Key takeaway

Dissolved-gas analysis produces five hydrocarbon numbers per sample. Triangle 1 turns three of them into a coordinate inside a ternary diagram with seven fault zones. Pentagon 1 turns all five into a centroid coordinate inside a pentagonal diagram with eight zones. The zone boundaries were not chosen by formula — they were drawn around clusters of inspected transformer cases where the fault was later confirmed by tear-down. Knowing the arithmetic behind each method is what lets you read a diagnostic tool's output and judge whether the answer is robust, near a boundary, or signalling a multi-fault case the diagram alone cannot resolve.

1. Why Duval still wins#

Dissolved-gas analysis on a mineral-oil transformer produces five hydrocarbon numbers per sample. The task is to turn those five numbers into one of seven fault categories that a maintenance team can act on. Three families of methods exist, and only one of them solves the problem cleanly.

Two-gas ratios (IEC 60599:2022 Table 1; the historic Doernenburg and Rogers ratios) divide gases pairwise and look up a fault code. Ratios collapse to zero or infinity when a denominator gas is absent, and fail to identify a fault in about 15–20 % of DGA cases because the result falls outside the defined code zones — even when gas concentrations are well above typical values (CIGRE TB771:2019, §2.1, p. 13).

Key-gas methods identify the dominant gas. The Key Gas method gives typically 50 % wrong identifications when applied automatically with software, dropping to around 30 % when applied manually by experienced DGA users (IEEE C57.104:2019, Annex D.1, p. 61). CIGRE TB771:2019 §2.1 (p. 13) cites the same ~50 % software figure when discussing why TB771 prefers the Triangle and Pentagon methods over Key Gas.

Graphical methods — the Duval Triangle and Pentagon families — solve both problems geometrically. Every set of gas readings, no matter how extreme, plots to exactly one point inside a bounded zone. The zones themselves are drawn around inspected transformer cases where the fault was later confirmed by tear-down, not derived from threshold heuristics.

Triangle 1 and Pentagon 1 are the two graphical methods every transformer engineer should be able to draw on the back of an envelope. Triangle 1 covers three gases (CH₄, C₂H₄, C₂H₂) and seven zones; Pentagon 1 adds H₂ and C₂H₆ and gives an eighth zone — stray gassing. Both are adopted by IEC 60599:2022, IEEE C57.104:2019, and CIGRE TB771:2019. Both are running, right now, behind tribotech.dk's Duval Triangle and Duval Pentagon diagnostic tools. This article shows how the coordinates are computed and how the zones are bounded, so that when a tool plots a point and prints a fault zone you know exactly what it just did.

2. The five fault gases and what they mean#

Five hydrocarbon gases carry the diagnostic signal in mineral-oil DGA. The order of the five along the pentagon's perimeter is the order of increasing energy required to produce them (Duval & Lamarre 2014, p. 10). That order is what makes a 5-gas geometric layout meaningful: a point's position directly encodes the energy spectrum of whatever process produced the gas.

Hydrogen (H₂) — the lightest molecule, formed first from any C–H bond cleavage. Generated in bulk by cold-plasma corona discharges, by stray gassing of certain refined oils below 200 °C, and by water–steel reactions at sampling valves (IEC 60599:2022, §5.3 and §A.7). H₂ alone is rarely conclusive; its diagnostic value comes from being weighed against the C₂ hydrocarbons.

Methane (CH₄) — formed at low temperatures (~120 °C upward) and dominant in partial discharge and the lowest thermal band T1 (<300 °C). Together with C₂H₆, methane signals low-energy thermal stress (IEC 60599:2022, §5.3).

Ethane (C₂H₆) — formed at low to moderate temperatures, dominant in stray gassing and overheating below ~250 °C. C₂H₆ does not appear in Triangle 1 at all; this is the most specific limitation Pentagon 1 was designed to fix (D&L 2014, p. 10).

Ethylene (C₂H₄) — the canonical high-temperature thermal marker, rising sharply above ~500 °C and dominating T2 (300–700 °C) and T3 (>700 °C). C₂H₄ is the most common fault gas in the CIGRE database; in T3 hot-spot-in-oil cases the typical concentration value is 126 ppm and the pre-failure value 1 800 ppm (TB771 Table 3.8).

