Study of Arc Interruption Characteristics under Rated Current in Low Voltage Circuit Breakers

Abstract

The breaking capacity of rated current is one of the important indexes to evaluate the performance of circuit breakers, which is usually measured experimentally and cannot be analyzed in terms of the arcing characteristics of the opening process. Simulation methods based on the magnetohydrodynamic (MHD) model of the arc can be used to obtain the macroscopic motion of the arc within the interrupter and the interaction of the arc with the contacts, walls, and splitter plates. Therefore, this paper focuses on the arc interruption characteristics’ underrated current in low voltage circuit breakers by MHD simulation. A more accurate and effective field-circuit coupling MHD simulation model of low voltage circuit breaker products is developed in this paper. A nonlinear conductivity model of the sheath layer is considered to better simulate the near-pole voltage drop and bending processes after the arc has been cut by the splitter. The time-dependent magnetic field generated by the arc is considered in the calculation. Additionally, the real-time parameters of the external circuit are coupled to reflect the evolution of the arc characteristics under the action of the external circuit. The simulation results intuitively and clearly show the evolution of the arc during the breaking process. Through this, an arc extinguishing chamber can be designed to effectively regulate the arc interruption characteristics, thereby improving the breaking capacity of the circuit breaker. The accuracy and efficiency of the proposed simulation method is verified by experiments. This method can be extended to the performance analysis of AC/DC low voltage circuit breakers.

1. Introduction

Low voltage circuit breakers (LVCBs) are widely used in power distribution systems to protect the humans and for equipment safety. When the fault current occurs, an air arc is generated between movable and fixed contacts in LVCBs, and then extinguished to interrupt the circuit. During the arcing process, the arc may erode the contacts, side walls, and metallic splitter plates, which seriously affects the design lifetime of LVCBs [1]. Therefore, how to analyze the arc interruption characteristics accurately and reasonably is of great importance for the optimal design of LVCBs to improve their electrical lifetime.

The arc phenomenon involves the interaction of multiple physical fields, making it difficult to fully understand arc behavior through experiments. The arc burning process is a multi-coupled field involving an electromagnetic field, airflow field, temperature field, and radiation field [2,3,4]. In recent years, magnetohydrodynamic (MHD) modeling and simulation methods have been adopted to investigate the complex arcing characteristics in low voltage circuit breakers [5,6,7]. Yin et al. investigated the arc dynamics of air circuit breakers based on a three-dimensional MHD model, which initially reveals the arc motion law of the double parallel contact system [8]. The arc’s magnetic vector constraint is considered and the characteristics of the arc at different frequencies are discussed through a simplified MHD model in literature [9]. Zhao et al. discuss the effects of arc ignition position, exhaust size, and gas-producing material on arc dynamics through an MHD model with a parallel pole-plate structure [10]. Pawel et al. analyze the vacuum circuit breaker using the MHD method [11]. Rahimpour et al. optimize the structure of solid-state circuit breaker using the MHD method [12].

However, less attention has been paid to the sheath layer of the electrode and the influence of the external circuit on arc evolution behavior in real time.

In this paper, the MHD models of double-break molded case circuit breaker (MCCB) and miniature circuit breaker (MCB) products are developed based on air plasma chemical composition, thermodynamic properties, transport coefficient, and other physical parameters. A model that considers the nonlinear conductivity of the sheath layer is proposed to better simulate the near-electrode voltage drop and bending processes after the arc is cut by the splitter plates. The time-dependent magnetic field generated by the arc is considered in the calculation. In addition, real-time parameters of the external circuit are coupled to reflect the change in characteristics of the arc under the external circuit. The arc interruption characteristics are analyzed by temperature and pressure distribution. An arc interruption experiment of the corresponding product was carried out, from which the arc evolution pattern, arc voltage, and arc current curves were obtained. The results show that the proposed simulation method fits well with the experimental results. This method provides an effective method for the optimal design of the LVCBs.

2. Numerical Models and Control Equation

2.1. Basic Conditions

The arc can be regarded as an air plasma whose physical parameters can be considered as predefined functions of temperature and gas pressure [13,14].

