The relationship between current load and temperature for quasi-steady state and transient conditions

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1 The relationship between current load and temperature for quasi-steady state and transient conditions Bernard R. Lyon Jr., Gary L. Orlove, and Donna L. Peters Infrared Training Center, 16 Esquire Road, North Billerica, MA ABSTRACT Infrared thermographers involved in predictive maintenance programs often use temperature measurement as a means of quantifying the severity of a problem. Temperature is certainly an important factor in evaluating equipment. However, if you follow guidelines that are based solely on absolute temperature measurement -or on a temperature rise (Delta T) you run the risk of incorrectly diagnosing your problems. The consequences of such actions can lead to a false sense of security, equipment failure, fire, and even the possibility ofpersonal injury. Understanding the additional factors involved in diagnosis is essential for obtaining productive results. One of these factors is the load or current flowing through conductors. The load can have a drastic effect on the temperature of a component. Changing loads can cause additional concerns because temperature changes lag behind load changes. The purpose of this paper is to illustrate the relationship between load and temperature of a faulty connection. The thermal response of a changing load is also investigated. Keywords: Keywords: infrared, thermography, predictive maintenance, temperature, current, load, electrical inspections, fused cut out, switch 1. INTRODUCTION An experienced thermographer can inspect numerous components quickly with an infrared imager. In addition he or she can make an informed recommendation to prioritize repair schedules based on the condition of the equipment rather than according to a timetable. For the most part, these recommendations are based on temperature criteria. In a perfect world, electrical equipment supply manufacturers would provide these threshold criteria. Currently, very little information is available from the manufacturers. Thermographers are therefore faced with the problem of deciding how to classify equipment as properly functioning, requiring more frequent monitoring, or critical. The problem lies in the fact that there is a wide variety of equipment in the field that was produced by many manufacturers and installed as long as 30 years ago. Thermally characterizing this equipment would be resource intensive. To add to the problem, variability in the conditions under which the equipment is surveyed will have dramatic effects on the results. Several independent organizations have begun to address this need by publishing severity criteria recommendations including the International Testing Association and the Electric Power Research Institute. The printed word carries a lot of weight, and many people are inclined to follow established guidelines, confident that they are "going by the book." Inevitably, an anomaly will be found and classified as normal; or at the most, requiring maintenance when it is convenient to do so. This anomaly then causes the equipment to fail even though all the guidelines were followed to the letter. So, what went wrong? There are many factors that can cause this situation. Some ofthese factors are: load, wind, solar heating, emissivity, variations in material properties (i.e. thermal conductivity), and the structure of the target. All too often in the tables, load is ignored, loosely defmed, or grouped in with other parameters, such as equipment type, temperature ratings, etc. The following five aspects relating to the importance of current load are examined in this paper: temperature as a severity criteria, using delta-t's vs. absolute temperatures, compensation equations, transient vs. steady state evaluation, and minimum load requirements for accurate thermograms. 2. TEMPERATURE AS A SEVERITY FACTOR How hot is too hot? New thermographers ask this question often. It is a legitimate inquiry. If a sincere effort is made to conduct a thermographic inspection in the most efficient manner, it is necessary to locate and repair problems that truly need corrective measures; and, to avoid misdiagnosis of problems, so that efforts are not expended in fixing components that are working properly. So, thermographers are constantly searching for a means of identifying real problems. It is inevitable that temperature is going to be one of the factors, if not the primary factor, involved in the identification of problems. The In Thermosense XXII, Ralph B. Dinwiddie, Dennis H. LeMieux, Editors, 62 Proceedings of SPIE Vol (2000) X!OO/$1 5.00

