Arc Voltage and Current Characteristics in Low-Voltage Direct Current

Recently, Low-Voltage DC (direct current) distribution systems have received high lights according to the expansion of DC generations and DC loads such as photovoltaics (PV) generations, electric vehicles (EVs), light emitting diodes (LEDs), computers, DC homes, etc. Low-Voltage DC distribution systems have optimistic perspectives since DC has various good aspects compared to alternating current (AC). However, ensuring safety of human and electric facility in Low-Voltage DC is not easy because of arc generation and difficulty of arc-extinguishing. This paper constructs a low-voltage DC circuit and studies the arc interruption that occurs when separating electrodes from where load currents flow. Also, arc extinguishers are experimented upon and analysed in various levels of source voltage and load currents conditions. Voltage and current characteristics for arc interruption are identified based on experimental results, and we establish the electric generation for arc interruption. Further, the voltage–current characteristics and the correlation of arc during arc duration time arc are verified, and the voltage–current equation and DC arc resistance model for the breaking arc are developed.


Introduction
With the recent increase in loads using direct current (DC) power, such as TVs, computers, Light Emitting Diodes (LED) lights, and the like, and increase of renewable power sources in the form of distributed generation, demand for DC distribution is increasing [1,2].The rapid development of the information society has led to an increase in the direct current loads such as Information Technology (IT)-related digital devices.In electricity-isolated areas where the people do not receive electricity, renewable power generation with distributed generation form is the most effective means to provide electric energy.In this situation, it is possible to reduce the power conversion step to supply DC load by changing the power distribution system from Alternating Current (AC) system to DC system, which reduces installation cost and increase energy efficiency.These advantages are expected to increase the demand for DC distribution system in homes and buildings.
However, in order to enable the DC distribution system, it is important to solve the problem of melting of contacts, fire, etc. caused by the arc in a socket-outlet plug [3] and circuit breaker [4].However, knowledge of the arc in DC system has not been fully discovered, and there has not yet been a clear definition of the arc in DC power system.
In 1889, Paschen experimented to find that the voltage at which gas discharge begins depends on the type of gas and is proportional to the product of the pressure of the gas and the distance between electrodes.Paschen experimented with a situation where a so-called parallel arc was generated by Energies 2018, 11, 2511 2 of 14 applying a constant voltage to a test circuit where the distance between electrodes are fixed with no initial current.Through this experiment, it is possible to find that the parallel arc arises when the distance between the electrodes is reduced to a certain level during by applying a constant voltage [5].
Compared with the parallel arc, a series arc is generated when contact electrodes are separated in condition that initial current flows.The series arc has been applied in the principle of arc lamp and arc welding from the 1800s to the present.Since 1902, various models for the series arc have been suggested.In these models, an arc voltage is defined as a function of an arc current and a gap distance [6][7][8][9][10].As the conventional studies for the series arc are concentrated on the arc lamp applications, only the quasi-static arc characteristic was investigated when the arc is continuously sustained in the fixed gap distance.
Recently, a series-breaking arc in circuit breakers, switches, and socket outlets and plugs as a protective device for DC distribution has been researched [11].The series-breaking arc generated in the protective devices is likely to cause fire by high temperature plasma generation.The problem in the protective devices should be properly solved to install them in electric facilities.Therefore, it is necessary to understand precisely the initiation, sustenance, and extinguishment of the series breaking arc generated in the protective device during the contact electrodes are separating.Until now, many researches have been made on DC breaking arc generated at electrodes during load currents flow without clearly clarified, the relationship between the voltage and current characteristics at the electrodes [12][13][14].
This paper has composed a low-voltage DC circuit, and experimented on breaking arc that occurs when separating electrodes at various levels of source voltage and load current conditions.