The variation of air plasma thermodynamic parameters and transport characteristics’ parameters with the temperature at different pressures can be found in the related research [15]. From Figure 1, it can be seen that the variation of various physical quantities with temperature is nonlinear. The higher the pressure, the lower the enthalpy and sound velocity. For thermal conductivity above 15,000 K, it increases with the increase of pressure, which is beneficial for the cooling of the arc and makes it easier for the arc to be extinguished. Conductivity is basically 0 below 6000 K, because at lower temperatures, gas molecules only decompose and do not ionize, resulting in lower conductivity. Subsequently, the rate of change in conductivity decreases as the temperature increases rapidly to above 25,000 K, resulting in complete ionization of the gas. As the pressure increases, the conductivity increases. For the viscosity coefficient, it reaches its peak at 10,000 K, and above 10,000 K, the viscosity coefficient increases with the increase of pressure. The increase in viscosity is not conducive to the rapid movement of the arc. The constant pressure-specific heat represents the energy required to increase the temperature of a unit mass of gas by 1 K. The specific heat at constant pressure shows two peaks with temperature changes at approximately 7000 K and 15,000 K, respectively, and the peak decreases with increasing pressure.

The MHD model is based on the basic theories of thermodynamics, hydrodynamics, plasma physics, and electromagnetic fields, and lists the mass, momentum, and energy control equations that describe the relationship between the parameters of the arc, as well as additional equations for the electric and magnetic fields, and then relies on the finite volume method to solve numerically to obtain the characteristics of the arc under given conditions. Solving the above partial differential equations requires the following assumptions [15,16,17].

(1)

The arc plasma satisfies the states of local thermodynamic equilibrium (LTE) and local chemical equilibrium (LCE), which can be described by a uniform thermodynamic temperature for different types of particles.

(2)

Arc plasma is a continuous physical medium and is assumed to be a laminar flow.

(3)

The effect of ablative vapors from walls and contacts on the physical parameters of the air is not considered.

2.2. Control Equations and External Circuit Model

The arc burning process can be described by the Navier-Stokes equations [18,19,20,21,22,23]. The non-equilibrium state of the near-polar zone results in a high conductivity in the near-electrode zone, which needs to be considered in MHD modeling to take into account the near-electrode voltage drops and the extrusion and elongation of the arc column by the splitter plates. The near-polar region can be physically characterized as a space charge layer, an ionized layer, and a thermodynamically non-equilibrium layer [24,25,26,27].

The arc model needs to be expanded because of the interrelationship between the LVCBs and the external circuit, which can greatly affect the characteristics of the arc. The difficulty in describing this relationship lies in the need to solve the problem of real-time coupling between the multi-physical field of the arc extinguishing chamber and the external circuit. The Mayer model was used in the paper to simplify the physical behavior of the arc. To simplify the calculation, the external circuit is equated to an RL series circuit. According to Kirchhoff’s first law, the circuit equation can be obtained as shown in Equation (1).

$$U_h+R{I}_h+L\frac{d{I}_h}{dt}=U$$

(1)

where U is the equivalent external electric potential, U_h is the equivalent arc electric potential, I_h is the equivalent external current, R and L are the equivalent external resistance and inductance, respectively.

In this paper, the nonlinear differential Equation (1) is discretized and solved iteratively. For the equivalent external current in each iteration step, it can be expressed by Equation (2), namely, the current of the next time step is equal to the current of the time step, plus the change value of the current in Δt.

$$I_h^{(i+1)}=I_h^{(i)}+\frac{\Delta t}{L}(U-U_h(I_h^{(i)})-R{I}_h^{(i)})$$

(2)

where $I_h^{(i+1)}$ and $I_h^{(i)}$ is the equivalent external current of step i and step i + 1, respectively. Due to the complex functional relationship between the external current I_h and external potential U_h, U_h can be expressed as a function of I_h, which can be expressed as $U_h(I_h^{(i)})$.

3. Simulation Model and Boundary Conditions

MCB and MCCB are both circuit breakers used to provide protection against human hazards and appliance damage. MCB is used for low energy requirements such as for domestic purposes or small electronic circuits. MCCB is used for high energy requirements such as large industries or commercial purposes. The structure of the arc chamber of MCCB and MCB is shown in Figure 2.

In this paper, the corresponding three-dimensional MHD simulation model was established according to the main structural characteristics of the MCCB and MCB. The fluid calculation model is shown in Figure 3. The size of the MCCB model is 100 mm and 80 mm in x and y directions, respectively; the thickness of the splitter is 2 mm and the spacing of each splitter is 3 mm. The moving contact is used as the anode, and the arc runners are used as the cathode. There are two air outlets on the left and right sides, as shown in Figure 3a. The size of the MCB model is 100 mm and 50 mm in x and y directions, respectively, the thickness of the splitter is 2 mm and the spacing of each splitter is 7 mm. The upper arc runner is used as the anode, the DC current input is 16 A, the moving contact and the lower arc runner are used as the cathode, and the potential is zero. The lower left part of the model is set as an air outlet, and the outlet pressure is 1 atm, as shown in Figure 3b.

