Introduction to Transformer Loss of Life – based on models from IEC and IEEE loading guides
This work introduces the concepts of Hot-Spot Temperature (HST) and transformer ageing due to temperature and how the HST affects transformer life expectancy. The relative ageing rate of two models are compared for various scenarios and the Transformer Loss of Life (LoL) is estimated for two HST profiles.
LoL is the term used to express how much life a transformer has lost since being commissioned. One factor which accelerates ageing of the transformer and increases its LoL is the HST. The IEEE  and the IEC  loading guides provide models for estimating the LoL utilising the HST.
Determination of the HST
Figure 1 shows a simplified model of the temperature distribution within an oil-immersed power transformer, with the following assumptions :
the oil temperature inside the windings increases linearly from bottom to top regardless of the cooling mode;
the temperature rise on the conductor at any position up the winding increases linearly and parallel to the oil temperature rise, with a constant temperature difference of ‘g’; and
the HST rise is higher than that of the conductor at the top of the winding to allow for increases in stray losses and is accounted for by multiplying ‘g’ by the hot-spot factor ‘H’; which may vary from 1.1 to 1.5, (1.0 to 2.1 ) depending on transformer size, short-circuit impedance and winding design.
The HST is the sum of the ambient temperature θA, top oil temperature rise ∆θTOP , and the hot-spot to top oil temperature rise ∆θH.
Ageing of the transformer paper insulation is dependent on temperature and contents of moisture, oxygen, and acid. Models presented here focus only on temperature and in particular the HST since deterioration is normally highest at the top of the winding.
The IEC standard refers to the relative ageing rate, V whereas the IEEE standard refers to the ageing acceleration factor, FAA . Both are utilised in the same way to calculate lifetime consumption. In this work we adopt V .
Model A: Non-thermally upgraded paper. The relative (thermal) ageing rate, V , is referenced to unity for a HST of 98°C [θHref], at an ambient of 20°C where the HST rise over ambient is 78°C and operating in the range of 80°C to 140°C.
V doubles for every 6°C rise in HST.
Model B: Thermally upgraded paper. V is referenced to unity for a HST of 110°C [θHref], at an ambient of 30°C where the HST rise over ambient is 80°C. 15000 is an empirical constant provided in Annex I . Equation (3) may also be used to model non-thermally upgraded insulation, with V referenced to unity in the case where the average winding temperature rise is 55°C and at a HST of 95°C, with a HST rise over ambient of 65°C.
Equations (2) and (3) are based on the Montsinger  and Dakin  life expectancy models, a simplification of the Arrhenius relation equation given in A.1 .
Figure 2 (left) compares the performance of hot-spot on paper types and shows that the use of thermally upgraded paper can decrease ageing by a factor of as little as 3.4 and at most by 7.4.
Figure 2 (right) compares the models for non-thermally upgraded paper insulation. The results for both models are plotted for the hot-spot range 80°C to 140°C and for the restricted (rest.) range of 80°C to 124°C so as to better highlight the differences. The two models are monotonically increasing, initially with Model B yielding higher values of V, and intersect at a HST of approximately 123°C, after which they commence to diverge and Model A yields higher values of V. The value of V below͢͢ 80°C is negligible for both curves.
Figure 2: Transformer ageing models. Left: Comparing insulation paper types. Right: Comparing models for non-thermally upgraded paper.
Lifetime consumption (loss of life)
Under constant conditions the relative lifetime consumption L can be calculated by the product of V and time elapsed, t2-t1. In practice the load and transformer temperatures change over time, and in which case L is given by (4) .
Worked Example: Lifetime consumption estimation for non-thermally upgraded paper.
Consider the HST profile of a transformer over a 24-hour period as provided by the first three columns in Table 1. Assume that the temperature transition times are negligible. Inserting the HST into equations (2) and (3) yields V for those periods (given in columns 4 and 5). The lifetime consumption for each time period is calculated by multiplying V with the time interval and given in columns 6 and 7.
Summing the lifetime consumptions over the 24-hour period shows the transformer actually aged 61.159 hours (Model A) [0.034%] or 74.636 hours [0.041%] (Model B), of its total life span. The percentages are based on a transformer lifespan of 180,000 hours or 20.55 years and assumes the transformer running constantly at the rated HST. This means that if a transformer was subjected to the same daily load profile as in Table 1, its lifespan would be reduced to 70636 hours [8.06 years] (Model A) or 57881 hours [6.61 years] (Model B).
Figure 3 (left) represents the values in Table 1. Figure 3 (right) represents the values in Table 1 but where the HST for the last six hours is changed to 128°C. The profiles are purposely changed to highlight a scenario where Model A can yield a higher LoL if the HST is beyond 123°C.
Figure 3: Transformer ageing for non-thermally upgraded paper and for two hot-spot profiles. Left: HST=110°C for last six hours. Right: HST=128°C for last six hours.
CHK Power Quality Pty Ltd offers the Miro-F TxM Transformer Monitor and Logger (TxM), an instrument purposely suited for comprehensive monitoring of transformer health and can provide LoL calculations based on the IEC and IEEE Standards.
The TxM includes two temperature sensors which can be software configured to measure the top oil and ambient temperatures. Where the transformer is equipped with multiple winding temperature sensors the TxM, together with the Miro Auxiliary I/O module (Miro Aux), can utilise these inputs in its LoL calculations.
Setting up and configuring the TxM requires the user to populate a template with relevant transformer ratings and other known parameters specific to the transformer. Alternatively, the user can use default values, provided in the TxM, for parameters that are not readily available on the transformer’s name plate.
The TxM together with the Miro Aux can expand the monitoring to include: geomagnetic DC current; dissolved gases such as oxygen; moisture; on load tap changer (OLTC) operation; bushing leakage current; and fan operation. All these parameters can, not only be displayed alongside critical power quality information, but also correlated for in depth analysis.
Please contact us for a free and no obligation demonstration or trial.
 “IEEE Guide for loading mineral-oil-immersed transformers and step-voltage regulators”, IEEE Standard C57.91, 2011.
 “IEC Power transformers, Part 7: Loading guide for oil-immersed power transformers”, IEC 60076-7, 2018.
 “Loading guide for oil-immersed power transformers”, IEC 60354 second edition, 1991-09.
 M. Srinivasan, A. Krishnan, “Prediction of Transformer Insulation Life with an Effect of Environmental Variables”, International Journal of Computer Applications, Vol. 55-No.5, pp 43-48, October 2012.
 V. M. Montsinger, “Loading Transformers by Temperature”, Winter Convention of the A.I.E.E, New York, USA, Jan. 27-31, 1930, p. 783.
 T. W. Dakin: “Electrical Insulation Deterioration Treated as a Chemical Rate Phenomenon”, AIEE Trans., Vol. 67, pp. 113-122, 1948.
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