Electric Cleanliness Algorithm based on Multi-Unit Interaction and
Reallocation
NIKOLAOS E. FRAGIADAKIS, ANARGYROS T. BAKLEZOS,
THEODOROS N. KAPETANAKIS, IOANNIS O. VARDIAMBASIS,
CHRISTOS D. NIKOLOPOULOS
Laboratory of Telecommunications and Electromagnetic Applications,
Department of Electronic Engineering,
Hellenic Mediterranean University,
Romanou 3, Chalepa, 73133, Chania, Crete,
GREECE
Abstract: - Authors prior to this work proposed a methodology providing electric or magnetic cleanliness on
spacecraft implementation by reordering equipment units. More precisely, since the mission's scientific goal
relies on the payload's high sensitivity and accuracy for capturing the space environment, field minimization in
measuring instrument location is imperative. Electromagnetic cleanliness is a constant open issue, since the
mission target relies on clean measurements without including spacecraft self-emissions. A lot of science
missions of ESA, NASA, or JAXA select usually a set of a couple of basic units as standard payload, i.e.
batteries, Radio Frequency switches, Command units or Data Handling Management units, S-Band
Transceivers, Power Distribution Units, etc. The later is usually measured and electromagnetically
characterized by employing the on-ground facilities providing equivalent radiating models. This work provides
a supplementary module to the formerly created framework for an entire unit positioning approach, taking into
account the unit’s test-level data, for suitable allocation of the space vessel’s equipment toward electric
cleanliness purposes taking into consideration the unit’s induced behavior.
Key-Words: - Differential Evolution, Electric and Magnetic Cleanliness, Induced Dipole, Spacecraft Units
Allocation, Inverse Electromagnetic Problems
Received: October 19, 2022. Revised: January 21, 2023. Accepted: February 24, 2023. Published: March 30, 2023.
1 Introduction
By definition, most space equipment consists of
sophisticated systems and sensors that present
tremendous sensitivity to electromagnetic
interference (EMI), necessitating specific testing
conditions and stringent cleanliness prerequisites
[1], [2], [3]. To avoid EMI/EMC problems at the
system level, assessment and analysis of the radiated
fields, electric as well as magnetic, of the
devices/harnesses on board a satellite, are required
throughout the design phase, [4], [5], to make it
possible for the on-site technical and scientific team
to put together an arrangement of the platform units
with field emissions at the various sensitive sensor
sites in accordance with the specific mission
requirements, the units are identified with regard to
their electric and/ or magnetic emissions.
Additionally, it is standard practice to model the
aforementioned devices at the unit level as a means
to get the ability to extrapolate all measured fields in
the nominal position of the sensors for an initial
placement of each unit that represents the best
engineering guess.
Naturally, this frequently results in emission
fields that much exceed the needs of the
technological and scientific objectives. The typical
solution for these problems is the relocation of the
units with considerable field emissions as far away
from the chosen locations of the sensors, [6]. Given
that there is a certain amount of platform space
available, this solution has a limited range of
applications. Booms were therefore used to
introduce a further distance between the sensors and
the rest of the platform, but as missions become
more complicated and carry more units, the
requirements also become more demanding.
For these kinds of problems, more sophisticated
methods have been used, namely shielding in its
passive form, [7], [8], of either custom sub-
components, [7], or whole units of equipment, for
example, reaction wheels, that commonly have
emission problems. Metglass or Mu-metal, [6], [9]
are often used materials that are suitable for this
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Nikolaos E. Fragiadakis, Anargyros T. Baklezos,
Theodoros N. Kapetanakis, Ioannis O. Vardiambasis,
Christos D. Nikolopoulos
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operation. Shielding is a solution that
unintentionally increases the platform's overall bulk
and can only be used on a select few units in order
to maintain operational efficiency.
To further reduce emissions, at the cost of
complexity, a technique known as active mitigation
which targets the cancelling out of the emitted
fields, is used. This technique uses additional,
carefully chosen, "artificial" sources placed
precisely in the platform in order to generate the
suitable opposing fields that abolish effectively
either a selected unit’s field, [7], [10], or the
platform's entire field in chosen spots, regions or
areas of interest, with the more sensitive equipment,
devices, or sensors, [7], [10], [11]. This method
includes low-frequency active systems, [10], [11],
as well as DC issue remedies like compensatory
magnets, [6], [7].