Acetylene (C₂H₂) — formed only at very high temperatures (>700 °C) or in the core of an electric arc (>3 000 °C in the arc plasma). C₂H₂ is the unambiguous arcing marker: essentially absent in thermal-only faults, present in any discharge above the low-energy threshold.

CO and CO₂ track cellulose involvement and are evaluated separately. They do not enter Triangle 1 or Pentagon 1.

3. Triangle 1 — the math#

Triangle 1 reduces three gas concentrations to a single point inside an equilateral triangle. Three steps.

Step 1 — normalisation. Define the three relative percentages on the three carbon-bearing gases (IEC 60599:2022, Annex B, Figure B.3, p. 37):

$$\%\text{CH}_4 = \frac{100 \cdot [\text{CH}_4]}{[\text{CH}_4] + [\text{C}_2\text{H}_4] + [\text{C}_2\text{H}_2]}$$ $$\%\text{C}_2\text{H}_4 = \frac{100 \cdot [\text{C}_2\text{H}_4]}{[\text{CH}_4] + [\text{C}_2\text{H}_4] + [\text{C}_2\text{H}_2]}$$ $$\%\text{C}_2\text{H}_2 = \frac{100 \cdot [\text{C}_2\text{H}_2]}{[\text{CH}_4] + [\text{C}_2\text{H}_4] + [\text{C}_2\text{H}_2]}$$ The three formulas all share the same denominator: the sum of methane, ethylene, and acetylene in parts per million. Each gas's relative percentage is one hundred times its own concentration divided by that sum. So if the three concentrations are 75, 45, and 30, the denominator is 150 and the percentages come out as 50, 30, and 20.

The three percentages sum to exactly 100 % by construction, regardless of the absolute concentrations. Absolute concentrations are used separately to decide whether plotting is meaningful at all — at least one of the three gases must be above 10 ppm and rising for the result to be diagnostic (IEC 60599:2022, §6.1; TB771 §2.2).

Step 2 — ternary to Cartesian. With %CH₄ at the top vertex, %C₂H₂ at the bottom-left and %C₂H₄ at the bottom-right (IEC 60599 Figure B.3 convention as implemented in the production Duval Triangle):

$$x = 50 + 5 \cdot \%\text{C}_2\text{H}_4 + 2.5 \cdot \%\text{CH}_4$$ $$y = 50 + \tfrac{5\sqrt{3}}{2} \cdot \%\text{CH}_4 \quad \text{(mapped to SVG by Y-flip into the viewBox } 600 \times 533\text{)}$$ The x coordinate equals fifty, plus five times percent ethylene, plus two-and-a-half times percent methane. The y coordinate equals fifty, plus five times the square root of three, divided by two, times percent methane — that second factor is roughly four-and-a-third. The y value is then flipped into the SVG viewBox of six hundred by five hundred and thirty-three pixels.

Sanity checks: pure CH₄ → SVG (300, 50) apex; pure C₂H₄ → SVG (550, 480) bottom-right; pure C₂H₂ → SVG (50, 480) bottom-left. The graphical convention itself is fixed by IEC 60599 Annex B; the affine scaling and Y-flip into the SVG viewBox are the production tool's pixel convention, not standardised. A different implementation choosing a different vertex placement would derive different Cartesian coordinates from the same percentages but produce identical zone classifications, because Triangle 1 zones are defined by percentage inequalities — see the companion article on Duval construction.

Step 3 — zone classification. Triangle 1 has seven zones bounded by lines parallel to the triangle sides. Boundary percentages (CIGRE TB771:2019, App Table H.1, p. 69):

The table lists seven fault zones bounded by simple percentage thresholds on methane, ethylene, and acetylene. Corona partial discharge sits at the top — almost pure methane, ninety-eight percent or more. Thermal faults T1, T2, and T3 climb the ethylene axis from below twenty percent up past fifty, with very little acetylene. The two discharge zones D1 and D2 occupy the lower middle and lower-right, where acetylene rises past thirteen and twenty-nine percent. The mixed zone DT sits between them.

IEC 60599:2022 Annex B Figure B.3 (p. 37) gives the same boundaries in its "Limits of zones" tabulation.

