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Hierarchical Digital Twin of a Naval Power System
Kerry Sado*, Student Member, IEEE, Jack Hannum, Student Member, IEEE, Eric Skinner, Student Member, IEEE,
Herbert L. Ginn, Senior Member, IEEE, and Kristen Booth, Member, IEEE
Department of Electrical Engineering
University of South Carolina
Columbia, United States
*ksado@email.sc.edu
Abstract—A hierarchical digital twin of a Naval DC power
system has been developed and experimentally verified. Similar
to other state-of-the-art digital twins, this technology creates
a digital replica of the physical system executed in real-time
or faster, which can modify hardware controls. However, its
advantage stems from distributing computational efforts by
utilizing a hierarchical structure composed of lower-level digital
twin blocks and a higher-level system digital twin. Each digital
twin block is associated with a physical subsystem of the
hardware and communicates with a singular system digital twin,
which creates a system-level response. By extracting information
from each level of the hierarchy, power system controls of the
hardware were reconfigured autonomously. This hierarchical
digital twin development offers several advantages over other
digital twins, particularly in the field of naval power systems. The
hierarchical structure allows for greater computational efficiency
and scalability while the ability to autonomously reconfigure
hardware controls offers increased flexibility and responsiveness.
The hierarchical decomposition and models utilized were well
aligned with the physical twin, as indicated by the maximum
deviations between the developed digital twin hierarchy and the
hardware.
Index Terms—digital twin, power systems, electrical ships,
hierarchical digital twin, control system, power electronics
I. INTRODUCTION
Generally, the term Digital Twin (DT) refers to the virtual
representation of a physical system or subsystem, also known
as the Physical Twin (PT). According to NASA, a DT is
defined as a highly accurate simulation that incorporates
multiple physics, scales, and probabilities and mirrors the state
of its corresponding PT based on a combination of historical
data, live sensor readings, and physical models [1]. DTs are the
collection of dynamic digital models that accurately represent
an existing physical system or subsystem [2]. The goal of
the DT is to generate high fidelity virtual representations of
each physical entity, capable of simulating their states and
behaviors to assess, optimize, and predict current and future
scenarios [3]. The significance of DTs is rapidly gaining
recognition from both academic and industrial sectors as DTs
have potential applications across multiple sectors, including
aerospace, renewable energy, and naval applications [4]–[8].
The maritime industry recognizes the potential of DT
technology as an opportunity for improvement [9]. There
This work is supported by the Office of Naval Research (ONR) under ONR
contract N00014-22-C-1003.
has been a growing emphasis on digitalizing the maritime
industry, as new technologies are expected to enhance the
speed of processes and inform data-driven decisions through-
out the maritime value chain [10]. DTs have the potential
to revolutionize and enhance various aspects of naval power
systems, encompassing performance, efficiency, maintenance,
fault analysis, and resiliency. By collecting and analyzing real-
time data from naval power systems, DTs can effectively
identify and address performance bottlenecks. By providing
a comprehensive view of the power system, DTs can help
identify potential problems before they cause outages or other
disruptions; this proactive approach can contribute to improv-
ing maintenance and fault analysis. If a fault does occur,
the DT can determine a stable reconfiguration to enable safe
return to port. Given the potential benefits of DTs, it is a
significant tool for enhancing the performance, efficiency, and
reliability of naval power systems. The ultimate goal for DTs
is to achieve a completely autonomous system that gathers
information about its operation and simulates its effects. This
would enable the DT to support any decision-making regarding
the asset [13].
Recently, the International Maritime Organization (IMO)
enacted a strategic plan aimed at decreasing greenhouse gas
emissions in shipping by 50% from 2008 levels by 2050
with the ultimate goal of phasing them out entirely by the
end of the century [14]. This leads to the electrification of
ships, which requires developing innovative technologies that
can enhance ship design and maintain operational efficiency
has become a critical matter [15]. The United States Navy is
transitioning towards the electrification of its vessels, requiring
a higher demand for electric power than previous generations.
This transformation in power usage will not only escalate in
magnitude but also become more dynamic with large pulsed
loads, such as air and missile defense radars and directed
energy weapons [16].
As a result of the increasing usage of DC power sources
in naval systems, the Navy is investigating the possibility of
adopting DC distribution systems [17]. The implementation of
DC systems for vessels is anticipated to result in the power
system having a greater number of power electronic converters
and Energy Storage (ES) units. While converters and ES can
provide fast response to pulsed loads, they also increase the
control complexity for power sharing within the system. For
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these increasingly complex interactions, DTs can be utilized to
mirror the physical system using multiphysics simulations and
historical data to monitor and predict system responses. The
integration of DTs on various power system components on
shipboards will significantly enhance the overall success of the
fleet [18]. By implementing DTs, a range of benefits can be
achieved, such as decreased operational costs and streamlined
processes, enhanced productivity, improved decision-making,
advanced predictive and preventive maintenance.
Although DT technology offers several potential benefits, it
also faces significant challenges. One obstacle is the difficulty
of integrating data from various sources and maintaining
synchronization between the DT and its PT. Additionally, the
computational effort may increase beyond the capabilities to be
held within a single DT or available computational hardware
as the level of detail increases due to system complexity.
In systems, such as naval ships, with constantly updating
equipment, a single, comprehensive DT must be reconfigured
whenever a component is replaced or added to the system.
Therefore, a Digital Twin Hierarchy (DTH) is proposed to
enable increased complexity, future system modifications, and
faster computation speeds by distributing computational effort.
The number of layers in the hierarchy can be determined by
system complexity, resolution needed, and physical measure-
ments collected.
The closest concepts found in the literature to the proposed
DTH provide a generic architecture that captures the essential
components of a DT aligned with the layers of the Reference
Architecture Model Industry 4.0 for manufacturing [19] or
highlight how mechanical parts can be categorized by feature
using a hierarchical digital mapping [20]. The “layers” of these
hierarchical digital twins are the IT layers and the material
properties, drawings, and heterogeneous data, respectively.
Ultimately, the information was condensed into a single DT.
In the presented DTH, the models are maintained and modeled
independently.
A hierarchical digital twin offers several benefits, including
the distribution of computational effort, the integration of
dissimilar computing hardware, and the expansion of modeled
quantities. However, it is important to limit the amount of
information transferred between layers of the hierarchy to
obtain these benefits. In this work, an electrical domain DTH
was conceptualized and demonstrated for managing the power
system of naval ships and validated experimentally. Though a
DTH can be used for a variety of domains and performance
outcomes, the DTH presented in this paper is capable of
power sharing prediction and is used for dynamic control
reconfiguration autonomously during operation.
In Section II, an introduction to the DTH and definitions
are provided. An application of the DTH and its layers are
provided in Section III. The hardware used for this work,
the validation of DTBs in isolation, and their integration
into the hierarchy are provided in Section IV. Section V
provides results of the digital twin-based dynamic control
reconfiguration, and the autonomous operation of the DTH.
Finally, Section VI highlights conclusions and future work.
