2015 3rd International Conference on Electric Power Equipment - Switching Technology (ICEPE-ST) Oct. 25-28, 2015 Busan, Korea Coupled Simulation of Eddy-Current Thermal Field in Medium Voltage Switchgear Hong Lü, Liuhuo Wang / Electric Power Research Inst. of Guangdong Power Grid Corp., Guangzhou, Guangdong, China Wensong Zheng, Lijun Wang, Jing Lin / State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an, China Email: lijunwang@mail.xjtu.edu.cn Abstract—The temperature rise is very critical for the normal operation of switchgear, in which eddy current and contact resistance are the two important influence factors. In this paper, firstly, the main conductive circuit model of one kind of 12kV medium voltage switchgear is established using commercial software Solidworks. Secondly, the effect of the eddy current and contact resistance on the temperature rise of switchgear is simulated with consideration of heat conduction, convection and radiation, and also reasonable boundary conditions. Simulation results show that the loss of eddy current accounts for 20% of the total loss, which indicates the eddy current is so significant that it can’t be neglected. Then, the effect of the different position of the contact resistance on temperature rise is also studied. Simulation results show that when the contact resistance is close to the edge, the heat loss of the contact increases significantly due to the longer conductive path. The temperature of the contact near the edge grows significantly due to the skewed-slots coil structure of the axial magnetic field contact, which is unfavorable for the energy transfer through heat conduction. And because of the higher temperature at the edge, the temperature of other positions can also be increased. Keywords— Medium-voltage switchgear; eddy loss; contact resistance; temperature rise; simulation I. INTRODUCTION As important electrical equipment, switchgears are widely used in power system and play a great role in opening and closing, control and protection of electrical equipment. Based on the voltage rank, they can be divided into high voltage, middle voltage and low voltage switchgears. During the switchgears’ normal operation, the components inside them will generate ohmic loss due to the current flow, including Joule heat and eddy loss because of induced current. When the Sine current level is higher, the eddy loss will not be ignored. After a long time of normal operation, due to the increase of contact resistance and relatively closed structure, the heat dissipation characteristic gets worse. The temperature on some positions of the conductive path gets very high, and some even close to or bigger than permitted temperature. This can not only affect the characteristic and lifetime of the insulation facility but also influence the steady and safely operation of power grid. A lot of works on temperature rise of switch facilities have been done by many researchers. J.K. Kim and S.C. Hahn analyzed the single phase bus-bar of the GIS using the coupling method between electromagnetic and thermal fields in which eddy current was taking into account, but it was just a simple two-dimensional model [1]. J. Paulke et al built the threedimensional model of low voltage switch facility and carried out thermal analysis of different operating state with consideration of influence of contact resistances [2]. N. Benjemaa and R. Abdi proposed the way to calculate contact resistance under the force region of copper bus-bar and also carried out simulation and experiment on fixed and slide contact [3]. F. Song studied eddy current and related loss problem of GIS facility and showed the eddy loss and temperature distribution of the disconnect switch room and bus-bar room [4]. Literatures [5-8] also carried out simulation calculation of thermal field on solid insulation and air-insulated switchgear. In the paper [6], the concept of heat network was introduced to make the results more accurate combining with CFD, and a special analysis was carried out on instantaneous temperature of switchgear during short-circuit fault. In summary, simulation and analysis on electromagnetic thermal coupling of medium-voltage switchgear main circuit are less. And many related study didn’t consider the combined effect of contact resistance, eddy current, convection and radiation, and the impact of contact structure on the results was not considered either. In this paper, a model of a kind of 12kV switchgear is established and a simulation of temperature rise of its normal operation based on Ansys Workbench combining eddy current field and steady state thermal field considering the several influence factors above is carried out. II. COUPLED METHOD OF EDDY-CURRENT THERMAL FIELD Eddy current field Thermal field Model import Share model Solver selection Material reassigned,mesh Excitation, material, boundary condition Import loss Adaptive meshing Thermal field Boundary condition Solve after cheking Thermal field Fig. 1 Simulation overall framework chart Fig. 1 shows the framework of the simulation. Firstly, eddy current field is calculated, then the loss value is imported into 978-1-4673-7414-9/15/$31.00 ©2015 IEEE Authorized licensed use limited to: Xian Jiaotong University. Downloaded on January 07,2021 at 08:57:24 UTC from IEEE Xplore. Restrictions apply. 