Experimental Setup
As shown in Figure 1, a switching device is developed to experiment occurrences of arcs when electrodes are separated during load current flows.The experiment device was installed on horizontal level, and the material for electrodes is pure bronze.In 1889, Paschen experimented to find that the voltage at which gas discharge begins depends on the type of gas and is proportional to the product of the pressure of the gas and the distance between electrodes.Paschen experimented with a situation where a so-called parallel arc was generated by applying a constant voltage to a test circuit where the distance between electrodes are fixed with no initial current.Through this experiment, it is possible to find that the parallel arc arises when the distance between the electrodes is reduced to a certain level during by applying a constant voltage [5].
Compared with the parallel arc, a series arc is generated when contact electrodes are separated in condition that initial current flows.The series arc has been applied in the principle of arc lamp and arc welding from the 1800s to the present.Since 1902, various models for the series arc have been suggested.In these models, an arc voltage is defined as a function of an arc current and a gap distance [6][7][8][9][10].As the conventional studies for the series arc are concentrated on the arc lamp applications, only the quasi-static arc characteristic was investigated when the arc is continuously sustained in the fixed gap distance.
Recently, a series-breaking arc in circuit breakers, switches, and socket outlets and plugs as a protective device for DC distribution has been researched [11].The series-breaking arc generated in the protective devices is likely to cause fire by high temperature plasma generation.The problem in the protective devices should be properly solved to install them in electric facilities.Therefore, it is necessary to understand precisely the initiation, sustenance, and extinguishment of the series breaking arc generated in the protective device during the contact electrodes are separating.Until now, many researches have been made on DC breaking arc generated at electrodes during load currents flow without clearly clarified, the relationship between the voltage and current characteristics at the electrodes [12][13][14].
This paper has composed a low-voltage DC circuit, and experimented on breaking arc that occurs when separating electrodes at various levels of source voltage and load current conditions.

Experimental Setup
As shown in Figure 1, a switching device is developed to experiment occurrences of arcs when electrodes are separated during load current flows.The experiment device was installed on horizontal level, and the material for electrodes is pure bronze.In this experiment, the maximum separation distance of the electrodes was 20 mm and the electrode separation speed was set at 150 mm/s.The power supply voltage varied from 50 V to 400 V and the load current varied from 0.5 A to 10 A to investigate DC breaking arcs at various voltages and currents.Each experiment was performed 3 times to reduce measurement error.Voltage and current were measured using an oscilloscope during the electrodes are separating.Experimental conditions are as shown in Table 1.In this experiment, the maximum separation distance of the electrodes was 20 mm and the electrode separation speed was set at 150 mm/s.The power supply voltage varied from 50 V to 400 V and the load current varied from 0.5 A to 10 A to investigate DC breaking arcs at various voltages and currents.Each experiment was performed 3 times to reduce measurement error.Voltage and current were measured using an oscilloscope during the electrodes are separating.Experimental conditions are as shown in Table 1.

Experiment of DC Arc
In this study, the arc experiment of DC circuit as shown in Figure 2 was constructed to investigate the arc generation during the electrode is separating in a state in which initial load current flows.

Experiment of DC Arc
In this study, the arc experiment of DC circuit as shown in Figure 2 was constructed to investigate the arc generation during the electrode is separating in a state in which initial load current flows.Figure 3 shows the relation between the separation time (t) and the distance between electrodes (d) with a separating speed of 150 mm/s.Figure 4 shows the relation between the separation time (t) and the source voltage (V S ).