2 classical approach to the identification of faults has been the utilization of a criteria table with temperatures and characterizations, grade assignments, or suggested actions. Here is a typical guideline, from the International Testing Association Maintenance Testing Specifications, 1997 (NETA MTS-1997): 1 C 3 C 0 C 10 C Possible deciency; warrants investigation 4 C 15 C 11 C 20 C Indicates orobable deficiency; repair as time permits C 40 C Monitor continuously until corrective measures can be accomplished > 16 C > 40 C Major discrepancy; repair immediately Table 1. Thermographic Survey - Suggested Actions Based on Temperature Rise Temperature specifications vary depending on the exact type of equipment. Even in the same class of equipment (i.e. cables) there are various temperature ratings. Heating is generally related to the square of the current; therefore, the load current will have a major impact on temperature rise. In the absence of consensus standards for temperature rise, the values in this table will provide reasonable guidelines. We have examined several guidelines and standards used by various industries and utility companies and, with respect to current load, most oftheir procedures have statements similar to the following: ' "... Corrective measures required as scheduling permits or ASAP, depending on the class of load and the severity oftemperature rise in this range." "... The criteria are based on fully loaded circuits." "... Decision as to priorities and order of maintenance should be determined by the degree of temperature rise and criticality of the equipment or process involved." We are confident that in the future we can expect to see further refmement of tables, including more variables, such as load, wind, thermal insulating factors (elbows, splices) etc. 3. TEMPERATURE RISE A single temperature reading, of and by itself, is usually insufficient information with respect to diagnosing a potential problem. One must take into account the environmental temperature as well as any other heat loss or gain that can take place. In a transformer heat is generated by eddy currents, (in the core) and by resistance, (in the windings). A correct understanding of the equipment being inspected is essential if one is to make a proper thermographic diagnosis. And, as we shall see, understanding how current loads contribute to temperature is an integral factor in evaluating the severity of a fault. 4. HOW RESISTANCE GENERATES HEAT To understand why current load is important with respect to temperature measurements, it is necessary to understand how heat is generated in electrical equipment. There is a fairly straightforward relationship between current I, resistance R, and power P. The power generated in a circuit is the product ofthe current squared and the resistance. Or: P=12R. (1) All current carrying conductors used in electrical equipment have some resistance. Therefore, power will be generated in any conductor carrying a load. Properly operating electrical equipment will have a thermal signature that depends on the type of equipment, environmental temperatures, current load, and how long the equipment has been under load. In general, conductors that have been carrying a reasonable current load continuously, over an extended period of time, will look hotter than their surroundings. It is normal for conductors to heat up. Most guidelines, as indicated, suggest that thermographic surveys should be conducted at maximum load, or at some reasonable percentage of maximum. Most electrical faults are 63

3 essentially high resistance paths, caused by loose connections, corrosion, etc. If we assume that resistance remains fairly constant, consider what happens as the load increases.. Ifthe load doubles, the power increases by a factor of four.. Ifthe load triples, the power increases by a factor of nine.. Ifthe load quadruples, the power increases by a factor of sixteen. These values clearly indicate the importance of current load with respect to power dissipated through a high resistance path. To quantify and examine this more closely, a special test fixture was constructed. The resistance was kept constant, current load was varied, and temperature measurements were taken. 5. TEST FIXTURE In order to simulate a real electrical fault, a fused cutout switch was used. The fuse and copper arc-shorting rod were removed from the fuse tube. A heating element was installed in the cap end of the fuse holder; simulating a high resistance contact between the fuse cap and the top contact. Thermographers experienced in inspecting these devices have stated that they cannot tell the difference between the simulated fault and a real one. Figure 1. Test Setup The heating element was connected to a BK isolated variable AC power supply. The output was adjusted from 0 to 120 volts AC. A meter on the supply was used to measured voltage or current, selected by using switches. A current probe, connected to a digital multimeter, was used to measure the current. A type K thermocouple was used to monitor the temperature at the contacts. Thermographic temperature data were taken with a Fur ThennaCam PM 390 and saved on a PCMCIA card as 12 bit TIFF files. TherMonitor 95 Pro thermal image processing and Plot 95were used to analyze the thermal images. An area on the cap of the fuse clip was outlined and the maximum, mean and minimum temperatures were recorded for each image. 64

