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1 INTRODUCTION AND MOTIVATION
Ensuring quality of life through provision of
communal infrastructure across the society is one of
the cornerstones of modern civilisation. Technology is
to devise solutions for robust and uninterrupted
telecommunications and logistics services, and water
and power provision to remote and/or isolated
communities that contribute to societal development.
Power supply to remote and isolated communities has
become a burning problem, since electricity drives
numerous essential technology systems, thus
providing fundamentals of developments and
survival. Provision of electricity for societies on
remote and isolated islands is a category within the
general problem, concerned by numerous research
teams across the world. Self-sustainable approaches
usually take into account the opportunities to
generate electricity from resources at hand, and
manage the supply through smart micro-grid
solutions [1].
We contribute to the problem solution through our
research in model development for a spatially
constrained remote island micro-grid, that will
optimise resource utilisation through advanced
compliance of resources availability quality and
utilisation costs, and the micro-grid capacity, load,
and operational cost [2]. The over-all model
development requires evidence-based model
development of the micro-grid components, as well as
the model of their optimised system integration into
an intelligent self-tuning micro-grid [1, 4]. Here we
present the results of experimental data-based model
development of a small wind turbine output in
relation to the essential set of wind energy predictors.
Three candidate models were developed using
machine learning model development approach [3, 4],
A Small Wind Turbine Output Model for Spatially
Constrained Remote Island Micro-Grids
D. Žigman
1
, K. Meštrović
1
& T. Tomiša
2
1
Zagreb University of Applied Sciences, Zagreb, Croatia
2
University of Zagreb, Zagreb, Croatia
ABSTRACT: Modelling operation of the power supply system for remote island communities is essential for its
operation, as well as a survival of a modern society settled in challenging conditions. Micro-grid emerges as a
proper solution for a sustainable development of a spatially constrained remote island community, while at the
same time reflecting the power requirements of similar maritime subjects, such as large vessels and fleets. Here
we present research results in predictive modelling the output of a small wind turbine, as a component of a
remote island micro-grid. Based on a month-long experimental data and the machine learning-based predictive
model development approach, three candidate models of a small wind turbine output were developed, and
assessed on their performance based on an independent set of experimental data. The Random Forest Model out
performed competitors (Decision Tree Model and Artificial Neural Network Model), emerging as a candidate
methodology for the all-year predictive model development, as a later component of the over-all remote island
micro-grid model.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 16
Number 1
March 2022
DOI: 10.12716/1001.16.01.16
144
and assessed for their performance, thus distilling the
optimal small turbine output model as a component
of the spatially constrained remote island micro-grid
model. Research results presented in this manuscript
may serve additional purpose of modelling the
alternative power source on vessels, either as a single
energy source, or as a component of the vessel’s
micro-grid.
2 METHODOLOGY
The approach taken utilised experimental data, and
followed the essential statistical research principles of
experimental model development [3, 4].
2.1 Over-all concept
Experimental data observed were analysed
statistically, and the machine learning approach [3, 4]
was utilised in development of three candidate
predictive models of a small wind turbine output
based on two wind predictors: wind speed and wind
direction. Model performance assessment was
conducted for all three models, using a common set of
descriptors, including Predicted-vs-Observed (P-O)
diagram, and the adjusted R-squared coefficient.
2.2 Data
Observations were taken at the experimental research
facility Sotavento in Santiago de Compostela, Galicia,
Spain (Figure 1), and provided in tabular format on
the internet [5]. A small wind turbine used was
manufactured as Bornay 1500 Inclin, extended the 1.5
kWh power rating with fibre-glass, and carbon fibre-
blades. In this research, we were concerned with the
Spring-time period, with the following duration of the
experiment selected: 1 May, 2019 – 31 May, 2019. The
experimental data set was split between input and
output data using variable selection, as follows: (i)
inputs (predictors): wind speed [m/s], wind direction
[°], (ii) output (target): cumulative generated energy
[kWh].
Figure 1. Location of a small wind turbine experimental site
2.3 Model development methodology
Machine learning-based approach was utilised in the
predictive model development procedure [3, 4]. Three
machine learning-based candidate models were
developed: (i) decision tree, (ii) random forest, and
(iii) artificial neural network with a single hidden
layer. The selection of candidate model approaches
was taken based on results of the statistical properties
of data.
Decision tree [3] is an optimisation-based model
development approach that returns a tree-like
structured model, comprising the root- (upper),
decision- (intermittent), and leaf-nodes (model
decisions). The model develops in two essential steps:
(i) the feature vector space (X1, X2, …, Xp) is divided
into non-overlapping regions Ri, and (ii) every new
observation of feature vector is assigned to region Ri
based on the mean value of the previous (training)
observations in the same region Ri. Decision tree is a
simple and clear model easily deployed for both the
human assessment and as a computer algorithm. Its
shortcomings include potential over-fitting
(modelling noise rather than a signal) and poor
performance with continuous data.
Random forest utilises the decision-tree concept to
form a forest of decisions that eventually yield the
random forest decision. The random forest
development approach requires the original data set
to be split into a number of sub-sets with randomly
selected data. Then, decision tree models are
developed with every sub-set. Decision, or, estimate,
related to new set of observations is performed by all
the decision trees, and then integrated using either the
democratic procedure (majority/average of votes of
separate decision trees) or using weighted approach,
favouring influential decision trees. Random forest
model encompass variance in data successfully and
tackles over-fitting efficiently, but is computationally
intensive, and not suitable for real-time predictions.