II. INTRODUCTION TO THE DIGITAL TWIN HIERARCHY
To introduce the hierarchical digital twin technique, a 2-
level hierarchy is implemented, as shown in Fig. 1. The
lowest level represents each individual converter; these are
defined as Digital Twin Blocks (DTBs). The DTBs have no
communication between one another but communicate with
the higher level System Digital Twin (SDT). The SDT is the
upper level of the DTH that combines data received from
DTBs and models the behavior of the entire system.
The DTH consists of decomposed but interconnected mod-
els with varying degrees of detail and complexity. This design
enables the distribution of complexity among DTBs, allowing
for the modeling of larger systems by replicating power system
components as separate DTBs. The data generated by DTBs
are fed up to the SDT, which integrates the information to
provide a comprehensive representation of the power system.
This approach enables larger systems to be modeled at varying
timescales, depending on the query from the decision maker.
The decision maker can be autonomous or incorporate a
human-in-the-loop to define potential scenarios or determine
a system response.
A. System Digital Twin (SDT)
As systems grow in size and complexity, it can become
increasingly challenging to model them in detail in a single,
comprehensive simulation, especially in real-time or faster
than real-time applications. Despite having suitable tools and
algorithms, including artificial intelligence, applying data di-
rectly from complex power systems to DT models can be
difficult. However, the SDT needs only to capture the essential
dynamics of the power system and inform the decision-making
process by incorporating all relevant data to be passed to the
decision maker.
To implement a SDT, the model should only include interac-
tions between components at the next level of the hierarchy, re-
sulting in less computationally expensive models. This means
that only the necessary quantities are calculated to predict the
Maintenance
Services
Decision Maker
Load
Scenario
Predictive states
Model
replicas
DTB1
Behavior
simulation data Digital Twin
Blocks
Control parameters
System Digital Twin
Control
Services
Prediction
Services
Monitoring
Services
System
Digital Twin
System
behavior data
Physical Twin Hardware
Reference points
& sensor data
Model
replicas
DTB2
Behavior
simulation data
Model
replicas
DTBn
Behavior
simulation data
Fig. 1: Generic hierarchical digital twin.
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behavior of the entire system. Any system quantities that are
not required to model the component interactions are delegated
to DTBs. The SDT aggregates the quantities returned from
DTBs and informs a decision maker, which is considered
external to the DTH.
B. Digital Twin Block (DTB)
A DTB is a representation or model of a component or
subsystem of the PT. The level of detail developed in a
DTB is dependent on the hardware measurements, timescale
of study, and system-level relationships. Models may be of
high fidelity or low fidelity and infer quantities not measured
in hardware. Complex models may require longer simulation
times to complete the DT study, so a simpler model may
be more beneficial, depending on the application, timescale,
or decision to be made. DTBs may employ more advanced
modeling techniques and use smaller time steps than those
used in SDT models. Ultimately, the fundamental requirement
of a DTB is to provide data that will enable the SDT to create
a system-level response based on the provided information.
III. AN APPLICATION OF THE DIGITAL TWIN HIERARCHY
To validate the concept of the proposed DTH, a system
to be twinned must first be defined. The demonstrator is a
simplified representation of the power system of a ship and
contains both constant and pulsed loads. The power system
consists of a DC bus, which is supplied by a 3-ϕ generator
and an energy storage, as shown in Fig. 2. By utilizing this
simplified yet practical system, the proposed DTH concept
can be validated, and its effectiveness in monitoring and
controlling the power system performance can be presented.
The validation implementation includes a SDT and two DTBs.
Figure 3 highlights the details of this particular DTH example
and the information being communicated up and down the
hierarchy. Specifically, DTB1 and DTB2 represent a 3-ϕ diode
bridge rectifier with a boost converter output stage and an
energy storage interface converter, respectively. Further details
on the modeling of the experimental DTH layers are available
in the subsequent subsections.
A. Modeling of System Digital Twin (SDT)
The SDT is being used to enable dynamic current sharing
between the 3-ϕ source and the ES using Extended Droop
Control [21]. Extended Droop Control allocates portions of the
load current to each converter on the bus and is a variation of
well-known resistive droop control. Extended Droop Control
uses a virtual RC filter created by the virtual impedances to
divide the load current by frequency and allocate it to each of
Energy
storage
3-ϕ
Source
Pulsed
load
Other
loads
DTB1 DTB2
Fig. 2: Demonstration system for implementing a hierarchical digital twin.
Physical Twin
System Digital Twin
Extended Droop Control
Reference points
sensor data
EDC parameters
Load current
Converter currents
Battery SoC
Decision Maker
Load
Scenario
Model
replicas
Rectifier
Model
replicas
DTB2
ES Interface
DTB1
Fig. 3: Demonstration specific hierarchical digital twin.
the converters connected to a bus. This division is especially
useful when two sources with vastly different response times,
like a generator and a battery, are connected to the same bus.
In the context of an RC load filter, the cutoff frequency can
be established in such a way to ensure all power source ramp
rate constraints are met. The maximum tolerable bus voltage
deviation, ∆Vmax, and the maximum converter current, Imax,
are used to specify the virtual resistor in (1), while the desired
cutoff frequency, fc, of the load filter determines the virtual
capacitance in (2) [22], [23].
Rd =
∆Vmax
Imax
(1) Cd =
1
2πfcRd
(2)
Rd and Cd are the virtual resistance and capacitance of
the droop control, respectively. The voltage reference supplied
to the generator rectifier is altered by the virtual resistor.
Similarly, the virtual capacitor impacts the voltage reference of
the ES interface converter. As the virtual capacitor is charged,
the ES current output is reduced.
The desired cutoff frequency may change in response to the
dynamic operating environment in which the system runs. For
a cruising ship, it may be desired that the ES is used less to
preserve its health. In this case, the cutoff frequency can be
increased which leads to reducing the value of Cd, and hence,
decrease the ES contribution to current pulses by ramping the
generator to match the load more quickly. By replacing the
capacitor with a variable capacitor, the cutoff frequency of
the system can be continuously tuned to match the operating
environment.
To develop the DTH, the initial phase involves constructing
a model that characterizes the dynamic responses of the bus
voltage and the current distribution between the two sources
under Extended Droop Control. Subsequently, the Extended
Droop Control equivalent circuit, as illustrated in Fig. 4, is
integrated into the DTH in the SDT. In the circuit, Ifast and
Islow correspond to the current provided by the ES and the
generator interface converters, respectively. This model can
be solved quickly since it does not require a small time-step,
is suitable for look-ahead simulations, and can be used for
real-time shadowing of the system as it operates.
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V
ref
I
load
Rd
I
fast
I
slow
V
ref
Cd
Fig. 4: Equivalent circuit model of Extended Droop Control [21].
B. Modeling of Digital Twin Blocks (DTBs)
The demonstrator, shown in Fig. 2, consists of two power
converters. Each of which can be decomposed into separate
subsystems as DTBs. DTBs can be employed to anticipate
the behavior and performance of the converter under different
operating conditions. Moreover, DTBs can be utilized for real-
time monitoring and control during operation, enabling predic-
tive maintenance and detecting potential problems before they
occur. The creation of a DTB for a power electronic converter
requires considering the impact of parameters, such as input
voltage and current, on the performance of the converter.
For the purpose of enabling a simple DTH for this work,
an averaged switching model is used in this study; however,
other models can be used in accordance with the system being
described and the required control decisions to be made.