63 steady state thermal field, finally the temperature distribution is obtained. III. SWITCHGEAR CALCULATION MODEL The switchgear entity is shown in Fig. 2, whose rated current is 3150A. The main circuit is composed of bus-bars, isolating circuit breaker and current transformers. The current is introduced from bus-bar and the conductive path is up and down through. Instrument room (b) Model details Fig. 3 Simplified switchgear calculation model Busbar IV. Isolated breaker Current transformer Fig. 2 Switchgear entity In this paper, the 3D model is established by Solidworks. As there are insulating materials between the conductive circuit and the switchgear shell, only the model of the conductive path is established and the shell is not taking account. In the model, the electrical contact between the contact fingers and the contacts is fully considered. The vacuum interrupter is wrapped in solid epoxy seal pole. In the model, since the relative permeability of the insulting material is close to 1, which would not affect the calculation of electromagnetic field and its thermal conductivity is so low to affect the thermal field, at the same time, in order to save the computing time, the interrupter shell and the epoxy parts are ignored. But for the current transformer, as the epoxy is close to the metal parts, it is also modeled. The model of other parts is exactly in agreement with the entity, but the contact fingers are simplified when modeling. The model is shown in Fig. 3. Busbar Contact Soft connection Current transformer Feeder busbar (a) Calculation model of main circuit THEORETICAL BASIS OF EDDY CURRENT LOSS AND THERMAL FIELD CALCULATION A. Eddy Current Calculations Equations of the electromagnetic field are described by a set of Maxwell equations [9], including four laws: Ampere's law, Faraday's law of electromagnetic induction, Gauss's electric flux law and Gauss magnetic flux law. For quasi-static electromagnetic field, the electric flux density can be ignored compared with the conduction current density, which means the changes in the magnetic field generated by an electrical field are not considered. The quasi static field that contains conductive material is also called as eddy current field. The differential equations can be expressed as: & u+ & u( & % & & (1) w% wW (2) (3) & In which: +& ——The strength of the magnetic field vector, A/m; - ——The total current density vector, A/m2; & (& ——The electric field intensity vector, V/m; % ——The magnetic induction vectorヤWb/m2 (T); t ——Time, s. Auxiliary equation: & & V( & & (4) (5) % P+ In which: P ——Permeability, H/m; V ——Electrical conductivity, 1/Ωm. In this paper, the electromagnetic field solving part is completed by Maxwell eddy current solver. The Maxwell 3D eddy current solver is used to analyze the time-varying magnetic field caused by time-varying current in the conductor or external alternating magnetic source. After the definition of the current source and necessary boundary conditions, the 3D eddy current field adopts the following two kinds of combined methods to calculate magnetic field [10]. In the case there exists eddy current inside the conductor, the direct method is used to solve the magnetic field strength. 64 Authorized licensed use limited to: Xian Jiaotong University. Downloaded on January 07,2021 at 08:57:24 UTC from IEEE Xplore. Restrictions apply. u 1 u H = jZP H (6) V + jZH Magnetic scalar potential method is adopted to calculate magnetic field strength. (PI )= (7) For the object that eddy current is not specified, the solver will adopt magnetic scalar potential method to calculate magnetic field. And if eddy current calculation is needed, the solver will adopt direct method to calculate eddy current. At the boundary side, the solver forces H continuous, then continuous magnetic field calculation is generated in the model. Because the Maxwell software adopts adaptive meshing technology, computing error can be reduced to any specified value. And energy