# A Distributed Event-Triggered Control Strategy for DC Microgrids Based on
Publish-Subscribe Model Over Industrial Wireless Sensor Networks

Seyed Amir Alavi, Kamyar Mehran, Yang Hao, Ardavan Rahimian, Hamed Mirsaeedi,
and Vahid Vahidinasab Manuscript received December 5, 2017; revised March 5,
2018, April 25, 2018, and June 30, 2018; accepted July 6, 2018.© 2018 IEEE.
Personal use of this material is permitted. Permission from IEEE must be
obtained for all other uses, in any current or future media, including
reprinting/republishing this material for advertising or promotional purposes,
creating new collective works, for resale or redistribution to servers or
lists, or reuse of any copyrighted component of this work in other works.S. A.
Alavi, K. Mehran, Y. Hao, and A. Rahimian are with the School of Electronic
Engineering and Computer Science, Queen Mary University of London, London E1
4NS, U.K. (e-mail: k.mehran@qmul.ac.uk).H. Mirsaeedi is with the School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran.V.
Vahidinasab is with the Department of Electrical Engineering, Abbaspour School
of Engineering, Shahid Beheshti University, Tehran, Iran.

###### Abstract

This paper presents a complete design, analysis, and performance evaluation of
a novel distributed event-triggered control and estimation strategy for DC
microgrids. The primary objective of this work is to efficiently stabilize the
grid voltage, and to further balance the energy level of the energy storage
(ES) systems. The locally-installed distributed controllers are utilised to
reduce the number of transmitted packets and battery usage of the installed
sensors, based on a proposed event-triggered communication scheme. Also, to
reduce the network traffic, an optimal observer is employed which utilizes a
modified Kalman consensus filter (KCF) to estimate the state of the DC
microgrid via the distributed sensors. Furthermore, in order to effectively
provide an intelligent data exchange mechanism for the proposed event-
triggered controller, the publish-subscribe communication model is employed to
setup a distributed control infrastructure in industrial wireless sensor
networks (WSNs). The performance of the proposed control and estimation
strategy is validated via the simulations of a DC microgrid composed of
renewable energy sources (RESs). The results confirm the appropriateness of
the implemented strategy for the optimal utilization of the advanced
industrial network architectures in the smart grids.

###### Index Terms:

DC microgrid, distributed state estimation, event-triggered control, publish-
subscribe model, WSN.

##  I Introduction

In the future modern smart grids, a direct current (DC) microgrid is becoming
a natural substitution for the traditional power grid, mainly due to the ease
of integration of the RESs. The DC microgrids have found the ever-increasing
importance for the efficient realization of a number of crucial applications
in the electric power industry, as they differentiate themselves from the AC
grid counterparts in having the non-zero-crossing current and reactive power
[1, 2, 3]. However, controlling of the DC microgrid subsystems poses a
considerable challenge, e.g., grid voltage stabilization is still a major
problem due to the limitations in the voltage compensation techniques, when
compared to the conventional AC power system [4, 5, 6].

The microgrid control strategies are categorized as centralized,
decentralized, and distributed [7, 8, 9]. In the centralized architecture, all
the data should be centrally processed where there is a single point of
failure for the entire power system, which potentially reduces the reliability
of the operation of the microgrid, as well as increasing the computational
complexities of the measured data processing [10, 11, 12]. In the
decentralized system architecture, a set of local controllers are distributed
over the DC microgrid, e.g., the load controllers, distributed generation (DG)
controllers, and converter controllers. The control objectives are achieved
without any direct communication between the controllers, which is
specifically useful in cases when the direct communication is not feasible or
costly to establish. However, there are disadvantages to this method, such as
the voltage offset and inadequate response time to load variations, which can
both lead to the voltage and frequency instabilities in the DC microgrid. One
of the most famous decentralized control methods is the droop control, where a
number of investigations are conducted to overcome the deficiencies of the
distributed control methods [13, 14, 15].

The main advantages of a distributed control architecture include the seamless
real-time operation, no single point of failure, reduction in the
computational and communication complexities, and distribution of the tasks
among the local controllers in the microgrid [16, 17]. The quality of power
primarily relies on the fast real-time communication between the distributed
controllers. Different approaches are proposed in order to effectively
minimize the communication time and complexity. In [16], it is suggested that
only one controller can communicate with its neighbor controllers rather than
all the controllers. However, to satisfy the overall control objectives, the
limitations of the main protocol candidates for the network should be
appropriately considered, hence, the separation of concerns (SoCs) would not
be held anymore [18].

The networked control systems (NCSs) are proved to be an essential framework
for the implementation of a distributed control architecture in a number of
applications, such as the power systems [19], industrial process control [20],
power substation automation [21], aircraft control [22], and autonomous
vehicles [23]. In an NCS, controllers are programmed on digital embedded
platforms, and are connected to sensor/actuator nodes via a shared
communication link. This offers a flexible structure where remote devices can
be added, removed, and located with a minimum wiring and maintenance cost.
With the advent of the Internet of things (IoT), the NCSs are moving towards
wireless operation, where a channel may be shared among thousands of sensing
nodes in the microgrid. Therefore, considering the fact that the channel
bandwidth is limited, the NCS objectives should include reduction of the
network traffic, as well as increasing the battery life of the sensors, while
guaranteeing the overall performance. Hence, to fulfill such objectives and to
address the issues regarding implementation of the intended control scheme, an
event-triggered control and estimation strategy is further proposed in this
work. The main objective in the event-triggered control is to efficiently
reduce the communication packets generated in the sensor-controller-actuator
loop [24]. Exchanging information can only be executed among the components,
when an event is generated to satisfy the control performance. Furthermore,
different datasets can be employed for the event-generation, e.g., the plant
output signals [25, 26], or state feedback signals [27, 28, 29].

Several works are already reported regarding the application of event-based
control for microgrids. In [30], a multi-agent control system is proposed
which uses the reinforcement learning to estimate the state of other agents
using the event-based message passing, with the objective of the load
frequency control (LFC) in AC grids. Moreover, a similar approach is followed
in [31] using the adaptive dynamic programming (ADP) for LFC of AC microgrids.
The authors in [32] have developed a power sharing control strategy among the
hybrid microgrids using the event-based distributed consensus. Communication
time delays and reactive power support are considered in the mentioned work.
The problem of economic dispatch has been addressed in [33] using the event-
based communication and fast gradient distributed optimization among different
microgrids, forming a resilient grid. The power sharing problem is addressed
in [34] to reduce the burden over the network. This idea has been extended in
[35, 36] only for DC microgrids but without considering the communication
models.

The main challenge of integrating the event-generation in an event-triggered
control loop is the stabilization of the overall system. Several approaches
are reported in the available literature, based on the use of the Lyapunov
theorem for the stability analysis. In [37], to guarantee the global
asymptotic stability, the problem of scheduling the event-based control tasks
in the embedded processors is addressed. In [38], the event-triggered
strategies to control the discrete-time systems are proposed, along with the
results for the self-triggered control strategy. In [37, 39], the discrete-
time systems are studied using a model-based Lyapunov triggering mechanism, in
which the values of the Lyapunov functions are calculated at each sampling
instant to maintain the system in the stable region. On the other hand, an
event-triggered control system is considered as a hybrid system where the
robustness analysis is rather a difficult task. In order to overcome the
stabilization and robustness problems, we propose an approach by dividing the
control problem into two different tasks. First, a distributed event-triggered
optimal observer using the KCF [40] is designed to estimate the state of the
DC microgrid via the sensing devices. Then, the distributed state feedback
controller regulates the output voltage of the DC-DC converters to stabilize
the average voltage of the microgrid to a set value.

Figure 1: Block diagram of the proposed distributed event-triggered control
and estimation strategy for the DC microgrids.

Figure 1 presents the diagram of the distributed controller. A state estimator
is proposed to reduce the number of data transmissions with relatively small
degradation in the estimation performance. The send on delta (SoD) event-
generation condition (i.e., $\delta$) is used in which the sensor data is
transmitted only if its values go beyond the $\delta$ value. A case study of
10-bus microgrid is used to validate the proposed scheme, where the control
objectives are chosen as the voltage stability and power sharing within the ES
systems. Furthermore, multiple distributed ES systems replace a central ES
system, to increase the reliability, power quality, and sensors’ battery life,
and to reduce the losses during the operation.

The contributions of this work can be summarized as:

  1. 1.

Regulating the voltage of the DC microgrid using a novel distributed control
strategy, in order to effectively control the output voltages of the DC-DC
converters connected to the ES systems. Also, the controller is fulfilling two
objectives, i.e., balancing the energy level of the storages together with the
voltage regulation.

  2. 2.

Proposing an SoD-based Kalman filter, as a state estimator, for feedback
control of the DC-DC converter, to balance the energy level by the distributed
controller, along with the voltage regulation in the microgrid. The developed
filter receives the real-time sensor data from the WSN, where the event-
triggering function is based on the SoD sampling. The energy cost at each
sensor node is also analyzed and compared to the traditional digital control
system with the time-triggered sampling functionality. It is shown the network
traffic is significantly reduced, due to the deployed procedure.

  3. 3.

Utilizing the publish-subscribe model for the appropriate implementation of
the event-based control strategy. It is shown that the model is seamlessly
suitable for the event-based coordination of the distributed controllers.

