# Analysis of Short-Circuit and Dielectric Recovery Characteristics of Molded Case Circuit Breaker according to External Environment

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## Abstract

**:**

_{10}, t

_{21}, and t

_{32}are 1.58, 1.53, and 1.79, respectively, in short-circuit characteristics and t

_{i}, t

_{m}, and t

_{l}are 1.59, 1.69, and 1.53, respectively, in dielectric recovery strength. Depending on the external magnetic field, the short-circuit characteristics decreased by 8.56% only in the t

_{21}period. The dielectric recovery strength decreases by 4.92% in the initial section (t

_{i}) and 14.45% in the later section (t

_{l}), respectively. It has been confirmed that the external magnetic field interferes with the emission of hot gas.

## 1. Introduction

## 2. Consideration of External Environmental Conditions

#### 2.1. Temperature

#### 2.2. Magnetic Field

## 3. Experiment Studies

_{S}charged by the rectifier generates overcurrent at the desired frequency with inductor L. An overcurrent generated by the operation of Thyr flows into the circuit breaker, and capacitor C

_{0}connected in parallel to the circuit breaker is installed to model a recovery voltage of the system and arbitrarily perform re-ignition. In addition, an experiment is constructed by selecting the ambient temperature and the external magnetic field as external conditions in the circuit breaker. These experimental setups appear in Section 3.1 and Section 3.2, respectively.

_{0}is the time that the overcurrent flows into the breaker, and t

_{1}is the time when the electrodes begin to separate. t

_{2}is the time when the arc formed after electrode separation reaches the splitter plate, and t

_{3}is the timing of the current reaching zero after the arc is extinguished on the splitter plate. Therefore, t

_{10}represents the time until the moving electrode is separated from the fixed electrode after the inflow of overcurrent, and t

_{21}represents the time the arc moves to the splitter plate after the contact is disconnected. t

_{31}represents the time at which the arc reaching the splitter plate is extinguished. Figure 4b shows each point of the dielectric recovery characteristics of the circuit breaker after the current reaches zero. When a recovery voltage exceeding the dielectric strength is applied between the fixed electrode and the moving electrode after the current reaches zero, the arc is re-formed and the voltage is discharged. The voltage at this time is V

_{DRV}, and the time taken from the current zero to the re-ignition is t

_{DRV}.

#### 3.1. Temperature Test Results

_{10}when the external temperatures are 25 °C, 35 °C, and 45 °C are 2.77 ms, 2.14 ms, and 1.78 ms, respectively. Compared to the value at 25 °C, the values of 35 °C and 45 °C are reduced by −22.5% and −35.6%, respectively. The electrodynamic repulsion force that determines the value of t

_{10}consists of the Holm force and the Lorentz force [18]. Before the fixed electrode and the moving electrode are opened, the current flows intensively in a very small area. The electromagnetic repulsive force generated by the magnetic flux density between these electrodes is called the Holm force. Before the overcurrent enters the fixed electrode, it flows in opposite directions. This repulsive force is called the Lorentz force. The Holm force and the Lorenz force are expressed by the following formula.

_{10}shortening.

_{21}when the external temperatures are 25 °C, 35 °C, and 45 °C are 4.24 ms, 4.91 ms, and 5.27 ms, respectively. Compared to the value at 25 °C, the values of 35 °C and 45 °C increased by +15.9% and +24.3%, respectively. t

_{21}is the period where the arc current generated between the fixed electrode and the movable electrode moves in the direction of the splitter plate. At this time, the force acting on the arc current is largely due to the centrifugal force caused by the movable electrode and the pressure difference of the heated gas generated by the arc discharge. Assuming that the centrifugal force is constant, the pressure difference is as follows.

_{32}when the external temperatures are 25 °C, 35 °C, and 45 °C are 1.45 ms, 1.54 ms, and 1.60 ms, respectively. Compared to the value at 25 °C, the values of 35 °C and 45 °C are increased by +5.7% and +10.2%, respectively. It is predictable that the lower the temperature of the splitter plate, the more advantageous it is to extinguish the arc current. The t

_{10}, t

_{21}, and t

_{32}values at 35 °C and 45 °C were compared based on the values of t

_{10}, t

_{21}, and t

_{32}at 25 °C, respectively. The ratios of these values at 35 °C and 45 °C are 1.58, 1.53, and 1.79 at t

_{10}, t

_{21}, and t

_{32}, respectively. It can be seen that it changes at a similar rate in all periods, and in the case of t

_{32}, it is slightly more affected. That is, it can be seen that the temperature affects the metal more than the air.

_{0}values (0.47, 1, and 10 μF) and their corresponding average voltage and average time, respectively. Using these voltages and times, Figure 13 illustrates the DRV V-t curve according to the temperature.

