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Duval’s Pentagon Method for Transformer Fault Diagnosis

Introduction

Duval’s Pentagon Method makes use of the five combustible gases Hydrogen (H2), Methane (CH4), Ethane (C2H6), Ethylene (C2H4), and Acetylene (C2H2) with the relative percentages transformed for representation in a pentagon plot to diagnosis internal faults in power transformers.

Identification of Fault Types using Duval’s Pentagon

Duval’s Pentagon is able to differentiate the fault types of Partial Discharge (PD), Thermal Fault of temperature T1 < 300°C, Thermal Fault of temperature 300°C < T2 < 700°C, Thermal Fault of temperature T3 > 700°C, Discharges of Low Energy – Sparking (D1), Discharges of High Energy – Arcing (D2), and Stray Gassing (S). Figure 1 presents Duval’s Pentagon with the definition of the seven fault diagnosis regions.

Figure 1: Duval’s Pentagon [1]

How to plot Duval’s Pentagon

The relative percentage of each combustible gas is calculated by dividing the specific gas by the sum of the 5 gasses e.g., for Methane (CH4) it will be:

% CH4 = (ppm of CH4) / (sum of ppm H2 + CH4 + C2H6 + C2H4 + C2H2)

From Figure 2 it is observed that each apex of the pentagon represents one of the combustible gases starting with H2 on the vertical axis and then in a counterclockwise direction C2H6, CH4, C2H4, and C2H2. This is based on the increasing energy required to produce the combustible gases. The relative percentages are then plotted on each of the axes (in Blue). As an example for the following dissolved gas results H2 = 40ppm, C2H6 = 120ppm, CH4 = 200ppm, C2H4 = 40 ppm, and C2H2 = 0 ppm the relative percentage of each gas are 10%, 30%, 50%, 10%, and 0% respectively. This is now plotted on the respective axes as displayed in green.

Figure 2: Plotting the Pentagon

The next point to calculate is the centre of these five points which forms the centroid of the plotted points. To identify these points the coordinates of each of these points must be calculated using X-Y axis.

To calculate the coordinates:

  • H2: X = 0, Y = %H2 as it is plotted on the Y-axis
  • C2H6: X = %C2H6 * cos(18), Y = %C2H6 * cos(90-18)
  • CH4: X = %CH4 * cos(126), Y = %CH4 * sin(-54)
  • C2H4: X = %C2H4 * cos(-54), Y = %C2H4 * sin(-54)
  • C2H2: X = %C2H2 * cos(18), Y = %C2H2 * sin(18)

For this example, the coordinates for H2, C2H6, CH4, C2H4, and C2H2 are (0,10), (-28.53, 9.27), (-29.39, -40.45), (5.88, -8.09), (0, 0) respectively.

The final X-Y coordinates of the centroid are calculated using these individual coordinates and the following formulas:

where A is the surface of the centroid

This is the final point of the oil sample representation which in this example is represented as the orange square with the x-y-coordinates being (-15.54, -9.52).

Conclusion

Duval’s Pentagon is an effective dissolved gas analysis method to identify the main types of internal faults within oil-filled power transformers. It is also effective in supporting the diagnosis that may be identified by other methods.

Use the following link to the “Analysis” section to get the Duvals Pentagon diagnosis of the oil samples.

References

  1. Duval, M., Lamarre, L., “The Duval Pentagon – A new Complementary Tool for the Interpretation of Dissolved Gas Analysis in Transformers, IEEE Electrical Insulation Magazine 30, no 6 (2014):9-12
  2. Duval, M., “A Review of Faults Detectable by Gas-in-oil Analysis in Transformers,” IEEE Electrical Insulation Magazine, Vol. 18, No. 3, Pages 8-17, May/June 2002
  3. Duval, M., “New Frontiers of DGA Interpretations for Power Transformers and Their Accessories,” Techcon Canada, Montreal 27-28 September 2012

Other dissolved gas analysis methods that may be of interest are:

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