The rest of this paper is organized as follows. Section II describes the
components of the DC microgrid, in which a microgrid model is developed based
on the proposed distributed control and estimation strategy. A number of
communication models have been thoroughly analyzed in terms of the event-based
communication, and the publish-subscribe communication model is further
proposed for the event-based sampling scenarios in Section III. In Section IV,
the proposed distributed controller design is discussed, and the structure of
the Kalman filter as a state estimator is described, where a modification is
suggested for the filter in order to adapt to the SoD event-based sampling.
The stability and steady-state analyses are provided in Section V. In Section
VI, a case study is given to validate the performance of the controller using
the simulations of a 10-bus DC microgrid. The paper is concluded in Section
VII.

##  II DC Microgrid Model Analysis

A DC microgrid essentially consists of four main components, including the DG,
ES systems, power converters (DC-DC or DC-AC), and loads. Figure 2 indicates
the common configuration of a microgrid, along with its constituent
components.

Figure 2: Schematic of a DC microgrid with the main constituent components.

The main objective of the ES systems is to compensate for the fast voltage
dynamics caused by the load fluctuations in the DC microgrid. They are
utilized to stabilize the voltage, and to increase the power quality. The
widely used ES devices are electrochemical batteries, super capacitors, and
flywheels which are easily deployable in a microgrid due to their natural DC
output. A DC microgrid has two main operating modes: islanded mode and
connected mode. The distributed secondary controller proposed in this work can
operate in the both modes. A maximum power point tracking (MPPT) scheme is
used to ensure that maximum power is absorbed from the intermittent
distributed energy sources (DERs) such as photovoltaics. Here, the DGs and DC-
DC converters in the main grid are modeled as the current sources, in which
the variable injected current is related to their output power. In this way,
the DC microgrid only gets connected to the main grid if enough power is not
available from the installed DGs for load balance.

##  III Communication Models for Microgrids

There are several communication models that can be integrated into a control
system. Each model has both advantages and disadvantages, and the system
designer has to effectively decide which model to employ for the
implementation of the control system. In this work, several communication
models are studied in detail and are compared with each other. In the
following, a comparative analysis has been given for a number of the intended
communication models, for the purpose of the appropriate employment in the DC
microgrids.

  1. 1.

Request/Response: This communication model is one of the most commonly known
models. It consists of a client that requests a service from a server, as
shown in Figure 3 (a). It is a useful model for the client-server or master-
slave architectures [41]. However, a drawback of this model is the inequality
of participants, which is apparent in the network topology. This makes it
difficult for the bidirectional communication scenario, in which both the
parties request information from each other, especially if firewalls are
present. Consequently, either events, event-subscriptions, or security is
difficult to manage, and require additional services and substantial resources
if firewalls are used in the network.

Figure 3: The communication models for the bidirectional communication
scenario: (a) request/response model; (b) event-subscription model.

  2. 2.

Event-Subscription: This communication model allows a client to subscribe to
events of a given type from a server. The server then informs the client each
time the event is triggered, without having to constantly poll the server, as
in Figure 3 (b). Advanced event-subscription mechanisms can include
client-specific requirements of when events are desired and under what
conditions. The benefits of using this communication model are that half of
the messages are not needed over time, and the latency of updates is kept to a
minimum. The problem with this model is that it is not designed for the
multiparty communication scenario. This can be further solved using the
publish-subscribe model.

  3. 3.

Multicasting: The previous models are primarily considered for the
communication purposes between two entities. However, a more efficient model
is required in cases when the same information has to be sent to multiple
entities at the same time. Here, a sender sends one message through an
intermediary (i.e., a broker or a router) which then distributes it to
multiple recipients that have all requested participation in the
communication. This model saves the bandwidth because the sender does not have
to send individual messages to all the parties by itself. Also, the sender
does not even have to know who the recipients are.

Although one can use this model in order to save the bandwidth, it is often
used as a means of overcoming the restrictions in the chosen protocol, and its
support of the event-subscription model, as well. In addition, multicasting is
inherently difficult to secure, and it is more efficient in terms of the
bandwidth only if the recipients actually use most of the transmitted values.
In the case where frequent multicasting for decreasing the latency in the
network is desired but not possible, the multicasting model might result in
the increase rather than decrease in the required bandwidth [42].

  4. 4.

Queues: The first-in, first-out queues, is a model that allows one or more
entities to post the messages or tasks into a queue, and then lets one or more
receivers receive the messages in an ordered fashion. The queues reside on an
intermediary node or network to which all participants are connected. This
model is an excellent tool for the load balancing purposes, where the
collected tasks from multiple sources need to be distributed among the
existing workers, perhaps having different performances. Queues can hardly be
used for real-time communications in control systems, since the message should
be saved at first, and then be processed at the controller via an intermediary
node.

Publish/Subscribe: This communication model is an extension of the
multicasting model, with the difference that messages transmitted are stored
in the intermediary node. The messages, or a reference to the messages, are
distributed to the corresponding subscribers, depending on the protocol. Also,
only the latest message is stored, a given number of messages are stored, or
all messages are stored in the intermediary, depending on the chosen protocol,
as well as the settings of the intermediary [43]. The difference between
distributing the entire message and distributing only a reference to the
message is important and affects the performance of the solution in terms of
the consumed bandwidth. If the subscribers consume most of the messages,
forwarding the messages themselves is more efficient, as in the case of
multicasting. If, however, consumption occurs only on demand, then sending
shorter references is more efficient because these messages are smaller and
subscribers would use only a minority of them to fetch an actual message. In
order to fetch a message in the latter case, a separate request/response
action needs to be performed [44].

The behavior of each model has been analyzed from the control point of view.
In this treatise, the publish-subscribe communication model is used for the
practical implementation of the distributed event-based control strategy. In
the publish-subscribe model, a node can act as a publisher, subscriber, or
both simultaneously. The network roles can be dynamically changed to ensure a
flexibility to reconfigure the directions of the data exchange. The main
advantage of this model is that the data can be exchanged intelligently
between the devices (i.e., the publishers send the data to the specific
subscribers without having a subscription knowledge of each node). This keeps
the setup process easier for the overall maintenance of the network, and
enables the self-configuration of the devices, as one of the primary
characteristics of the industrial ad-hoc networks. The process of selecting
messages for the reception and processing is called filtering. The topic-based
and content-based filtering are the two common forms of filtering used in new
communication protocols introduced in the context of IoT. In the publish-
subscribe network setup, a server manages the topics and contents, which is
called a broker. The broker-free setup can be achieved with the distributed
topics/contents suitable for the proposed distributed control structure [45].
The topic-based publish-subscribe communication model also enables the
selective message distribution among a number of sources and sinks [46].
Messages are associated with the topics and are selectively routed to
destinations with matching topic interests. Subscribers show their interest in
receiving data with a given topic and data sources publish messages on the
topics.

The main advantages of the publish/subscribe communication model compared with
the aforementioned models can be summarized as:

  * •

Adaptive role change in a dynamic environment from the publisher to the
subscriber and vice versa.

  * •

Intelligent data exchange among the nodes without having a subscription
knowledge of each node.

  * •

Automatic self-configuration of the nodes in the ad-hoc network without a
central configurator which enables the plug and play operation of the
microgrid.

  * •

Intrinsic discrete event transmission support which suits it as an ideal
choice for the event-triggered control.

Figure 4: Block diagram of the topic-based publish-subscribe model for the
industrial distributed communication scenario.

Figure 4 also presents the concept of the topic-based publish-subscribe
communication protocol model. Multiple subscribers can listen for a
predetermined topic, and also multiple publishers can publish new data to
certain topics. The only drawback with this model is that when subscribers
initially subscribe to a certain topic or content, their initial value remains
undefined until the next publishing cycle. A number of communication protocols
are proposed to tackle this issue, such as the message queue telemetry
transport (MQTT) protocol, which uses the retained value in the broker-based
structures. Consequently, when a subscriber connects to the broker, it will
release the retained value of the most updated publish to the subscriber [47,
48]. The protocol stack of MQTT is depicted in Figure 5.

TABLE I: Comparison Between the Different Communication Models for the Distributed Event-Triggered Control of DC Microgrids. Communication Model | Support for Dynamic Environment | Smart Message Delivery | Plug & Play Capability | Event Transmission Support
---|---|---|---|---
Request/Response | Weak | Weak | Not supporting | Not supporting
Event-Subscription | Weak | Medium | Not supporting | Strong
Multicasting | Strong | Medium | Medium | Medium
Queues | Medium | Medium | Not Supporting | Medium
Publish/Subscribe | Strong | Strong | Strong | Strong
Figure 5: The MQTT protocol stack for the event-based implementation.

##  IV Distributed Control Strategy Analysis

A bidirectional DC-DC boost converter provides an interface between the ES
system and the DC microgrid. The boost converter also acts as a bidirectional
charger. A voltage-current (V-I) droop controller regulates the DC-DC
converter output voltage with the reference voltage of $v^{*}_{i}$, which is
calculated based on the microgrid voltage reference $v^{mg}$ and the locally
measured output current $i_{i}$. In the proposed strategy, the droop control
is improved by considering two extra control signals $u^{\overline{v}}_{i}$,
$u^{e}_{i}$ in the current reference signal $v^{\mathrm{*}}$:

$v^{\mathrm{*}}_{i}\mathrm{=}v^{mg}\mathrm{-}F_{i}r_{i}\mathrm{(}i_{i}\mathrm{-}u^{\overline{v}}_{i}\mathrm{-}u^{e}_{i}\mathrm{)}$
(1)

where the voltage stabilization control signal $u^{\overline{v}}_{i}$ is
defined to regulate the average microgrid bus voltage, and the power sharing
control signal $u^{e}_{i}$ is proposed to balance the energy level between the
ES systems and to maintain it through the load sharing. In a decentralized V-I
droop control, the load is normally shared between the ES systems in inverse
proportion to their virtual resistances $r_{i}$. The virtual resistance (i.e.,
$r_{i}$) is merely used for the voltage regulation at the converters of the ES
systems, therefore it is lossless.