Experiment of DC Arc
In this study, the arc experiment of DC circuit as shown in Figure 2 was constructed to investigate the arc generation during the electrode is separating in a state in which initial load current flows.When the electrode is separated in a state in which the initial load current flows, the measured experimental waveforms are as follows in Figure 5.In Figure 5, the instantaneously increased voltage between the electrodes during arc initiation is defined as arc initiation threshold voltage Vth; and the instantaneously decreased current during arc initiation is defined as arc initiation threshold current Ith.
Figure 6 shows the relation of arc voltage between electrodes (varc) and separation time (t). Figure 7 shows the relation of arc current (iarc) and arc separation time (t).When the electrode is separated in a state in which the initial load current flows, the measured experimental waveforms are as follows in Figure 5.When the electrode is separated in a state in which the initial load current flows, the measured experimental waveforms are as follows in Figure 5.In Figure 5, the instantaneously increased voltage between the electrodes during arc initiation is defined as arc initiation threshold voltage Vth; and the instantaneously decreased current during arc initiation is defined as arc initiation threshold current Ith.
Figure 6 shows the relation of arc voltage between electrodes (varc) and separation time (t). Figure 7 shows the relation of arc current (iarc) and arc separation time (t).In Figure 5, the instantaneously increased voltage between the electrodes during arc initiation is defined as arc initiation threshold voltage V th ; and the instantaneously decreased current during arc initiation is defined as arc initiation threshold current I th .
Figure 6 shows the relation of arc voltage between electrodes (v arc ) and separation time (t).When the electrode is separated in a state in which the initial load current flows, the measured experimental waveforms are as follows in Figure 5.In Figure 5, the instantaneously increased voltage between the electrodes during arc initiation is defined as arc initiation threshold voltage Vth; and the instantaneously decreased current during arc initiation is defined as arc initiation threshold current Ith.
Figure 6 shows the relation of arc voltage between electrodes (varc) and separation time (t). Figure 7 shows the relation of arc current (iarc) and arc separation time (t).varc(t0) is voltage between electrodes at separation start time, which is equal to zero.varc(text) is voltage between electrodes at the arc extinguishing point, which is equal to the source voltage (Vs).The voltage between electrodes increase rapidly between t0 and t1 and an arc occurs at t1.The voltage between electrodes at t1 is varc(t1) = Vth.The arc begins from t1 and continues to text, and the voltage between electrodes gradually increases.
Also, the arc current iarc(t0) is equal to load current IL at the electrode separation point.iarc(text) is equal to zero at the arc extinguishing point.The arc current rapidly decreases between t0 and t1, and the arc current at t1 is iarc(t1) = ILoad − Ith.The arc current continuously decreases from the arc initiation time (t1) to the arc extinguishing time (text).

Analysis of Arc Initiation Threshold Voltage ( )
On the several source voltage levels in the experiment circuit in Figure 2 (50 V, 100 V, 200 V, 300 V, 400 V), load currents were variously changed and examined.After separation of the electrodes, arc initiation threshold voltage ( ) was confirmed at the arc initiation time ( ).
From the experimental results of DC breaking arc initiation, the arc initiation threshold voltage ( ) at the arc initiation point ( ) distributed within 9.45-10.54V as shown in Figure 8 and Table 2, regardless of the magnitude of the source voltage and load currents.That is, breaking arc initiation voltage at DC can be confirmed as constant at about 10 V.  v arc (t 0 ) is voltage between electrodes at separation start time, which is equal to zero.v arc (t ext ) is voltage between electrodes at the arc extinguishing point, which is equal to the source voltage (V s ).The voltage between electrodes increase rapidly between t 0 and t 1 and an arc occurs at t 1 .The voltage between electrodes at t 1 is v arc (t 1 ) = V th .The arc begins from t 1 and continues to t ext , and the voltage between electrodes gradually increases.Also, the arc current i arc (t 0 ) is equal to load current I L at the electrode separation point.i arc (t ext ) is equal to zero at the arc extinguishing point.The arc current rapidly decreases between t 0 and t 1 , and the arc current at t 1 is i arc (t 1 ) = I Load − I th .The arc current continuously decreases from the arc initiation time (t 1 ) to the arc extinguishing time (t ext ).

Analysis of Arc Initiation Threshold Voltage (V th )
On the several source voltage levels in the experiment circuit in Figure 2 (50 V, 100 V, 200 V, 300 V, 400 V), load currents were variously changed and examined.After separation of the electrodes, arc initiation threshold voltage (V th ) was confirmed at the arc initiation time (t 1 ).
From the experimental results of DC breaking arc initiation, the arc initiation threshold voltage (V th ) at the arc initiation point (t 1 ) distributed within 9.45-10.54V as shown in Figure 8 and Table 2, regardless of the magnitude of the source voltage and load currents.That is, breaking arc initiation voltage at DC can be confirmed as constant at about 10 V. varc(t0) is voltage between electrodes at separation start time, which is equal to zero.varc(text) is voltage between electrodes at the arc extinguishing point, which is equal to the source voltage (Vs).The voltage between electrodes increase rapidly between t0 and t1 and an arc occurs at t1.The voltage between electrodes at t1 is varc(t1) = Vth.The arc begins from t1 and continues to text, and the voltage between electrodes gradually increases.
Also, the arc current iarc(t0) is equal to load current IL at the electrode separation point.iarc(text) is equal to zero at the arc extinguishing point.The arc current rapidly decreases between t0 and t1, and the arc current at t1 is iarc(t1) = ILoad − Ith.The arc current continuously decreases from the arc initiation time (t1) to the arc extinguishing time (text).