_{i}), medium time (t

_{m}), and late time (t

_{l}). In general, the initial time is affected by the cooling performance of the splitter plate, and the latter time is affected by the emission of hot gas generated by arc extinguishment [20]. The results are as follows. The average time corresponding to each of the C

_{0}values (0.47 μF, 1 μF, 10 μF) is 0.95 μs, 1.86 μs, and 4.45 μs, respectively. At t

_{i}, DRVs of 25 °C, 35 °C, and 45 °C are 279 V, 242 V, and 220 V, respectively. At t

_{m}, DRVs of 25 °C, 35 °C, and 45 °C are 381 V, 345 V, and 320 V, respectively. In this t

_{l}, DRVs of 25 °C, 35 °C, and 45 °C are 482 V, 408 V, and 369 V, respectively. The rate of change in the DRV of 35 °C and 45 °C based on the 25 °C DRV is as follows. When it is t

_{i}, the rates are−13.3% and −21.1%. When it is t

_{m}, the rates are −9.4% and −16.0%. When it is t

_{l}, the rates are −15.4% and −23.4%, respectively. Upon comparing t

_{i}and t

_{l}, the rates of change are similar. This result shows that the arc-cooling performance is poor due to the increased temperature of the splitter plate at the initial time. In addition, it can be seen that at the latter time, hot gas is not sufficiently emitted due to the high temperature outside. The rate of change of the DRV of 35 °C and 45 °C to 25 °C DRV is 1.59, 1.69, and 1.53, respectively, at t

_{i}, t

_{m}, and t

_{l}. It can be seen that it changes at a similar rate in all periods.

#### 3.2. Disturbing Magnetic Field Test Results

_{total}is the total magnetic resistance of the magnetic equivalent circuit. According to the equation, if the core is not saturated by the magnetic field, the magnetic flux by the magnetic field is proportional to the current applied to the coil. In addition, the force applied to the arc current is shown in the following equation.

**f**is the volume force density and is expressed in Equation (5) as the cross product of the current density (

_{v}**J**) and magnetic flux density (

**B**) and the product of the magnetic field (H) and divergence of

**B**, as shown. In this paper, when 5A flows through the core, the maximum values of magnetic field and force are approximately $4\times {10}^{4}$ A/m and $52$ mN, respectively. These values act in a direction that interferes with the motion of the arc current.

_{10}, there is little difference with +0.01 ms. This means that the influence of disturbing magnetic fields on the Holm force and the Lorentz force of t

_{10}is very little. In the case of the Holm force, the hardness of the material and the area of the electrode are not factors affected by the magnetic fields [21]. The Lorentz force may be affected by magnetic fields, but for the Lorentz force to be large, the reciprocating current path interval should be small, and for the Lorentz force to be greatly influenced by magnetic fields, the interval should be large. The two factors are inversely proportional. In fact, circuit breakers have small intervals, so the Lorenz force is insignificant.

_{21}, it increases by +0.35 ms compared to no magnetic fields. These disturbing magnetic fields generate forces in a direction that disturbs the arc current moving toward the splitter plate. The increase in time in this period may also affect the subsequent period t

_{32}, leading to interruption failure.

_{32}, it is not as meaningful as in the case of t

_{10}. Disturbing magnetic fields do not affect arc extinguishment in this period. The increase/decrease ratios of periods t

_{10}, t

_{21}, and t

_{32}of disturbing magnetic fields in preparation for the case of no magnetic fields are −0.27%, 8.56%, and 0.15%, respectively. t

_{21}shows a significant change ratio even in no disturbing magnetic fields. It can be seen that this also increases the overall time by 4.08%.

_{0}value (0.47, 1, and 10 μF) shows the average voltage and average time. Using these voltages and times, Figure 17 shows the DRV V-t curve under distanced magnetic fields.

_{0}values (0.47 μF, 1 μF, 10 μF) is 1.08 μs, 1.75 μs, and 4.73 μs, respectively. At t

_{i}, with and without disturbed magnetic fields, the DRVs are 320 V and 305 V, respectively. At t

_{m}, with and without disturbed magnetic fields, the DRVs are 382 V and 361 V, respectively. At t

_{l}, with and without disturbing magnetic fields, the DRVs are 491 V and 429 V, respectively.

_{i}, t

_{m}, and t

_{l}, respectively. This rate of change is approximately three times greater in the late period than in the early and medium periods. The initial DRV characteristics are affected by the cooling characteristics of the splitter plate, the temperature change of the arc current, and energy loss in the air. On the other hand, the DRV characteristics of the later stage are affected by the heat gas emission after arc extinguishing. This ionized heat gas is greatly affected by the magnetic field and is prevented from moving to the exhaust. For this reason, it is judged that there is a large difference in the late period (t

_{l}).

