the arc suppression method
In order to extinguish the fault arc reliably, the influence of the line voltage drop cannot be ignored, so the reference value of the neutral point voltage needs to be revised.When the neutral point voltage is regulated according to (13), the fault point voltage can be suppressed to zero, and the fault current at this time is correspondingly reduced to zero.
If the influence of the harmonic component is also taken into account, (13) needs to be further revised.
In the above formulas, only l is an unknown quantity.If the fault distance can be estimated, then Uref can be determined.Combined with the active inverter injection device, a new fault distance estimation method is proposed in this paper.

Fault distance calculation
When the power system is running normally, a small current İi1 is injected into the system by the active inverter at a certain time interval.The selection of this current should avoid causing excessive neutral point voltage offset.After injecting the small current, the neutral point voltage UN1 and the zero-sequence current İmA01 at the beginning of the fault line can be obtained, and the total zero-sequence admittance Y of the system can be roughly estimated according to (15).
In this operating state, the system does not contain the fault component, and the zero-sequence equivalent network and current equation are shown in Fig. 5a and (16), respectively.
When a single-phase grounding fault occurs, but the active inverter is not put into operation, the zero-sequence equivalent network of the system is shown in Fig. 5b, and the corresponding current equation is as follows: where İ mA0 and İ f0 are the zero-sequence currents at the beginning of the fault line and the fault point, respectively, under the fault state.
According to the voltage relationship and the fault boundary conditions, the voltage U mA of the fault phase at the bus can be expressed as: After a few cycles of the fault, the active inverter is used to inject an initial compensation current İi2 into the distribution 5 Equivalent zero-sequence circuit of distribution network a normal state b fault state c state of injected current after the fault network.In order to meet the need of the safe operation of the distribution network, the injection current can be selected according to İi2 = − ĖA Y .In this operating state, the zero-sequence currents at the beginning of the fault line and the fault point are İ mA0 and İ f0 , respectively.The zerosequence equivalent network is shown in Fig. 5c, and the corresponding current relationship is as follows: At this time, the voltage U mA of the fault phase at the bus is: By substituting ( 16) into (20) and eliminating K 2 , (21) can be obtained.
Combining ( 18) and ( 21) to eliminate K 1 R f , the formula for calculating l can be obtained. where In addition, considering the existence of phase-to-phase capacitance and phase-to-ground capacitance, İmA and İmA0 will change along the line, so the average value of the current between the bus and the fault point is selected when using (13) to calculate the neutral point reference voltage.The average value of İmA can be obtained by subtracting the average value of the phase-to-phase capacitive current from the measured value at the beginning of the fault line.The average value of İmA0 can be obtained by subtracting the average value of the phase-to-ground capacitive current from the measured value at the beginning of the fault line.

Fault distance error analysis
In practice, due to the influence of factors such as measurement errors of electrical quantities and distribution parameters, there will be a certain error between the calculation result of the fault distance and the actual fault distance, which may affect the arc suppression effect, so it is necessary to analyze the maximum fault distance error of reliable arc suppression.
Generally speaking, the voltage drop U on the line after a single-phase grounding fault does not exceed 5% of the supply voltage.For a distribution network with a voltage level of 10 kV, the maximum voltage drop on the line is 0.5 kV.
Assuming that the line voltage drop is evenly distributed along the line, and the full length of the line is l * , in order to ensure the reliable extinguishment of the arc, it is necessary to suppress the current after the fault below the threshold 5A, the maximum allowable error l of the fault distance is as follows.
For the 10 kV distribution network model built in this paper, the length of the fault line is 10 km, according to (23), l = 0.1R f can be obtained, that is, the allowable error of fault distance calculation is proportional to the transition Fig. 6 Flowchart of the arc suppression method resistance.The larger the transition resistance, the stronger the ability of the arc suppression method to withstand the fault distance error.Even for a low-resistance ground fault with a size of 10 , the fault distance can still guarantee a margin of at least 1 km.

