thermal performance evaluation of air circuit breaker

THERMAL PERFORMANCE EVALUATION OF AIR CIRCUIT BREAKER (ACB) USING COUPLED ELECTRIC-THERMAL ANALYSIS

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Subhash NN, Vikrant Deshmukh, Sonil Singh, Arnab Guha (EATON India Engineering Centre, INDIA); [email protected] [email protected] [email protected] [email protected] Ramdev Kanapady, Ph.D, ASME Fellow (EATON, USA). [email protected]

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Abstract: Air circuit breaker (ACB) protects the circuit of electrical equipment from fault conditions due to abnormal current. The abnormal current arises due to overload faults, short circuit faults and ground faults. The size of ACB has been decreasing in accordance with voice of customers, which resulted in higher power density and internal heat generation which causes higher component temperature. The heat sources of ACB are the current carrying conductors. Therefore, proper knowledge of thermal characteristics of ACB current conducting path is essential for the accurate thermal design to ensure safe and reliable operation.

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This paper describes a new iterative sequentially coupled electric-thermal finite element modeling methodology to accurately predict the temperature rise in ACB. The proposed approach 1) capture the effect of resistance rise with temperature, 2) accurately account for electrical contact resistances which are modeled as contact volumes validated by measured values, 3) incorporate accurate heat transfer coefficients required at surfaces of inside the circuit breaker current path, heat dissipation from the plastics and mounting frame which are obtained from a separate CFD model that account for both convective cooling and radiative heat transfer and 4) inclusion of thermal contact resistance at various contact surfaces to accurately model the heat barriers to the heat flow along the path of the current path. The proposed approach is validated with temperature rise test results. Key words: Air circuit breaker (ACB), Coupled electric-thermal analysis, Finite Element Method (FEM), Heat Transfer Coefficient (HTC), Computational Fluid Dynamics (CFD).

1.

Introduction

Circuit breakers protect the electrical equipment from fault conditions due to excessive or abnormal current. The abnormal current arises due to overload faults, short circuit faults and ground faults.

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Circuit breakers are manufactured in wide variety of sizes, from small devices for a single household appliance up to large switchgear for high voltage circuits of an entire city. Low-voltage circuit breakers (LVCB) are common in domestic, commercial and industrial applications in the range 200-1000 VAC. LVCB can be a miniature circuit breaker (MCB) with rated currents less than 100A are used in domestic, commercial and light industrial applications. Molded case circuit breaker (MCCB) with rated currents less than 1000A used in low voltage switchboards, motor control center and panel boards. Low voltage power circuit breakers (LVPCB) with rated currents in the range 800 to 6300A are used in multi-tiers low voltage switchboards or switchgear cabinets. Insulated case circuit breaker (ICCB) low voltage switchboard are same as LVPCB used in motor control centers and some transfer switches. LVPCB are also called as air circuit breakers (ACB). General discussions of the low-voltage circuit breaker and the principle of working can be found in the literature for instance in the book edited by Flurscheim [1]. Schematic description of single pole of an ACB is in depicted in Figure 1 showing the different elements of current path.

Figure 1: Different elements of current path in air circuit breaker.

The continuous current rating of a circuit breaker is the number of amperes that the device can carry continuously without the temperature of any insulation component becoming greater than its rated temperature. The maximum permissible temperature rise at rated current is defined and limited by international standards such as IEEE C37.13 and IEC 62271 [2] for circuit breakers. According to IEEE C37.13 temperature rise shall not exceed the values given in Table 1. Temperature rise in various

components of the ACB are due to Joule heat generated by the specific resistance of each individual part and the contact resistance at the contacts, junctions, connections and bolt joints. Referring to Figure 1, the current path include line-side terminal, lineside junction, line-side conductor, main contact, movable conductor, flexible conductor, load-side conductor, load-side junction and load-side terminal, in that order. Along this path it is important to identify heat sources, heat sinks and heat barriers to accurately predict temperature rise of each individual part so that hot spots can be identified. In addition to meeting temperature rise requirements of the standards, prediction capability will also help in overcoming correct topology identification of circuit-breakers to be installed inside switchgear assembly for given maximum continuous current which the circuit-breaker can carry without damages for specific switchgear operating/boundary conditions.

