IEEE Electrification Magazine - December 2019 - 108

The shipboard power
distribution system
can reach thousands
of kilometers when
installed, and
therefore, the study
and development of
a trustworthy
mathematical
modeling approach
is needed.

perform exhaustive analysis regarding
the high-frequency disturbance propagation in shipboard IPES.

High-Frequency Disturbances
Propagation in Power Cables

The previous section presented the
useful features provided by the CSI
software usage, but these features are
not enough to correctly evaluate the
high-frequency disturbance propagation in the IPES. The shipboard power
distribution system can reach thousands of kilometers when installed,
and therefore, the study and development of a trustworthy mathematical
modeling approach is needed. The
onboard integration of several power
electronics devices and pulsed power
loads in military applications (such
as innovative weapon systems) should be assessed with
the least adverse effect on the IPES power quality. It is
important to correctly evaluate the model to be used to
analyze the harmonic pollution propagation in the system
because different simplifying hypotheses lead to distinct
cable models.
In this respect, loads installed onboard naval vessels
and cruise ships have characteristics that make them
work in the range of the medium-frequency transients (up
to megahertz). Consequently, the conventional steadystate models are not usable, and new frequency-de pendent models have to be developed for the system
components. Regarding shipboard power cables, the general resistance, inductance, conductance, capacitance

I1(x)

I2 (x ′)

V1(x )

∆x

V2 (x ′)

x′

Figure 15. The RLGC distributed cell for Δx cable length.

(RLGC) cable model (Figure 15) is used
here for the study of the disturbance
propagation in the system.
The assessment of high-frequency
disturbance propagation in a shipboard IPES is crucial and depends
on several factors: skin and proximity effect, complex permittivity variation, geometry, cable shield bonding,
and layout. Each of these phenomena is well known in literature and
has been ascertained through different studies. Turning briefly to the
details of the aspects mentioned, the
skin effect is the tendency of ac current to be more distributed in the
external part of the conductor in a
way proportional to the inverse of the
frequency square root. Therefore, the
skin effect leads mainly to an increase
in conductor resistance (while the conductor inductance
is slightly decreased), resulting in higher cable power
losses. The proximity effect instead consists of an apparent increase in resistance, especially with high-frequency
ac due to the currents' mutual effect in tightly adjacent
conductors (e.g., cable harnesses in parallel). The complex permittivity variation with frequency then results in
frequency-dependent capacitance value. Moreover, the
cable shield bonding can impact on the harmonic propagation through cables connected at the same earth reference, resulting in system dissymmetry and unbalance.
Naturally, the cable geometry affects the RLGC reference
parameters since, for example, simply different arrangements of two conductors (as depicted in Figure 16) bring
two different formulas to calculate the cable inductance
and capacitance. Finally, the layout is a key factor to correctly model the cable parameters and their mutual electromagnetic interactions. The cable parameters variations
can be affected by environmental factors, and thus, the
cable path through the ship must be known to properly
calculate its parameters.
The high-frequency disturbances are not negligible in
such a complex system since their propagation can have
an undesired effect on the IPES performance; they

TABLE 2. The data of the case study cable.
r

b
r

(a)

(b)

Figure 16. The different arrangements of two conductors: the (a) socalled Lecher wire, and (b) coaxial cable.

108

I E E E E l e c t r i f i cati o n M agaz ine / DECEMBER 2019

Resistivity [Ω * mm2/m]

0.028

Conductor radius [mm]

9.2

Outer radius [mm]

19.2

Relative permeability

Relative permittivity

2.3

Dissipation factor

0.002

IEEE Electrification Magazine - December 2019

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