
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13484-6
10.1016/j.heliyon.2024.e37453
e37453
Research Article
Cloud-fog architecture-based control of smart island microgrid in master-slave organization using disturbance observer-based hybrid backstepping sliding mode controller
Azizi Mohammad Ali
Niknam Taher niknam@sutech.ac.ir
⁎
Dehghani Moslem mo.dehghani@sutech.ac.ir
⁎⁎
Jokar Hossein
Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran
⁎ Corresponding author. niknam@sutech.ac.ir
⁎⁎ Corresponding author. mo.dehghani@sutech.ac.ir
05 9 2024
15 9 2024
05 9 2024
10 17 e3745326 2 2024
9 8 2024
4 9 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Distributed control is an effective method to coordinate the microgrid with various components, and also in a smart microgrid, communication graph layouts are essential since changing the topology unexpectedly could disrupt the operation of the distributed controllers, and also an imbalance may occur between the production and load. Hence, reducing the exchanged data between units and system operator is essential in order to reduce the transmitted data volume and computational burden. For this purpose, an islanded microgrid with multiple agents which is using cloud-fog computing is proposed here, in order to reduce the computing burden on the central control unit as well as reducing data exchange among units. To balance the production power and loads in a smart island with a stable voltage/frequency, a hybrid backstepping sliding mode controller (BSMC) with disturbance observer (DO) is suggested to control voltage/frequency and current in the MG-based master-slave organization. Therefore, this paper proposes a DO-driven BSMC for controlling voltage/frequency, and power of energy sources within a Master-Slave organization; in addition, the study proposes a clod-fog computing for enhancing performance, reducing transferred data volume, and processing information on time. In the extensive simulations, the suggested controller shows a reduction in steady-state error, a fast response, and a lower total harmonic distortion (THD) for nonlinear and linear loads less than 0.33 %. The fog layer serves as a local processing level, so it reduces the exchanged data between cloud and fog nodes.

Highlights

• Using multi-layer cloud-fog computing to increase computing speed and reduce computational burden on the cloud layer.

• This study proposes a master-slave organized inverter-driven smart island microgrid.

• The backstepping controller and sliding mode controller are combined to ensure global robustness and improve performance.

• Designing a disturbance observer to estimate uncertainties in real-time to improve robustness and effective compensation.

• Using a hybrid backstepping sliding mode controller with disturbance observer to improve the steady-state parameters.

Keywords

Smart island microgrid
Hybrid backstepping sliding mode control
Disturbance observer
Master-slave organization
Cloud-fog computing
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pmc1 Introduction

Recently, environmental concerns and power demands have grown rapidly, so supplying power at high voltages over long distances isn't the most efficient way to satisfy the needs of advancing progress, in particular in places lacking main grid access. Power generation by renewable energy resources like solar energy and wind power is known as distributed generation (DG) systems [[1], [2], [3]]. A smart island that includes several DGs and electric vehicles needs to consider emerging challenges such as cybersecurity enhancements, cyber-attacks detection, faults detection, designing robust controllers, renewable energy integration, energy management, smart building scheduling, computation burden, communication networks, etc. Also, a reasonable economic method is to supply electricity in an island state by distributed and renewable energy resources (DER/RER), which produce and consume power nearby [4].

Since communication technology has enabled things as diverse as keys, electronic devices, and vehicles to have network capacities, the concept of the Internet of Things (IoT) must be modified to cover these new types of equipment [5]. Therefore, the original cloud-managed networking concept of the IoT has evolved into a network of interconnected smart devices, that are considered independently operational physical components that are capable of being sensed, actuated, processed, stored, and networked [5].

As the IoT's initial concept is changed, its initial aims have been extended and matured [5]. By Incorporating the network with equipment such as sensors and actuators, the possibility of executing control tasks using the sources of the IoT appeared, which are more closely related to the networked cyber-physical systems from the control perspective [6]. As a result, the computing, sensing, and actuating capabilities of the IoT constitute a strong structure for controlling external processes [7]. There is, nevertheless, no standard method to use IoT as a control structure. In addition, applying classical constant control loops to a large-scale system that is undergoing dynamic changes does not seem regular. It makes sense and enchanting to use a flexible reconfigurable control loop architecture in this scheme instead of the classical constant control loop architecture, since it generates and consumes on a demand basis, as well as makes use of the advantages of many devices connected to the IoT such as actuators, sensors, and plants, which are capable of reorganizing themselves automatically as required.

