a software implementation of the duval triangle method (ok)

A Software Implementation of the Duval Triangle

MethodA. Akbari*, A. Setayeshmehr, H. Borsi, E. Gockenbach

Institute of Electric Power Systems, High Voltage Engineering Section (Schering-Institut)Leibniz Universitat Hannover, Callinstr. 25 A, 30167 Hannover, Germany

E-mail:

Abstract- Monitoring and diagnosis of electrical equipment, in PDparticular power transformers, has attracted considerableattention for many years. It is of great importance for the utilities

80 0to find the incipient faults in these transformers as early as

T2

possible. Dissolved gas analysis (DGA) is one of the most usefultechniques to detect incipient faults in oil-filled power 60/ A C2H4transformers. Various methods have been developed to interpretDGA results such as IEC ratio code, Rogers method and Duval DI / 60triangle method. One of the most frequently used DGA methodsis Duval triangular. It is a graphical method that allows one tofollow the faults more easily and more precisely. In this paper a 20 D2 TD 13 80detailed 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 80 60 40 20

used for this software because of its growing importance in %CHmodern application development. VI Dv Tr1n mthod

I. INTRODUCTION

A. The Duval Triangle DGA methodThe Duval Triangle diagnostic method for oil-insulated

high-voltage equipment, mainly transformers, was developedby Michel Duval in 1974 [1]. It is based on the use of 3hydrocarbon gases (CH4, C2H4 and C2H2) corresponding to theincreasing energy levels of gas formation in transformers inservice. This method has proven to be accurate anddependable over many years and is now gaining in popularity.One advantage of this method is that it always provides adiagnosis, with a low percentage of wrong result. Duvalmethod is special since fault diagnosis is performed based onvisualisation of the location of dissolved gases in thetriangular 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 hotspots of various temperature ranges (thermal fault) [2]. Thesefault types will be determined in 6 zones of individual faultsmentioned in Table I (PD, DI, D2, Ti, T2 or T3), anintermediate zone DT has been attributed to mixtures ofelectrical and thermal faults in the transformer. Since noregion is designated for normal ageing condition, carelessimplementation of Duval triangle will result in the diagnosisof either one of the mentioned faults. To avoid this problem,dissolved gases should be assessed for their normality beforebeing interpreted using Duval triangle. The three sides of theTriangle are expressed in triangular coordinates (P1, P2, P3)representing the relative proportions of CH4, C2H4 and C2H2,from 0 to 100 for each gas.

These three gases in ppm, CH4 = g1, C2H4 = g2 and C2H2 = g3,must be transformed into triangular coordinates before beingplotted onto the triangle. First the sum of these three values,g1+g2+g3, should be calculated and then the relative proportionof the three gases: P1 = %CH4 = 100 x gl/(gl+g2+g3), P2 =

%C2H4 = 100 x g2/(g1+g2+g3), P3 = %C2H2 = 1O0xg3/(g1+g2+g3).

TABLE IExamples of faults detectable by DGA

Symbol Fault Examiples

Discharges of the cold plasma (corona)PD Partial discharges type in gas bubbles or voids, with the

possible formation ofX-wax in paper.Partial discharges of the sparking type,

Discharges of low inducing pinholes, carbonized punctures inDI energy paper. Low energy arcing inducing

carbonized perforation or surface trackingof paper, or the formation of carbonparticles in oil.Discharges in paper or oil, with power

Discharges of follow-through, resulting in extensiveD2 high energy damage to paper or large formation of

carbon particles in oil, metal fusion,tripping of the equipment and gas alarms.

T1 Thermal fault, T Evidenced by paper turning brownish (><300 °C 200 °C) or carbonized (> 300 °C).

T2 Thermal fault, Carbonization of paper, formation of300 <T<700 °C carbon particles in oil.

T3 Thermal fault, T Extensive formation of carbon particles in>700 °C oil, metal coloration (800 °C) or metalI_________I____ fusion (> 1000 °C).

978-1-4244-2092-6/08/$25.00 ©2008 IEEE

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For example, if the DGA results are g, = 70, g2 = 110, g3 =

20 ppm, P1 = 35%, P2 = 55%, P3 = 10%, which corresponds toonly one point called R in the right side of the Triangle, asindicated in Fig. 2 and determined as a T3 fault.

