This document summarizes electromagnetic analyses of different configurations of integrated production umbilical cables. Umbilical cables can have multiple independent power circuits and steel tubes. Three configurations (A, B, C) are analyzed using a combined 2D finite element and transposition methodology to evaluate performance considering load terminal voltages and induced voltages. Configuration B, where each power circuit rotates around its own center, has the best performance with balanced terminal voltages and minimized induction effects along the cable length.

1. IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010 3317
Electromagnetic Analysis of Submarine Umbilical
Cables With Complex Configurations
M. B. C. Salles1 , M. C. Costa1 , M. L. P. Filho2 , J. R. Cardoso1 , and G. R. Marzo1
Applied Electromagnetism Laboratory (LMAG),PEA-EPUSP, São Paulo, Brazil
Institute for Technological Research-IPT, São Paulo, Brazil
These studies present the electromagnetic analyses of different configurations of the so called “Integrated Production Umbilical,” or
simply Umbilical Cables. Modern Umbilical Cables can have more than 4 independent 3-phase power circuits as well as steel tubes.
There is no 2-D symmetry for these cable configurations and the 3-D simulations are very undesirable due to cable length. The adopted
methodology to evaluate cable performance is a combination of 2-D-finite element analyses (coupled with electric circuit) and the trans-
position technique. The results have shown that the configuration B in which all power circuits rotates along its own center has better
performance considering the load terminal voltages due to the compensation of the induction effect along the cable.
Index Terms—Finite element analysis, integrated production umbilical, power quality, submarine power cable, umbilical cable.
I. INTRODUCTION pump. The main electrical characteristics of the voltage supplied
by the converters (C1, C2, C3 and C4) are: frequency range
T HE OIL exploration on offshore platforms represents an
activity of high investment, where the risk of fails and the
maintenance must be minimized. The oil exploration process
( – Hz); supply voltage (
constant; constant current ( A).
–
The cross-sections number 1 of the analyzed UC configura-
V); V/F
requires cables composed by hydraulic steel tubes, independent tions are shown in Fig. 2 and in Fig. 3. One can see the 4 power
3-phase power circuits, signal conductors, etc., these compo- circuits on the inner layer (configurations A and B) and on the
nents can be integrated in an Umbilical Cable (UC). The new outer layer (configuration C) of the cables with their respective
concept of umbilical cables are composed by more than only phases A (dark grey), B (black) and C (white). Each power con-
one independent power circuit operating in a wide range of vari- ductor has its own copper shield. There are 8 steel tubes in the
able frequency and voltage values. The operation of the UC must outer layer (configurations A and B) and in the inner layer (con-
follow strong power quality requirements. The UC internal con- figuration C) used to transport fluid. All configurations have an
figuration can affect the magnetic coupling between the compo- external metallic armor mainly used for mechanical purposes.
nents derating the ampacity of the power circuits [1]–[3] and The outer diameter of the three configurations is 280 mm with
also degrading the quality of the voltage on the load terminals. 10 km of length. The main data of the cable are given in the
There are no analytical equations to evaluate the interactions Appendix.
inside the cables or to evaluate the power quality during oper- For better mechanical resistance, the internal structure of the
ation in unsymmetrical and complex geometries. Although the cable must rotate in relation to the center along its length. In
use of 3-D-Finite Element Models overcomes the lack of ana- this specific case, the entire inner layer rotates in anticlockwise
lytical equations, the number of finite elements required by this direction (1 turn every 1000 mm), while the entire outer layer
type of cable geometry would lead to an undesirable simulation rotates in clockwise direction (1 turn every 1500 mm). In ad-
time. In order to determine the voltage wave form at the load dition, the configuration B includes the rotation of each power
terminals, the authors has developed a combined methodology circuit in relation to its own center completing one turn every
to evaluate the mutual coupling effects between power conduc- 750 mm.The oil pump terminal voltages can be strongly affected
tors, power shields, metal tubes and armors (the metallic parts depending on the internal configuration of the UC. In order to
inside the cable). This methodology combines the transmission guarantee the lifetime and the required maintenance of the oil
line transposition method with 2-D-Finite Element Method re- pumps, the voltage at the load terminals should be not only bal-
ducing drastically the simulation time with no loss of accuracy. anced but the influence of induced voltage from the surrounding
This paper is organized as follows. In Section II, one presents conductors (modulation) should be minimized.
the investigated geometries and the electrical characteristics
of the UC system. The combined methodology is presented in
III. COMBINED METHODOLOGY
Section III. Section IV discusses the results.
