1. INFLUENCE OF METAL INSTALLATIONS INVOLVED WITH MAGNETIC FIELD OF FEEDING LINE ON GROUND FAULT CURRENT DISTRIBUTION IN A SUPPLIED HV/MV SUBSTATION
Dr Ljubivoje M. Popović

2. RELEVANT DATA ABOUT THE FEEDING LINE USED FOR THE EXPERIMENTAL MEASUREMENTS
- length of the feeding cable line to the TS ”Obilić” is: km
length of the feeding cable line to the TS ”Pionir” is: km
type of single-core cables is: XHE49-A, 1x 1000 m2 , sheath: Cu 95 mm2
cables are laid in triangle formation and the crossbonding is not applied
equivalent specific soil resistivity is estimated within the range from 30 to 50 Ωm
grounding impedances of supply and supplied TS are: between 0.02 and 0.05 Ω

3. DESIGN CHARACTERISTICS OF THE XLPE CABLES OF 110 kV-

4. RESULTS OF MEASUREMENTS OF THE PHASE CONDUCTOR SELF IMPEDANCE AND THE LINE REDUCTION FACTOR
For the line of the length of 2.32 km:
Zph = ( j ) Ω and
r = – j0.1505
For the line of the length of 6,59 km:
Zph = ( j ) Ω and
r = – j0.1724
Equivalent specific soil resistivity, ρ = ?

5. EQUIVALENT SOIL RESISTIVITY EARTH PENETRATION DEPTH
shorter line: ρ = Ωm and δ = 20.9 m
longer line: ρ = Ωm and δ = m

6. EXPERIMENTAL TEST OF THE ANALYTICAL EXPRESSIONS FOR THE REDUCTION FACTOR OF CABLE LINES CONSISTING OF THREE SINGLE–CORE CABLES
- shorter line: r = – j and
longer line: r = – j0.1693

7. TESTING ANALYTICAL EXPRESSION FOR THE REDUCTION FACTOR FOR THE FAULT ANYWHERE ALONG A CABLE LINE
Measured value: r(l = 2.32 km) = j0.0641
- Formula that should be tested:
Values obtained by using the given formulas:
r(l = 2.32 km) = – j0.0607

8. APPARENTLY PARADOCSAL DIFFERENCE BETWEEN THE RESULTS OF MEASUREMENTS AND THE RESULTS OF THE CALCULATIONS
MEASUREMENT RESULTS:
- Shorter line: r = – j ;
- Longer line: r = – j i
- Fault on the line: r(l = 2.32 km) = – j0.0641
CALCULATION RESULTS:
- For both lines: r(ρ = 30 Ωm) = – j and
- Fault on the line: r(ρ = 30 Ωm, l = 2.32 km) = – j0.0365

9. INFLUENCE OF THE NUMBER OF GROUNDED SHEATHS ON THE VALUE OF CURRENTS THROUGH THE SHEATHS
Relative participation in conducting ground fault current through the sheath of the cable through which it passes:
reduction is from 60.66% to 46.31% , when the number of grounded sheaths is increased from one to two and
reduction is from % to 37.49% , when the number of grounded sheaths is increased from two to three

10. FISICAL MODEL OF THE CABLE FEEDING LINE INCLUDING THE FICTIVE CONDUCTOR SUBSTITUTING ALL OTHER METAL INSTALATIONS

11. EQUIVALENT CIRCUIT WHEN ONLY THE SHEATH OF THE CABLE THROUGH WHICH THE GROUND FAULT CURRENT PASSES IS GROUNDED AT BOTH LINE ENDS

12. SYSTEM OF EQUATIONS THAT IS OBTAINED FOR THE FORMERLY PRESENTED EQUIVALENT CIRCUIT

13. THE GEOMETRICAL SHAPE AND THE SPACE POSITION OF THE FICTIVE CONDUCTOR IN RELATION TO THE CABLE LINE

14. ANALYTICAL EXPRESSIONS FOR THE IMPEDANCES OF THE FICTIVE CONDUCTOR
Active resistance of the fictive conductor per unit length, R’c = ?
Medium radius of the fictive conductor, rc = ?

