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Conductor temperature monitoring for the fully insulated busbar prefabricated joint considering contact resistance

Conductor temperature monitoring for the fully insulated busbar prefabricated joint considering... INTRODUCTIONDue to the large current carrying capacity, good insulation performance and compact structure, the fully insulated busbars have been increasingly widely utilized and developed in the industries such as electric power, chemical industry, petroleum, metallurgy and shipbuilding around the world[1–5]. The total length of the fully insulated busbar used in China was nearly 200 km during 2014[6, 7].The length of the single busbar is within 10 m so that the fully insulated busbar routes usually consist of dozens or even hundreds of busbar segments connected in series through joints. There are mainly two types of joints for insulated busbar, namely prefabricated type and taped type, and the former one is more commonly used in practice. According to the statistics, the defects or failures of fully insulated busbar owing to product quality, installation process and operating environment have spread to dozens of substations in over ten provinces in China. Statistical results from more than 40 defects and failures of fully insulated busbar show that the joints and terminations are the weakest point of the fully insulated busbar system with the fault proportion of 70%. Moreover, the main causes for the joint and termination defects include poor sealing, poor contact and main insulation defects, where more than one third of the faults were caused by poor contact. Poor conductor contact will lead to overheating of the joint, which will further increase the contact resistance, thus forming a vicious circle. Excessive temperature will aggravate the thermal aging of the insulation, cause the joint sealing failure and eventually lead to insulation breakdown [8]. Therefore, it is of great significance to monitor the conductor temperature of the fully insulated busbar joint so as to realize the early warning of overheating faults.In view of the high similarity in the structure between the fully insulated busbar and the power cable, the temperature monitoring of the cable joint can be used for reference. Although there has been extensive research regarding the thermal behaviour of the cable joint, most of them focus on the steady‐state analysis for determining the ampacity rather than real‐time online monitoring [9–12]. It is difficult to directly measure the conductor temperature because of high voltages being applied to busbar. The most common indirect real‐time measurement for conductor temperature of cable joint is based on the thermal circuit model [13–15]. In our previous papers, an alternative indirect approach was put forward to realize the hotspot temperature monitoring for the cable joint in two steps [16], which shows strong robustness with the variable thermal environments and uncertain thermal parameters of the joint [17]. Afterwards, the authors applied this method to the fully insulated busbar taped joint, which indicates the high model precision and strong robustness to the solar radiation impact [18]. The validity of the above method to the prefabricated joint, where air convection and thermal radiation are the main forms of heat transfer, has yet to be verified. Moreover, almost all of the existing models assume that the contact resistance of the joint is known, but in fact, affected by the installation quality or operating conditions, the contact resistance may become larger, thereby resulting in overheating defect or failure. It is clear that the contact resistance plays a key role in the model accuracy, but to the best of our knowledge, such investigations have not yet been performed either theoretically or experimentally. For this reason, this paper aims to improve our previous algorithm so as to monitor the conductor temperature of the fully insulated busbar prefabricated joint under uncertain contact resistances in real time.METHODOLOGYBasic idea and analysis stepsSince this paper is an improvement on the basis of our previous work, the general introduction of its basic idea and analysis steps is given below first [18].Due to the high thermal conductivity of the conductor, most of the heat flux will be transported in the conductor from connector to both sides. Meanwhile, in the radial direction of the busbar, the heat will be transferred from the hot conductor to the cold surface. According to the direction of heat flux, the joint hotspot temperature Tj can be obtained through radial direction temperature calculation (RDTC) in the busbar and axial direction temperature calculation (ADTC) in the conductor from two surface temperatures Ts1 and Ts2 as seen in Figure 1.1FIGUREThe path for obtaining the hotspot temperature of fully insulated busbar jointThe analysis steps are as follows:In RDTC, the 1‐D transient thermal network is adopted to calculate the conductor temperatures T1 and T2 in real time on the basis of the current and surface temperatures Ts1 and Ts2.In ADTC, the transient thermal analysis of the insulated busbar joint under single‐step load currents ranging from 100 A to the rated current is carried out, from which the conductor temperature data are extracted as training samples. On this basis, the axial function between the hotspot temperature Tj and the conductor temperature T1 and T2 can be established. In real‐time temperature monitoring, the conductor temperatures T1 and T2 calculated in RDTC are substituted into the axial function, and then the hot spot temperature Tj can be obtained, as illustrated in Figure 2.2FIGUREThe algorithm for hotspot temperature monitoring of fully insulated busbar jointRDTC modelThe establishment process of RDTC model is introduced in [18] in detail, and only the main points are given below.The structural and thermal parameters of the fully insulated busbar are illustrated in Table 1.Each layer of the busbar can be represented by lumped π‐type RC thermal circuit branches as per IEC 60853[19] and thus the transient thermal network is provided in Figure 3.3FIGUREThe 1‐D transient thermal network of the fully insulated busbarAs per Kirchhoff's law, the state equations in Figure 3 can be written as1(C0+C1n)dTc0dt+Tc0−Tc1R1−G=0Tc0−Tc1R1+Tc2−Tc1R2−(C1w+C2n)dTc1dt=0Tc1−Tc2R2+Ts−Tc2R3−(C2w+C3+C4n)dTc2dt=0$$\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {({C}_0 + {C}_{1n})\dfrac{{d{T}_{c0}}}{{dt}} + \dfrac{{{T}_{c0} - {T}_{c1}}}{{{R}_1}} - G = 0}\\[12pt] {\dfrac{{{T}_{c0} - {T}_{c1}}}{{{R}_1}} + \dfrac{{{T}_{c2} - {T}_{c1}}}{{{R}_2}} - ({C}_{1w} + {C}_{2n})\dfrac{{d{T}_{c1}}}{{dt}} = 0}\\[12pt] {\dfrac{{{T}_{c1} - {T}_{c2}}}{{{R}_2}} + \dfrac{{{T}_s - {T}_{c2}}}{{{R}_3}} - ({C}_{2w} + {C}_3 + {C}_{4n})\dfrac{{d{T}_{c2}}}{{dt}} = 0} \end{array} } \right.\end{equation}$$The conductor temperature can be obtained by solving the above differential equation using the surface temperature and the power loss.ADTCIn order to obtain the training samples for the axial function in ADTC, it is necessary to perform transient thermal analysis of the insulated busbar prefabricated joint. Unlike the taped joint, the main heat dissipation medium of the prefabricated joint is closed air, where heat is transferred through thermal convection and radiation. Hence, the 3‐D fluid‐thermal analysis is carried out in this paper.The half longitudinal section structure of the prefabricated joint is depicted in Figure 4. A terminal pad is welded at the end of the busbar conductor and connected with the connecting copper bar by bolts. The joint is enclosed in the prefabricated sleeve and the end of the sleeve is sealed by the flange. The thermal parameters of the joint are provided in Table 2 [20].4FIGUREThe half longitudinal section structure of the prefabricated joint1TABLEThe structural and thermal parameters of the insulated busbarComponentsOuter radius (mm)Thermal conductivity (W/(m·K))Volumetric specific heat (kJ/(m3·K))Air26//Copper conductor303833450PTFE insulation320.2592290XLPE insulation36.50.2862400Aluminum earth screen36.82182500XLPE oversheath40.10.28624002TABLEThe thermal parameters of the insulated busbar prefabricated jointComponentsThermal conductivity (W/(m·K))Volumetric specific heat (kJ/(m3·K))Dynamic viscosity (kg/(m·s))Thermal expansion coefficient (1/K)Air0.0261.2981.831×10−53.356×10−3Prefabricated sleeve (Resin impregnated paper)0.352400//Heat shrink tube (XLPE)0.2862400//Flange (aluminium)2372440//Considering the symmetry of the fully insulated busbar prefabricated joint, a quarter 3‐D simulation model is established in Figure 5 including the joint and adjacent busbar.5FIGUREThe quarter 3‐D simulation modelThe effect of contact resistance is equivalent