# Redefinition of Digital Twin and its Situation Awareness Framework Designing
Towards Fourth Paradigm for Energy Internet of Things

Xing He, , Yuezhong Tang, Shuyan Ma, Qian Ai, Fei Tao, Robert Qiu E-mail
address of the corresponding author Xing HE<EMAIL_ADDRESS>This work was
partly supported by National Key R&D Program of China (2021YFB2401204),
National Natural Science Foundation of China (52277111), and Science and
Technology Commission of Shanghai Municipality (21DZ1208300).

###### Abstract

Traditional knowledge-based situation awareness (SA) modes struggle to adapt
to the escalating complexity of today’s Energy Internet of Things (EIoT),
necessitating a pivotal paradigm shift. In response, this work introduces a
pioneering data-driven SA framework, termed digital twin-based situation
awareness (DT-SA), aiming to bridge existing gaps between data and demands,
and further to enhance SA capabilities within the complex EIoT landscape.
First, we redefine the concept of digital twin (DT) within the EIoT context,
aligning it with data-intensive scientific discovery paradigm (the Fourth
Paradigm) so as to waken EIoT’s sleeping data; this contextual redefinition
lays the cornerstone of our DT-SA framework for EIoT. Then, the framework is
comprehensively explored through its four fundamental steps: digitalization,
simulation, informatization, and intellectualization. These steps initiate a
virtual ecosystem conducive to a continuously self-adaptive, self-learning,
and self-evolving big model (BM), further contributing to the evolution and
effectiveness of DT-SA in engineering. Our framework is characterized by the
incorporation of system theory and Fourth Paradigm as guiding ideologies, DT
as data engine, and BM as intelligence engine. This unique combination forms
the backbone of our approach. This work extends beyond engineering, stepping
into the domain of data science—DT-SA not only enhances management practices
for EIoT users/operators, but also propels advancements in pattern analysis
and machine intelligence (PAMI) within the intricate fabric of a complex
system. Numerous real-world cases validate our DT-SA framework.

###### Index Terms:

big data analytics, complex system, digital twin, energy internet of things,
Fourth Paradigm, situation awareness

##  I Introduction

Energy internet of things (EIoT) emerges as a potential solution to energy
crisis and environmental problems. EIoT encompasses heterogeneous distributed
energy resources units (DERs) [1], including uncertain distributed generation
units (e.g., photovoltaic, wind turbines), flexible demand-side units (e.g.,
air conditioning, thermal energy storage), and energy prosumer (e.g., electric
vehicles, energy storage). EIoT is a complex system in essence [2], and its
complexity is ever increasing in various aspect [3]: a) connecting nearby
utilities improves security and efficiency, resulting in a vast interconnected
system; b) continuous injection of cell units, DERs as typical ones, that are
large in number, small in size, distributed in deployment, diverse in
behaviors, smart in response, and uncertain in control [4]; and c) multiple
physical disciplines (electrical, magnetomechanics, etc.) are closely coupled
[5]. All these driving forces lead to an open, flat, and non-linear complex
EIoT as illustrated in Figure 1 [6].

For such a complex EIoT, situation awareness (SA) holds critical significance
for its routine operation. Reference [7] defines SA as the perception of
environmental elements, the comprehension of their meaning, and the projection
of their status in the near future. In the realm of EIoT, SA plays a pivotal
role in supporting decision-making for both the individual behaviors of DER as
well as the collective actions of DER aggregation. Moreover, SA contributes to
the stable operation of EIoT—inadequate SA was identified as a root cause for
the world’s biggest blackout in history, the US–Canada Blackout [8]. This
underscores the crucial role of SA in preventing and mitigating potentially
catastrophic events in the daily operation of EIoT.

Figure 1: Development trend of modern EIoT [6]

###  I-A Motivation for DT-based Situation Awareness

Traditional SA modes are in urgent need of change, since their struggle to
keep pace with EIoT’s escalating complexity. This complexity frequently gives
rise to emergence [9] and chaos [10] phenomena that go beyond the scope of
reductionism111 Reductionism is any of several related philosophical ideas
regarding the associations between phenomena which can be described in terms
of other simpler or more fundamental phenomena. It is also described as an
intellectual and philosophical position that interprets a complex system as
the sum of its parts [11]., as discussed in Section II-B.

Taking a step back, even if reductionism may sometimes effectively model
certain EIoT scenarios, the complexity of EIoT modeling often requires
addressing comprehensive and flexible scenarios, taking into account multi-
stakeholder dynamics, multi-objective requirements, diverse paths, and high
levels of uncertainty. In this regard, both knowledge-based modes and solely
data-driven modes exhibit limitations. Knowledge-based algorithms are
vulnerable to insufficient model accuracy [12] or even the absence of domain-
specific model [13]. Yet, despite a solely data-driven model (e.g., neural
network) appearing successfully in building a “black-box” for specific purpose
(e.g., anomaly detection [14, 15]), it still struggles to meet SA requirements
in EIoT, mainly due to two factors: a) inadequate samples for model training,
especially those with “abnormal operating conditions” labels, and b) the
inherent lack of interpretability for “black-box” models.

###  I-B Contribution and Organization of this Work

Thanks to data-intensive scientific discovery paradigm (i.e., the Fourth
Paradigm [16]), this paper, by integrating the ongoing digitalization progress
of EIoT and its overall digital architecture, introduces an SA framework based
on our redefined digital twin (DT), termed DT-SA. DT-SA is designed to
systematically explore various potential evolutionary paths of EIoT in the
virtual space, with a coverage of the simulation, analysis, decision-making,
and verification procedures. The ever-increasing growth of data in EIoT,
coupled with emerging data technologies/disciplines, sets the stage for our
DT-SA.

The exploration of DT-SA begins by redefining the concept of DT. Although DT’s
origins lie in fields like aviation and workshops, the DT tailored for EIoT
demonstrates distinctive characteristics that deserve a redefinition. In
contrast to domains heavily reliant on computer vision and precise control
[17], EIoT-DT prioritizes deduction and decision-making on the action and
interaction of DERs within a complex system. Specifically, EIoT-DT endeavors
to project physical entities (PEs) in the real EIoT onto virtual entities
(VEs) in the digital space, contributing to the facilitation of big model (BM)
(refer to Section II-D). The BM, by integrating a system simulator, a
situational awareness, and a decision-maker, serves a pivotal role in
converting extensive field data and expert experience into informative
criteria for domain-specific decision-making, surpassing mere for
visualization. The BM acts as a data-intensive intelligence engine for various
downstream domain-specific tasks, with the goal of enhancing management and
adding value to environmental PEs through monitoring (understanding the state
of EIoT and its DERs), testing (comprehending the reaction to environment
changes and its consequences), and optimizing (striving for improved decision-
making).

To support such a BM, the VE undergoes an evolution beyond being a mere
replica of the real-world PE. Instead, VE is empowered for “free-style”
evolution in a “parallel universe” or “mateverse”, needing only to follow a
few basic laws. This evolution of VE enables the generation of multi-scenario
(virtual) data for BM training. In concrete, our research progresses by
customizing the VE (image) based on its corresponding PE (inverse image), with
an emphasis on DERs’ fundamental properties and potential behaviors (refer to
Section V). Subsequently, Monte Carlo simulations—accounting for various
scenarios, multiple time-scales, distinct evolution-paths, etc.—are conducted
to generate nearly full-coverage data in parallel universe. These data
facilitate the self-adaptive, self-learning, and self-evolving BM for EIoT at
a macro-level. In such a manner, DT provides a natural systematic life-cycle
SA in a virtual space, termed DT-SA. In general, our DT-SA comprises four key
steps—digitalization, simulation, informatization, and intellectualization;
the details are elaborated in Section IV-C.

