The resonance of transmission
MacNeill, El-Hawary, and Molloy highlight the unique
electrical characteristics of submarine cables that
need to be taken into account when specifying the
transmission of power from marine energy converters.
Aaron MacNeill
Mohamed E. El-Hawary
Sue Molloy
Who should read this paper?
All those with an interest in or responsibility for the design and development of
marine energy power systems.
Why is it important?
There is a fundamental difference between transmitting electrical power
through overhead conductors and submarine cables. For overhead lines, a
bare conductor can be used because, under normal conditions, air is a good
natural insulator. Salt water, on the other hand, is electrically conductive and,
therefore, the cable must be isolated from its surroundings. In simple terms,
this means that the conductor must be wrapped in three different layers –
one to electrically isolate the conductor from the seawater, one to keep out
moisture, and a third to protect the cable from abrasion. The thickness and
composition of these layers of wrapping, together with the design of the
conductor (single or triple core), impart unique characteristics to the cable in
terms of resistance (the opposite of conductance), capacitance (the ability to
store electrical energy), and inductance (a unique characteristic of AC circuits
whereby current flowing through a conductor produces a magnetic field,
which in turn induces a current, both in the conductor itself and the surrounding
area). The authors simulate the performance of various designs of submarine
cables in terms of these three parameters. Their findings will assist in
tailoring cable geometry for specific marine energy applications such that
power quantity and quality is optimized.
About the authors
Aaron MacNeill is a PhD candidate in electrical engineering at Dalhousie
University. His research interests include power system network modelling,
transient analysis and operation/control. Mohamed El-Hawary is a Professor
of electrical and computer engineering at Dalhousie University and has pioneered
many computational and artificial intelligence solutions to problems in economic/
environmental operation of power systems. Sue Molloy is the engineer in
residence for tidal power research in the Faculty of Engineering at Dalhousie
University, where she specializes in marine renewable energy and eco-ships.
104 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
Copyright Journal of Ocean Technology 2013
SUBMARINE POWER CABLE ELECTRICAL PERFORMANCE EVALUATION
FOR MARINE ENERGY APPLICATIONS
Aaron M. MacNeill, Mohamed E. El-Hawary, Sue Molloy
Dalhousie University, Halifax, NS, Canada
ABSTRACT
This paper reviews the constructional details of single-core and three-core AC power submarine
cables. The inductance and capacitance electric circuit parameters are then evaluated in terms
of the geometry, electromagnetic, and electrostatic (dielectric) properties of the conductors and
insulation of the cable. Given the electric circuit parameters, two-port network models are then
evaluated which allows the determination of steady state electrical performance characteristics
of the cables. The study examines the effect of the cable length on the receiving end (cable
output) voltage, active, reactive power and performance indices such as transmission efficiency
and voltage regulation.
KEY WORDS
Submarine power cable; Underwater cable; Cable performance; Line parameters; Marine energy
NOMENCLATURE
σ
ω
ε
μ
L
Z
a
b
=
=
=
=
=
=
=
=
=
conductivity
radial frequency
permittivity
permeability
inductance
impedance
inner radius of the sheath
radius of the core conductor
length of transmission line
Copyright Journal of Ocean Technology 2013
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 105
INTRODUCTION
Ocean current power generation systems use
the power of wave and tidal currents to generate
renewable energy. Bringing electric power to
shore requires electrical cables. Submarine
power cables have been used for offshore wind
transmission, bulk power transmission or to
link power to offshore structures and islands.
Submarine power cables are also used in
applications such as offshore wind farms. The
choice of cable will affect both the quality of
received power and the security of the power
link. There are various cable design types that
could be used to transmit power to and from
shore. A cable’s line parameters must be
evaluated in order to determine how the cable
performs at transmitting electrical energy
under various operational conditions. The
selection of cable is site-specific and there
are many other criteria other than cable
electrical characteristics that will inform the
cable selection.
The steady state electrical performance of a
cable under normal operating conditions is
defined by the following variables: the receiving
end voltage, active power, reactive power,
voltage regulation, and the transmission
efficiency. Line parameters are evaluated based
on studying the magnetic and electric fields
established by power flow in the cable. They
depend solely on the materials used and
geometry of the cable. This implies that, by
varying the materials and geometry used for
the different cable layers, the quality of the
power at the receiving end of the transmission
line could be controlled. There are specific
challenges associated with transmitting marine
energy ashore since the power generated varies
106 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
depending on the height of the wave or
velocity of tidal current that vary with time.