Control flow of the arc suppression method
The flowchart of the active voltage-type arc suppression method considering the line voltage drop is shown in Fig. 6.
Continuously measuring the zero-sequence voltage of the system and the three-phase current of each outgoing line to detect whether a single-phase grounding fault occurs.When the system is running normally, use the active inverter to inject a small current into the system every set time interval, record the zero-sequence voltage of the system and the zerosequence current at the beginning of each line, then use (15) to estimate the zero-sequence admittance.When a single-phase grounding fault is detected, measure and record the voltage of the fault phase at the bus, the current and the zero-sequence current of the grounded phase at the beginning of the fault line before and after the active inverter is put into operation.Subsequently, calculate l according to (22) and substitute it into (13) to obtain Uref , and then adjust the operating state  the distribution network side, İh is the equivalent harmonic current source on the distribution network side.The parameters of the distribution network and inverter are selected according to Table 1.
Ignoring the influence of Ėeq and İh , according to Fig. 8, the open-loop transfer function of voltage outer loop is as (24).
In order to ensure the stability of the system, the gain of the current inner loop proportional controller should not exceed L 0 f S /G INV [17], so let G P = 0.06.If G PRU = 1, substitute the data in Table 1 into (24) to obtain the Bode diagram of the open-loop transfer function of the system without adding the quasi-PR, as shown in Fig. 9.
It can be seen that the phase margin of the open-loop transfer function is 36.7°,which is within the range of 30°~60°F ig. 10 Bode diagram of open-loop transfer function with the quasi-PR controller required to ensure the stability of the control system.However, the cutoff frequency of the system and the gain at the fundamental frequency are too small, and further regulation is required to reduce the steady-state error and improve the harmonic output capability.
A quasi-PR controller is introduced to achieve accurate tracking of the output voltage to the reference voltage and achieve no static error control.The transfer function is as shown in (25).
where K P , K R , ω i are the proportional coefficient, resonance coefficient and resonance cutoff frequency of the quasi-PR controller, respectively, ω 0 is the resonance point of the quasi-PR controller, and the value is 100π rad/s.Increasing K P can improve the proportional gain of the system, but the ability to resist high-frequency interference will be reduced; Increasing K R will increase the cutoff frequency and the gain near the resonance point, but the phase margin will decrease, which will affect the system stability; ω i not only affects the bandwidth of the cutoff frequency, but also affects the gain of the controller, and is positively correlated with both.Considering the above influence relationships, taking K P = 6, K R = 200, ω i = π rad/s, the Bode diagram of the open-loop transfer function of the system with the quasi-PR controller is shown in Fig. 10.
It can be seen from Fig. 10 that the gain at the fundamental frequency of the system increases to 72.9 dB after adding the quasi-PR controller, which greatly reduces the steady-state error and has good tracking performance.The open-loop cutoff frequency is 1.36 × 10 4 rad/s, which can ensure the low-order harmonic output capability of the system.However, the phase margin of the open-loop transfer function is only 14.46°, which cannot meet the requirement of stability.In order to increase the phase margin and improve the transient performance of the control system, the lead correction link is introduced, and its transfer function is as follows.
According to the knowledge of automatic control theory, the time parameters in (26) are set, let T 1 = 1 × 10 −4 s, T 2 = 3 × 10 −5 s, then the Bode diagram of the open-loop transfer function after adding the correction link is shown in Fig. 11.At this time, the gain of fundamental frequency and the cutoff frequency of the system all meet the requirements of the stability of the control system.
For the actual fault, the transition resistance is random and variable.When changing the size of the transition resistance, the Bode diagram of the open-loop transfer function using the above control strategy is shown in Fig. 12.
According to Fig. 12, it can be seen that no matter how the transition resistance changes, the phase margin of the system can always be controlled within the range of 30°~60°, and the impact on the system is smaller when the transition resistance is large, and the high-resistance fault is more practical in practice, therefore, the designed control strategy has wide applicability.

Simulation model
In order to verify the effectiveness of the proposed arc suppression method, a simulation model of the distribution network is built in MATLAB/Simulink following Fig. 1.
The voltage level of the distribution network is 10 kV, and four lines are drawn from the bus, of which L 1 and L 2 are overhead lines, L 3 and L 4 are cable lines, and their lengths are 8 km, 12 km, 12 km, and 10 km, respectively.The line parameters are selected according to Table 2, all four lines are connected to a delta-connected load with a size of 2MVA and a power factor of 0.9.Set the parameters of the active inverter according to Table 1.Suppose the single-phase grounding fault occurs on phase A of L 4 .

Fault distance simulation verification
In order to verify the accuracy of the fault distance estimation method proposed in this paper, the simulation was carried out under different fault conditions.The results of the fault distance calculation are shown in Table 3.
It can be seen from Table 3 that the measurement error of the fault distance increases with the increase in the transition resistance.At the same time, when the fault point gradually moves away from the bus, the error will also increase.However, under different fault conditions, the calculation errors of the fault distance are all within the maximum allowable error range specified by (23), which indicates that the fault distance calculated according to Sect. 3 can limit the fault current below the threshold of reliable arc suppression.Even if there is still a certain voltage drop between the fault point  and the bus, but the value of this voltage drop is very small, and it will not affect the overall effect of the arc suppression.