The rest of this paper is structured as follows: Section II delves into the
roadmap of DT-SA in EIoT, with an emphasis on the spatial-temporal data
utilization (refer to Section III). Section IV presents a redefinition of DT
(more like metaverse), along with the designed DT-SA framework, focusing on VE
model (refer to Section V). Section VI backs DT-SA up with case studies using
field data. Section VII concludes our work.

##  II Roadmap of DT-SA in Fourth Paradigm

A concise roadmap of DT-SA, as depicted in Figure 2, is presented first to
provide an overview of this work. Rooted in system theory and the Fourth
Paradigm, DT-SA is deeply intertwined with state-of-the-art data technologies
and disciplines. In DT-SA framework, DT serves as the data engine, BM as the
intelligence engine, and BDA as the core.

Figure 2: A brief roadmap of DT-SA for EIoT

###  II-A Background of Twin $\rightarrow$ Digital Twin $\rightarrow$ DT-SA

The concept of “twin” dates back to the 1960s Apollo Program. In Apollo
Program, 15 simulators were created as twins for various tests, preparing for
the unexpected. These twins, positioned in an earth-based mode, allowed
engineers to simulate each condition of the space vehicle (PE) during a flight
mission using real-time flight data, thereby assisting astronauts in critical
situations. The twin played a vital role in the rescue mission, successfully
bringing the astronauts home when disaster struck the Apollo 13 in 1970 [18].

With the development of digital technology [19, 20, 21], the physical
component of the twin had been gradually replaced by its digital counterpart,
giving rise to the digital twin (DT). Initially proposed by Grieves in 2002
[22], DT gained practical definition and public acknowledgment in NASA’s
integrated technology roadmap in 2012 [23]. Various definitions of DT found in
the literature are summarized in Table I.

TABLE I: Definitions of DT used in literature Ref. |  Definition
---|---
[24] |  An integrated multiphysics, multiscale, probabilistic simulation of an as-built vehicle or system that uses the best available physical models, sensor updates, fleet history, etc., to mirror the life of its corresponding flying twin. (2012)
[23] |  An integrated multiphysics, multiscale simulation of a vehicle or system that uses the best available physical models, sensor updates, fleet history, etc., to mirror the life of its corresponding flying twin. DT is ultra-realistic and may consider one or more important and interdependent vehicle system, including propulsion/energy storage, avionics, life support, vehicle structure, thermal management/TPS, etc. Manufacturing anomalies that may affect the vehicle may also be explicitly considered. (2012)
[25] |  A set of virtual information constructs that fully describes a potential or actual physical manufactured product from the micro atomic level to the macro geometrical level. At its optimum, any information that could be obtained from inspecting a physical manufactured product can be obtained from DT. (2017)
[26] |  A digital copy of the physical system to perform real-time optimization. (2017)
[27] |  A real time digital replica of a physical device. (2017)
[28] |  A real mapping of all components in the product lifecycle using physical data, virtual data and interaction data between them. (2018)
[29] |  A dynamic virtual representation of a physical object or system across its lifecycle, using real-time data to enable understanding, learning and reasoning. (2018)
[30] |  A digital replica of a living or non-living physical entity. By bridging the physical and the virtual world, data is transmitted seamlessly allowing the virtual entity to exist simultaneously with the physical entity. (2018)
[31] |  A realistic digital representation of assets, processes or system in the built or natural environment. (2018)
|  Definition in this work, see Section IV for details
|  A self-evolving digital organism in the context of the Fourth Paradigm,
with massive VEs as molecules/cells/tissues and a built-in BM as brain. These
living VEs are closely linked to their real-world PEs through data, with the
goal of enhancing management and adding value for numerous downstream domain-
specific tasks in practice, through monitoring (understanding the state of
EIoT units), testing (comprehending the reaction to environment changes and
its consequences), and optimizing (striving for improved decision-making) in
the virtual space. (2023)

In the context of the Fourth Paradigm, DT has evolved into a cross-
disciplinary product, involving integrants such as data, data
technologies/disciplines, domain-specific knowledge, simulation, and analysis.
DT stands out as a promising enabling technology, bridging the gap between
data and demands. With significant advancements in a range of domain-specific
tasks, DT has been successfully implemented in numerous engineering fields to
date [32], including the field of energy [33, 34]. DT market is estimated to
grow from USD 3.1 billion in 2020 to USD 48.2 billion by 2026 [35].

SA, as defined in Section I-A, strives to translate the presented system into
the perceived system for decision-making. Analogous to the Apollo twins
(PE–vehicle in orbit, VE–twins on earth) assist astronauts, DT provides a
natural systematic DT-SA to help EIoT operators/users in making reliable
decisions under normal or urgent conditions.

###  II-B Challenge of DT-SA: Complexity, Emergence Phenomenon

Our exploration of DT-SA is primarily motivated by comprehending the intricate
emergence phenomena within complex EIoT. This motivation is anchored in our
quest to harness the positive emergence, as it plays a pivotal role in the
effective functioning of EIoT.

####  II-B1 Aggregation behaviors and its emergence phenomena

A standard EIoT at the distribution network level is depicted in Figure 3. In
essence, EIoT [36] is a network connecting DERs, characterized by their small
size, large number, distributed deployment, hierarchical structure, diverse
behavior, smart response, and uncertain control. To enhance management
efficiency, aggregation behaviors are implemented to those DERs, leading to a
hierarchical complex EIoT—these DERs converge to create an aggregation termed
“energy cell” (e.g., intelligent building, microgrid), and furthermore form
some advanced aggregation termed “energy tissue”(e.g., microgrid cluster,
virtual power plant).

Figure 3: Motivation and engineering background of DT-SA: Aggregation behavior
and its emergence phenomena in EIoT.

Aggregation behaviors may give rise to emergence phenomena, either positive or
negative. Emergence occurs when an entity exhibits traits that its components
do not possess individually—in other words, the whole is more than the sum of
its parts. Emergence phenomena are common in real-life but typically beyond
reductionism, as depicted in Figure 4.

Figure 4: Schema of emergence phenomena and reductionism.

It is paramount to emphasize that not every aggregation behavior or complexity
leads to emergence phenomena. Certain instances, such as Vaucanson’s automatic
duck and power flow calculation, fall in the scope of reductionism. Despite
their precision and complexity, their intricate patterns can be methodically
modeled piece-by-piece, yielding analytical formulations in the form of
$\bm{x}\\!=\\!f(t)$. In contrast, reductionism proves inadequate when applied
to some behavior exhibited by insect colonies. A holistic perspective, beyond
reductionism, becomes imperative in such cases, as these behaviors are
indivisible. For instance, ants construct fancy underground palaces through a
rather simple cooperative mode without a super-brain conductor; for each
individual ant, it is impossible to formulate its trajectories using an
analytical description in the form of $\bm{x}\\!=\\!f(t)$.

Back to EIoT as depicted in Figure 3, user-side DERs are aggregated aiming to
induce positive emergence: a) the emergence of intelligence, fostering a
smarter decision-maker, and b) the emergence of value, enhancing operational
efficiency.