The frequency range at which the various
mission-specific sensors operate is another crucial
feature of the cleanliness topic that is highlighted by
this frequency diversification. These mission’s
specific parameters define the cleanliness criteria,
which consecutively determine the scope of the
required unit characterization and the proper
problem-solving techniques. Direct Current’s (DC)
issues are widely known and have to be prevented
or limited from the mission's planning phase, [12],
using the help of existing rules. Avoiding permanent
magnets, and decreasing current loops’ areas, [13],
to back-wire solar panels, [14], are only some of the
DC magnetic field’s precautionary measures. The
system’s design is significantly influenced by the
electrostatic problem. Furthermore, the differential
electric potential of any two places on the space
vessel’s surface must be kept minimum, because
surface charges change the platform’s electrostatic
environment (commonly below 1V). All of the
spacecraft's surfaces must be highly conducting for
this to occur, [15]. On the other hand, the cleaning
difficulties of the Alternating Currents (AC) of low
frequency are a relatively new area, that is drawing
more and more focus, [9], [10], [11], [13].
As previously noted, any whole system-level
EMC project must adhere to high magnetic and
electric cleanliness standards, containing magnetic
and electric fields originating from any harness,
device, or equipment mounted on the mission’s
platform. In the present paper, we suggest a
methodology for DC and low frequencies, which
focuses on (without being limited to) the electric
field, in a manner suitable for the minimization of
the field, which is emitted at the location of the
sensor, taking into account the induced fields. This
is accomplished by shifting the onboard equipment's
position and orientation. The authors have
previously addressed different problems with
similar field reductions, [16], [17]. However,
usually, in missions, the instruments measuring the
fields are extremely sensitive. In these cases, an
arrangement appropriate for the electric field’s
minimization at the desirable position of the electric
sensor based solely on the unit models of the units
might be quite different from the reality due to the
effect of the induced dipoles on the other units. This
work provides a methodology that also considers the
induced behavior of the units and showcases that the
environment is indeed very different so a solution
neglecting the induced dipoles is not adequate.
Works related to the description of the induced
dipole participation in the total electric field can be
found in [18], [19]. It should be emphasized that the
suggested methodology ignores emissions from
cables and harnesses and only considers emissions
from individual units.
The prediction of the complete spacecraft’s
radiated emissions, starting from unit-level or
component-level measurements (characterization),
(i) streamlines the testing process, (ii) lowers the
overall EMC campaign cost, and (iii) also offers a
way to allocate the space platform's equipment as a
means to accomplish the required magnetic and
electric cleanliness at particular locations, [16], [17].
Fig. 1: Layout of sensor placement on the boom of
Solar Orbiter signifying the areas with electric and
magnetic cleanliness requirements. Credit: ESA.
2 Electric Field Equations & Problem
Definition
The reduction of electric and/ or magnetic emissions
at a site where multiple sensitive devices or sensors
are intended to be installed is the essence of
electromagnetic purity. Each unit's electromagnetic
behavior is described and assigned to typical
equivalent sources (such dipoles) as part of the unit-
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level modeling process, which enables the
identification of all units’ field emissions throughout
the space vessel for different operational routines.
The vectorial summation of all the units' emissions,
or at least those that have been shown to be
significant contributions to the area of interest, is
then used to estimate the system-level behavior. For
the rest of the paper, the focus will be solely on the
DC and low-frequency electric field.
2.1 Electric Field Formulation
In the current work, the frequency spectrum of
interest ranges from 0 Hz to low frequencies below
300 kHz. The radiated fields from any source are
thought to be quasistatic at these frequencies,
especially near a source at distance considerably
lower than one wavelength. Therefore the fields,
electric and magnetic, are treated separately. The
near-field approximation is appropriate for the
particular circumstances of low frequencies and
regions of interest in the vicinity of several unit
sources. For any frequency of interest, another
electric dipole serves as the primary representation
for each unit's electric behavior in this work, which
focuses on the electric field. The analysis presented
completely supports a method with more dipoles per
unit, but since this is not a frequent practice, it will
not be expressly discussed in this study. In any
instance, the moment and position variables inside
the unit space are used to represent each such dipole
for each frequency.
Denoting the vectors of a dipole source’s
position as
, of the dipole’s moment as ,
and of the observation point’s position as
,
and employing the near-field’s approximation, we
can express our electric field as:
(1)
Having in mind that denotes the moment
vector of the dipole, ,
and
, the electric field
at with
can be analyzed into its three
components for every prominent emissions’
frequency :
(2a)
(2b)
(2c)
where
and .
Consequently, the magnitude of a single
dipole’s total field for the frequency is:
(3)
When N number of units are considered to
contribute to spacecraft’s emissions, corresponding
either to N distinct dipoles or to N (N>Q) dipoles
associated with only Q units (when some units
correlate to more than one dipole), each
component of the total electric field on the m
evaluation spot is given by:
(4)
resulting in a total electric field’s magnitude:
(5)
2.2 Emissions on System Level Assembly
The dipole parameters have to be stated in the same
coordinate system in order to complete the
computations of (2) and the summations of (3) and
(4). Commonly, this is chosen as the Spacecraft's
Coordinate System (SCS), within which each unit,
that describes the location of the various units in the
spaceship's scheme, is capable of rotation around the
three axes and movement in three dimensions,
naturally within the limits of the spacecraft.
