The Analysis of the Thermal Processes Occurring in the Contacts of Vacuum Switches During the Conduction of Short-Circuit Currents

Abstract

This article presents the results of research on the thermal state of vacuum switch contacts during the conduction of short-circuit currents. This state is directly related to the value of the flowing current and the operating conditions of the switch. These conditions are mildest in the case of the conduction of operating currents through closed contacts. The situation worsens significantly when short-circuit currents are conducted, and the greatest destructive effects occur during commutation processes. Exceeding a certain level of contact destruction usually leads to the loss of the switching capacity of the switch. In vacuum switches, tracking the thermal state of the contacts is particularly difficult due to the inaccessibility of transducers or measurement sensors inside the chamber. In such a case, simulation studies verified by experimental results are important. This paper presents the results of such studies, directed at their practical implementation in the design and operation of vacuum switches. Simulation studies were conducted to analyze the thermal processes occurring in the contacts of vacuum switches during the conduction of short-circuit currents. Special attention was paid to the influence of contact parameters on the thermal processes occurring during the conduction of short-circuit currents. In addition to simulations, experimental studies were carried out to verify the simulation results. Ultimately, the research results presented are intended to provide practical knowledge of the design and operation of vacuum switches, particularly with regard to the contact heating processes during the conduction of short-circuit currents.

1. Introduction

In recent years, a number of important studies have been carried out on vacuum chambers and contacts in vacuum chambers. One of these represents research into the electrical strength of vacuum chambers, particularly for medium-voltage switchgear. This includes a modified vacuum chamber design that allows for the direct observation of physical phenomena, such as electrical failures and arc ignition processes [1]. In contrast, another paper [2] presents a model for the analysis of contact temperature rise. This work highlights the importance of understanding the thermal dynamics taking place in a vacuum chamber to ensure reliable operation in high-voltage applications. The recent innovations include the integration of infrared cameras and multiple temperature sensors in vacuum chambers [3]. These systems enable the precise monitoring and control of temperature gradients in devices under test (DUTs), improving the accuracy of the thermal modeling and test results. This dual approach helps to mitigate the uncertainty in temperature measurements caused by environmental factors in the chamber. Extensive research has also been focused on developing mathematical models that simulate thermal behavior under vacuum conditions. These models aim to predict the temperature rise in contacts during short-circuit flows [2,4].

In the design of electrical switches, there are two contacts responsible for switching on and off current circuits (called switching contacts) and contacts forming movable or non-movable connections (called non-switching contacts) [5,6,7,8]. The contacts forming a disconnecting contact are most often pressed against each other by the switch mechanism. Their actual area of adhesion depends, among other things, on the state of smoothness of the surfaces of the two electrodes, their cleanliness, and the pressing force exerted by the switch drive [9,10,11,12]. Due to the varying surface area of the electrodes (caused in a new fastener by machining processes and in an in-service one by the erosive effects of the switching processes), the resultant (total) size of the contact area is the total area at the points of contact and represents only a few percent of the apparent area (resulting from the geometric dimensions of the contacting electrodes). The number of actual micro points of contact is largely dependent on the method and accuracy of machining the working surfaces and the hardness of the contact materials [13,14,15,16,17]. The thickening of the current flow in the contact areas hinders current flow. This manifests in an increase in voltage drop in the contact zone, which is equivalent to the occurrence of an increase in resistance of the current path there (the formation of the so-called transition resistance) [18,19]. Under typical operating conditions, this resistance is made up of the resistance of the track constriction and the resistance of the tarnish layers formed on the contact surfaces [20,21,22]. In the case of vacuum fasteners, the effect of tarnish layers is negligible, and therefore ignored in the considerations presented [10].

During the operation of electrical devices, both during the conduction of operating currents and fault currents (including short-circuit currents), it is the switching contacts that are most exposed to the thermal effects of current flow [22,23,24,25]. According to Joule’s law, heat is emitted both on the resistance of the current paths and on the contact resistance itself. The thermal state of contacts operating in a vacuum under established operating conditions, as well as the temperature distribution along the current paths of the contact system for exemplary vacuum quench chambers, is presented in this paper [13]. From the design and operational points of view, the evaluation of the maximum contact temperature and its spatial distribution in the switch tracks under the flow of short-circuit currents is also of important cognitive significance [5,9,26,27,28]. The simulation and verification studies presented in this paper were performed with a focus on the possibility of determining the short-circuit thermal load capacity of contacts in the quench chambers of vacuum switches. This load capacity is defined in regulations by the n-second permissible value of the thermal current, which the contact can withstand (during n seconds) without damage, understood as welding or permanent deformation.

