Dissolved gas analysis calculator: Duval triangles and pentagons, IEC 60599 and IEEE

What this calculator does

It takes the chromatograph concentrations in ppm and applies each interpretation method in its own tab, so they can be compared without mixing them up:

• Summary: the result of every method in one table.
• Duval Triangles 1 to 7 and Duval Pentagons 1 and 2, with the point plotted on the figure.
• IEC 60599:2022: Table 1 by equipment type, the simplified scheme of Table 2, the typical values of Annex A, rates of increase, CO₂/CO, O₂/N₂ and C₂H₂/H₂.
• IEEE C57.104-2019: DGA Status 1, 2 or 3 with Tables 1 to 4 by transformer age and O₂/N₂ ratio, variations between analyses and multi-point regression rates.
• IEEE C57.104-2008: Conditions 1 to 4, the Table 3 sampling interval, litres of gas per day the Rogers and Doernenburg ratios and the key gas method.
• IEEE C57.146-2005: thresholds and key gases for silicone-immersed transformers.

If you enter previous analyses with their dates (up to five), the calculator adds the variations and the generation rates, which are the figures that really decide. If the sample is free gas from the Buchholz relay, it converts it to its dissolved equivalent with the IEC 60599 Ostwald coefficients.

Where the gases come from

Each degradation mechanism inside the transformer breaks certain molecules and not others, which is why the gas mixture identifies the fault:

• Hydrogen (H₂): appears with almost everything, and is the first to show in partial discharges.
• Methane and ethane (CH₄, C₂H₆): moderate overheating of the oil.
• Ethylene (C₂H₄): severe overheating, above 300 °C.
• Acetylene (C₂H₂): electrical arcing. It needs temperatures above 700 °C and is produced no other way.
• Carbon monoxide and dioxide (CO, CO₂): degradation of cellulose, that is, of the insulating paper.

IEEE C57.104-2019 DGA Status

The 2019 edition no longer classifies the transformer with fixed limits: it classifies the analysis into three statuses based on statistics from a large population of transformers.

• Status 1: low gas levels and no sign of gassing. Routine sampling.
• Status 2: a gas between Table 1 (90th percentile) and Table 2 (95th percentile), or a confirmed increase between analyses. Investigate and sample more often.
• Status 3: a gas above Table 2, or a generation rate above Table 4. Probable active gassing.

Tables 1 and 2 depend on transformer age (unknown, 1 to 9, 10 to 30 or over 30 years) and on the O₂/N₂ ratio (up to 0.2 or above); without O₂ and N₂ the above-0.2 section is used. Table 3 sets the maximum variation between two consecutive analyses: if it is exceeded, a confirmation sample is needed within a month. Table 4 sets the maximum rate in ppm/year, calculated by linear regression of the last 3 to 6 analyses over the last two years, with at least four months of history; for acetylene any increase counts.

The calculator also applies the Annex D.8 criteria for CO and CO₂ (high CO without hydrocarbons points to oil oxidation, not to a fault in paper) and reminds you that, with every gas below Table 1, the guide advises against identifying the fault type.

IEEE C57.104-2008 conditions

The calculator classifies the analysis into four conditions with Table 1 of the 2008 edition, which corrected the 1991 values and remains the most widely used field reference for units with no history. The condition is that of the worst gas or of the total combustible gas, not the average.

With the previous analysis, Table 3 gives the sampling interval and operating procedure from the total combustible gas and its generation rate (below 10, 10 to 30 or above 30 ppm per day). With the oil volume, Equation (1) is also applied: more than 2.8 litres of combustible gas per day points to an active fault.

The 2019 edition replaced this approach with the DGA Status described in the previous section. The calculator applies both editions, each in its own tab.

IEC 60599

The standard uses three quotients — C₂H₂/C₂H₄, CH₄/H₂ and C₂H₄/C₂H₆ — and a table that translates them into six fault types: PD (partial discharges), D1 and D2 (low- and high-energy discharges) and T1, T2 and T3 (thermal faults below 300 °C, between 300 and 700 °C and above 700 °C). When the ratios fit no row, the calculator says so and applies the simplified scheme of Table 2, which at least distinguishes partial discharges, discharges and thermal faults.

The CH₄/H₂ limit for partial discharges depends on the equipment: 0.1 in transformers, 0.2 in instrument transformers and 0.07 in bushings, which also have their own simplified scheme (Table A.10). In a tap-changer compartment Table 1 does not apply: Duval Triangle 2 and the C₂H₄/C₂H₂ ratio are used there.

The calculator compares each gas with the 90 % typical values of Annex A and, with the previous analysis, the rate of increase with Table A.3. If every gas is at the low end of the typical values, the analysis is normal and the standard advises against diagnosing with the ratios. Three auxiliary ratios complete the reading: CO₂/CO (paper involvement), O₂/N₂ (oxygen consumption, below 0.3) and C₂H₂/H₂ (above 2, contamination from the tap changer).

Duval triangles

Each triangle takes three gases, expresses them as a percentage of their sum and places the point in a ternary diagram divided into zones. The calculator draws each triangle from the same inequalities it uses to classify the point, so the drawing and the diagnosis cannot disagree.