In order to avoid the use of the 3-D models, one has developed
a combined methodology using 2-D models and the transposi-
II. DESCRIPTION OF UMBILICAL CABLE SYSTEMS tion technique. In the following, we briefly discuss the idea in-
volved in this combined methodology to analyze complex Um-
The analyzed configurations of the umbilical cable have four bilical Cables (UC).
3-phase power circuits (Circuit #1, Circuit #2, Circuit #3 and
Circuit #4). Each circuit feeds independently one submerged oil A. Limitations of the 2-D Finite Element (FE) Model
As indicated in Section II, the analyzed cable has no sym-
Manuscript received December 10, 2009; revised February 20, 2010; metry along the domain depth. The metallic components (con-
accepted February 21, 2010. Current version published July 21, 2010. Corre-
ductors, shields, tubes and armors) of UC change their relative
sponding author: M. B. C. Salles (e-mail: mausalles@gmail.com).
Color versions of one or more of the figures in this paper are available online position along the cable length by performing a helicoidal path.
at http://ieeexplore.ieee.org. Therefore, in order to analyze the cable performance the simu-
Digital Object Identifier 10.1109/TMAG.2010.2044484 lations must consider different cross sections which represents
0018-9464/$26.00 © 2010 IEEE

2. 3318 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010
Fig. 1. Unifilar diagram of the 3-phase system. Fig. 5. Cross sections used to represent the variation of relative position.
C. Methodology: 2-D FE Model Transposition
In this way, the cable performance is evaluated using 2-D
finite element models coupled to the transposed multiple seg-
ments technique (transposition) [4]. In the particular case of UC,
the interchanges are obtained performing various 2-D steady-
state analyses considering several cross sections to model the
different relative positions between the power cables and the
metallic components.
D. Least Common Multiple (LCM)
Fig. 2. Cross-sections number 1 of the configuration A and B. As described in Section II, the inner layer of this UC com-
pletes 1 turn every 1000 mm while its outer layer completes 1
turn every 1500 mm. The LCM between the layer lengths is then
3000 mm. In other words, there is a repetition of the cable pat-
tern every 3000 mm.
E. Accuracy of the Analysis Method
The number of cross sections defines the accuracy which is
linked to the LCM of the cable layers, as shown in Fig. 5. For
this UC one has compared the results for two values of cross
sections number ( and ) and the difference was
not significant. Fig. 7(a) presents 3 of the 50 cross sections used
to compute the simulations of the configuration A and B.
Fig. 3. Cross-sections number 1 of the configuration C. F. 2-D Finite Element Analysis
From the electromagnetism theory, the induced voltage in one
conductor increases proportionally with the level and the fre-
quency of the current of the surrounded conductors. The con-
verters supply the oil pumps with a constant relation between
voltage and frequency. Considering the operation characteris-
tics, one of the worst conditions is when 3 circuits #1, #2 and #3
supply the pumps on 80 Hz and 1 circuit #4 supplies on 30 Hz.
The general idea of the methodology is summarized in Fig. 6.
Fig. 4. Transmission Lines phase transposition. The computational package FLUX-2-D [6] is used to evaluate
each cross section the configurations.
the variation of the relative position between the metallic cable IV. UMBILICAL CABLE ANALYSIS
components.
In order to compare the performance of the UC with the eval-
B. Transposition Technique uation of the coupling effects between the internal components,
three different configurations are verified:
The concept of transposition is addressed in classical 3-phase • Configuration A: the tubes and the power circuits turn
high voltage transmission lines (TL) theory [4], [5]. The idea is around the cable center, but the power circuits do not turn
to change the position of phases through the TL length, aiming around their own centers, as in Fig. 7(a).
to obtain balanced values for the TL parameters (inductances, • Configuration B: the tubes and the power circuits turn
capacitances and so on). The TL parameters are then calculated around the cable center and the power circuits turn also
from the average values on each phase. Fig. 4 illustrates a TL around their own centers, completing 1 turn every 750
transposition with three interchanges with lengths L/3. mm, as shown in Fig. 7(b).