calculation error is less than 1%. By calculating electromagnetic field, the ohmic loss can be obtained by using the following law: P 1 J · J *dV (8) ³ 2V V And the relationship between ohmic losses and resistance is as follows: P I 2 RRMS (9) In engineering practice, a variety of electrical contact has a direct impact on the resistance value. Any refined and processed flat is actually rough. When the surfaces are contacted, even if a large contact force is applied on the contact face, actual contact still occurs in few points. These actual contacted surfaces bear all of the contact force. And because of the oxide film effect of metal surface, only the surfaces where oxide film is crushed have actual contact. These contact points are called conductive points. When current flows through the contact spots, the current line shrinks to produce contact resistance. In the switchgears, the contact resistance between separable static and dynamic contact is particularly evident. For engineering applications, the general assumption is that there is only one contact spot between contact surfaces. This article assumes that there is a cylinder (conductive bridge model) which is equivalent to contact resistance between static and dynamic contacts. The material property of conductive bridge is the same as contact material, and the radius is determined by Holm equation [11]. r F (10) ¯± H In the formula, F means contact pressure, ξ stands for surface contact coefficient which is generally between 0.3 and 0.6, and H stands for material hardness. In this study, the contact pressure of the isolation breaker at its operation position is 4800N, and the contact coefficient is set as 0.3. The material of the contact blade is CuCr50, the hardness of which is 128. The cylindrical radius can be calculated to be 4mm. And since the main circuit resistance of the isolation breaker is under 50μΩ, the height of the cylinder can be identified as 4mm. Fig. 4 Contact resistance model In the eddy current calculation, 3150A current is loaded as excitation, and the phase difference of three phases is 120o, the frequency is power frequency 50Hz. The meshing method is based on the depth of the surface, which fully takes the impact of skin effect into account, and the displacement current is ignored. B. Steady-State Thermal Field Calculation In thermal analysis, three kinds of main heat transfer ways are included: thermal conduction, thermal convection and thermal radiation. As the conductive components in the switchgear are in a closed environment, thermal conduction is the main cooling mode. And there is still small amount of thermal convection and thermal radiation. The threedimensional steady-state thermal conduction is described by the following formula [12]: ¬ w 7 w 7 w 7 w] w[ w\ q (11) In whichヲ TĘĘTemperature (K); ƉĘĘThermal conductivity (W/m·K); q——Energy produced per unit volume (W/m3). In steady-state thermal field calculation, the conduction equations are calculated by the methods in which thermal conductivity is given to the materials. But for thermal convection and radiation, surface convection coefficient and thermal emission coefficient are given to the surface to be equivalent to convection and radiation process. In practice, the two coefficients have important influence on the temperature rise in the calculation. For the boundary conditions of this paper, the conductor pole and contact parts in the interrupter are only given the radiation emission coefficient of 0.4 as their vacuum environment. And the convection coefficient is set as 6W/m·K for the bus-bar and contact base. The mechanical connection part is given the coefficient of 3 W/m·K as its relative closed environment. What’s more, the epoxy part surround the current transformer is given the coefficient of 6W/m·K. The ambient temperature is set as 22Ȕ. The material of conductor pole, contact base, bus-bar and mechanical part is copper. The contact support is made of steel stainless. And the material of contact plate is made from 65 Authorized licensed use limited to: Xian Jiaotong University. Downloaded on January 07,2021 at 08:57:24 UTC from IEEE Xplore. Restrictions apply. TAB 1 MATERIAL PROPERTY OF THE MAIN PARTS Name thermal conductivity (W/m·K) Bus-bar Cu 401 Conductive clip Cu 401 Contact base Cu 401 Conductive pole Cu 401 Contact blade CuCr50 330 Contact support steel stainless 15.1 Insulation epoxy 0.29 V. material SIMULATION RESULTS AND DISCUSSION A. Influence of Eddy current on total loss To illustrate the effect of eddy current on the total loss, the electromagnetic field is calculated in two kinds of conditions: with and without eddy current. Maxwell