2. Test Object and Its Rated Parameters

The subject of the tests described in this paper are the contacts located in a three-phase SV-7 vacuum contactor with a rated current of 250 A, which has been manufactured for more than 40 years by Oram Grupa Martech in Lodz. These contactors are designed for connecting AC electric circuits with a frequency of 50 Hz and 60 Hz (use in DC circuits is not allowed). Due to its reliable operation and robust design, this device has been widely used for the following [29]:

• Controlling electric motors at voltages up to 1200 V;
• Use in drive systems in the mining industry;
• Connecting power consumers in the chemical industry due to arc quenching in a vacuum chamber, which protects the contacts from the effects of an aggressive atmosphere;
• Use in drive systems within sealed or explosion-proof enclosures due to low thermal losses;
• Use in automation systems requiring the long-term and reliable switching operation of the contactor.

The actuating elements of the SV-7 contactor (Figure 1a,b) are three vacuum quench chambers VK-7 (Figure 1b).

The simulation studies presented in this paper directed at the possibility of experimental verification were performed with reference to the typical designs and operating parameters of vacuum contactors; hence,

Table 1. Selected technical parameters of SV-7 vacuum circuit breaker.

Rated voltage Ui		V	1500
Switching voltages Ue		V	400, 500, 690, 1000, 1200
Frequency		Hz	50–60
Rated current		A	250 *, 400 **
Connectivity	max switch on current	A	2000
	max switch off current	A	1600
Rated current 1 s		A	4500
Rated current 8 s		A	1700
Rated current 10 s		A	1480
Main contact pressure		N	43 ÷ 54
Maximum voltage drops across the main contacts at 100 A direct current		mV	35
Max limiting temperature rise of main track connection terminals		°C	50 * 70 **
Max temperature increases limit of flexible connections—in the immediate vicinity of the attachment to the vacuum chamber		°C	85 * 105 **
Max temperature increases limit of the vacuum chamber housing sleeve		°C	85 * 105 **
Control voltage		V	110, 220 d.c., 24, 110, 230, 400, 500 a.c.

* for ambient temperature of 55 °C, ** for ambient temperature of 35 °C.

lists the more important technical data of the vacuum circuit breaker in question used in the analytical calculations.

The experimental studies presented in another paper [30] showed that the voltage drops at the vacuum circuit breakers of SV-7 contactors are 2–5 times smaller than those at the connection terminals of the entire contactor. Thus, the resulting contactor resistance R_p = 350 μΩ (calculated) from Table 1 [29] is not representative of these vacuum chambers. For a number of tested VK-7 vacuum chambers, with which the heating tests performed met the permissible temperature increments given in Table 1, their measured resistances were found to be in the range of 50–162 μΩ. As expected, the temperature increments of all the components heated by the rated current of the contactors are smaller for the smaller resistances of the contactor quench chambers. The time constants for heating of all the parts of the current paths are not less than 20 min.

3. Assumptions and Calculation Procedures

In the case of thermal processes under short-circuit conditions, due to the short durations of these phenomena, it is assumed that there is no heat exchange between the current paths and the surroundings. This simplification is justified, especially for the current paths of contactors, where the intensity of the short-circuit current and the short duration of the short circuit make heat exchange with the surroundings negligible. However, to further simplify the procedure for calculating the temperature in the contacts, the temperature rises of the supply tracks caused by adiabatic resistive heating were also neglected. In fact, this temperature rise can be determined, taking into account the variation in resistivity and specific heat of the current track material using classical methods described in the industry literature and standards, such as [5,31,32,33,34].

In addition, the model presented here disregards the temperature rise in the tracks caused by the flow of the operating current, such as the rated current. The determination of these temperature rises and the analysis of temperature distribution along the current leads of the VK7 vacuum chamber contacts are described in detail in another paper [13]. It should be remembered, however, that this type of simplification, consisting of ignoring the effect of the operating current on the temperature of the current tracks, can be mitigated by using the superposition of the obtained results with the results of the resistance heating calculations. Such a combination allows for the more precise modelling of the actual course of thermal phenomena in the system.

