In short: The Duval Triangle converts three hydrocarbon gases into a single point inside a triangle and names the fault type occupying the zone where that point lands. It is a closed system, so it never abstains. That is its strength and its main failure mode. Check the absolute concentrations before you compute the coordinates, and treat the resulting zone as a hypothesis for a qualified engineer to test.
What is the Duval Triangle and what does it actually tell you?
The Duval Triangle is a graphical fault identification method for dissolved gas analysis. Take three hydrocarbon gases from an oil sample, express each as a percentage of their sum, and plot the result inside an equilateral triangle whose interior is divided into named fault zones. The zone containing the point gives the suggested fault type. That is the whole mechanism.
What makes it worth using is not the geometry, which is trivial, but where the zone boundaries came from. Michel Duval drew them by plotting transformers whose faults had been confirmed by physical inspection after the unit was opened, then tracing the lines that separated the clusters. The zones summarise what inspected machines looked like in gas space. They are not derived from a chemical model of oil decomposition, and nobody has claimed they were.
This matters when you decide how much weight to give the output. A zone assignment tells you which population of previously inspected faults your sample most resembles. It does not tell you that your transformer has that fault. IEEE C57.104-2019, clause 6.2.3, draws the line in one sentence: “The fact that a possible fault type is identified is not in itself a confirmation of the presence of a fault.” Everything sensible about using the triangle follows from taking that sentence literally.
Plot successive samples from the same unit and fault evolution becomes a track across the triangle. A stationary point with rising absolute concentrations means the same fault getting worse. Migration between zones usually means the fault changed character, or that a second one started contributing gas.
How to read it
Triangle 1 uses methane, ethylene and acetylene. Sum the three concentrations in ppm, divide each by the total, and you have three percentages adding to 100. Those are barycentric coordinates: they define exactly one point, and every point corresponds to exactly one such triple. Each side carries the scale for one gas, and the graduations run in a rotational direction that people get wrong constantly when plotting by hand.
The normalisation deserves suspicion. Dividing by the sum throws away the magnitude entirely: a sample with 2 ppm methane, 1 ppm ethylene and 0.3 ppm acetylene produces the same point as one with 2000, 1000 and 300. The triangle cannot tell them apart and will name the same fault for both. One of those transformers has a problem. The other probably has a laboratory rounding artefact.
So the reading order is fixed, and reversing it is the most common misuse of the method. Absolute concentrations first, against a reference appropriate to that unit’s age and its oxygen to nitrogen ratio. Rate of change second. Coordinates last, and only if the first two steps established that something is worth diagnosing. What counts as an abnormal level, and why fixed universal ppm limits were abandoned by the 2019 IEEE revision, is covered in our guide to normal dissolved gas levels in transformers.
Why three gases and not seven
Routine DGA reports seven or nine gases. Triangle 1 uses three, and the choice is thermodynamic rather than statistical.
Methane, ethylene and acetylene form at increasing energy. C57.104-2019 states the ordering directly: methane for low energy and low temperature faults, ethylene for high temperature faults, acetylene for very high temperature and arcing faults. Acetylene requires conditions ordinary overheating does not supply, which is why its presence dominates the geometry. Three gases ordered along an energy axis give a two-dimensional space in which severity has a direction, and the zone layout exploits that.
Hydrogen and ethane are excluded, and their exclusion costs real information. Hydrogen is the most sensitive indicator of partial discharge and of stray gassing. Ethane distinguishes low temperature overheating from ordinary ageing. Carbon oxides say whether cellulose is involved, which usually matters more for the repair decision than the fault class does. None of that enters Triangle 1. Duval’s own answer was to build the additional triangles and the pentagons, which use the full hydrocarbon set.
The seven zones and what each means for the asset
Triangle 1 partitions its interior into seven named regions covering the six basic fault types of Annex C of C57.104-2019 plus one mixed zone. We are not going to publish the boundary coordinates. They belong to IEEE, IEC and CIGRE, and reproducing the grid as a dataset is precisely what a licensed subscriber may not do. Where each zone sits and what it implies is the useful part anyway.
PD, partial discharge of the corona type, occupies a narrow strip at the methane vertex. A PD assignment means methane almost completely dominates the three gas mixture, with very little ethylene and essentially no acetylene. Physically this is cold plasma discharge, and C57.104-2019 associates it with possible X-wax deposition on paper. It is rarely urgent by itself and frequently a sign that hydrogen deserves a closer look than the triangle can give it.
T1, T2 and T3 are thermal faults ordered by temperature, occupying a band along the low acetylene edge. The standard defines T1 as below 300 degrees Celsius with paper turned brownish, T2 between 300 and 700 with paper carbonised, and T3 above 700 with strong evidence of oil carbonisation, metal discoloration around 800 degrees and metal fusion above 1000. Moving from T1 to T3, the ethylene fraction rises and the methane fraction falls. Once you see that ordering principle the layout stops looking arbitrary.