In this context, the DTB of the generator interface is
modeled as a 3-ϕ diode bridge rectifier with a boost converter
output stage, as shown in Fig. 5. The DTB of the ES interface
converter is modeled using the averaged switching model
shown in Fig. 6. In the hierarchy developed to model the
system shown in Fig. 4, State of Charge (SoC) of the ES
could be inferred at the SDT but not explicitly measured.
Since the SoC is a key limiter of the ES current contribution
to pulses, it needs to be calculated by the DTB and passed up
the hierarchy. In addition to calculating the SoC of the ES, the
replication of the control logic makes the DTB a more accurate
representation of the interface converter than could be achieved
by the passive components at the SDT level. Through the
replication of the nested loop controls of the power converter,
the DTB is capable of compensating for non-linearities caused
by saturation limits on the voltage and current controllers
of the hardware. The SDT computes transient load sharing
between the two converters and relays it down the hierarchy to
be simulated by their respective DTBs. Corresponding results
are sent back to the SDT for analysis.
C. Decision Maker Modeling
In this work, the focus is on the proposed DTH, and
the decision maker is considered external to it. However, to
A
B
C
L
Vo
rL
V
o
D
D IL
IL
C
rc
C
rc
3-ϕ source
Fig. 5: Three-phase diode bridge rectifier with a boost converter output stage.
L rL
V
o
D
D IL
IL C
rc
Vin Vo
Fig. 6: Averaged switching model of the boost converter.
validate the concept of the DTH, a fuzzy logic-based decision
maker was modeled. The decision maker is developed using
an ontological technique called Posture-Based Alignment [25].
Posture-Based Alignment enables the ship to attain a posture
relevant to the active mission segment. In one posture, a
specific response can be vital, but in another, that same activity
is completely irrelevant to the success of the mission segment.
In this application, the various postures determine load current
contribution from the ES and generator. Accordingly, three
postures were adopted: “Port, “Cruise,” and “Battle;” each
represents a distinct set of objectives for the decision maker
to follow. In “Port,” the ship is presumed to be at minimal
readiness, and the land-tie connection or generator should
serve the load demand. In “Cruise,” the ship is at a higher
state of readiness, and the current distribution depends on the
ES SoC. When the SoC is greater than 90%, more current is
provided by the ES, and it is reduced below this SoC level.
This approach ensures that the ES is ready to respond to any
shift in posture or other events. The primary objectives of
this posture are to maintain ES readiness, reduce the wear
and fuel expenses of the generators, and ease generator stress.
In “Battle,” the ES operates without any SoC constraints and
supplies the maximum allowable energy during transient load
conditions. Therefore, the generator and ES operate at their
peak rating to meet the demands from propulsion, weapons,
and other crucial systems. The predefined posture-based align-
ment boundaries are arbitrary values; these values can be
updated based on the type of ES or generator capabilities.
Postures and their objectives are summarized in Table I.
IV. EXPERIMENTAL TESTBED VALIDATION
The hardware testbed used for for this work is shown
Fig. 7. The power converters were implemented using Im-
perix PEB8032 Silicon IGBT half-bridge modules [26]. The
modules were operated at a frequency of 20 kHz. A 1.25
mH inductor was used in the boost converter design. The bus
voltage was monitored using an Imperix DIN800V sensor, and
the inductor currents were monitored with the built-in current
sensors of the PEB8032 modules. Imperix external DIN50A
current sensors were connected with converters output to
measure the load current of each converter. A Chroma DC
TABLE I: DECISION MAKER POSTURES
Posture Objectives fc (Hz)
Port
ES serves minimum.
Load is assigned to the generator.
10
Cruise
SoC>90%:ES serves portion of the load.
SoC<90%: ES serves minimum.
0.05
0.25
Battle ES supplies maximum allowable energy. 0.01
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ES
3-ϕ
transformer
Electronic
DC load
System digital twin
DTB1
DTB2
Controller
Physical twin 2 Physical
twin 1
Fig. 7: Hardware testbed.
electronic load was utilized to handle both constant and pulsed
loads, serving as a current sink that drew a baseline load of
a 1 A baseload and 2 A pulsed loads. The converters were
controlled using the Imperix B-Box real-time control platform.
The SDT is running an equivalent circuit model of the EDC
using a timestep of 1 ms, depicted in Fig. 4. Simulink was used
to implement the model, and RT-LAB was used to deploy the
model in real-time on an Opal-RT OP5607 real-time simulator.
The real-time SDT simulator sent current contributions to
each DTB. The DTBs also received sensor measurements
for initialization over Ethernet, including input voltages, load
currents, and set points applied to each physical converter. The
B-Box communicated to the SDT and DTBs over Ethernet for
coupling and dynamic control reconfiguration.
The DTB models were converted into C code and deployed
on the FPGA boards of NI-CRIO 9035. The models had a
fixed-step size of 10 µs. To facilitate communication, LabView
was employed to manage the Ethernet connectivity between
the OPAL-RT system and the DTBs. This setup allowed for
the reception of current contributions and the transmission of
important data, such as the SoC of the ES and converters
currents. Data were measured through Imperix sensors and
exchanged among the physical twins and the hierarchical
structure through the use of Ethernet as the primary commu-
nication protocol.
Before running the entire hierarchy autonomously, several
tests were performed to validate the components and the
hierarchy as a whole. The first test validated individual DTBs
against their respective hardware components. Once the DTBs
were validated, the SDT was validated against the hardware
measurements. Finally, the DTH was validated against the
hardware, and details are provided in the following subsec-
tions.
A. Digital Twin Blocks (DTBs) Experimental Validation
Verifying the fidelity between a DTB and its physical
counterpart is an important step in ensuring an accurate
representation of the behavior of the physical system. An
40 45 50 55 60 65
390
400
410
420
Voltage
(V)
PT Rec DTB
40 45 50 55 60 65
0
5
10
Current
(A)
IL
Rec PT IL
Rec DT
40 45 50 55 60 65
0
10
20
Current
(A)
IL
ES PT IL
ES DT
40 45 50 55 60 65
Time (s)
88
90
92
SoC
(%)
PT DT
Fig. 8: Validation of Digital Twin Blocks.
effective method to evaluate the dynamic response of the
system involves subjecting it to pulsed loads. This approach
enables the assessment of the DTB response to load changes
and facilitates the identification of any inconsistencies between
the DTB and the physical system that may not be evident
under steady-state conditions. The purpose of this test was
to validate the accuracy of DTB models by comparing them
with their respective physical converters. The nested loop
controls of the hardware were replicated in the DTBs, ensuring
regulation of the bus voltage at 400 V. During the test, both
the DTBs and the hardware ran simultaneously while a pulsed
load was applied to the common bus. The total load current
was measured and sent to the SDT, which decomposed the
load current by frequency and allocated portions to each
load converter. While the SDT was employed in this test,
the comparison focused only on the agreement between the
inductor currents, IL, of the two converters and their respective
DTBs. Figure 8 presents the comparison of the output voltage
and inductor current between DTB1 and the hardware rectifier
in the first and second plots, respectively. The third and fourth
plots compare the inductor current and SoC extracted from
the ES interface converter. These plots clearly demonstrate the
agreement between the physical and digital systems, thereby
validating the operation of DTBs.