The DC microgrid is subject to high frequency harmonics due to the pulse width
modulation (PWM) switching control scheme used for the converters. A low-pass
filter with the cut-off frequency of ${\omega}^{c}_{i}$ should be used to
reduce the harmonics, and to prevent the resulting instabilities in the grid.

$F_{i}\mathrm{=}\frac{{\omega}^{c}_{i}}{{s\mathrm{+}\omega}^{c}_{i}}$ (2)

where ${\omega}^{c}_{i}$ is a time-variant parameter considering the switching
control of the DC-DC converters. However, with an appropriate selection of an
upper-bound value, it can be approximated to a time-invariant parameter.

The current regulation can be achieved in two stages [49]. At the first stage,
a proportional-integral (PI) voltage controller $G^{v}_{i}$ is defined in (3)
to set the converter current reference to regulate the output voltage of the
ES system:

$i^{\mathrm{*}}_{i}\mathrm{=}G^{v}_{i}\left(v^{\mathrm{*}}_{i}\mathrm{-}v_{i}\right)\mathrm{,\
}\mathrm{\ }G^{v}_{i}\mathrm{=}p^{vp}_{i}\mathrm{+}\frac{p^{vi}_{i}}{s}$ (3)

At the second stage the current controller sets the duty cycle of the PWM
switching to control the bipolar junction transistors (BJTs) of the converter,
and to regulate the output current.

In order to balance the energy level, a PI controller $G^{e}_{i}$ is defined
in (4) to set the energy level $e_{i}$ to the local estimate of the average
energy level of the ES systems. Due to different capacities for the energy
storages, per-unit energy level is used for the power balancing signal.

$u^{e}_{i}\mathrm{=}G^{e}_{i}\left(e_{i}\mathrm{-}{\overline{e}}_{i}\right)\mathrm{,\
\ }G^{e}_{i}\mathrm{=}p^{ep}_{i}\mathrm{+}\frac{p^{ei}_{i}}{s}$ (4)

Another PI controller $G^{\overline{v}}_{i}$ is used for the voltage
regulation of the microgrid, where the local estimate of the average bus
voltage is regulated to the voltage reference of the microgrid:

$u^{\overline{v}}_{i}\mathrm{=}G^{\overline{v}}_{i}\left(v^{mg}\mathrm{-}{\overline{v}}_{i}\right)\mathrm{,\
}\
G^{\overline{v}}_{i}\mathrm{=}p^{\overline{v}p}_{i}\mathrm{+}\frac{p^{\overline{v}i}_{i}}{s}\mathrm{+}\frac{p^{\overline{v}ii}_{i}}{s^{\mathrm{2}}}$
(5)

In (5), the double-integral is used to maintain the overall stability, and to
eliminate the steady-state error. An average state estimator is designed for
each ES system, using the local measurements and information from the
neighboring ES systems. The estimator updates the local estimates of the
average energy level and bus voltage of the ES system, then the controller
tries to regulate the average estimates to the nominal values of the
microgrid.

###  IV-A Distributed Average Consensus Protocol

Each ES system has an average state estimator that uses the local measurements
and information from the neighboring ES systems to update the local estimates
of the average ES system per-unit energy level $\overline{e}_{i}$, average
microgrid bus voltage $\overline{v}_{i}$, and average ES system output
current. The average state estimator implements a distributed average
consensus protocol for tracking the dynamic signals from [50].

The ES systems are connected by a sparse communication graph
$\mathcal{G(V,E)}$ with the nodes $\mathcal{V}=(1,...,\mathcal{N)}$ and edges
$\mathcal{E}$. Each graph node represents an ES system, and the graph edges
represent communication links between them. $(i,j)\in\mathcal{E}$ if there is
a link allowing information flow from node $i$ to node $j$. The neighbors of
$i$ node are given by $\mathcal{N}_{i}$, where $j\in\mathcal{N}_{i}$ if
$(j,i)\in\mathcal{E}$. The graph adjacency matrix is given by $A=[a_{ij}]\in
R^{N\times N}$, where $a_{ij}>0$ if $(j,i)\in\mathcal{E}$ and $a_{ij}=0$
otherwise.

For the $i$th ES system, let $x_{i}$ be a local state variable, and let
$\overline{x}_{i}$ be a local estimate of the average value of that state for
the ES systems. The $i$th ES system receives the average state estimates from
its neighbors $j\in\mathcal{N}_{i}$, and its average state estimator
implements the following distributed average consensus protocol:

$\overline{x}_{i}=x_{i}+\int\sum\limits_{j\in\mathcal{N}_{i}}{a_{ij}(\overline{x}_{j}-\overline{x}_{i})dt}$
(6)

Each node in the network has in-degree $d_{i}=\sum_{j=1}^{N}a_{ij}$ and out-
degree $d_{i}^{o}=\sum_{j=1}^{N}a_{ji}$. Moreover, the graph is balanced if
$d_{i}=d_{i}^{o}$ for all the nodes. The graph degree matrix is given by
$\textbf{D}=diag\\{d_{i}\\}$ and the graph Laplacian matrix is also given by
$\textbf{L}=\textbf{D}-\textbf{A}$. The global dynamics of the distributed
average consensus protocol are given by:

$\dot{\overline{\textbf{x}}}=\dot{\textbf{x}}-\textbf{L}\overline{\textbf{x}}$
(7)

Applying the Laplace transform yields the following transfer function matrix
for the average consensus protocol [50]:

$G^{avg}=\frac{\overline{\textbf{X}}}{\textbf{X}}=s(sI_{N}+\textbf{L})^{-1}$
(8)

$\overline{\textbf{X}}$ and X are the Laplace transforms of $\overline{x}$ and
$x$, respectively.

For a balanced communication graph with a spanning tree, the steady-state gain
of the average consensus protocol is given by the averaging matrix [51]:

$\lim_{s\to 0}G^{avg}=Q\mathrm{,where}\ [Q]_{ij}=\frac{1}{N}$ (9)

The final value theorem shows that for a vector of step inputs, the elements
of $\overline{\textbf{x}}(t)$ converge to the global average of the steady-
state values $\textbf{x}^{ss}$:

$\lim_{t\to\infty}\overline{\textbf{x}}(t)=\lim_{s\to
0}G^{avg}\lim_{t\to\infty}s\textbf{X}=Q\textbf{x}^{ss}=\left\langle\textbf{x}^{ss}\right\rangle\underline{1}$
(10)

###  IV-B Event-Based Kalman Filter Design

Consider the following linear system which is the state space realization of
distributed average consensus protocol transfer function in each controller:

$\displaystyle\dot{x}=Ax\left(t\right)+w\left(t\right)$ $\displaystyle
y(t)=Cx(t)+v(t)$ (11)

where $x\mathrm{\ }\mathrm{\in}\mathrm{\ }{\mathrm{R}}^{\mathrm{n}}$ is the
estimated state and $y\ \mathrm{\in}\mathrm{\
}{\mathrm{R}}^{\mathrm{p}}\mathrm{\ }$is the output measurement. The process
noise $w\left(t\right)$ and measurement noise $v(t)$ are the uncorrelated,
zero-mean white Gaussian random signals, fulfilling the following:

$\displaystyle E\left\\{w(t)\;w(s)^{\prime}\right\\}=Q\;\delta(t-s)$ (12)
$\displaystyle E\left\\{v(t)\;v(s)^{\prime}\right\\}=R\;\delta(t-s)$ (13)
$\displaystyle
E\left\\{w_{i}\left(t\right){v_{j}\left(s\right)}^{\prime}\right\\}=0,\;\;1\leq
i\leq n,\;\;1\leq j\leq p$ (14)

where $w_{i}$ and $v_{j}$ are the i-th and j-th elements of the $w$ and $v$,
respectively. Also, $R$ is the measurement noise covariance, and $Q$ is the
process noise covariance. It is assumed that the i-th sensor only transmits
the data when the difference between the current sensor value and the
previously transmitted value is greater than ${\delta}_{i}$.

The states are also estimated periodically with the period of $T$. For
simplicity, it is assumed that there is no delay in the sensor data
transmission. Using the SoD method, the estimator continuously with a period
of $T$ demands the data from the sensors no matter the data becomes available.
For example, if the last received $i$-th sensor value is $y_{i}$ at the time
$t_{last,i}$, and there is no $i$-th sensor data received for
${t>t}_{last,i}$, then the estimator can estimate $y_{i}(t)$ as:

$y_{i}\left(t_{last,i}\right)-{\delta}_{i}\leq\ y_{i}\left(t\right)\leq
y_{i}\left(t_{last,i}\right)+{\delta}_{i}$ (15)

The last received i-th sensor data is used to compute the output
$y_{computed,i}$ even if there is no sensor data transmission:

$y_{computed,i}\left(t\right)=y_{i}\left(t_{last,i}\right)=C_{i}x\left(t\right)+v_{i}\left(t\right)+{\Delta}_{i}\left(t,t_{last,i}\right)$
(16)

where
${\mathrm{\Delta}}_{i}\left(t,t_{last,i}\right)\mathrm{=}y_{i}\left(t_{last,i}\right)\mathrm{-}y_{i}\left(t\right)$
and:

$\left|{\Delta}_{i}\left(t,t_{last,i}\right)\right|\leq{\delta}_{i}$ (17)

In (16), the measurement noise increases from $v_{i}\left(t\right)$ to
$v_{i}\left(t\right)+{\Delta}_{i}\left(t,t_{last,i}\right)$. If
${\Delta}_{i}\left(t,t_{last,i}\right)$ is assumed to have the uniform
distribution with (17), then the variance of
${\Delta}_{i}\left(t,t_{last,i}\right)$ is
$\frac{{\delta}^{\mathrm{2}}_{i}}{\mathrm{3}}$, which is added to the
measurement noise covariance in standard Kalman filter R$\left(i,i\right)$
when (16) applies.