to an increase in conductor resistivity in the simulation. This part of the conductor is shown as the red volume in Figure 6, and its equivalent heat generation rate can be calculated by the following formula:2G=I2×ρjS2=I2×ρjW2H2$$\begin{equation}G = \frac{{{I}^2 \times {\rho }_j}}{{{S}^2}} = \frac{{{I}^2 \times {\rho }_j}}{{{W}^2{H}^2}}\end{equation}$$where I is the current; the width W and height H of the equivalent volume are 0.1 and 0.03 m, respectively; ρj is the equivalent resistivity which is k times the resistivity of copper. k is called the contact factor and specified to be 9 in this section.6FIGUREThe schematic diagram of equivalent heat sourceSince the length of the busbar is 5 m in the simulation, there is almost no axial heat flux at the end, where the adiabatic boundary condition is applied. The heat transfer between the outer surfaces and the surroundings is governed by both convection and radiation. For simplicity and convenience, the combined heat transfer coefficient that includes the effects of both convection and radiation is introduced [20]. Therefore, only the convective heat transfer boundary conditions are applied at the outer surfaces of the busbar and joint. The combined heat transfer coefficient is taken as 12 W/(m2·K) and the ambient temperature is taken as 25°C.There is enclosed air inside the joint that transfers heat from the conductor to the prefabricated sleeve through convection and radiation. The thermal convection is governed by the laws of conservation of mass, momentum and energy and its governing equations are expressed as [21]:3∇·ρv+∂ρ∂t=0ρ∂v∂t+(v·∇)v=f−∇p+μ∇2v∂T∂t+v·∇T=λρc∇2T+Gρc$$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\nabla \cdot \rho {\bm{v}}+\dfrac{{\partial \rho }}{{\partial t}} = 0}\\[12pt] {\rho \left( {\dfrac{{\partial {\bm{v}}}}{{\partial t}} + ({\bm{v}} \cdot \nabla ){\bm{v}}} \right) = {\bm{f}} - \nabla p + \mu {\nabla }^2{\bm{v}}}\\[12pt] {\dfrac{{\partial T}}{{\partial t}} + {\bm{v}} \cdot \nabla T = \dfrac{\lambda }{{\rho c}}{\nabla }^2T + \dfrac{G}{{\rho c}}} \end{array} \end{equation}$$where ρ is air density and v is the velocity vector; ∇ is Hamiltonian; p is pressure and μ is dynamic viscosity; f is the external force on the fluid per unit volume, if only gravity is considered, then f = ρg, where g is the acceleration of gravity; λ and c are thermal conductivity and specific heat capacity, respectively. In this paper, the commercial finite volume CFD code CFX is used to solve the above equations.The fundamental equation for the thermal radiation is expressed as [22]4dIds=−ka+ksI+kaσT4π+ks4π∫4πPΩ,Ω′IΩ′dΩ′$$\begin{equation}\frac{{{\rm{d}}I}}{{{\rm{d}}s}} = - \left( {{k}_a + {k}_s} \right)I + {k}_a\frac{{\sigma {T}^4}}{\pi } + \frac{{{k}_s}}{{4\pi }}\int_{{4\pi }}{{P\left( {\Omega ,\Omega ^{\prime}} \right)I\left( {\Omega ^{\prime}} \right){\rm{d}}\Omega ^{\prime}}}\end{equation}$$where I and s are the radiant intensity and distance in the direction of Ω, respectively; σ is Stefan‐Boltzmann constant, 5.67 × 10−8 W·m−2·K−4; ka and ks are the gas absorption and scattering coefficients. P(Ω, Ωʹ) is the probability that incident radiation in the direction Ωʹ will be scattered into the increment of solid angle dΩ about Ω. The Discrete Transfer model [22], a widely used numerical method of thermal radiation, is adopted in CFX.Since the air is nearly transparent to thermal radiation, only the surface emissivity is considered here. There are various solid materials in the joint including copper, resin impregnated paper and XLPE. The emissivity of non‐metals is usually around 0.9 while the emissivity of metals is related to the degree of oxidation and usually between 0.5 and 0.8[20]. In this paper, the emissivities of the solid surface inside the joint are all set to 0.8 in the simulation.The turbulent flow model is not used in the solution setting. After the solution, the average value of the Rayleigh number Ra of the field is 1.2 × 107, which is less than 108. That is to say, the flow state of the air inside the joint is laminar, so it is reasonable not to use the turbulent flow model.Considering the calculation accuracy and time cost, the simulation time step is taken as 20 s.The steady‐state temperature distributions of the prefabricated joint on the transverse and longitudinal sections at rated current are provided in Figure 7. Due to the thermal expansion, closed air moves upwards and takes away the heat of the conductor. Since the air first reaches the top and the moves down to the bottom, the temperature at the upper layer is significantly higher than that of the lower layer. The simulation results are consistent with the above‐mentioned laws of natural convection, showing the rationality of the simulation to a certain extent.7FIGUREThe steady‐state temperature distributions of the fully insulated busbar prefabricated jointAccording to [18], ADTC needs only two measuring spots in the busbar, with one spot adjacent to the joint end and the other one remote enough from the joint for longitudinal heat flow to be zero. In this paper, the distances between the two points and the joint end are set to 0.2 and 2.2 m, respectively. After completing the thermal analysis, extract the joint hotspot temperature Tj and conductor temperatures (T1, T2) at the measuring spots every 20 s to constitute the training samples.The form of the axial function can be written as follows [18]:5Tj=f(T1,T2)=aT1+(1−a)T2$$\begin{equation}{T}_{\rm{j}} = f({T}_1,{T}_2) = a{T}_1 + (1 - a){T}_2\end{equation}$$Fit formula (5) by the use of the training samples and then the axial functional expression of ADTC is calculated as follows:6Tj=f(T1,T2)=2.85T1−1.85T2$$\begin{equation}{T}_{\rm{j}} = f({T}_1,{T}_2) = 2.85{T}_1 - 1.85{T}_2\end{equation}$$Model correction considering contact resistanceIn the previous analysis the contact resistance is known, but in practice the contact resistance of the joint is often uncertain. When the contact resistance in the simulation is different from the actual one, both RDTC and ADTC will produce errors.For RDTC, only heat flux from the conductor is considered in the transient thermal network. However, in reality, the heat flux will also be transferred from the joint to the busbar because of the higher temperature of the joint. Hence, the closer to the joint, the greater the radial heat flux to the busbar, as sketched in Figure 8. That is to say, the contact resistance will affect the calculation accuracy of T1 in RDTC.8FIGUREThe schematic diagram of heat flux in the insulated busbar jointIn fact, there is a corresponding relationship between the radial heat flux of the busbar and the contact resistance. If one can establish this functional relationship and determine the contact resistance, the radial heat flux at T1 can be corrected, thereby reducing the error of RDTC when the contact resistance is abnormal.The above RDTC correction method requires: (1) establishment of the functional relationship between the contact resistance and the radial heat flux of busbar, (2) identification of contact resistance of joint. The former is relatively easy to implement through the steady‐state thermal analysis and function fitting. The main difficulty lies in how to identify the contact resistance in the joint.The hotspot temperature is closely related to the contact resistance. Therefore, this paper utilizes the calculation result of hotspot temperature based on RDTC and ADTC in steady state to characterize the contact resistance. In an ideal situation where there is no wind, rain and sunshine, the load current is I and the ambient temperature is stable at T∞. At this time, the calculation value of the joint hotspot temperature is Tjc, and then the equivalent thermal resistance Rj of the joint is defined as7Rj=Tjc−T∞I2R$$\begin{equation}{R}_{\rm{j}} = \frac{{{T}_{{\rm{jc}}} - {T}_\infty }}{{{I}^2R}}\end{equation}$$where R is the conductor resistance per unit length of busbar.Obviously, under the condition that the joint structure is fixed, Rj can uniquely determine the contact resistance, so it is reasonable to use Rj to characterize the contact resistance. In fact, the acquisition of Rj is feasible. According to the typical daily load curve [23], there is almost always a period of time when the load is relatively stable from 6 o'clock in the evening to 6 o'clock in the morning. At this time, if the ambient temperature fluctuates little and the conductor temperature is relatively stable, it can be considered that the joint has reached a thermal steady state. In this paper, if the fluctuation of the load does not exceed 10%, and the changes of the ambient temperature and the calculation value of the hotspot temperature are less than 0.5 K within Δt (Δt≥ 2 h), the joint reaches a steady state. The formula for