Harmonic component suppression performance verification
Figure 13 shows the waveforms of fault current and fault point voltage under the action of the proposed arc suppression method.At 0.12 s, the single-phase grounding fault occurs, the fault point is 10 km from the bus, the transition resistance is set to 100 , the initial compensation current is injected at 0.18 s, and the control neutral point voltage of the active inverter is adjusted as the reference value at 0.24 s.
As can be seen from Fig. 13, the current at the fault point increases rapidly after the fault occurs, and its amplitude is close to 40A, if not handled in time, the safe operation of the distribution network will be endangered; After the initial compensation current is injected, the current and voltage at the fault point are greatly reduced; Then, according to the calculated reference value of neutral point voltage, the operation state of the active inverter is adjusted.It is obvious that the fault current decreases rapidly to near zero, which makes the arc can be extinguished reliably, the fault point voltage is also suppressed to a very low level, effectively preventing the repeated re-ignition of the arc.
In order to more fully verify the arc suppression effect of the AVAS-CLVD, change the fault conditions, and carry out simulations under different transition resistances and fault distances, the fault currents under four conditions, including no arc suppression device (NASD), arc suppression coil (ASC), AVAS-RLVD and AVAS-CLVD, were listed and compared, as shown in Table 4.Among them, the ASC works in the over-compensation state, and the compensation degree is 10%.
From Table 4, the transition resistance affects the residual current at the fault point.No matter what arc suppression method is used, the fault current will decrease with the increase in the transition resistance.When the ASC is used, the closer the fault point is to the bus, the greater the fault current.In the case of a short-distance low-resistance fault, the residual current of the fault point after the ASC compensation is still much larger than the 5A threshold requirement for reliable arc suppression, and the arc is difficult to extinguish reliably.Comparing the AVAS-RLVD and AVAS-CLVD, the fault current will decrease with the decrease in the fault distance, but AVAS-RLVD still has a large fault residual under the long-distance, low-resistance grounding fault, the value may even exceed 20A, at this time the arc will be difficult to extinguish naturally.When the influence of line voltage drop is considered, the fault current and fault voltage can be suppressed to a very low level, which can effectively extinguish the fault arc and avoid the repeated re-ignition of the arc.

Harmonic component suppression performance verification
The harmonic suppression ability of the proposed method is verified by injecting the fifth harmonic current with an amplitude of 10A from the A phase of the bus, and the existing arc suppression methods are introduced for comparative analysis.Changing the fault conditions, the magnitude of the fault harmonic current under the action of different arc suppression methods is shown in Table 5.
According to Table 5, the ASC has no inhibitory effect on the fault harmonic components, which indicates that in some extreme cases, even if the ASC can suppress the fault fundamental current close to zero, if there is a large fault harmonic current in the system, the fault arc still cannot be reliably extinguished.For both AVAS-RLVD and AVAS-CLVD, they can effectively suppress harmonic components regardless of fault conditions.

Conclusion
In view of the problem that the existing active voltage-type arc suppression methods have poor arc suppression effect in the case of low-resistance grounding faults at the end of the heavy-load line, this paper proposes a new active voltagetype arc suppression method that takes into account the line voltage drop.The conclusions are as follows: (1) The performance of the AVAS-RLVD without considering the line voltage drop is analyzed.Due to the existence of the line voltage drop between the fault point and the bus, the fault point will still have a large fault residual current after AVAS-RLVD acts, and the arc is difficult to extinguish reliably.(2) A current is injected into the neutral point of the distribution network before and after the fault.According to the zero-sequence network of the system in different states, the calculation of the fault distance is realized, and then the best reference value of the neutral point voltage for controlling the arc extinguishing can be obtained.(3) In order to achieve accurate tracking of the reference voltage, a double closed-loop control strategy of current inner loop + voltage outer loop is introduced, and it is verified by analysis that the control strategy can still maintain good dynamic and steady-state performance when the transition resistance changes.(4) In order to verify the effectiveness of the proposed method, a simulation model is built in MAT-LAB/Simulink, the results show that the proposed method has high fault distance estimation accuracy, and under different fault distances and different transition resistances, the fundamental and harmonic components of the fault can be suppressed to a safe range.The effectiveness of the proposed arc suppression method is verified.

Fig. 1
Fig. 1 Schematic diagram of the active voltage-type arc suppression

Fig. 2
Fig. 2 Equivalent circuit diagram of distribution network

Fig. 3
Fig. 3 Equivalent zero-sequence circuit of distribution network

Fig. 4
Fig. 4 Diagram of the residual current at the fault point

7Fig. 8
Fig. 8 Structure block diagram of the double closed-loop control

Fig. 13
Fig. 13 Effect diagrams of arc suppression method considering line voltage drop a Fault current waveform b Fault voltage waveform

Table 1
System parameters

Table 2
Line impedance parameters

Table 3
Fault distance calculation results