SINTEF Energy Research

Optimal design of a subsea power grid

T. Trötscher, M. Korpås, J. O. Tande

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SINTEF Energy Research

Setting and drivers

More exchange capacity between countries

Large scale integration of off-shore wind

Shore power for oil and gas rigs

Scandinavian hydro power for balancing

New HVDC technology

2

Take a holistic approach

Do not build parallel infrastructure

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NORD.LINK / NorGer

Ekofisk Oil rig

Wind farm

•Hydro power•Reservoirs•Regulating

power

?

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The problem to be addressed…

4

…the number of possible cable configurations grows exponentially with the number of connection points. It is impossible to evaluate all combinations.

…and the challenge to overcome

0 5 10 15 20 25 3010

0

1020

1040

1060

1080

10100

10120

10140

Number of nodes

Nu

mb

er

of c

ab

le c

on

figu

ratio

ns

Problem: Connect off-shore wind farms and oil-rigs to the on-shore grid

Objective: Maximize social economic benefit

Exogenous variables:

Location and power rating of wind farms, possible land connection points, statistical description of wind and power prices. Consumption at off-shore loads

Unknowns: Where to build cables and with what power rating

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Solution It’s possible to formulate the problem as a standard

linear or quadratic optimization program by making some assumptions: Constant or linear marginal costs Linear representation of the underlying physical power grid

Stochastic nature of wind power generation and power prices are represented by a random sample of historical data

5

ii

im

mg

gmgm CLwfPXLXF ,,),(

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Example model

6

0o 3oE 6oE 9oE 12oE

54oN

57oN

60oN

63oN

Ber.

Sta.

Troll

Eko.

Møre

DE

Node CommentMøre Wind farm 1000MW

Troll Wind farm 1000MW and load 200MW

Ekofisk Wind farm 1000MW and load 200MW

Bergen Generation capacity 3000MW and load 2000MW

Stavanger Generation capacity 3000MW and load 2000MW

Wilhelmshafen Generation capacity 4800MW and load 2400MW

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Results

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0o 3oE 6oE 9oE 12oE

54oN

57oN

60oN

63oN

Ber.

Sta.

Troll

Eko.

Møre

DE

406

706

888

506

200

1519

112

881

0o 3oE 6oE 9oE 12oE

54oN

57oN

60oN

63oN

Ber.

Sta.

Troll

Eko.

Møre

DE

800

1000

800

1537

0o 3oE 6oE 9oE 12oE

54oN

57oN

60oN

63oN

Ber.

Sta.

Troll

Eko.

Møre

DE

200

800

1000

1000

Optimized grid Optimized grid, locked to radial connections

Optimized grid without wind power

788 mill. EUR 7531 mill. EUR!

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How large does the random sample need to be?

To take into account the stochastic nature of wind power generation and power prices, the optimization is conducted with regard to a random sample that represent various wind conditions and prices levels. How large must the random sample be?

9

Convergence for a sample size of 150. Model dependent!

1 2 3 4 5 6 7 80

1

2

3

4

5x 10

9 N=5 samples

Solution number

Co

st

1 2 3 4 5 6 7 80

1

2

3

4

5x 10

9 N=10 samples

Solution number

Co

st

1 2 3 4 5 6 7 80

1

2

3

4

5x 10

9 N=20 samples

Solution number

Co

st

1 2 3 4 5 6 7 80

1

2

3

4

5x 10

9 N=50 samples

Solution number

Co

st

1 2 3 4 5 6 7 80

1

2

3

4

5x 10

9 N=150 samples

Solution number

Co

st

1 2 3 4 5 6 7 80

1

2

3

4

5x 10

9 N=400 samples

Solution number

Co

st

Operation Cost Line cost

1 2 3 4 5 6 7 8 90

200

400

600

800

1000

1200

1400

1600

Line number

Line

rate

MW

Mean

1: Bergen-Troll2: Bergen-Ekofisk3: Bergen-Møre4: Stavanger-Troll5: Stavanger-Ekofisk6: Stavanger-Wilhelmshafen7: Troll-Ekofisk8: Troll-Møre9: Ekofisk-Wilhelmshafen

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Conclusion

The model provides plausible results Optimized grid is better than radial solution Value of wind power is given implicitly

Useful as a decision support tool Systematic approach Stepwise grid expansion

Future work Cost function for cables

Input Result Sensitivity analysis

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