B. System Digital Twin (SDT) Experimental Validation
Section III-A describes the SDT model as an equivalent
circuit used to predict the load contribution from each source
connected to the DC bus using Extended Droop Control.
In this experiment, both the hardware and the SDT model
were assigned constant control parameters, Rd and Cd. Then,
a pulsed load was applied to the hardware and the SDT
model. The predicted load currents from the SDT model
were compared to the load currents measured from each
hardware converter, as shown in Fig. 9. The first plot depicts
a comparison between the load contribution of the rectifier
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40 45 50 55 60 65
0
2
4
Current
(A) Rectifier PT Rectifier DT
40 45 50 55 60 65
Time (s)
-2
0
2
Current
(A)
ES PT ES DT
Fig. 9: System Digital Twin validation.
interface converter and its corresponding response from the
SDT, and the second plot compares the load contribution of the
ES interface converter with its corresponding response from
the SDT. Although the utilization of passive components in
the SDT model may result in certain current spikes generated
by the switching components of the physical converters not
being accounted for, the effect on the system is minimal. This
experiment shows that the load contribution between the ES
and the generator interfaces is observed to be in alignment for
both the SDT model and the physical converters in accordance
with the EDC scheme explained in Section III-A.
In order to measure the deviation between the outcomes
generated by digital models and the physical hardware, it is
necessary to conduct a quantitative comparison. To achieve
this, the Mean Absolute Percentage Error (MAPE) serves as
an indicator of the average percentage deviation between the
predicted and actual values and is defined as
MAPE = mean

Xact − Xpred
Xact

∗ 100% (3)
where Xpred denotes the output data of the digital models and
Xact represents the corresponding output data of the physical
hardware. A lower MAPE value indicates higher accuracy in
the digital models. The data obtained from physical converters
and the DTH were compared using (3) to evaluate the average
percentage deviation of the DTH from the hardware, as shown
in Table II.
C. Hierarchy Experimental Validation
To validate the fidelity of the DTH as a complete system,
DTBs were connected to the SDT, and a pulsed load scenario
was applied with the posture set to cruising. The SDT suc-
cessfully received the load scenario and effectively transmitted
the rectifier and ES current components to the corresponding
DTBs for simulation. The DTB results were then transmitted
back to the SDT, including the ES SoC.
TABLE II: ACCURACY OF HIERARCHICAL DIGITAL TWIN
DTH component Parameter Deviation from PT(%)
DTB1 Rectifier current ±5
DTB2 ES SoC ±1
SDT EDC rectifier current ±2
SDT EDC ES current ±1.85
40 45 50 55 60 65
Port
Cruise
Battle
Posture
40 45 50 55 60 65
-2
0
2
4
6
8
Current
(A)
Load
ES PT
ES DTB
Rectifier PT
Rectifier DTB
40 45 50 55 60 65
Time (s)
88
90
92
SoC
(%)
SoC PT SoC DTB
Fig. 10: Validation of the hierarchical digital twin.
Subsequently, the same load scenario was applied to the PT,
allowing for the measurement and recording of its response.
The response of the DTH and the physical hardware to the load
scenario, are depicted in Fig. 10. The second plot of the figure
clearly demonstrates that the load sharing between the ES and
rectifier DTBs aligns well with that of the physical converters.
This alignment signifies the successful synchronization and
coordination between the physical system and the virtual
models within the DTH. Due to the utilization of a single
cutoff frequency, the current contribution from each source
remained consistent throughout the experiment.
V. AUTONOMOUS OPERATION
During the autonomous test, the DTH and the physical
hardware were connected to transmit instantaneous hardware
results to the DTH and for the decision maker to change
the controls of the physical hardware in situ. When a load
was applied to the system, the decision maker transmitted
the load profile to the SDT for simulation. The SDT then
decomposed the load profile by frequency and forwarded
the currents of the generator and ES interface converters to
be simulated by their corresponding DTBs. The responses
from DTBs were subsequently transmitted back to the SDT.
Based on the simulation results obtained from DTBs and
according to the selected posture and SoC of the ES, new
Extended Droop Control parameters were provided by the
decision maker to the hardware controller, altering the current
sharing action. The response of the autonomous operation of
the hierarchy to different postures is shown in Fig. 11. The
cutoff frequency was adjusted, as defined by the objectives of
the decision maker, such that the ES contributed a varying
proportion of the load applied to the power system based
on the posture and prescribed rules of the decision maker.
For example, when the posture was changed to battle, the
cutoff frequency was lowered to its minimum value, thereby
increasing the value of the virtual capacitor. This modification
resulted in the maximum contribution from the ES system,
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30 35 40 45 50 55 60
Port
Cruising
Battle
Posture
f
c
= 0.05 Hz
f
c
=
0.01
Hz
f
c
= 0.25 Hz
f
c
= 0.05 Hz
30 35 40 45 50 55 60
-2
0
2
4
6
Current
(A)
Load Current
ES PT
ES DT
Rectifier PT
Rectifier DT
30 35 40 45 50 55 60
Time (s)
88
90
92
94
SoC
(%)
PT DT
Fig. 11: Autonomous operation of the hierarchy.
as evidenced in the second plot of Fig. 11 from 35 to 40
seconds. Upon changing the posture from battle to cruising,
the cutoff frequency was adjusted to the preset value from 40
to 53 seconds. Since the SoC dropped below the preset value
of 90% at 53 seconds, the ES contribution was reduced.
The successful completion of this test verifies the ability of
the proposed DTH to function independently and confirms that
the controls of the PT can be reconfigured in real-time using
a hierarchical digital twin. By leveraging advanced control
algorithms, the DTH can regulate and maintain the behavior
of the entire system, ensuring its stability and efficiency. The
autonomous operation of the DTH is essential for maintaining
system reliability and minimizing downtime. With the ability
to operate independently, the DTH can promptly respond to
changes in the system and adjust accordingly, thereby ensuring
reliable and uninterrupted system operation.
Modeling DTs presents a significant challenge, particularly
in sensor calibration, as the accuracy of the DT heavily relies
on precise measurements from the PT. Even minor discrep-
ancies in sensor readings can result in noticeable disparities
between the virtual and physical systems. Therefore, ensuring
proper calibration and maintenance of sensors is crucial to
obtain accurate data. In real-world scenarios, high-frequency
noise often interferes with sensor measurements, introducing
inaccuracies. To mitigate this noise and improve measurement
accuracy, appropriate filtering techniques can be applied to the
sensor signals. Implementing filtering enhances the accuracy
of the DTs by refining the received signals from the sensors.
VI. CONCLUSIONS  FUTURE WORK
A hierarchical digital twin of a naval DC power system was
developed and experimentally verified through an implementa-
tion example which enabled modifications to the system-level
controls in real-time. Detailed definitions for each layer of the
DTH were provided, along with the corresponding hardware
used. The developed DTH, based on the proposed defini-
tions and system decomposition, successfully autonomously
reconfigured the hardware controls during system operation.
This capability offers increased flexibility and responsiveness,
bearing significant implications for the advancement of next-
generation power systems in naval applications. The maximum
deviations observed between the developed DTH and the
hardware demonstrate a strong alignment between the DTH
decomposition and the physical twin.