15. RELEVANT PARAMETERS OF THE FICTITIOUS CONDUCTOR BY USING THE MEASUREMENT RESULTS
Re{r} = Re{ }
Im{r} = Im{ } }

16. RELEVANT PARAMETERS OF THE FICTIVE CONDUCTOR IN THE CASE OF THE CONSIDERED CABLE LINES
SHORTER LINE:
R’c = 0.08 Ω/km i rc = 12.3 m,
LONGER LINE:
R’c = Ω/km i rc = 8.1 m.

17. - Shorter line: r = - 0.056 - j0.105, or | r | = 0.119 and
REDUCTION FACTOR IN THE CASE WHEN ONLY THE SHEATH OF THE CABLE WITH THE GROUND FAULT CURRENT IS GROUNDED
- Shorter line: r = j0.105, or | r | = and
- Longer line: r = j 0.083, or | r | =

18. EQUIVALENT CIRCUIT IN THE CASE WHEN ALL THREE SHEATHS ARE GROUNDED AT THE LINE ENDS

19. SYSTEM OF EQUATIONS ENABLING DETERMINATION OF THE ACTUAL REDUCTION FACTOR

20. THE WRONG/CRITICAL CASE: CABLES ARE LAID IN FLAT FORMATION AND GROUND FAULT CURRENT PASSES THROUGH ONE OF THE AUTER CABLES

21. PARAMETERS OF EQUIVALENT SHEATH SUBSTITUTING ALL THREE ACTUAL SHEATHS OF CABLES LAID IN TRIANGLE FORMATION

22. PART OF THE GROUND FAULT CURRENT PASSING THROUGH THE EARTH
ACTUAL VALUES OF THE REDUCTION FACTOR FOR THE LINE USED FOR THE EXPERIMENTAL MEASUREMENTS
SHORTER LINE:
r = j0.0245, or | r | ≈ 0.036
LONGER LINE:
r = j0.0170, or | r | ≈ 0.029
PART OF THE GROUND FAULT CURRENT PASSING THROUGH THE EARTH
without surrounding metal installations: 10.6% ;
with surrounding metal installations: 3.6% and 2.9%, respectively.

23. COMPARISON OF THE PREVIOUSLY KNOWN AND ACTUAL POTENTIAL AND POTENTIAL DIFFERENCES AT GROUNDING SYSTEMS OF SUPPLIED TS 110/10 kV
SHORTER LINE:
LONGER LINE:

24. CONCLUSIONS
Presented analytical procedure enables observing the whole grounding problem of distribution HV/MV substations into an realistic frame work.
It was shown that the part of the ground fault current passing through the earth is dramatically smaller than it was considered until recently.
3. General conditions for solving grounding problem of distribution HV/MV substations located in urban and suburban areas are much favorable than it was considered until recently.

25. REFERENCES
IEC , Ed. 2 (2003): ”Currents during two separate simultaneous line - to – line short circuits amd partial short – circuit currents through earth”
Lj. Popovic: ”Determination of the Reduction Factor for Feeding Cable Lines Consisting of Three Single-Core Cables”, IEEE Transactions on Power Delivery, Vol.18, No.3, July 2003, pp
Lj. Popovic: ”Improved Analytical Expressions for the Reduction Factor of Feeding Lines Consisting of three single-core cables”, ETEP, European Transactions on Electrical Power, Vo. 18, No. 2, March 2008, pp. 190 – 203.
Lj. Popovic: ”Influence of the Metallic Installation Surrounding the Feeding Cable Line on the Ground Fault Current Distribution in Supplied Substations”, IEEE Transactions on Power Delivery, Vol. 23, No. 4, October 2008, pp