Worked example (based on IEEE C57.104:2019, Annex D.4, p. 63, Figure D.2 — absolute concentrations scaled 3× to clear the 10 ppm plotting threshold of IEC 60599:2022 §6.1, ratio preserved). Take CH₄ = 75 ppm, C₂H₄ = 45 ppm, C₂H₂ = 30 ppm. (The IEEE-published values are CH₄ = 25, C₂H₄ = 15, C₂H₂ = 10; Triangle 1 zone classification depends only on the ratio, so the normalised point and zone are unchanged.)

1. Sum: 75 + 45 + 30 = 150 ppm.
2. Normalise: %CH₄ = 50, %C₂H₄ = 30, %C₂H₂ = 20.
3. Compute Cartesian: $x = 50 + 5 \cdot 30 + 2.5 \cdot 50 = 325$; $y_{\text{math}} = 50 + (5\sqrt{3}/2) \cdot 50 \approx 266.5$, which maps into the SVG viewBox by Y-flip ($\text{SVG-}y \approx 265$). The point therefore lands at SVG coordinate $(325, 265)$ — exactly where the Duval Triangle tool plots the same input.
4. Classify: %C₂H₂ = 20 sits between the D1/D2 boundary at 13 and the D2/DT boundary at 29; %C₂H₄ = 30 sits between the D1/D2 boundary at 23 and the D2/DT boundary at 40. The point lands in zone D2 — high-energy arcing

To walk through the arithmetic: the three concentrations sum to one hundred and fifty parts per million. Dividing each by that sum gives fifty percent methane, thirty percent ethylene, and twenty percent acetylene. Feeding those into the affine formulas places the point at x equals three hundred and twenty-five, y around two hundred and sixty-five in the SVG canvas. Acetylene at twenty percent sits in the high-energy discharge band; ethylene at thirty percent sits in the same band. So the point lands cleanly in zone D2 — high-energy arcing — and refines to the D2-H oil sub-zone under the 2022 Duval and Buchacz refresh.

(IEEE C57.104:2019 Annex D.4, p. 63, verbatim: "in zone D2"). Duval & Buchacz published companion papers in 2022 introducing D1-P/D2-P (paper) and D1-H/D2-H (oil) sub-zones — Part I defines them on Pentagons 1 and 2 (EIM 38(1), pp. 19–21) and Part II extends the same scheme to Triangle 1 (EIM 38(6), pp. 12–14, Figure 1). Under that refresh, this worked example resolves to the D2-H sub-zone — high-energy arcing in oil.

The figure shows Triangle 1 with methane at the apex, acetylene at the bottom-left, and ethylene at the bottom-right. The worked example dot sits inside the D2 zone in the lower middle of the triangle — visually confirming the high-energy arcing diagnosis the arithmetic just produced.

This is the canonical worked example in the IEEE guide and the cleanest concrete demonstration of Triangle 1 mechanics. tribotech.dk's Duval Triangle tool classifies the same input identically.

How is this triangle actually constructed?

The 60° geometry is not a stylistic choice. Three gas percentages sum to 100 by construction — that single algebraic identity constrains the original 3D point to a 2D plane inside 3-space, and the equilateral triangle is the only orientation that treats the three gases as equals. Pentagon 1 is built differently: the single diagnostic point is an area-weighted polygon centroid, and the choice of centroid formula matters at zone boundaries. The full derivation — including how the Pentagon 1 zone vertices are calculated and why Triangle 1 zones are robust to vertex-placement convention while Pentagon 1 zones are not — is in the companion post: How Duval diagrams are constructed.

4. Pentagon 1 — the math#

Pentagon 1 takes all five hydrocarbon gases at once. The construction was introduced by Duval and Lamarre in 2014 and the zone boundaries were corrected for transcription errors in Paulhiac & Duval 2023.

Step 1 — 5-gas normalisation. Let $\Sigma_G = \text{H}_2 + \text{CH}_4 + \text{C}_2\text{H}_6 + \text{C}_2\text{H}_4 + \text{C}_2\text{H}_2$ (all in ppm). For each gas, %Gas = 100 · Gas / Σ_G. The five percentages sum to 100 % (D&L 2014, p. 9).