While this study primarily focused on modeling the electri-
cal domain of the hardware, future developments can broaden
the scope of the DTH to encompass additional simulation do-
mains. One potential progression is to explore the integration
of thermal models for electrical components. By incorporating
thermal models of the ES, converters, and power cables
into multiple DTBs, control parameters can be dynamically
adjusted based on thermal information received by the SDT.
This modeling capability empowers the SDT to request the
thermal profile of physical subsystems from their correspond-
ing DTBs, providing valuable insights into remaining life
while improving power distribution to load buses. Moreover,
real-world scenarios and naval load profiles can be applied,
utilizing historical data to validate system stability.
ACKNOWLEDGMENT
This work is supported by the Office of Naval Research
(ONR) under ONR contract N00014-22-C-1003.
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Hierarchical Digital Twin of a Naval Power System

  • 1. Hierarchical Digital Twin of a Naval Power System Kerry Sado*, Student Member, IEEE, Jack Hannum, Student Member, IEEE, Eric Skinner, Student Member, IEEE, Herbert L. Ginn, Senior Member, IEEE, and Kristen Booth, Member, IEEE Department of Electrical Engineering University of South Carolina Columbia, United States *ksado@email.sc.edu Abstract—A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware. Index Terms—digital twin, power systems, electrical ships, hierarchical digital twin, control system, power electronics I. INTRODUCTION Generally, the term Digital Twin (DT) refers to the virtual representation of a physical system or subsystem, also known as the Physical Twin (PT). According to NASA, a DT is defined as a highly accurate simulation that incorporates multiple physics, scales, and probabilities and mirrors the state of its corresponding PT based on a combination of historical data, live sensor readings, and physical models [1]. DTs are the collection of dynamic digital models that accurately represent an existing physical system or subsystem [2]. The goal of the DT is to generate high fidelity virtual representations of each physical entity, capable of simulating their states and behaviors to assess, optimize, and predict current and future scenarios [3]. The significance of DTs is rapidly gaining recognition from both academic and industrial sectors as DTs have potential applications across multiple sectors, including aerospace, renewable energy, and naval applications [4]–[8]. The maritime industry recognizes the potential of DT technology as an opportunity for improvement [9]. There This work is supported by the Office of Naval Research (ONR) under ONR contract N00014-22-C-1003. has been a growing emphasis on digitalizing the maritime industry, as new technologies are expected to enhance the speed of processes and inform data-driven decisions through- out the maritime value chain [10]. DTs have the potential to revolutionize and enhance various aspects of naval power systems, encompassing performance, efficiency, maintenance, fault analysis, and resiliency. By collecting and analyzing real- time data from naval power systems, DTs can effectively identify and address performance bottlenecks. By providing a comprehensive view of the power system, DTs can help identify potential problems before they cause outages or other disruptions; this proactive approach can contribute to improv- ing maintenance and fault analysis. If a fault does occur, the DT can determine a stable reconfiguration to enable safe return to port. Given the potential benefits of DTs, it is a significant tool for enhancing the performance, efficiency, and reliability of naval power systems. The ultimate goal for DTs is to achieve a completely autonomous system that gathers information about its operation and simulates its effects. This would enable the DT to support any decision-making regarding the asset [13]. Recently, the International Maritime Organization (IMO) enacted a strategic plan aimed at decreasing greenhouse gas emissions in shipping by 50% from 2008 levels by 2050 with the ultimate goal of phasing them out entirely by the end of the century [14]. This leads to the electrification of ships, which requires developing innovative technologies that can enhance ship design and maintain operational efficiency has become a critical matter [15]. The United States Navy is transitioning towards the electrification of its vessels, requiring a higher demand for electric power than previous generations. This transformation in power usage will not only escalate in magnitude but also become more dynamic with large pulsed loads, such as air and missile defense radars and directed energy weapons [16]. As a result of the increasing usage of DC power sources in naval systems, the Navy is investigating the possibility of adopting DC distribution systems [17]. The implementation of DC systems for vessels is anticipated to result in the power system having a greater number of power electronic converters and Energy Storage (ES) units. While converters and ES can provide fast response to pulsed loads, they also increase the control complexity for power sharing within the system. For 20230702 Approved, DCN# 543-691-23 DISTRIBUTION STATEMENT A. Approved for public release, distribution unlimited. 1 of 8
  • 2. these increasingly complex interactions, DTs can be utilized to mirror the physical system using multiphysics simulations and historical data to monitor and predict system responses. The integration of DTs on various power system components on shipboards will significantly enhance the overall success of the fleet [18]. By implementing DTs, a range of benefits can be achieved, such as decreased operational costs and streamlined processes, enhanced productivity, improved decision-making, advanced predictive and preventive maintenance. Although DT technology offers several potential benefits, it also faces significant challenges. One obstacle is the difficulty of integrating data from various sources and maintaining synchronization between the DT and its PT. Additionally, the computational effort may increase beyond the capabilities to be held within a single DT or available computational hardware as the level of detail increases due to system complexity. In systems, such as naval ships, with constantly updating equipment, a single, comprehensive DT must be reconfigured whenever a component is replaced or added to the system. Therefore, a Digital Twin Hierarchy (DTH) is proposed to enable increased complexity, future system modifications, and faster computation speeds by distributing computational effort. The number of layers in the hierarchy can be determined by system complexity, resolution needed, and physical measure- ments collected. The closest concepts found in the literature to the proposed DTH provide a generic architecture that captures the essential components of a DT aligned with the layers of the Reference Architecture Model Industry 4.0 for manufacturing [19] or highlight how mechanical parts can be categorized by feature using a hierarchical digital mapping [20]. The “layers” of these hierarchical digital twins are the IT layers and the material properties, drawings, and heterogeneous data, respectively. Ultimately, the information was condensed into a single DT. In the presented DTH, the models are maintained and modeled independently. A hierarchical digital twin offers several benefits, including the distribution of computational effort, the integration of dissimilar computing hardware, and the expansion of modeled quantities. However, it is important to limit the amount of information transferred between layers of the hierarchy to obtain these benefits. In this work, an electrical domain DTH was conceptualized and demonstrated for managing the power system of naval ships and validated experimentally. Though a DTH can be used for a variety of domains and performance outcomes, the DTH presented in this paper is capable of power sharing prediction and is used for dynamic control reconfiguration autonomously during operation. In Section II, an introduction to the DTH and definitions are provided. An application of the DTH and its layers are provided in Section III. The hardware used for this work, the validation of DTBs in isolation, and their integration into the hierarchy are provided in Section IV. Section V provides results of the digital twin-based dynamic control reconfiguration, and the autonomous operation of the DTH. Finally, Section VI highlights conclusions and future work. II. INTRODUCTION TO THE DIGITAL TWIN HIERARCHY To introduce the hierarchical