Taking into account the spacecraft origin SCS,
the jth equipment unit’s center (DUT’s center) is
assumed at . All the characteristics are
shown in Fig. 3, where each unit is assumed to be
represented by () dipoles.
The transformation matrices shown in eq. (6)
are used to calculate the positioning of the relevant
electric moment’s vector, when a DUT rotates in
every possible direction (according to a respective
orientation angle of the 3-axial SCS):
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(6)
resulting in the below effect on the spatial
coordinates and moments:
(7)
(8)
The rotation sequence to the DUT's center
follows a consistent pattern starting from the x-,
continuing with the y-, and ending with the z-axis,
using (7) and (8) to calculate the dipole source’s
coordinates and moment vectors.
Fig. 2: Translation of DUT’s electric moment vector
from DCS to SCS.
The Device Coordinate System (DCS)
coordinates of the dipole with respect to
unit’s origination are . For
computing the total electric field using (4) - (5), the
( DCS coordinates must be
translated to the corresponding SCS coordinates by:
(9)
DUT’s electric moment vector and orientation
center are then stated in SCS for every potential
rotation and/or displacement, using (7) and (9),
respectively.
Fig. 3: Translation of DUT’s center from DCS to
SCS.
2.3 Problem Description and Definitions
Numerous DUTs are present on board every space
mission and are bound by the spacecraft's hull. This
has allowed us to replicate the spacecraft container
with a cuboid volume that has dimensions of 2.5 m
by 2.5 m by 3 m. (Fig. 2). The boundary area for the
displacement of all the units is also included in this
volume. To clarify, as stated in the Introduction, a
number of real spacecraft devices (DUTs) of ESA’s
Earth Explorer “GOCE” mission are characterized
and measured, [20], offering the base range from
which the electric moments (and also the magnetic
moments, if the same approach is followed) for this
paper’s artificial DUTs are drawn. These artificial
DUTs are intended to highlight the practical features
of this work.
In typical space missions, several different
equipment units and instruments constitute the
entire onboard real platform. The fusion of all the
units and devices creates the precise and complete
electromagnetic environment. However, only 3 or 4
of the devices often make a significant contribution,
defining the behavior of the system's
electromagnetic signature as a whole. Others are
either mass-modeled with a predetermined moment
value or deleted during the design phase, [21].
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Table 1. Moments of the Electric Field for the 4
DUTs
DUT/Dipole
px
py
pz
1
-31
-38.5
-71
2
-42.7
26.6
17.7
3
-12.6
45.3
-94.1
4
10.1
-27.3
170
Table 2. Dipole’s Coordinates in its Unit DCS
DUT/Dipole
1
0.01
0
0
2
0
0.005
0
3
0
0
-0.03
4
0
0.01
0.01
Each of the four DUTs used in this study is
modeled with one equivalent dipole given to it and
is positioned in accordance with Table II. The four
DUTs are thought to operate at a single similar
frequency. Table I provides the associated electric
moments for each DUT. The DUTs can be placed
anywhere within the spacecraft's boundary
constraints.
The aforementioned methodology can also be
used when the DUT models include multiple
electric (or with minor modifications, magnetic)
dipoles, in order to take into consideration the
induced electric moments, which can be modeled
either typically also by additional dipoles, as
demonstrated in this work, or precisely by more
detailed representations, [3], [18], [19], [22], [23].
The position (), where electric and/or
magnetic cleanliness needs to be attained, is where
measuring probes or other victim devices exposed to
space-vessel emissions need to be installed. In this
study, the sensor volumes are shaped like cubes,
each with a 0.2 m-long edge. The electric sensor’s
center is used for identification in the SCS
. To match various scenarios,
the precise volume form of the observation site may
be modified. The precise configuration is shown in
Fig. 1. The allowable orientation of the DUTs in this
work has a restriction. The DUTs must always
sustain a face that is parallel to the space-vessel's
base surface, which is necessary in order to mount
the DUTs on the inside surfaces or walls of the
spacecraft. The discretized numbers
for the angles and are used to describe this
constraint, and the units are only permitted to rotate
about the z-axis (when .
Assuming a specific set of DUTs, the orientation
and positioning of artificial DUTs in relation to the
sensor position can drastically alter the observed
electric field there (modelled as electric moments).
Equations (2) and (3) provide evidence for this. The
positioning and orientation of the units at the sensor
positions must be carefully chosen in order to
reduce the electric field that they emit.
