A Software Implementation of the Duval Triangle Method A. Akbari*, A. Setayeshmehr, H. Borsi, E. Gockenbach Institute of Electric Power Systems, High Voltage Engineering Section (Schering-Institut) Leibniz Universität Hannover, Callinstr. 25 A, 30167 Hannover, Germany *
E-mail:
[email protected]
Abstract- Monitoring and diagnosis of electrical equipment, in particular power transformers, has attracted considerable attention for many years. It is of great importance for the utilities to find the incipient faults in these transformers as early as possible. Dissolved gas analysis (DGA) is one of the most useful techniques to detect incipient faults in oil-filled power transformers. Various methods have been developed to interpret DGA results such as IEC ratio code, Rogers method and Duval triangle method. One of the most frequently used DGA methods is Duval triangular. It is a graphical method that allows one to follow the faults more easily and more precisely. In this paper a detailed implementation of Duval triangle method was presented for researchers and utilities interested in visualizing their own DGA results using a software program. The Java language is used for this software because of its growing importance in modern application development.
PD T1 T2 40
60
%CH4 40
%C2H4 60
D1 D2
20
80
I. INTRODUCTION
60
DT
40 %C2H2 Fig. 1. Duval Triangle method
T3
80
20
These three gases in ppm, CH4 = g1, C2H4 = g2 and C2H2 = g3, must be transformed into triangular coordinates before being plotted onto the triangle. First the sum of these three values, g1+g2+g3, should be calculated and then the relative proportion of the three gases: P1 = %CH4 = 100 × g1/(g1+g2+g3), P2 = %C2H4 = 100 × g2/(g1+g2+g3), P3 = %C2H2 = 100× g3/(g1+g2+g3).
A. The Duval Triangle DGA method The Duval Triangle diagnostic method for oil-insulated high-voltage equipment, mainly transformers, was developed by Michel Duval in 1974 [1]. It is based on the use of 3 hydrocarbon gases (CH4, C2H4 and C2H2) corresponding to the increasing energy levels of gas formation in transformers in service. This method has proven to be accurate and dependable over many years and is now gaining in popularity. One advantage of this method is that it always provides a diagnosis, with a low percentage of wrong result. Duval method is special since fault diagnosis is performed based on visualisation of the location of dissolved gases in the triangular map. The Triangle method is indicated in Fig. 1. Generally, three types of faults are detectable, i.e. partial discharge, high and low energy arcing (electrical fault) and hot spots of various temperature ranges (thermal fault) [2]. These fault types will be determined in 6 zones of individual faults mentioned in Table I (PD, D1, D2, T1, T2 or T3), an intermediate zone DT has been attributed to mixtures of electrical and thermal faults in the transformer. Since no region is designated for normal ageing condition, careless implementation of Duval triangle will result in the diagnosis of either one of the mentioned faults. To avoid this problem, dissolved gases should be assessed for their normality before being interpreted using Duval triangle. The three sides of the Triangle are expressed in triangular coordinates (P1, P2, P3) representing the relative proportions of CH4, C2H4 and C2H2, from 0 to 100 for each gas.
978-1-4244-2092-6/08/$25.00 ©2008 IEEE
20
80
Symbol
PD
Partial discharges
D1
Discharges of low energy
D2
Discharges of high energy
T1 T2 T3
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TABLE I Examples of faults detectable by DGA Fault Examples
Thermal fault, T 300 °C). Carbonization of paper, formation of carbon particles in oil. Extensive formation of carbon particles in oil, metal coloration (800 °C) or metal fusion (> 1000 °C).
For example, if the DGA results are g1 = 70, g2 = 110, g3 = 20 ppm, P1 = 35%, P2 = 55%, P3 = 10%, which corresponds to only one point called R in the right side of the Triangle, as indicated in Fig. 2 and determined as a T3 fault.
For example if point R is located on vertex B, it means that P1 and P2 are zero and P3 is 100. A. Cartesian coordinates and triangular coordinates To plot Duval triangle, the triangle coordinate should be converted to Cartesian coordinate using simple trigonometry. Consider the triangle ABC in Fig. 4. The triangle is equilateral, therefore: AB = BC = AC = L. First we consider vertex B at Cartesian coordinate (Bx , By), which can be a point anywhere in our coordination system. The coordinates of point A (Ax , Ay) can be considered as follow: Ax = Bx + 0.5×L, Ay = By + AH = By + L×cos 30°
100 20
P2 = %C2H4
P1 = %CH4 40
R
100 60 P3 = %C2H2
100
The coordinates of point C (Cx , Cy) can be considered as follow: Cx = Bx + L, Cy = B y
Fig. 2. Example of a point displayed in triangle II.
