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only [Cerveira et al., 2016] has considered power loss
in cables. However, [Cerveira et al., 2016] does not
take into account variable cable loads due to fluc-
tuating wind. [Bauer and Lysgaard, 2015] proposes
an Open Vehicle Routing approach for this problem
adding the planarity constraints on the fly. In this
Open Vehicle Routing version of the problem, only
one cable can enter a turbine, even if this is often
not the case in the reality. In [Bauer and Lysgaard,
2015], the possibility of branching cables in the tur-
bines (as we are doing), is mentioned as a future work.
However, the substation limits, that could be a major
constraint in practical applications, are not considered
in [Bauer and Lysgaard, 2015]. Different approaches
for the cable network design are provided in [Berzan
et al., 2011]. The suggested approach is a divide-and-
conquer heuristic based on the idea of dividing the
big circuit problem into smaller circuit problems. The
proposed MILP model cannot deal with more than 11
turbines. In [Hertz et al., 2012] the cable layout prob-
lem for onshore cases is studied. The onshore cable
problem is similar to the offshore one with the fol-
lowing differences. First of all, the cable can be of
two types: underground cables (connecting turbines
to other turbines or to the above-ground level), and
above-ground cables. In the first case, the cables need
to be dug in the ground. Due to the fact that parallel
lines can use the same dug hole, parallel structures are
preferred (until a fixed number). The above-ground
level cables need to follow existing roads. Such con-
straints do not exist in the offshore case.
The main contribution of this paper is to anal-
yse how the inter-array cable routing of real-world
wind farms can be improved by using modern opti-
mization techniques. A particularly challenging as-
pect in the cable routing design, is to understand if
one could limit power losses by optimizing cable rout-
ing. As a general rule, cables with less resistance are
also more expensive, therefore we would like here to
make a proper trade-off between investments and ca-
ble losses. We formulate the optimization problem
with immediate costs (CAPEX) and losses-related
costs as two separate goals. The two objectives can be
merged into a single objective by proper weighing of
the two parts. The weighing factor can be considered
fixed or can vary: this makes it possible to perform
various what-if analyses to evaluate the impact of dif-
ferent preferences (i.e. of different weighing factors).
The latter approach is important in cases where a pos-
itive pay-back is demanded within a short time hori-
zon, or where liquidity problems hinder choosing the
best long-term solution. We report a study of both
approaches on a set of real-world instances.
In order to perform the above analysis, we devel-
oped a MIP approach to optimize the routing. In the
computation of power losses, it is shown that wind
scenarios can be handled efficiently as part of data
preprocessing, resulting in a MIP model of tractable
size. Tests on a library of real-life instances proved
that substantial savings can be achieved.
The rest of the paper is organized as follows: Sec-
tion 2 describes our MILP model, first presenting a
basic model and then improving and extending the
formulation. In particular, we show how to model
power losses, and propose a precomputing strategy
that is able to handle this non-linearity efficiently, thus
avoiding sophisticated quadratic models that would
make our approach impractical. Section 3 compares
our optimized solutions with an existing cable layout
for a real wind farm (Horns Rev 1), showing that mil-
lions of euro can be saved. Section 4 is dedicated to
various what-if analyses. Subsection 4.1 describes the
real-world wind farms that we considered in our tests
while Subsection 4.2 shows the results of our opti-
mization on a testbed of real-world cases, reporting
the impact of considering power losses for all the in-
stances. Subsection 4.3 is dedicated to the Pareto opti-
mality study. Some conclusions are finally addressed
in Section 5.
2 MATHEMATICAL MODEL FOR
CABLE ROUTING
OPTIMIZATION
2.1 Basic Model
In the present paper we assume that the location of the
turbines has already been defined. We wish to find an
optimal cable connection between all turbines and the
given substation(s), minimizing the total cable costs.
The optimization problem considers that:
• the energy flow leaving a turbine must be sup-
ported by a single cable;
• the maximum energy flow (when all the turbines
produce their maximum) in each connection can-
not exceed the capacity of the installed cable;
• different cables, with different capacities, costs
and impedances, can be installed;
• cable crossing should be avoided;
• a given maximum number of cables can be con-
nected to each substation;
• cable losses (dependent on the cable type, the ca-
ble length and the current flow through the cable)
must be considered in the optimization.
On the Impact of using Mixed Integer Programming Techniques on Real-world Offshore Wind Parks
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