PSI - Issue 36

Roman Dzhala et al. / Procedia Structural Integrity 36 (2022) 17–23 Roman Dzhala et al. / Structural Integrity Procedia 00 (2021) 000 – 000

21 5

z z H

 −

(5)

,

(

)

x r H x y z y , ,

= + H

s

s





s 

s

x

(6)

,

(

)

= − , ,

H x y z

 H

y

r

x H

)  − = s

(

(7)

,

H x y z , ,

z

s



s 

   

    

2 J

z z −

J r



(

) 2

2

2 2 r x y = + ,

where:

(8)

,

,

( ) ,

s x z z = + − 

s

s

2

1

,

H r z

 

= −

s

 +

r

) 2

(

2

r z z + −

s

s

   

   

y

(   s s

)

(9)

.

,

1

H

= y J

−

s

4

s 

2

2

y

+

s 

As can be seen from the above given formulas, over UP at x = 0 the vertical and longitudinal components of MF are zero. Only horizontal transverse component of MF remains above the route, as for the ideal one without damage to UP. However, the current flowing from the insulation damage changes the distribution of this main largest component H x ( r , z ) along the route. Changes in the distribution of MF caused by leakage of current through local insulation defects of UP, calculated by formulas (5) - (9), are shown in Fig. 4; the values of MF are normalized per unit current and depth of UP. a b

1

1

0 .97

0 .97

0 .93

0 .93

0 .9

0 .9

2  Hx 0 z  ( )

2  Hx 0 z  ( )

0 .87

0 .87

0 .83

0 .83

0 .8

0 .8

10

5

0

5

10

15

10

5

0

5

10

15

z

z

Fig. 4. Changes in horizontal transverse component of MF along power line H х ( z ) over UP with ( a ) one and ( b ) two at distance z 2 -z 1 =5h of UP insulation damages. The occurrence of the longitudinal component of MF H z caused by the leakage of current from UP is essential for non-contact measurements. It takes place on both sides of UP route with different signs (directions). Over the route ( θ = 0, θ = π) there is the transverse component MF of current leakage: ( )   cos , H H y s x = . It is important that it changes sign when moving the observation point over the current leakage (over the damage to the insulation of UP). CCM at different points z of UP is carried out on the basis of the following formula: ( ) J z h z H h z x ( ) 2 ( ) 0, ,  =  . (10)