55% Load, 18 K Phase Difference: Pass or Shut Down?
A 400 A molded-case circuit breaker in a main switchboard carries 220 A, 55% of rating. Ambient inside the board is 25 °C. With ε set to 0.95 on the terminals, phase A reads 68 °C; phases B and C read 50 °C. The client's maintenance standard states: investigate if any terminal exceeds 70 °C or is more than 15 °C above similar phases. The thermographer notes phase A is below 70 °C but 18 °C above the others, and recommends no action until the next annual shutdown. Production is at maximum, so the board cannot be loaded higher for a re-scan. The breaker feeds a variable-frequency drive load with noticeable 5th-harmonic current.
1. Evaluate the recommendation to wait until the annual shutdown. Support your answer with an I² scaling estimate.
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The recommendation is not defensible. Phase A is 43 K above ambient and 18 K above the sister phases at only 55% load. The client's own standard already triggers investigation at more than 15 K above similar phases, so 'no action' contradicts the acceptance criteria.
For the same connection resistance, resistive heating is approximately proportional to I². If the temperature rise were to scale with I² and the connection resistance stayed constant:
Rise at 100% ≈ 43 K / (0.55²) = 43 / 0.3025 ≈ 142 K Estimated terminal temperature ≈ 25 + 142 = 167 °C
Convection and radiation increase with temperature and will reduce this upper-bound estimate, but the result still points to a severe hot spot at rated load. The 18 K phase difference at 55% load is a strong indicator of a high-resistance connection: loose lug, corrosion, damaged contact or wrong torque. Recommend immediate inspection and re-torque, not an annual wait.
2. What follow-up measurements and records would you require, and how do the 5th-harmonic currents affect the interpretation?
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Record per-phase true-RMS current, ambient temperature, emissivity setting, reflected temperature, distance, lens, camera model and time. Compare all three phases at the same load and angle. Use a micro-ohmmeter or contact-resistance test and a torque check on the suspect connection. Re-scan after repair at the same load.
The 5th harmonic increases RMS current and adds eddy and skin-effect losses, so the heating can be higher than the fundamental current alone suggests. A meter that reads only fundamental current will understate the heating. Use a true-RMS meter and note the harmonic distortion. Also check whether the breaker's thermal element or trip unit is affected by the distortion; the thermal image shows the result, not the cause.
3. The client says '68 °C is below our 70 °C limit, so it passes.' How do you respond?
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Explain that the 70 °C absolute limit is not a stand-alone pass criterion at 55% load. Acceptance criteria for electrical connections are load-dependent: a joint that is only 43 K above ambient at 55% load will be much hotter at rated load. The relative criterion - 18 K above similar phases - has already been exceeded, and that is the more sensitive indicator at partial load. The correct response is to treat phase A as a high-resistance connection requiring prompt inspection, not to use the absolute limit as a reason to defer. If the client insists on a load-corrected judgement, state the limitation clearly and recommend re-scanning at the highest available load after repair.