In the analysis of VK-7 contact heating processes, a value of 294.75 °K (21.6 °C) was used as the initial temperature. This value corresponded to the air temperature prevailing in the laboratory during the verification tests.

Simulation calculations were carried out using the Agros2D program, which is a multi-platform tool for solving field and flow problems. This program developed at Western University in Pilsen belongs to the category of open source software [34], which makes it particularly attractive in the context of academic and engineering research. Agros2D allows for the modelling and analyzation of physical phenomena in two-dimensional systems, which is sufficient for the study of the temperature distribution of symmetrical contacts of the SV-7 vacuum circuit breaker.

Agros2D software (version 3.2.0.20140521) was used to model the thermal processes occurring in the contacts of the vacuum switches during the flow of short-circuit currents [35]. These processes were described by partial differential equations taking into account both heat conduction and convection. The basic equation describing the heat flow takes the following form:

$$-div\left(\lambda gradT\right)+\rho c_p\left({\displaystyle \frac{\delta T}{\delta t}}+V·gradT\right)=Q$$

(1)

where

• λ is the thermal conductivity of the material;
• ρ is the density;
• c_pc is the specific heat;
• T is the temperature;
• V is the velocity of the medium;
• Q represents the heat source in the medium.

This equation allows for the temperature distribution at interfaces to be modelled, taking into account adiabatic effects and heat transfer by conduction and convection.

In order to accurately model the thermal processes in the contacts of a vacuum connector, it is also necessary to take into account the volumetric density of active power (dissipated power), which describes the amount of energy dissipated per unit volume. In the case of copper, this expression takes the following form:

$$q_v=\left|j\right|·\left|E\right|={\displaystyle \frac{{\left|j\right|}^2}{{\gamma }_{cu}}}$$

(2)

where

• q_v is the volume density of active power (W/m³);
• j is the current density (A/mm²);
• E is the electric field strength;
• γ_cu is the electrical conductivity of copper (55 × 10⁶ S/m).

This expression allows us to determine the amount of heat generated as a result of current flow through the contact, which is crucial for estimating the maximum temperatures reached during the flow of short-circuit currents.

In view of future verification possibilities in test circuits, a rated 8 s short-circuit current of I = 1700 A was assumed for the calculations (Table 1). Simulations were carried out for contacts with a diameter of 30 mm and a total length, including the leads, of 20 mm. These parameters reflect the actual contact dimensions of the SV-7 switch.

The empirical formula that can be used to determine the value of contact resistance, taking into account the average layer resistance values for a given contact material, is

$$R_p={\displaystyle \frac{c\rho }{{\left(0.1·F_k\right)}^m}}$$

(3)

where

• ρ—resistivity of the contact material;
• c—constant depending on the state of the contact surface, taking into account also the influence of tarnish layers (for Cu the product of cρ = 0.08–0.14 mΩN^m);
• F_k—contact force (Table 1 and the test results [30]);
• m—contact type-dependent constant (due to the contact model, m = 0.5 was assumed for the calculation).

Determining the actual area of contact (and indirectly the radius of contact) is very difficult in practice. For a given contact force, the number of contact points depends on the so-called contact hardness αH of the contact material. For a single-point contact, it is expressed by the following formula [36,37,38]:

$${\displaystyle \frac{F}{\pi ·r^2}}=\alpha H$$

(4)

Therefore, in practical calculations, the formula for determining the contact radius can be used:

$$r=\sqrt{{\displaystyle \frac{S_p}{\pi }}}=\sqrt{{\displaystyle \frac{F}{\pi ·\alpha H}}}=\sqrt{{\displaystyle \frac{F}{\pi ·{\sigma }_o}}}$$

(5)

where

• S_p—the contact area;
• σ_o = αH—the hardness of the material.