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This paper focus on developing three dimensional (3D) finite element based coupled electric-thermal model using Maxwell [3] and Ansys [4]. This is two-way iterative sequentially coupled thermal-electric model accurately predict the temperature rise for rated current. Results presented for low voltage circuit breaker with an operating voltage range between 250-600V and rated current of 4000A. The organization of this paper is as follows. A brief introduction and motivation was described in Section 1. In Section 2 previous work on thermal modeling of low-voltage circuit breaker is given. Section 3 presents the governing equations for pertaining to electrical and thermal physics with boundary conditions and the solution strategy for sequentially coupled electric-thermal approach followed by illustrative example and validation in Section 4. Concluding remarks are provided in Section 5.

Limit of Total Temp (oC)

Class 90 Insulation

50

90

Class 105 Insulation

65

105

Class 130 Insulation

90

130

Class155 Insulation

115

155

Class 180 Insulation

140

180

Class 220 Insulation

180

220

Circuit-breaker contacts, conducting joints, and other parts except the following

85

125

Fuse terminals

(1)

(1)

Series coils with over Class 220 insulation or bare

(1)

(1)

Terminal connections

55

95

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Limit of Temp Rise Over Air Surrounding Enclosure

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Table 1: Temperature rise limit IEEE C37.13

2.

Review of Previous Work

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It is common practice in the ACB industry to employ thermal network theory techniques such as described in Cherukury [5] to predict the temperature rise of the conductors and terminals of the circuit breakers. However, this technique limits the prediction capability during the design phase when the conductors in the current paths have complex geometry and shapes. Plesca [6] presented a thermal model based on the finite element method (FEA) for an ACB where measured values of electrical resistances from test data was used to model the heat sources thereby assuming the current densities are uniform in the current carrying conductor cross sections. This technique not only limits the designers to optimize the weight of copper conductors based on the current density distributions (current density crowding etc.) but also temperature effects on the resistance are assumed to be negligible, under-predicting the temperature rise. Frei et al [7] reported FEA thermal model for MCCB employing direct electric-thermal multi-physics coupling to predict the temperature rise of components. Plastic molded parts are included in the model along with the conductors. Thermal and electric contact resistances were calculated analytically and included in the model. The convective heat dissipation is considered only from the molded plastic casing to the surroundings and convective heat dissipation from current path components to inner air cavity is assumed to be negligible based on the work of Barcikowski [8] and Barcikowski et al. [9] for relatively similar size of MCCB. Dilawer et al. [10] presented a direct multi-physics electric-thermal analysis for predicting the thermal behavior of ACB. Electrical contact resistances were modeled as volumes and experimentally measured data was employed. Effects of thermal resistance were neglected and heat transfer coefficients values for convective cooling were adjusted to correlate the predicted temperature results with test results.

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This paper describes a 2-way iterative sequentially coupled thermal-electric model to accurately predict the temperature rise of the current path components. DC conduction electrical analysis was performed using MAXWELL [2]. The heat sources of Ohmic losses are sequentially used as the input to steady state thermal model in ANSYS [3]. The novel features of the proposed model are 1) capturing the effect of resistance rise with temperature, 2) accurately accounted electrical contact resistances which are modeled as contact volumes validated by measured values, 3) incorporate accurate heat transfer coefficients required for surface heat dissipation inside the ACB current path cavity and heat dissipation from the plastics and mounting frame that are obtained from a separate CFD model that account for both convective cooling and radiative heat transfer and 4) inclusion of thermal contact resistance at various contact surfaces to accurately model the heat barriers to the heat flow along the path of the current path. The proposed approach is validated with temperature rise test results. 3. Sequentially Coupled Electric-Thermal Model for Air Circuit Breakers It is well known that the temperature distribution in the conductors of circuit breaker under continuous current is a very complex phenomenon, which involves the coupled interactions between thermal and electromagnetic processes. An applied current flowing in electrically conducting path causes Ohmic losses which cause the temperature rise.