Analysis of Arc Initiation Threshold Voltage ( )
On the several source voltage levels in the experiment circuit in Figure 2 (50 V, 100 V, 200 V, 300 V, 400 V), load currents were variously changed and examined.After separation of the electrodes, arc initiation threshold voltage ( ) was confirmed at the arc initiation time ( ).
From the experimental results of DC breaking arc initiation, the arc initiation threshold voltage ( ) at the arc initiation point ( ) distributed within 9.45-10.54V as shown in Figure 8 and Table 2, regardless of the magnitude of the source voltage and load currents.That is, breaking arc initiation voltage at DC can be confirmed as constant at about 10 V.This can be confirmed that the arc starts when the voltage between the electrodes (voltage formed across the electrodes of the circuit breaker or switch) is about 10 V.

Analysis of Arc Initiation Threshold Current (I th )
On the several source voltage levels in the experiment circuit in Figure 2 (50 V, 100 V, 200 V, 300 V, 400 V), load currents were variously changed and examined.Based on the experimental results, i arc (t 0 ) and i arc (t 1 ) are measured and the difference is calculated.The arc initiation threshold current (I th ) was confirmed at the arc initiation time (t 1 ).
With the arc initiation experimental results, the arc initiation threshold current (I th ) was found to be inversely proportional to the source voltage (V s ) and proportional to the load current (I L ) as shown in Figure 9 and Table 3.This can be confirmed that the arc starts when the voltage between the electrodes (voltage formed across the electrodes of the circuit breaker or switch) is about 10 V.

Analysis of Arc Initiation Threshold Current ( )
On the several source voltage levels in the experiment circuit in Figure 2 (50 V, 100 V, 200 V, 300 V, 400 V), load currents were variously changed and examined.Based on the experimental results, ( ) and ( ) are measured and the difference is calculated.The arc initiation threshold current ( ) was confirmed at the arc initiation time ( ).
With the arc initiation experimental results, the arc initiation threshold current ( ) was found to be inversely proportional to the source voltage ( ) and proportional to the load current ( ) as shown in Figure 9 and Table 3.

Analysis of Relationship between Arc Voltage (v arc (t)) and Arc Current (i arc (t)) between Electrodes
Equation ( 1) is derived based on the characteristics of the arc initiation threshold current (I th ) inversely proportional to the source voltage (V s ) and proportional to the load current (I L ).
To find the value of a random constant the following equation ( 2) is used.The constant K was approximately 10 V, equal to the arc initiation threshold voltage (V th ).
The result of Equation ( 2) can be applied as with Equation (3), and it is confirmed that the value of dividing the arc initiation threshold voltage by the arc initiation threshold current is equal to the load resistance (R L ).
Since I th = i arc (t 0 ) − i arc (t 1 ) and V th = v arc (t 1 ), Equation ( 4) can be as follows.
It has been confirmed that Equation (4) satisfies any random time between t 1 to t ext .In conclusion, Equations (5-7) can be as follows.
Figure 12 shows the relationship between r arc (t) and i arc (t) under source voltage condition V s1 < V s2 .When load current is I L1 = I L2 , the load resistance R L is proportional to the magnitude of the source voltages V s1 , V s2 , therefore R L1 < R L2 .
Energies 2018, 11, x FOR PEER REVIEW 9 of 15 Figure 12 shows the relationship between ( ) and ( ) under source voltage condition .When load current is , the load resistance is proportional to the magnitude of the source voltages , , therefore .Figure 13 is the experimental result graph of and according to the changes in source voltage.Figure 13 is the experimental result graph of and according to the changes in source voltage.Figure 17 shows the graph of applying the experimental result of 200 V/5 A to Equation ( 13).This result demonstrates that the arc power has its maximum value at 2.5 A where .Figure 17 shows the graph of applying the experimental result of 200 V/5 A to Equation ( 13).This result demonstrates that the arc power has its maximum value at 2.5 A where i arc = 2 I L . Figure 18 shows the experimental results of arc voltage, arc current, arc resistance, and power between electrodes during electrodes separation.As shown in Figures 16 and 17, the power between electrodes becomes its maximum when arc current becomes .As shown in Figure 18, and are rapidly decreased and is rapidly increased when the arc power is maximum, and it is ascertained that arc is rapidly extinguished.