To evaluate the effect of transition resistance on temperature distribution, simulations were performed for two extreme values of transition resistance: 162 μΩ and 50 μΩ. These values represent, respectively, the upper and lower ranges of resistances that were recorded in the vacuum chamber studies described in [30]. It should be emphasized that from a computational point of view [30], a transition resistance of 162 μΩ is more reliable compared to a resistance of 50 μΩ. For the 162 μΩ resistance value, the calculated contact force is about 46 N, which is consistent with the rated contact force given in Table 1 (main contact pressure 43–54 N). This consistency confirms the correctness of the model and the assumptions made. On the other hand, for a transition resistance of 50 μΩ, the calculated contact force is as high as 484 N, which significantly exceeds the rated values declared by the manufacturer. Such a large difference suggests that a resistance of 50 μΩ is less likely to occur under actual operating conditions given the physical limitations on contact force that can be achieved in vacuum chamber contacts.

Similarly, for a comparative evaluation of the effect of short-circuit durations on temperature distribution, simulations were carried out for a time equal to 8 s and, for comparison, 1 s. The computational model implemented in Agros2D software is shown in Figure 2.

In the computational model of contact transition resistance, the contact area between electrode surfaces is assumed to be spherical; although in more detailed analyses, it can be modelled as an ellipsoid. The diameter of this sphere corresponds to the so-called equivalent contact area, which is a simplified model of the actual contact between the electrodes. The values of the radius of this area depend on the contact pressure and the properties of the contact material, and example results for various combinations of these parameters are presented in another paper [39,40]. It is worth noting that the accurate determination of the equivalent contact radius is crucial for the accurate modelling of transition resistance and temperature distribution.

In the adopted calculation procedure, the purpose of which is to analyze the heat flow in the contacts, the existence of a volumetric heat source was assumed. The power of this source, expressed by the formula Ri² (where i is a sinusoidal current, i(t) = 1700√2sin(ωt) A, f = 50 Hz), is generated in a sphere-shaped area whose radius corresponds to the equivalent contact radius of the contacts. This area is located in the plane of contact of the electrodes (closed contacts).

4. Simulation Results

In the computational procedure for heat distribution, characteristic computational points were selected, lying both along the contact axis and on the contact surface. The location of the points at key points makes it possible to capture significant differences in heating dynamics, especially in areas with increased current density. The simulation results of the temperature distribution both in the contacts themselves and on their surface are shown in Figure 3. They show the temperature changes under short-circuit conditions for two different short-circuit durations, 8 s and 1 s, and two extreme resistance values of 162 μΩ and 50 μΩ.

With a transition resistance of 162 μΩ and an 8 s flow of a rated short-circuit current of 1700 A, the temperature at the contact point reaches about 1280 °C, which far exceeds the melting points of typical contact materials, such as copper (1083 °C), silver (960 °C), and silver tungsten (960 °C). Such a result suggests that under the conditions of a prolonged short circuit, the extreme heating of the contacts occurs, which can lead to material degradation, and consequently even contact damage. In the case of a short circuit with a duration of 1 s, for the same transition resistance (162 μΩ) and current of 1700 A, the temperature also exceeds the melting point of the contact materials. Although the short-circuit time is shorter, the heat released turns out to be sufficient to lead to heating with a similar temperature value (about 1180 °C). Interestingly, the rated value of 1 s short-circuit current for the SV-7 contactor is 4500 A; nevertheless, the results show that even at a current of 1700 A, the melting temperature is exceeded, which may raise doubts about the resistance of the contacts to such operating conditions. It is also worth noting that for a transition resistance of 162 μΩ, limiting the short circuit duration to 1 s does not significantly change the temperature distribution. Even with a shorter short-circuit time, the heat generated is sufficiently high to reach temperatures exceeding the permissible values for contact materials. This suggests that in the case of increased transition resistance, the short-circuit duration has less of an influence on the heating process, and the key factor determining the intensity of heating is the resistance itself.

On the other hand, for a transition resistance of 50 μΩ during both the 8 s and 1 s short circuits, there were no significant temperature increases. The temperatures at the point of contact ranged from 113 °C to 143 °C, indicating that the contact material stays within a safe thermal range, well below the melting point. Such a low level of heating suggests that the lower transition resistance effectively limits the amount of heat released, which translates into the thermal stability of the contacts even during prolonged short circuits.