A
TRIANGULAR COORDINATES
90 P2
As shown in Fig. 3 the system consists of an equilateral triangle ABC with three vertices A, B and C and three components namely P1, P2 and P3 that are determined with points D, E and F respectively. These three fractions are between 0 and 100, and (P1 + P2 + P3) should always have the value of 100. Plotting P1, P2 and P3 in the Triangle provide only one point inside the Triangle. To obtain this point that is determined as R in Fig. 3, three parallel lines should be drawn from D, E and F. For point D a line should be drawn parallel to BC, for point E a line should be drawn parallel to AB and for point F a line should be drawn parallel to AC. The intersection of these three lines will be the point R that is somewhere inside the triangle.
P1
) 60°
90 60° (
) 60° 90
D
H
F
G
Fig. 4. Cartesian coordination of a point inside the triangle
To calculate the Cartesian coordinates of a point R (Rx , Ry) which are obtained from three fractions P1, P2 and P3 , the following calculations should be done. In triangle EBD: ED = BE×cos 30° = P1×L×cos 30° = RG In triangle ABC: AH = AB×cos 30° = L×cos 30° From these follow that ED = P1×AH , ED = RG and RG = P1×AH Hence Ry = By + RG = By + P1×L×cos 30° (1)
90 P2
E D
R (Rx,Ry)
E
R
P1 90
Calculation of Rx needs consideration using two similar triangles ABH and RFG in ABC. From the similarity of triangles ABH and RFG it can be concluded that:
F
90
P3 Fig. 3. Example of a point displayed in triangle
FR/AB = RG/AH = P1×AH/AH = P1
The point R at edges AB, BC or AC represents one of the components P1, P2 and P3 is zero. For example if point R is located on point D in Fig. 3, it means that P2 is zero. Also Point R at vertices A, B or C means that two of the components P1, P2 and P3 are zero and one of them is 100.
and therefore FR = P1×AB = P1×L In triangle RFG: FG = FR×cos 60° = P1×L×cos 60° BG = BF + FG = P2×L + P1×L×cos 60° = L×(P2 + P1×0.5)
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consequently Rx = Bx + BG = Bx + L×(P2 + P1×0.5)
and CartesianX() was used to calculate (1) and (2) respectively.
(2)
We consider the mentioned example in section I again and calculate the point R inside the triangle. The fractions are calculated according to input DGA gases as P1 = 35%, P2 = 55%, P3 = 10%, or P1 = 0.35, P2 = 0.55, P3 = 0.1. The Point B(Bx , By) consider to be placed at origin (0,0) and the length of triangle side L is 200 . For this example, (1) and (2) can be calculated as below:
Area D1
Ry = By + RG = By + P1×L×cos 30° = 0 + 0.35 × 200 × 0.866 = 60.62 Rx = Bx + L × (P2 + P1×0.5)= 0 + 200 × (0.55 + 0.35 × 0.5) = 145
D2
B. Duval triangular fault zones coordinates To determine different zones of Duval triangular method, we need to define a polygon for each zone. As depicted in Fig. 5, we need seven polygons to define different fault zones. The four points of zone D1 is specified as D11, D12, D13, D14. Each point such as D11 is defined by its fraction values P1, P2 and P3 that can be determined according to Fig. 5. Table I shows all points of each polygon of Duval triangle.
DT
T1
PD T2
T1 20
80 D14 P1 = %CH4 40
T2 D13
60
40
P2 = %C2H4
T3
60
D1
PD D2
20 D11
D12 80
60
DT
40
T3
80
TABLE II Triangular coordinates for Duval triangle zones Points P1 P2 D11 0 0 D12 0 0.23 D13 0.64 0.23 D14 0.87 0 D21 0 0.23 D22 0 0.71 D23 0.31 0.40 D24 0.47 0.4 D25 0.64 0.23 DT1 0 0.71 DT2 0 0.85 DT3 0.35 0.5 DT4 0.46 0.5 DT5 0.96 0.0 DT6 0.87 0.0 DT7 0.47 0.4 DT8 0.31 0.4 T11 0.76 0.2 T12 0.8 0.2 T13 0.98 0.02 T14 0.98 0.0 T15 0.96 0.0 T21 0.46 0.5 T22 0.5 0.5 T23 0.8 0.2 T24 0.76 0.2 T31 0.0 0.85 T32 0.0 1 T33 0.5 0.5 T34 0.35 0.5 PD1 0.98 0.02 PD2 1 0.0 PD3 0.98 0.0
P3 1 0.77 0.13 0.13 0.77 0.29 0.29 0.13 0.13 0.29 0.15 0.15 0.04 0.04 0.13 0.13 0.29 0.04 0.0 0.0 0.02 0.04 0.04 0.0 0.0 0.04 0.15 0.0 0.0 0.15 0.0 0.0 0.02
C. Recognizing DGA fault To find out the DGA fault according to the seven defined fault zones or polygons, the input DGA fractions P1, P2 and P3 should be calculated as described before in section I. The fractions will be converted to Cartesian coordinates that will lead the point R and then the zone in which it falls, allowing the identification of the fault corresponding to the DGA data. To determine which one of the seven zones contains point R, a Java built in function called contains() that is applicable for each defined polygon can be used. But if the point is located in the boundary of a polygon it cannot be recognized using this function. To overcome this problem a small circle with centre R and radius r can be considered. The radius r should be selected carefully. In developed program the assigned value to r was 5 and there were about 105 points inside it. All points belonging to this circle should be tested to see whether belong to each of the seven polygons. Finally a percentage value can be assigned to each polygon according to the number of points that are inside each polygon divided by the total number of points of this circle in our case 105.