The results of our work indicate that when
practically feasible, and for the same power
carrying capacity and transmission length,
overhead lines outperform an equivalent
submarine power cable. Cables provide positive
reactive power compensation for the system.
As the transmission distance increases, the
active power delivered is reduced and DC
power transmission is required.
SUBMARINE CABLES
An electrically conductive substance, fresh
or salt water, surrounds submarine cables.
Therefore, a layer of insulation must be wrapped
around the conductor to confine the current
flow through the core conductor and not leak
to the surrounding seawater. A protective layer
is used to protect against water damage. A
metallic (lead, aluminum, or copper) or polymer
sheath is introduced around the insulation to
keep water and water vapour from reaching the
insulation. Lead is the ideal metal to use for
the sheath because it can completely keep
moisture away from the insulation [Worzyk,
2009; Pieroni and Fellows, 1979; Thue, 1998].
An armour is a layer or multiple layers of steel
or copper round wire that make up the outermost
layers of the cable required to protect the cable
from random external causes of possible damage
such as the tensional forces produced when
laying the cable, or external sources.
There are many considerations in designing the
different layers of the cable. The differences in
construction impact the performance of
submarine power cables. The cable’s electrical
Copyright Journal of Ocean Technology 2013
Figure 1: Assumed geometrical cable model.
performance characteristics are the focus of
this paper. Figure 1 shows a simplified geometric
model for submarine cables with single and
three conductors [Sadiku, 2007; Pieroni and
Fellows, 1979; Hauge et al., 1988; El-Hawary,
1995; Thue, 1998; Worzyk, 2009].
The electrical resistance of the core conductor
affects the cable’s efficiency and depends on
factors such as the conductor’s material;
construction type such as a solid core, stranded
core, profiled core, or segmental core conductor;
and electromagnetic phenomena such as
proximity effect and skin effect [Worzyk,
2009; Sadiku, 2007; Thue, 1998].
The sheath/armour and armour/seawater
insulation layers are used for protection between
the sheath and armour and to keep water out
of the armour, respectively [Worzyk, 2009;
Pieroni and Fellows, 1979].
While the actual construction of submarine
cables is not that simple, valid approximations
are available. In three-core submarine cables
there is a conductor screen between each of the
core conductors and the insulation; outside the
insulation layer there is an insulation screen,
water swellable tapes, a metallic shield, and a
polyethylene jacket. These layers are used to
Copyright Journal of Ocean Technology 2013
prevent water and humidity from attacking the
cable’s insulation as well as electrically shield
each of the core conductors from themselves.
Around the bundle of three conductors there is
a binder tape and polypropylene string bedding.
This keeps the three cables and filler bound
together. Encompassing this are layers of
galvanized steel armour with a polypropylene
separator between armour layers and
polypropylene serving outside the final layer
of armour [ABB, 2010]. Noting that a metallic
shield surrounds each of the conductors and
knowing that this shield is electrically grounded
means that each of the core conductors is
electrically shielded from the others and the
outside environment. This allows for the
disregard or combination of materials that have
relative permeability of one. The separation
layers between the armour can be safely
neglected since the layer is very thin and exists
a significant distance away from the cable’s
centre. The model developed to analyze the
submarine cables does not account for the
presence of extra conductors that are not core
conductors. The assumptions are summarized as:
• The conductor screen is part of the insulation.
• Water swellable tape is part of the insulation.
• Binder tape and polypropylene string bedding are part of the insulation layer between the bundle and armour layers.
• Water swellable tape and polyethylene jacket that surround the individual core sheaths are part of the filler.
•
The armour layers are stacked directly on top of each other; the polypropylene insulation serves as the outer insulation layer of the cable.