Artificial neural network mimics a human or
animal ones, with artificial neurons being kicked-off
by the appropriate input level, and exchanging their
outputs with other neurons it is connected with.
The artificial neural network (ANN) consists with
neuron layers that receive the inputs (input layer),
those that reside internally within the network
(hidden layers), and the one that provides
decision/estimation results (output layer). While
theoretically an ANN may consist of many internal
layers, a one- or two-hidden layer-architecture may
produce optimal results. ANN is suitable for
modelling the complex systems, where prediction of
behaviour is required without explaining the system.
Model performance assessment was conducted
using two essential model performance indicators: (i)
Predicted-Observed diagram, (ii) adjusted R-squared
coefficient. The P-O diagram is a simple graphical
indicator of model’s performance, designed as a
graphical presentation of observed-predicted pairs.
The adjusted R-squared indicator is defined as
follows. Let denote observations as
y
, and model-
derived estimates as
x
. The Coefficient of
Determination (R-squared) indicator is then defined
as given in (1), with the
y
denoting mean of
observations.
( )
( )
2
2
1
2
1
1
n
ii
i
n
i
i
yx
R
yy
=
=
−
−
−


(1)
145
The Coefficient of Determination may mislead
mode comparison, so the adjustment to model
structure given in (2) is suggested, yielding the
adjusted R-squared indicator, with:
sn … number of observations,
p … number of predictors.
( )
22
1
11
n
n
s
adjR R
sp
−
= − − 
−
(2)
3 RESEARCH RESULTS
This Section contains research results in a form of
developed predictive models definition and
performance assessment, as described in Section 2.
Predictive model development procedure was coded
in the open-source R framework for statistical
computing, using the R library rattle and associated R
libraries.
3.1 Decision Tree Model (DTM)
Decision tree model was developed using a common
approach. Statistical analysis embedded in the model
development procedure found wind direction
statistically insignificant, rendering the model based
on the wind speed only. DTM is shown in Figure 2.
Validation sub-set of data was used in the DTM
assessment procedure, with the results presented in
Figure 3. Although performance analysis returned a
rather high adjusted R-squared value, the model’s P-O
diagram returns layered structure with significant
variations from the central line. Further to this, DTM
model tends to increase inaccuracy for values at the
edge of the modelling range.
Figure 2. Decision tree model of a small wind-turbine
output
Figure 3. DTM performance assessment
3.2 Random Forest Model (RFM)
Model consisted of 500 decision trees build-up on the
randmised sub-sets of the original observations. The
RFM performance analysis returned a very high
adjusted R-squared index value, in justification of the
good model fit. Again, RFM was assessed based on a
separate validation data, compiled as a sub-set of the
original population. P-O diagram (Figure 4) shows
that observation-predicted values tie up with the P-O
line firmly, with just a handful of exceptions.
Figure 4. RFM performance assessment
3.3 Single Hidden Layer Neural Network Model
(SHLNNM)
The SHLNNM was developed using the training set
of experimental data, with definition given in Table 1.
Table 1. Definition of the SHLNNM
_______________________________________________
Weights for node h1 (hidden layer)
_______________________________________________
b → h1 i1 → h1 i2 → h1
120.80 -352.85 306.06
_______________________________________________
Weights for node o (output layer)
_______________________________________________
b → o h1 → o i1 → o i2 → o
-768.10 254.34 166.94 -0.10
_______________________________________________
The SHLNNM parameters (Table 1) are described
as follows:
b … denotes the bias associated with the node
h1 … marks the hidden layer node 1
i1 … marks the input node 1 (or: the input variable, or
predictor, 1)
i2 … marks the input node 2 (or: the input variable, or
predictor, 2)
o … marks the output node
146
Figure 5. SHLNNM performance assessment
The SHLNNM performance assessment revealed
considerable adjusted R-square value, but the model
is outperformed by the other candidates.
Additionally, the P-O diagram (Figure 5) shows a
remarkable deviations from the linear fit for excessive
(very small and very high) values.
4 DISCUSSION AND CONCLUSION
The research presented aims at development of a
small wind turbine model, based on experimental
data collected during May 2019 in near coastal are of
northern Spain, and deployment of machine learning
techniques, related to statistical properties of the
experimental data set. The model is set to become a
component of the over-all micro-grid model supposed
to be deployed in small remote and isolated island
communities, or on vessels or fleets.
Three candidate machine learning-based models of
a small wind turbine output were developed using the
R framework for statistical computing: (i) Decision
Tree Model (DTM), (ii) Random Forest Model (RFM),
and (iii) Artificial Neural Network Model. While all
three models extends high goodness-of-fit, their
response stability over the range of observation values
varies significantly. The RFM performance extends far
the best adjusted R-squared, with a a linearity of
prediction across the range of observation, rendering
it as the most suitable model of a small wind turbine
output.
Research will continue with the model
development that will encompass variance of wind
scenarios throughout the year, followed by its
integration within the over-all spatially constrained
remote island micro-grid model.
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https://windexchange.energy.gov/small-wind-
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