####  II-B2 Chaos, Lorenz system, and multi-body system

It is crucial to acknowledge that the aggregation behaviors may inevitably
result in negative emergence phenomena, such as chaos, a special outcome of
complexity that is beyond the scope of reductionism. To quickly grasp the
concept of chaos, consider a classical chaotic system, the Lorenz system,
represented as Eq. (1):

$\displaystyle\dot{x}_{1}$ $\displaystyle=\sigma({x}_{2}-{x}_{1})$ (1)
$\displaystyle\dot{x}_{2}$ $\displaystyle=\rho{x}_{1}-{x}_{2}-{x}_{1}{x}_{3}$
$\displaystyle\dot{x}_{3}$ $\displaystyle=-\beta{x}_{3}+{x}_{1}{x}_{2}$

Mathematically, an analytical solution in the form of $\bm{x}\\!=\\!f(t)$
cannot be deduced from Eq. (1), classifying the Lorenz system as a “chaotic
system”. Further details about this experiment can be found in Reference [37].

Similar to the Lorenz system, a three-body system may also exhibit chaotic
behavior, as illustrated in the bottom-right part of Figure 3. In EIoT, a
multi-body system with chaotic effects, the intricate interactions among DERs
or their aggregations may induce unintended consequences or even serious
incidents. Therefore, a profound understanding of both positive and negative
emergence is pivotal for the effective management of DERs, contributing to
advanced decision-making within the complex EIoT landscape.

####  II-B3 Chaos in EIoT and ideas for solutions

In the domain of power systems, a chaotic system can be triggered when a
single generator bus (Bus 1) supplies power to a local load bus (Bus 2) and
connects to a slack bus (Bus 3), as depicted in Figure 5a [38].

(a) Chaotic power system model with three buses

(b) Time-series waveforms

(c) Phase portrait strange attractor

Figure 5: The chaotic power system [38].

The dynamics of the system depend on various parameters
($\delta_{m}$–generator angle, $s_{m}$–generator slip,
$E^{\prime}_{q}$–generator q-axis transient potential , $E_{fd}$–excitation
potential, $\delta_{L}$–load phase angle, and $V_{L}$–load bus voltage
amplitude), as expressed in Eq. (2). Figure 5b and 5c, respectively,
illustrate the time series waveforms of each variable and the phase portrait
strange attractor in 3-dimensional space, confirming the chaotic nature of the
power system. Details of this chaotic power system can be found in Reference
[38].

$\left\\{\begin{array}[]{l}\dot{\delta}_{m}=\omega_{B}s_{m},\\\
\dot{s}_{m}=\frac{1}{2H}\left(-ds_{m}+P_{m}-P_{g}\right)\\\
\dot{E}_{q}^{\prime}=\frac{1}{T_{d0}^{\prime}}\left(-E_{q}^{\prime}+\left(x_{d}-x_{d}^{\prime}\right)I_{d}+E_{fd}\right),\\\
\dot{E}_{fd}=\frac{1}{T_{A}}\left(-E_{fd}+K_{A}\left(V_{ref}-V_{t}\right)\right),\\\
\dot{\delta}_{L}=\frac{1}{q_{1}}\left(Q-Q_{1d}-Q_{0}-q_{2}V_{L}-\left(q_{3}-B_{c}\right)V_{L}^{2}\right)\\\
\dot{V}_{L}=\frac{1}{p_{2}}\left(P-P_{1d}-P_{0}-p_{3}V_{L}-{p_{1}}\dot{\delta}_{L}\right).\end{array}\right.$
(2)

In analyzing such a system, we should set aside reductionism, acknowledging
that the chaotic trajectory cannot be analytically formulated. Fortunately,
while chaos and emergence may appear random, they inherently follow some
patterns hidden in the spatial-temporal data, such as the time-series
waveforms in Figure 5c. This viewpoint will be exemplified through a case (see
Section III-C) only, and will not be further explored in this paper. Moreover,
the emergence phenomenon, usually composed of numerous simple behaviors, is
relatively easy to reproduce through simulations. Therefore, for the analysis
of a chaotic EIoT with aggregation behaviors and emergence phenomena, we
endorse data-intensive solutions, with an emphasis on data-driven mode,
systematic analysis, and numerical expression. In this context, DT technology
sets a solid cornerstone for gaining insight into EIoT.

###  II-C Guiding Ideologies: Fourth Paradigm, System Theory

The scientific paradigm continues its evolution in history: starting with
empirical science focused on direct observation, transitioning to theoretical
science with mathematical models, advancing to computational science using
simulations for complex phenomena, and culminating in today’s eScience, which
integrates theory, experiment, and simulation through data exploration,
leveraging large datasets and advanced data management techniques. Presently,
with the influx of heterogeneous data from sensors/simulations, all scientific
paradigms—experimental, theoretical, and computational—are influenced by this
data deluge. Insights from the data are gained farily late in the data-
processing pipeline, marking a paradigm shift towards a data-intensive
scientific discovery. Today’s scientific paradigm, along with its tools,
techniques & technologies, is so different that it deserves distinguishing
data-intensive science from computational science as a new, the Fourth
Paradigm for data-intensive scientific discovery [16].

In the context of the Fourth Paradigm, our approach involves employing system
theory and statistics to tackle complexity. General system theory, introduced
by Bertalanffy in 1950 [39], aims to establish universal principles applicable
to systems regardless of their specific elements and forces. Nothing
prescribes that we have to end with analytically results. In fact, this view
was not altered but rather reinforced when deterministic laws were gradually
replaced by statistical laws [40].

Starting from original general system theory, the term complex adaptive system
(CAS) was coined by sociologist Buckley in 1968 [41]. Holland further
developed CAS, defining it as “systems that have a large number of components,
often called agents, that adapt or learn as they interact” [42], with an
emphasis on system’s complexity, emergence, and other macroscopic properties
[9]. Our work extends the concept of agent into molecule–cell–tissue–system,
reflecting the hierarchical structure with aggregation behavior of DERs in
complex EIoT (refer to Figure 3). This extension influences the design of our
unified Virtual Entity (VE) model (refer to Section V).

###  II-D Big Model for Complex System

Human behaviors inspire the concept of the big model (BM). We, as human
beings, start our lives by learning a wide range of knowledge, without domain-
specific problem-solving, to form our initial outlook. This initial outlook
has a potential influence on our decision-making in many aspects as we grow
up. In light of this, the traditional model construction pattern “different
models for different tasks” is gradually being replaced by “one data-intensive
pre-built BM for various tasks”—researchers collect massive data and develop
advanced algorithms, in order to build a BM for a large-scale system with
different demands [43]. From this point, BM is a data-intensive by-product of
Fourth Paradigm.

The BM functions as a built-in intelligence engine that absorbs the laws and
patterns hidden in data. Its utilization significantly reduces the reliance of
downstream tasks on vast amounts of high-quality data. As a result, scenarios
that were previously challenging due to limited labeled data become more
tractable. This paradigm shift can be compared to our power system in
particular—BM serves as a ”slack bus,” generating high-quality intelligence
and thus serving a number of downstream applications.