D1 and D2 are discharge faults and they live where acetylene is significant. D1 is low energy discharge or sparking, evidenced by pinholes and carbonised perforations in paper. D2 is high energy discharge with power follow-through, and its physical signature is severe: extensive carbonisation, metal fusion at the discharge extremities, sometimes a trip. A D2 with high absolute acetylene is one of the few DGA results that justifies pulling a unit before the next scheduled sample.
DT is the seventh zone and it is the honest one. It sits between the thermal band and the discharge region and means the gas pattern is consistent with a mixture of electrical and thermal faults, or with a fault the method cannot resolve into one class. CIGRE Technical Brochure 771 shows that a real mixture of a T3 and a D1 can land anywhere along a path between the two pure zones depending on the relative contribution of each, and that some of those mixtures land squarely inside D2. A DT assignment is the method reporting ambiguity, and it should be read as an instruction to bring in the pentagons, the carbon oxides and the operating history.
The trap: it always gives you an answer
Three normalised percentages must sum to one, so a point defined by them must fall somewhere in the simplex. The zones tile the simplex completely, no gaps and no overlaps. Any three non-negative numbers you feed the triangle will therefore produce a zone assignment. There is no arithmetic path to “not classified”.
C57.104-2019 states the property as an advantage and immediately qualifies it. The triangle “always proposes a fault identification (it is a ‘closed’ system as compared to 2-gas ratios methods)”, and then: “because it always gives a diagnostic, it should be used only to identify a fault when other information indicates that a fault is likely to exist.” Read those two clauses together. The closure that makes the method attractive is what makes it dangerous without a gate in front of it.
This is where a lot of DGA software goes wrong. Compute coordinates, look up zone, print fault name, colour the badge. That pipeline produces output on every sample and looks authoritative on a dashboard. It will also label a healthy transformer with an arcing fault because a laboratory reported 0.4 ppm of acetylene at the edge of its detection limit and the normalisation amplified that noise into a dominant coordinate.
When the coordinates are noise
Below a few ppm, gas ratios are measurement error dressed up as chemistry. That is arithmetic, not nuance: if two gases are each measured with plus or minus thirty percent uncertainty, their ratio carries roughly sixty, and a point computed from three such quantities can sit in a different zone depending on which end of the error bar you take.
The standards are explicit about the gate. TB 771 requires that at least one gas value used meet the IEC accuracy requirement, and adds that where a laboratory cannot vouch for its ppm values, fault identification should only be attempted above typical levels. C57.104-2019 advises against fault identification when all gas levels sit below its reference table, notes that relative measurement uncertainty becomes large below roughly five times the detection limit, and singles out acetylene as the only elevated gas as a case for particular caution.
An engine that respects those clauses has to be able to return nothing. Returning “not determined” when the gases sit under the analytical floor is correct behaviour, not a coverage gap. It costs something real: a system that abstains scores worse on any accuracy benchmark, because an honest abstention counts the same as a wrong diagnosis. Taking that hit is better than reporting a fault name computed from noise. Why raw accuracy is a poor metric for diagnostic engines is covered in our overview of dissolved gas analysis of power transformers.
Triangle 4 and Triangle 5, and when they apply
Triangle 1 resolves six fault classes. Duval defined two further triangles to split those classes into sub-types, using different gas triples and different zone layouts.
Triangle 4 uses hydrogen, methane and ethane, and targets the low temperature end. It separates stray gassing of the oil from overheating, from partial discharge, and from catalytic reactions between water and galvanised steel in sampling valves. Stray gassing is worth calling out because it is not a fault at all: it is chemical instability in some modern refined oils, producing gas below 200 degrees. Mistaking it for an incipient thermal fault has sent healthy transformers for unnecessary internal inspection.
Triangle 5 uses methane, ethylene and ethane and works at the hot end. It distinguishes high temperature thermal faults in oil alone from those involving paper, which is the distinction that changes what you do next. Oil-only overheating is usually a circulating current or a bad joint. Paper carbonisation is loss of solid insulation, and solid insulation does not recover. C57.104-2019 attaches a caveat to those zones that is easy to skip: they indicate a possibility of paper carbonisation, “not a 100% certainty”, and further investigation with carbon oxides and furans is called for.
Why gating matters
Triangles 4 and 5 are refinements, not independent classifiers, and the standard is unusually direct about their preconditions. C57.104-2019 lists three rules for their use, and they are worth enforcing as a hard gate rather than treating as advice:
The reason to enforce this in code is the same closure property discussed above. Triangles 4 and 5 are closed systems too. Run Triangle 5 on an arcing sample and it will not complain, it will return a thermal sub-type, because a thermal sub-type is the only thing it can return. Its zones were fitted on inspected thermal cases, and outside that population the boundaries carry no evidence at all. The safe order is to evaluate Triangle 1 first and dispatch to Triangle 4 or Triangle 5 only inside the domains the standard defines. Outside them, no sub-type should be reported at all.