Boundary conditions are necessary for the solution of a system of equations, and reasonable boundary conditions will provide good convergence and solution accuracy for the solution of the system of equations. Combined with the actual interrupter chamber boundary situation, the paper mainly follows the following treatment to give the boundary conditions of each equation variable on the calculation model. To make all control equations closed, the following boundary conditions are used [28].

(1)

Velocity boundary conditions: all walls are slip-free walls.

(2)

Pressure boundary condition: one atmosphere in the initial interrupter chamber.

(3)

Temperature boundary condition: ambient temperature of 300 K.

(4)

Current boundary conditions: a static contact for the use of the average current density method to set the current density boundary, the other static contact end face for the zero potential surfaces. The average current density expression is shown in Equation (3).

$$J_{ave}=\frac{i_c{}^{(i)}}{S}$$

(3)

where J_ave is the current density of the current inlet surface, and S is the area of the current inlet surface.

4. Simulation Analysis

According to the experimental determination, the external circuit was set up with a resistance of 0.9873 Ω, an inductance of 0.005314 H, an RMS voltage of 251 V, a power factor of 0.509, an RMS current of 189 A, an initial current value of 139.86 A, and a voltage initial phase angle of 0.63 pis. The calculated arc temperature, flow field velocity, and arc voltage are used to describe the bending and elongation of the arc during circuit breaker opening and the arc movement into the splitters. From the distribution of the temperature of the arc at different moments of the ignition phase, it can be concluded that the evolution of the arc can be divided into the following stages. (1) The initial arc between the contacts in the air field and magnetic field under the action of continuous expansion, and an arc column with moving contact movement, expansion, and elongation. (2) The arc moves in the direction of the splitter, during which the arc is constantly bent and elongated, the arc voltage rises, and when it reaches the vicinity of the splitter, the arc column is squeezed by the splitter. (3) The arc enters the splitter area, the arc column elongates, and is cut. (4) Arc extinguished.

4.1. Analysis of the Arc Interruption Characteristics of the MCCB at the Rated Current

The movable and fixed contacts are separated when an arc is generated with the temperature distribution at different moments, as shown in Figure 4. As can be seen from the cloud diagram, the burning of the arc is consistent with the change in current. The arc starts to burn at the moment the contact is first split; the arc radius is small and confined to the static contact area. At the moment of 1.8 ms, the current increases to about 100 A, the arc spreads between the grating and the contact; the maximum temperature at this point is about 20 K, the radius of the arc increases, and the arc root on the moving contact has moved to the side of the contact. The arc spreads toward the splitter, starts to enter the splitter, and is squeezed and stretched at 2.2 ms; the arc is squeezed and cut by the splitter, and the arc voltage is raised further by the combined effect of cooling and the near-pole voltage drop from the cut at 2.7 ms. The current is reduced to approximately 150 A, at which point the energy injected into the arc is reduced and the arc radius becomes thinner at 3.6 ms. With a current of approximately 75 A, the overall temperature of the arc drops at 4.3 ms, and as the current decreases, the arc is completely extinguished at 5 ms. The arc continuously expands under the action of airflow and the magnetic field, and expands and elongates with the movement of the moving contact. When moving in the direction of the grid, the arc is continuously bent and stretched, and the arc voltage continuously rises. After reaching the vicinity of the grid, the arc column is squeezed by the grid.

When the arc is generated, its high temperature will cause the gas pressure in the arc and its immediate area to rise significantly. Figure 5 shows the distribution of gas pressure within the arc chamber at different times during the arc ignition period. When the arc has just started, the arc area is very small. As the current continues to increase, the contacts are pulled further apart and the internal pressure increases under the heating effect of the arc. The large production of ablative vapor is also one of the reasons for the increase in internal gas.

As shown in Figure 6, at the moment t = 2.2 ms, air vortices form in the splitter due to the pressure near the splitter area being higher than the contact area, which causes the arc to stagnate and is not conducive to the cutting action of the splitter on the arc. The arc begins to bend into the splitter and is elongated, and its path is almost along the surface of the splitter, greatly increasing the contact area between the arc and the metal material and accelerating the arc cooling at 2.7 ms. This also explains the rapid increase in arc voltage at this stage in Figure 7.

