Analysis of the magnetic coupling influence

between different feeders on unbalanced

distribution networks

Code: 12.004

Nélio Alves do Amaral Filho, Mariana Simões Noel da Silva,

Leandro Ramos de Araujo, Débora Rosana Ribeiro Penido

Araujo

Electrical Engineering, Federal University of Juiz de Fora,

Minas Gerais - Brazil

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• Electrical distribution systems (DS) have attracted the attention of a

growing number of researchers

✓ Electric power quality

▪ Unbalances

✓ Increased demand for electricity

▪ Operation under harsher conditions

✓ Greater need to represent all DS-related characteristics and effects

✓ An efficient representation of the system components

✓ Tools able to evaluate and analyze the DS more accurately

Introduction

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• Several possible analyses can be performed in distribution systems

studies

✓ Electromagnetic coupling (mutual coupling) that occurs between

two or more feeders when physically arranged in parallel

✓ Practice done by the utilities

✓ Feeders can be found traveling along▪ the same path and sharing a common pole;

▪ the same power corridor on separate poles.

✓ The existing mutual coupling can significantly affect the system

✓ This coupling is usually neglected in most studies

Introduction

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• Analysis of the electromagnetic coupling influence between different

feeders

• Backward/Forward Sweep (BFS) Method

• Different constructive characteristics

✓ Length of the distribution feeders sections

✓ Separation distance between the conductors

✓ Phase sequences and geometry of the conductors on the poles

Objectives

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Model of the distribution feeders in parallel

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  (1)1

0,07537 ln 6,74580ii c d

i

Z r r jRMG

        (2)1

0,07537 ln 6,74580ij d

ij

Z r jD

                       '      '      '

                       '      '      '

                       '       '      '

'     '     '     ' '    ' '    ' '

aa ab ac aa ab ac

ba bb bc ba bb bc

ca cb cc ca cb cc

phase

a a a b a c a a a b a c

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z Z ZZ

Z Z Z Z Z Z

'     '     '     ' '    ' '    ' '

'     '     '     ' '    ' '    ' '

   (3)

b a b b b c b a b b b c

c a c b c c c a c b c c

Z Z Z Z Z Z

Z Z Z Z Z Z

, 1 1    , 1 2

, 2 1 , 2 2

  (4)  

abc F F abc F F

phase

abc F F abc F F

Z ZZ

Z Z

A B C

B C A

n

Mutual: same feeder

Mu

tual

: di

ffe

ren

t fe

ede

r

FEEDER 1

FEEDER 20,76m

1,37m

0,6m

0,6m

Backward Forward Sweep Algorithm

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1

VS=8kV

3

4

6

5

9

7

12

15

11 14

8

F1

F2

2

10

13

16

2 4

1

3 7 5

6

9

813

12

10

11 15

14

16

Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

Layer 6

S1

S2

F1 F2

, 1 , 1 1    , 1 2 , 1

, 2 , 2 1 , 2 2 , 2

        (5)  

abc F abc F F abc F F abc F

abc F abc F F abc F F abc F

V Z Z I

V Z Z I

Layer separation

Calculation of

Nodal Currents

Backward

Sweep

E1

Variables

initialization

Forward Sweep

Stop when a coupling

section is found

Mutual coupling:

Forward Sweep

using eq. (5)

Convergence Test

|ΔV| < ε

Y

N

Have all voltages

been updated?

Y

N

E2

E3

E4

E6.1

E6.2

E6.3E7

Identification of

sections that share

the same pole

E5

End

.

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Simulated systems

650

651

VS=4,16 kV

632

671

675

6320

67506710

800

VS=24,9 kV

802 806

808

810

812 814 850

890

IEEE 13M IEEE 34M

• To investigate the impact of the mutual coupling, 2 cases were

analyzed✓ Case 1: ignoring the effect of the mutual impedances between different

feeders (without the mutual coupling representation)

✓ Case 2: considering the effect of these mutual impedances (mutual

coupling)

• For comparison and results presentation✓ It was calculated the difference between the absolute values obtained from

each case, for a same variable (voltage, current or electrical losses)

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Simulated systems

2 1

 1

  (6)k k

k

C C

kC

V VV

V

Feeders length

Experimental results

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IEEE 13M

0

2

4

6

8

10

12

14

16

18

20

0,1 0,5 1 1,5 2

Phase A

Phase B

Phase C

Factor k

Max

imum

vol

tage

dif

fere

nce

(%

)

0

2

4

6

8

10

12

14

16

18

20

0,1 0,5 1 1,5 2 2,5 3 3,5

Factor k

Max

imum

vol

tage

dif

fere

nce

(%

) Phase A

Phase B

Phase C

IEEE 34M

Distance between conductors

Experimental results

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0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,15 0,3 0,5 0,75 1 1,25 1,5 1,75 2

Phase A

Phase B

Phase C

Distance between the center conductor and the left conductor (m)

Vo

ltag

e d

iffer

ence

in b

us 6

75 (

pu)

IEEE 13MIEEE 34M

0

0,5

1

1,5

2

2,5

0,2 0,3 0,6 1 2 4 10 50

Vertical distance between feeders on pole (m)

Vo

ltag

e d

iffer

ence

in b

us 8

90 (

%) Phase A

Phase B

Phase C

B A C

A B C

n

FEEDER 1

FEEDER 2

Dx

Dy

Different phase sequences or conductor geometry on the pole

Experimental results

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Voltage - Phase A

Voltage - Phase B

Voltage - Phase C

Current - Phase A

Current - Phase B

Current - Phase C

Losses

Eq. Triangle

ABC - C'B'A'

ABC - A'B'C'

BAC - C'A'B'

BAC - B'A'C'

Maximum difference (%)

0 0,25 0,5 0,75 1 1,25 1,5 1,75 2

Voltage - Phase A

Voltage - Phase B

Voltage - Phase C

Current - Phase A

Current - Phase B

Current - Phase C

LossesEq. Triangle

ABC - C'B'A'

ABC - A'B'C'

BAC - C'A'B'

BAC - B'A'C'

Maximum difference (%)

IEEE 34MIEEE 13M

A B C

B C A

n

FEEDER 1

FEEDER 2

C B C

A

n

FEEDER 1 FEEDER 2A

B

0,6m

2,13m

• The effect of the mutual coupling may become significant in certain

conditions

✓ System configuration;

✓ Long length of feeders sections that are in parallel;

✓ Small distances between the phase conductors, both vertically and

horizontally;

✓ Specific phase sequences.

• The mutual coupling influence can be considerable not only in the

voltage, but also in both current and electrical losses

• The mutual coupling representation in the power flow analysis

algorithms for distribution systems should not be neglected

Conclusions

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The authors thank the Pos-Graduate Program in Electrical Engineering

(PPEE) of the Federal University of Juiz de Fora, CNPq, FAPEMIG, and

CAPES for the incentive and support.

Acknowledgments

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References

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