calculating the equivalent thermal resistance of the joint is as follows:8Rj=T¯jc−T¯∞I¯2R$$\begin{equation}{R}_{\rm{j}} = \frac{{{{\bar{T}}}_{{\rm{jc}}} - {{\bar{T}}}_\infty }}{{{{\bar{I}}}^2R}}\end{equation}$$where the line above the physical quantity represents the average value within Δt.In order to characterize the influence of the joint on the radial heat flux at T1, the heat flux correction factor m is defined as the ratio of the radial heat flux at T1 to the radial heat flux of busbar far away from the joint. The relationship between Rj and m can be obtained through the steady‐state thermal analysis of the joint and is found to be linear. The fitting function is9m=0.4766Rj+0.6676$$\begin{equation}m = 0.4766 {R}_{\rm{j}} + 0.6676\end{equation}$$After identifying the equivalent thermal resistance Rj of the joint, substitute it into formula (9) to obtain m, and then the heat flux at T1 can be corrected. However, since the identification of Rj depends the hotspot temperature calculation value Tjc where the radial heat flux has not been corrected yet, Rj will be lower than the actual value. For this reason, it is necessary to perform repeated iteration until it converges as seen in Figure 9.9FIGUREThe iterative relationship between the equivalent thermal resistance Rj of joint and the heat flux correction factor mIn ADTC, the axial function is also related to the contact resistance. Referring to the correction method used in RDTC, the function relationship between the Rj and coefficient a in formula (5) is obtained through thermal analysis as shown in Figure 10. It can be seen that the relationship is approximately a power function. As the contact resistance increases, the coefficient a in axial function gradually increases, but there is a saturation trend. The functional relationship between Rj and a is obtained by fitting as follows:10a=4.93−0.69Rj−2.92$$\begin{equation}a = 4.93 - 0.69{R}_{\rm{j}}^{ - 2.92}\end{equation}$$10FIGUREThe relationship between the equivalent thermal resistance Rj of joint and the coefficient a in axial functionAccording to the above formula, the coefficient a in axial function can be determined by using the equivalent thermal resistance Rj of the joint. The identification of Rj is based on the hotspot temperature calculation value Tjc, while Tjc depends on the coefficient a in axial function. Hence, repeated iterative calculations are also required until convergence. Combined with the correction process in RDCT, the overall iterative relationship is shown in the Figure 11.11FIGUREThe overall iterative process for model correctionARRANGEMENT OF TEMPERATURE RISE TESTOverview of platformThe test platform is placed outdoors in the open air at Wuhan University and the overall layout is shown in Figure 12. A rectangular loop is formed by connecting the fully insulated busbars, prefabricated joint and copper bars in series. The geometry of the busbar and joint is consistent with the previous simulation. The length of the busbar is about 5 m to ensure that the temperature near the joint is unaffected by the end of the busbar. The inducing transformer is used to provide large current which is adjusted by the voltage regulator and measured by the current transformer. Platinum resistance thermometers with tolerance class of A [24] are employed to measure the temperatures of the air, the surface and the conductor. In order to reduce the measurement error, two sensors are placed inside the joint and three sensors are placed on each surface measuring spot. Both the temperature and current data are uploaded to the computer through the data logger for real‐time acquisition and storage.12FIGUREThe schematic diagram of the overall layout of the temperature rise test platformThe assembly of the fully insulated busbar prefabricated jointThe assembly process of the fully insulated busbar prefabricated joint is shown in Figure 13. Connect two busbar conductors through the copper bar and insert the temperature sensors inside the conductor at one end. Fix the sensors at the copper bar and install the prefabricated sleeve on the joint. The end of the sleeve is sealed by the flange and sealing ring.13FIGUREThe assembly of the fully insulated busbar prefabricated joint. (a) Insert the temperature sensors, (b) connect the conductor and fix the sensors, (c) install the prefabricated sleeve, and (d) seal by flangeRESULTSNormal contact resistanceThe temperature rise test was carried out for the joint with normal contact resistance first. The hotspot temperature of the prefabricated joint was calculated using the surface temperatures and current through RDTC and ADTC, and the results are illustrated in Figure 14.14FIGUREThe measured and calculated hotspot temperature under normal contact resistanceIt can be seen from the figure that under the conditions of current fluctuation and environmental change, the maximum calculated error of the hotspot temperature is not more than 4 K, and the steady‐state error at night is basically less than 0.5 K. A short‐term rainfall occurred at noon on 17 August, and the temperature of the hot spot dropped sharply and then returned to normal. The calculated temperature curve agrees very well with the measured one during the whole process, indicating that the algorithm can effectively overcome the impact of environmental sudden changes and is strongly robust. In addition, the steady‐state temperature rise of the joint is about 30 K, and the maximum hotspot temperature reaches 80.5°C under the rated current. There is a safety margin of 10 K compared to the temperature limit of 90°C, and thus the contact resistance is normal.Abnormal contact resistanceDisassemble the sleeve and loosen the copper bar bolts inside the joints to simulate the abnormal contact resistance. After reinstalling the sleeve, a temperature rise test was performed. The test duration is about 5 days, and the measured and calculated curve of the hotspot temperature are depicted in Figure 15. The steady‐state hotspot temperature rise under the rated current reached about 50 K, and the hot spot temperature exceeded the temperature limit of 90°C at noon on August 31, showing an abnormal contact resistance.15FIGUREThe measured and calculated hotspot temperature under abnormal contact resistanceIt can be seen that the calculated temperature is in good agreement with the measured one in general, and the steady‐state error under rated current is between 0 and 5 K. In the early morning of 29 to 30 August and 3 September, the steady‐state error is very small, while in the early morning of 1 to 2, September the steady‐state error is a little bit larger, which may be related to the changes in the weather. This implies that the calculated temperature under the abnormal contact resistance is more affected by environmental changes. Even so, the steady‐state error of 5 K is still within the acceptable range. In the process of current sudden change, the transient error is relatively large with the maximum error of about 10 K.DISCUSSIONSThe effect of current and environmental factors on TjFurther analysis of the temperature curves can reveal an interesting phenomenon. When the current drops in Figure 14, the hotspot temperature changes only slightly. On the other hand, with the decreasing current the hotspot temperature drops much more rapidly in Figure 15. In fact, the joint hotspot temperature is affected by both current and environmental factors, which must be kept in mind when analyzing the temperature change.At around 8:00 on 18 August, the current was reduced stepwise, decreasing 200 to 300 A every 1.5  h until the current dropped to zero at 13:00 and then lasted for 1.5 h. During this period, the temperature rise caused by the Joule heat must be greatly reduced but the measured hotspot temperature only dropped by less than 8 K. This is because the sun rises at the same time and the solar thermal radiation together with the increasing ambient temperature caused the joint temperature to rise. According to the data of 17 August in Figure 14, the temperature rise of the joint caused by environmental factors alone reached 20 K with almost constant current before rainfall. On the basis of the above analysis, if only the influence of current is considered, the hotspot temperature will drop by about 28 K. But this impact is largely weakened by environmental factors. This explains why the measuring equipment and temperature calculations (RDTC and ADTC) did not detected the sharp drop in the value of current.Similarly, at 13:00 on 31 August the current was suddenly reduced from 1250 A to zero and held it for almost 6.5 h, where the hotspot temperature dropped by 54 K. During the same time period on 1 September in Figure 15, the temperature drop of the joint caused by environmental factors