There are mainly three types of models in the built-in BM: a) white
box—mechanism model; b) black box—deep neural network model; c) gray
box—statistical model. It’s imperative to underscore that the preceding
sections (Section I-A, II-B) have emphatically conveyed that relying solely on
either white box or black box models falls short in effectively addressing
emergence and chaos phenomena within the EIoT. As a natural progression, our
focus now shifts to the gray box, specifically the high-dimensional analysis
in Section III. Furthermore, we delve into BM’s ecosystem, DT, in Section IV.

##  III Spatial-temporal Analysis for DT-SA

As previously discussed, spatial-temporal analysis holds paramount importance
within the realms of DT-SA and BM. However, a significant portion of existing
analyses, primarily mechanism-based and white-box, tends to be carried out in
an isolated (spatial-temporally disjointed) manner within a low-dimensional
space, as depicted in the central segment of Figure 6. Unfortunately, these
analyses frequently grapple with limitations, as they are predominantly geared
towards addressing ideal, typical, or extreme scenarios. In light of these
constraints, we embark on a comprehensive exploration of spatial-temporal
analysis for DT-SA.

Figure 6: Independently spatial-temporal analysis paradigm V.S. jointly
spatial-temporal analysis paradigm

###  III-A Spatial-temporal Data and its Mining

As emphasized earlier, spatial-temporal analysis plays a pivotal role in the
context of DT-SA and BM. In spatial-temporal analysis, we routinely handle
multiple variables (spatial space, $N$), where each variable
($i\\!=\\!1,...,N$) samples time-series data for a given duration (temporal
space, $T$) of observation. For instance, the time-series waveforms, as
illustrated in Figure 5b, represent the chaotic behavior of the power system
(Figure 5a).

Traditional statistical theory usually deals with a fixed $N$ (commonly $N$ is
small, typically $N\\!<\\!6$ [44]). For instance, for Part Transformation
(ABC–DQ0, in the power system domain), $N\\!=\\!3$. This fixed small $N$ is
referred to as the low-dimensional regime. In engineering scenarios, however,
we are often interested in cases where $N$ can vary arbitrarily in size
compared to $T$ (commonly $T$ is large, typically $T\\!>\\!60$, $N\\!>\\!10$,
$N/T\\!>\\!0$ [44]). This fundamental requirement serves as the primary
driving force for our exploration of BDA (big data analytics). Consequently,
we adopt a (large-dimensional) data matrix, rather than a vector or a scalar,
as the foundation of BDA. These data matrices can be viewed as data points in
high-dimensional vector space.

For DT-SA in EIoT, (spatial-temporal) data mining is expected to yield high-
dimensional information with domain-specific significance. The data resource
(_input_) primarily comprises sampled spatial-temporal data denoted as
$\mathbf{X}\\!\in\\!\mathbb{R}^{N\\!\times\\!T}$. Concerning high-dimensional
information (_output_), there are mainly two types: a) High-dimensional
indicators for high-dimensional statistics, and b) deep features for deep
learning.

Once the input and output are established, attention turns to information
extraction tools. Traditional mathematical tools often prove inadequate for
handling spatial-temporal data [44]. This inadequacy has greatly spurred the
development of data science, particularly in the fields of AI (artificial
intelligence) and BDA. Accordingly, we highlight a focal tool for each field:
a) AI field—deep learning (DL), which does well in massive data modeling, and
b) BDA field—High-dimensional statistics, specifically random matrix theory
(RMT), which is good at spatial-temporal data analytics. Both tools involve a
series of high-dimensional methods for jointly spatial-temporal modeling and
analysis, and have already made profound impacts in various fields.

####  III-A1 Deep Learning and the Advantages

DL stands as the state-of-the-art data mining algorithm. It aims to extract
high-level, complex abstractions (i.e. deep features) through a hierarchical
learning process. In this process, deep features are learnt at a given level
based on relatively lower features (i.e., the features in the lower layer of
the network) [45]. Throughout this learning process, DL utilizes extensive
data, represented by $\mathbf{x}$, in a non-handcrafted manner, facilitating
the construction of a deep network model

$\mathbf{y}\\!=\\!{{\bm{f}}^{L}}\left({{\mathbf{W}}^{L}}\\!\cdots\\!{{\bm{f}}^{2}}\left({{\mathbf{W}}^{\text{2}}}{{\bm{f}}^{1}}\left({{\mathbf{W}}^{1}}\mathbf{x}\\!+\\!{{\mathbf{b}}^{1}}\right)\\!+\\!{{\mathbf{b}}^{\text{2}}}\right)\\!\cdots\\!\\!+\\!{{\mathbf{b}}^{L}}\right)$

DL models are inherently data-driven, allowing them to adaptively adjust their
parameters with little prior knowledge of the physical mechanism or causal
relationship. Consequently, DL can be generalized to different scenarios or
even different systems without significant modifications.

####  III-A2 Big Data Analytics & RMT and the Advantages

BDA aims to extract valuable insights (in the form of high-dimensional
statistics) from matrix-based variables (such as eigenvalues or the matrix
variate itself [46]) through jointly temporal-spatial analysis. Handling data
that is high in dimensionality, rather than large in size, poses challenges in
making BDA tractable. The theoretical aspects are discussed in more detail in
the next subsection, Subsection III-B, while case studies are presented in
Subsections III-C and VI-A.

###  III-B Random Matrix Theory and its LES Indicator for BDA

Given the scarcity of labeled data in engineering scenarios, especially data
annoteated with “abnormal operating condition” labels, there is significant
potential for the exploration and effectiveness of unsupervised algorithms. In
this regard, RMT stands out as a noteworthy unsupervised algorithm. RMT has
recently become analytically tractable [44], offering transparency and
rigorous handling of data matrices.

The primary goal of RMT is to comprehend the joint eigenvalue distribution,
which serves as statistical analytics for data matrices in the asymptotic
regime—high-dimensional analysis and visualization are treated as functionals
of eigenvalue distributions. For example, linear eigenvalue statistics
(LES)[47] of the matrix exhibit Gaussian distributions under very general
conditions. Recent breakthroughs in probability, particularly the Central
Limit Theorem (CLT) for the LES[44], have allowed the study of other
statistical variables, making their properties derivable and provable. In this
sense, RMT is much more fundamental than DL. Besides, RMT excels in handling
moderate-size (unlabeled) data, a common scenario in the EIoT landscape. For
the sake of completeness of this paper, we provide a brief expansion on the
LES. Additional details can be found in [48]

####  III-B1 Definition of LES

Consider a random matrix
$\mathbf{\Gamma}\\!\in\\!{{\mathbb{R}}^{N\\!\times\\!T}}$, and $\mathbf{M}$ is
the covariance matrix
${{\mathbf{M}}}\\!=\\!{\frac{1}{N}\mathbf{\Gamma}\mathbf{\Gamma}^{\mathrm{H}}}$.
The LES $\tau$ of $\mathbf{\Gamma}$ is defined in [49, 47] via the continuous
test function ${\varphi:\mathbb{C}\rightarrow\mathbb{C},}$

$\tau_{\varphi}=\sum_{i=1}^{N}{\varphi({\lambda_{i}})}=\text{Tr}\varphi\left(\mathbf{M}\right),$
(3)

where the trace of the function of a random matrix is involved.