field solver can calculate the total loss of each part, and the loss of the main parts of the model under the two conditions is shown in Table 2. TAB 2 OHMIC LOSSES OF VARIOUS PARTS Parts name Without eddy With eddy Bus-bar 22.31W 28.80W Conductive clip 0.75W 1.40W Contact Base 5.70W 7.77W Soft Connection 4.01W 4.50W Contact plate 108.25W 113.73W Conductive bridge 11.90W 12.03W As can be seen, the losses of various parts increase significantly after the eddy current is taken into account. The total loss is 1400W when eddy current is ignored, but when it is considered, the total loss increase to 1847W. That is to say eddy current loss is about 24% of total ohmic loss, and is a very important factor leading to conductor heating. Meanwhile, the contact resistance and contact plate are two sources that contribute to the losses of the conductive circuit, which take account for 6% of the total loss. Therefore, improving the material property of the contact plate or reducing the contact resistance is important way to reduce the losses. B. Influence of convection coefficient and radiation emissivity on temperature rise In the setting of the thermal field boundary conditions, the convection coefficient and emissivity of the model surface are given according to the empirical values. So the different coefficients will have some impacts on the results. To verify these impacts, extreme cases are considered in which several groups of different simulation conditions are conducted. In some cases, only radiation emissivity is given to the model surface and in others convection coefficient is added. Thus, the impacts on the thermal field are compared under different coefficients. The simulation results are shown in Fig. 5. Without radiation With radiation Temperature CuCr50. Table 1 shows the material property of the main parts of the model. Convection coefficient Fig. 5 Impacts of convection heat transfer coefficients and radiation emissivity Since the convection coefficient on the metal surfaces is generally between 2 and 10 [12], the results are only compared in this range. The radiation efficient on copper surface is fixed at 0.4. As can be seen from the comparison results, the radiation begins to play a significant role when the temperature is higher than 100oC. There is almost no difference with or without radiation coefficient when the temperature is lower than 100oC. When the convection coefficient is set from 2 to 10, the temperature gradually decreases, but the rate of decline slows down which shows that changes of the convection coefficient begin to affect more significantly as the temperature goes higher. And the minimum temperature rise difference between them (with and without radiation) is about 5K. When the convection coefficient is selected as different values, the maximum difference between them is 30K. The effect of radiation is significant. C. Steady-state Thermal Field Results Based on the comparison of above simulation results, in the steady-state thermal field calculation of this paper, radiation emissivity is only set on the arc chamber surfaces since it is the main high temperature area. And as the vacuum environment, no convection heat exchange is nearly zero. The convection coefficients of other parts are set according to actual situation. The final steady-state thermal simulation results are shown in Fig. 6. ć Temperature/ć 166.82 152.46 138.10 123.74 109.38 95.02 80.66 66.30 51.94 37.58 23.22 Fig. 6 Steady-state thermal field As can be seen from the results, the highest temperature of the main circuit is located near the contact, and the value is 66 Authorized licensed use limited to: Xian Jiaotong University. Downloaded on January 07,2021 at 08:57:24 UTC from IEEE Xplore. Restrictions apply. D. Influence of contact resistance location on thermal field In the above model, the contact resistance is assumed to be located in the electrode center. But in practice, duo to the uneven force on the end of the conductive poles and slightly ablation on the contact plates, the actual contact points is likely to deviate from the electrode center. To explore the impact of this case on the circuit temperature rise, another two cases are specially considered: contact resistance off the center and contact resistance located in the edge. Three kinds of positions of contact resistance are shown in Fig.7. In order to compare the result with above, the diameter and height of the contact resistance value is fixed. Contact resistance (a) (b) (c) Fig. 7 Contact resistance position (a) center; (b) off the center; (c) edge The set of electromagnetic and thermal boundary conditions is the same as when the contact