alone is about 9 K. Based on the above analysis, if only the influence of current is considered, the hotspot temperature will decrease by about 45 K, about 1.6 times 28 K. This is very reasonable considering that the contact resistance is larger and the current drops faster in Figure 15.Evaluation of the contact stateAccording to the above analysis, using the hotspot temperature alone cannot sense the state of the contact resistance. Because temperature is not only related to the contact resistance, but also depends on the current and environmental factors, and is a dynamically changing quantity. But the contact state of joint will not change in a short period of time.In fact, the equivalent thermal resistance Rj introduced in Section 2.4 is exactly a good characterization of contact resistance, so the contact state of the joint can be evaluated based on Rj. According to data from temperature rise test, the maximum conductor temperature of the outdoor insulated busbar can reach 55°C without load, and thus the maximum allowable temperature rise ΔTm should be set to 35 K with the temperature limit of 90°C. Therefore, the critical equivalent thermal resistance Rjcr under rated load I0 is calculated as 0.9 K/W based on the following formula:11Rjcr=ΔTmI02R$$\begin{equation}{R}_{{\rm{jcr}}} = \frac{{\Delta {T}_{\rm{m}}}}{{{I}_0^2R}}\end{equation}$$With the equivalent thermal resistance of the actual joint Rj, the safety margin A is defined as follows:12A=Rjcr−RjRjcr×100%$$\begin{equation}A = \frac{{{R}_{{\rm{jcr}}} - {R}_{\rm{j}}}}{{{R}_{{\rm{jcr}}}}} \times 100{\rm{\% }}\end{equation}$$The contact state of a joint can be quantitatively evaluated through the safety margin A. In this paper, if the safety margin A≥10%, the contact state can be considered as normal. If 0≤A < 10%, the contact resistance is in a warning state, and further deterioration may lead to an abnormal state. If A < 0%, the contact state is abnormal, the conductor temperature may exceed 90°C with high current and ambient temperature.The equivalent thermal resistance Rj of the joint can be identified at night as described in Section 2.4. In Figure 14, the identification value of Rj is about 0.81 K/W, and its corresponding safety margin A is 10.0%, indicating that the contact state is normal. On the other hand, the identification value of Rj in Figure 15 is about 1.23 K/W with the safety margin A of ‐36.7%. It can be judged that the contact state of the joint were severely abnormal and the hotspot temperature can easily exceed 90°C under rated load in hot weather as shown in Figure 15.Analysis of the transient calculated errorThe transient error during the abrupt change of current is about 10 K, which is not a small number. It is necessary to thoroughly analyze the reasons for the transient error.Formula (5) can be transformed into the following form:13a=Tj−T2T1−T2$$\begin{equation}a=\frac{T_{\rm j}-T_{2}}{T_{1}-T_{2}}\end{equation}$$That is to say, the coefficient a is the ratio of (Tj−T2) to (T1−T2). Assume that the initial temperature of the busbar and joint is equal to the ambient temperature. When the current suddenly increases from zero to the rated value, the joint hotspot temperature will rise more rapidly than adjacent conductor temperature. In the initial stage, the heat inside the joint has not been sufficiently transferred to the surrounding busbar yet. At this time, (T1−T2) is almost zero, and thus the corresponding coefficient a is very large. As the heat inside the joint gradually diffuses towards the busbar, a will decrease and eventually reach a steady‐state value. The coefficient a is time‐varying, but in our proposed algorithm a is set to a constant close to the above steady‐state value, so the calculated temperature based on RDTC and ADTC is always lower than the measured value with increasing step current. When the contact resistance is small, the difference between the joint hotspot temperature and adjacent busbar conductor temperature is not very large, so the corresponding error is relatively small as seen in Figure 14. On the contrary, when the contact state is abnormal, the temperature difference between the joint and the busbar is so great that it produces a large transient error as seen in Figure 15. Similarly, transient error with decreasing step current can be analyzed. After the rated current is cut off, the joint hotspot temperature drops faster than the busbar conductor temperature, so the coefficient a gradually decreases from the steady‐state value. Since a is set to a constant close to the steady‐state value, the calculated temperature based on RDTC and ADTC is always higher than the measured value with decreasing step current. The larger the contact resistance, the greater the transient error.In conclusion, the fundamental cause of transient error lies in that the essentially time‐vary coefficient a is approximated to a constant in the proposed method. Obviously, this is a systematic error of the model that is difficult to eliminate.Nevertheless, this transient error is actually acceptable from an engineering point of view. This is because a large number of daily load curve data indicate that the current in the power substation hardly changes drastically and suddenly as in Figure 15, so the actual transient error must be fairly reduced. Moreover, the maximum calculated error usually corresponds to the midpoint of the temperature curve during descending or ascending phase. But in actual temperature monitoring, it doesn't matter how the temperature curve changes, it is the peak value of the curve that most matters. Near the peak, the hotspot temperature has tended to be steady, and the error will be greatly reduced. For example, the calculated errors at the peak points on 29 to 31 August and 1 to 2 September in Figure 15 are only 1.3, 3.6, 1.9, 0.2 and 2.8 K, respectively, which are much lower than the maximum transient error of 10 K.In summary, the proposed algorithm can effectively monitor the joint hotspot temperature.CONCLUSIONSThis paper presents an approach to indirectly monitor the conductor temperature of the fully insulated busbar prefabricated joint based on RDTC and ADCT using surface temperatures and current. The influence of contact resistance is analyzed and the algorithm is corrected by establishing the relationship between the contact resistance and model coefficients.A series of temperature rise tests were carried out under various service conditions to verify the proposed approach. During the test, the contact resistance was adjusted artificially to simulate different contact states. When the contact state was normal, the transient error and the steady‐state error did not exceed 4 and 1 K, respectively, showing the high model precision. When the state is abnormal, the steady‐state error under rated current is between 0 and 5 K, and the transient error during the abrupt change of current is about 10 K. The reason of this transient error as well as its influence is fully discussed and the evaluation method of the contact state is presented. From an engineering point of view, the proposed algorithm can effectively monitor the joint hotspot temperature and evaluate the contact state.AUTHOR CONTRIBUTIONSLiezheng Tang: Investigation; Methodology; Software; Validation; Writing – original draft. Jiangjun Ruan: Conceptualization. Rou Chen: Writing – review & editing. Guohua Zhou: Funding acquisition; Writing – review & editing.ACKNOWLEDGEMENTThe authors would like to thank Hubei Xinghe Electric Power New Material Co., Ltd., who assembled the fully insulated busbar prefabricated joint.CONFLICT OF INTERESTThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.FUNDING INFORMATIONFunding information is not applicable.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available on request from the corresponding author. 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Energies 10(12), 1–17 (2017). https://doi.org/10.3390/en10122050Nakamura, S., Morooka, S., Kawasaki, K.: Conductor temperature monitoring system in underground power transmission XLPE cable joints. IEEE Trans. Power Deliv. 7(4), 1688–1697 (1992). https://doi.org/10.1109/61.156967Bragatto, T., Cresta, M., Gatta, F., et al.: A 3‐D nonlinear thermal circuit model of underground MV power cables and their joints. Electr. Power Syst. Res. 173, 112–121 (2019). https://doi.org/10.1016/j.epsr.2019.04.024Bragatto, T., Cresta, M., Gatta, F., et al.: Underground MV power cable joints: A nonlinear thermal circuit model and its experimental validation. Electr. Power Syst. Res. 149, 190–197 (2017). https://doi.org/10.1016/j.epsr.2017.04.030Ruan, J., Liu, C., Huang, D., et al.: Hot spot temperature inversion for the single‐core power cable joint. Appl. Therm. Eng. 104, 146–152 (2016). https://doi.org/10.1016/j.applthermaleng.2016.05.008Tang, L., Ruan, J., Qiu, Z., et al.: Strongly robust approach for temperature monitoring of power cable joint. IET Gener. Transm. Distrib. 13(8), 1324–1331 (2019). https://doi.org/10.1049/iet‐gtd.2018.5924Tang, L., Ruan, J., Yang, Z., et al.: Hotspot temperature monitoring of fully insulated busbar taped joint. IEEE Access 7, 66463–66475 (2019). https://doi.org/10.1109/ACCESS.2019.2918556IEC Standard. Calculation of the cyclic and emergency current rating of cables ‐ part 2: Cyclic rating of cables greater than 18/30 (36) kV and emergency ratings for cables of all voltages. IEC 60853‐2:1989/AMD1:2008Cengel, Y.: Heat Transfer – A Practical Approach. Mc‐Graw Hill, New York (2003)Welty, J., Wicks, C., Wilson, R., et al.: Fundamentals of Momentum, Heat and Mass Transfer. 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Conductor temperature monitoring for the fully insulated busbar prefabricated joint considering contact resistance