The sum sigma-G is just the total of all five gases in parts per million — hydrogen, methane, ethane, ethylene, and acetylene added together. Each gas's percentage is then a hundred times itself divided by that total, so the five percentages sum to a hundred.

Step 2 — vertex angles. The five vertices sit at 72° spacing in order of increasing energy of formation, counterclockwise from H₂ at the top (D&L 2014, p. 10; P&D 2023 §V):

The five vertices sit at seventy-two degree spacing around the pentagon, ordered by energy of formation. Hydrogen sits at the top at ninety degrees. Going counter-clockwise: ethane upper-left at one hundred and sixty-two degrees, methane lower-left at two hundred and thirty-four degrees, ethylene lower-right at three hundred and six degrees, and acetylene upper-right at eighteen degrees.

Paulhiac & Duval 2023 §V writes the same angles in equivalent signed form (90°, 18°, −54°, −126°, 162°). The two notations differ only by 360°; they describe the same pentagon.

Step 3 — per-gas Cartesian coordinates. Each gas's plotted point lies on the radial line from the pentagon centre (0, 0) toward its 100 % vertex, at radial distance equal to its percentage:

$$x_i = \%\text{Gas}_i \cdot \cos\theta_i, \quad y_i = \%\text{Gas}_i \cdot \sin\theta_i$$ Each gas gets its own point. The x and y coordinates are simply the gas's percentage multiplied by the cosine and sine of its assigned vertex angle. Five gases give five points.

Five gases, five points (D&L 2014, p. 9).

Step 4 — polygon centroid. The single DGA result is represented not by five points but by the area-weighted centroid of the irregular pentagonal polygon they define. The standard Bourke formulae give, with indices taken modulo 5 so the polygon closes:

$$A = \tfrac{1}{2} \sum_{i=0}^{n-1} (x_i \cdot y_{i+1} - x_{i+1} \cdot y_i)$$ $$C_x = \frac{1}{6A} \sum_{i=0}^{n-1} (x_i + x_{i+1}) \cdot (x_i \cdot y_{i+1} - x_{i+1} \cdot y_i)$$ $$C_y = \frac{1}{6A} \sum_{i=0}^{n-1} (y_i + y_{i+1}) \cdot (x_i \cdot y_{i+1} - x_{i+1} \cdot y_i)$$ The Bourke formula computes the centroid of the irregular pentagon in two stages. First the signed area A is half the sum of cross products between adjacent vertices — each cross product is x of vertex i times y of vertex i plus one, minus x of vertex i plus one times y of vertex i. Then the centroid coordinates are weighted sums of the same cross products, divided by six times the area. The vertices are traversed counter-clockwise so the polygon closes and the signed area stays positive.

The centroid is not the arithmetic mean of the five point coordinates. The area-weighted centroid is what the zone boundaries were calibrated against, and the 2014 paper is explicit about this preference (D&L 2014, p. 10).

Maximum centroid radius. Even if one gas is 100 % and the other four are 0 %, the centroid does not reach the 100 % vertex. Paulhiac & Duval 2023 derive the limit by taking ε → 0 in the four near-zero terms: the result is 100 / 3 ≈ 33.33 % (P&D 2023, §V). All DGA centroids therefore live inside a smaller pentagon of radius 33.33 %, drawn as the inner red dashed pentagon in the layout figure. The 2014 paper's stated practical limit of 40 % was a small over-approximation, corrected in 2023.

The figure shows the pentagon vertex layout. The outer pentagon marks the hundred-percent pure-gas envelope; the inner red dashed pentagon marks the thirty-three-point-three-three percent maximum centroid radius. The five per-gas points for the 2014 worked example form an amber polygon, and the area-weighted centroid — drawn as a red dot — lands inside zone T1, the low-temperature thermal zone below three hundred degrees Celsius.

Worked example (D&L 2014, p. 9, Figure 1). Take H₂ = 31 ppm, C₂H₆ = 130 ppm, CH₄ = 192 ppm, C₂H₄ = 31 ppm, C₂H₂ = 0 ppm.