It can be demonstrated that the contact areas have an extremely short heating time constant. According to the data presented by Krynski [6], for a contact force of 50 N, this time is of the order of 10⁻⁴ s. The flow of sinusoidal current through the contact resistance causes the release of heat, the power of which, expressed by the formula RI², has a periodic character with a frequency twice the frequency of the current. This value arises from the transformation of electrical energy into heat at the resistance, which leads to a doubling of the frequency relative to the current signal.

The period of variation in heat source power equal to 10 ms is 1–2 orders of magnitude longer than the heating time constant of the contact point of the contact. This means that microscopic contact areas are able to dynamically respond to periodic changes in heat source power, which means that the local temperatures can quickly adapt to momentary changes in the current. This situation is confirmed by the course of temperature changes over time, as shown in Figure 4.

It is useful for verification studies to evaluate the temperature on the surface of electrodes after heating with a short-circuit current. The temperature build-up on the surface of the model contact during 8 and 1 s short circuits with a current of 1700 A is shown in Figure 5a–d.

For a short circuit with a duration of 8 s, the temperature rise at the surface of the electrodes remains relatively small. For transition resistance R_p = 162 μΩ, an increase of about 43 °C was recorded, while for R_p = 50 μΩ, the increase was only 23 °C. Such a result confirms that a higher transition resistance leads to more heat release, but even with a longer short circuit, the electrode surface does not heat up intensively (as it does at the point of contact). For the 1 s short circuit, the temperature rise is even smaller. For R_p = 162 μΩ, the increase was only 4 °C, and for R_p = 50 μΩ only 3 °C. The low temperature rises at the short-circuit times confirms that the effect of transition resistance on temperature rise becomes less important at very short current pulses due to the limited amount of time in which energy can be transferred to the contact material.

In all the simulations, a significant delay in the heating of the surface of the electrodes relative to the heating of the contact point was noted. This fact confirms the limited speed of temperature equalization at the electrode surface, which is directly related to the low thermal diffusivity of the electrode material. Low thermal diffusivity limits the rate of heat propagation from the point of contact to the surface, which leads to a significant delay in reaching temperature equilibrium between the different areas of contacts.

5. Preliminary Evaluation of Research Results and Their Analysis

The flow of electric current through conductive elements causes their heating. Based on the theory of contact heating, it can be shown that the temperature rise in the contact zone satisfies the following relation [6,20,21,22]:

$$\Delta T={\displaystyle \frac{U_p^2}{8\lambda {\rho }_{\vartheta }}}$$

(6)

where

• U_p—the voltage drop across the contact resistance (U_p = I R_p);
• λ—the coefficient of thermal conductivity of the contact material;
• ρ_ϑ—the resistivity of the current path material (temperature-dependent ϑ).

The simulation studies show that the expected temperatures of the contact materials are high (more than 150 °C), so the applicability of the Wiedemann–Franz–Lorenz law [5,38,39,40] can be assumed for the contact materials:

$$\rho \lambda =L\mathsf{\Theta }$$

(7)

where

• L—the Lorenz constant equal to about 2.4 × 10⁻⁸ V² K⁻²;
• θ—the temperature in absolute scale.

Then,

$${{\displaystyle \int }}_{{\theta }_m}^{{\theta }_p}L\theta ={\displaystyle \frac{\Delta U_p^2}{8}}$$

(8)

where

• θ_p—the absolute temperature of the point of contact;
• θ_m—the absolute temperature of the environment of the point of contact.

After solving Equation (8), we obtain

$$U_p=\sqrt{4L\left({\theta }_p^2-{\theta }_m^2\right)}$$

(9)

The maximum temperature of the point of contact is then equal to

$${\theta }_p=\sqrt{{\theta }_m^2+{\displaystyle \frac{U_p^2}{4L}}}$$

(10)

By substituting the value of U_p = R_pI and the material data for the contacts made of AgW50/50, the contact temperature value was obtained (with the simplifications assumed earlier regarding the omission of resistive heating of the current paths):

• approx. 935 °K (662 °C) for a transition resistance of 162 μΩ;
• about 403 °K (128 °C) for a transition resistance of 50 μΩ.

These values are lower than the simulation studies show; although due to the lack of unambiguous data on the actual material parameters of the electrodes, the comparison of the obtained temperatures can be considered satisfactory.