20
P3 = %C2H2 Fig. 5. Different fault zone inside the triangle
It is obvious that some points are common in neighbouring polygons, e.g. points D12 and D21 of polygons D1 and D2 are the same, which can also be seen in Table II. To define each polygon, the points defined in Table II should be converted to Cartesian coordinates using (1) and (2). To implement the Duval triangle DGA method the java programming language was used because of its growing importance in modern application development and its popularity. Java is platform independent and there are a lot of free compilers and tools for that. Using java Polygon() function, all the seven zones can be defined. The function addpoint() can be used to add each single Cartesian point to a polygon. Fig. 6 shows the source code needed for defining polygon D1. The four points D11, D12, D13, D14 should be added to this polygon using addpoint() function. The methods CartesianY()
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converting is straight forward just by changing Y Cartesian coordinate as below: Ynew = H - Y
Polygon D1 = new Polygon(); P1=0; P2=0; P3=1; //Point D11 xPoint = CartesianX(P1,P2,Bx,L); yPoint = CartesianY(P1,By,L); D1.addPoint(xPoint,yPoint);
X
0,0
P1=0; P2=0.23; P3=0.77; //Point D12 xPoint = CartesianX(P1,P2,Bx,L); yPoint = CartesianY(P1,By,L); D1.addPoint(xPoint,yPoint);
width , 0
Y
P1=0.64;P2=0.23;P3=0.13; //Point D13 xPoint = CartesianX(P1,P2,Bx,L); yPoint = CartesianY(P1,By,L); D1.addPoint(xPoint,yPoint);
0 , height width , height
P1=0.87; P2=0; P3=0.13; //Point D14 xPoint = CartesianX(P1,P2,Bx,L); yPoint = CartesianY(P1,By,L); D1.addPoint(xPoint,yPoint);
Fig. 8. Graphics coordinate system, circles represent coordinates, and squares represent pixels.
H is the window’s height, the triangle should be drawn inside it. Fig. 9 shows the program user interface and the result of the diagnosis for the example mentioned in section I.
Fig. 6. A brief Java code for defining D1 zone as a polygon
This value shows the percentage of the circle in each of the polygons. If the circle is out of a polygon range the percentage value will be zero. Fig. 7 shows an example that point R located in zones D1 and D2. 100 20
P1 = %CH4 40
D1
P2 = %C2H4
D2
Fig. 9. Example of a diagnosis by designed program
R
IV. 100
60
100
P3 = %C2H2
Fig. 7. Example of a point displayed in triangle
The calculated percentage value in this case for D1 is 32% and for D2 is 68% and for other zones zero. III.
THE GRAPHICS COORDINATE SYSTEM AND DISPLAYING
CONCLUSION
In this paper an implementation of Duval Triangle DGA diagnostic method was investigated. This method is widely in use for interpreting DGA data. The developed java program can be used as a stand alone system or as a part of a DGA diagnostic system that includes other DGA methods such as Rogers or IEC. This program can also be used for investigating on other type of insulation fluids such as Ester as a tool for simplifying the process of finding the best zone for each fault.
TRIANGLE
REFERENCES
To display Duval triangle and polygons inside it, a conversion from Cartesian coordinate to graphics coordinate is necessary. The graphics coordinate system is anchored in the upper left-hand corner of a component, with coordinates increasing down and to the right, as depicted in Fig. 8. The
[1] Michel Duval, Fault gases formed in oil-filled breathing EHV power transformers- The interpretation of gas analysis data, IEEE PAS Conf., Paper No C 74 476-8, 1974. [2] Michel Duval, James Dukarm, Improving the Reliability of Transformer Gas-in-Oil Diagnosis, IEEE Elec. Insul. Mag., Vol.21, No.4, pp. 21-27, 2005.
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