####  III-B2 Law of Large Numbers for LES

The Law of Large Numbers tells us that $N^{-1}\tau_{\varphi}$ converges in
probability to the limit

$\lim_{N\to\infty}\frac{1}{N}\sum_{i=1}^{N}{\varphi({\lambda_{i}})}\\!=\\!\int\varphi(\lambda)\rho(\lambda)\,d\lambda,$
(4)

where $\rho(\lambda)$ is the probability density function of the eigenvalue
$\lambda$. Therefore, we deduce that

$\mathbb{E}(\tau_{\varphi})=N\\!\int\varphi(\lambda)\rho(\lambda)\,d\lambda,$
(5)

####  III-B3 Central Limit Theorem for LES

As the natural second step, CLT aims to study the variations of LES
$\tau_{\varphi}$. CLT tells that

######  Theorem III.1 (M. Sheherbina, 2009, [47]).

Let the real valued test function $\varphi$ satisfy condition
${{\left\|\varphi\right\|}_{3/2+\varepsilon}}\\!<\\!\infty\left(\varepsilon>0\right)$.
Then $\\!\tau_{\varphi}\\!$, as defined in Eq. (3), in the limit
$N,T\\!\to\\!\infty,{c}\\!=\\!{N/T}\leq 1$, converges in the distribution to
the Gaussian random variable with the mean $\mathbb{E}(\tau_{\varphi})$,
according to Eq. (5), and the variance:

$\displaystyle\sigma^{2}(\tau_{\varphi})=$
$\displaystyle\frac{2}{c\pi^{2}}\iint\limits_{-\frac{\pi}{2}<{{\theta}_{1}},{{\theta}_{2}}<\frac{\pi}{2}}{{{\psi}^{2}}\left({{\theta}_{1}},{{\theta}_{2}}\right)}\left(1-\sin{{\theta}_{1}}\sin{{\theta}_{2}}\right)d{{\theta}_{1}}d{{\theta}_{2}}$
(6)
$\displaystyle+\frac{{{\kappa}_{4}}}{{\pi}^{2}}\left(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}{\varphi\left(\zeta\left(\theta\right)\right)\sin\theta
d{{\theta}}}\right)^{2},$

where
$\psi\left({{\theta}_{1}},{{\theta}_{2}}\right)\\!=\\!\frac{\left[\varphi\left(\zeta\left(\theta\right)\right)\right]\arrowvert_{\theta={{\theta}_{2}}}^{\theta={{\theta}_{1}}}}{\left[\zeta\left(\theta\right)\right]\arrowvert_{\theta={{\theta}_{2}}}^{\theta={{\theta}_{1}}}},$
${\left[{\zeta\left(\theta\right)}\right]\arrowvert_{\theta={\theta_{2}}}^{\theta={\theta_{1}}}}\\!=\\!\zeta\left({{\theta_{1}}}\right)\\!-\\!\zeta\left({{\theta_{2}}}\right),$
and
$\zeta\left(\theta\right)\\!=\\!1\\!+\\!1/c\\!+\\!{2}\\!/\\!{\sqrt{c}}\sin\theta;$
$\kappa_{4}\\!=\\!\mathbb{E}\left({{X_{ij}}^{4}}\right)\\!-\\!3$ is the $4$-th
cumulant of entries of $\mathbf{X}$.

###  III-C LES for Insight into Chaotic Systems

Let’s consider the Lorenz system expressed in Eq. (1), with parameters
$\sigma\\!=\\!10,\beta\\!=\\!8/3$, and $\rho\\!=\\!24$. Then we initiate the
simulation of the chaotic system with the following steps:

  1. a)

Set the simulation frequency to 100 Hz.

  2. b)

Introduce change points (CPs) of parameter $\rho$. 1) CP1:
$28\\!\rightarrow\\!30$ at 60s; and 2) CP2: $30\\!\rightarrow\\!31$ at 120s.

  3. c)

Generate simulation sequences with a total length of 18000 (3 minutes,
$18000\\!=\\!3\\!\times\\!60\\!\times\\!100$).

  4. d)

Employ a moving sliding window (MSW) of length 2000 to sample spatial-temporal
data matrix ($X\\!\in\\!\mathbb{R}^{3\\!\times\\!2000}$) from the sequence,
and then calculate LES indicator $\tau_{\varphi}$ for $X$.

The performance is obtain as illustrated in Figure 7.

Figure 7: Performance of Lorenz system with parameter changes

When the parameter $\rho$ undergoes a slight jump at both change points (CP1:
at 60s, $\rho\\!:28\\!\rightarrow\\!30$, CP1: at 120s,
$\rho\\!:30\\!\rightarrow\\!31$), the raw data appear insensitive. However,
employing LES $\tau_{\varphi}$ allows us to easily distinguish their different
patterns in the high-dimensional space.

This case serves as a practical illustration of applying the LES indicator to
gain insights into chaotic systems, aligning with the Fourth Paradigm’s
emphasis on data-intensive scientific discovery. In this context, spatial-
temporal data analysis, specifically RMT, severs as a powerful tool for DT-
SA—it enables the extraction of informative patterns and insights from the
extensive data within the complex EIoT.

##  IV Redefinition of DT toward Metaverse

This section presents a cutting-edge redefinition of DT, aimed at seamless
integration with the Fourth Paradigm, system theory, and BM.

###  IV-A Redefinition of Digital Twin: Extend DT into Metaverse

As discussed in Section II, today’s EIoT urgently demands an advanced DT that
surpasses the limitation of being merely an 1-1 replica of its physical
counterpart. In response to this demand, we propose a redefinition of DT to
align it with the Fourth Paradigm, CAS, and BM: _DT is a self-evolving digital
organism, with massive VEs as molecules/cells/tissues and a built-in data-
intensive BM as the brain. These living VEs are closely linked to their real-
world PEs through data, with the goal of enhancing management and adding value
for numerous downstream domain-specific tasks in practice, through monitoring
(understanding the state of PEs), testing (comprehending the reaction to
environment changes and its consequences), and optimizing (striving for
improved decision-making) in the virtual space._

This redefined DT signifies a departure from the original concept of a 1-1
mirror world. Instead, it advances towards digital parallel universes,
enabling a comprehensive and holistic consideration in the landscape of
complex EIoT. In this context, our redefined DT aligns more closely with the
concept of the metaverse, an emerging paradigm finding extensive applications
in various fields such as gaming, military, and sociology. Importantly, both
the original DT and the metaverse adhere to IEEE 2888 Standards [50], with the
metaverse expanding into a broader and more intricate scope.

This redefined DT marks a departure from the original DT, a 1-1 mirror world.
Instead, it advances towards digital parallel universes, allowing for a
comprehensive and holistic consideration in the landscape of complex EIoT. In
this sense, the redefined DT is more akin to metaverse, an emerging concept
gaining extensive applications in various fields such as gaming, military,
sociology. Notably, both the original DT and the metaverse conform to IEEE
2888 Standards [50], with the metaverse expanding into a broader and more
intricate scope. Currently, these two paradigms are converging, as
demonstrated in Figure 8. DT, originating from the industrialization with a
focus on manufacturing production, is progressing towards globalization; in
contrast, the metaverse, rooted in games and media with a focus on
constructing relationships, is moving towards industrialization.

Figure 8: Metaverse V.S. DT: A technological evolution view [51]

Our extension of DT into the metaverse for DT-SA in EIoT brings several
advantages:

  1. -

(To researchers) Metaverse emphasizes “relationships,” whereas DT primarily
focuses on “Entities.”

  2. -

(To dispatchers) Metaverse utilizes virtual simulation technology to create a
virtual world supporting “what if” discussions, whereas DT pursues an image as
close to the real world as possible.