Improved Kalman Measurement Update Algorithm: An algorithm is proposed here to
appropriately improve the measurement update part of the standard Kalman
filter algorithm, which is adapted to the SoD event-generation condition by
increasing the measurement noise covariance $\overline{R}_{k}$:

  1. 1.

Initialization set

$\displaystyle\hat{x}^{-}(0),{P}^{-}_{0}$ $\displaystyle
y_{last}=C\hat{x}^{-}\left(0\right)$ (18)

  2. 2.

Measurement update

$\overline{R}_{k}=R$ (19)

if i-th measurement data are received

$\hat{y}_{last,i}=y_{i}\left(kT\right)$ (20)

else

$\overline{R}_{k}\left(i,i\right)=\overline{R}_{k}\left(i,i\right)+\frac{{\delta}^{2}_{i}}{3}$
(21)

end if

$\displaystyle
K_{k}={P}^{-}_{k}C^{\prime}(C{P}^{-}_{k}C^{\prime}+\overline{R}_{k})^{-1}$
$\displaystyle\hat{x}\left(kT\right)=\hat{x}^{-}\left(kT\right)+K_{k}(\hat{y}_{last}-C\hat{x}^{-}(kT))$
$\displaystyle P_{k}{=(I-K_{k}C)P}^{-}_{k}$ (22)

  3. 3.

Project ahead

$\displaystyle\hat{x}^{-}\left((k+1)T\right)=\exp{\left(AT\right)}\hat{x}\left(kT\right)$
$\displaystyle{P}^{-}_{k+1}=\exp{\left(AT\right)}P_{k}\exp{\left(A^{\prime}T\right)}+Q_{d}$
(23)

where $Q_{d}$ is the process noise covariance for the discretized dynamic
system; $y_{last}$ is defined as (24):

$y_{last}=[y_{last,1},y_{last,2},\dots,y_{last,p}]^{\prime}$ (24)

The presented event-triggered Kalman filter has been developed to implement
the distributed controller and estimator as an NCS. It should be noted that in
the proposed event-triggered observer, convergence is obtained by using the
Kalman optimal observer. However, choosing the lower values of ${\delta}_{i}$
would result in the considerable reduction in the convergence time [40]. The
controllers only receive updates from their neighbor controllers which is
reflected in the L matrix of the transfer function that has been realized.
Distributed average consensus is then achieved for each controller based on
the number of neighbor controllers. Also, the higher the number of adjacent
controllers are, the faster the estimator would converge.

##  V Global Dynamics and Stability Analysis

Figure 6 presents the block digram of the feedback loop for each of the
distributed ES controllers. The voltage regulation dynamics of the grid forms
a multiple-input multiple-output (MIMO) linear system. If $V^{mg}$ is the
Laplace transform of the voltage reference of the grid, the distributed
control dynamics can be expressed as (25):

$V^{*}=V^{mg}\underline{1}-Fr\left(I-G^{\overline{v}}\left(V^{mg}\underline{1}-\overline{V}\right)-G^{e}\left(E-\overline{E}\right)\right),\
\ $ (25)

where

$\displaystyle F=diag\left\\{F_{i}\right\\}$ (26) $\displaystyle
r=diag\left\\{r_{i}\right\\}$ (27) $\displaystyle
G^{\overline{v}}=diag\left\\{{G_{i}}^{\overline{v}}\right\\}$ (28)
$\displaystyle G^{e}=diag\left\\{G^{e}_{i}\right\\}$ (29)
$\displaystyle\overline{V}=G^{avg}V\ and\ \overline{E}=G^{avg}E$ (30)

The grid-connected rectifier, the constant power loads, as well as the
generation sources (i.e., operate under the MPPT algorithm) can act as the
positive or negative current sources, while the ES systems act as the bus
voltage regulation units in the DC microgrid. To formulate the bus voltage
regulation dynamics, power sources can be modeled by a parallel current source
and resistance. Modern DC-DC converters operate at a high switching frequency
with one switching period delay (i.e., $T_{s}$) in the current control mode.
In order to model the DC-DC converter, a control structure as shown in Figure
7 is used, in which the bus voltage regulation dynamics is designed as an
outer-loop between the output voltage of the ES system $v^{\mathrm{*}}_{i}$,
and the local bus voltage $v_{i}$ [52]. Moreover, the transfer function for
the internal loop is given by $H^{v_{ol}}_{i}$.

Figure 6: Internal model of the ES system: (a) DC-DC converter circuit; (b)
block diagram of the local converter controller. Figure 7: Block diagram of
the proposed distributed feedback controller.

$H^{v_{cl}}_{i}=\frac{H^{v_{ol}}_{i}}{1+H^{v_{ol}}_{i}}\ ,\ \
H^{v_{ol}}_{i}=\frac{G^{v}_{i}}{sC_{i}(T_{s}s+1)}$ (31)

Therefore, the local bus voltage closed-loop transfer function of the DC
microgrid is given by:

$V\mathrm{=}H^{v_{cl}}V^{\mathrm{*}}\mathrm{,\ }{\ \ \ \ \ \ \ \
H}^{v_{cl}}\mathrm{=}diag\\{H^{v_{cl}}_{i}\\}$ (32)

The output currents of the ES system can be obtained from multiplying the bus
voltages with the bus admittance matrix, constructed based on the line and
load impedances:

$I=YV$ (33)

A first order model is used for the battery per-unit energy level charging and
discharging:

${\dot{e}}_{i}=-\frac{v_{i}i_{i}}{e^{max}_{i}}$ (34)

where $e^{max}_{i}$ is the maximum energy capacity of the i-th ES system. The
global energy level dynamics is modeled as (35):

$E=MYV,\ \ M=diag\\{-\frac{v^{mg}}{e^{max}_{i}s}\\}$ (35)

The global closed-loop voltage regulation dynamics can be described by the
multiple output linear system as (V):

$\displaystyle
V=[{\left(H^{v_{cl}}\right)}^{-1}+FrY+FrG^{\overline{v}}G^{avg}$
$\displaystyle-
FrG^{e}\left(I_{N}-G^{avg}\right)MY]^{-1}V^{mg}\left(I_{N}+FrG^{\overline{v}}\right)\underline{1}$
(36)

In the above strategy, it is assumed the local distributed controllers can
exchange data with the other controllers in a continuous mode. It should also
be noted that this assumption is not feasible in the cases involving the NCSs.
An event-based Kalman filter is proposed to overcome this problem. Using this
filter, the distributed control system can be realized with the SoD event
triggering condition.

###  V-A Stability and Steady-State Analysis

Assuming $v^{mg}$ be the control reference voltage. In this case, input to the
global closed-loop voltage dynamics is given by:

$V^{mg}=\frac{v^{mg}}{s}$ (37)

The steady-state DC microgrid bus voltages are obtained by applying the final
value theorem to (37):

$\displaystyle v^{ss}=\lim_{s\to 0}sV$ $\displaystyle=\lim_{s\to
0}[s^{2}\left(H^{v_{cl}}\right)^{-1}+s^{2}FrY+s^{2}FrG^{\overline{v}}G^{avg}$
$\displaystyle-s^{2}FrG^{e}\left(I_{N}-G^{avg}\right)MY]^{-1}s^{2}v^{mg}\left(I_{N}+FrG^{\overline{v}}\right)\underline{1}$

The steady-state bus voltages can be reached to based on the following limits:

$\displaystyle\lim_{s\to
0}s^{2}G^{\overline{v}}=G^{\overline{v}ii},\mathrm{where}\
G^{\overline{v}ii}=\mathrm{diag}\\{k_{i}^{\overline{v}ii}\\}$
$\displaystyle\lim_{s\to 0}sG^{e}=G^{ei},\mathrm{where}\
G^{ei}=\mathrm{diag}\\{k_{i}^{ei}\\}$ $\displaystyle\lim_{s\to
0}sM=M_{0},\mathrm{where}\
M_{0}=\mathrm{diag}\\{-\frac{v^{mg}}{e_{i}^{max}}\\}$ $\displaystyle\lim_{s\to
0}G^{avg}=Q,\lim_{s\to 0}Y=Y_{0},\ \lim_{s\to 0}F=I_{N},$
$\displaystyle\mathrm{and}\lim_{s\to 0}{\left(H^{v_{cl}}\right)}^{-1}=I_{N}$

therefore

$\displaystyle
v^{ss}=\left[r\left(G^{\overline{v}ii}Q-G^{ei}(I_{N}-Q)M_{0}Y_{0}\right)\right]^{-1}v^{mg}(rG^{\overline{v}ii})\underline{1}$

which yields

$\displaystyle\left[(G^{ei})^{-1}G^{\overline{v}ii}Q-(I_{N}-Q)M_{0}Y_{0}\right]v^{ss}=v^{mg}(G^{ei})^{-1}G^{\overline{v}ii})\underline{1}$