Esters change the picture
Natural and synthetic esters are not mineral oil with a green label. IEEE C57.155-2014, moved to inactive-reserved status in March 2025 and still the clearest published statement on the subject, puts it bluntly: the differences between an ester liquid and mineral oil are far greater than the differences between any two mineral oils. The fault gases are the same species, which is convenient, but the ratios and the rates of generation are not.
The consequence for the triangle runs in one direction. C57.155-2014 records that methane, ethane and ethylene are produced in greater amounts and at lower temperatures from overheating in esters, and in different proportions than in mineral oil. Some esters also generate ethane under no-fault conditions, driven by linolenic acid content. Plot an ester sample against mineral oil boundaries and the elevated ethylene fraction pushes the point toward the hot end of the thermal band. The error is systematic and it overestimates the thermal class every time.
Duval defined Triangle 3 for non-mineral liquids for this reason, with boundaries fitted to ester behaviour, and Triangles 6 and 7 to refine the thermal sub-types. The family matters too: soybean-based, high-oleic and synthetic esters gas differently enough that one set of boundaries does not cover them. Triangle 3 therefore has to be selected by declared liquid family, with Triangles 6 and 7 gated behind it, the same way Triangles 4 and 5 sit behind Triangle 1 for mineral oil.
Where the published zones stop
Three gaps in the published ester coverage are worth knowing before trusting any tool that claims to cover them.
Pentagon 3 for non-mineral liquids is published as a figure. TB 771 presents it graphically and refers the reader elsewhere for the numerical boundary values. Anyone can measure the vertices off that image and get something that looks about right, but the result is an estimate wearing the name of a published method, and that is the difference between an engineering product and a plausible-looking one.
Triangles 6 and 7 are published for FR3 and soybean chemistry only. Extending them to high-oleic or synthetic esters by assumption is inventing a diagnosis and attributing it to Duval.
Silicone fluids have no interpretation criteria comparable to the mineral oil canon. Without them, a verdict on a silicone-filled unit is a guess with a citation stapled to it.
Where Duval sits next to the ratio methods
The IEC 60599:2022 ratio scheme takes a different approach to the same problem. It computes ratios between gas pairs, checks them against defined ranges, and returns a fault class only when a combination matches one of the listed cases. When a combination falls outside every range, the table returns nothing. The standard says that such a case “can be considered a mixture of faults, or new faults that combine with a high background gas level”, and directs the reader to the graphical representations in Annex B to see which characteristic fault is nearest.
That abstention is not free. TB 771 quantifies it: the IEC method and the other two-gas ratio methods fail to identify faults in about fifteen to twenty percent of DGA cases, even when ppm values are well above typical levels and a fault is obviously present. The Key Gas method fares worse, at around fifty percent wrong identifications when applied automatically in software and around thirty percent applied manually by an experienced user.
TB 771 chose the triangles and pentagons over the ratio methods for its own database work on exactly these grounds, describing them as closed systems with a high proportion of correct predictions because they rest on a large number of inspected cases. No headline accuracy percentage belongs on that. Figures in the high eighties circulate for Triangle 1 against inspection-confirmed cases and they are plausible, but the primary standards do not state one, and a number that cannot be traced to its evaluation dataset and its abstention policy is a marketing number rather than evidence.
The useful move is not to pick a winner. Run both, and read the disagreement. When the ratios abstain and the triangle names a fault, you have learned that your sample sits outside the region the ratio method was defined on, which is worth knowing. Agreement makes the diagnosis stronger than either method alone justifies. Conflict points to a mixture of faults or a data quality problem, and either is something you want surfaced rather than averaged away.
Putting it in the right order
A sound Triangle 1 implementation covers the simplex completely, with no gaps and no overlapping zones, and that is something to verify by execution rather than by reading the code. Triangles 4 and 5 belong behind Triangle 1 for mineral oil, under the gating rules above. Triangle 3 belongs to esters by liquid family, with Triangles 6 and 7 gated behind it for the chemistries the source publishes. The pentagons run alongside for mineral oil, and the IEC 60599 ratios run in parallel and abstain where the standard says they should.
Before any of that, absolute concentrations are evaluated against percentiles conditioned on transformer age and oxygen to nitrogen ratio, per the 2019 IEEE revision, and rate of change is treated as a diagnostic signal of equal standing rather than a footnote. Acetylene gets its own handling, because the standard’s language on it is “any increase” rather than a threshold. If the gates do not open, no zone is reported.
What comes out of a chain like this is decision support. It is not an expert opinion, not a statement of condition, and not a substitute for a qualified engineer who knows the unit, its loading history and its maintenance record. The triangle narrows the hypothesis space and shows how the point has moved since the last sample. Deciding what to do about it stays where it belongs. How we implement that chain, and how its abstentions are reported, is on the RONIN platform page.