digital twin technique, a 2- level hierarchy is implemented, as shown in Fig. 1. The lowest level represents each individual converter; these are defined as Digital Twin Blocks (DTBs). The DTBs have no communication between one another but communicate with the higher level System Digital Twin (SDT). The SDT is the upper level of the DTH that combines data received from DTBs and models the behavior of the entire system. The DTH consists of decomposed but interconnected mod- els with varying degrees of detail and complexity. This design enables the distribution of complexity among DTBs, allowing for the modeling of larger systems by replicating power system components as separate DTBs. The data generated by DTBs are fed up to the SDT, which integrates the information to provide a comprehensive representation of the power system. This approach enables larger systems to be modeled at varying timescales, depending on the query from the decision maker. The decision maker can be autonomous or incorporate a human-in-the-loop to define potential scenarios or determine a system response. A. System Digital Twin (SDT) As systems grow in size and complexity, it can become increasingly challenging to model them in detail in a single, comprehensive simulation, especially in real-time or faster than real-time applications. Despite having suitable tools and algorithms, including artificial intelligence, applying data di- rectly from complex power systems to DT models can be difficult. However, the SDT needs only to capture the essential dynamics of the power system and inform the decision-making process by incorporating all relevant data to be passed to the decision maker. To implement a SDT, the model should only include interac- tions between components at the next level of the hierarchy, re- sulting in less computationally expensive models. This means that only the necessary quantities are calculated to predict the Maintenance Services Decision Maker Load Scenario Predictive states Model replicas DTB1 Behavior simulation data Digital Twin Blocks Control parameters System Digital Twin Control Services Prediction Services Monitoring Services System Digital Twin System behavior data Physical Twin Hardware Reference points & sensor data Model replicas DTB2 Behavior simulation data Model replicas DTBn Behavior simulation data Fig. 1: Generic hierarchical digital twin. 20230702 Approved, DCN# 543-691-23 DISTRIBUTION STATEMENT A. 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  • 3. behavior of the entire system. Any system quantities that are not required to model the component interactions are delegated to DTBs. The SDT aggregates the quantities returned from DTBs and informs a decision maker, which is considered external to the DTH. B. Digital Twin Block (DTB) A DTB is a representation or model of a component or subsystem of the PT. The level of detail developed in a DTB is dependent on the hardware measurements, timescale of study, and system-level relationships. Models may be of high fidelity or low fidelity and infer quantities not measured in hardware. Complex models may require longer simulation times to complete the DT study, so a simpler model may be more beneficial, depending on the application, timescale, or decision to be made. DTBs may employ more advanced modeling techniques and use smaller time steps than those used in SDT models. Ultimately, the fundamental requirement of a DTB is to provide data that will enable the SDT to create a system-level response based on the provided information. III. AN APPLICATION OF THE DIGITAL TWIN HIERARCHY To validate the concept of the proposed DTH, a system to be twinned must first be defined. The demonstrator is a simplified representation of the power system of a ship and contains both constant and pulsed loads. The power system consists of a DC bus, which is supplied by a 3-ϕ generator and an energy storage, as shown in Fig. 2. By utilizing this simplified yet practical system, the proposed DTH concept can be validated, and its effectiveness in monitoring and controlling the power system performance can be presented. The validation implementation includes a SDT and two DTBs. Figure 3 highlights the details of this particular DTH example and the information being communicated up and down the hierarchy. Specifically, DTB1 and DTB2 represent a 3-ϕ diode bridge rectifier with a boost converter output stage and an energy storage interface converter, respectively. Further details on the modeling of the experimental DTH layers are available in the subsequent subsections. A. Modeling of System Digital Twin (SDT) The SDT is being used to enable dynamic current sharing between the 3-ϕ source and the ES using Extended Droop Control [21]. Extended Droop Control allocates portions of the load current to each converter on the bus and is a variation of well-known resistive droop control. Extended Droop Control uses a virtual RC filter created by the virtual impedances to divide the load current by frequency and allocate it to each of Energy storage 3-ϕ Source Pulsed load Other loads DTB1 DTB2 Fig. 2: Demonstration system for implementing a hierarchical digital twin. Physical Twin System Digital Twin Extended Droop Control Reference points sensor data EDC parameters Load current Converter currents Battery SoC Decision Maker Load Scenario Model replicas Rectifier Model replicas DTB2 ES Interface DTB1 Fig. 3: Demonstration specific hierarchical digital twin. the converters connected to a bus. This division is especially useful when two sources with vastly different response times, like a generator and a battery, are connected to the same bus. In the context of an RC load filter, the cutoff frequency can be established in such a way to ensure all power source ramp rate constraints are met. The maximum tolerable bus voltage deviation, ∆Vmax, and the maximum converter current, Imax, are used to specify the virtual resistor in (1), while the desired cutoff frequency, fc, of the load filter determines the virtual capacitance in (2) [22], [23]. Rd = ∆Vmax Imax (1) Cd = 1 2πfcRd (2) Rd and Cd are the virtual resistance and capacitance of the droop control, respectively. The voltage reference supplied to the generator rectifier is altered by the virtual resistor. Similarly, the virtual capacitor impacts the voltage reference of the ES interface converter. As the virtual capacitor is charged, the ES current output is reduced. The desired cutoff frequency may change in response to the dynamic operating environment in which the system runs. For a cruising ship, it may be desired that the ES is used less to preserve its health. In this case, the cutoff frequency can be increased which leads to reducing the value of Cd, and hence, decrease the ES contribution to current pulses by ramping the generator to match the load more quickly. By replacing the capacitor with a variable capacitor, the cutoff frequency of the system can be continuously tuned to match the operating environment. To develop the DTH, the initial phase involves constructing a model that characterizes the dynamic responses of the bus voltage and the current distribution between the two sources under Extended Droop Control. Subsequently, the Extended Droop Control equivalent circuit, as illustrated in Fig. 4, is integrated into the DTH in the SDT. In the circuit, Ifast and Islow correspond to the current provided by the ES and the generator interface converters, respectively. This model can be solved quickly since it does not require a small time-step, is suitable for look-ahead simulations, and can be used for real-time shadowing of the system as it operates. 20230702 Approved, DCN# 543-691-23 DISTRIBUTION STATEMENT A. Approved for public release, distribution unlimited. 3 of 8
