Shortest cable routing of heliostats
in solar tower power plants
Franziska Ossenbrink
Abstract
Data Cable: First Results
A software is implemented in Matlab that computes the optimal cable layout in a heliostat
field. To this day, cable routing in heliostat fields has not been optimized computer-based.
We will show that doing so is worthwhile. Our model considers acquisition and installation
costs as well as different types of cable and their characteristics.
Data and Power Cable
To maximize the energy output heliostats adjust their orientation every ten seconds. To be
able to rotate, each mirror is connected with a data cable for control and a power cable for
the motor to track the sun. Since both cable types have different requirements we consider
them as separate problems.
Data cable:
Fig. 6: One Hamiltonian path made of fiberglas. Cable length: 16.795,55m.
• Transmitted by fiberglas and copper cables
– Fiberglas cable: no length restriction, connects any number of heliostats
– Copper cable: has to be shorter than 100 meters, only connects two heliostats with
each other
Fiberglas Copper
Price [e/m]
2
1,29
The results of the computation of a Hamiltonian path can be seen in Figure 6.
We then modified the Esau Williams heuristic since only using fiberglas is expensive and we
thought that we might find a cheaper solution considering copper and fiberglas cables. The
most economic layout can be seen in Figure 7. Our approach:
• We divided the heliostat field into belts
• Three types of switches (see Figure 1 - 3), red = copper cable, blue = fiberglas cable
3
• We subdivided each of the belts in groups (dependent on how many heliostats belonged
to one belt and what kind of switch of type branching we chose)
2.5
7.6
• We chose the switch of type branching to have 8 copper cable outputs (and tried to
always connect 8 heliostats to these switches if it was possible)
2.5
2
7.4
2
1.5
7.2
1.5
1
7
1
0.5
6.8
0.5
0
6.6
0
Fig. 1: Switch endpoint.
6.4
-0.5
Fig. 2: Switch conductor.
-0.5
6.2
-1
Fig. 3: Switch branching with 8 copper
-1
-1.5
6
cable outputs.
-1.5
5.8
5.8
6
6.2
6.4
6.6
6.8
7
7.2
Power cable:
7.4
7.6
-2
-1.5
-1
-1
-0.5
0
0.5
1
1.5
2
2.5
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
3
• Consists of copper
• It matters how many heliostats are connected to a cable (the more heliostats the thicker
the cable)
Fig. 7: Connecting each group member to the center of the group with copper cables.
Red = copper cable, blue = fiberglas cable. Total cable length: 25.800,21m.
Comparison of the results
Fig. 4: Solar tower power plant PS10 placed near
Sevilla, Spain, cf [1].
Fig. 5: Assumed cable layout of PS10. Cable length: 21.089,25m.
Cost Model and Constraints
Cable length [m] Total costs of cabling [e]
Fiberglas Copper
Actual cable layout
21.089,25
42.178,50
Hamiltonian Path
16.795,55
33.591,1
Esau Williams heuristic 7.428,23 18.371.98
38.556,31
The installation costs that differ from country to country are not considered yet.
Our aim is to create a cable layout with minimal costs. The total costs consist of costs for
• Cable meters used to connect the heliostats
• Costs for cables and switches
• Installation costs (manpower)
In order to make our model as realistic as possible we consider the following constraints while
optimizing:
• Cables are allowed to branch
• Cables are not allowed to cross
• Further constraints relating to the particular cable type (e.g. different thicknesses for
the power cable, length restrictions, switches for the data cable)
What is next?
The computation and the software for the optimal layout for the data
cable is almost completed. Next, we focus on the power cable. We
want to modify the version of the Esau Williams heuristic that has been
used in [2] to consider different cable thicknesses dependent on how
many heliostats are connected to the respective cable. Finally, we want Fig. 8: Copper cable.
to test our software with the Redstone power plant that is going to be
equipped with 7560 heliostats. It is planned to be constructed in South Africa in 2019.
Collaboration
Joint work with Mark Schmitz and
Yibekal Gedle from TSK Flagsol
Algorithms
We use different heuristics to compute the layout as they yield to a good solution in an
acceptable lapse of time. The model is implemented stepwise.
At first we considered fiberglas cables only and did not allow branching. For this purpose we
created a Hamiltonian path by searching a solution for the travelling salesman problem. We
computed the nearest neighbors and then applied the 2-opt algorithm.
Then, we changed to the Esau Williams heuristic. We modified this algorithm several
times to avoid crossings and consider the different switches for the data cable.
References
[1] https://gothesolarway.files.wordpress.com/2015/06/spain.jpg, access 21st June 2017.
[2] Julia Lust. Shortest cable routing in offshore wind farms, Bachelor thesis, 2016.
[3] Raja Jothi and Balaji Raghavachari. Revisiting esau-williams- algorithm: on the design of local access networks. In Proceedings
7th INFORMS Telecommunications Conference (Telecom), Boca Raton, Florida, pages 104-107, 2004.
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