resistance is located in the center. The simulation results of the contact section faces are shown in Fig. 8. Temperature/ć ć 233.93 221.03 208.12 195.22 182.31 169.41 156.50 143.59 130.69 117.78 104.88 (c) Contact resistance at the edge Fig. 8 Contact thermal field of different contact resistance positions When the contact resistance is located at the center, the heat that generated by the contact resistance is conducted from the contact plates to the stainless steel support and side copper body below. Although the thermal conductivity of copper is far greater than the stainless steel, duo to the chute structure of axial magnetic field contact, the conductive path is so long to make the thermal field evenly. When the contact resistance is off the center, the current conduction path and heat conduction path get changed. The temperature increases slightly but doesn’t change significantly. And when the contact resistance is located at the edge, the current is conducted along the chute of the side. The conduction path gets much longer, so the heat generated by the contact resistance can’t be conducted well, resulting in the temperature of contact resistance much higher than the previous. The highest temperature reaches to 233.93oC. Similar to the foregoing, the temperature changes of busbar, contact base and conductive clip of three cases are compared. The results are shown in Fig. 9. Temperature/ć 166.82oC. The lowest temperature is 23.22oC which is located at the epoxy parts surrounding the current transformer. Thermal fields of three phases are basically the same. In steady-state thermal simulation, temperatures rise of bus-bar, contact base or other parts that are easy to be observed are more concerned. In this example, the bus-bar temperature rise is 59K, the contact base 63K, the conductive clip 74K. According to the national standards, the temperature rise of exposed parts in switchgear in steady state should not exceed 65K [13]. Simulation results show that it meets the standard requirements. 250 233 183 166 150 100 Temperature/ć ć 166.76 159.49 152.21 144.93 137.65 130.38 123.10 115.82 108,54 101.26 93.98 Highest Busbar Contact base Soft connection Lowest 200 122 111 106 82 88 83 90 90 97 50 23 23 23 0 At the center Off the center At the edge Fig. 9 Influence of contact resistance positions on temperature of different parts (a) Contact resistance at the center Temperature/ć ć 183.74 175.04 166.33 157.63 148.92 140.22 131.51 122.81 114.10 105.40 96.69 (b) Contact resistance off the center As can be seen from Fig. 9, when the contact resistance is off the center, the effects of temperature on other parts are limited. The temperature change of bus-bar and contact base doesn’t exceed 5K. But when the contact resistance is at the edge, significant temperature changes of each part can be seen. And the temperature rise of contact resistance is about 210K, which has direct effects on steady-state thermal field. Under the operation of switchgear, to maintain the mechanical moving parts work properly and to minimize the contact plate surface erosion will help to keep the contact resistance located at the central area to prevent the additional temperature rise duo to the contact resistance deviation. 67 Authorized licensed use limited to: Xian Jiaotong University. Downloaded on January 07,2021 at 08:57:24 UTC from IEEE Xplore. Restrictions apply. VI. CONCLUSIONS Based on the modeling and simulation of medium switchgear, the following conclusions can be drawn, 1) Eddy current loss is one important aspect of switchgear main circuit ohmic loss, which accounts for 20% of the total loss. Its impact on steady-state thermal during switchgear operation can’t be neglected. Effective reduction of eddy current loss can help to reduce the temperature rise. 2) The convection and radiation coefficients in the set of steady-state thermal field boundary conditions will have a significant impact on simulation results. In the actual calculation, based on the specific circumstances, different thermal boundary conditions should be set on different positions. 3) During the actual operation of switchgear, duo to the uneven force on the end of the conductive poles and slightly ablation on the contact plates, the actual contact points are likely to deviate off the center. When the contact resistance is close to the electrode edge, the maximum temperature will increase significantly. And the temperature of the bus-bars, contact base and conductive clip will also rise. [3] [4] [5] [6] [7] [8] [9] [10] REFERENCES [1] [2] J.K. Kim, S.C. Hahn, K.Y. Park, H.K. Kim, Y. H. Oh. 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