2.4. Unit-to-Unit Interaction
Since the frequency under investigation does not
exceed a couple of hundred kilohertz, the scatterers
near the remaining the (in total) units of the
spacecraft can be handled as oscillating dipoles,
which are coherently provoked upon the scatterers
by the incident fields, [18], [19]. These induced
dipoles’ calculations may be derived from boundary
value problems, either quasi-static or even static.
The medium around all scatterers have been
modeled with . Moreover, due to the
very long wavelength, the scatterer’s dimensions
may be considered excessively small, thus its
precise shape and dimensions have no effect.
Consequently, any scatterer may be handled as one
sphere with small radius in the interior of a uniform
total field generated by the rest N-1
components. On the basis of the above-mentioned
procedure, the interaction among units depends on
frequency and has to be addressed individually for
every single frequency of concern in which,
according to [24], [25], the material of the sphere-
scatterer is affecting the induced electric dipoles’
moments.
In the case of one perfectly conducting (PEC)
sphere of small radius , the induced electric
dipole’s moment is:
(10)
whilst, in the case of one dielectric sphere with a
small radius , , and isotropic, homogeneous,
and frequency-dependent dielectric constant :
(11)
where is the free-space dielectric permittivity.
For both events, we use as the radius of a
sphere circumscribing the unit’s volume
(given in m3):
(12)
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For example, a simple two-device interaction
() is calculated in the following manner. We
consider that unit 1 is the source (active) and in its
neighbourhood unit, 2 is the victim (scatterer). Thus,
when there is no electric field external to the unit
pair , is the electric field
caused by unit 1 at the position of unit 2 for the
frequency . Generally in the case of multiple units,
has to be the vector summation of the
electric fields generated from the rest of the units at
the designated unit’s position, assuming that each
unit’s AC electric behavior is expressed in its
respective DCS for the frequency, translated
through coordinate rotations/translations to the SCS,
characterized at the device level and modeled.
Then, in the scatterer’s spot (using the
notation) is only a straight computation of
the electric field caused by the source dipoles
(jth unit and kth dipole) as shown in Fig. 4 for a
two-dipole () easy case. Thereupon,
examining a small conducting sphere’s case, unit 2’s
provoked moment in the proximity of
unit 1 is computed by (1).
The aforementioned provoked moment is
coming from the dipole positioned at the
unit-scatterer’s center, following the
notation and describing unit 2’s provoked behavior.
Fig. 4: Illustration of Unit 1’s electric field effect on
Unit 2 and the corresponding calculation of the total
field on the sensor, ignoring induced field effects on
Unit 1.
2.5 Description of the Field Minimization
Heuristic Algorithm
The goal of this methodology is to offer a
systematic method for creating an appropriate
environment by jointly minimizing the electric field
at a predefined volume, appropriately positioning
and orienting the electric sources, and taking into
account each unit’s induced dipole under the
influence (field) of the others. The coordinates of
each cube center point identify the chosen volume
(sensor) for the electric field.
In order to effectively cancel out their electric
fields at the sensor's volume (centered at ), the
four units (the electric dipole sources of the DUTs)
must be rearranged, and their orientation must be
changed, according to the proposed stochastic
method. This results in electromagnetic cleanliness.
The well-known Differential Evolution (DE)
computational optimization technique is used in this
work to produce the answer, [26]. The set of 24
variables in total, corresponding to the 4 DUT
centers' Cartesian SCS coordinates and rotation
angles, is the answer. Figure 6 shows the proposed
methodology's flowchart.
DE is used to computationally solve the
minimization or maximization of a fitness/objective
function. Generally, this function is expressing the
rules regulating a prerequisite or an issue, through a
mathematical formula for the process's desirable
result. In this case, the best course of action would
be to reduce the electric field at the relevant site
, so as
(13)
The minimization method starts by initializing
the solution set, using the uniform distribution to
choose at random out of the proper solution search
space with 24 dimensions since each of the 4 DUTs
of this work has 6 variables (3 center coordinates
() and 3 rotation angles () (with
, , and
). We will talk about the
acceptable range for each DUT's center coordinates
shortly. For the minimization of the goal function,
the proposed algorithm is repeatedly seeking to
improve any prospect solution by using the
mutation, crossover, and selection operations (for
the electric field at the sensor location).
Each prospect solution is generated, and then its
viability is initially assessed in relation to DUT’s
impact. Note that, although the step is not included
in the method’s flowchart, we also perform this
evaluation for the initial population’s solutions (Fig.
4). Cuboid DUTs of dimensions , are
expressed along by their circumscribed spheres to
carry out the evaluations. The radius of each
sphere is given by
(14)
To prevent overlap the two DUTs must follow
the following rule
L1
W1
H1
Unit 1 (source)
y
x
z
OL2
W2
H2
Unit 2 (scatterer)
y
x
z
O
dind_2
d11
2
Einc2
d21
P
(Sensor Location)
E
E ind_2
E
E total
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(15)
where is the distance between DUT centers, while
and are the corresponding circumscribed
spheres’ radii, shown in Fig. 5. The DUT’s
dimensions are presented in Table III.