  3. -

(To patrol inspectors or system operators) In the metaverse, terminal users
are not only information demanders but also information creators.

These superiorities enhance DT’s capabilities in handling diverse, complex,
and uncertain scenarios in EIoT.

###  IV-B Redefined DT for DT-SA in EIoT

The redefinition of DT is meaningful to DT-SA in EIoT. On one hand, it serves
as an interface for existing knowledge and experience, thereby narrowing the
search space of BM, thus enhancing its efficiency, interpretability,
robustness, and generalization performance. On the other hand, it facilitates
systematic deduction across various time-scales, evolution paths, and
uncertainties, liberating simulations from the constraints of “reality” to
effectively address “what if” dilemma before practical implementation.

DT integrates mechanistic knowledge and digital technology to model the
abstract properties of Physical Entities (PEs), encompassing characteristics,
behavior, and configuration, thus forming corresponding Virtual Entities
(VEs). These VEs enable ergodic simulation, providing nearly full-coverage
data for the systematic exploration of ”what if” scenarios and other
considerations, especially in the context of DERs aggregation or broader EIoT
scenarios.

DT utilizes both mechanistic knowledge and digital technology to model the
abstract properties of PEs, such as characteristics, behavior, and
configuration, thus forming corresponding VEs. These VEs enable ergodic
simulation, providing nearly full-coverage data for the systematic exploration
of “what if” scenarios and other considerations, especially in the context of
DERs aggregation or broader EIoT scenarios.

Furthermore, the generated data become the cornerstone for constructing a
data-intensive BM under the Fourth Paradigm. From this sense, our DT actively
examines real-time sampling data with the assistance of the built-in BM,
inferring indirect indicators (e.g,. high-dimensional statistics, deep
features) for some domain-specific task. These indicators allows us to
evaluate the current situation, learn from past experience, and forecast
future trend. Overall, the redefined DT is dedicated to systematically
implementing SA of VEs throughout their life-cycle in the digital space,
considering associated uncertainty, risk, and opportunity.

###  IV-C Framework and Roadmap of DT-SA

This part, building upon our redefined DT and referencing our prior work [52,
34], introduces a DT-SA framework, as illustrated in Figure 9.

Figure 9: Schematic of DT-SA framework and its four steps: digitalization-
simulation-informatization-intellectualization.

In general, our DT-SA framework comprises four key steps:

  1. a)

Digitalization: the unified characterization of diverse PEs under the
condition of mutual operability between PE units in the real world and VE
models in the digital space;

  2. b)

Simulation: the generation of a batch of multi-scenario dataset in the digital
parallel space through intensive simulation using VE models;

  3. c)

Informatization: the extraction of high-dimensional statistics or deep
features from the dataset through BDA or AI for BM training;

  4. d)

Intellectualization: the customization of engineering criteria to assist
decision-making for domain-specific tasks.

In relation to these four steps, an ecosystem is suggested as depicted in
Figure 10, contributing to DT-SA’s evolution and effectiveness.

Figure 10: Ecosystem contributing to DT-SA’s evolution and effectiveness

This ecosystem explores three interconnected spaces: a) _virtual space_ for
digitalization and simulation, b) _high-dimensional space_ for
informatization, and c) _cognitive space_ for intellectualization. The
interdependence among the three spaces is illustrated through the flow of
data. The output of _virtual space_ (batched sampled data) is the input of the
_high-dimensional space_ , and the output of the _high-dimensional space_
(informative high-dimensional statistics and deep features) is the input of
the _cognitive space_. Finally, engineering indicators are customized in
_cognitive space_ for decision-making on domain-specific applications.

####  IV-C1 Virtual Space (Space I)

Manual/history (labelled) data are utilized to build VE models by pre-
learning, and to build or update the BM in the (early) stages of DT. Space I
takes data resources as input, generating full-coverage sample data and
decisions as outcomes. It involves two major components—DT as data engine and
BM as intelligence engine.

####  IV-C2 High-dimensional Space (Space II)

This space strives to transform the presented system, characterized by low-
dimensional raw data, into a perceived system with informative statistics and
features. Data utilization methodology, involving data modeling and analysis,
are at the heart.

####  IV-C3 Cognitive Space (Space III)

Manual intervention and ultra-realistic actuators are employed for virtual
test on domain-specific decisions within the metaverse. It provides a channel
for evaluating “what if” scenarios under normal or urgent conditions, in order
to pick out or even to generate reliable/prescient decisions.

Additionally, feedback establishes a closed-loop among these three spaces,
allowing us to update BM or to correct/adjust VE models in a continuous cycle.
With the closed-loop feedback attribute and successive iteration mechanism, DT
enables simulations of new ideas that can be tested to evaluate the
environmental impact and to confirm the performance in the seamless digital
space, before giving an implementation in practice. Furthermore, continuous
optimization of each module/algorithm within the DT-SA ecosystem can be
carried out in this successive iteration process, ensuring the nearly real-
time efficiency and adaptability of DT-SA in the complex EIoT.

##  V Modelling and Simulation of Virtual Entity

This section, aligned with our designed DT-SA framework in Section IV-C,
establishes a unified and refined VE model for PE characterization. This VE
model not only mirrors real-world PEs, but also possesses the capability to
self-evolve in the metaverse. Additionally, VE modeling is informed by systems
theory, which advocates for a holistic approach to studying the entire system,
placing emphasis on system’s openness, self-organization, and hierarchical
structure.

###  V-A Demanded Attributes of Virtual Entities

The VE model is formulated to describe PE’s abstract properties (e.g.,
characteristics, behavior, configuration, and performance) in a knowledge-data
hybrid manner. As discussed in Section II-D, three models for VE are
considered: a) white mechanism model; b) black deep network model; and c)
statistical model. Outlined below are key features expected of the VE model:

  1. -

Generality: VE is applicable to most PEs in existence, encompassing various
types, services, and levels.

  2. -

Representability: VE can “statically” profile PE by reflecting its basic
properties, functions, demands, and other attributes.

  3. -

Predictability: VE can “dynamically” simulate PE’s evolutionary behavior on
multiple time scales, deducing consequences with the help of incorporating
domain-specific knowledge and data science.

  4. -

(Real-time) Interactivity: VE can exchange data, information, and energy with
exteriors (PEs, other VEs, and the system) in nearly real time.

  5. -

Interoperability: Closure topologies and mathematical operators can be defined
to study the interaction of multiple environmental VEs.

  6. -

Subjectivity: VE can simulate motivation and decision-making processes to
derive the ”right” decision.

  7. -

Self-evolution: VE can self-learn, self-improve, and self-update through
accumulated data.

###  V-B Designing of Virtual Entity Model

To incorporate the aforementioned features, the VE model is structured as
follows:

$\textbf{VE}=(\textbf{VE}_{\text{Attr}},\textbf{VE}_{\text{Perf}},\textbf{VE}_{\text{Info}},\textbf{VE}_{\text{Agg}},\textbf{VE}_{\text{SA}})$

where

  1. -

$\textbf{VE}_{\text{Attr}}$: PE’s natural/social attributes, including its
components, resources and demand, adjustable volume, network
structure/parameters, and so on.

  2. -

$\textbf{VE}_{\text{Act}}$: PE’s optional action, such as energy
generation/consumption, which depends on $\textbf{VE}_{\text{Info}}$ and
$\textbf{VE}_{\text{SA}}$.