The attempt to assess the correctness of the simulation results was also carried out experimentally. Tests with a short-circuit current of 1700 A were realized using an unsealed vacuum chamber (assuming no heat exchange with the environment during the short-circuit tests) devoid of housing fragments. Unsealing the enclosure allowed for direct access to the contacts and the measurement of temperature. In both the cases, slight contact welds were noted, which indicates a local exceedance of the melting temperature at the contact point. This confirms the simulation results of intense heating in these areas (Figure 3a,b).

In order to evaluate the temperature distribution on the surface of the electrodes of the unsealed chamber, a detailed thermal imaging study was conducted using a Fluke Ti20 (Fluke Corporation, Everett, Washington, DC, USA) thermal imaging camera. This camera is capable of measuring temperatures in the range of −10 °C to 350 °C, which is sufficient to analyze the temperature conditions prevailing during the experiments since at no time during the tests was the upper measurement limit exceeded. The measurement accuracy of the device used is ±2 °C or 2% of the measured value, with the greater of the two values being chosen [41]. An image showing the experimental setup and the chamber used in the study is included in Figure 6.

Figure 7 shows a simplified version of the block diagram of the test rig built. The power source was a TW25 large-current transformer. It has a capacity of 25 kVA and allows for a continuous current load of up to 5400 A on the secondary side. The task of the PLC was to switch the contactor on and the current flow for a set time (1 and 8 s). The changes in contactor temperature were recorded using a thermal imaging camera.

Figure 8 shows the thermograms obtained during the short-circuit tests recorded during short circuits of different durations, 8 and 1 s, respectively.

Comparing the obtained experimental results with the simulations of heating the lateral surface of electrodes with a transition resistance of 162 μΩ (Figure 5a,b), there was a high correspondence between the measured and simulated results for short circuits of 8 and 1 s durations. Such convergence indicates the correctness of the simulation model selection. The slight measurement differences may be due to the influence of additional factors, such as the thermal conductivity of the chamber enclosure or local differences in the structure of the contact material, which were not fully accounted for in the model. Less agreement was observed for the short circuit with a transition resistance of 50 μΩ.

Figure 9 shows the recorded photos of the temperature rise on the lateral surface of the vacuum chamber contacts during the 8 s experiment. An initial temperature of 21.6 °C was derived from the ambient temperature. The photos were taken at 1 s intervals.

In research using a thermal imaging camera, temperature measurement is subject to errors due to several factors. The main sources of error include the emissivity of the surface, the reflection of radiation from the environment, and environmental conditions such as temperature and humidity. The errors can be systematic (resulting from camera calibration) or random (signal fluctuations). The accuracy of a thermal imaging camera, according to its technical specifications, is ±2 °C or 2% of the reading value, whichever is greater. In the present study, the error was estimated at ±2 °C of the measured value. This is larger than the calculated percentage error.

Figure 10 shows a graph of the temperature change as a function of time, corresponding to the data shown in Figure 9. The curve shows a gradual increase in temperature, with up to a maximum at the eighth second of the test. The exponential trend line indicated by the dashed line suggests a general trend in temperature increase for this test.

Thermographic recordings unequivocally confirmed earlier observations of a delay in the rise of temperature on the surface of the electrodes relative to when the test current flow is switched on and off. This delay is due to the limited thermal diffusivity of the electrode material, which results in the gradual equalization of temperature after the current flow ends. This result is consistent with the theoretical predictions for the dynamics of heat distribution in systems with high transition resistance.

In order to better illustrate the agreement between the simulation and experimental results, the temperatures obtained are summarized in

Table 2. A summary of the lateral contact temperature obtained from the simulation and experiment. The simulation parameters: lateral contact surface, current I = 1700 A, and current flow time t = 8 s.

Measurement Time	Simulation Agros2D	Experiment (Temp. Range)
[s]	[°C]	[°C]
0	21.6	19.6–23.6
1	25.8	21.1–25.1
2	31.2	29.6–33.6
3	36.6	32.5–36.5
4	42.1	36.4–40.4
5	47.5	43–47
6	53.1	45.3–49.3
7	58.5	51.2–55.2
8	64	54.6–58.6

. The column with experimental results shows the range of uncertainties, rather than a single measured value. This allows for the more accurate comparison of the simulation and experiment results. Despite some discrepancies (especially evident in the sixth, seventh, and eighth seconds of the tests), the overall trend of the temperature increase is similar.

