Decision about criticality of power transformers using whitenization weight functions on DGA caution levels

Figures & data

Figure 1. A typical whitenization function.

Figure 2. WW function of lower measures.

Figure 3. WW function of middle measures.

Figure 4. WW function of upper measures.

Table 1. Key gas concentration in ppm (IEEE Std. C.57.104)

Key gases	Level-1	Level-2	Level-3
H2	100	700	1,800
CH4	120	400	1,000
CO	350	570	1,400
CO2	2,500	4,000	10,000
C2H4	50	100	200
C2H6	65	100	150
C2H2	35	50	80

Table 2. Equations for lower measure WW function for caution level-1

Key gases	$f_j^1(x)$	$f_j^1(x)$	$f_j^1(x)$
H2 (j = 1)	0	1	(x−200)/100
	x ≤ 0 and x ≥ 200	x ≤ 0 and x ≤ 100	100 ≤ x ≤ 200
CH4 (j = 2)	0	1	(200−x)/80
	x ≤ 0 and x ≥ 200	0 ≤ x ≤ 120	120 ≤ x ≤ 200
CO (j = 3)	0	1	(400−x)/50
	x ≤ 0 and x ≥ 400	0 ≤ x ≤ 350	350 ≤ x ≤ 400
CO2 (j = 4)	0	1	(3,000−x)/500
	x ≤ 0 and x ≥ 3,000	0 ≤ x ≤ 2,500	2,500 ≤ x ≤ 3,000
C2H4 (j = 5)	0	1	(70−x)/20
	x ≤ 0 and x ≥ 70	0 ≤ x ≤ 50	50 ≤ x ≤ 70
C2H6 (j = 6)	0	1	(70−x)/5
	x ≤ 0 and x ≥ 70	0 ≤ x ≤ 65	65 ≤ x ≤ 70
C2H2 (j = 7)	0	1	(40−x)/5
	x ≤ 0 and x ≥ 40	0 ≤ x ≤ 35	35 ≤ x ≤ 40

Table 3. Equations for middle measure WW function for caution level-2

Key gases	$f_j^2(x)$	$f_j^2(x)$	$f_j^2(x)$	$f_j^2(x)$
H2 (j = 1)	0	(x−100)/600	1, when x = 700	(1,300−x)/600
	x ≤ 100 and x ≥ 1,300	100 ≤ x ≤ 700		700 ≤ x ≤ 1,300
CH4 (j = 2)	0	(x−120)/280	1, when x = 400	(680−x)/280
	x ≤ 350 and x ≥ 790	120 ≤ x ≤ 400		400 ≤ x ≤ 680
CO (j = 3)	0	(x−350)/220	1, when x = 570	(790−x)/220
	x ≤ 120 and x ≥ 680	350 ≤ x ≤ 570		570 ≤ x ≤ 790
CO2 (j = 4)	0	(x−2,500)/1,500	1, when x = 4,000	(5,500−x)/1,500
	x ≤ 2,500 and x ≥ 5,500	2,500 ≤ x ≤ 4,000		4,000 ≤ x ≤ 5,500
C2H4 (j = 5)	0	(x−50)/50	1, when x = 100	(150−x)/50
	x ≤ 50 and x ≥ 150	50 ≤ x ≤ 100		100 ≤ x ≤ 150
C2H6 (j = 6)	0	(x−65)/35	1, when x = 100	(135−x)/35
	x ≤ 65 and x ≥ 135	65 ≤ x ≤ 100		100 ≤ x ≤ 135
C2H2 (j = 7)	0	(x−35)/15	1, when x = 50	(65−x)/15
	x ≤ 35 and x ≥ 65	35 ≤ x ≤ 50		50 ≤ x ≤ 65

Table 4. Equations for middle measure WW function for caution level-3

Key gases	$f_j^3(x)$	$f_j^3(x)$	$f_j^3(x)$	$f_j^3(x)$
H2 (j = 1)	0	(x−700)/1,100	1, when x = 1,800	(2,900−x)/1,100
	x ≤ 700 and x ≥ 2,900	700 ≤ x ≤ 1,800		1,800 ≤ x ≤ 2,900
CH4 (j = 2)	0	(x−400)/600	1, when x = 1,000	(1,600−x)/600
	x ≤ 400 and x ≥ 1,600	400 ≤ x ≤ 1,000		1,000 ≤ x ≤ 1,600
CO (j = 3)	0	(x−570)/830	1, when x = 1,400	(2,230−x)/830
	x ≤570 and x ≥ 2,230	570 ≤ x ≤ 1,400		1,400 ≤ x ≤ 2,230
CO2 (j = 4)	0	(x−4,000)/6,000	1, when x = 10,000	(16,000−x)/6,000
	x ≤ 4,000 and x ≥ 16,000	4,000 ≤ x ≤ 10,000		10,000 ≤ x ≤ 16,000
C2H4 (j = 5)	0	(x−100)/100	1, when x = 200	(300−x)/100
	x ≤ 100 and x ≥ 300	100 ≤ x ≤ 200		200 ≤ x ≤ 300
C2H6 (j = 6)	0	(x−100)/50	1, when x = 150	(200−x)/50
	x ≤ 100 and x ≥ 200	100 ≤ x ≤ 150		150 ≤ x ≤ 200
C2H2 (j = 7)	0	(x−50)/30	1, when x = 80	(200−x)/50
	x ≤ 50 and x ≥ 110	50 ≤ x ≤ 80		80 ≤ x ≤ 110