4.2. Analysis of Arc Interruption Characteristics of MCB at Rated Current

Figure 8 shows the temperature field of the MCB model. It can be seen that the contact gap is broken through and a clear conductive channel is formed at 0.2 ms; the arc is taking shape and the temperature distribution has diverged significantly, with high temperature points appearing at the root of the arc in contact with the metal surface. With the contact open, the arc is gradually elongated at 1.2 ms, when the contact is completely open. In the process of contact opening, the distance between the moving contact and the lower arcing piece is constantly reduced, increasing the pressure behind the moving and static contacts and accelerating the movement of airflow, as shown in Figure 9. In the case of small currents, because the arc is subject to less Lorentz force and receives relatively more influence from the airflow field, the arc root near the static contact is moving faster than the moving contact.

From t = 1.2 ms the anode arc root moves slowly along the contact surface toward the arc chamber, but the cathode arc root is almost stagnant due to the restraint of the baffle below the moving contact. The air inside the interrupter is subjected to a rapid rise in temperature by the arc root airflow field at 3.6 ms, after which the arc column begins to move toward the splitter. The arc column begins to come into contact with the interrupter splitter at 3.6 ms, the arc column is squeezed under the action of splitter ablation, and the arc voltage increases significantly. Until t = 3.8 ms, the arc is found after the region of reignition. On the one hand, this is because the arc after the region in the arc chamber cyclonic airflow influence temperature gradually increased, ionization began to occur, and resistivity decreased. On the other hand, in the process of cutting with the splitter, violent ablation in the arc column occurs to change the physical parameters of the arc, while making the arc column narrower, with an overall increase in resistivity of the conductive path.

The reignited arc root moves back toward the arc extinguisher under the action of the Lorentz force at 4 ms, while the lower running arc path also makes full contact with the arc column to form a new arc root, and the current is transferred from the moving contact to the lower running arc path at 4.2 ms, as shown in Figure 10. From t = 5.0 ms onwards, the arc is fully in contact with the splitter and enters the arc extinguishing stage, but the arc does not cut through the splitter because the Lorentz force is not sufficient to overcome the viscous force at low currents. With the dissipation of the arc energy, the current gradually decreases and the arc is finally extinguished.

5. Experimental Analysis

5.1. Analysis of MCCB Experimental Results

To verify the correctness of the MCCB simulation results, an experimental system was built to capture the arc motion characteristics with a CCD. The images obtained from the experiment are shown in Figure 11. From the test high-speed video, it can be seen that at 0 ms, the static and moving contacts are still closed and no arc is generated. The moving and static contacts begin to arc at 0.1 ms, and the brightness of the arc gradually increases and continues until 1.5 ms when the arc begins to enter the splitter. The arc is driven into the splitter at the same time in the simulation, as shown in Figure 3. The arc exits the splitter increasing in brightness at 2.0 ms; the arc enters the splitter and the arc highlight area is located at the splitter position at 2.3 ms. The arc gradually brightens until 3.6 ms, when it appears that the arc has been completely divided by the splitter and will be driven to the outlet, which is consistent with the simulation results. After that the arc continues to brighten around the back of the moving contact, gradually darkening to 4.3 ms and finally extinguishing. The analysis of arc behavior is based on the moment when the arc starts, the moment when the arc enters the splitter plate, and the moment when the arc is extinguished, which is basically consistent with the description in the simulation.

The voltage and current waveform graph curves during the experiment and simulation are shown in Figure 12. It can be seen that the changing trend is the same, and the error between the simulated calculated voltage and current, and the experimental voltage and current is controlled within 20%, which verifies the accuracy of the simulation model. The rate of decline in arc current is small until 2 ms, mainly due to the low arc voltage. Whereas the rate of change of current is positively related to the difference between the system voltage and the arc voltage. Therefore, the higher the arc voltage, the better the current limiting performance. The arc enters the splitter region 2.7 ms later, and the arc voltage starts to increase due to the near-electrode voltage drop. As a result, the arc current drop rate increases depending on the external circuit change. The voltage and current trends obtained from the arc simulation are in good overall agreement with the experimentally obtained voltage trends.