The graph in Figure 11 shows the temperature increments obtained during the simulation and measured during the experiment. The solid line shows the side surface temperatures of the contacts during the computer simulation. The experimental results are shown with dashed lines, where the lower and upper lines mark the confidence interval of the temperature measurement recorded using the thermal imaging camera. This makes it possible to visually compare the compatibility of the two methods.

6. Discussion

The model tests carried out in this paper, partially verified by the results of experimental tests on real objects, confirm the possibility of determining the contact temperature of power switches by computational methods. This is particularly important from the point of view of diagnostics and prediction of the durability of these elements under operating conditions. It was shown that the prediction of the thermal short-circuit strength of switches based on the analysis of n-second currents can be useful in assessing their reliability during the conduction of short-circuit currents. The variability in instantaneous contact temperature, which dynamically “keeps up” with changes in the power dissipated at the transition resistance, underscores the importance of assessing the maximum temperature, especially in the case of large surge currents. In power circuits, these values can exceed the initial short-circuit current by up to 2.5 times, which significantly increases the risk of exceeding permissible contact temperatures.

By ensuring low contact transition resistance, which can be achieved by maintaining sufficiently high contact pressure or surface regeneration, the negative thermal effects in the contacts can be significantly reduced. In the simulations and the experimental studies, it has been shown that transition resistance has a significant effect on the temperature rise in the contacts of a vacuum chamber during short-circuit current flow. The simulation results show that with a transition resistance of 162 μΩ, the maximum temperature reached 1284 °C after 8 s of a short-circuit current flow of 1700 A. This temperature value significantly exceeded the melting point of the typical contact materials, (e.g., for copper, 1083 °C). In contrast, for a lower transition resistance of 50 μΩ, the maximum temperature did not exceed 143 °C (this is well below the melting point) even with longer short-circuit times. This means that controlling the technical condition of the contact surfaces is crucial to prevent thermal degradation, which has a direct impact on extending the life of the contacts.

The effect of short-circuit duration on the dynamics of the temperature rise proved to be equally significant. At a higher transition resistance of 162 μΩ, even a short, 1 s short-circuit led to temperatures close to the material’s melting point (1178 °C), indicating a significant risk to contact life at high short-circuit current values. In contrast, at a lower transition resistance of 50 μΩ, the temperature only reached 113 °C after 1 s of short-circuiting, and increased to 143 °C after 8 s. This confirms the thermal stability of the contacts at a low value of transition resistance.

The simulations also demonstrated a relationship between the transition resistance and the contact force. For a resistance value of 162 μΩ, the calculated contact force was approximately 46 N, which was within the range declared by the manufacturer (43–54 N). However, for a resistance of 50 μΩ, the calculated contact force reached 484 N, suggesting that such a low resistance is less likely under real operating conditions due to the physical limitations of the contact force that can be achieved in vacuum chamber contacts.

The comparison of the simulation results with the experimental data revealed a high degree of agreement, particularly for the 8 s tests, where the measured temperature varied between 54.6 °C and 58.6 °C. This is close to the values obtained in the simulations. The small differences between the simulated and experimental values may be due to the influence of additional factors, such as the thermal conductivity of the chamber enclosure or local differences in the structure of the contact material, which were not fully taken into account in the model.

In addition, the results indicate a significant role for the delay in heat propagation from the point of contact to the electrode surface due to the low thermal diffusivity of the material. During an 8 s short circuit at a resistance of 162 μΩ, the surface temperature only increased by 43 °C, indicating a limited rate of temperature equalization. This confirms the theoretical predictions regarding the dynamics of heat distribution in systems with high transient resistance and should be taken into account when analyzing the long-term temperature stability of contacts, especially in the context of current overloads. In this connection, it is proposed to consider the possibility of determining the permissible contact transition resistance, instead of focusing only on the voltage drop across the pole of the switch. Such a parameter could be used as a determinant for maintaining a compromise between the rated n-second current and the permissible contact temperature to ensure safe operation by preventing the melting temperature of the contact material from being exceeded.

Despite the simplifications used in the analysis presented here, the modelling of current track heating processes, especially with regard to the temperature variation in different parts of the system, can provide important information to better understand the dynamics of these processes and increase the accuracy of thermal predictions under real operating conditions.