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Abstract

INTRODUCTIONDue to the large current carrying capacity, good insulation performance and compact structure, the fully insulated busbars have been increasingly widely utilized and developed in the industries such as electric power, chemical industry, petroleum, metallurgy and shipbuilding around the world[1–5]. The total length of the fully insulated busbar used in China was nearly 200 km during 2014[6, 7].The length of the single busbar is within 10 m so that the fully insulated busbar routes usually consist of dozens or even hundreds of busbar segments connected in series through joints. There are mainly two types of joints for insulated busbar, namely prefabricated type and taped type, and the former one is more commonly used in practice. According to the statistics, the defects or failures of fully insulated busbar owing to product quality, installation process and operating environment have spread to dozens of substations in over ten provinces in China. Statistical results from more than 40 defects and failures of fully insulated busbar show that the joints and terminations are the weakest point of the fully insulated busbar system with the fault proportion of 70%. Moreover, the main causes for the joint and termination defects include poor sealing, poor contact and main insulation defects, where more than one third of the faults were caused by poor contact. Poor conductor contact will lead to overheating of the joint, which will further increase the contact resistance, thus forming a vicious circle. Excessive temperature will aggravate the thermal aging of the insulation, cause the joint sealing failure and eventually lead to insulation breakdown [8]. Therefore, it is of great significance to monitor the conductor temperature of the fully insulated busbar joint so as to realize the early warning of overheating faults.In view of the high similarity in the structure between the fully insulated busbar and the power cable, the temperature monitoring of the cable joint can be used for reference. Although there has been extensive research regarding the thermal behaviour of the cable joint, most of them focus on the steady‐state analysis for determining the ampacity rather than real‐time online monitoring [9–12]. It is difficult to directly measure the conductor temperature because of high voltages being applied to busbar. The most common indirect real‐time measurement for conductor temperature of cable joint is based on the thermal circuit model [13–15]. In our previous papers, an alternative indirect approach was put forward to realize the hotspot temperature monitoring for the cable joint in two steps [16], which shows strong robustness with the variable thermal environments and uncertain thermal parameters of the joint [17]. Afterwards, the authors applied this method to the fully insulated busbar taped joint, which indicates the high model precision and strong robustness to the solar radiation impact [18]. The validity of the above method to the prefabricated joint, where air convection and thermal radiation are the main forms of heat transfer, has yet to be verified. Moreover, almost all of the existing models assume that the contact resistance of the joint is known, but in fact, affected by the installation quality or operating conditions, the contact resistance may become larger, thereby resulting in overheating defect or failure. It is clear that the contact resistance plays a key role in the model accuracy, but to the best of our knowledge, such investigations have not yet been performed either theoretically or experimentally. For this reason, this paper aims to improve our previous algorithm so as to monitor the conductor temperature of the fully insulated busbar prefabricated joint under uncertain contact resistances in real time.METHODOLOGYBasic idea and analysis stepsSince this paper is an improvement on the basis of our previous work, the general introduction of its basic idea and analysis steps is given below first [18].Due to the high thermal conductivity of the conductor, most of the heat flux will be transported in the conductor from connector to both sides. Meanwhile, in the radial direction of the busbar, the heat will be transferred from the hot conductor to the cold surface. According to the direction of heat flux, the joint hotspot temperature Tj can be obtained through radial direction temperature calculation (RDTC) in the busbar and axial direction temperature calculation (ADTC) in the conductor from two surface temperatures Ts1 and Ts2 as seen in Figure 1.1FIGUREThe path for obtaining the hotspot temperature of fully insulated busbar jointThe analysis steps are as follows:In RDTC, the 1‐D transient thermal network is adopted to calculate the conductor temperatures T1 and T2 in real time on the basis of the current and surface temperatures Ts1 and Ts2.In ADTC, the transient thermal analysis of the insulated busbar joint under single‐step load currents ranging from 100 A to the rated current is carried out, from which the conductor temperature data are extracted as training samples. On this basis, the axial function between the hotspot temperature Tj and the conductor temperature T1 and T2 can be established. In real‐time temperature monitoring, the conductor temperatures T1 and T2 calculated in RDTC are substituted into the axial function, and then the hot spot temperature Tj can be obtained, as illustrated in Figure 2.2FIGUREThe algorithm for hotspot temperature monitoring of fully insulated busbar jointRDTC modelThe establishment process of RDTC model is introduced in [18] in detail, and only the main points are given below.The structural and thermal parameters of the fully insulated busbar are illustrated in Table 1.Each layer of the busbar can be represented by lumped π‐type RC thermal circuit branches as per IEC 60853[19] and thus the transient thermal network is provided in Figure 3.3FIGUREThe 1‐D transient thermal network of the fully insulated busbarAs per Kirchhoff's law, the state equations in Figure 3 can be written as1(C0+C1n)dTc0dt+Tc0−Tc1R1−G=0Tc0−Tc1R1+Tc2−Tc1R2−(C1w+C2n)dTc1dt=0Tc1−Tc2R2+Ts−Tc2R3−(C2w+C3+C4n)dTc2dt=0$$\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {({C}_0 + {C}_{1n})\dfrac{{d{T}_{c0}}}{{dt}} + \dfrac{{{T}_{c0} - {T}_{c1}}}{{{R}_1}} - G = 0}\\[12pt] {\dfrac{{{T}_{c0} - {T}_{c1}}}{{{R}_1}} + \dfrac{{{T}_{c2} - {T}_{c1}}}{{{R}_2}} - ({C}_{1w} + {C}_{2n})\dfrac{{d{T}_{c1}}}{{dt}} = 0}\\[12pt] {\dfrac{{{T}_{c1} - {T}_{c2}}}{{{R}_2}} + \dfrac{{{T}_s - {T}_{c2}}}{{{R}_3}} - ({C}_{2w} + {C}_3 + {C}_{4n})\dfrac{{d{T}_{c2}}}{{dt}} = 0} \end{array} } \right.