5.2. Analysis of MCB Experimental Results

The images obtained by the high-speed camera are shown in Figure 13. The dynamic characteristics of the test arc can be seen in general agreement with the simulation trend. When the moving contacts are opened, breakdown occurs between the contacts to form an initial arc at 0.2 ms, which is accompanied by the moving contacts being fully opened and the air plasma being fully ionized to form a bright arc column. In the simulation, the bright arc column is formed in about 0.2 ms, which is consistent with the experimental behavior. The arc begins to enter the interrupter chamber under the action of the Lorentz force and airflow field at 3.0 ms. The arc elongates to its maximum extent and comes into contact with the grating, undergoing violent ablation followed by reignition in the post-arc region at 3.6 ms; this phenomenon, that the arc root will re-ignite at about the same time, was also noticed in the simulation. This is accompanied by a slow development of the air ionization process on the down-running arc, with a new arc root forming at 4.2 ms and a complete transfer of cathodic current from the moving contact to the down-running arc at 4.4 ms. As the Lorentz force at a low current is not sufficient to overcome the viscous force between the arc and the splitter, the arc column is partially stagnated on the groove side of the splitter until the arc is completely extinguished at 5.6 ms, and the arc appears blue-purple and the air is gradually transformed from the ionized state to the insulated state. This phenomenon can be found in the simulation in Figure 8; with the dissipation of arc energy, the current gradually decreases and the arc finally extinguishes.

The voltage and current waveform curves during the experiment and simulation are shown in Figure 14. The arc is gradually elongated during the movement of the moving contact, and the arc diameter has a significant increase in the process to a certain extent; the arc column is the longest between 0~3.6 ms, showing a slow increase in the overall arc voltage. Between 3.6~3.8 ms, the arc column and the grating undergo violent ablation, forming a reignition in the post-arc region, which is manifested as a drop in arc pressure. This is partly because the temperature of the post-arc region in the arc extinguishing chamber is gradually increasing under the influence of the cyclonic airflow when ionization begins to occur and the resistivity decreases. On the other hand, the arc column undergoes violent ablation during the cutting process with the splitter, which changes the physical parameters of the arc, while making the arc column narrower and increasing the overall resistivity of the conductive path. Between 3.8~4.2 ms, after a short elongation of the reignited arc, the cathode arc root is transferred to the lower runner arc path, showing another drop in arc pressure. Between 4.4~4.9 ms, as the arc root moves, the arc is squeezed by the static contact and the lower lead, and then further elongated as the open distance increases. Throughout the process, the arc generally tends to lengthen, so the arc voltage generally tends to rise. As the arc gradually enters the splitter, the arc column is extruded by the ablation of the splitter and the arc voltage rises rapidly. As the arc energy is dissipated, the current drops rapidly at 4.9~5.4 ms, and the arc voltage shows a slow decline. The arc is finally extinguished at 5.8 ms. The proposed simulation method considers a nonlinear conductivity model of the sheath layer to better simulate the near-pole voltage drop and bending processes, which leads to more precise and truer current and voltage values compared to other works [10,11]. At the same time, the article simulated the actual product model, which was not achieved in previous articles because they only simulated an idealized model. The results in Figure 12 and Figure 14 also indicate that the simulation method presented in the article can effectively match the simulation results with the actual product results, and is thus a method with great promotion significance in engineering and product design.

6. Conclusions

In this paper, a more accurate and effective field-circuit coupling MHD simulation model of low voltage circuit breaker products was developed. An MHD model that integrates the nonlinear conductivity of the arc sheath layer and real-time coupling with the external circuit is proposed. The interruption characteristics of MCCB and MCB are analyzed by this method, and the conclusions are as follows.

(1)

A more accurate and effective MHD simulation model for LVCB, which considers the nonlinear conductivity model of the sheath layer and the real-time coupling with the external circuit, has been established. This modeling method provides theoretical and technical references for the optimization design of related products, becoming an important means to effectively improve product performance.

(2)

For MCCB, the movable and static contact is located in the splitter plate area. Therefore, the arc can quickly enter the splitter plate area after arcing, thus the arc voltage rises rapidly, which will play a good role in limiting current and is conducive to the rapid breaking of the arc. Moreover, there will be no back breakdown phenomenon.

(3)

For MCB, the air gap structure between the movable and static contacts can be changed to accelerate the airflow field. It accelerates the residence time of the arc in the contact area, and reduces the occurrence of reverse breakdown phenomenon.