Table 5. Critical values of three whitenization weight functions

${\mathit{\lambda }}_j^K$	H2 (j = 1)	CH4 (j = 2)	CO (j = 3)	CO2 (j = 4)	C2H4 (j = 5)	C2H6 (j = 6)	C2H2 (j = 7)
K = 1	100	120	350	2,500	50	65	35
K = 2	700	400	570	4,000	100	100	50
K = 3	1,800	1,000	1,400	10,000	200	150	80

Table 6. Dissolved gas-in-oil samples of testing transformers

Specimen	H2	CH4	CO	CO2	C2H4	C2H6	C2H2
Tx1	53	49	748	6,021	2,824	514	31
Tx2	12	325	12	787	1	3	108
Tx3	1	2	34	322	1	1	1
Tx4	1	19	140	1,879	1	57	1
Tx5	19	303	432	3,114	1	157	1
Tx6	1	46	219	9,909	6	16	1
Tx7	1	2	34	327	1	1	1
Tx8	1	19	159	3,303	47	60	1
Tx9	12	8,778	317	2,959	11,900	4,834	19
Tx10	1	73	124	66,261	1	88	1
Tx11	66	87	211	1,902	77	53	24
Tx12	111	102	377	2,496	34	62	36
Tx13	103	114	327	2,734	66	32	17
Tx14	92	103	351	2,496	37	41	22
Tx15	57	64	218	2,210	41	63	33
Tx16	109	76	507	2,910	48	22	13
Tx17	29	123	344	2,506	12	5	1
Tx18	77	98	259	2,496	38	52	26
Tx19	18	76	153	2,107	31	27	5
Tx20	89	113	302	1,992	59	63	29
Tx21	22	106	514	13,327	36	72	28

Table 7. Coefficient matrix of grey cluster with fixed weights

${\mathit{\sigma }}_i^k$	K = 1	K = 2	K = 3	${\mathit{\sigma }}_i^k$	K = 1	K = 2	K = 3
i = 1	0.4285	0.0272	0.0787	i = 12	0.8786	0.0296	0
i = 2	0.7143	0.1045	0.0095	i = 13	0.8146	0.0687	0
i = 3	1	0	0	i = 14	0.9971	0.0006	0
i = 4	1	0	0	i = 15	1	0	0
i = 5	0.4285	0.205	0.1228	i = 16	0.7271	0.1431	0
i = 6	0.8571	0	0.1406	i = 17	0.9929	0.0021	0
i = 7	1	0	0	i = 18	1	0	0
i = 8	0.8571	0.0764	0	i = 19	1	0	0
i = 9	0.4402	0.0437	0	i = 20	0.9357	0.0257	0
i = 10	0.7142	0.0938	0	i = 21	0.5714	0.135	0.0636
i = 11	0.8571	0.077	0

Table 8. Critical values for variable weight clustering

${\mathit{\eta }}_j^K$	H2 (j = 1)	CH4 (j = 2)	CO (j = 3)	CO2 (j = 4)	C2H4 (j = 5)	C2H6 (j = 6)	C2H2 (j = 7)
K = 1	0.0310	0.0372	0.1086	0.7763	0.0155	0.0201	0.0108
K = 2	0.1182	0.0675	0.0962	0.6756	0.0168	0.0168	0.0084
K = 3	0.1230	0.0683	0.0956	0.6835	0.0136	0.0102	0.0054

Table 9. Variable weights clustering coefficient matrix of grey subclass

${\mathit{\sigma }}_i^k$	K = 1	K = 2	K = 3	${\mathit{\sigma }}_i^k$	K = 1	K = 2	K = 3
i = 1	0.0791	0.0183	0.2507	i = 12	0.9203	0.0145	0
i = 2	0.9518	0.0494	0.0003	i = 13	0.6232	0.1114	0
i = 3	1	0	0	i = 14	0.9978	0.0004	0
i = 4	1	0	0	i = 15	1	0	0
i = 5	0.0574	0.3565	0.0088	i = 16	0.2518	0.2555	0
i = 6	0.2236	0	0.6731	i = 17	0.9892	0.0034	0
i = 7	1	0	0	i = 18	1	0	0
i = 8	0.2236	0.3617	0	i = 19	1	0	0
i = 9	0.2142	0.2067	0	i = 20	0.9930	0.0030	0
i = 10	0.2114	0.0111	0	i = 21	0.0947	0.0751	0.3045
i = 11	0.9844	0.0091	0