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This generates heat which is transported by conduction along the conductor path and also dissipated by convection and radiation from the surfaces of conductors and parts connected to it. This rise in temperature additionally causes the Ohmic losses to increase due to increase resistivity of the copper. This coupled electric-thermal physical phenomena in the proposed model is described in Figure . In addition, main contacts and contacts at the junctions (refer Figure 1) provides additional Ohmic losses to contact resistance and barrier to heat path by thermal contact resistance. The governing equations and boundary conditions related these physical phenomena are described in this section.

Figure 2: Sequentially Coupled Electric-Thermal Mode for Air Circuit Breakers.

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3.1 Electrical Model and boundary conditions In this section differential equations and associated boundary conditions governing the electrical model are presented and coupling variable, temperature, to the thermal model is introduced. The skin effects at 60Hz were expected to be insignificant hence steady state analysis is considered. Electric current density (J) is related to electric field (E) by Maxwell’s equations 𝑱 = 𝜎(𝑇)𝑬

(1)

𝑬 = −∇∅

(2)

where 𝜎 is electric conductivity in S/m, ∅ is scalar electric potential. This equation is analogous to Ohm’s law, where E is analogous to voltage, J is analogous to current and electrical conductivity is the inverse of resistivity. The Maxwell’s equation states that electric field in a material with non-zero conductivity produce an electric current. The governing equation for steady state electrical conduction is given by ∇∙𝑱=0

(3)

∇ ∙ (𝜎(𝑇)∇ ∅) = 0

(4)

1

𝜎(𝑇) = 𝜌(𝑇) = 𝜌

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subjected to boundary conditions ∅ = 0 at the ground surface and ∅ = 𝑉𝑝 𝑜𝑟 𝑱. 𝒏 = 𝐽𝑝 at the terminal surface. In the electric FE model, current source values were imposed on the free end of line-side bus bars and ground surfaces are were imposed on the free end of load-side bus bars. Since conductivity has significantly varies with temperature can be estimated through a linear variation of resistivity as (5)

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0 (1+𝛼(𝑇−𝑇𝑟𝑒𝑓 )

Where Tref is reference temperature for o and  is the temperature coefficient of copper (0.00386 per oC). The temperature variable T provides the coupling variable from the thermal model which is described in the Section 3.3. 3.2 Electrical Contact Resistance

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The contact resistance is one of the critical heat sources along with the conductor resistance. In a ACB contact resistances come into play at two contacts one at the main contact and another at the conductor and terminal junctions of both line and load side of the current path. The contact resistance between two any surfaces 1-2 can be expressed as 𝒏 ∙ 𝑱𝟏 = ℎ𝑐𝑜𝑛𝑡𝑎𝑐𝑡 (𝑉1 − 𝑉2 )

(6a)

𝒏 ∙ 𝑱𝟐 = ℎ𝑐𝑜𝑛𝑡𝑎𝑐𝑡 (𝑉2 − 𝑉1 )

(6b)

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Where n is outward normal at the contact surfaces, Ji is the current density at the surface i, Vi is the voltage at the surface i between the surface in contact, hcontact is the coefficient which depends on the contact pressure, material hardness, electrical conductivities of the material in contact and surface roughness. Just like the resistivity of the conductors, all these parameters are function temperature which is assumed to constant in this study. One could employ coefficients hcontact, in Eqs. 6 as described in [6, 11]. Our approach followed in the validation procedure is described in the subsequent sections. 3.3 Thermal Model and boundary conditions In this section differential equations and associated boundary conditions governing the thermal model are presented and coupling variable, current densities, to the electrical

model are introduced. For a steady state conduction problem the differential equations governing the thermal response of the system under thermal loads and associated boundary conditions are 𝑑2 𝑇

𝑑2 𝑇

𝑑2 𝑇

−𝐾 (𝑑𝑥 2 + 𝑑𝑦 2 + 𝑑𝑧 2 ) = 𝑄(𝑥)

(7)

subjected to following boundary conditions Essential BCs: 𝑇 = 𝑇𝑎 𝑑𝑇

(8a) (8b)

Convection BCs: −ℎ(𝑇 − 𝑇𝑖 ) = 𝒒𝒃

(8c)