## 4. Conclusions

_{10}, t

_{21}, and t

_{32}corresponding to short-circuit characteristics are 1.58, 1.53, and 1.79, respectively, and t

_{i}, t

_{m}, and t

_{l}, corresponding to dielectric recovery strength are 1.59, 1.69, and 1.53, respectively. In other words, when the external temperature increases from 25 °C to 45 °C, it can be seen that both short-circuit characteristics and dielectric recovery strength deteriorate at a similar rate. This shows a similar tendency to the case of the experiment conducted previously by changing the thermal conductivity of the splitter plate [14]. The second external environmental condition is disturbing magnetic fields. For this experiment, an external magnetic field is introduced in the direction in which the interruption of the circuit breaker was disturbed. As a result, the short-circuit characteristics only show a meaningful result at t

_{21}, and there is no significant difference in the other periods. However, if the distance between the current paths that generate the Lorentz force in other circuit breakers is increased, it is expected to show a difference at t

_{10}. The dielectric recovery strength shows a significantly larger difference in the latter time than in the initial time and the medium time. The ability of magnetic fields to interfere with the release of heat gases is evident. These external magnetic fields can be applied in various ways depending on the circuit breaker installation environment. The influence in one direction is dealt with in this paper. The external temperature and disturbing magnetic fields covered in this paper are not tested according to product standards. In addition, greater damage is expected due to the miniaturization of the environment in which the circuit breaker is installed and the complexity of peripheral devices. Based on this paper, it is expected that more performance evaluations of circuit breakers in various environments will be conducted.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Schematics of measurement points. (

**a**) Short-circuit characteristics, (

**b**) Dielectric recovery voltage.

**Table 1.**Measurement result of DRV in previous paper [14].

Material (Thermal Conductance) [kcal/°C] | Time [μs] | Voltage [V] | |
---|---|---|---|

Steel (62) | Initial Period | 1.1 | 217 |

0.8 | 189 | ||

1.2 | 208 | ||

Medium Period | 3.1 | 281 | |

2.6 | 266 | ||

2.3 | 236 | ||

Later Period | 4.2 | 311 | |

5.0 | 362 | ||

4.7 | 347 | ||

Aluminum (196) | Initial Period | 0.8 | 314 |

0.5 | 115 | ||

0.77 | 309 | ||

Medium Period | 2.76 | 371 | |

1.76 | 283 | ||

2.14 | 362 | ||

Later Period | 3.92 | 362 | |

3.91 | 380 | ||

3.90 | 380 | ||

Copper (320) | Initial Period | 0.65 | 287 |

0.78 | 327 | ||

0.78 | 345 | ||

Medium Period | 1.88 | 292 | |

1.88 | 371 | ||

2.18 | 371 | ||

Later Period | 3.32 | 336 | |

3.52 | 327 | ||

4.25 | 415 |

Temperature | Category | Test Number [V] | AVG. | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||

25 °C | t_{10} | 2.73 | 2.57 | 2.41 | 3.94 | 2.84 | 2.20 | 3.55 | 2.21 | 2.49 | 2.77 |

t_{21} | 4.17 | 4.36 | 4.62 | 2.88 | 4.29 | 4.83 | 3.34 | 5.02 | 4.68 | 4.24 | |

t_{32} | 1.49 | 1.47 | 1.45 | 1.65 | 1.32 | 1.39 | 1.57 | 1.35 | 1.43 | 1.45 | |

35 °C | t_{10} | 2.51 | 1.24 | 1.49 | 2.67 | 2.55 | 2.44 | 2.09 | 2.04 | 2.29 | 2.14 |

t_{21} | 4.98 | 5.44 | 5.75 | 4.22 | 4.40 | 4.48 | 5.10 | 5.01 | 4.88 | 4.91 | |

t_{32} | 1.50 | 2.00 | 1.42 | 1.57 | 1.41 | 1.59 | 1.43 | 1.51 | 1.44 | 1.54 | |

45 °C | t_{10} | 1.99 | 2.60 | 1.59 | 1.65 | 1.29 | 1.23 | 1.77 | 2.08 | 1.86 | 1.78 |

t_{21} | 5.05 | 4.40 | 5.29 | 5.56 | 5.74 | 5.81 | 5.41 | 5.04 | 5.17 | 5.27 | |

t_{32} | 1.89 | 1.54 | 2.11 | 1.39 | 1.56 | 1.51 | 1.43 | 1.46 | 1.57 | 1.60 |

Temperature | C_{0}[μF] | Category | Test Number | AVG. | ||
---|---|---|---|---|---|---|