O1
O2
R1
R2
a1
b1
c1
a2
b2
c2
d
R2
O2
a2
b2
c2
R1O1
a1
b1
c1
d
Fig. 5: Illustration of the overlap avoidance
condition for the minimum distance of the DUTs
centers placement.
Table 3. DUT’s Dimensions
DUT
1
0.4
0.4
0.2
0.3
2
0.2
0.25
0.3
0.2194
3
0.4
0.1
0.1
0.2121
4
0.3
0.3
0.2
0.2345
If the unit overlap criterion is not satisfied, as
shown in the algorithm's flowchart of Fig. 6, the
candidate solution is deleted and substituted by a
brand-new one. To further explore just physically
possible options, this is done.
Each created prospect solution must also avoid
setting the units outside of the spacecraft's
perimeter. The DUT centers produced by the
potential solution must be located more than
from the spacecraft boundary. The results of this
constraint are the max/min values of the seeking
area for the coordinates of the unit centers, which
are listed in Table IV.
Since each variable of Table IV is unable to
receive values beyond its permitted range, this
requirement is evidently always satisfied. It is rather
simple to impose additional regulations, such as
prohibited zones for particular units, precise relative
orientations or lengths among particular unit couples
or unit’s boundary couples, etc. Such guidelines and
statements are fully supported by the technique
while formulating a particular issue.
Fig. 6: Algorithm process in a flowchart.
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The induced dipoles are calculated and added to
the problem's dipole sources once each feasible
solution has been developed. Calculating the total
field at the sensor location entails iteratively
determining the device combination that reduces
this field value.
Table 4. Allowable Ranges of the Center
Coordinates of the 4 DUTs
Variables
Min Allowable
Values
Max Allowable
Values
-0.95m
0.95m
-0.95m
0.95m
-1.2m
1.2m
-1.0306m
1.0306m
-1.0306m
1.0306m
-1.2806m
1.2806m
-1.0379m
1.0379m
-1.0379m
1.0379m
-1.2879m
1.2879m
-1.0155m
1.0155m
-1.0155m
1.0155m
-1.2655m
1.2655m
3 Discussion on Simulations
Before continuing with the results of the
methodology, the importance of the inclusion of the
induced fields to the problem is highlighted. The
methodology was used to attempt to find a solution
for the optimal placement of the four devices
purposefully ignoring the induced dipoles. An
assortment of units was found that (ignoring the
induced dipoles) produced an electric field
distribution, a yz cut of which is presented in Fig. 7.
Obviously, the methodology managed to place the
electric sensor (red box) in the minimum field
location (deep blue area).
However, this result is erroneous since when
actually including the induced dipoles in the
calculation of the electric for that specific
assortment of the units, it becomes apparent (Fig. 8)
that the sensor (red box) is no longer in the
minimum of the electric field. This result clearly
showcases that the induced dipoles should always
be included in the calculation in order to accurately
predict the emitted field.
Correct algorithm execution results (including
the induced dipoles) are presented in Fig. 9 and
recorded in Table V. The DUTs are obviously
distinct from one another, and the particular
combination of DUTs produces an electric field
amplitude of 5.43e-23 (V/m) in the middle of the
sensor volume. It should be noted for the extraction
of the induced dipoles up to 10nth order interactions
was used with a field convergence limit equal to 1e-
30, [19]. Fig. 9 also depicts the boom (in blue
highlight) and the electric sensor (in yellow
highlight).
Fig. 7: E-field amplitude is calculated on the yz slice
of space at ), where the
E-field sensor’s center position is when optimized,
without considering induced dipoles.
Fig. 8: E-field amplitude is calculated on the yz slice
of space at ), where the
E-field sensor’s center position is, taking into
account induced dipoles.
Fig. 10, Fig. 11, and Fig. 12 show the magnitude
contours of the electric field at the sensor’s center,
revealing that the algorithm successfully rearranges
the various DUTs in order to place the electric
sensor on the site with the least electric field at the
xy, xz, and yz planes, respectively. Figure 10 and
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Figure 11 show three-dimensional electric field
magnitude’s cuts, that pass through the space
vehicle and reveal high field’s values because of the
sources' close proximity to the spacecraft (DUTs).
Therefore, it is typical to expect the sensor to be in a
lower amplitude region. However, in the slices of
Fig. 10 (xy plane near the sources), Fig. 11 (xz plane
near the sources), and Fig. 12 (yz plane out of the
sources) the sensor lies in the least field area. This is
also demonstrated in Fig. 13, which shows how the
electric field's amplitude varies with boom length
(but is not limited to).