For example if point R is located on vertex B, it means thatP1 and P2 are zero and P3 iS 100.A. Cartesian coordinates and triangular coordinatesTo 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 (B,, By),

which can be a point anywhere in our coordination system.The coordinates of point A (Ax, Ay) can be considered asfollow:

A, = B, + 0.5xL,Ay =By+AH = By+ Lxcos 300

The coordinates of point Cfollow:

(C, , Cy) can be considered as

C, = Bx +L,Cy = By

Fig. 2. Example of a point displayed in triangle A

II. TRIANGULAR COORDINATES

As shown in Fig. 3 the system consists of an equilateraltriangle ABC with three vertices A, B and C and threecomponents namely P1, P2 and P3 that are determined withpoints D, E and F respectively. These three fractions arebetween 0 and 100, and (P1 + P2 + P3) should always have thevalue of 100.Plotting P1, P2 and P3 in the Triangle provide only one point

inside the Triangle. To obtain this point that is determined asR in Fig. 3, three parallel lines should be drawn from D, E andF. For point D a line should be drawn parallel to BC, for pointE a line should be drawn parallel to AB and for point F a lineshould be drawn parallel to AC. The intersection of these threelines will be the point R that is somewhere inside the triangle.

P1

9o rE f

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 , thefollowing calculations should be done.In triangle EBD: ED = BExcos 300 = PIxLxcos 300 = RGIn triangle ABC: AH = ABxcos 30° = Lxcos 30°From these follow that

ED = PI xAH, ED = RGand

RG = P1xAHHence

Ry =By+RG =By+PxLxcos300 (1)

Calculation of Rx needs consideration using two similartriangles ABH and RFG in ABC. From the similarity oftriangles ABH and RFG it can be concluded that:

Fig. 3. Example of a point displayed in triangle

The point R at edges AB, BC or AC represents one of thecomponents P1, P2 and P3 iS zero. For example if point R islocated on point D in Fig. 3, it means that P2 is zero. AlsoPoint R at vertices A, B or C means that two of thecomponents P1, P2 and P3 are zero and one of them is 100.

FRIAB = RGIAH = PIxAHIAH = P

and therefore FR = PIxAB = P1 xL

In triangle RFG: FG = FRxcos 600 = PIxLxcos 600BG = BF + FG = P2xL +PI xLxcos 600 = Lx(P2 +PxO. 5)

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consequentlyRx = BX+BG = Bx +Lx(P2 +P1x0.5)

We consider the mentioned example in section I again andcalculate the point R inside the triangle. The fractions arecalculated according to input DGA gases as P1 35%, P255%o,P3 10O%,orP =0.35,P2 =0.55,fP3= 0..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:

Ry = By + RG = By + P1xLxcos 30° = 0 + 0.35 x 200 x 0.866= 60.62Rx = B±+ L x (P2 + P1x0.5)= 0 + 200 x (0.55 + 0.35 x 0.5)= 145

B. Duval triangularfault zones coordinatesTo 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 DI is specified as DlI, D12, D13,

D14. Each point such as DlI is defined by its fraction valuesP1, P2 and P3 that can be determined according to Fig. 5.Table I shows all points of each polygon of Duval triangle.

and CartesianX( was used to calculate (1) and (2)(2) respectively.

TABLE IITriangular coordinates for Duval triangle zones

Area Points PI P2 P3D1I 0 0 1

Dl D12 0 0.23 0.77D13 0.64 0.23 0.13D14 0.87 0 0.13D21 0 0.23 0.77D22 0 0.71 0.29

D2 D23 0.31 0.40 0.29D24 0.47 0.4 0.13D25 0.64 0.23 0.13DT1 0 0.71 0.29DT2 0 0.85 0.15DT3 0.35 0.5 0.15

DT DT4 0.46 0.5 0.04DT5 0.96 0.0 0.04DT6 0.87 0.0 0.13DT7 0.47 0.4 0.13DT8 0.31 0.4 0.29T1l 0.76 0.2 0.04T12 0.8 0.2 0.0

T1 T13 0.98 0.02 0.0T14 0.98 0.0 0.02T15 0.96 0.0 0.04T21 0.46 0.5 0.04

T2 T22 0.5 0.5 | 0.0T23 0.8 0.2 0.0T24 0.76 0.2 0.04T31 0.0 0.85 0.15T32 0.0 1 0.0

T3 T33 0.5 0.5 0.0T34 0.35 0.5 0.15PD1 0.98 0.02 0.0

PD PD2 1 0.0 0.0PD3 0.98 0.0 0.02

60 40

P3= %C2H2

Fig. 5. Different fault zone inside the triangle

It is obvious that some points are common in neighbouringpolygons, e.g. points D12 and D21 of polygons Dl and D2 arethe same, which can also be seen in Table II. To define eachpolygon, the points defined in Table II should be converted toCartesian coordinates using (1) and (2).To implement the Duval triangle DGA method the javaprogramming language was used because of its growingimportance in modern application development and itspopularity. Java is platform independent and there are a lot offree compilers and tools for that.Using java Polygono function, all the seven zones can be

defined. The function addpointo can be used to add eachsingle Cartesian point to a polygon. Fig. 6 shows the sourcecode needed for defining polygon Dl.The four points Dl], D12, D13, D14 should be added to thispolygon using addpointo function. The methods CartesianYQ