\end{equation}$$The conductor temperature can be obtained by solving the above differential equation using the surface temperature and the power loss.ADTCIn order to obtain the training samples for the axial function in ADTC, it is necessary to perform transient thermal analysis of the insulated busbar prefabricated joint. Unlike the taped joint, the main heat dissipation medium of the prefabricated joint is closed air, where heat is transferred through thermal convection and radiation. Hence, the 3‐D fluid‐thermal analysis is carried out in this paper.The half longitudinal section structure of the prefabricated joint is depicted in Figure 4. A terminal pad is welded at the end of the busbar conductor and connected with the connecting copper bar by bolts. The joint is enclosed in the prefabricated sleeve and the end of the sleeve is sealed by the flange. The thermal parameters of the joint are provided in Table 2 [20].4FIGUREThe half longitudinal section structure of the prefabricated joint1TABLEThe structural and thermal parameters of the insulated busbarComponentsOuter radius (mm)Thermal conductivity (W/(m·K))Volumetric specific heat (kJ/(m3·K))Air26//Copper conductor303833450PTFE insulation320.2592290XLPE insulation36.50.2862400Aluminum earth screen36.82182500XLPE oversheath40.10.28624002TABLEThe thermal parameters of the insulated busbar prefabricated jointComponentsThermal conductivity (W/(m·K))Volumetric specific heat (kJ/(m3·K))Dynamic viscosity (kg/(m·s))Thermal expansion coefficient (1/K)Air0.0261.2981.831×10−53.356×10−3Prefabricated sleeve (Resin impregnated paper)0.352400//Heat shrink tube (XLPE)0.2862400//Flange (aluminium)2372440//Considering the symmetry of the fully insulated busbar prefabricated joint, a quarter 3‐D simulation model is established in Figure 5 including the joint and adjacent busbar.5FIGUREThe quarter 3‐D simulation modelThe effect of contact resistance is equivalent to an increase in conductor resistivity in the simulation. This part of the conductor is shown as the red volume in Figure 6, and its equivalent heat generation rate can be calculated by the following formula:2G=I2×ρjS2=I2×ρjW2H2$$\begin{equation}G = \frac{{{I}^2 \times {\rho }_j}}{{{S}^2}} = \frac{{{I}^2 \times {\rho }_j}}{{{W}^2{H}^2}}\end{equation}$$where I is the current; the width W and height H of the equivalent volume are 0.1 and 0.03 m, respectively; ρj is the equivalent resistivity which is k times the resistivity of copper. k is called the contact factor and specified to be 9 in this section.6FIGUREThe schematic diagram of equivalent heat sourceSince the length of the busbar is 5 m in the simulation, there is almost no axial heat flux at the end, where the adiabatic boundary condition is applied. The heat transfer between the outer surfaces and the surroundings is governed by both convection and radiation. For simplicity and convenience, the combined heat transfer coefficient that includes the effects of both convection and radiation is introduced [20]. Therefore, only the convective heat transfer boundary conditions are applied at the outer surfaces of the busbar and joint. The combined heat transfer coefficient is taken as 12 W/(m2·K) and the ambient temperature is taken as 25°C.There is enclosed air inside the joint that transfers heat from the conductor to the prefabricated sleeve through convection and radiation. The thermal convection is governed by the laws of conservation of mass, momentum and energy and its governing equations are expressed as [21]:3∇·ρv+∂ρ∂t=0ρ∂v∂t+(v·∇)v=f−∇p+μ∇2v∂T∂t+v·∇T=λρc∇2T+Gρc$$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\nabla \cdot \rho {\bm{v}}+\dfrac{{\partial \rho }}{{\partial t}} = 0}\\[12pt] {\rho \left( {\dfrac{{\partial {\bm{v}}}}{{\partial t}} + ({\bm{v}} \cdot \nabla ){\bm{v}}} \right) = {\bm{f}} - \nabla p + \mu {\nabla }^2{\bm{v}}}\\[12pt] {\dfrac{{\partial T}}{{\partial t}} + {\bm{v}} \cdot \nabla T = \dfrac{\lambda }{{\rho c}}{\nabla }^2T + \dfrac{G}{{\rho c}}} \end{array} \end{equation}$$where ρ is air density and v is the velocity vector; ∇ is Hamiltonian; p is pressure and μ is dynamic viscosity; f is the external force on the fluid per unit volume, if only gravity is considered, then f = ρg, where g is the acceleration of gravity; λ and c are thermal conductivity and specific heat capacity, respectively. In this paper, the commercial finite volume CFD code CFX is used to solve the above equations.The fundamental equation for the thermal radiation is expressed as [22]4dIds=−ka+ksI+kaσT4π+ks4π∫4πPΩ,Ω′IΩ′dΩ′$$\begin{equation}\frac{{{\rm{d}}I}}{{{\rm{d}}s}} = - \left( {{k}_a + {k}_s} \right)I + {k}_a\frac{{\sigma {T}^4}}{\pi } + \frac{{{k}_s}}{{4\pi }}\int_{{4\pi }}{{P\left( {\Omega ,\Omega ^{\prime}} \right)I\left( {\Omega ^{\prime}} \right){\rm{d}}\Omega ^{\prime}}}\end{equation}$$where I and s are the radiant intensity and distance in the direction of Ω, respectively; σ is Stefan‐Boltzmann constant, 5.67 × 10−8 W·m−2·K−4; ka and ks are the gas absorption and scattering coefficients. P(Ω, Ωʹ) is the probability that incident radiation in the direction Ωʹ will be scattered into the increment of solid angle dΩ about Ω. The Discrete Transfer model [22], a widely used numerical method of thermal radiation, is adopted in CFX.Since the air is nearly transparent to thermal radiation, only the surface emissivity is considered here. There are various solid materials in the joint including copper, resin impregnated paper and XLPE. The emissivity of non‐metals is usually around 0.9 while the emissivity of metals is related to the degree of oxidation and usually between 0.5 and 0.8[20]. In this paper, the emissivities of the solid surface inside the joint are all set to 0.8 in the simulation.The turbulent flow model is not used in the solution setting. After the solution, the average value of the Rayleigh number Ra of the field is 1.2 × 107, which is less than 108. That is to say, the flow state of the air inside the joint is laminar, so it is reasonable not to use the turbulent flow model.Considering the calculation accuracy and time cost, the simulation time step is taken as 20 s.The steady‐state temperature distributions of the prefabricated joint on the transverse and longitudinal sections at rated current are provided in Figure 7. Due to the thermal expansion, closed air moves upwards and takes away the heat of the conductor. Since the air first reaches the top and the moves down to the bottom, the temperature at the upper layer is significantly higher than that of the lower layer. The simulation results are consistent with the above‐mentioned laws of natural convection, showing the rationality of the simulation to a certain extent.7FIGUREThe steady‐state temperature distributions of the fully insulated busbar prefabricated jointAccording to [18], ADTC needs only two measuring spots in the busbar, with one spot adjacent to the joint end and the other one remote enough from the joint for longitudinal heat flow to be zero. In this paper, the distances between the two points and the joint end are set to 0.2 and 2.2 m, respectively. After completing the thermal analysis, extract the joint hotspot temperature Tj and conductor temperatures (T1, T2) at the measuring spots every 20 s to constitute the training samples.The form of the axial function can be written as follows [18]:5Tj=f(T1,T2)=aT1+(1−a)T2$$\begin{equation}{T}_{\rm{j}} = f({T}_1,{T}_2) = a{T}_1 + (1 - a){T}_2\end{equation}$$Fit formula (5) by the use of the training samples and then the axial functional expression of ADTC is calculated as follows:6Tj=f(T1,T2)=2.85T1−1.85T2$$\begin{equation}{T}_{\rm{j}} = f({T}_1,{T}_2) = 2.85{T}_1 - 1.85{T}_2\end{equation}$$Model correction considering contact resistanceIn the previous analysis the contact resistance is known, but in practice the contact resistance of the joint is often uncertain. When the contact resistance in the simulation is different from the actual one, both RDTC and ADTC will produce errors.For RDTC, only heat flux from the conductor is considered in the transient thermal network. However, in reality, the heat flux will also be transferred from the joint to the busbar because of the higher temperature of the joint. Hence, the closer to the joint, the greater the radial heat flux to the busbar, as sketched in Figure 8. That is to say, the contact resistance will affect the calculation accuracy of T1 in RDTC.8FIGUREThe schematic diagram of heat flux in the insulated busbar jointIn fact, there is a corresponding relationship between the radial heat flux of the busbar and the contact resistance. If one can establish this functional relationship and determine the contact resistance, the radial heat flux at T1 can be corrected, thereby reducing the error of RDTC when the contact resistance is abnormal.The above RDTC correction method requires: (1) establishment of the functional relationship between the contact resistance and the radial heat flux of busbar, (2) identification of contact resistance of joint. The former is relatively easy to implement through the steady‐state thermal analysis and function fitting. The main difficulty lies in how to identify the contact resistance in the joint.The hotspot temperature is closely related to the contact resistance. Therefore, this paper utilizes the calculation result of hotspot temperature based on RDTC and ADTC in steady state to characterize the contact resistance. In an ideal situation where there is no wind, rain and sunshine, the load current is I and the ambient temperature is stable at T∞. At this time, the calculation value of the joint hotspot temperature is Tjc, and then the equivalent thermal resistance Rj of the joint is defined as7Rj=Tjc−T∞I2R$$\begin{equation}{R}_{\rm{j}} = \frac{{{T}_{{\rm{jc}}} - {T}_\infty }}{{{I}^2R}}\end{equation}$$where R is the conductor resistance per unit length of busbar.Obviously, under the condition that the joint structure is fixed, Rj can uniquely