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5 6. THERMAL DATA FROM LOAD CHANGES The intent of this experiment was twofold: First, to observe the effects of different loads under conditions where the apparatus has reached steady state and second, to observe the transient effect of a load change. The load was changed and the apparatus was given ample time to reach a state ofthermal equilibrium. An increase or decrease in load of25% was found to stabilize well within one hour. For this experiment, we defmed a full load condition when the output voltage was set at 120 volts AC. As observed below, this resulted in a current flow of 0.23 amperes. And, as expected, we found a linear relationship between the voltage and current, simply because the resistance did not change appreciably with temperature. The voltage was raised in four steps of 25% - simulating 25% load changes. During this time, the thermal camera was recording an image every minute. After the first hour, the current was recorded and the voltage was raised another 25%. After stabilizing at 100% load, the voltage was set to zero volts, and the camera recorded data for two hours, an image saved every minute, to observe transient cooling. The switch was allowed to stabilize overnight, and the voltage was set to 120 volts. Again, the camera recorded thermal images every minute for two hours to observe transient heating. The environment was kept at a uniform temperature without any convectional cooling from wind, or heating by means of solar loading. According to Ohm's law, the power dissipated by the fault (resistor) is equivalent to the product ofthe current squared and the resistance. Even if the resistance remains constant and the fault reaches a reasonable steady state condition, the temperature cannot be assumed to rise proportionally with respect to the power. Heat transfer by means of radiation, conduction and convection will all increase as the temperature increases based on the thermal properties of the component and its environment. Table 1 illustrates the data collected for steady state conditions. Figures 4 and 5 compare the increase in power and increase in temperature rise with respect to increasing current load.. Reference temperature: 22.2 C. Voltage Current Power Load Hot Spot Temperature Temperature (V) (I) (W) Watts Percentage Temperature Rise Above Rise as % of : Volts AC Amperes. V x I Measured C Reference C Full Load Rise % % 26.5 C 4.3 5% % 44.8 C % % 74.2 C 52 62% % 106 C % Table 1. Load and Temperature Data 90 Cl) c 0 (I) E I- 0% 20% 40% 60% 80% 100%, Load (%) 0% 20% 40% 60% 80% Load (%) I 00% Figure 4. Power Dissipation as a Function of Load Figure 5. Temperature Rise as a Function of Load 66

6 7. LOAD - TEMPERATURE CORRECTION FACTORS Correction factors have been offered as solutions for dealing with load problems. The data clearly shows that temperature rises will vary considerably with different loads. If the load doubles, from 0.11 amperes to 0.23 amperes, as indicated above, the temperature rise increases almost by a factor of four (3.7). If one considers this, as well as the fact that the power produced by a resistive element is proportional to the current squared, it is not difficult to ascertain how correction factors have been developed using current ratios squared in their computations. Here is such a correction factor: Temperature rise at full load (C ) =(full load current I measured urr2 x measured temperature rise in C. (2) Variations of the above equation substitute the exponent for different values ranging from 1.6 to 2.0, depending on the material or equipment involved. If one applies this correction factor to the data taken with the fused cutout switch, a temperature rise of 22.6 C, with a current load of 0.11 amperes, should result in a rise of 98.8 C, at full load: (O.23amperes/O.llamperes) 2x 22.6 C 98.8 C. (3) This is 15 C0 higher than the measured temperature. If the exponent 1.6 is applied, the answer is 10.3 C lower than the measured value or 73.5 C. If 1.8 is used as an exponent, the answer is much closer, 85.3C. Ifyou apply this same exponent to the data for a 52 C rise, you get the following results: (O.23amperes/O.l7amperes) 1.8 x 52 C = 89.5 C. (6) This error is only 5.7 C high. However, if 1.6 is used as an exponent, the results are much closer, 84.3 C. The error here is only 0.5 C high. The exponents were calculated for currents of amperes and 0.23 amperes. If 1.78 is used as an exponent for a currentof amperes the full