Fig. 9: The DUTs’ placement inside the spacecraft,
in compliance with the algorithm’s solution to
prevent overlap.
Fig. 10: E-field magnitude calculated on the xy slice
of space at ), where the
E-field sensor’s center position is.
The electric field’s magnitude has its minimum
upon the sensor’s site, where it is reduced nearly 2
orders of magnitude in comparison to every other
location along the boom, i.e. initiating from the
spaceship’s point () with the
attached boom and moving along the boom’s line
toward the sensor. The increased field’s amplitude
further along the boom shows emphatically how
clean the sensor has become.
Fig. 11: The electric field magnitude calculated
upon the xz slice of space at
).
The boom line depicted in Fig. 13, being the
blue line of Fig. 9, is totally residing on the xz-plane
().
Fig. 12: The electric field magnitude calculated
upon the yz slice of space at
).
Table 5. Optimized Orientations and Center
Positions of DUTs 1-4
DUT
θ(0)
φ(0)
ω(0)
x(m)
y(m)
z(m)
1
0
0
0
0.4316
-0.9347
-0.3644
2
270
185.54
90
0.0994
-1.0306
0.2703
3
90
343.29
90
0.0549
-0.0971
0.1778
4
90
359
0
-0.9632
-0.9373
-0.1472
Figure 13 showcases the importance of adding
the units’ induced performance, as the minimization
is not only substantially worst when an interaction
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2023.18.9
Nikolaos E. Fragiadakis, Anargyros T. Baklezos,
Theodoros N. Kapetanakis, Ioannis O. Vardiambasis,
Christos D. Nikolopoulos
E-ISSN: 2224-2856
91
Volume 18, 2023
between units is not taken into consideration, but
also the minimum has been moved to another
location (at least 30 cm away).
Fig. 13: Electric field’s magnitude calculated across
the boom’s length, with the field minimum observed
at the E-field sensor’s position.
Fig. 14: Electric field’s magnitude calculated upon
the xz slice of space at (
).
The electric field’s amplitude is estimated
across the space vessel over a broader cubical region
(approximately 15×15×15 m3), which further
illustrates the electric field’s reduction attained due
to the herein outlined algorithm. The magnitude of
the electric field in this region is shown in an xz
plane cut in Fig. 14. It is clear that no other location
in the study's area offers so a low-level field. This
shows how our methodology can present unit
layouts that achieve electric purity at levels
sufficient for at least early mission design thoughts.
4 Conclusions
The methodology presented in the herein study uses
heuristics to determine the best possible placement
of DUTs (regarding their orientation and exact
position), when their electric moments are known
and predefined at the unit-level measurement
procedure within any spacecraft. Τhis study’s
objective is the minimization of the total electric
field’s amplitude at chosen sensor positions while
accounting for the units’ induced performance. This
work demonstrates (i) how the field could be
decreased at several preselected locations of
interest, and (ii) where the sensor needs to be
positioned, given the electric and unit models. At
the site of the sensor, the method is able to lower the
field by around two orders. It is simple to implement
limitations and restrictions on the placement of the
units. Additionally, the concept is simple to
combine with active strategies to improve the
outcomes even more.
In the future, the process may be expanded to
take into account cable emissions as well as harness
ones, in order to produce harness paths that will
satisfy both cleanliness goals. For results with
significantly more accuracy and methodology with
improved robustness, the algorithm has to
additionally take into account the shielding effects
of the spacecraft walls. This will make it possible to
automatically provide a great beginning point for
creating clean from electromagnetic fields
platforms, using the proposed methodology.
Additionally, the ultimate validation test should
involve thorough system measurements and full use
of the suggested methodologies in a real spaceship
environment.
References:
[1] M. Pudney, S. King, T. Horbury, M.
Maksimovic, C.J. Owen, and P. Laget, “Solar
orbiter strategies for EMC control and
verification,” in Proc. 2019 ESA Workshop on
Aerospace EMC, Budapest, Hungary, May
2019, pp. 1-6.
[2] R.D. Leach and M.B. Alexander, “Failures and
anomalies attributed to spacecraft charging,”
NASA Ref. Publ. 1375, 1995.
[3] A. Junge and F. Marliani, “Prediction of DC
magnetic fields for magnetic cleanliness on
spacecraft,” in Proc. 2011 IEEE Int. Symp.
Electromagnetic Compatibility, Long Beach,
USA, Aug. 2011, pp. 834-839.
