Duval's Triangle 1

Introduction

Duval’s Triangle 1 Method makes use of the three combustible gases Methane (CH₄), Ethylene (C₂H₄), and Acetylene (C₂H₂) which are transformed for representation in a triangular plot. The triangle can differentiate the fault types of partial discharges, electrical faults (high and low energy arcing), and thermal faults (hot spots of various temperature ranges). Each point is derived from the percentage volume of the sum of the three gases. The triangle has a clockwise direction in terms of increasing percentage gas levels. Figure 1 presents the triangle with the definition of the seven fault diagnosis regions.

Regions in the Triangle

Duval’s Triangle 1 is very useful in providing diagnoses when a fault condition is already identified since two of the three gases used (ethylene and acetylene) are products of high-energy conditions. The conditions identified are Partial Discharges (PD), Discharges of Low Energy (D1), Discharges of High Energy (D2), Thermal Faults of temperature < 300°C (T1), Thermal Faults of temperature 300°C < T2 > 700°C, and Thermal Faults of temperature > 700°C (T3) [1].

How to Plot Duval’s Triangle

Duval’s Triangle is a ternary plot which is a triangle representation of the relative percentage of the three combustible gases CH₄, C₂H_4, and C₂H₂. This is plotted in a cartesian X-Y axes.

Figure 2 is used to explain Duval’s Triangle and may be used to plot in Excel. Each side of the triangle starts from 0% and ends at 100% on the other end.

To calculate the percentages the following example will be used; CH₄ = 30ppm, C₂H₄ = 50ppm and C₂H₂ = 70ppm. The relative percentages are:

%CH₄ = ppm CH₄ / (ppm CH₄ + ppm C₂H₄ + ppm C₂H₂) = 30ppm / 150ppm = 20 %

%C₂H₄ = ppm C₂H₄ / (ppm CH₄ + ppm C₂H₄ + ppm C₂H₂) = 50ppm / 150ppm = 33.33 %

%C₂H₂ = ppm C₂H₂ / (ppm CH₄ + ppm C₂H₄ + ppm C₂H₂) = 70ppm / 150ppm = 46.67 %

This is plotted as the green dot in Figure 2.

Using Excel to draw the triangle the following can be used:

Cartesian Coordinates (x, y) for the Triangle are (0, 0), (1, 0), (0.5, 0.866)
Plotting the sample point:

X = [(%C₂H₄/0.866) + (%CH₄/1.732)] * 0.866

Y = %CH₄ * 0.866

For the above example, the (x, y) is (0.433, 0.173)

Plotting the Regions points (x, y):

a = (0.49, 0.849), b = (0.51, 0.849), c = (0.48, 0.831), d = (0.58, 0.658), e = (0.6, 0.693), f = (0.73, 0.398), g = (0.75, 0.433), h = (0.675, 0.303), I = (0.85, 0), J = (0.71, 0), k = (0.555, 0.268), l = (0.635, 0.407), m = (0.55, 0.554), n = (0.435, 0.753), o = (0.23, 0)

Conclusion

Duval’s Triangle is an excellent technique that has proven itself to diagnose internal faults in power transformers.

One of the key challenges of this method is that there is no region in the triangle to indicate a normal aging state for the transformer. Thus this method is not as effective in identifying a change from a normal state to a defective state. The Low Energy Degradation Triangle (LEDT) method however can provide a trend from Normal operation to a developing fault.

Duval’s Triangle 1 can be used in a health index as applied in the Transformer Age Index Model to assess the health of the transformer.

In an updated version, Duval’s Triangle 4 is composed of the three gases Hydrogen (H₂), Methane (CH₄), and Ethane (C₂H₆) which are more specific for low energy or temperature (PD, T1, and T2) [2].

Duval’s Triangle 5 is composed of the gases Methane (CH₄), Ethylene (C₂H₄), and Ethane (C₂H₆) which are formed more specifically for the identification of faults of high temperature to ascertain more information about thermal faults in paper and oil [2].

Use the application below to assess your oil sample (in ppm) using Duval’s Triangle 1, or follow this link to the “Analysis” section to fully analyse your oil samples.

Interactive Duval Triangle 1