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Neumann BCs: −𝐾 (𝑑𝑛) = 𝒒𝒃

where qb is heat flux (W/m2), K is thermal conductivity (W/mK) and n is the outward unit normal to the surface and Q(x) is Ohmic losses given by |𝐽(𝑥)|2 𝜎(𝑇)

(9)

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𝑄(𝑥) =

where J(x) is the current density which provides the coupling variable from the electrical model. 3.4 Thermal Boundary Conditions

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Heat transfer due to convection (qconv) from the current path conductors to the surrounding is modeled as convective boundary and is defined by in the thermal model by heat transfer coefficient (HTC), surface area of components (A) and temperature difference given by

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𝑞𝑐𝑜𝑛𝑣 = ℎ(𝑥)𝐴(𝑇𝑠𝑢𝑟𝑓𝑎𝑐𝑒 − 𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡 )

(10)

Where h is the HTC, A is the surface area of the conductor and Tsurface is the surface temperature of the conductors and Tambient is the ambient temperature.

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3.5 CFD Model for Heat Transfer Coefficients The HTC defined in Eq. 10 is obtained from CFD model with steady state conjugate heat transfer model with radiation. The heat sources are included as Ohmic losses in the current path conductors with the assumption that the current densities are uniformly distributed across the cross section of the conductors. External air domain extends beyond the ACB frame. Boundary conditions for the external domain is set as atmospheric pressure (P = Patm) and reverse flow temperature equal to atmosphere (T = Tatm). Air has been modelled as incompressible ideal gas to allow change in density only due to temperature. Radiation has been modelled using S2S model. In this method view factor is calculated before the simulation begins and extent of radiative heat exchange is calculated with

respect to view factor. In S2S model, view factor for finite surfaces i with respect to j is given as 1

𝐹𝑖𝑗 =

cos 𝜃𝑖 cos 𝜃𝑗

∫𝐴 ∫𝐴

𝐴𝑖

𝑖

𝜋𝑟 2

𝑗

𝛿𝑖𝑗 𝑑𝑨𝑖 𝑑𝑨𝑗

(11)

𝜕 𝜕𝒕

(𝜌𝑘) +

(𝜌Є) +

𝜕 𝜕𝒙𝑖

𝜕 𝜕𝒙𝑖

(𝜌𝑘𝒖𝑖 ) =

(𝜌Є𝒖𝑖 ) =

𝜕

𝜕 𝜕𝒙𝑗

𝜇

𝑘

𝜇

𝜕𝒙𝑗

𝜕𝑘

[(𝜇 + 𝜎 𝑖 ) 𝜕𝒙 ] + 𝑮𝑘 + 𝑮𝑏 - 𝜌Є – 𝑌𝑀 + 𝑺𝑘 𝑗

𝜕Є

Є

[(𝜇 + 𝜎𝑖 ) 𝜕𝒙 ] + 𝐶1Є 𝑘 (𝑮𝑘 + 𝐶3Є 𝑮𝑏 ) − 𝐶2Є 𝜌 𝑗

Є

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𝜕 𝜕𝒕

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Where, r is the distance between the surface centroids, θ is the angle between lines joining the surface centroids and their respective normal and δ is equal to 1 if surfaces are visible to each other and 0 otherwise. Turbulence has been modelled using standard K-epsilon RANS model. Standard K-epsilon is considered as this model is being widely used industrial applications. Standard K-epsilon turbulence (Launder & Sharma) models turbulent viscosity using equations for Turbulence kinetic energy (k) and dissipation (Є) as given below.

Є2 𝑘

+ 𝑺Є

(12a) (12b)

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Advantage of using CFD thermal model is elimination of need to approximate HTC at conductor surfaces as it includes buoyancy effects. But due to higher computational effort required, CFD has been limited to one time analysis to calculate HTC distribution along the surfaces of the conductors. Since radiation is included in the CFD model, this unique approach alleviates need of modelling radiation in conduction thermal model. The HTC values from CFD not only improve fidelity but also reduce time required in conduction thermal model.