C. Recognizing DGA faultTo find out the DGA fault according to the seven defined

fault zones or polygons, the input DGA fractions P1, P2 andP3 should be calculated as described before in section I. Thefractions will be converted to Cartesian coordinates that willlead the point R and then the zone in which it falls, allowingthe 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 containsO that is applicable foreach defined polygon can be used. But if the point is located inthe boundary of a polygon it cannot be recognized using thisfunction. To overcome this problem a small circle with centreR and radius r can be considered. The radius r should beselected carefully.In developed program the assigned value to r was 5 and

there were about 105 points inside it. All points belonging tothis circle should be tested to see whether belong to each ofthe seven polygons. Finally a percentage value can beassigned to each polygon according to the number of pointsthat are inside each polygon divided by the total number ofpoints of this circle in our case 105.

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Polygon Dl = new Polygono;

P1=0; P2=0; P3=1; //Point DllxPoint = CartesianX(Pl,P2,Bx,L);yPoint = CartesianY(Pl,By,L);Dl.addPoint(xPoint,yPoint);

P1=0; P2=0.23; P3=0.77; //Point D12xPoint = CartesianX(Pl,P2,Bx,L);yPoint = CartesianY(Pl,By,L);Dl.addPoint(xPoint,yPoint);

P1=0.64;P2=0.23;P3=0.13; //Point D13xPoint = CartesianX(Pl,P2,Bx,L);yPoint = CartesianY(Pl,By,L);Dl.addPoint(xPoint,yPoint);

P1=0.87; P2=0; P3=0.13; //Point D14xPoint = CartesianX(Pl,P2,Bx,L);yPoint = CartesianY(Pl,By,L);Dl.addPoint(xPoint,yPoint);

Fig. 6. A brief Java code for defining DI zone as a polygon

converting is straight forward just by changing Y Cartesiancoordinate as below:

Ynew = H- Y

O 0 X width,0

O o O o o3 a O o o:

)~~~~~~I[1[1[1[1[1[1[I]QE1O, height o[ aQ[1 00[0[1Q 0[EQ[1

t ~~~~~~~~~width,height

Fig. 8. Graphics coordinate system, circles represent coordinates, and squaresrepresent pixels.

H is the window's height, the triangle should be drawn insideit. Fig. 9 shows the program user interface and the result of thediagnosis for the example mentioned in section I.

This value shows the percentage of the circle in each of thepolygons. If the circle is out of a polygon range the percentagevalue will be zero. Fig. 7 shows an example that point Rlocated in zones DI and D2.

t ~~~~~~~~CH4:

4 | C2H4: FK--

N ~~~~~~~~~~~DIDisrhag-s of iow e=ergy -->1[1%X _ ~~~~~~~~~DZFi-sh-rge pE high-e,Iegy 0-li%

60-- g4 DT EWedtta a6dthemal -> 0 %,

%/ CH4 1 11%C2H4 T 1 Therfri.1 faultr 3ao c --W.

_ _} ~~~~~~~~~~TZ The-mIfaultt30f<1T<70 "C 0%: 1 M

40 - _60 _ T3 Thqt"I lF-ItulT>rG700l-C> 109N

%/ C2H2

Fig. 9. Example of a diagnosis by designed program

100 604- ~~P3 = %C2H2

Fig. 7. Example of a point displayed in triangle

The calculated percentage value in this case for DI is 32%and for D2 is 68% and for other zones zero.

III. THE GRAPHICS COORDINATE SYSTEM AND DISPLAYINGTRIANGLE

To display Duval triangle and polygons inside it, aconversion from Cartesian coordinate to graphics coordinate isnecessary. The graphics coordinate system is anchored in theupper left-hand corner of a component, with coordinatesincreasing down and to the right, as depicted in Fig. 8. The

IV. CONCLUSION

In this paper an implementation of Duval Triangle DGAdiagnostic method was investigated. This method is widely inuse for interpreting DGA data. The developed java programcan be used as a stand alone system or as a part of a DGAdiagnostic system that includes other DGA methods such asRogers or IEC. This program can also be used forinvestigating on other type of insulation fluids such as Ester asa tool for simplifying the process of finding the best zone foreach fault.

REFERENCES

[1] Michel Duval, Fault gases formed in oil-filled breathing EHV powertransformers- The interpretation ofgas analysis data, IEEE PAS Conf.,Paper No C 74 476-8, 1974.

[2] Michel Duval, James Dukarm, Improving the Reliability of TransformerGas-in-Oil Diagnosis, IEEE Elec. Insul. Mag., Vol.21, No.4, pp. 21-27,2005.

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a software implementation of the duval triangle method (ok)

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