Furthermore, as shown in (V-A), without the double-integral gain of the
voltage controller, the steady-state response would be dominated by the energy
balancing control signal; to verify that the average steady-state voltage is
equal to the reference voltage of the microgrid, each side of (V-A) is
multiplied by the averaging matrix $Q$. Since the column sums of $(I_{N}-Q)$
are equal to zero, $Q(I_{N}-Q)=0_{N\times N}$. Following (10) yields:

$\displaystyle
Q\left((G^{ei})^{-1}G^{\overline{v}ii}Qv^{ss}\right)=v^{mg}Q\left((G^{ei})^{-1}G^{\overline{v}ii}\underline{1}\right)$
$\displaystyle\left\langle
v^{ss}\right\rangle\left\langle(G^{ei})^{-1}G^{\overline{v}ii}\underline{1}\right\rangle\underline{1}=v^{mg}\left\langle(G^{ei})^{-1}G^{\overline{v}ii}\underline{1}\right\rangle\underline{1}$
$\displaystyle\left\langle v^{ss}\right\rangle=v^{mg}$ (42)

##  VI Results and Discussion

The performance evaluation of the proposed controller is thoroughly presented
in this section through a case study of a 10-bus microgrid. As also depicted
in Figure 1, each distributed controller receives the events from neighbor ES
sensors. The deployed sensors measure the bus voltages and currents.

It has been discussed in detail that the network traffic, and the battery
energy usage of sensor nodes in a WSN, would be reduced significantly if an
event-triggered strategy is used. The event-triggered control stops the
unnecessary data exchange in a shared medium. Once an event is generated, the
data must be sent to the controller as fast as possible, in order to prevent
the deviation of system behavior from the stable margin.

In the proposed distributed control, there are two different variables that
are evaluated in the event-generation condition. First is the bus voltage in
which the distributed controller is installed, and second is the ES system
per-unit energy level. The conditions of the SoD event-generation for these
variables are independent, therefore two thresholds are evaluated in each
controller. Each event is then matched with its corresponding topic in the
publish-subscribe model; e.g., in the presented case study of the 10-bus
system, each bus controller publishes data in two topics related to that bus.
Since the network is assumed to be connected, each distributed controller
subscribes to the topics of the other neighbors. This is shown in Table II.
The MATLAB & Simulink software is employed for the simulation of the DC
microgrid and distributed control strategy. Also, the Simscape toolbox is used
to simulate the electrical distribution system of the DC microgrid.

TABLE II: Distributed Controllers and Their Corresponding Topics. Bus Controller | Voltage SoD Event Topic | Energy SoD Event Topic
---|---|---
Bus 1 | voltageBus1 | energyBus1
Bus 2 | voltageBus2 | energyBus2
Bus 3 | voltageBus3 | energyBus3
Bus 4 | voltageBus4 | energyBus4
Bus 5 | voltageBus5 | energyBus5
Bus 6 | voltageBus6 | energyBus6
Bus 7 | voltageBus7 | energyBus7
Bus 8 | voltageBus8 | energyBus8
Bus 9 | voltageBus9 | energyBus9
Bus 10 | voltageBus10 | energyBus10

###  VI-A DC Microgrid Configuration

The microgrid used for the case studies is shown in Figure 8. The presented DC
microgrid incorporates a 10-bus distribution system with the PV generation and
10 battery ES systems.

At bus 1, a 150 kW rated rectifier provides main connection of the microgrid.
Bus 1 also includes 500 $m^{2}$ PV generation operated with the MPPT
algorithm, rated for 80 kW. Based on the analysis of conventional wiring
configurations of the DC microgrids shown in [53] for data centers, $50m\times
24mm$ cables are selected to connect the load buses to bus 1. The buses 1 to 7
have 25 kWh lithium-ion batteries, while the buses 8 to 10 ES systems have
12.5 kWh lithium-ion batteries. The battery ES systems are connected by a
sparse communication network to support the proposed distributed event-
triggered control. The communication links between the ES systems are
bidirectional, meeting the requirements of the distributed control strategy
for a balanced communication network. Based on the ETSI EN 300 132-3-1
telecommunications DC distribution standard for data centers, the voltage
limits are defined as 380 V$\pm 5\%$ [54].

Figure 8: Proposed case study of the 10-bus DC microgrid with the ES systems.
Figure 9: Data of the PV solar irradiance used in this case study.

For the case study, 15 kW constant power loads are installed at buses 1 to 5,
and 5 kW constant power loads are installed at buses 6 to 10, hence the total
load of the microgrid would be 100 kW. The battery ES systems begin with
values around half of their energy levels, and are chosen randomly. The bus 1
PV generation with MPPT was simulated based on the modeling approach from
[55], using the 1 min resolution irradiance and temperature data for 2 p.m. to
4 p.m. on June 1, 2014 from the NREL Solar Radiation Research Laboratory
(SRRL): Baseline Measurement System (BMS), in Colorado. Moreover, the used
irradiance data is shown in Figure 9. The simulation parameters are also
provided in Table IV. The graph adjacency matrix $A$ elements $a_{ij}$ are
chosen as ”1” if there is a connection and ”0” if there is no communication
link between the buses. The DC load and battery parameters for each bus are
given in Table III. The parameters of the proposed event-based Kalman filter
are also provided in Table V for the proposed control strategy.

TABLE III: Values of the Loads and Batteries at Each Bus. Bus | Load Power | Battery Capacity (380 V)
---|---|---
Bus 1 | 15 kW | 25 kWh
Bus 2 | 15 kW | 25 kWh
Bus 3 | 15 kW | 25 kWh
Bus 4 | 15 kW | 25 kWh
Bus 5 | 15 kW | 25 kWh
Bus 6 | 5 kW | 25 kWh
Bus 7 | 5 kW | 25 kWh
Bus 8 | 5 kW | 12.5 kWh
Bus 9 | 5 kW | 12.5 kWh
Bus 10 | 5 kW | 12.5 kWh

###  VI-B Simulation Scenario

The simulation scenario is divided into four sections to represent the
different modes of operation of the proposed control strategy. The scenario is
simulated for both with and without the proposed event-triggered estimation,
in order to compare the results of both the implementations. Moreover, in
another simulation, the performance of the proposed estimator is tested by
adding 100 ms delay in the event transmission. The simulation time is set at
120 minutes (i.e., 7,200 seconds).

####  VI-B1 Islanded Operation With Load Switching, 0 to 10 min

The DC microgrid begins in the islanded mode. The start load is 60% at all the
employed buses. After 5 minutes, the loads are switched at all buses to their
100% nominal values. As shown in Figure 12, the energy level of the ES systems
at the buses are increased, as the total power from the PV exceeds the total
load of the microgrid. After the load switching, storages starting to
discharge the energy, and the voltage is stabilized around 380 V with the zero
error, as shown in Figure 10 (C).

####  VI-B2 Grid Connected Operation With Rectifier Providing Load Balancing,
10 to 40 min

At min 10, a grid connection is made with the rectifier in the load balancing
mode. Moreover, the ES systems use their 30 kW power capacity to reach a
balanced per-unit energy level, as shown in Figure 12. A per-unit energy level
of 0.45 is reached by the ES systems; 11.25 kWh for the 25 kWh ES systems at
buses 1 to 7, and 5.62 kWh for the 12.5 kWh ES systems at buses 8 to 10. The
voltage controllers limit the bus voltages of the DC microgrid between 377.3
and 381.6 V (i.e., 1% error), and ensure the average bus voltage remains at
the voltage reference of the microgrid, as shown in Figure 12 (B). As desired,
the average ES system per-unit energy level remains constant around the
operating point.

####  VI-B3 Grid Connected Operation With Main Grid Providing ES Charging, 40
to 80 min

At min 40, the rectifier operating mode is changed from the load balancing to
the ES charging mode, and the injected power increases. The rectifier uses its
maximum power capacity of 150 kW to raise the average ES system per-unit
energy level to the value of 0.62, as shown in Figure 12 (B). The per-unit
energy balancing is maintained between the ES systems. The 25 kWh ES systems
are charged at a common rate and the 12.5 kWh ES systems are charged at half
of this rate. As the ES systems are charged, they adjust their output powers
to balance the variable PV generation, and to further regulate the average DC
microgrid voltage within 0.05 V of the reference of 380 V, as shown in Figure
10 (B).

####  VI-B4 Islanded Operation With Sudden Main Grid Disconnection, 80 to 120
min

At min 80, the grid connected rectifier is suddenly disconnected, initiating
the islanded operation. The sudden power imbalance causes the bus voltages of
the DC microgrid to fall, with a minimum level of 377.4 V reached. The ES
systems react to the fall in the voltage by increasing the corresponding
output powers, restoring the microgrid load balance and returning the average
bus voltage to the reference with less than 1% (i.e., 2 V) steady-state
deviation.