determine the contact resistance, so it is reasonable to use Rj to characterize the contact resistance. In fact, the acquisition of Rj is feasible. According to the typical daily load curve [23], there is almost always a period of time when the load is relatively stable from 6 o'clock in the evening to 6 o'clock in the morning. At this time, if the ambient temperature fluctuates little and the conductor temperature is relatively stable, it can be considered that the joint has reached a thermal steady state. In this paper, if the fluctuation of the load does not exceed 10%, and the changes of the ambient temperature and the calculation value of the hotspot temperature are less than 0.5 K within Δt (Δt≥ 2 h), the joint reaches a steady state. The formula for calculating the equivalent thermal resistance of the joint is as follows:8Rj=T¯jc−T¯∞I¯2R$$\begin{equation}{R}_{\rm{j}} = \frac{{{{\bar{T}}}_{{\rm{jc}}} - {{\bar{T}}}_\infty }}{{{{\bar{I}}}^2R}}\end{equation}$$where the line above the physical quantity represents the average value within Δt.In order to characterize the influence of the joint on the radial heat flux at T1, the heat flux correction factor m is defined as the ratio of the radial heat flux at T1 to the radial heat flux of busbar far away from the joint. The relationship between Rj and m can be obtained through the steady‐state thermal analysis of the joint and is found to be linear. The fitting function is9m=0.4766Rj+0.6676$$\begin{equation}m = 0.4766 {R}_{\rm{j}} + 0.6676\end{equation}$$After identifying the equivalent thermal resistance Rj of the joint, substitute it into formula (9) to obtain m, and then the heat flux at T1 can be corrected. However, since the identification of Rj depends the hotspot temperature calculation value Tjc where the radial heat flux has not been corrected yet, Rj will be lower than the actual value. For this reason, it is necessary to perform repeated iteration until it converges as seen in Figure 9.9FIGUREThe iterative relationship between the equivalent thermal resistance Rj of joint and the heat flux correction factor mIn ADTC, the axial function is also related to the contact resistance. Referring to the correction method used in RDTC, the function relationship between the Rj and coefficient a in formula (5) is obtained through thermal analysis as shown in Figure 10. It can be seen that the relationship is approximately a power function. As the contact resistance increases, the coefficient a in axial function gradually increases, but there is a saturation trend. The functional relationship between Rj and a is obtained by fitting as follows:10a=4.93−0.69Rj−2.92$$\begin{equation}a = 4.93 - 0.69{R}_{\rm{j}}^{ - 2.92}\end{equation}$$10FIGUREThe relationship between the equivalent thermal resistance Rj of joint and the coefficient a in axial functionAccording to the above formula, the coefficient a in axial function can be determined by using the equivalent thermal resistance Rj of the joint. The identification of Rj is based on the hotspot temperature calculation value Tjc, while Tjc depends on the coefficient a in axial function. Hence, repeated iterative calculations are also required until convergence. Combined with the correction process in RDCT, the overall iterative relationship is shown in the Figure 11.11FIGUREThe overall iterative process for model correctionARRANGEMENT OF TEMPERATURE RISE TESTOverview of platformThe test platform is placed outdoors in the open air at Wuhan University and the overall layout is shown in Figure 12. A rectangular loop is formed by connecting the fully insulated busbars, prefabricated joint and copper bars in series. The geometry of the busbar and joint is consistent with the previous simulation. The length of the busbar is about 5 m to ensure that the temperature near the joint is unaffected by the end of the busbar. The inducing transformer is used to provide large current which is adjusted by the voltage regulator and measured by the current transformer. Platinum resistance thermometers with tolerance class of A [24] are employed to measure the temperatures of the air, the surface and the conductor. In order to reduce the measurement error, two sensors are placed inside the joint and three sensors are placed on each surface measuring spot. Both the temperature and current data are uploaded to the computer through the data logger for real‐time acquisition and storage.12FIGUREThe schematic diagram of the overall layout of the temperature rise test platformThe assembly of the fully insulated busbar prefabricated jointThe assembly process of the fully insulated busbar prefabricated joint is shown in Figure 13. Connect two busbar conductors through the copper bar and insert the temperature sensors inside the conductor at one end. Fix the sensors at the copper bar and install the prefabricated sleeve on the joint. The end of the sleeve is sealed by the flange and sealing ring.13FIGUREThe assembly of the fully insulated busbar prefabricated joint. (a) Insert the temperature sensors, (b) connect the conductor and fix the sensors, (c) install the prefabricated sleeve, and (d) seal by flangeRESULTSNormal contact resistanceThe temperature rise test was carried out for the joint with normal contact resistance first. The hotspot temperature of the prefabricated joint was calculated using the surface temperatures and current through RDTC and ADTC, and the results are illustrated in Figure 14.14FIGUREThe measured and calculated hotspot temperature under normal contact resistanceIt can be seen from the figure that under the conditions of current fluctuation and environmental change, the maximum calculated error of the hotspot temperature is not more than 4 K, and the steady‐state error at night is basically less than 0.5 K. A short‐term rainfall occurred at noon on 17 August, and the temperature of the hot spot dropped sharply and then returned to normal. The calculated temperature curve agrees very well with the measured one during the whole process, indicating that the algorithm can effectively overcome the impact of environmental sudden changes and is strongly robust. In addition, the steady‐state temperature rise of the joint is about 30 K, and the maximum hotspot temperature reaches 80.5°C under the rated current. There is a safety margin of 10 K compared to the temperature limit of 90°C, and thus the contact resistance is normal.Abnormal contact resistanceDisassemble the sleeve and loosen the copper bar bolts inside the joints to simulate the abnormal contact resistance. After reinstalling the sleeve, a temperature rise test was performed. The test duration is about 5 days, and the measured and calculated curve of the hotspot temperature are depicted in Figure 15. The steady‐state hotspot temperature rise under the rated current reached about 50 K, and the hot spot temperature exceeded the temperature limit of 90°C at noon on August 31, showing an abnormal contact resistance.15FIGUREThe measured and calculated hotspot temperature under abnormal contact resistanceIt can be seen that the calculated temperature is in good agreement with the measured one in general, and the steady‐state error under rated current is between 0 and 5 K. In the early morning of 29 to 30 August and 3 September, the steady‐state error is very small, while in the early morning of 1 to 2, September the steady‐state error is a little bit larger, which may be related to the changes in the weather. This implies that the calculated temperature under the abnormal contact resistance is more affected by environmental changes. Even so, the steady‐state error of 5 K is still within the acceptable range. In the process of current sudden change, the transient error is relatively large with the maximum error of about 10 K.DISCUSSIONSThe effect of current and environmental factors on TjFurther analysis of the temperature curves can reveal an interesting phenomenon. When the current drops in Figure 14, the hotspot temperature changes only slightly. On the other hand, with the decreasing current the hotspot temperature drops much more rapidly in Figure 15. In fact, the joint hotspot temperature is affected by both current and environmental factors, which must be kept in mind when analyzing the temperature change.At around 8:00 on 18 August, the current was reduced stepwise, decreasing 200 to 300 A every 1.5  h until the current dropped to zero at 13:00 and then lasted for 1.5 h. During this period, the temperature rise caused by the Joule heat must be greatly reduced but the measured hotspot temperature only dropped by less than 8 K. This is because the sun rises at the same time and the solar thermal radiation together with the increasing ambient temperature caused the joint temperature to rise. According to the data of 17 