Arc Extinguishing Threshold Point
Previous Section 3.4, it is shown that increase of and decrease of are accelerated and the variation width becomes larger based on the time point passing .The relationship between the time ( ) to reach and the arc extinguishing time ( ) is analyzed as shown in Table 4.According to the experimental conditions in Table 1, / was analyzed to be 0.80 on the average.It is ascertained that arc extinguishing duration time is 20% of the total arc duration time.Figure 18 shows the experimental results of arc voltage, arc current, arc resistance, and power between electrodes during electrodes separation.As shown in Figures 16 and 17, the power between electrodes becomes its maximum when arc current becomes 1  2 I L .As shown in Figure 18, v arc and i arc are rapidly decreased and r arc is rapidly increased when the arc power is maximum, and it is ascertained that arc is rapidly extinguished.Figure 18 shows the experimental results of arc voltage, arc current, arc resistance, and power between electrodes during electrodes separation.As shown in Figures 16 and 17, the power between electrodes becomes its maximum when arc current becomes .As shown in Figure 18, and are rapidly decreased and is rapidly increased when the arc power is maximum, and it is ascertained that arc is rapidly extinguished.

Arc Extinguishing Threshold Point
Previous Section 3.4, it is shown that increase of and decrease of are accelerated and the variation width becomes larger based on the time point passing .The relationship between the time ( ) to reach and the arc extinguishing time ( ) is analyzed as shown in Table 4.According to the experimental conditions in Table 1, / was analyzed to be 0.80 on the average.It is ascertained that arc extinguishing duration time is 20% of the total arc duration time.

Arc Extinguishing Threshold Point
Previous Section 3.4, it is shown that increase of r arc and decrease of i arc are accelerated and the variation width becomes larger based on the time point passing P max .The relationship between the time (t max ) to reach P max and the arc extinguishing time (t ext ) is analyzed as shown in Table 4.
According to the experimental conditions in Table 1, t max /t n was analyzed to be 0.80 on the average.It is ascertained that arc extinguishing duration time is 20% of the total arc duration time.

Conclusions
In this paper, arc initiation voltage and arc initiation current characteristics were shown through arc initiation experiments.Electrodes were separated under various source voltages and load currents conditions.After arc occurred, voltage between electrodes and current changes were measured and experimental results were analyzed.
After the electrode separation, the voltage between electrodes rose instantaneously and the arc was initiated.Here it was confirmed that the instantaneous increased voltage level was about 10 V regardless of the source voltage and the load current value.After the electrode separation, the load current decreased instantaneously.This value was inversely proportional to the supply voltage (V s ) and proportional to the load current (I L ).By applying these characteristics to experimental values, it is confirmed that the value of dividing the arc initiation threshold voltage by the arc initiation threshold current is equal to the load resistance (R L ).Based on this, the voltage-current characteristics and the correlation of the breaking arc were verified, and the voltage-current equation and DC arc resistance model for the breaking arc were developed.
The characteristics of v arc , i arc and r arc of the breaking arc at random point during arc duration time were analyzed.The variation width of r arc and i arc was shown to increase as the arc approached extinguishing point, and P max was 1  4 of the load power before electrode separation.The increase of r arc and decrease of i arc were accelerated at the point reaching P max and the arc was rapidly extinguished.