TABLE IV: Parameters of the Case Study and Controller. $R_{dc}$ | 36 m$\Omega$ | Voltage | 380 V | $p_{i}^{\bar{v}p}$ | 500
---|---|---|---|---|---
$L_{dc}$ | 7 $\mu H$ | $p_{i}^{vi}$ | 10 | $p_{i}^{\bar{v}i}$ | 10
$r$ | 0.2533 | $w_{i}^{c}$ | 100 rad/s | $p_{i}^{\bar{v}ii}$ | 0.1
$p_{i}^{vp}$ | 10 | $p_{i}^{ep}$ | 5000 | $p_{i}^{ei}$ | 50
TABLE V: Parameters of the Event-Triggered Kalman Filter. $\delta_{i}(Voltage)$ | 0.1 V
---|---
$\delta_{i}(Energy)$ | 0.01 p.u.
$Q$ | 0
$R$ | 1
$T$ | 1 Second
Figure 10: Simulation results of the bus voltages for the case study of the
10-bus DC microgrid: A) without the proposed estimator; B) with the proposed
estimator; C) error between the two approaches. Figure 11: Simulation results
of the bus voltages for the case study of the 10-bus DC microgrid: A) without
the proposed estimator; B) with the proposed estimator (100 ms delay); C)
error between the two approaches. Figure 12: Simulation results of the energy
level of the storages for the case study of the 10-bus DC microgrid: A)
without the proposed estimator; B) with the proposed estimator; C) error
between the two approaches. Figure 13: Simulation results of the output power
of storages using the proposed distributed event-triggered estimator.

Furthermore, by manually adding the delay of 100 ms in the event transmission
via the communication network, it can be seen in Figure 12 that the stability
throughout the simulation is maintained. It should be noted that the event-
triggered control is more prone to the instability, due to the delay in the
event-transmission. This is the reason the voltage profile is higher compared
with the ideal scenario. This fact is reflected in the error graph of Figure
12 (C).

In the simulation without applying the event-based Kalman filter, each sensor
is driven by a synchronous clock, as in a traditional digital control system.
For instance, with a sampling period of 1 ms, there should be 40,000 events in
the time frame of 40 s. For this specific case study, in 7,200 seconds there
should be $7,200\times 1000=72\times 10^{5}$ number of generated messages at
each bus, but this is much lower with the event-triggered control strategy
proposed in this work. The number of generated events at each distributed
controller unit of each bus is given in Table VI. This also shows that the
acceptable performance of the microgrid is kept with a minimum number of
transactions among the neighboring controllers. The total energy loss in the
communication is compared in Table VII, where the average power consumption of
each transceiver is assumed to be 50 mA in the duration of 10 ms at the
voltage of 3.3 V (i.e., $e=v\times i\times t$), and the sampling interval is
100 ms for the time-triggered control. When comparing the values of the
consumed energy in the nodes in the traditional sample-based control, as well
as the proposed event-based one, the effectiveness of the event-based control
strategy in terms of the utilization of the resources is evident, as the
energy lost in the communication is reduced nearly by 40%. Additionally, the
network traffic is considerably reduced comparing the number of packets
generated at each bus with the proposed control strategy to the traditional
sample-based control scheme.

TABLE VI: Generated Events at Each Bus. Bus | Number of Published Messages
---|---
Bus 1 | 44,064
Bus 2 | 44,159
Bus 3 | 43,920
Bus 4 | 43,942
Bus 5 | 44,198
Bus 6 | 44,180
Bus 7 | 44,060
Bus 8 | 44,184
Bus 9 | 44,693
Bus 10 | 43,945
TABLE VII: Comparison of the Energy Cost Between the Time-Triggered and Event-Based Control Implementations. Traditional Digital Control | 720,000 messages total | 0.34 Wh
---|---|---
Event-Based Control | 441,345 messages total | 0.2084 Wh

##  VII Concluding Remarks

This investigation has thoroughly presented the design and performance
evaluation of a novel distributed event-triggered control and estimation
strategy. The objective of this controller is to effectively stabilize the
voltage of a DC microgrid only by controlling the output voltages of the DC-DC
converters connected to the ES systems. The controller is able to balance the
energy level of the ES systems and to regulate the output voltage of the
microgrid. An event-based Kalman filter has been developed for the state
feedback controller of the DC-DC converters. The Kalman measurement update
algorithm has also been modified for the distributed controllers to exchange
the data over industrial WSNs. The publish-subscribe model has been proposed
for the optimal implementation of the distributed controller, in which the
publishers send the data to the specific subscribers without having a
subscription knowledge of each node. This has consequently resulted in the
intelligent data exchange, as well as the self-configuration of the devices.
The simulated results confirm a significant reduction in the network traffic,
while maintaining the performance threshold comparing to the digital control
schemes. The total energy cost at each sensor node is considerably reduced
compared to the traditional time-triggered sampling control systems. This work
can be extended to include the comparative analysis of the existing protocols
for the proposed controller, along with the performance evaluations using the
other estimation methods.

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|  Seyed Amir Alavi (GS’16) received the B.Sc. and M.Sc. degrees in electrical
engineering from Power and Water University of Technology (PWUT), Tehran,
Iran, and Shahid Beheshti University (SBU), Tehran, Iran, in 2013 and 2017,
respectively. He is currently pursuing the Ph.D. degree in electronic
engineering at Queen Mary University of London (QMUL). He is the supervisor of
the Real-Time Microgrid Lab. at QMUL. He has conducted a number of industrial
projects on implementation of smart energy management services based on IoT
solutions. He is also working as an embedded systems designer in a London-
based electricity data intelligence company Voltaware. His research interests
include embedded control systems, microgrids, event-based control and signal
processing, networked control systems, and wireless sensor networks.
---|---
|  Kamyar Mehran is a Lecturer in Power Engineering at Queen Mary University
of London (QMUL), U.K. He is the founder of the Real-Time Power and Control
System (RPCS) Lab. at QMUL. He is active in the field of intelligent control,
fuzzy systems, and multi-sensory fusion systems with a number of publications
and book chapters in the field. His research interests include energy storages
(vehicular, grid), low-cost DC/AC microgrids, SiC-based inverters, and energy
management systems. His recent research grants include a condition monitoring
system for aged Lithium-Ion batteries in rural micro-grids (EPSRC Global
Challenge Research Fund), and Innovate UK Faraday Battery Challenge “Current
Density Imaging in EV battery modules”. He worked as a research fellow in
University of Warwick (2013-2015), and Newcastle University (2010-2013). He
was the commercialization manager for a spin-off company, OptoNeuro Ltd.,
commercializing disruptive GaN devices for optoelectronics. Prior to his
academic career, he collected over 8 years of industrial experience in
companies like Sun Microsystems (Oracle) and National Iranian Oil Company. He
received B.Sc. (Tehran, 99), M.Sc. (Newcastle, 2004) and Ph.D. (Newcastle,
2010) all in electronic and electrical engineering.
---|---
|  Yang Hao (M’00-SM’06-F’13) received the Ph.D. degree on computational
electromagnetics from the Centre for Communications Research (CCR) at the
University of Bristol, U.K., in 1998. He is currently a Professor of antennas
and electromagnetics in the Antennas & Electromagnetics Research Group, Queen
Mary University of London. Prior to his appointment at QMUL, he was a
postdoctoral research fellow at the School of Electronic, Electrical and
Computer Engineering, University of Birmingham. Over the years, Prof. Hao
developed several fully-integrated antenna solutions based on novel artificial
materials to reduce mutual RF interference, weight, cost, and system
complexity for security, aerospace, and healthcare. He developed, with leading
UK industries, novel and emergent gradient index materials to reduce mass,
footprint, and profile of low frequency and broadband antennas. He co-
developed the first stable active non-Foster metamaterial to enhance usability
through small antenna size, high directivity, and tunable operational
frequency. He has coined the term body-centric wireless communications, i.e.,
networking among the wearable and implantable wireless sensors on the human
body. He was the first to characterize and include the human body as a
communication medium between on-body sensors using surface and creeping waves.
He contributed to the industrial development of the first wireless sensors for
healthcare monitoring. He is a strategic advisory board member for the
Engineering and Physical Sciences Research Council (EPSRC), where he is
committed to championing RF/microwave engineering for reshaping the future of
UK manufacturing and electronics. Prof. Hao is active in a number of areas,
including computational electromagnetics, microwave metamaterials, graphene
and nanomicrowaves, antennas and radio propagation for body centric wireless
networks, active antennas for millimeter/sub-millimeter applications, and
photonic integrated antennas. He has published over 140 journal papers, and he
was a co-editor and co-author of the books Antennas and Radio Propagation for
Body-Centric Wireless Communications (Boston, MA, USA: Artech House, 2006,
2012), and FDTD Modeling of Metamaterials: Theory and Applications (Boston,
MA, USA: Artech House, 2008), respectively. Prof. Hao is currently a founding
Editor-in-Chief of EPJ Applied Metamaterials, a new open access journal
devoted to applied metamaterials research. He was an Editor-in-Chief of the
IEEE Antennas and Wireless Propagation Letters during 2013-2017. He was an
Associate Editor of the same journal, IEEE Transactions on Antennas and
Propagation during 2008-2013, and also a Co-Guest Editor for the IEEE
Transactions on Antennas and Propagation in 2009. He is a member of Board of
the European School of Antenna Excellence, a member of EU VISTA Cost Action
and the Virtual Institute for Artificial Electromagnetic Materials and
Metamaterials, Metamorphose VI AISBL. He was a Vice Chairman of the Executive
Team of IET Antennas and Propagation Professional Network. He has served as an
invited and keynote speaker, conference General Chair, session chair and short
course organizer at many international conferences. He won the IET A F Harvey
Prize in 2016, BAE Chairmans Silver award in 2014, and Royal Society Wolfson
Research Merit Award in 2012. He was elected as a Fellow of the ERA Foundation
in 2007, Fellow of the IET in 2010, and Fellow of the IEEE in 2013.
---|---
|  Ardavan Rahimian (S’07-M’09) received the M.Eng. (Hons.) degree in
electronic and communications engineering from the University of Birmingham,
U.K., in 2009. He is currently pursuing the Ph.D. degree in electronic
engineering at the Queen Mary University of London, U.K. He was the winner of
the Rohde & Schwarz Technology Prize in 2009. His research interests include
antennas, microwaves, millimeter-waves, smart grid, and wireless
communications. He has authored or co-authored a number of papers in these
areas.
---|---
|  Hamed Mirsaeedi (S’16) received the B.Sc. and M.Sc. degrees both in
electrical engineering from Power and Water University of Technology (PWUT),
Tehran, Iran, and the University of Tehran, Iran, in 2013 and 2017,
respectively. He works as a research assistant at the System and Machine
Research Lab. (SMRL), Control and Intelligent Processing Center of Excellence
(CIPCE), School of Electrical and Computer Engineering, University of Tehran.
His research interests include reliability-centered maintenance, asset
management, distribution system reliability, smart grid, and power system
analysis.
---|---
|  Vahid Vahidinasab (M’10-SM’17) received the B.Sc. degree from K. N. Toosi
University of Technology (KNTU), Tehran, Iran, in 2004, and the M.Sc. and
Ph.D. degrees from Iran University of Science and Technology, Tehran, Iran, in
2006 and 2010, respectively, all in electrical engineering. He is currently an
Assistant Professor of electrical engineering at Shahid Beheshti University
(SBU). He is the founder and director of the SOHA Smart Energy Systems Lab. at
SBU. He has demonstrated a consistent track record of attracting external
funds, and he has managed several projects and has closely worked with several
large complex national/international projects. His research interest is
oriented to different research and technology aspects of energy systems
integration, including the integration of storage and renewable energy
resources, PHEVs, demand response, IoT, smart grid/microgrids/nanogrids
design, operation and economics, power markets, reliability assessment of
power components/systems, and application of artificial intelligence and
optimization methods in power system studies.
---|---