Electronic converters are used in most DERs/RERs to connect to MGs. Developing an effective nonlinear controller is crucial due to the disturbances, load changes, and nonlinear variables of the system. As the power electronic switches have non-continuous characteristics, the sliding mode control (SMC) and backstepping control (BSC) techniques could be used directly to power electronic converters [8]. Chattering is the greatest weakness of the SMC method. on the other hand, the zero steady-state error (SSE) of the BSC method is more than the SMC method. Also, using an observer-based BSC could overcome the drawbacks of BSC in comparison to SMC. There are drawbacks to such approaches, like harmonics in output signals of voltage and current, the maximum of which is 5 % for the distribution voltage according to IEEE 1547 standard [9,10]. The majority of centralized control strategies use the master-slave approach. In this approach, a unit is in charge of voltage/frequency regulation, while slave units serve as current controllers and exchange reactive and active power with the upstream network [10,11].

The inverter output voltage control and power management systems have been handled by a variety of methods. There have been numerous studies on the design of controllers, which are responsible for controlling DC/AC power converters. Microgrids' balanced operation has traditionally been controlled by proportional-integral (PI) controllers because of their ease of use and effectiveness [12]. There are, however, some challenges associated with tuning cascaded PI controllers. The system model must be accurate to achieve a minimal total harmonic distortion (THD) and quick dynamic response and must operate within a small range of stable operation at low switching frequencies. In addition, new control methods, including droop-based [13], model predictive [14], and adaptive control schemes [15], are being explored. Such techniques, despite their advantages, have a few drawbacks. It is likely that predictive controllers are worried about their insufficiency in robustness because they need precise system variables to achieve optimal performance, therefore they fail to perform well if the microgrid (MG) has unbalanced or nonlinear loads or model uncertainty. By using the droop controller, it is possible to provide active and reactive power by reverse voltage deviation. Droop control is limited in its use due to its slow transient response [13]. Active/reactive power, unbalanced, and harmonic power are controlled by droop control [16]. Also, in Ref. [17], the negative sequence reactive power-based droop control scheme is applied to compensate for the voltage unbalance. In Ref. [18] a capacitive virtual impedance layout is suggested to compensate for distortion of the output voltage of the voltage source inverters with LCL filters. However, the quality of the filter output voltage has been ameliorated by the increasing voltage distortion at filter capacitance. In addition, resistive virtual impedances have been added to prepare a suitable load-sharing, that the voltage drop on the virtual resistances resulted through the output voltage distortion. The unbalance and harmonics of bus voltage of the sensitive loads are managed by using the secondary control level [19], which is caused by sending suitable control signals to the primary level. A decentralized control scheme is proposed in Ref. [20] to control the output voltage of an MG, but a multi-agent energy resource with current control scheme is not considered. Also, the disturbances and unknown variables are not considered in the controller design procedure. An adaptive SMC with state observer is presented to control voltage-frequency and current in an MG with several renewable energy resources [21], but the disturbance and unknown variables are not considered in the controller design, and also the chattering problem in SMC strategy is not discussed [21].

Over the past decade, with the appearance of cloud computing, Internet data management has dramatically improved, as well as the aggregation and sharing of data has been solved. As IoT technology has spread and become more popular, the smart equipment and demand of associated services have been increased rapidly. Data collection and analysis must be efficient and rapid in IoT as an essential requirement. IoT demands high bandwidth, huge computing power, data management, and fast response speed in which cloud computing cannot satisfy these requirements, because it relies too heavily on centralized cloud servers. To overcome this limitation, the concepts of edge computing and fog computing are expressed as novel computing schemes. Network performance can be improved by using distributed idle resources located at the edge. IoT systems based on fog and device computing which is a new scheme, can provide better services due to high interconnection.

This study proposes a multi-layer architecture that utilizes cloud-fog computing (CFC) as a means of implementing energy management and control computing in fog layers and appliances, such as smart homes, distributed, thereby reducing computing burdens on the cloud (central control unit). The suggested hybrid backstepping sliding mode controller (BSMC) controls the current and voltage/frequency of an inverter-driven MG composed of DGUs that is organized as a smart island master-slave hybrid network. Accordingly, the master unit is in charge of voltage control status, and the slave units are in charge of current control mode. In the suggested architecture, one of the DGUs which is called the master unit sets the voltage/frequency of the smart island according to the reference signal, and also, the current control scheme is provided by the other DGUs. The slave units generate a defined load power according to the current reference signal which is computed instantaneously based on the local load's current and specified power from the cloud layer. In this paper, the hybrid backstepping sliding mode controllers (HBSMC) incorporating disturbance observers (DO) are proposed to eliminate the influence of the disturbances, also the theoretical concepts, requirements, and necessary conditions are considered to guarantee the stability and robustness of the system. Simulations in the time domain are conducted in MATLAB/Simulink to evaluate the performance of the suggested controller, and it is evaluated in comparison to other classical control methods [10,22,23].

