# FAQ Duval

##### Frequently asked questions (and their answers) related to the Duval family of DGA interpretation methods

#### How many Duval methods are there?

When people speak of the "Duval method", they often mean the Duval Triangle 1 as defined in IEEE Std C57.104. However, there are actually three Duval triangles and two Duval pentagons.

#### What is the technical difference between the Duval methods?

The Duval triangles use the relative percentages of three gasses. You are supposed to use the Triangle 1 first. Depending on the result, you are supposed to do Triangle 4 and 5 next to further classify the sub-type of a fault. This makes sense since the Triangles 4 and 5 use different gasses for classification.

The Duval pentagons use the relative percentages of five gasses. You are supposed to use Pentagon 1 first. If thermal faults are identified, you are supposed to do Pentagon 2 next to further classify the sub-type of a fault. This makes *no* sense since Pentagon 2 uses the same gasses for classification - those two pentagons could have been combined.

#### What are the advantages of the Duval Triangles (vs Duval Pentagons)?

For the Duval triangles, only a subset of the gasses is needed. Also, the implementation is simpler. When using pen and paper, the three lines of the three gasses have to intersect, this can be used for validation. When using a computer, a simple in-range check can be used.

#### What are the disadvantages of the Duval Triangles (vs Duval Pentagons)?

With the Triangle 1 alone, stray gassing cannot be distinguished from fault cases. Triangles 4 and 5 are needed for this, taking away from the advantage of simplicity.

#### What are the requirements for the Duval methods?

- You have to be sure that a fault has occured
- Triangle 1 requires measurements of CH4, C2H4 and C2H2
- Triangle 4 requires measurements of H2, CH4 and C2H6
- Triangle 5 requires measurements of CH4, C2H4 and C2H6
- Pentagon 1 requries measurements of H2, C2H2, C2H4, CH4, C2H6
- Pentagon 2 requries measurements of H2, C2H2, C2H4, CH4, C2H6
- All Duval methods require measurements from transformers, although modified versions for OLTC DGA have been published
- All Duval methods require measurements from mineral oil, although modified versions for natural esters have been published

#### How can these methods be implemented as an algorithm?

The triangle methods can be implemented using simple in-range-checks using two of the three gas percentages. For the pentagons, the centroid point has to be calculated first using trigonometry, then the jordan curve theorem can be used to identify the fault type.

#### What happens at the border between two fault regions?

For Triangles 4 and 5, the fault zone boundaries from IEEE Std C57.104 can be used (Table D.3 and D.4). For Triangle 1 and the pentagons, the behavior is undefined. In practice, it doesn't matter.

#### How can I include measurement uncertainties in a Duval triangle?

For each of the three gasses, the minimum and maximum possible percentage has to be evaluated, based on measurement uncertainty.

Then, the corresponding lines are drawn onto the triangle. This results in a hexagon-like shape. The percentage of the area of the hexagon included inside the fault area of the nominal point gives an indication about the sensitivity of the result.

#### How can I include measurement uncertainties in a Duval pentagon?

With pen and paper, this might be difficult. On a computer, a simple Monte Carlo approach can be used.

#### How can I interpret temporal changes using the Duval methods?

The Duval methods cannot be used to track changes in fault severity, because only relative gas percentages are used. However, changes in fault type can be tracked by repeating the method regularly. A good way to visualize the results is to use a color gradient based on measurement age, with older samples fading away.