# SoftEDA: Rethinking Rule-Based
Data Augmentation with Soft Labels

Juhwan Choi, Kyohoon Jin, Junho Lee, Sangmin Song, Youngbin Kim
Chung-Ang University, Seoul, Republic of Korea
<EMAIL_ADDRESS>

###### Abstract

Rule-based text data augmentation is widely used for NLP tasks due to its
simplicity. However, this method can potentially damage the original meaning
of the text, ultimately hurting the performance of the model. To overcome this
limitation, we propose a straightforward technique for applying soft labels to
augmented data. We conducted experiments across seven different classification
tasks and empirically demonstrated the effectiveness of our proposed approach.
We have publicly opened our source code for reproducibility.

##  1 Introduction

Data augmentation is a common strategy for mitigating overfitting and
enhancing the robustness and generalizability of a model by augmenting the
existing data or generating new data for training. Rule-based data
augmentation is a prevalent approach to data augmentation that involves
modifying the current data according to predefined policies. Examples of such
policies for image data include rotation, flipping, and cropping (Yang et al.,
2022).

Rule-based data augmentation methods are also frequently utilized for text
data due to their simplicity and efficiency. One such method is easy data
augmentation (EDA) (Wei & Zou, 2019), which consists of four operations:
synonym replacement, random insertion, random swap, and random deletion. These
operations enable the generation of augmented data that are similar to the
original data, but with small variations. However, some researchers have
raised concerns that the EDA method may hurt the meaning of a sentence. As an
alternative, they proposed “an easier data augmentation” (AEDA) (Karimi et
al., 2021), which is based solely on the random insertion of punctuation marks
in {”.”, ”;”, ”?”, ”:”, ”!”, ”,”}.

In this work, we aimed to improve existing rule-based text data augmentation
methods and propose a novel, yet simple data augmentation strategy called easy
data augmentation with soft labels (softEDA). Traditional EDA techniques
generate noisy and perturbed data from the original text by randomly
inserting, swapping, or deleting words. This is different from rule-based
image data augmentation methods, such as cropping and rotating, which preserve
the fundamental semantics and thus allow original labels for augmented images
to be maintained. However, in traditional EDA, these perturbed data keep the
original one-hot label, making it coarse to the model and potentially reducing
performance as a result.

To mitigate this performance degradation, softEDA incorporates noise-to-label
values of the noisy augmented data. Label smoothing (Szegedy et al., 2016) is
applied to the original data labels to acquire noisy labels. We assign these
soft labels to augmented data and organize them with original data for
training. By leveraging this straightforward technique, the model can enhance
its robustness and performance by learning the relatively weaker signal of a
soft label instead of the one-hot label.

To the best of our knowledge, this is the first study to introduce soft labels
into rule-based text data augmentation methods. We evaluated softEDA on seven
different text classification tasks and empirically showed its effectiveness
compared to the previously proposed EDA and AEDA. We have opened our source
code for further study and
reproducibility.111https://github.com/c-juhwan/SoftEDA

##  2 Method

As EDA generates data through perturbing original data, augmented data may
have uncertainty compared to original data. Despite this uncertainty, EDA
assigns the exact same one-hot label to augmented data. SoftEDA, on the other
hand, adheres to the fundamental concept of EDA and employs its four sub-
operations. However, unlike EDA, softEDA introduces uniform noise distribution
across every class through label smoothing considering the uncertainty. For
data $({\bm{x}},{\bm{y}})$ in dataset $D$, the label of augmented data
$\hat{{\bm{y}}}$ is defined according to the following equation:

$\displaystyle\hat{{\bm{y}}}$
$\displaystyle=(1-\alpha){\bm{y}}+\frac{\alpha}{N_{Class}}=\begin{cases}(1-\alpha)+\frac{\alpha}{N_{Class}}&if\;y=y_{i}\\\
\frac{\alpha}{N_{Class}}&Otherwise\end{cases}$

##  3 Experiment

We evaluated softEDA with seven different text classification tasks. To assess
the effectiveness of softEDA, we constructed text classification models based
on convolutional neural networks (CNN) (Kim, 2014), long short-term memory
(LSTM) (Liu et al., 2016), and pretrained BERT (Devlin et al., 2019). For our
experiments, we used $\alpha=[0.1,0.15,0.2,0.25,0.3]$ to determine the optimal
value for each model. Further details about experimental setup can be found in
Appendix A and B.

The results of the experiment are provided in table 1. We found that, in most
cases, softEDA significantly improved the performance of the model compared to
other methods. Furthermore, softEDA was able to boost the model even when
other methods exhibited degrading performance.

It is noteworthy that softEDA demonstrated promising performance on the Corpus
of Linguistic Acceptability (CoLA) (Warstadt et al., 2019) dataset, which
measures the grammatical acceptability of given sentences. While EDA and AEDA
failed to achieve good result because they use one-hot labels and do not
maintain the syntactic structure of a sentence, softEDA improved performance
by manipulating the label of augmented data.

Table 1: Accuracy (%) and gain (%p) across seven datasets. For softEDA, we denoted the best outputs among various smoothing values. Full results with each $\alpha$ can be found in Appendix C. | Dataset
---|---
Model | SST2 | CR | MR | TREC | SUBJ | PC | CoLA
CNN w/o Aug | 77.84 | 77.29 | 74.94 | 86.76 | 90.18 | 91.62 | 69.13
w/ EDA | +0.12 | -0.02 | +0.70 | +0.15 | +0.05 | +0.81 | -1.50
w/ AEDA | +0.72 | -0.36 | -0.40 | +0.90 | -0.50 | +0.04 | -2.23
w/ softEDA | +0.83 | +0.91 | +1.84 | +2.03 | +0.99 | +1.29 | +0.21
LSTM w/o Aug | 75.80 | 74.26 | 74.05 | 86.37 | 88.84 | 92.74 | 69.18
w/ EDA | +0.82 | +1.70 | +0.70 | -3.24 | +1.69 | +0.49 | -0.07
w/ AEDA | +2.97 | +0.28 | +0.49 | -1.37 | +0.64 | -0.15 | -0.37
w/ softEDA | +2.59 | +2.90 | +1.41 | +1.95 | +2.18 | +0.60 | +0.18
BERT w/o Aug | 89.74 | 89.08 | 84.28 | 95.47 | 96.18 | 93.44 | 75.38
w/ EDA | +0.71 | -0.41 | -0.92 | +0.51 | -0.35 | +0.58 | -0.45
w/ AEDA | +0.22 | +1.84 | +0.19 | -0.67 | -0.30 | -0.15 | -0.34
w/ softEDA | +0.83 | +2.10 | +0.19 | +1.17 | +0.15 | +0.67 | +1.50

##  4 Conclusion

We have shown that rule-based text data augmentation methods can be refined by
applying soft labels to augmented data. By using this simple approach, we
found it possible to further boost existing rule-based data augmentation
methods with a simple modification. Future work could extend the softEDA
approach to other rule-based methods, including AEDA and character-level noise
injection (Belinkov & Bisk, 2018), and could include an investigation of the
best parameters for each method.

### Acknowledgements

We would like to express our sincere gratitude to the reviewers and organizers
of this track. This research was supported by Basic Science Research Program
through the National Research Foundation of Korea(NRF) funded by the Ministry
of Education(NRF-2022R1C1C1008534), and Institute for Information &
communications Technology Planning & Evaluation (IITP) through the Korea
government (MSIT) under Grant No. 2021-0-01341 (Artificial Intelligence
Graduate School Program, Chung-Ang University).