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3.6 Thermal Contact Resistance

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There is no temperature drop at the interface of bolted joints. Hence it is assumed that there is perfect thermal contact conductance (TCC) between these joints. But at the contacts between moving arms-spacers (main contacts) and fingers-conductors (auxiliary contacts), the heat flow across the contact surface is defined in ANSYS using 𝑞 = 𝑇𝐶𝐶 (𝑇𝑡𝑎𝑟𝑔𝑒𝑡 − 𝑇𝑐𝑜𝑛𝑡𝑎𝑐𝑡 )

(13)

where Ttarget and Tcontact are the temperature of corresponding nodes at the contact surfaces. Negus [12] presented a model for TCC of Eq. 13 as 𝑇𝐶𝐶 = 1.25𝑘𝑠

𝑚 𝑠

𝑃 0.95

(𝐻 ) 𝑐

(14)

Where P is apparent pressure on interface, Hc is hardness of softer material, ks is effective thermal conductivity, m is effective absolute surface slope and s is effective 2𝑘1 𝑘2 surface roughness given below, as 𝐾𝑠 = 𝑘 +𝑘 , 𝑆 = √𝑠1 2 + 𝑠2 2 , 𝑚 = √𝑚1 2 + 𝑚2 2 . For most practical applications: 10

−6

𝑃

1

2

≤ 𝐻 ≤ 2 ∗ 10−2 . If m value is not known, 𝑚𝑖 = 𝑐

0.125 (𝑠𝑖 ∗ 106 )0.402 for 0.216 ≤ 𝑠𝑖 ≤ 9.6 𝜇𝑚. Using Eq.14 TCC is calculated and incorporated in ANSYS thermal model. 4.

Simulation Results

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The Figure 3 shows the current path components of the ACB that is being investigated in this study. The 3D CAD model created in Pro-E was imported to Maxwell. DC conduction analysis was performed in Maxwell and the heat load data was imported to the ANSYS thermal module. HTC values obtained from CFD analysis was used as input in the ANSYS thermal model. The HTC coefficients obtained from CFD model account for heat loss due to both convection and radiation. In the ACB configuration, the lineside components is vertically above the load-side components, hence CFD analysis correctly predicts that the HTC values of line-side components are lower from the loadside components. For example, varying HTC values along the length of the bus bar on the line-side is 6.9 - 9 W/m 2K compared to load-side is 6.9 - 8.1 W/m 2K.

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1. Figure 3: Terminal Resistance measurement points

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The contact resistances need at surfaces of the moving arm and the line conductor, and at the primary disconnects which connect conductor extensions and adaptors both at line and load sides. The electrical contact resistances were derived from the resistances measurements between points A-B, C-D and E-F shown in Figure and listed in Error! Not a valid bookmark self-reference.. In the electrical model without thermal model, the contact parameters were varied so that total electrical resistances of 3 measurements matched with test results. This resulted in main terminal contact resistance of 2.5 µΩ and junction contact resistance of 0.5 µΩ between primary disconnects and extensions and adaptors. In ANSYS thermal model material properties and TCC were assigned to the ACB components. The material properties used for thermal analysis is shown in Table . For electrical analysis a reference electrical conductivity of 5.8×107 S/m is used for copper. Using Eq. 14 resulted in TCC of 7000 W/m2 0C employed for main contacts and junction contacts.

Table 2: Test and simulation terminal resistances. Measurement points

Resistance (µΩ)

A-B

14

C-D

10.3

E-F

7

Table 3: Material properties for thermal model. Thermal Conductivity (W/mK)

Copper

390

Plastic

0.6

Steel

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Material

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The percentage error between the predicted and the test results are significant if effect of increase in resistance with temperature rise is not included in the model. The increase in resistance with temperature rise effectively captured by 2-way iterative sequential coupling of electric and thermal model. The internal heat generation and resulting operating temperature of current path can be reduced by decreasing electrical contact resistance. The percentage error between the predicted and the test results are significant for conductors inside the ACB if thermal contact resistance is not included in the model. The temperature rise will be lower if the TCC is high. The TCC depends on various control factors such as force on contact interface, hardness of materials, radius of contact spot, surface roughness of materials, thermal conductivity of materials in contact and void area. HTC values from CFD also increases the thermal prediction performance significantly. If time and resource permits, then sequentially coupled electric-CFD model needs to be employed as this model will allow to explore further cooling options related to internal chamber of ACB to bring down the temperature rise.

