You measure water in the oil. You care about water in the paper. Those are not the same number, and the gap between them is where most moisture mistakes happen.
Karl Fischer gives you a clean figure for the oil — a few parts per million. But the oil holds almost none of the water in a transformer. The overwhelming share, often more than 99% of it, lives in the paper and pressboard. And it’s the paper that decides how fast the insulation ages and how close you are to trouble under load. The oil number is just the part you can reach.
Equilibrium moisture curves are the bridge between the two. Feed in an oil moisture reading and a temperature, and the curve hands back an estimate of how wet the paper is. This is the tool that turns a routine oil sample into a statement about the part you can’t sample. Used carefully, it’s invaluable. Used carelessly, it produces confident numbers that are flat wrong.
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The one idea that makes them work
Here’s the principle the whole thing stands on: at a fixed temperature, once the system has settled, water shares itself between the oil and the paper so that the relative saturation is the same in both.
Relative saturation — sometimes called water activity — is how full of water something is compared to how much it could hold at that temperature. Express it as a percent. The insight, worked out by Fabre-Pichon in the 1960s and built into usable charts by Oommen in the 1980s, is that at equilibrium the oil and the paper sit at the same relative saturation, even though their absolute water contents are wildly different.
That’s why it works. The paper can be carrying 30,000 times more water by weight than the oil, but if you know the oil is, say, 20% saturated, then the paper is also about 20% saturated — and from a paper sorption curve you can read off what 20% saturation means in percent moisture by dry weight.
So the recipe behind every equilibrium curve is: take the oil’s water-holding behaviour, take the paper’s water-holding behaviour, line them up at equal relative saturation, and you get a chart linking oil ppm to paper percent.
Reading a curve
In practice the chart usually plots oil water content (ppm) up one side against temperature along the bottom, with a family of curves drawn across it — one curve for each level of paper moisture.
To use it:
- Take an oil sample and measure water by Karl Fischer. Get your ppm.
- Record the oil temperature at the moment you sample. Not optional — it’s half the input.
- Find your temperature on the bottom axis, go up to your ppm, and see which paper-moisture curve you land on.
That curve is your estimate of paper dryness, in percent by dry weight. For orientation: new, well-dried insulation sits around 0.5 to 1%. Paper above roughly 2 to 3% is treated as wet and a candidate for drying. The paper saturates somewhere around 6 to 8%, which is as wet as cellulose gets before water starts coming out as a free phase.
Why temperature is the whole story
If you take one thing from this, take this: a moisture reading without its temperature is close to meaningless.
The reason is in how the two materials respond to heat. Warm the transformer up and the oil’s capacity for water climbs steeply, so water is pulled out of the paper and into the oil. The oil ppm shoots up. But the paper barely changes — it’s a huge reservoir, and shedding a tiny fraction of its water moves the oil number a lot while moving the paper number almost not at all.
Put concretely: the same transformer, same actual paper moisture, can read low ppm cold and high ppm hot. If you compare a winter sample to a summer sample and ignore temperature, you’ll “see” the insulation getting wetter or drier when nothing has changed. The curve exists precisely to undo that illusion — but only if you feed it the right temperature.
There’s a second-order version of the same problem inside the tank. Top oil runs hotter than bottom oil, so the relative saturation differs between the top and bottom of the same transformer at the same moment. The sample location and its temperature both matter.
The curves are not one thing
There isn’t a single official equilibrium curve. There’s a family of them, drawn by different researchers from different data, and they don’t fully agree.
The lineage runs roughly like this. Fabre-Pichon’s French work in the 1960s laid the groundwork, though it was published through CIGRE and was hard to get hold of — so others redrew it and the original often got lost. The Piper chart was a widely used early version, later criticised for its accuracy. Oommen’s charts in the 1980s became the reference most people cite, built by combining paper absorption data with oil humidity behaviour. Later sets from Griffin, Fessler, Nielsen, and an MIT group around 1999 extended and refined the picture, especially at the low end.
The practical consequence: for the same oil ppm and temperature, two different curve sets can give you paper-moisture estimates that differ by a meaningful margin. The disagreement is worst where you often care most — at low moisture and low temperature, where the oil ppm is tiny and small errors blow up. Oommen himself flagged the low-moisture region of his own charts as the least reliable.
What to do about it: pick one curve set and stay on it. The absolute paper number from any single chart carries real uncertainty, but the trend you build by always using the same method is solid. Consistency beats theoretical precision here.