  • 4. V ref I load Rd I fast I slow V ref Cd Fig. 4: Equivalent circuit model of Extended Droop Control [21]. B. Modeling of Digital Twin Blocks (DTBs) The demonstrator, shown in Fig. 2, consists of two power converters. Each of which can be decomposed into separate subsystems as DTBs. DTBs can be employed to anticipate the behavior and performance of the converter under different operating conditions. Moreover, DTBs can be utilized for real- time monitoring and control during operation, enabling predic- tive maintenance and detecting potential problems before they occur. The creation of a DTB for a power electronic converter requires considering the impact of parameters, such as input voltage and current, on the performance of the converter. For the purpose of enabling a simple DTH for this work, an averaged switching model is used in this study; however, other models can be used in accordance with the system being described and the required control decisions to be made. In this context, the DTB of the generator interface is modeled as a 3-ϕ diode bridge rectifier with a boost converter output stage, as shown in Fig. 5. The DTB of the ES interface converter is modeled using the averaged switching model shown in Fig. 6. In the hierarchy developed to model the system shown in Fig. 4, State of Charge (SoC) of the ES could be inferred at the SDT but not explicitly measured. Since the SoC is a key limiter of the ES current contribution to pulses, it needs to be calculated by the DTB and passed up the hierarchy. In addition to calculating the SoC of the ES, the replication of the control logic makes the DTB a more accurate representation of the interface converter than could be achieved by the passive components at the SDT level. Through the replication of the nested loop controls of the power converter, the DTB is capable of compensating for non-linearities caused by saturation limits on the voltage and current controllers of the hardware. The SDT computes transient load sharing between the two converters and relays it down the hierarchy to be simulated by their respective DTBs. Corresponding results are sent back to the SDT for analysis. C. Decision Maker Modeling In this work, the focus is on the proposed DTH, and the decision maker is considered external to it. However, to A B C L Vo rL V o D D IL IL C rc C rc 3-ϕ source Fig. 5: Three-phase diode bridge rectifier with a boost converter output stage. L rL V o D D IL IL C rc Vin Vo Fig. 6: Averaged switching model of the boost converter. validate the concept of the DTH, a fuzzy logic-based decision maker was modeled. The decision maker is developed using an ontological technique called Posture-Based Alignment [25]. Posture-Based Alignment enables the ship to attain a posture relevant to the active mission segment. In one posture, a specific response can be vital, but in another, that same activity is completely irrelevant to the success of the mission segment. In this application, the various postures determine load current contribution from the ES and generator. Accordingly, three postures were adopted: “Port, “Cruise,” and “Battle;” each represents a distinct set of objectives for the decision maker to follow. In “Port,” the ship is presumed to be at minimal readiness, and the land-tie connection or generator should serve the load demand. In “Cruise,” the ship is at a higher state of readiness, and the current distribution depends on the ES SoC. When the SoC is greater than 90%, more current is provided by the ES, and it is reduced below this SoC level. This approach ensures that the ES is ready to respond to any shift in posture or other events. The primary objectives of this posture are to maintain ES readiness, reduce the wear and fuel expenses of the generators, and ease generator stress. In “Battle,” the ES operates without any SoC constraints and supplies the maximum allowable energy during transient load conditions. Therefore, the generator and ES operate at their peak rating to meet the demands from propulsion, weapons, and other crucial systems. The predefined posture-based align- ment boundaries are arbitrary values; these values can be updated based on the type of ES or generator capabilities. Postures and their objectives are summarized in Table I. IV. EXPERIMENTAL TESTBED VALIDATION The hardware testbed used for for this work is shown Fig. 7. The power converters were implemented using Im- perix PEB8032 Silicon IGBT half-bridge modules [26]. The modules were operated at a frequency of 20 kHz. A 1.25 mH inductor was used in the boost converter design. The bus voltage was monitored using an Imperix DIN800V sensor, and the inductor currents were monitored with the built-in current sensors of the PEB8032 modules. Imperix external DIN50A current sensors were connected with converters output to measure the load current of each converter. A Chroma DC TABLE I: DECISION MAKER POSTURES Posture Objectives fc (Hz) Port ES serves minimum. Load is assigned to the generator. 10 Cruise SoC>90%:ES serves portion of the load. SoC<90%: ES serves minimum. 0.05 0.25 Battle ES supplies maximum allowable energy. 0.01 20230702 Approved, DCN# 543-691-23 DISTRIBUTION STATEMENT A. Approved for public release, distribution unlimited. 4 of 8
  • 5. ES 3-ϕ transformer Electronic DC load System digital twin DTB1 DTB2 Controller Physical twin 2 Physical twin 1 Fig. 7: Hardware testbed. electronic load was utilized to handle both constant and pulsed loads, serving as a current sink that drew a baseline load of a 1 A baseload and 2 A pulsed loads. The converters were controlled using the Imperix B-Box real-time control platform. The SDT is running an equivalent circuit model of the EDC using a timestep of 1 ms, depicted in Fig. 4. Simulink was used to implement the model, and RT-LAB was used to deploy the model in real-time on an Opal-RT OP5607 real-time simulator. The real-time SDT simulator sent current contributions to each DTB. The DTBs also received sensor measurements for initialization over Ethernet, including input voltages, load currents, and set points applied to each physical converter. The B-Box communicated to the SDT and DTBs over Ethernet for coupling and dynamic control reconfiguration. The DTB models were converted into C code and deployed on the FPGA boards of NI-CRIO 9035. The models had a fixed-step size of 10 µs. To facilitate communication, LabView was employed to manage the Ethernet connectivity between the OPAL-RT system and the DTBs. This setup allowed for the reception of current contributions and the transmission of important data, such as the SoC of the ES and converters currents. Data were measured through Imperix sensors and exchanged among the physical twins and the hierarchical structure through the use of Ethernet as the primary commu- nication protocol. Before running the entire hierarchy autonomously, several tests were performed to validate the components and the hierarchy as a whole. The first test validated individual DTBs against their respective hardware components. Once the DTBs were validated, the SDT was validated against the hardware measurements. Finally, the DTH was validated against the hardware, and details are provided in the following subsec- tions. A. Digital Twin Blocks (DTBs) Experimental Validation Verifying the fidelity between a DTB and its physical counterpart is an important step in ensuring an accurate representation of the behavior of the physical system. An 40 45 50 55 60 65 390 400 410 420 Voltage (V) PT Rec DTB 40 45 50 55 60 65 0 5 10 Current (A) IL Rec PT IL Rec DT 40 45 50 55 60 65 0 10 20 Current (A) IL ES PT IL ES DT 40 45 50 55 60 65 Time (s) 88 90 92 SoC (%) PT DT Fig. 8: Validation of Digital Twin Blocks. effective method to evaluate the dynamic response of the system involves subjecting it to pulsed loads. This approach enables the assessment of the DTB response to load changes and facilitates the identification of any inconsistencies between the DTB and the physical system that may not be evident under steady-state conditions. The purpose of this test was to validate the accuracy of DTB models by comparing them with their respective physical converters. The nested loop controls of the hardware were replicated in the DTBs, ensuring regulation of the bus voltage at 400 V. During the test, both the DTBs and the hardware ran simultaneously while a pulsed load was applied to the common bus. The total load current was measured and sent to the SDT, which decomposed the load current by frequency and allocated portions to each load converter. While the SDT was employed in this test, the comparison focused only on the agreement between the inductor currents, IL, of the two converters and their respective DTBs. Figure 8 presents the comparison of the output voltage and inductor current between DTB1 and the hardware rectifier in the first and second plots, respectively. The third and fourth plots compare the inductor current and SoC extracted from the ES interface converter. These plots clearly demonstrate the agreement between the physical and digital systems, thereby validating the operation of DTBs. B. System Digital Twin (SDT) Experimental Validation Section III-A describes the SDT model as an equivalent circuit used to predict the load contribution from each source connected to the DC bus using Extended Droop Control. In this experiment, both the hardware and the SDT model were assigned constant control parameters, Rd and Cd. Then, a pulsed load was applied to the hardware and the SDT model. The predicted load currents from the SDT model were compared to the load currents measured from each hardware converter, as shown in Fig. 9. The first plot depicts a comparison between the load contribution of the rectifier 20230702 Approved, DCN# 543-691-23 DISTRIBUTION STATEMENT A. Approved for public release, distribution unlimited. 5 of 8
