# Circuit Model and Analysis of Molded Case Circuit Breaker Interruption Phenomenon

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[15,16]. Various studies have been conducted on these arc currents [17]. In particular, it was found that, the smaller the electrode size of the contacts, the higher the arc voltage [18,19]. Arc movement during contact separation is also an important factor in analyzing interruption. The reaction force at the contact electrode is proportional to the magnitude of the current, and it is confirmed that it reacts at about ten times the rated current. Therefore, the more the fault current flows into the wiring circuit breaker, the faster the current-time response.

## 2. Interruption Phenomenon and Background Theory

_{2}and t

_{3}are the starting times for section II and section III, respectively.

^{2}). This force exerts its force when the contact is attached, and when the contact begins to fall, it is exponentially less powerful. The maximum value of this force may be affected by the opening of the contact point, but in most cases, the circuit breaker application is omitted owing to its weak force.

_{e}is the length of the electrode arm, in units (m); and d

_{e}is the distance between the electrodes, in units (m). The application requires additional application of the angle changing in Equation (3). If the current flowing is large enough, the Lorentz force not only operates before the contact opens, but also can have an effect after the contact is opened.

_{sb}is the Strfan=Boltzman constant ($5.67\times {10}^{-8}\mathrm{W}/{\mathrm{m}}^{2}{K}^{4}$), A

_{s}is the surface area of the arc, η is the percentage of electrical power that is converted into radiation, I is the arc current, and V

_{colu}is the arc voltage. η is assumed to be 70%.

_{arc}is length of arc; j

_{root}is the average current density of arc root, in units (a/mm

^{2}); and a is the arc column expansion coefficient. This value is set to 1.

_{1}is the pressure changed by the arc current, P

_{0}is the ambient pressure, and A is the cross section of the space affected by the force. Based on the arc current, there is less space inside, and the outside is trapped by the splitter plate. Among these, the upper part of the splitter plate direction has a relatively large amount of space, and exhaust also exists in that direction. Because of this, the generated arc current extends upward towards the plate. The Lorentz force, which we have looked at earlier, can help the arc current extend further upward. Some circuit breakers are designed to induce movement of arc current by utilizing ferrite cores and other surrounding conductors such as splitter plates.

_{arc}is the arc temperature, in units (K). The voltage drop of the plate is obtained as follows:

## 3. Circuit Modeling

#### 3.1. Modeling of Section I

#### 3.2. Modeling of Section II

_{arc}) value of section II is obtained. (Figure 7). Section II of this modelling is measured from 1.2 ms to 7.3 ms. The resistance values are fitted as a primary function, and the error rate is 2.13%. This linearized resistance value is used as the resistance (R

_{arc}) in section II in the circuit model.

^{2}and the ambient temperature is 300 K.

#### 3.3. Modeling of Section III

_{3}for starting section III is determined based on the results of the experiment, and t

_{3}values per case are as follows: 7-plates is 6 ms, 5-plates is 6.2 ms, 3-plates is 7.2 ms, and 1-plate is 7.3 ms.

_{sp}) between electrodes during section III. This voltage (V

_{sp}) consists of voltage drop by plate (V

_{plat}

_{e}) and voltage drop by arc length (V

_{arc}), as shown in Equation (13).

_{plate}) is as follows. The energy of one plate over a specified time is calculated using Equation (10), and the voltage of one plate is calculated using Equation (12). Table 1 shows the temperature and voltage drop when the arc first touches the splitter plate in each case. Here, the specific heat of one plate is 0.447 J/(g·K), the weight is set to 4 g, and the top one plate weighs 2 g.

_{arc}). This value is obtained using Equation (6), as shown in the modeling of section II. At this time, the arc length is required, which consists of the shortest distance and a number of distances (2 mm) between plates. For example, in the case of 7-plates (basic state), this is the sum of the shortest distance and seven distances between plates (2 mm) (Figure 11). The shortest distance of cases is as follows: 7-plates is 12 mm, 5-plates is 12 mm, 3-plates is 14 mm, and 1-plate is 19 mm. The constant voltage (V

_{sp}) generated in this section is modeled on the circuit using the zener diode.

_{2}and t

_{3}is determined experimentally. In section II, the variable resistance (R

_{arc}) is obtained as shown in Figure 7, and in section III, the voltage (V

_{sp}) is obtained through Equation (13).

## 4. Comparison of Simulation Model and Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Case | Temperature (K) | Voltage Drop of One Plate (V) | Total Voltage Drop (V) |
---|---|---|---|

7-plates | 21,138 | 8.18 | 53.17 |

5-plates | 20,576 | 8.52 | 42.59 |

3-plates | 16,493 | 11.87 | 35.61 |

1-plate | 15,927 | 12.51 | 12.51 |

Section II | Section III | |||||
---|---|---|---|---|---|---|

Model | Simulation Value (V) | Experiment Value (V) | Error Rate (%) | Simulation Value (V) | Experiment Value (V) | Error Rate (%) |

7-plates | 70.8 | 75 | −5.6 | 167 | 143 | 16.8 |

5-plates | 68.7 | 62.5 | 14.7 | 135 | 132 | 2.3 |

3-plates | 69.6 | 73.5 | −1.1 | 96 | 128 | −25.0 |

1-plate | 69.3 | 53.1 | 36.5 | 73 | 88 | −17.0 |

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**MDPI and ACS Style**

Lee, K.-A.; Cho, Y.-M.; Lee, H.-J.
Circuit Model and Analysis of Molded Case Circuit Breaker Interruption Phenomenon. *Electronics* **2020**, *9*, 2047.
https://doi.org/10.3390/electronics9122047

**AMA Style**

Lee K-A, Cho Y-M, Lee H-J.
Circuit Model and Analysis of Molded Case Circuit Breaker Interruption Phenomenon. *Electronics*. 2020; 9(12):2047.
https://doi.org/10.3390/electronics9122047

**Chicago/Turabian Style**

Lee, Kun-A, Young-Maan Cho, and Ho-Joon Lee.
2020. "Circuit Model and Analysis of Molded Case Circuit Breaker Interruption Phenomenon" *Electronics* 9, no. 12: 2047.
https://doi.org/10.3390/electronics9122047