• Triangle 1 (CH₄, C₂H₄, C₂H₂): the classic IEC 60599 triangle for mineral oil. Boundaries: 98 % CH₄ for PD; 4, 13, 15 and 29 % C₂H₂; 20, 23, 40 and 50 % C₂H₄. The DT zone covers mixtures of thermal and electrical faults.
• Triangle 2 (same gases): for oil from oil-type on-load tap changers, where arcing is part of normal operation. Zone N for normal operation and zones D1, X1, X3, T2 and T3 for abnormal operation.
• Triangle 3: Triangle 1 with three boundaries shifted for each alternative fluid.
• Triangles 4 and 5: for low-temperature faults in mineral oil. Triangle 4 uses H₂, CH₄ and C₂H₆; Triangle 5, CH₄, C₂H₄ and C₂H₆. They separate stray gassing of the oil (S), overheating below 250 °C (O) and hot spots with carbonisation of paper (C). IEEE C57.104-2019 says to apply Triangle 4 to faults that Triangle 1 identifies as PD, T1 or T2, and Triangle 5 to T2 or T3 faults.
• Triangles 6 and 7: the equivalents of 4 and 5 for FR3 natural ester, whose stray gassing produces much more ethane.

Sources: IEC 60599:2022 (Figures B.3 and B.4) and M. Duval, The Duval Triangle for LTCs, alternative fluids and other applications (2009). Triangles 4 and 5 follow Tables D.3 and D.4 of IEEE C57.104-2019.

Duval pentagons

The pentagon (Duval and Lamarre, 2014) uses all five hydrocarbons at once. Each gas has its own axis, from the centre (0 %) to the vertex (100 %), in this order: H₂, C₂H₆, CH₄, C₂H₄ and C₂H₂. The five percentages form an irregular polygon and the point of the analysis is its centroid, which never goes beyond 40 % on an axis. The zone boundaries are those of Annex D of IEEE C57.104-2019.

• Pentagon 1: the six basic faults (PD, D1, D2, T1, T2, T3) and stray gassing S.
• Pentagon 2: the same discharges, but the thermal faults are split into T3-H (in oil only), C (with carbonisation of paper) and O (overheating below 250 °C).

They do not replace Triangles 1, 4 and 5. If the pentagons and the triangles disagree, a mixture of faults is the most likely explanation.

Rogers, Doernenburg and key gases

These are the two ratio methods of IEEE C57.104-2008. Rogers uses CH₄/H₂, C₂H₂/C₂H₄ and C₂H₄/C₂H₆ and assigns one of six cases, from unit normal to thermal fault above 700 °C. Doernenburg uses four ratios (CH₄/H₂, C₂H₂/C₂H₄, C₂H₂/CH₄ and C₂H₆/C₂H₂) and checks that there is enough gas before diagnosing: if no key gas exceeds twice its L1 limit, or if neither ethane nor CO exceeds L1, there is no fault (Figure 4), and if a ratio has no gas above L1 it is not significant. For free gas from the relay it applies the gas-space columns.

The key gas method (Figure 3) compares the proportions of the six combustible gases with four typical profiles — overheated oil (ethylene), overheated cellulose (CO), partial discharge (hydrogen) and arcing (acetylene) — and shows the closest one together with the principal gas measured.

Silicone-immersed transformers

IEEE C57.146-2005 gives its own thresholds for silicone: 200 ppm H₂, 100 CH₄, 1 C₂H₂, 30 C₂H₄ and C₂H₆, 3,000 CO, 30,000 CO₂ and 3,361 total combustible gas. Below them, normal surveillance; above them, resample to confirm and look for the fault type. The calculator also compares the proportions of the combustible gases with the guide’s four key gas profiles (overheated silicone, overheated cellulose, partial discharge and arcing) and shows the closest one. In silicone, any amount of acetylene may indicate a serious problem.

Worked example

Power transformer with H₂ 180, CH₄ 95, C₂H₆ 30, C₂H₄ 210, C₂H₂ 4 and CO 320 ppm.

• Total combustible gas: 839 ppm. Condition 2 for the total, hydrogen and acetylene, and Condition 4 for ethylene, which is above 200 ppm: the worst gas decides.
• IEC 60599: C₂H₂/C₂H₄ = 0.02; CH₄/H₂ = 0.53; C₂H₄/C₂H₆ = 7.0. Hydrogen exceeds the highest typical value (150 ppm), so the ratios are significant, but they fit no row of Table 1; Table 2 gives a thermal fault.
• Duval Triangle 1: CH₄ 31 %, C₂H₄ 68 %, C₂H₂ 1 %, zone T3. As it is not PD, T1 or T2, Triangles 4 and 5 do not apply.
• Pentagon 1: zone T3. Pentagon 2: T3-H, a thermal fault in oil with no sign of paper carbonisation.

Reading: thermal fault above 700 °C, with some acetylene that calls for close monitoring. The usual suspect is a poor internal connection or a circulating current in the core or tank.

What this calculator does not do

It does not know whether the sample was taken properly, whether the unit has only recently returned to service after a repair or degassing, or anything of its history beyond the previous analysis you give it. The IEC 60599 typical values are ranges observed across many networks: you should calculate those of your own equipment population. And every graphical method returns a zone even when there is no real generation; the diagnosis only makes sense when the gases and their rate of increase are above typical levels.

What measures it

The analysis is run by a laboratory from an oil sample, or by a dielectric oil analyser on site. For critical units the alternative is on-line monitoring: hydrogen and dissolved gas sensors that flag a change in trend between samples, instead of waiting for the six-monthly analysis. Oil treatment — drying and degassing — is the other half of the job.