  • 6. 40 45 50 55 60 65 0 2 4 Current (A) Rectifier PT Rectifier DT 40 45 50 55 60 65 Time (s) -2 0 2 Current (A) ES PT ES DT Fig. 9: System Digital Twin validation. interface converter and its corresponding response from the SDT, and the second plot compares the load contribution of the ES interface converter with its corresponding response from the SDT. Although the utilization of passive components in the SDT model may result in certain current spikes generated by the switching components of the physical converters not being accounted for, the effect on the system is minimal. This experiment shows that the load contribution between the ES and the generator interfaces is observed to be in alignment for both the SDT model and the physical converters in accordance with the EDC scheme explained in Section III-A. In order to measure the deviation between the outcomes generated by digital models and the physical hardware, it is necessary to conduct a quantitative comparison. To achieve this, the Mean Absolute Percentage Error (MAPE) serves as an indicator of the average percentage deviation between the predicted and actual values and is defined as MAPE = mean Xact − Xpred Xact ∗ 100% (3) where Xpred denotes the output data of the digital models and Xact represents the corresponding output data of the physical hardware. A lower MAPE value indicates higher accuracy in the digital models. The data obtained from physical converters and the DTH were compared using (3) to evaluate the average percentage deviation of the DTH from the hardware, as shown in Table II. C. Hierarchy Experimental Validation To validate the fidelity of the DTH as a complete system, DTBs were connected to the SDT, and a pulsed load scenario was applied with the posture set to cruising. The SDT suc- cessfully received the load scenario and effectively transmitted the rectifier and ES current components to the corresponding DTBs for simulation. The DTB results were then transmitted back to the SDT, including the ES SoC. TABLE II: ACCURACY OF HIERARCHICAL DIGITAL TWIN DTH component Parameter Deviation from PT(%) DTB1 Rectifier current ±5 DTB2 ES SoC ±1 SDT EDC rectifier current ±2 SDT EDC ES current ±1.85 40 45 50 55 60 65 Port Cruise Battle Posture 40 45 50 55 60 65 -2 0 2 4 6 8 Current (A) Load ES PT ES DTB Rectifier PT Rectifier DTB 40 45 50 55 60 65 Time (s) 88 90 92 SoC (%) SoC PT SoC DTB Fig. 10: Validation of the hierarchical digital twin. Subsequently, the same load scenario was applied to the PT, allowing for the measurement and recording of its response. The response of the DTH and the physical hardware to the load scenario, are depicted in Fig. 10. The second plot of the figure clearly demonstrates that the load sharing between the ES and rectifier DTBs aligns well with that of the physical converters. This alignment signifies the successful synchronization and coordination between the physical system and the virtual models within the DTH. Due to the utilization of a single cutoff frequency, the current contribution from each source remained consistent throughout the experiment. V. AUTONOMOUS OPERATION During the autonomous test, the DTH and the physical hardware were connected to transmit instantaneous hardware results to the DTH and for the decision maker to change the controls of the physical hardware in situ. When a load was applied to the system, the decision maker transmitted the load profile to the SDT for simulation. The SDT then decomposed the load profile by frequency and forwarded the currents of the generator and ES interface converters to be simulated by their corresponding DTBs. The responses from DTBs were subsequently transmitted back to the SDT. Based on the simulation results obtained from DTBs and according to the selected posture and SoC of the ES, new Extended Droop Control parameters were provided by the decision maker to the hardware controller, altering the current sharing action. The response of the autonomous operation of the hierarchy to different postures is shown in Fig. 11. The cutoff frequency was adjusted, as defined by the objectives of the decision maker, such that the ES contributed a varying proportion of the load applied to the power system based on the posture and prescribed rules of the decision maker. For example, when the posture was changed to battle, the cutoff frequency was lowered to its minimum value, thereby increasing the value of the virtual capacitor. This modification resulted in the maximum contribution from the ES system, 20230702 Approved, DCN# 543-691-23 DISTRIBUTION STATEMENT A. Approved for public release, distribution unlimited. 6 of 8
  • 7. 30 35 40 45 50 55 60 Port Cruising Battle Posture f c = 0.05 Hz f c = 0.01 Hz f c = 0.25 Hz f c = 0.05 Hz 30 35 40 45 50 55 60 -2 0 2 4 6 Current (A) Load Current ES PT ES DT Rectifier PT Rectifier DT 30 35 40 45 50 55 60 Time (s) 88 90 92 94 SoC (%) PT DT Fig. 11: Autonomous operation of the hierarchy. as evidenced in the second plot of Fig. 11 from 35 to 40 seconds. Upon changing the posture from battle to cruising, the cutoff frequency was adjusted to the preset value from 40 to 53 seconds. Since the SoC dropped below the preset value of 90% at 53 seconds, the ES contribution was reduced. The successful completion of this test verifies the ability of the proposed DTH to function independently and confirms that the controls of the PT can be reconfigured in real-time using a hierarchical digital twin. By leveraging advanced control algorithms, the DTH can regulate and maintain the behavior of the entire system, ensuring its stability and efficiency. The autonomous operation of the DTH is essential for maintaining system reliability and minimizing downtime. With the ability to operate independently, the DTH can promptly respond to changes in the system and adjust accordingly, thereby ensuring reliable and uninterrupted system operation. Modeling DTs presents a significant challenge, particularly in sensor calibration, as the accuracy of the DT heavily relies on precise measurements from the PT. Even minor discrep- ancies in sensor readings can result in noticeable disparities between the virtual and physical systems. Therefore, ensuring proper calibration and maintenance of sensors is crucial to obtain accurate data. In real-world scenarios, high-frequency noise often interferes with sensor measurements, introducing inaccuracies. To mitigate this noise and improve measurement accuracy, appropriate filtering techniques can be applied to the sensor signals. Implementing filtering enhances the accuracy of the DTs by refining the received signals from the sensors. VI. CONCLUSIONS FUTURE WORK A hierarchical digital twin of a naval DC power system was developed and experimentally verified through an implementa- tion example which enabled modifications to the system-level controls in real-time. Detailed definitions for each layer of the DTH were provided, along with the corresponding hardware used. The developed DTH, based on the proposed defini- tions and system decomposition, successfully autonomously reconfigured the hardware controls during system operation. This capability offers increased flexibility and responsiveness, bearing significant implications for the advancement of next- generation power systems in naval applications. The maximum deviations observed between the developed DTH and the hardware demonstrate a strong alignment between the DTH decomposition and the physical twin. While this study primarily focused on modeling the electri- cal domain of the hardware, future developments can broaden the scope of the DTH to encompass additional simulation do- mains. One potential progression is to explore the integration of thermal models for electrical components. By incorporating thermal models of the ES, converters, and power cables into multiple DTBs, control parameters can be dynamically adjusted based on thermal information received by the SDT. This modeling capability empowers the SDT to request the thermal profile of physical subsystems from their correspond- ing DTBs, providing valuable insights into remaining life while improving power distribution to load buses. Moreover, real-world scenarios and naval load profiles can be applied, utilizing historical data to validate system stability. ACKNOWLEDGMENT This work is supported by the Office of Naval Research (ONR) under ONR contract N00014-22-C-1003. REFERENCES [1] E. H. Glaessgen and D. S. 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