Figure 3
Figure3shows the relation between the separation time (t) and the distance between electrodes (d) with a separating speed of 150 mm/s.Figure4shows the relation between the separation time (t) and the source voltage (VS).

Figure 3
Figure3shows the relation between the separation time (t) and the distance between electrodes (d) with a separating speed of 150 mm/s.Figure4shows the relation between the separation time (t) and the source voltage (VS).

Figure 3 .
Figure 3. Distance between the electrode.Figure 3. Distance between the electrode.

Figure 3 .
Figure 3. Distance between the electrode.Figure 3. Distance between the electrode.
Figure 7   shows the relation of arc current (i arc ) and arc separation time (t).

Figure 6 .
Figure 6.Arc voltage between the electrodes.Figure 6. Arc voltage between the electrodes.

Figure 6 .
Figure 6.Arc voltage between the electrodes.Figure 6. Arc voltage between the electrodes.

Figure 8 .
Figure 8. Characteristics of arc initiation threshold voltage as source voltage and load current.

Figure 8 .
Figure 8. Characteristics of arc initiation threshold voltage as source voltage and load current.Figure 8. Characteristics of arc initiation threshold voltage as source voltage and load current.

Figure 8 .
Figure 8. Characteristics of arc initiation threshold voltage as source voltage and load current.Figure 8. Characteristics of arc initiation threshold voltage as source voltage and load current.

Figure 9 .
Figure 9. Characteristics of arc initiation threshold current as source voltage and load current.Figure 9. Characteristics of arc initiation threshold current as source voltage and load current.

Figure 9 .
Figure 9. Characteristics of arc initiation threshold current as source voltage and load current.Figure 9. Characteristics of arc initiation threshold current as source voltage and load current.

Figure 12 .
Figure 12.Relation between arc resistance and arc current with the parameter of source voltage change.

Figure 13 .
Figure 13.Arc resistance and arc current experimental results (source voltage change).

Figure 12 .
Figure 12.Relation between arc resistance and arc current with the parameter of source voltage change.

Figure 13
Figure 13 is the experimental result graph of r arc and i arc according to the changes in source voltage.

Figure 12 .
Figure 12.Relation between arc resistance and arc current with the parameter of source voltage change.

Figure 13 .
Figure 13.Arc resistance and arc current experimental results (source voltage change).Figure 13.Arc resistance and arc current experimental results (source voltage change).

Figure 13 .
Figure 13.Arc resistance and arc current experimental results (source voltage change).Figure 13.Arc resistance and arc current experimental results (source voltage change).

Figure 14
Figure 14 is a graph of the relation between r arc and i arc under load current conditions I L1 < I L2 .When the source voltage is equal, R L is inversely proportional to the magnitude of the load currents I L1 and I L2 , and therefore R L1 > R L2 .

Figure 14 .
Figure 14.Relation between arc resistance and arc current with the parameter of load current change.

Figure 15
Figure 15 is an experimental result graph of and according to the changes in source voltage.

Figure 15 .
Figure 15.Arc resistance and arc current experimental results (load current change).

Figure 14 .
Figure 14.Relation between arc resistance and arc current with the parameter of load current change.

Figure 15
Figure 15 is an experimental result graph of r arc and i arc according to the changes in source voltage.

Figure 14 .
Figure 14.Relation between arc resistance and arc current with the parameter of load current change.

Figure 15
Figure 15 is an experimental result graph of and according to the changes in source voltage.

Figure 15 .
Figure 15.Arc resistance and arc current experimental results (load current change).Figure 15.Arc resistance and arc current experimental results (load current change).

Figure 15 .
Figure 15.Arc resistance and arc current experimental results (load current change).Figure 15.Arc resistance and arc current experimental results (load current change).

Table 2 .
Arc initiation threshold voltage experimental results.

Table 2 .
Arc initiation threshold voltage experimental results.

Table 3 .
Arc initiation threshold current experimental results.

Table 4 .
t max (time at maximum arc power) at P max (maximum arc power) and t ext (arc extinguishing time) relationship.