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 107
• Potential pilot and fibre optic wires are neglected.
performed to determine the surface impedances
of the various cable layers. Applying the
method of composition of impedances
• The cable is totally surrounded by seawater. [MacNeill, 2012; Bianchi and Luoni, 1976;
[Bianchi and Luoni, 1976]
Schelkunoff, 1934] will allow the determination
of the net total impedance – based on the
LINE PARAMETERS
resistance as the real part, and the inductive
reactance 2πfL, with L= inductance – of the
The line parameters – resistance, capacitance,
cable layers in terms of geometry and material
and inductance of the cables – are developed
properties. The surface impedances of a hollow
for single-core and three-core submarine cables. cylinder with an inner radius a, and outer
These line parameters will be used in the tworadius b are given by [MacNeill, 2012;
port network model of transmission links such Schelkunoff, 1934; Carson and Gilbert, 1921]:
that the cable’s steady state performance can
be evaluated.
(1)
Single-Core Cable Line Parameters
The line parameters for a single-core submarine
cable are determined based on the geometrical
model shown in Figure 1. Figure 2 shows the
cross sectional view of this cable, denoting the
various layers of conductors and insulators and
their associated thicknesses.
(2)
(3)
Where
,
σ is the conductivity of the cylindrical shell, ω
is the radial frequency of the applied
electromagnetic wave, ε is the permittivity of
the cylindrical shell, and μ is the permeability
of the cylindrical shell. Applying the principle
of composition of impedances to the cross
section shown in Figure 2, the following
equation relating to the surface impedances of
the various cable layers can be developed
[MacNeill, 2012]:
(4)
Figure 2: Cross sectional view of cable model.
Electromagnetic field analysis of the cables
(cross section is shown in Figure 2) can be
108 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
Where L0, L01, and L02 are the inductances of
the insulator layers given by [Schelkunoff,
1934]:
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(5)
where
The value obtained, Z, represents the resistance
and inductance of the cable through the
following relationship [El-Hawary, 1995;
Schelkunoff, 1934]:
(6)
and
To find the capacitance of the cable while noting
that the sheath is grounded [Westerwell and
Price, 2006; Doyen et al., 1989; Wolff and
Elberling, 2000; Thue, 1998] helps in reducing
the capacitance model to that of the non-ideal
coaxial cable given by [Sadiku, 2007;
Schelkunoff, 1934]:
(7)
Where a is the inner radius of the sheath, and
b is the radius of the core conductor of the cable.
Three-Core Cable Line Parameters
The line parameters of a three-core submarine
cable are determined using the assumed
geometrical configuration shown in Figure 1.
Analyzing the magnetic field produced by the
three-core conductors can be used to approximate
the inductance of the three-core submarine
cable. Figure 3 shows the geometry for the
three-core cable.
From this figure the inductance of all the cable
layers just outside the bundle can be found using
the following expression [MacNeill, 2012]:
(8)
Copyright Journal of Ocean Technology 2013
Figure 3: Three-core cable geometry.
This can be applied to find the inductance
contribution of the various cable layers that
surround the bundle of core conductors. The
inductance of the cable’s outer layers can be
combined with the self-inductance of each
core conductor and the mutual inductance of
each core conductor with its adjacent conductors.
It is assumed that the core conductors are
transposed, such that the mutual inductance
between core conductors is equalized. The
mutual and self-inductance for each phase
of the cable can then be evaluated as
[El-Hawary, 1995]:
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 109
(9)
The total equivalent inductance can be evaluated
combining components of the inductance.
(10)
The capacitance of a three-conductor submarine
cable can be determined effectively for two
different sheathing configurations: sheaths
surrounding each of the core conductors or a
sheath surrounding the bundle. It is possible to
have sheaths around each core conductor and
another sheath that surrounds the total bundle,
where one of the sheaths is required to be
metallic and the other sheath may be metallic
or polymer. Any of these combinations can be
reduced to the same approach as that for the
two sheathing techniques discussed above. In
the first case where the metallic sheath surrounds
each of the core conductors, the capacitance
can be found from the non-ideal coaxial cable
case [Sadiku, 2007; Schelkunoff, 1934].
(12)
To support this assumption, we use the following
observation concerning the resistance of
submarine cables: the resistance is proportional
to the energy lost in the core conductor and the
energy lost in each of the cable’s layers due to
the magnetic field’s induced electromotive
force (EMF). This applies to both cable types;
however, for the three-conductor submarine
cable, there is a cancellation effect for balanced
phase voltages, which are separated by 120
electrical degrees. This results in a sum of
currents that is zero at each time instant. Due
to the offsetting of each conductor from the
centre of the cable, the magnetic field outside
of the bundle will not be zero. The out of
phase voltages reduce the magnetic field
(11)
This is true based on the same reasoning used
for the single-core submarine cable. The
capacitance can then be found from Equation 7.