The equilibrium catch
The word “equilibrium” is doing a lot of work in the name, and it’s the assumption that breaks most often.
The curves describe a settled system — oil and paper that have sat at a steady temperature long enough to stop exchanging water. A real transformer in service is rarely that. Load cycles, ambient swings, and cooling changes keep the temperature moving, which keeps water sloshing between paper and oil and never quite arriving anywhere. Under those conditions, pulling an accurate paper-moisture figure from an oil sample through a published curve is, honestly, almost impossible.
How long is “settled”? The figure cited in the literature is steady temperature for more than about three weeks before the paper and oil have genuinely equilibrated. So the reading is trustworthy when the transformer has held a stable, fairly steady temperature for roughly that long — a long stretch of constant load, or a settled outage. It’s least trustworthy right after a load swing, a sharp ambient change, or anytime the oil temperature is clearly on the move. If you must sample a unit that’s been cycling, treat the paper estimate as a rough indication, not a measurement, and weight your judgement toward the trend rather than the single value.
The more robust way: work in relative saturation
Because the whole system is driven by relative water content rather than absolute, modern practice leans on relative saturation directly instead of converting everything to ppm and back.
A capacitive moisture probe installed in the oil reads relative saturation continuously and on the spot. That sidesteps two weaknesses of the absolute-ppm route at once. First, it removes a conversion step and its error. Second, it’s far less sensitive to oil aging — aged, acidic oil holds more water than fresh oil, which quietly distorts the absolute curves, but the relative-saturation relationship between oil and paper holds up much better.
The workflow is clean: measure the oil’s relative saturation, take the paper’s equilibrium relative humidity as equal to it, then use a paper sorption curve to get percent moisture. Same physics as the classic charts, fewer ways to go wrong. If you have an actual pressboard sample, you can also measure its water directly by Karl Fischer using the oven method at around 130–140°C per IEC 60814 — but in a sealed, in-service unit you rarely do, which is the entire reason these curves exist.
Why any of this matters
Two reasons it’s worth getting right.
Aging. Water is a catalyst for the breakdown of cellulose, so wetter paper ages faster — and not by a little. The numbers in the literature are stark: each extra 0.5% of moisture in the paper roughly halves its remaining strength (its degree of polymerization), and paper at around 4% moisture has been found to age on the order of 20 times faster than the same paper at 0.5%. The paper moisture you estimate from these curves feeds directly into how much life the insulation has left — far more usefully than the oil ppm alone ever could.
Bubbling under load. This is the sharp-edged one. Push a transformer hard and the hotspot temperature climbs. If the paper is wet enough, that heat can drive water out as vapour — bubbles — right in the high-stress region. Bubbles are gas, gas is a weak dielectric, and bubbles in the wrong place can trigger a failure. How much overload margin a transformer really has before it bubbles depends on how wet the paper is. The oil number won’t tell you that. The paper estimate, read off an equilibrium curve, will.
That’s the value of these curves in one line: they take the number you can measure and turn it into the number that actually governs how the transformer ages and how hard you can run it.
FAQ
What are equilibrium moisture curves?
They’re charts that relate the water content of transformer oil to the water content of the paper insulation, at a given temperature. Because you can sample oil but not paper in a sealed transformer, the curves let you estimate paper moisture from an oil moisture reading.
What principle do they rely on?
At a fixed temperature and once the system has reached equilibrium, the relative saturation (water activity) is the same in the oil and the paper. Equal relative saturation, very different absolute water content — that’s the link the curves capture.
Why do I need the oil temperature to use them?
Because the oil’s water capacity rises steeply with temperature. The same paper moisture produces a low oil ppm when cold and a high one when hot. Without the temperature, the ppm can’t be placed on a curve, and comparisons between samples become misleading.
Are the Oommen curves the only ones?
No. There are several sets — Fabre-Pichon, Piper, Oommen, Griffin, Fessler, Nielsen, and MIT curves among them — and they disagree, especially at low moisture and low temperature. Pick one set and use it consistently for trending rather than mixing them.
How accurate are the paper-moisture estimates?
Treat the absolute number with caution. The curves assume equilibrium, which service transformers rarely reach, and different curve sets disagree. The trend over time, measured the same way each time, is far more reliable than any single absolute value.
What paper moisture counts as wet?
As a rough guide, around 0.5–1% is dry and healthy, above roughly 2–3% is treated as wet and a candidate for drying, and cellulose saturates near 6–8%.