load temperature rise is calculated to be 84.0 C. This is an error of only 0.2 C. If 1.58 is used as an exponent for a current ofo. 17 amperes, the calculated full load temperature rise is 83.8 C. The error here is only 0.03 C. This correction factor was applied to the following data taken on a 20 ampere, 1 10-volt breaker connection. The measured temperature rise at 1 00% load was 50 C. If 2 was used as the exponent, 63.9 C was calculated as the rise. If 1.6 was used, the calculated rise was 53.7 C. From the information above, one can see that changing the exponents can result in a correction factor that agrees with the experimental data. However, one would expect the exponents to remain constant with the same equipment, in the same environment, where essentially, the only variable introduced was the load. From these observations, we would suggest a modification of the correction factor to account for the errors observed. This would set limits, which would give us an error budget. The modified correction factor is: Mm. temp. rise at full load (C ) =(full load current I measured current)'5 x measured temp rise in C. (8) Max. temp. rise at full load (C ) =(full load current Imeasured current)'8 x measured temp rise in C. (9) If we apply this modified correction factor for a current load of amperes we get a temperature rise from 68.3 C to85.3 Co at full load. The measured rise of 83.8 C falls into this 17 C window. For a current load of 0.17 amperes, we get a temperature rise from 81.8 C to 89.6 C. Again, the measured temperature rise falls nicely into the error budget window, which now is 7.8 C. Correction factors should be used with a skeptical eye. There are just too many factors involved in the generation and dissipation of heat in electrical equipment to quantify temperature and current in a reasonably defmitive manner. Here are some variables to consider: Emissivity variations - This can result in differential radiative cooling. Thermal conductivity - Agood thermal conductor will act as a heat sink and conduct heat away from the source. 67

7 . Insulation A component that is well insulated electrically, such as an elbow connector, is also well insulated thermally. It is very difficult to ascertain the real internal temperature rise without extrapolating about load increases.. Electrical resistance - Faulty connections will change resistance.. Loadvariations - Changes in load do not result in immediate changes in temperature. Experience has shown that it takes forty-five minutes or more for a component to become thermally stable after a load change. This concept will be discussed in more detail.. Wind The movement of air over a component can drastically affect its temperature. We do not want to discourage thermographers from using correction factors. If a circuit is observed operating at a reduced load, some kind of prediction or extrapolation, inevitably, will be utilized to make a judgment as to what will happen when the load increases. Through experience in the field, and experimentation in the laboratories and classrooms, thermographers are constantly refining their methods. Like anything else, there is an error budget to consider. Do not become over confident, simply because you have an equation. One should recognize that these correction factors have a limited value. If used with caution, they can assist in fmding real problems. If accepted and used as defmitive scientific laws, they can lead to errors. These errors, as shown above, may be unacceptable with respect to severity criteria used for inspections. 8. LOAD CHANGE WITH TIME ITIME CONSTANTS Many predictive maintenance thermographic reports have a place to enter the current load, expressed as a percentage, or as an actual reading in amperes. This entry by itself has little relevance, unless the component being measured has reached steady state operation. For the fused cutout switch at 50% load the temperature rise was 22.6 C ; at 75% load, it increased to 52 C. This 29.4 C increase does not take place instantaneously when the load is switched from 50% to 75%. One good recommendation is to wait at least 45 minutes after a load change before taking any temperature readings. The reason is fairly straightforward: it takes time for components to heat up. Different components will heat up at different rates due to differing thermal properties and environmental conditions. In order to quantify the temperature change, the concept of a time constant was used. A time constant is the amount oftime it takes for a 63% change in a certain value, such as temperature. For our load change, a thermal time constant would be the amount of time it takes the temperature difference to change by 63%. From the plot below, we can see that the time constant for a change in load from 0.11 amperes to 0.17 amperes is about 14 minutes. Note that the time constant is the same for the maximum, mean, or minimum temperatures Multi - Image Plot 154. /Max. [161.6F] u E 0) F /Mean [149.7F] /Min. [125.0F] :00 08:20 16:40 25:00 33:20 41:40 50:00 58:20 Duration (Curs At-OO:14:16) Figure 6. Temperature Plots for 50% to 75% Load Change. 68