  3. -

$\textbf{VE}_{\text{Info}}$: Information from the inner and exterior of PE.

  4. -

$\textbf{VE}_{\text{Agg}}$: Aggregation/decomposition of PEs, relevant to the
entire procedure including its motivation, decision, action, and consequence,
with an emphasize on the emergence of intelligence & value (see Section II-B).

  5. -

$\textbf{VE}_{\text{SA}}$: DT-SA module, taking $\textbf{VE}_{\text{Attr}}$ &
$\textbf{VE}_{\text{Info}}$ as inputs, and $\textbf{VE}_{\text{Agg}}$ &
$\textbf{VE}_{\text{Act}}$ as outputs.

In such a manner, the VE model is designed to map the PE’s operations in the
physical world and its responses to the external environment. For instance, if
$\textbf{VE}_{\text{Info}}$ module anticipates an upcoming peak in power
consumption, $\textbf{VE}_{\text{Attr}}$ module will be activated to assess
potential flexible resources, in order to assist $\textbf{VE}_{\text{SA}}$
module in making demand-response decisions for $\textbf{VE}_{\text{Act}}$.

Our study on the VE model emphasizes aggregation behavior, with three
indicators describing motivation, participants, and effectiveness of
aggregation:

  1. -

Aggression degree: tendency towards change or evolution, largely influenced by
$\textbf{VE}_{\text{Attr}}$. A flexible and intelligence unit has a high level
of aggression degree.

  2. -

Fitness degree: VE’s fitness for other VEs or the environment, depending on
$\textbf{VE}_{\text{Attr}}$ and $\textbf{VE}_{\text{Info}}$. Energy storages,
for example, have a high fitness degree with DGs. For rigorous quantization of
this degree, a “binary operation” and “distance” should be defined.

  3. -

Emergence degree: benefit as the consequence of aggregation, such as emergence
phenomena of new characteristics, ability, and behavior, or the alleviation of
uncertainty caused by the mixing of DGs and energy storages.

###  V-C Quick Start and Self-evolution of DT-SA with VE

Creating an omniscient DT that covers every facet of EIoT is both impractical
and unnecessary, especially in the near future. For domain-specific
engineering tasks, a sub-DT—essentially a condensed version of the omniscient
DT—is often adequate. For example, when the EIoT is on the verge of
instability, economic considerations might take a backseat.

In practice, engineers may initiate a quick DT by creating simple VEs,
offering early-cycle technical support in the program. Once deployed, these
VEs, simple at first, may evolve over time, driven by the accumulation of
operating data or through the feedback from manual interventions. This quick
start capability enhances DT-SA’s adaptability to the complex EIoT. In
general, instead of adhering to a fixed model, the VE embraces a self-
adaptive, self-learning, and self-evolve model with an iterative process:
modeling$\rightarrow$deployment$\rightarrow$testing$\rightarrow$updating$\rightarrow$remodeling$\cdots$.

##  VI Case Studies of DT-SA in EIoT

This section introduces practical applications of DT-SA through three case
studies. These cases demonstrate how the framework is applied in real-world
engineering projects and the development of relevant standards, and verify the
superiority and necessity of our proposed DT-SA.

###  VI-A Case#1 DT-Based Substation Equipment Fault Diagnosis

This part, as depicted in Figure 11, by taking fault diagnosis as a domain-
specific SA task, makes a comparison among traditional mode, DT mode, and
metaverse mode. The result demonstrates how far our efforts have come.

Figure 11: DT-SA for Fault Diagnosis

####  VI-A1 Engineering Background and Classical Indicator

Small current ground fault, often with insignificant fault characteristics, is
a common fault in the distribution network. Several measurements, such as
fault recorder (FR), $\mu$PMU, and PT/CT (potential transformer/current
transformer), are deployed for sampling $V$ and $I$ on heterogeneous buses, as
illustrated in Fig. 12.

Figure 12: Waveform of $V$ and $I$ in a real distribution network

Classical indicator for this type of fault is zero-sequence current, which is
a low-dimensional indicator depended on only 3-dimensional raw data, i.e.,
$I_{\text{A}},I_{\text{B}},I_{\text{C}}$ confined to each single FR, as
depicted in center part of Figure 6. There are several disadvantages for zero-
sequence current indicator: a) FR is vulnerable to external environment,
communication and other factors, its own accuracy and precision is not highly
reliable; b) Considering both sensitivity and reliability, the fault threshold
is difficult to set—a high threshold is unreliable and prone to missed alarms;
conversely, it is too sensitive and prone to trigger false alarms. In general,
zero-sequence current indicator does not make full use of the spatial-temporal
data (from heterogeneous lines) and their correlation..

####  VI-A2 DT-SA Indicators for Fault Diagnosis

We take a real case using field data in some distribution network. When a
fault occurs, 7 FRs are turned on to record 42-dimensional data (each FR
records 6-dimensional data: three-phase voltage, i.d., $1,2,3$, and three-
phase current, i.d., $4,5,6$). The FR records 10 cycles before and after its
start-up, covering the life-cycle of the fault, as shown in Figure 13a.

On one hand, a built-in module for each FR, separately, calculates its
corresponding classical zero-sequence current indicator (7 indicators in all).
Without loss of generality, suppose they are
$I_{4-6},I_{10-12},I_{16-18},I_{22-24},I_{28-30},I_{34-36},I_{40-42}$, and the
classical indicators are sensitive to the fault for the last 3 FRs
($I_{28-30},I_{34-36},I_{40-42}$), and are insensitive for the first 4 FRs
($I_{4-6},I_{10-12},I_{16-18},I_{22-24}$).

On the other hand, the 42-dimensional spatial-temporal data, in the form of
$N\times T$ matrix, compose the VE model of the life-time of the fault (pre-
fault, post-fault). We get to look at the data from multiple FRs as a matrix,
and implement spatial-temporal analysis to the matrix, as depicted in the
right part of Figure 6. In concrete, we, according to Eq. 3, extract a high-
dimensional spectral indicator LES based on RMT as a novel indicator, i.e.,
$\tau_{1-42}$. The proposed LES $\tau_{1-42}$ indicator does make use of the
spatial-temporal correlation of all the 7 strongly associated FRs. Figure 13b
shows that the LES indicator $\tau_{1-42}$ has the same trend as classical
indicators $I_{28-30},I_{34-36},I_{40-42}$, which are also sensitive
indicators.

Then we move to the digital space (metaverse). If we suppose that the data
from 3 sensitive FRs are unreliable or even totally missing, as shown in
Figure 13c, then we can not make a correct SA about our distributed network
using the left classical zero-sequence current indicators
($I_{4-6},I_{10-12},I_{16-18},I_{22-24}$). However, the LES indicator
$\tau_{1-24}$, which can be calculated out using 24-dimensional data only from
the left 4 (insensitive) FRs, is still competent in the SA task. In such a
manner, our DT-SA offers a data-intensive discovery for fault diagnosis
application. This fault diagnosis module has already been deployed to real
systems, and it exhibits better performance.

(a) Raw Data & LES $\tau_{1-42}$

(b) LES $\tau_{1-42}$ V.S. Zero-sequence Current (Sensitive)

(c) LES $\tau_{1-24}$ V.S. Zero-sequence Current (Insensitive)

Figure 13: Test and improve the engineering indicators in virtual digital
world: classical indicators V.S. LES indicator

In addition, this case tells how to test our VE in metaverse. Our case says
that our LES indicator $\tau_{1-24}$ is still effective when all the 3
sensitive FRs are unreliable. Then it is reasonable to believe that our
algorithm is still valid for several arbitrary FR data missing/anomalous, and
hence we need not test these scenarios in our metaverse.

