Origin of the Duval Triangle
Michel Duval of Hydro Quebec developed this method in the 1960s using a database of thousands of DGAs and transformer problem diagnosis. More recently, this method was incorporated in the Transformer Oil Analyst Software version 4 (TOA 4), developed by Delta X Research and used by many in the utility industry to diagnose transformer problems. This method has proven to be accurate and dependable over many years and is now gaining in popularity. The method and how to use it are described below.
Picture 1: The Duval Triangle
How to Use the Duval Triangle
1. First determine whether a problem exists by using the IEEE® method above, and/or table shown on Picture 2 below. At least one of the hydrocarbon gases or hydrogen must be in IEEE® Condition 3 and increasing at a generation rate (G2), from table shown on Picture 2, before a problem is confirmed. To use this table without the IEEE® method, at least one of the individual gases must be at L1 level or above and the gas generation rate must be at least at G2. The L1 limits and gas generation rates from table on Picture 2 are more reliable than the IEEE® method; however, one should use both methods to confirm that a problem exists. If there is a sudden increase in H2 with only carbon monoxide and carbon dioxide and little or none of the hydrocarbon gases, we need to determine if the cellulose insulation is being degraded by overheating.
2. Once a problem has been determined to exist, use the total accumulated amount of the three Duval Triangle gases and plot the percentages of the total on the triangle to arrive at a diagnosis. An example is shown below. Also, calculate the amount of the three gases used in the Duval Triangle, generated since the sudden increase in gas began. Subtracting out the amount of gas generated prior to the sudden increase will give the amount of gases generated since the fault began. Detailed instructions and an example are shown below.
- a. Take the amount (ppm) of methane in the DGA and subtract the amount of CH4 from an earlier DGA, before the sudden increase in gas. This will give the amount of methane generated since the problem started.
- b. Repeat this process for the remaining two gases, ethylene and acetylene.
3. Add the three numbers (differences) obtained by the process of step 2 above. This gives 100 % of the three key gases, generated since the fault, used in the Duval Triangle.
4. Divide each individual gas difference by the total difference of gas obtained in step 3 above. This gives the percentage of increase of each gas of the total increase.
5. Plot the percentage of each gas on the Duval Triangle, beginning on the side indicated for that particular gas. Draw lines across the triangle for each gas, parallel to the hash marks shown on each side of the triangle. An example is shown below.
Picture 2: L1 Limits and Generation Rate Per Month Limits
CAUTION: Do not use the Duval Triangle (Picture 1) to determine whether or not a transformer has a problem. Notice, there is no area on the triangle for a transformer that does not have a problem. The triangle will show a fault for every transformer whether it has a fault or not. Use the above IEEE method or table on Picture 2 to determine if a problem exists before applying the Duval Tirangle. The Duval Triangle is used only to determine what the problem is. As with other methods, a significant amount of gas (at least L1 limits and G2 generation rates in table on Picture 2) must already be present before this method is valid.
NOTE: In most cases, acetylene will be zero, and the result will be a point on the right side of the Duval Triangle.
Compare the total accumulated gas diagnosis and the diagnosis obtained by using only the increase-in-gases after a fault. If the fault has existed for some time, or if generation rates are high, the two diagnoses will be the same. If the diagnoses are not the same, always use the diagnosis of the increase in gases generated by the fault, which will be the more severe of the two. See the example below of a transformer where the diagnosis using the increase in gas is more severe than when using the total accumulated gas.
Picture 3: Duval Triangle Diagnostic Example
Example:
Using Picture 3 and the information below (Picture 4), two diagnoses of a transformer were obtained. The first diagnosis (Point 1) was obtained using the total amount of the three gases used by the Duval Triangle. The second diagnosis (Point 2) was obtained using only the increase in gases between the two DGAs. CO and CO2 are used to evaluate cellulose.
Picture 4: DGA Table
Steps to Obtain the First Diagnosis (Point 1) on the Duval Triangle (Picture 3):
1. Use the total accumulated gas from DGA 2 = 369
2. Divide each gas by the total to find the percentage of each gas of the total.
% CH4 = 192/369 = 52%, % C2H4 = 170/369 = 46%,
% C2H2 = 7/369 = 2%
3. Draw three lines across the Duval Triangle starting at the percentages obtained in step 2. These lines must be drawn parallel to the hash mark on each respective side. See the black dashed lines in Picture 1 above.
4. Point 1 is obtained where the lines intersect within the T2 diagnostic area of the triangle, which indicates a thermal fault between 300 and 700 °C. See Picture 1, Legend, above.
Steps to Obtain the Second Diagnosis (Point 2) on the Duval Triangle (Picture 3):
1. Use the total increase in gas = 139.
2. Divide each gas increase by the total increase to find the percentage of each gas of the total:
% increase CH4 = 50/139 = 36%
% increase C2H4 = 86/139 = 46%
% increase C2H2 = 3/139 = 2%
3. Draw three lines across the Duval Triangle starting at the percentages obtained in step 2. These lines must be drawn parallel to the hash mark on each respective side. See the white dashed lines in Picture 3 above. Note that C2H2 was the same percentage (2%) both times, and, therefore, both lines are the same.
4. Point 2 is obtained where the lines intersect within the T3 diagnostic area of the triangle, which indicates a thermal fault greater than 700 °C. See Picture 1, Legend, above.
The ratio of total accumulated gas is CO2/CO = 2,326/199 = 11.7. The ratio of increase is CO2/CO = 1,317/23 = 57. Neither of these ratios is low enough to cause concern. This shows that the thermal fault is not close enough to the cellulose insulation to cause heat degradation of the insulation. The large increase in CO2 could mean an atmospheric leak.
NOTE:
1. Point 2 is the more severe diagnosis obtained by using the increase in gas rather than the total accumulated gas. It is helpful to perform both methods as a check. Many times both diagnoses will come out the same.
2. CO and CO2 are included to show that the fault does not involve severe degradation of cellulose insulation.
The fault is probably a bad connection on a bushing bottom, a bad contact or connection in the tap changer, or a problem with a core ground. These problems are probably all reparable in the field. Any of these problems can cause the results revealed by the Duval Triangle diagnosis above. These are areas where a fault will not degrade cellulose insulation, which would cause the CO2/CO ratio to be much lower than what was obtained.
Expertise Needed
A transformer expert should be consulted if a problematic trend is evidenced by a number of DGAs. The transformer manufacturer should be consulted along with DGA lab personnel and others experienced in transformer maintenance and diagnostics. Never make a diagnosis based on one DGA. A sample may have been mishandled or mislabeled, either in the field or lab.
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