[4] F.S. de Adana, M.F. Catedra, J.M. Gomez, and
R. Mittra, “Effective technique for system level
prediction of the radiated emissions of
electronic devices and cables inside satellites
from unit level measurements,” in Proc. 2007
IEEE Int. Symp. Electromagnetic
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2023.18.9
Nikolaos E. Fragiadakis, Anargyros T. Baklezos,
Theodoros N. Kapetanakis, Ioannis O. Vardiambasis,
Christos D. Nikolopoulos
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Compatibility, Honolulu, USA, July 2007, pp.
1-5.
[5] F.S. de Adana, M.F. Catedra, J.M. Gomez, R.
Mittra, J.B. Renuncio, F. Gutierrez, and M.A.
Prieto, “An effective technique for system-
level prediction of the radiated emissions of
unknown sources inside low-Q cavities using
unit-level measurements,” IEEE Trans.
Electromagnetic Compatibility, vol. 51, no. 2,
pp. 181-191, May 2009.
[6] M. de Soria-Santacruz, M. Soriano, O.
Quintero, F. Wong, S. Hart, M. Kokorowski,
B. Bone, B. Solish, D. Trofimov, E. Bradford,
C. Raymond, P. Narvaez, C. Keys, P. Lord, J.
Ream, R. Oran, B.P. Weiss, C. Ru8sell, K.
Ascrizzi, and L. Elkins-Tanton. “An approach
to magnetic cleanliness for the Psyche
mission,” in Proc. 2020 IEEE Aerospace
Conference, Big Sky, USA, Mar. 2020, pp. 1-
15.
[7] M. Boghosian, P. Narvaez, and R. Herman,
“Magnetic testing, and modeling, simulation
and analysis for space applications,” in Proc.
2013 IEEE Int. Symp. Electromagnetic
Compatibility, Denver, USA, Aug. 2013, pp.
265-270.
[8] M. Pudney, S. King, C. Trenkel, F. Liebold, S.
Strandmoe, P. Meyer, and M. Ehinger,
“Advances in reaction wheel design for
magnetic cleanliness,” in Proc. 2019 ESA
Workshop Aerospace EMC, Budapest,
Hungary, May 2019, pp. 1-6.
[9] K. Dang, P. Narvaez, J. Berman, K. Pham, and
A. Curiel, “Magnetic shielding concepts for
reaction wheel assembly on NASA Europa
clipper spacecraft,” in Proc. 2020 IEEE Int.
Symp. Electromagnetic Compatibility and
Signal/Power Integrity (EMCSI 2020), Reno,
USA, Aug. 2020, pp. 305-311.
[10] A. Nicolai, S. Stoltz, O. Hillenmaier, J.
Ludwig, C. Strauch, D. Grivon, L. Rossini, E.
Onillon, T. Hellwig, and S. Scheiding,
“Towards a magnetically clean reaction wheel
with active magnetic field mitigation,” in Proc.
2019 ESA Workshop on Aerospace EMC,
Budapest, Hungary, May 2019, pp. 1–6.
[11] A. Nicolai, S. Stoltz, L. Hafemeister, S.
Scheiding, O. Hillenmaier, and C. Strauch,
“The magnetically clean reaction wheel:
Results and performance,” in Proc. 2022 ESA
Workshop on Aerospace EMC, May 2022, pp.
1–7.
[12] A. Lassakeur and C. Underwood, “Magnetic
cleanliness program on cubesats for improved
attitude stability,” in Proc. 9th Int. Conf.
Recent Advances in Space Technologies (RAST
2019), Instabul, Turkey, June 2019, pp. 123-
129.
[13] R. Kallenbach, T. Behnke, S. Engelke, K.
Bubeck, and R. Henkelmann, “AC and
transient magnetic emissions of the Juice
Ganymede laser altimeter,” in Proc. 2022 ESA
Workshop Aerospace EMC, May 2022, pp. 1-6.
[14] T.G. Stern and S. DeLapp, “Techniques for
magnetic cleanliness on spacecraft solar
arrays,” in Collection of Technical Papers -
2nd International Energy Conversion
Engineering Conf., 2004.
[15] V.A. Davis, M.J. Mandell, N.R. Baker, M.
Brown-Hayes, G.T. Davis, R.H. Maurer, and
C. Herrmann, “Surface-charging analysis of the
radiation belt storm probe and magnetospheric
multi scale spacecraft,” IEEE Trans. Plasma
Science, vol. 40, no. 2, pp. 262-273, Feb. 2012.
[16] G.I. Koutantos, C.D. Nikolopoulos, A.T.
Baklezos, and C.N. Capsalis, “Proper
equipment ordinance for achieving EM
cleanliness in space missions: The case of ELF
electric sources,” IEEE Trans. Electromagnetic
Compatibility, vol. 62, no. 5, pp. 1686–1692,
Oct. 2020.
[17] C.D. Nikolopoulos, A.T. Baklezos, and C.N.