###  VI-B Case#2 DT-SA Project and Relevant Standards for EIoT in Lingang,
China

The implementation of EIoT stands as a strategic initiative in alignment with
sustainable development and a low-carbon economy. In Lingang New District,
Shanghai, China, a prominent project exemplifies the implementation of our DT-
SA framework within the international free-trade zone.

####  VI-B1 Background and Overview of Lingang DT-SA Project

Lingang is endowed with abundant resources, making it an ideal locale for
investigating the behavior of DERs within a complex EIoT. Lingang has a rich
array of climate-susceptible natural energy resources, along with diverse
users with varying resources, characteristics, and demands.

  1. -

Natural Energy Resources—approximately 500MW (installed capacity) wind
turbine, 200MW photovoltaics, etc.

  2. -

Demand Response Users—electric vehicle (EV) charging stations with a
considerable scale, etc.

  3. -

Important users—integrated circuit manufacturers, electric vehicle
manufacturers, and large aircraft manufacturers, etc.

The deliberate and interconnected deployment of these elements positions
Lingang as a compelling exemplar.

In this context, the collaborative efforts between State Grid Shanghai
Municipal Electric Power Company (Author 2) and Shanghai Jiao Tong University
(Authors 1, 3, 4) initiated the Lingang DT-SA Project for EIoT within the
Lingang regional distribution network. This project is funded by the Science
and Technology Commission of Shanghai Municipality (Project No: 21DZ1208300,
2021.11$\sim$2024.11), and titled “Research and Application of Situation
Awareness and Efficient Operation Technology for EIoT in a Digital City”. Its
overarching goal is to contribute to the advancement of city digitalization,
energy optimization, and urban management. Figure 14 illustrates this project.

Figure 14: Demonstration scheme of DT-SA Framework for EIoT in Lingang, China

The project develops a digital infrastructure for managing DERs within EIoT,
leveraging our proposed DT-SA framework (refer to Figure 9). The DT-SA
Framework seamlessly integrates technology platform, data base, and user
subjects to organically construct the EIoT-DT and a digital space for the
Lingang metaverse. It is noteworthy that the construction of the Lingang
metaverse aligns with the motivations and engineering principles of the DT-SA
framework, as illustrated in Figure 4—for instance, we may conceptualize the
EV user as an EM (energy molecule), the EV charging stations as an EC (energy
cell), and the virtual power plant (VPP [53]) containing these EV charging
stations as an ET (energy tissue). The behaviors of the above DERs and their
aggregation in the metaverse (corresponding VM, VC, VT) are influenced by
factors such as traffic condition and climate environment. Utilizing the
Lingang metaverse, we can conduct a comprehensive and systematic exploration
on DERs behaviors and their impact on the EIoT in Lingang with minimal trial-
and-error costs.

####  VI-B2 DT-Based Automatic Control of Air Conditioning

Illustrating the effectiveness of the DT-SA framework, we focus on the
automatic control of air conditioning (refer to Fig. 15a) within the broader
context of the Lingang Project. Air conditioning load, recognized as a large-
scale adaptable demand-side resource, has the capacity for conducting load
response (as either an independent entity or part of a VPP), contributing to
EIoT dispatching strategies such as load peak shaving or network congestion
management.

(a) DT-based automatic control of air conditioning

(b) Use Case: electrical vehicle

(c) Use Case: energy storage

Figure 15: Power Metaverse: Use Cases

Our project establishes a sub-DT dedicated to air conditioning by mapping
real-world parameters (climate, pedestrian flow, set temperature, etc.) into
the digital space. Within this DT system, various air conditioning output
strategies are simulated, including load shifting (Strategy 1), load reduction
(Strategy 2), etc. Utilizing those batch-generated sample data, the DT-SA
platform, with the help of BM, determines the optimal strategy. In such a
manner, we give a comprehensive consideration on the uncertainty of
environment and interests of multiple-stakeholder, balancing the needs of
power dispatchers (load peak shaving), mall customers (thermal comfort
experience), and mall operators (minimizing electricity expenses). This case
reflects the superiority of our DT-SA framework in DERs management in EIoT.

####  VI-B3 Development of Relevant Standard—Power Metaverse

The Lingang DT-SA Project has introduced an ITU technical standard titled
“Power Metaverse: Use Cases Relevant to Grid Side and User Side” (refer to
[54]). This report provides a comprehensive overview of the power metaverse,
presenting a roadmap and detailing seven use cases, including the air
conditioning case discussed earlier. These cases showcase the application of
the power metaverse in the power system, addressing both user and grid
perspectives. Each use case offers a thorough description of the application
scenario, including assumptions, service scenarios, and requirements.

  1. -

The user-side cases illustrate how the metaverse can be employed to balance
the supply and demand of the power grid by promoting the participation of
adjustable and controllable resources on the user-side, including air
conditioning, electric vehicles, combined heat and power, energy storage, and
multienergy complementarity; these cases resemble scenarios like air
conditioning control, as depicted in Figures 15b and 15c.

  2. -

The grid-side cases illustrate how the metaverse can be employed to enhance
the automation and intelligence of core businesses in the distribution
network, including resilient power grid, and DGA (dissolved gas analysis)
inspection.

The specification outlined in this technical report serves as a valuable
reference for intelligent decision-making, technical research, and practical
applications, underscoring the significance of the Lingang DT-SA framework in
both engineering applications and theoretical guidance.

##  VII Conclusion

This work introduces a cutting-edge redefinition of DT in the context of
Fourth Paradigm, CAS, and BM. The redefined DT extends beyond its original
form, transforming from a limited “1-1 mapping” mirror world towards an
expansive “free” metaverse. The redefined DT, evolving from a confined “1-1
mapping” mirror world towards a expansive “free” metaverse, enables us to
proactively address hypothetical scenarios before practical implementation,
thereby reducing trial-and-error costs. Additionally, the metaverse
contributes substantially to the BM training by providing extensive virtual
data.

Next, we delve into a concise yet comprehensive DT-SA framework, focusing on
its role in gaining systematic and quantitative insights into complex systems
through spatial-temporal data. Notably, we emphasize the merits of DT-SA,
including its model-free nature, theoretical support from RMT, compatibility
with existing knowledge, and resilience against uncertainties and data errors.
This positions DT-SA as a compelling alternative for DT-SA in the complex
EIoT. Positioned as the future development direction of EIoT, DT-SA offers
valuable insights and intelligence across various technical aspects (e.g.,
aggregation and system modeling, analysis of chaotic systems with emergence
phenomena), with a coverage of wide applied domains such as fault diagnosis,
peak shaving dispatching.

In conclusion, the development of the DT-SA encompasses various aspects
spanning industry, academia, and research. Our DT-SA framework is compatible,
so it serves as a novel foundation for collaboration among experts from
diverse fields. Besides, the DT-SA framework demonstrates adaptability beyond
the EIoT realm, showing promise in implementation within other systems, such
as intelligent cities and brilliant factories. This broad exploration holds
potential benefits for both the engineering community and data science,
underscoring the versatility and significance of DT-SA in advancing our
understanding and management of complex systems.

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