1. Σ_G = 384 ppm.
2. Normalise: %H₂ ≈ 8, %C₂H₆ ≈ 34, %CH₄ ≈ 50, %C₂H₄ ≈ 8, %C₂H₂ = 0.
3. Plot the five points:
   • H₂ at 90°: (0, 8.1)
   • C₂H₆ at 162°: (−32.3, 10.5)
   • CH₄ at 234°: (−29.4, −40.5)
   • C₂H₄ at 306°: (4.8, −6.5)
   • C₂H₂ at 18°: (0, 0) — sits on the centre because %C₂H₂ = 0
4. Apply the Bourke centroid formula to the five points. The 2014 paper publishes the result: centroid at (−17.3, −9.1) (D&L 2014, p. 10).
5. Classify: with $C_x = -17.3$ and $C_y = -9.1$, the centroid sits inside the T1 polygon (zone vertices per P&D 2023 Table 5). The paper labels this case T1.

Walking through the numbers: the five gases sum to three hundred and eighty-four parts per million. After normalising, methane is about fifty percent, ethane thirty-four, hydrogen and ethylene around eight each, acetylene zero. Two of the five per-gas points collapse to the origin because acetylene is absent; the other three sit in the lower-left half of the plane. The Bourke centroid lands near minus seventeen, minus nine — inside the T1 zone, low-temperature thermal fault below three hundred degrees Celsius.

This is the reference example tribotech.dk's Duval Pentagon tool reproduces.

Corrected zone vertices (P&D 2023 Table 5). Implementations should use the 2023 coordinates, not the 2014 paper's. Small transcription errors in 2014 propagated into TB771 and IEEE C57.104; the authoritative coordinates have always sat in the algorithm file referenced by P&D 2023 and are reproduced in Table 5 of that paper.

5. When Triangle 1 alone is enough — and when Pentagon 1 earns its place#

Triangle 1 and Pentagon 1 are complementary, not competing.

Triangle 1 alone is sufficient when the dominant gases are unambiguous and the case sits well inside a single zone, away from boundaries. Three cleanly Triangle-classifiable archetypes: high-energy arcing D2 (significant C₂H₂ together with significant C₂H₄, point in the lower centre); high-temperature thermal T3 (C₂H₄-dominated, very low C₂H₂, point in the lower-right corner); and pure corona PD (essentially all-methane, narrow strip at the top).

Pentagon 1 earns its place when Triangle 1 leaves an ambiguity that the two missing gases — H₂ and C₂H₆ — can resolve. Three concrete situations.

1. Stray gassing of mineral oil. Some refined oils produce H₂, CH₄ and C₂H₆ at moderate temperatures (~120–200 °C) by a non-fault mechanism. Triangle 1 cannot see H₂ or C₂H₆, so stray gassing maps into the T1/PD region and looks like a low-temperature thermal fault. Pentagon 1 has a dedicated S zone that captures it correctly (D&L 2014, p. 10). For the longer story, see our blog Stray gassing — what it is and isn't.
2. Pure corona with very high H₂ and negligible hydrocarbons. Triangle 1 cannot plot a point at all because the three gases it consumes may all be below detection limits. Pentagon 1 plots the case at the H₂ vertex and classifies as PD or S (TB771 §H.3).
3. Multiple simultaneous faults. Superposed gases from two coexisting faults can place the Triangle 1 point in a zone that matches neither component fault. Pentagon 1 weights gases differently and, where Triangle 1 and Pentagon 1 disagree on the fault label for the same sample, that disagreement is itself the diagnostic signal: "multiple faults suspected, comparative analysis needed" (TB771 §H.6; D&L 2014, p. 11).

The practical workflow is straightforward. Always plot Triangle 1 first. If the point sits well inside a single zone, the diagnosis is usually settled. If the point sits near a boundary, falls in DT, or absolute H₂ is high while the hydrocarbons it consumes are low, run Pentagon 1 and check whether the two methods agree. For deeper sub-type resolution (T3-H vs C, D1-H vs D1-P, S vs O), Triangles 4–5 and Pentagon 2 enter the workflow — covered in our blog Navigating the DGA Maze.