August in Figure 14, the temperature rise of the joint caused by environmental factors alone reached 20 K with almost constant current before rainfall. On the basis of the above analysis, if only the influence of current is considered, the hotspot temperature will drop by about 28 K. But this impact is largely weakened by environmental factors. This explains why the measuring equipment and temperature calculations (RDTC and ADTC) did not detected the sharp drop in the value of current.Similarly, at 13:00 on 31 August the current was suddenly reduced from 1250 A to zero and held it for almost 6.5 h, where the hotspot temperature dropped by 54 K. During the same time period on 1 September in Figure 15, the temperature drop of the joint caused by environmental factors alone is about 9 K. Based on the above analysis, if only the influence of current is considered, the hotspot temperature will decrease by about 45 K, about 1.6 times 28 K. This is very reasonable considering that the contact resistance is larger and the current drops faster in Figure 15.Evaluation of the contact stateAccording to the above analysis, using the hotspot temperature alone cannot sense the state of the contact resistance. Because temperature is not only related to the contact resistance, but also depends on the current and environmental factors, and is a dynamically changing quantity. But the contact state of joint will not change in a short period of time.In fact, the equivalent thermal resistance Rj introduced in Section 2.4 is exactly a good characterization of contact resistance, so the contact state of the joint can be evaluated based on Rj. According to data from temperature rise test, the maximum conductor temperature of the outdoor insulated busbar can reach 55°C without load, and thus the maximum allowable temperature rise ΔTm should be set to 35 K with the temperature limit of 90°C. Therefore, the critical equivalent thermal resistance Rjcr under rated load I0 is calculated as 0.9 K/W based on the following formula:11Rjcr=ΔTmI02R$$\begin{equation}{R}_{{\rm{jcr}}} = \frac{{\Delta {T}_{\rm{m}}}}{{{I}_0^2R}}\end{equation}$$With the equivalent thermal resistance of the actual joint Rj, the safety margin A is defined as follows:12A=Rjcr−RjRjcr×100%$$\begin{equation}A = \frac{{{R}_{{\rm{jcr}}} - {R}_{\rm{j}}}}{{{R}_{{\rm{jcr}}}}} \times 100{\rm{\% }}\end{equation}$$The contact state of a joint can be quantitatively evaluated through the safety margin A. In this paper, if the safety margin A≥10%, the contact state can be considered as normal. If 0≤A < 10%, the contact resistance is in a warning state, and further deterioration may lead to an abnormal state. If A < 0%, the contact state is abnormal, the conductor temperature may exceed 90°C with high current and ambient temperature.The equivalent thermal resistance Rj of the joint can be identified at night as described in Section 2.4. In Figure 14, the identification value of Rj is about 0.81 K/W, and its corresponding safety margin A is 10.0%, indicating that the contact state is normal. On the other hand, the identification value of Rj in Figure 15 is about 1.23 K/W with the safety margin A of ‐36.7%. It can be judged that the contact state of the joint were severely abnormal and the hotspot temperature can easily exceed 90°C under rated load in hot weather as shown in Figure 15.Analysis of the transient calculated errorThe transient error during the abrupt change of current is about 10 K, which is not a small number. It is necessary to thoroughly analyze the reasons for the transient error.Formula (5) can be transformed into the following form:13a=Tj−T2T1−T2$$\begin{equation}a=\frac{T_{\rm j}-T_{2}}{T_{1}-T_{2}}\end{equation}$$That is to say, the coefficient a is the ratio of (Tj−T2) to (T1−T2). Assume that the initial temperature of the busbar and joint is equal to the ambient temperature. When the current suddenly increases from zero to the rated value, the joint hotspot temperature will rise more rapidly than adjacent conductor temperature. In the initial stage, the heat inside the joint has not been sufficiently transferred to the surrounding busbar yet. At this time, (T1−T2) is almost zero, and thus the corresponding coefficient a is very large. As the heat inside the joint gradually diffuses towards the busbar, a will decrease and eventually reach a steady‐state value. The coefficient a is time‐varying, but in our proposed algorithm a is set to a constant close to the above steady‐state value, so the calculated temperature based on RDTC and ADTC is always lower than the measured value with increasing step current. When the contact resistance is small, the difference between the joint hotspot temperature and adjacent busbar conductor temperature is not very large, so the corresponding error is relatively small as seen in Figure 14. On the contrary, when the contact state is abnormal, the temperature difference between the joint and the busbar is so great that it produces a large transient error as seen in Figure 15. Similarly, transient error with decreasing step current can be analyzed. After the rated current is cut off, the joint hotspot temperature drops faster than the busbar conductor temperature, so the coefficient a gradually decreases from the steady‐state value. Since a is set to a constant close to the steady‐state value, the calculated temperature based on RDTC and ADTC is always higher than the measured value with decreasing step current. The larger the contact resistance, the greater the transient error.In conclusion, the fundamental cause of transient error lies in that the essentially time‐vary coefficient a is approximated to a constant in the proposed method. Obviously, this is a systematic error of the model that is difficult to eliminate.Nevertheless, this transient error is actually acceptable from an engineering point of view. This is because a large number of daily load curve data indicate that the current in the power substation hardly changes drastically and suddenly as in Figure 15, so the actual transient error must be fairly reduced. Moreover, the maximum calculated error usually corresponds to the midpoint of the temperature curve during descending or ascending phase. But in actual temperature monitoring, it doesn't matter how the temperature curve changes, it is the peak value of the curve that most matters. Near the peak, the hotspot temperature has tended to be steady, and the error will be greatly reduced. For example, the calculated errors at the peak points on 29 to 31 August and 1 to 2 September in Figure 15 are only 1.3, 3.6, 1.9, 0.2 and 2.8 K, respectively, which are much lower than the maximum transient error of 10 K.In summary, the proposed algorithm can effectively monitor the joint hotspot temperature.CONCLUSIONSThis paper presents an approach to indirectly monitor the conductor temperature of the fully insulated busbar prefabricated joint based on RDTC and ADCT using surface temperatures and current. The influence of contact resistance is analyzed and the algorithm is corrected by establishing the relationship between the contact resistance and model coefficients.A series of temperature rise tests were carried out under various service conditions to verify the proposed approach. During the test, the contact resistance was adjusted artificially to simulate different contact states. When the contact state was normal, the transient error and the steady‐state error did not exceed 4 and 1 K, respectively, showing the high model precision. When the state is abnormal, the steady‐state error under rated current is between 0 and 5 K, and the transient error during the abrupt change of current is about 10 K. The reason of this transient error as well as its influence is fully discussed and the evaluation method of the contact state is presented. From an engineering point of view, the proposed algorithm can effectively monitor the joint hotspot temperature and evaluate the contact state.AUTHOR CONTRIBUTIONSLiezheng Tang: Investigation; Methodology; Software; Validation; Writing – original draft. Jiangjun Ruan: Conceptualization. Rou Chen: Writing – review & editing. Guohua Zhou: Funding acquisition; Writing – review & editing.ACKNOWLEDGEMENTThe authors would like to thank Hubei Xinghe Electric Power New Material Co., Ltd., who assembled the fully insulated busbar prefabricated joint.CONFLICT OF INTERESTThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.FUNDING INFORMATIONFunding information is not applicable.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available on request from the corresponding author. 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"IET Generation, Transmission & Distribution" – Wiley

Published: Jan 1, 2023

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