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DC Current excitation of 4000A was applied at the bus bar free end and the coupled analysis was performed analysis for single pole of the ACB. Proximity effects among poles were assumed negligible. Analysis was performed for several iterations. After 5 cycles of iteration, there was no significant change in temperature values. Figure 4 shows current density distribution pattern and the Figure 4 shows the final temperature distribution for a specific design instance. The ratio of temperature rise to maximum temperature from the model and lab test data is shown in the Figure 5for various components along the current path. There is a good correlation between experimental and FE results. The results from the study bring out the following inferences.

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Figure 4: (a) Ohmic loss and (b) temperature distribution.

1.00

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0.60 0.40

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T/Tmax

0.80

FEM

0.20

Busbar line

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0.00

Adapter

Finger Cluster

Test

Extension

Line Moving Load Busbar Conductor Arm Conductor load

Thermistor Location

Figure 5: The ratio of temperature rise to maximum temperature for simulation results and lab test data for various components along the current path.

5.

Conclusions

A new iterative sequentially coupled electric-thermal finite element modeling methodology to accurately predict the temperature rise for ACB is presented. For the first time, incorporating all the following key features are proposed for ACB. They key features are 1) captured the effect of resistance rise with temperature, 2) accurately

model of electrical contact resistances which are modeled as contact volumes validated by measured values, 3) incorporated accurate heat transfer coefficients required for surface heat dissipation inside the circuit breaker current path cavity and heat dissipation from the plastics and mounting frame are obtained from a separate CFD model that account for both convective cooling and radiative heat transfer and 4) inclusion of thermal contact resistance at various contact surfaces to accurately model the heat barriers to the heat flow along the path of the current path. The proposed approach is validated with temperature rise test results. 6.

Acknowledgements

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Authors would like to thank entire ACB design team at Eaton, especially Paul Rakus and Dr. Michael Slepian for their ACB product technical inputs to this project. References

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C. H. Flurscheim, Power Circuit Breaker Theory and Design, Peter Peregrinus Ltd., London, 2nd Edition, 1985. IEC 62271 (2004), International Electro technical Commission Low voltage switchgear and control gear assemblies- part 1. ANSYS Maxwell 3D v16: user Guide. ANSYS: Inc. Theory Reference [online]. K. S. Cherukury (2007), Thermal Network Theory for Switchgear under Continuous Current, MS Thesis, National Institute of Technology, Rourkela. T. P. Adrian (2012), Thermal analysis of the current path from circuit breakers using finite element method: World academy of science, Engineering and Technology, Vol: 72, 12-29, 2012. P. U. Frei and H. O. Weichert (2004), Advanced thermal simulation of a circuit breaker, Electrical Contacts: Proceedings of the 50th IEEE Holm Conference on Electrical Contacts and the 22nd International Conference on Electrical Contacts. F. Barcikowski (2003), Numerische Berechnungen zur W¨arme- und Antriebsauslegung von Schaltger¨aten, Ph.D. dissertation, Technische Universit¨at Braunschweig, G¨ottingen: Cuvillier. F. Barcikowski and M. Lindmayer (2000), Simulations of the heat balance in lowvoltage switchgear, in Proc. 20th Int. Conf. on Electrical Contacts, Stockholm. I. S. Dilawer, M. A. R. Junaidi, M. A. Samad, M. Mohinoddin (2013), Steady state thermal analysis and design of air circuit breaker: International journal of engineering & technology, Vol. 2, Issue 11. R. Holmes, Electric Contacts: Theory and Applications, Springer-Verlag, 4th Edition. K. J. Negus, M. M. Yovanovich (1988), Co relation of the gap conductance integral for conforming rough surfaces: Journal of Thermo Physics, Vol. 2, No 3. http://www.mecheng.osu.edu/documentation/Fluent14.5/145/wb_sim.pdf, 22 July 2014.

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