6. Try it yourself — interactive widget#

The widget above lets you move two sliders that mix six real CIGRE TB771 inspected cases — three thermal faults at increasing severity (T1, T2, T3) and three electrical faults at increasing energy (PD, D1, D2). The sliders interpolate between cases linearly and add the thermal and electrical contributions together so you can see how the resulting point moves on both diagrams. This is a teaching aid, not a kinetic prediction: real combined faults do not superpose linearly. Each detent is a published case, but the path between detents is just interpolation. For real diagnosis on a real sample, use the production Duval Triangle and Duval Pentagon tools.

About the anchor cases. Anchor values come from CIGRE TB771:2019 Chapter 3 inspected-case examples. There is no published 5-gas archetype vector keyed to fault zone in IEC 60599 or TB771; the anchors are illustrative reference points, not population medians. Interpolation between anchors and additive mixing of thermal and electrical contributions are teaching devices, not kinetic predictions. For diagnosis on real samples, use the production Duval tools linked above.

Two patterns are worth watching as you move the sliders. First, push thermal severity from T1 to T3 with electrical fixed at zero: the Triangle 1 point sweeps from the top-left (high %CH₄, low %C₂H₄) down through the T2 band into T3 in the lower-right. The Pentagon 1 centroid travels along a roughly horizontal line in the lower-left quadrant. Second, add electrical energy with thermal fixed: the Triangle 1 point lifts off the bottom edge — %C₂H₂ rises — and crosses through D1 into D2. The Pentagon 1 centroid pulls toward the C₂H₂ vertex in the upper-right. The two diagrams trace different geometries through the same fault space, and the comparison is the diagnostic value.

7. Reading a real result#

Two illustrative case patterns. Both are sanitised: the asset class, fluid type and gas magnitudes are real; client identifiers, sites and serial numbers are not.

Pattern A — clean T3 hot spot, single-zone agreement. A mid-life mineral-oil transformer in a generation application reports CH₄ = 180 ppm, C₂H₄ = 950 ppm, C₂H₂ = 4 ppm, H₂ = 60 ppm, C₂H₆ = 110 ppm. Triangle 1: %CH₄ = 16, %C₂H₄ = 83, %C₂H₂ = 0.4 — point well inside T3, far from the T2 boundary. Pentagon 1 centroid sits unambiguously in T3 as well. The diagnosis is robust without further geometric refinement; the next step is Triangle 5 (T3-H vs C, hot spot in oil vs carbonisation of paper) and a furanic-compound check on cellulose involvement.

Pattern B — Triangle and Pentagon disagree, multi-fault suspected. A wind-park generator transformer reports CH₄ = 80 ppm, C₂H₄ = 90 ppm, C₂H₂ = 25 ppm, H₂ = 220 ppm, C₂H₆ = 40 ppm. Triangle 1: %CH₄ = 41, %C₂H₄ = 46, %C₂H₂ = 13 — the point lands on the D2/DT boundary. Pentagon 1 centroid sits in D1. The two methods disagree because the elevated H₂ that Pentagon 1 sees and Triangle 1 ignores carries weight only in the five-gas geometry. The signal is not "one method is right and the other wrong" but "a single fault is unlikely". The next step is a load-correlated trend on H₂ and C₂H₂ and a tank-bottom sample for free-water and particulate confirmation; the diagnostic decision waits for the second sample.

For any real DGA result on your own equipment, the production tools on tribotech.dk accept a five-gas input and return both Triangle 1 and Pentagon 1 classifications with their boundary distances: Duval Triangle, Duval Pentagon.

8. Limitations and where to go next#

Triangle 1 and Pentagon 1 are not the whole DGA story.

Paper involvement. Triangle 4 and Triangle 5 resolve sub-types of low-energy and thermal faults, including the critical distinction between hot spots in oil only (T3-H) and carbonisation of paper (C). For low-temperature thermal faults the same Triangles 4 and 5 separate stray gassing of oil (S) from genuine overheating (O). Cellulose-derived CO and CO₂, and furanic compounds, enter the workflow at this point — they sit outside the five hydrocarbon gases Triangle 1 and Pentagon 1 consume.

Alternative fluids. Triangle 1 and Pentagon 1 are calibrated for mineral oil. Pentagon 2 is also mineral-oil-only — it sub-classifies thermal faults (S, O, C, T3-H) after Pentagon 1 indicates T1, T2, or T3. Natural and synthetic ester fluids use Triangle 3 and Pentagon 3 instead, with fluid-specific zone calibrations for each variant (rapeseed, soybean, sunflower, synthetic ester); Pentagons 4 and 4b refine thermal faults in those same alternative fluids. Silicone fluids use Triangle 3 with their own calibration but have no Pentagon analog.