In the case where the metallic sheath surrounds
the bundle of conductors the method of images
can be applied for a coaxial cable with several
off centre cores.
The resistance of a three-conductor submarine
cable can be found from the AC resistance of
each core conductor given by:
110 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
Figure 4: Variation of magnetic field outside three-core cable with
distance from centre.
Figure 5: Variation of magnetic field outside single-core cable with
distance from centre.
Copyright Journal of Ocean Technology 2013
appreciably outside the bundle of conductors.
This allows for the approximations that there
will be minimal magnetic field induced EMF
in the outer layers of the submarine cable.
Figures 4 and 5 show the magnetic field
surrounding a triple-core and single-core cable
where the line current is assumed to be 1 amp.
(13A)
(13B)
Where the values A, B, C, and D are defined
as follows [El-Hawary, 1995]:
In Figures 4 and 5 each curve represents the
magnetic field around the perimeter of the
three-conductor cable, where the horizontal
axis corresponds to the angular position around
the cable. Each line in each figure corresponds
to a distance away from the cable’s centre; the
distance from the cable’s centre is given in the
legend of each figure.
These assumptions yield close approximations
for the line parameters for a three-core
submarine cable.
Two-Port Network Analysis
Having obtained the line parameters from the
submarine cable geometry and material
properties, a two-port network analysis can be
used to find the relationship between the cables’
input (sending end) and output (receiving end)
variables. The two-port network is an
equivalent circuit that can be used to represent
a transmission line as shown in Figure 6.
(14)
(15)
(16)
(17)
where
and
,
is the length of the transmission line.
With the sending-end voltage, apparent power,
and power factor specified, the receiving end
voltage, voltage angle, power, reactive power,
power factor, efficiency, voltage regulation,
and Thevenin equivalent impedance can be
determined. These indices define the steady
state performance of the line. The receiving
end voltage and current are found directly
from knowledge of the sending end voltage
and current and solving Equations 13A and
13B [El-Hawary, 1995].
The receiving end power is given by:
Figure 6: Two-port network model.
Analyzing this equivalent circuit, the following
relationships relate the input (sending end) to
the output (receiving end) of the cable
[El-Hawary, 1995]:
Copyright Journal of Ocean Technology 2013
(18)
The receiving end reactive power is given by:
(19)
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 111
The transmission efficiency is given by:
(20)
The receiving end power factor is then:
Figure 7: Thevenin’s equivalent model.
(21)
The voltage regulation at the receiving end of
the transmission line is defined as the difference
between rated and no load voltages normalized
by the rated voltage. The no load voltage can be
found from Equation 13A by setting Ir=0. The
voltage regulation is then expressed as follows:
(22)
The Thevenin equivalent impedance of the
cable is defined as follows:
(23)
The Thevenin equivalent voltage is the receiving
end voltage at no load (zero receiving end
current).
(24)
This and the transmission line’s Thevenin
equivalent impedance can be used to model
the transmission line interconnection with the
grid. Note also that the grid can be represented
as a Thevenin equivalent circuit. Figure 7
shows the interconnection between the Thevenin
equivalent models for the submarine cable
and the grid.
112 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
In Figure 7 it is important to note that under
normal operating conditions, power is meant to
flow from the receiving end of the submarine
cable to the grid. The current flow through this
equivalent circuit model is defined as the
difference between the grid voltage and
receiving end voltage divided by the sum of
the equivalent Thevenin impedances. If the
receiving end voltage and grid voltage are of
the same magnitude then to have a current
flow there must be a difference in phase
between the two sources. If the receiving end
phase angle is assumed to be zero degrees,
then the grid phase angle must be a small
negative angle in order to have the correct
current flow.