Capsalis, “On achieving spacecraft level
magnetic cleanliness with proper equipment
ordinance of DC and ELF magnetic sources,”
IEEE Trans. Electromagnetic Compatibility,
vol. 62, no. 6, pp. 2714–2724, Dec. 2020.
[18] A.T. Baklezos, C.D. Nikolopoulos, P.K.
Papastamatis, T.N. Kapetanakis, I.O.
Vardiambasis, and C.N. Capsalis, “Early
considerations for unit’s induced electric
behaviour characterization in the extreme low
frequency domain,” in Proc. 2022 Int. Symp.
Electromagnetic Compatibility (EMC Europe
2022), Gothenburg, Sweden, Sep. 2022, pp.
744–747.
[19] A.T. Baklezos, C.D. Nikolopoulos, S.T.
Spantideas, A.E. Giannopoulos, and C.N.
Capsalis, “On the unit-to-unit interaction for
electric field estimation up to the low
frequency band,” in Proc. 2022 ESA Workshop
Aerospace EMC, May 2022, pp. 1-4.
[20] A.T. Baklezos, C.D. Nikolopoulos, S.T.
Spantideas, E.G. Chatzineofytou, M. Nicoletto,
I. Marziali, D. Boschetti, and C.N. Capsalis,
“Steady state emissions modeling of low
frequency magnetic and electric fields
generated by GOCE CDMU,” in Proc. 2019
ESA Workshop Aerospace EMC, Budapest,
Hungary, May 2019, pp. 1-5.
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2023.18.9
Nikolaos E. Fragiadakis, Anargyros T. Baklezos,
Theodoros N. Kapetanakis, Ioannis O. Vardiambasis,
Christos D. Nikolopoulos
E-ISSN: 2224-2856
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[21] H.H. Park, H. Jin, T.Y. Kim, K.H. Kim, H.J.
Lee, J.H. Shin, Y.H. Jang, and W.H. Jo,
“Analysis of the KPLO magnetic cleanliness
for the KMAG instrument,” Advances in Space
Research, vol. 69, no. 2, Jan. 2022.
[22] A.S.K. Habila and W.H. Steyn, “In-orbit
estimation of the slow varying residual
magnetic moment and magnetic moment
induced by the solar cells on CubeSat
satellites,” in Proc. 2020 Int. Conf. Computer,
Control, Electrical and Electronics
Engineering (ICCCEEE 2020), Khartoum,
Sudan, Feb. 2021, pp. 1-6.
[23] M.A. Pudney, G. Kapfunde, and L. Trougnou,
“Induced magnetic field due to reaction wheel
shielding,” in Proc. 2016 ESA Workshop
Aerospace EMC, Valencia, Spain, May 2016,
pp. 1-6.
[24] C.S. Obiekezie, D.W.P. Thomas, A. Nothofer,
S. Greedy, L.R. Arnaut, and P. Sewell,
“Complex locations of equivalent dipoles for
improved characterization of radiated
emissions,” IEEE Trans. Electromagnetic
Compatibility, vol. 56, no. 5, pp. 1087-1094,
Oct. 2014.
[25] C.D. Nikolopoulos, “Extremely low frequency
electric field emissions for space applications:
Measuring and modeling techniques,” in
Electromagnetic Compatibility for Space
Systems Design. Hershey, USA: IGI Global,
2018, ch. 1, pp. 1-37.
[26] R. Storn and K. Price, “Differential evolution -
A simple and efficient heuristic for global
optimization over continuous spaces,” Journal
of Global Optimization, vol. 11, pp. 341-359,
Dec. 1997.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
-Nikolaos Fragiadakis carried out part of the paper’s
conceptualization, methodology, software,
validation, investigation, data curation, and
writing—original draft preparation.
-Anargyros Baklezos carried out part of the paper’s
conceptualization, methodology, software,
validation, investigation, resources, data curation,
writing—original draft preparation, and writing—
review, and editing.
-Theodoros Kapetanakis carried out part of the
paper’s software, validation, investigation, and data
curation.
-Ioannis Vardiambasis carried out part of the
paper’s conceptualization, methodology,
investigation, resources, writing—original draft
preparation, writing—review and editing,
supervision, and project administration.
-Christos Nikolopoulos carried out part of the
paper’s conceptualization, methodology, software,
validation, investigation, resources, data curation,
writing—original draft preparation, writing—review
and editing, supervision, and project administration.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This research received no external funding.
Conflict of Interest
The authors have no conflict of interest to declare
that is relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2023.18.9
Nikolaos E. Fragiadakis, Anargyros T. Baklezos,
Theodoros N. Kapetanakis, Ioannis O. Vardiambasis,
Christos D. Nikolopoulos
E-ISSN: 2224-2856
94
Volume 18, 2023