8 Time constants were determined for all of the load changes using the mean temperature data. As the table below indicates, the time constants agree quite well with each other for load changes above 50%. The time constant of 18 minutes for the load change from 0% to 25% may seem unusual. However, the difference between the temperature rise at 18 minutes and 14 minutes is only 1.1 C! Consider what this means when conducting a thermographic inspection of this fused cutout. If the load were changed 14 minutes prior to inspection, the temperature rise would be only 63% ofthe fmal value. A rise of 50 C at steady state would read only C. One can see the importance oftime with respect to changes in load. After 45 minutes, the temperature rise is within 2 C of its fmal value. This agrees nicely with previous results. Thermal Time Constants Load Change I Time Constant O%-25% 18 minutes 25%-50% 16 minutes 50%-75% 14 minutes 75%-100% 14 minutes O%-100% 14 minutes 100%-O% 14 minutes Table 3. Time Constants 9. CONCLUSIONS Current load is an important factor to consider when conducting thermographic inspections of electrical equipment. For a resistive fault, the power generated is proportional to the current squared and the resistance (P12R). It would seem that there is a fairly straightforward relationship between the load and the temperature rise. However, there are just too many variables to consider to accurately predict the temperature rise expected at increased loads; even if there are no emissivity errors, and the component has reached steady state operation. Experimentation has shown that correction factors used to calculate temperature rises might not be accurate enough to comply with severity guidelines. The correction factors can provide a reasonable error budget, which can assist thermographers in analyzing potential problems. The element of time must be considered when trying to correlate current load and temperature rises. The thermal time constant of components is a means of quantifying the time delay between load change and thermal stabilization. For a typical fused cutout switch, it takes about forty-five minutes to reach steady state (adequate for a reasonably accurate temperature measurement) after a load change. Thermographers need to understand how current load, time, and temperature relate to one another. This knowledge will improve efficiency when conducting electrical inspections. 10. ACKNOWLEDGMENTS The authors would like to thank Robert P. Madding, and Ronald Lucier of the Infrared Training Center for their assistance with the materials involved in setting up the experiments; and for their review and comments on this manuscript. A debt of gratitude is extended to Robert Loggins and James Sprecher of Pacific Gas & Electric for their contributions of components, images, and advice concerning electrical systems. Appreciation and applause to Jon L. Giesecke, substation authority and magician extraordinaire, for his many contributions as a knowledgeable and entertaining guest speaker at our training center. And, a note of thanks to the many students who have attended training courses and shared their knowledge and valuable experience with us. 11. REFERENCES 1. Baird, G.S., The Effect of Circuit Loading on Electrical Problem Temperature, Thermosense IX, R.P. Madding, Editor, Proc. SPIE Vol. 780 pp Orlando, FL, May Hurley, T.L., Infrared Qualitative and Quantitative Inspectionsfor Electric Utilities, Thermosense XII, S.A. Semanovitch Editor, Proc. SPIE Vol pp Orlando, FL, April Kaplan, H., Practical Applications of Infrared Thermal Sensing and Imaging Equipment, SPIE Optical Engineering Press, Vol. TT13,

9 4. Lucier, RD., Kaplan, H.L., Infrared Thermography Guide, NP-6973 Research Project , Research Reports Center, Palo Alto CA, Maldague, X.P.V., InfraredMethodology and Technology, Gordon and Breach, NETA Technical Committee, Maintenance Testing Speccationsfor Electric Power Distribution Equipment and Systems, InterNational Electrical Testing Association,, Morrison, CO, Newport, R., The Question ofload in Electricallnspections, Spectrum, Vol. 4, Issue 1, The Academy of Infrared Thermography, March Perch-Nielson, T, Sorensen, J.C., Guidelines to Thermographic Inspection of Electrical Installations, Thermosense XVI, Snell, JR., Editor, Proc. SPIE Vol pp Orlando, FL, March Snell, J.R., Problems Inherent to Quantitative Thermographic Electrical Inspections, Thermosense XII, S.A. Semanovitch Editor, Proc. SPIE Vol pp Orlando, FL, April Stout, D., Environmental Effects On Indicated Delta T On Outside Electrical Connections, Reliability Magazine, June