RESULTS
Based on manufacturer supplied cable
specification sheets, the line parameters for
both a single-core and three-core submarine
cable can be calculated. Simulation results
establish three curves for each of the performance
indices. One curve (red) represents the simulation
using line parameters provided by the
manufacturer of the specific cable type; a second
curve (blue) uses the line parameters that were
calculated from the manufacturer’s cable
geometry; and finally a curve (green) represents
the equivalent set of overhead transmission
lines. The equivalent set of overhead
transmission lines uses the same core conductor
radius as used for the submarine cable. The
Copyright Journal of Ocean Technology 2013
Table 1: Cable geometry case study.
phase separation and height for the equivalent
set of overhead conductors are the standard
values used for the voltage class considered.
The overhead lines study was included as a
reference to compare with the submarine cables
electrical characteristic. The cable geometry
used is shown in Table 1 [ABB, 2010].
Single-core submarine cable spacing of 10 m
is assumed. The equivalent set of overhead
transmission lines is assumed to have a height
of 10 m and phase separation of 0.813 m
[El-Hawary, 1995]. This is based on the
assumption of a 32.5 kV sending end voltage.
A line frequency of 60 Hz has been assumed.
It is also assumed that there are no harmonics
introduced on the transmission line. The
sending end power is assumed to be 3 MVA at
a 0.95 lagging power factor. A lagging power
factor is chosen because this would simulate
the sending end generator being an induction
machine operating as a generator. The
performance indices evaluated are the receiving
end voltage, voltage angle, real power, reactive
power, line efficiency, voltage regulation, and
the Thevenin equivalent impedance at the
receiving end of the transmission line.
Copyright Journal of Ocean Technology 2013
Single-Core Cable Steady State Performance
Figures 8 through 16 show the steady state
performance of the single-core submarine
cable for both the calculated values of the line
parameters and the measured values of line
parameters provided by the cable manufacturer
Figure 8: Receiving end voltage magnitude, single-core.
Figure 9: Receiving end voltage angle, single-core.
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 113
in Table 1 [ABB, 2010]. In addition the
equivalent set of overhead transmission lines
will be analyzed for comparison purposes.
reactive power zero crossing for a certain line
length. This zero crossing is possible since the
sending end power factor is lagging.
Figure 8 shows that a submarine cable’s
receiving end voltage reaches a maximum
value when the receiving end reactive power is
zero. For the overhead transmission lines the
voltage increases over the whole range of line
lengths. Figure 9 shows that the receiving end
voltage phase angle decreases at a faster rate
than for the overhead transmission line.
Figures 12 and 13 display the transmission line
efficiency and voltage regulation, respectively.
These figures provide the following information:
the overhead transmission lines are more
efficient than the submarine cables. This is due
to the extra losses incurred in the submarine
cable’s layers. The voltage regulation is better
for the overhead transmission lines than for
submarine cable. This means that the submarine
cable’s receiving end voltage will be more
sensitive to load changes.
Figure 10 shows that the real power delivered
to the shoreline station decreases with line
length, and decreases at a faster rate for
submarine cables. Figure 11 shows that the
reactive power for overhead lines is nearly
constant, while for submarine cables it is
increasing with line length. This results in a
Figure 12: Transmission line efficiency, single-core.
Figure 10: Receiving end power, single-core.
Figure 13: Receiving end voltage regulation, single-core.
Figure 11: Receiving end reactive power, single-core.
114 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
Figure 14 shows the power factor at the
receiving end of the transmission line. The
power factor for the overhead transmission
line is approximately constant, while for the
Copyright Journal of Ocean Technology 2013
submarine cable it achieves a maximum at a
certain line length. This means that for this
specific cable, there is a line length where the
generated reactive power and added reactive
power from the transmission line sum to zero.
This implies that a cable could potentially be
tailored to a specific marine application so as
to achieve improved power factors at the
receiving end.
Figure 14: Receiving end power factor, single-core.
Figure 15: Thevenin equivalent impedance, single-core.
Figure 16: Thevenin equivalent impedance angle, single-core.
Copyright Journal of Ocean Technology 2013
Figures 15 and 16 show that the Thevenin
equivalent impedance increases linearly with
transmission line length, and that the impedance
phase angle is approximately constant with
line length.
From Figures 8 to 16 it can be seen that the
calculated values for the line parameters provide
very good approximations of the performance
indices for line lengths less than 20 km.
Three-Core Cable Steady State Performance
Figures 17 through 25 show the steady state
performance of the three-core submarine cable
for both the calculated values of the line
parameters and the measured values of line
parameters provided by the cable manufacturer
in Table 1 [ABB, 2010]. In addition the
equivalent set of overhead transmission lines
will be analyzed for comparison purposes.