### URM Statement

First author Juhwan Choi meets the URM criteria of ICLR 2023 Tiny Papers
Track. He is outside the range of 30-50 years, non-white researcher. This work
is his first submission and accepted paper at ICLR or other top-tier
conferences.

## References

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##  Appendix A Dataset Specifications

Table 2: Dataset used for the experiment. | Dataset
---|---
Dataset | Task | $N_{Class}$ | $N_{Train}$ | $N_{Test}$
SST2 (Socher et al., 2013) | Sentiment | 2 | 6,919 | 1,820
CR (Hu & Liu, 2004) (Liu et al., 2015) | Sentiment | 2 | 3,011 | 752
MR (Pang et al., 2002) | Sentiment | 2 | 9,593 | 1,067
TREC (Li & Roth, 2002) | Question Type | 6 | 5,452 | 500
SUBJ (Pang & Lee, 2004) | Subjectivity | 2 | 8,000 | 2,000
PC (Ganapathibhotla & Liu, 2008) | Pro-Con | 2 | 39,418 | 4,506
CoLA (Warstadt et al., 2019) | Linguistic Acceptability | 2 | 8,551 | 527

##  Appendix B Experimental Setup

In this section, we demonstrate experimental setups and implementation details
for reproduction. We have opened our source code for further information.

SoftEDA Implementation. SoftEDA leverages all four sub-operations of EDA for
augmentation and involves three distinct steps. Firstly, a sub-operation is
randomly selected from the available four operations. Subsequently, the chosen
operation is applied to a given sentence to attain augmented sentence.
Finally, in contrast to conventional EDA techniques, SoftEDA applies label
smoothing to the label of augmented data to obtain a soft label. It is
recommended to refer to the accompanying code for further information.

Models. For the LSTM model, we used bidirectional two-layer LSTM and passed
extracted hidden states to the linear classifier. For the CNN model, we mainly
followed the core architecture of Kim (2014) to extract features. For the BERT
model, we used the bert-base-uncased model at Hugging
Face222https://huggingface.co/bert-base-uncased. Extracted features from the
models were passed to the linear classifier, with a hidden size of 768 and
dropout with $p=0.2$, followed by a gaussian error linear unit (Hendrycks &
Gimpel, 2016) activation and the final linear layer.

Training Hyperparameters. We used AdamW (Loshchilov & Hutter, 2019) as the
optimizer, with a learning rate of 1e-4 and weight decay of 1e-5. There was no
scheduler used. We trained every model with a batch size of 32 and applied
early stopping with a patience of 5 epochs.

Other Details. We randomly selected 20% of the training data as a validation
set if there was no predefined validation set. Every model used the BERT
tokenizer from Hugging Face, with a maximum token length of 100. The training
was conducted using a single NVIDIA RTX 3090 GPU.

##  Appendix C Full Experiment Results

Table 3: Accuracy (%) of the full experiment results. | Dataset
---|---
Model | SST2 | CR | MR | TREC | SUBJ | PC | CoLA
CNN w/o Augmentation | 77.84 | 77.29 | 74.94 | 86.76 | 90.18 | 91.62 | 69.13
w/ EDA | 77.96 | 77.27 | 75.64 | 86.91 | 90.23 | 92.43 | 67.63
w/ AEDA | 78.56 | 76.93 | 74.54 | 87.66 | 89.68 | 91.66 | 66.90
w/ softEDA $\alpha=0.1$ | 78.67 | 76.13 | 74.88 | 87.50 | 90.33 | 92.61 | 68.05
w/ softEDA $\alpha=0.15$ | 77.07 | 75.48 | 73.99 | 88.79 | 89.88 | 92.91 | 68.79
w/ softEDA $\alpha=0.2$ | 77.90 | 78.20 | 74.75 | 87.73 | 90.13 | 92.35 | 68.79
w/ softEDA $\alpha=0.25$ | 78.10 | 77.91 | 75.18 | 88.01 | 90.67 | 92.49 | 68.97
w/ softEDA $\alpha=0.3$ | 75.48 | 76.10 | 76.78 | 87.54 | 91.17 | 92.69 | 69.34
LSTM w/o Augmentation | 75.80 | 74.26 | 74.05 | 86.37 | 88.84 | 92.74 | 69.18
w/ EDA | 76.62 | 75.96 | 74.75 | 83.13 | 90.53 | 93.23 | 69.11
w/ AEDA | 78.77 | 74.54 | 74.54 | 85.00 | 89.48 | 92.59 | 68.81
w/ softEDA $\alpha=0.1$ | 78.39 | 77.16 | 73.62 | 87.46 | 88.94 | 93.12 | 69.18
w/ softEDA $\alpha=0.15$ | 74.15 | 72.99 | 73.71 | 86.68 | 89.93 | 93.34 | 69.18
w/ softEDA $\alpha=0.2$ | 76.09 | 75.73 | 73.01 | 88.32 | 89.53 | 93.07 | 69.00
w/ softEDA $\alpha=0.25$ | 77.23 | 75.48 | 71.48 | 86.84 | 90.48 | 92.92 | 67.34
w/ softEDA $\alpha=0.3$ | 77.18 | 75.61 | 75.46 | 86.09 | 91.02 | 92.63 | 69.36
BERT w/o Augmentation | 89.74 | 89.08 | 84.28 | 95.47 | 96.18 | 93.44 | 75.38
w/ EDA | 90.45 | 88.67 | 83.36 | 95.98 | 95.83 | 94.02 | 74.93
w/ AEDA | 89.96 | 90.92 | 84.47 | 94.80 | 95.88 | 93.29 | 75.04
w/ softEDA $\alpha=0.1$ | 89.63 | 89.37 | 83.18 | 94.02 | 96.33 | 93.87 | 76.72
w/ softEDA $\alpha=0.15$ | 89.52 | 89.74 | 83.82 | 95.00 | 95.68 | 93.43 | 75.40
w/ softEDA $\alpha=0.2$ | 89.62 | 91.18 | 84.47 | 95.20 | 96.23 | 93.87 | 76.19
w/ softEDA $\alpha=0.25$ | 89.51 | 91.18 | 83.36 | 96.64 | 96.08 | 94.11 | 76.88
w/ softEDA $\alpha=0.3$ | 90.57 | 88.18 | 82.48 | 94.69 | 96.18 | 94.11 | 75.61
Table 4: F1 scores of the full experiment results. | Dataset
---|---
Model | SST2 | CR | MR | TREC | SUBJ | PC | CoLA
CNN w/o Augmentation | .7726 | .7351 | .4350 | .8400 | .8982 | .5165 | .4516
w/ EDA | .7749 | .7532 | .4520 | .8278 | .8982 | .5328 | .5262
w/ AEDA | .7799 | .7325 | .4489 | .8593 | .8933 | .5273 | .4821
w/ softEDA $\alpha=0.1$ | .7805 | .7418 | .4334 | .8430 | .8993 | .5369 | .4595
w/ softEDA $\alpha=0.15$ | .7645 | .7287 | .4481 | .8726 | .8951 | .5449 | .5500
w/ softEDA $\alpha=0.2$ | .7740 | .7558 | .4366 | .8516 | .8977 | .5397 | .4240
w/ softEDA $\alpha=0.25$ | .7747 | .7551 | .4379 | .8489 | .9037 | .5399 | .4206
w/ softEDA $\alpha=0.3$ | .7481 | .7266 | .4434 | .8422 | .9076 | .5440 | .4407
LSTM w/o Augmentation | .7528 | .6978 | .4369 | .8204 | .8839 | .5373 | .4070
w/ EDA | .7592 | .7219 | .4365 | .7645 | .9105 | .5420 | .4847
w/ AEDA | .7827 | .7173 | .4346 | .8230 | .8908 | .5263 | .4230
w/ softEDA $\alpha=0.1$ | .7787 | .7548 | .4446 | .8521 | .8856 | .5558 | .4070
w/ softEDA $\alpha=0.15$ | .7354 | .6932 | .4465 | .8564 | .8954 | .5492 | .4070
w/ softEDA $\alpha=0.2$ | .7563 | .7394 | .4323 | .8525 | .8922 | .5521 | .4190
w/ softEDA $\alpha=0.25$ | .7564 | .7239 | .4229 | .8403 | .9010 | .5517 | .4193
w/ softEDA $\alpha=0.3$ | .7670 | .7335 | .4517 | .8412 | .9075 | .5439 | .4139
BERT w/o Augmentation | .8942 | .8820 | .4812 | .9475 | .9606 | .5605 | .6779
w/ EDA | .9012 | .8775 | .4798 | .9430 | .9569 | .5738 | .6749
w/ AEDA | .8963 | .9017 | .4839 | .9340 | .9573 | .5495 | .6802
w/ softEDA $\alpha=0.1$ | .8932 | .8849 | .4925 | .9274 | .9617 | .5543 | .6998
w/ softEDA $\alpha=0.15$ | .8910 | .8890 | .4820 | .9345 | .9550 | .5569 | .6883
w/ softEDA $\alpha=0.2$ | .8928 | .9036 | .4830 | .9329 | .9610 | .5831 | .6934
w/ softEDA $\alpha=0.25$ | .8916 | .9030 | .4797 | .9655 | .9596 | .5656 | .6985
w/ softEDA $\alpha=0.3$ | .9023 | .8691 | .4614 | .9341 | .9601 | .5586 | .6659


See pages 1-last of regularization.pdf