Kinetics. Neither Triangle 1 nor Pentagon 1 models how gases evolve in time. Trending and rate-of-change analysis sit on top of the geometric classification and remain the diagnostic engineer's job. Run rates against IEEE C57.104:2019 Tables 4 and 5 for percentile context, not against the Duval diagrams.

The tools at tribotech.dk implement the full Duval family (Triangles 1, 2, 3, 3b, 4, 5, 6, 7; Pentagons 1, 2, 3, 3b, 4, 4b, and the Unified Pentagon per CIGRE 2023) and accept the same five-gas input. The blogs Navigating the DGA Maze and DGA in synthetic ester transformers walk through the wider workflow.

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Bibliography#

Full expansion of abbreviated citations used above.

IEC 60599:2022. International Electrotechnical Commission. Mineral oil-filled electrical equipment in service — Guidance on the interpretation of dissolved and free gases analysis. IEC, 2022. Annex A (Tables A.1–A.13, typical concentration values by equipment type), Annex B (Figures B.1–B.4 graphical methods; Figure B.3 Duval Triangle 1 with "Limits of zones" tabulation), §5.3 (gas formation), §6.1 (interpretation criteria).

IEEE C57.104:2019. Institute of Electrical and Electronics Engineers. IEEE Guide for the Interpretation of Gases Generated in Mineral Oil-Immersed Transformers. IEEE Std C57.104-2019, IEEE Power and Energy Society, Transformers Committee. Annex C (basic faults and sub-types), Annex D.1 (Key Gas), Annex D.3 (Pentagon 1), Annex D.4 (Triangle 1, Figure D.2, p. 63 worked example).

CIGRE TB771:2019. CIGRE Joint Working Group D1/A2.47 (M. Duval, convenor). Technical Brochure 771: Advances in DGA interpretation. CIGRE, Paris, June 2019. §2 (method selection rationale), Chapter 3 (per-fault concentration tables 3.1, 3.4, 3.8, 3.11 and inspected-case examples 3.5, 3.6, 3.9, 3.10), Appendix C (typical-value calculation methodology), Appendix H (graphical methods: H.1 Triangle 1, H.3 Pentagons, App Table H.1 zone boundary numerics).

Duval & Lamarre 2014 ("D&L 2014"). Duval, M., and Lamarre, L. "The Duval Pentagon — A New Complementary Tool for the Interpretation of Dissolved Gas Analysis in Transformers." IEEE Electrical Insulation Magazine, vol. 30, no. 6, pp. 9–12, November/December 2014.

Paulhiac & Duval 2023 ("P&D 2023"). Paulhiac, L., and Duval, M. "Unified Pentagon for DGA in Mineral Insulating Oil." CIGRE International Conference on Transformers (ICTRAM), Paper ICTRAM06, 2023. §V (per-gas formulae, maximum centroid radius derivation), Table 5 (corrected zone vertices for Pentagon 1 and Pentagon 2).

Duval & Buchacz 2022 Part I. Duval, M., and Buchacz, J. "Identification of Arcing Faults in Paper and Oil in Transformers — Part I: Using the Duval Pentagons." IEEE Electrical Insulation Magazine, vol. 38, no. 1, pp. 19–21, January/February 2022. Introduces D1-P/D2-P (paper) and D1-H/D2-H (oil) arcing sub-zones on Pentagons 1 and 2 with explicit (X, Y) summit coordinates.

Duval & Buchacz 2022 Part II. Duval, M., and Buchacz, J. "Gas Formation from Arcing Faults in Transformers — Part II." IEEE Electrical Insulation Magazine, vol. 38, no. 6, pp. 12–14, November/December 2022. Figure 1 extends the D1-H/D1-P/D2-H/D2-P sub-zone scheme to Triangle 1.

Bourke. Bourke, P. "Calculating the Area and Centroid of a Polygon." paulbourke.net/geometry/polyarea. Geometric reference cited by D&L 2014.

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