Figure 17: Receiving end voltage magnitude, three-core.
Figure 18: Receiving end voltage angle, three-core.
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 115
It can be seen from Figures 17 and 18 that for
three-core submarine power cables, the receiving
end voltage decays as the line length increases.
For the overhead lines the voltage increases over
the whole range of line lengths. The receiving
end voltage phase angle decreases at a slower
rate than for the overhead transmission line.
Figure 19 shows that the real power decreases
with line length, and decreases at a faster rate
for submarine cables. Figure 20 shows that the
reactive power for overhead lines is nearly
constant, while for submarine cables it is
increasing with line length; this results in a
receiving end reactive power zero crossing for
the submarine cable.
Figures 21 and 22 display the transmission line
efficiency and voltage regulation, which provides
the following information: the overhead
transmission lines are marginally more efficient
than the submarine cable. This is due to the
minimal losses incurred in the cable’s extra
layers. The voltage regulation for the overhead
transmission line is much better than for the
submarine cable. This means that the submarine
cable receiving end voltage will be more sensitive
to load changes.
Figure 23 shows the power factor at the receiving
end of the transmission line. The results are
similar to the single-core cable case. Again, a
cable could potentially be tailored to achieve a
desired power factor.
Figure 19: Receiving end power, three-core.
Figure 20: Receiving end reactive power, three-core.
Figure 21: Transmission line efficiency, three-core.
Figures 24 and 25 show that the Thevenin’s
equivalent impedance increases linearly with
transmission line length, and that the impedance
phase angle is constant with line length.
The trends of the performance indices for both
116 The Journal of Ocean Technology, Vol. 8, No. 1, 2013
Figure 22: Receiving end voltage regulation, three-core.
Copyright Journal of Ocean Technology 2013
maximum receiving end voltage; and the
receiving end power factor approaches unity
for a certain line length.
CONCLUSIONS
Figure 23: Receiving end power factor, three-core.
This study has shown that submarine cables
have unique electrical characteristics that need
to be considered when specifying underwater
transmission of power.
• Submarine cables provide considerable reactive power to the system.
•
Figure 24: Thevenin equivalent impedance, three-core.
Figure 25: Thevenin equivalent impedance angle, three-core.
single-core submarine cables and three-core
submarine cables are very similar. The difference
between the two cables can be found by looking
at the rate of change of the performance indices
with respect to line length. The design of
three-core cable lines is more complex than
single-core. The important characteristics of
submarine cables are as follows: submarine
cables are less efficient; the cables incur a
Copyright Journal of Ocean Technology 2013
In the case where sending end power factor is lagging there is a line length where the receiving end power factor could be close to unity.
• The receiving end voltage magnitude fluctuates (rises, maximizes, and then decreases).
One of the advantages is that a submarine
cable is able to feed the reactive power
demand of the electric power generator
(induction and permanent magnet generators)
that are commonly used in offshore wind and
marine energy converters. This balancing of
reactive power demand from the generator and
production from the cable means that there is
an enhanced quality of power reaching shore.
The consequence of this is the possibility of
introducing resonances in the transmission
line. The findings from this evaluation would
assist in tailoring the cables’ geometry to
improve electrical characteristics of the
submarine cables and hence improve the
quality of electric power transmission to shore,
contributing to overall reliability of marine
energy electric generation. In general,
determining submarine cable performance
characteristics has important implications on
The Journal of Ocean Technology, Vol. 8, No. 1, 2013 117
how to analyze underwater power systems and
offshore generation interconnections with
specific focus on marine energy.
ACKNOWLEDGEMENTS
The authors would like to thank
CanmetENERGY/Natural Resources Canada
(NRCan) for providing funding support for
this study; it was funded under the Program
for Integrated Renewable Electricity Systems
allocated by the Program of Energy Research
and Development POL 5.1 Marine Renewable
Energy. Funding support from Natural Sciences
and Engineering Research Council of Canada
Discovery Grant and support of Dalhousie
University (Electrical and Computer
Engineering Department and Faculty of
Engineering) are hereby acknowledged.
Finally, the advice and support of NRCan’s
Ghanashyam Ranjitkar are hereby
acknowledged.
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