1 | 2 | 3 | ||||

25 °C | 0.47 | t_{DRV} [μs] | 0.96 | 1.23 | 1.01 | 1.06 |

V_{DRV} [V] | 423 | 386 | 230 | 346 | ||

1 | t_{DRV} [μs] | 1.74 | 1.90 | 2.02 | 1.88 | |

V_{DRV} [V] | 368 | 375 | 411 | 384 | ||

10 | t_{DRV} [μs] | 4.37 | 4.53 | 4.63 | 4.51 | |

V_{DRV} [V] | 467 | 491 | 489 | 482 | ||

35 °C | 0.47 | t_{DRV} [μs] | 0.83 | 0.90 | 1.44 | 0.99 |

V_{DRV} [V] | 318 | 312 | 209 | 279 | ||

1 | t_{DRV} [μs] | 1.79 | 1.87 | 1.83 | 1.83 | |

V_{DRV} [V] | 413 | 429 | 245 | 362 | ||

10 | t_{DRV} [μs] | 4.61 | 4.68 | 3.86 | 4.38 | |

V_{DRV} [V] | 399 | 437 | 376 | 404 | ||

45 °C | 0.47 | t_{DRV} [μs] | 0.62 | 1.20 | 0.57 | 0.79 |

V_{DRV} [V] | 238 | 169 | 236 | 214 | ||

1 | t_{DRV} [μs] | 1.77 | 1.92 | 1.94 | 1.87 | |

V_{DRV} [V] | 369 | 352 | 338 | 353 | ||

10 | t_{DRV} [μs] | 4.25 | 4.59 | 4.53 | 4.45 | |

V_{DRV} [V] | 334 | 435 | 333 | 367 |

Magnetic Field | Category | Test Number [V] | AVG. | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||

No magnetic fields (I = 0 A) | t_{10} | 3.56 | 2.57 | 2.41 | 3.94 | 2.61 | 2.20 | 3.55 | 2.83 | 2.49 | 2.90 |

t_{21} | 3.33 | 4.36 | 4.62 | 2.88 | 4.62 | 4.83 | 3.34 | 4.25 | 4.68 | 4.10 | |

t_{32} | 1.54 | 1.47 | 1.45 | 1.65 | 1.28 | 1.39 | 1.57 | 1.35 | 1.43 | 1.45 | |

Disturbing magnetic fields (I = 5 A) | t_{10} | 3.37 | 1.80 | 1.67 | 4.31 | 2.93 | 2.78 | 2.95 | 2.50 | 3.78 | 2.89 |

t_{21} | 3.69 | 5.14 | 5.19 | 2.73 | 4.64 | 4.59 | 4.57 | 5.02 | 4.50 | 4.45 | |

t_{32} | 1.33 | 1.86 | 1.73 | 1.47 | 1.40 | 1.14 | 1.47 | 1.45 | 1.30 | 1.46 |

Magnetic field | C_{0}[μF] | Category | Test Number | AVG. | ||
---|---|---|---|---|---|---|

1 | 2 | 3 | ||||

No magnetic field (I = 0 A) | 0.47 | t_{DRV} [μs] | 0.96 | 1.28 | 1.01 | 1.08 |

V_{DRV} [V] | 423 | 465 | 230 | 372 | ||

1 | t_{DRV} [μs] | 1.74 | 2.05 | 2.02 | 1.93 | |

V_{DRV} [V] | 368 | 384 | 411 | 387 | ||

10 | t_{DRV} [μs] | 4.88 | 4.53 | 4.63 | 4.68 | |

V_{DRV} [V] | 498 | 491 | 489 | 492 | ||

Disturbing magnetic field (I = 5 A) | 0.47 | t_{DRV} [μs] | 1.26 | 1.33 | 0.65 | 1.08 |

V_{DRV} [V] | 348 | 315 | 349 | 337 | ||

1 | t_{DRV} [μs] | 1.13 | 1.64 | 1.96 | 1.57 | |

V_{DRV} [V] | 298 | 384 | 410 | 364 | ||

10 | t_{DRV} [μs] | 4.69 | 4.56 | 5.13 | 4.79 | |

V_{DRV} [V] | 460 | 399 | 427 | 428 |

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**MDPI and ACS Style**

Cho, Y.-M.; Park, H.-J.; Lee, H.-J.; Lee, K.-A.
Analysis of Short-Circuit and Dielectric Recovery Characteristics of Molded Case Circuit Breaker according to External Environment. *Electronics* **2022**, *11*, 3575.
https://doi.org/10.3390/electronics11213575

**AMA Style**

Cho Y-M, Park H-J, Lee H-J, Lee K-A.
Analysis of Short-Circuit and Dielectric Recovery Characteristics of Molded Case Circuit Breaker according to External Environment. *Electronics*. 2022; 11(21):3575.
https://doi.org/10.3390/electronics11213575

**Chicago/Turabian Style**

Cho, Young-Maan, Hyun-Jong Park, Ho-Joon Lee, and Kun-A Lee.
2022. "Analysis of Short-Circuit and Dielectric Recovery Characteristics of Molded Case Circuit Breaker according to External Environment" *Electronics* 11, no. 21: 3575.
https://doi.org/10.3390/electronics11213575