3. SALLES et al.: ELECTROMAGNETIC ANALYSIS OF SUBMARINE UMBILICAL CABLES 3319
Fig. 8. Magnetic potential lines obtained for the cross section 1 of the Config-
uration A and B (only the first cross section has the same values). (a) 80 Hz,
(b) 30 Hz.
Fig. 6. General steps of the methodology.
Fig. 9. Real components of induced voltage (80 Hz) in phase C of circuit
#4—Configuration A.
Fig. 7. Cross sections along the length of configurations A (a) and B (b).
• Configuration C: the tubes and the power circuits turn
around the cable center (Fig. 3).
Due to the magnetic permeability of the armor ( u0),
the boundary conditions were defined considering a tangential
magnetic field in the outer diameter of the UC. The supply cir-
cuits are modeled with ideal 3-phase voltage sources and the oil
pumps are modeled as a pure resistive load of eight ohms on
each phase. The circuit coupling represents each finite element
region (power conductors, power shields, tubes and armor) by
an electric circuit component.
A. Terminal Voltage Computation
Fig. 10. Imaginary components of induced voltage (80 Hz) in phase C of circuit
Fig. 8(a) shows the equipotential lines obtained from the anal- #4—Configuration A.
ysis of the circuits #1, #2 and #3 supplied on 80 Hz. Fig. 8(b)
shows the analysis of circuit #4 supplied on 30 Hz. These two
separately analyses are necessary to determine the influence of
Fig. 12. The induced voltage in configuration C (not showed)
the 80 Hz on the 30 Hz circuits for frequency domain simulation.
has similar performance of configuration A.
The converter voltages of each phase A of the 3-phase circuits
are at its maximum value.
B. Power Quality Analysis
The average values of the real and the imaginary components
of terminal voltage of the circuit #4 are calculated considering Voltage modulation indicates the induced voltage level in a
each cross section. The terminal voltage of the configuration A phase of a circuit by the surrounding circuits. The computation
and B obtained by the combined methodology are shown from of the induced voltage on phase A of circuit as a result of
Figs. 9 to 12. current flowing through circuit can be calculated individually
The induced voltages are almost constant for the configura- by the (1), (2) and (3)
tion A, as shown in Fig. 9 and in Fig. 10. For the configuration
B, the rotation of the 3-phase power circuits around their own
centers results on a variable induced voltage along the length (1)
of the UC which compensates itself, as shown in Fig. 11 and in

4. 3320 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010
TABLE II
SIMULATION DATA OF DIMENSIONS AND MATERIAL PROPERTIES
Fig. 11. Real components of induced voltage (80 Hz) in phase C of circuit Configuration B is the most appropriate one which guarantee
#4—Configuration B. the balanced voltage at the load terminals and the low level of
modulation on the most sensible circuit (30 Hz).
V. CONCLUSION
The combined methodology presented in this paper enables
the evaluation of the power quality of UC using 2-D steady-
state models, without compromising the accuracy of the results.
One has verified that the rotation of the power circuits results
in a reduction of the voltage modulation. These characteristics
will also guarantee a better oil pump operation, diminishing the
maintenance and enlarging the lifetime.
This analysis gives faster results compared to 3-D steady-
state or 2-D transient. Besides that, the results of the 2-D tran-
sient analysis (not showed in this paper) for the configuration
B are very similar to the one obtained by the frequency domain
analysis. Even thought this methodology mainly analyses the in-
duced voltage in the circuit #4 by the others 3 circuits, different
analysis could also be done modifying the last two steps of the
Fig. 12. Imaginary components of induced voltage (80 Hz) in phase C of circuit Fig. 6, for example, to “loss computation” or “thermal analysis”.
#4—Configuration B.
APPENDIX
TABLE I The main data of the cable geometry and the material prop-
VOLTAGE MODULATION IN THE 30 HZ CIRCUIT (%) erties are given in Table II.
ACKNOWLEDGMENT
The authors gratefully acknowledge the financial support
from the Brazilian government via FAPESP (State of São
Paulo Research Foundation), CNPq (National Counsel of
Technological and Scientific Development) and CAPES (“Co-
ordenação de Aperfeiçoamento de Pessoal de Nível Superior,”
in Portuguese).
Computing total rms voltage on phase A of circuit
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