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Technology for Decentralised Generation and Storage Part II Project work

Grid Assets

Brandenburg University of Technology

Department of Power Distribution and High Voltage Technology Pfeiffer 2

Solution

First step: Calculation of impedances

110-kV-grid( )

6MVA2000

kV110Z1Q 05

2

,==

1102 = 0,05110

6,05Z1Q ==

0,0498Z0,995X 1Q1Q ==

0,0049X0,1R 1Q1Q ==

TransformerCorrection factor for transformer impedance will be neglected

( )0,551

MVA20

kV10,50,1Z

2

1T ==

( )0,055

MVA20

kV10,50,01R

2

1T ==

0,548RZX2

1T

2

1T1T ==

0,521X0,95X 1T0T == (Z0m is there included)

Cable 10,48km10/km0,0967

2

1R1K ==

0,9km10/km0,1792

1X1K ==

F9,12km10F/km0,4562C1K ==

Cable 2 0,48km5/km0,0967R1K ==

0,9km5/km0,179X1K ==

F2km5F/km0,456C1K 28,==

Zero-sequence impedances of the cable:

Because data for the zero-sequence impedance of the cable are not available, we use the

following estimated values:

1K0K R4R =

1K0K X4X =

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Technology for Decentralised Generation and Storage Part II Project work

Grid Assets

Brandenburg University of Technology

Department of Power Distribution and High Voltage Technology Pfeiffer 3

Second step: Definition of the symmetrical component networks

Zero-sequence system

Positive-sequence system

Negative-sequence system

Calculation of the impedances (from capacitances)

698jF4,56314sj

1

Cj

1Z

1C=

==

2792jF1,14314sj

1

Cj

1Z

1C=

==

559jF5,7314sj

1

Cj

1

Z 1C ===

Third step: Interconnection of the symmetrical component networks

From lecture EDS II we know:

210 III ==

0F210 IZ3UUU =++

This means, the symmetrical component networks have to be connected in series at faultlocation.

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Technology for Decentralised Generation and Storage Part II Project work

Grid Assets

Brandenburg University of Technology

Department of Power Distribution and High Voltage Technology Pfeiffer 4

In the next step we can simplify the three equivalent circuit diagrams.

Zero-sequence system

Due to the very large values of the impedances of the capacitances we can neglect the

impedances of cable 1 and cable 4 and get the parallel connection of the four capacitances:

( )279j

F1,142F4,562314sj

1

Cj

1Z

1C=

+==

Positive-sequence system

Negative-sequence system

The simplified equivalent component networks we can now interconnect:

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Technology for Decentralised Generation and Storage Part II Project work

Grid Assets

Brandenburg University of Technology

Department of Power Distribution and High Voltage Technology Pfeiffer 5

It is to be seen, that

- the impedance in the zero-sequence system is equivalent to the zero capacitance

- the shunt impedance in the positive sequence system is equivalent to the effective

capacitance

- the positive current is not flowing over the effective capacitance, because the

impedance in the parallel branch is smaller

- the impedance in the negative sequence system is very small and can therefore be

neglected

Fourth step:Calculation of the currents in 012-system

Due to the fact, that the voltage in negative-sequence system is negligible we can assume,

that10 UU =

( )Aj21kA0,02069

j2793

kV10I0 =

= (completely capacitive current)

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Technology for Decentralised Generation and Storage Part II Project work

Grid Assets

Brandenburg University of Technology

Department of Power Distribution and High Voltage Technology Pfeiffer 6

Fifth step:Calculation of earth fault current

Aj63I3I 0CE ==

Verification: A623kV10F11,4s3143C3I 1ECE === YU

Fifth step:Calculation of the voltages in 012-system

3

kV10U0

3

kV10U1

0U2

Sixth step:Calculation of the voltages in abc-system

003

kV10

3

kV10UUUU 210a =++=++=

03

kV10a

3

kV10aUUaUU 221

20b ++=++=

( )kVja10

3

kV103ja

3

kV101aU 2

b

===

03

kV10a

3

kV10UaaUUU 2

210c ++=++=

( ) kV10ja3

kV103ja

3

kV101aU 22c ===

Seventh step:Calculation of earth fault factor

3

3

kV10

kV10==

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Technology for Decentralised Generation and Storage Part II Project work

Grid Assets

Brandenburg University of Technology

Department of Power Distribution and High Voltage Technology Pfeiffer 7

Eighth step:Phasor diagrams