To summarize, this study has made the following contributions:1) Multi-layer CFC implementation using multiple fog layers and device layers for increased computing speed and reduced computing burden on the cloud layer (central control unit).

2) This study proposes a master-slave organized inverter-driven smart island MG (SIMG).

3) BSC and SMC are combined to ensure global robustness and improve performance.

4) DO is designed to estimate system uncertainties in real-time for effective compensation and enhanced system robustness.

5) Using the BSMC with DO to improve the steady-state system efficiency;

The paper continues with the following: The SIMG using the state space model is introduced in Section 2. Section 3 presents a hybrid controller using an observer for slave and master units. Section 4 presents the CFC framework. In Section 5, the proposed approach is discussed alongside simulation outcomes. Finally, section 6 expresses the main conclusion.

2 SIMG model

2.1 SIMG definition

In the face of increasing populations, a smart island has a chance to outperform a conventional island, which will increase life quality, support future generations, and reduce costs. The island is expected to gain a greater number of tourists due to the advantages of creating jobs and increasing local incomes. It is challenging for the island to be created due to its insufficient cooperation among organizations, the lack of confidence, inadequate engagement, and insufficient education, equipment installation costs, issues relating to telecommunications and communication among systems, subversive, resistant, and cyber-attacks, and effective use of renewable energy [24,25]. A SIMG is shown in Fig. 1 with cloud, fog, and device layers where computations are done locally, and just the outcomes exchanged between agents.Fig. 1 A general schematic of a CFC-based SIMG.

Fig. 1

2.2 State-space model

As shown in Fig. 1, the SIMG consists of DGUs and several loads comprising nonlinear and linear loads like smart homes, electric vehicles, protection relays, smart sensors voltage, transformers, and distribution lines, which work in fog-computing layers that each fog layer including several device layers. Network infrastructure that uses optical fiber or wireless exchanges data among device, fog, and cloud layers. The main purpose of this study is to design a SIMG in CFC architecture that transfers data between layers and also an HBSMC with DO is suggested to control the master and slave units, hence, this paper does not consider fiber cable communications and wireless networks as communication links. It has been assumed the data of devices and layers are available in layers.

A diagram of the DGUs using RERs, such as solar cells, fuel cells, and wind turbines, is shown in Fig. 2. This diagram shows a power source, a converter, an LC filter, a single-phase full-bridge inverter, and diverse kinds of loads. RERs consist of solar cells/wind turbines with AC/DC, and DC/DC converters that have been replaced with a DC voltage unit.Fig. 2 The standalone DGU configuration with inverter and LC filter.

Fig. 2

Kirchhoff's current and voltage laws are applied to obtain the state equations of the system which is shown in Fig. 2 [23]:(1) LdiLdt+Vout=Vinv

(2) iL=ic+iout,ic=CdVoutdt

in which, Vinv shows the inverter output voltage and it is the coefficient of input voltage as Vinv=uVdc. u shows the input controller signal. The inductor is shown by L, as well as the capacitance of the LC filter is depicted by C. The value of the load consumption current is shown by Rout.(3) {diLdt=−1LVout+uLVdcdVoutdt=1CiL−1C.RloadVout

The derivative of Eq. (3) is obtained as follows:(4) {diLdt=−1LVout+uLVdcd2Voutdt2=1CdiLdt−1RLoadCdVoutdt

Eq. (1) can be applied to Eq. (3) to derive the following:(5) {diLdt=−1LVout+uLVdcd2Voutdt2=uLCVdc−1LCVout−1RLoadCdVoutdt

It is convenient to measure Vout, its derivative, and Vdc, therefore the real model of the inverter could not be described by Eq. (4), since external disturbances and variable changes affect the inverter, hence, Eq. (4) should be reformed. Since the inverter model has nonlinearity variables, Eq. (5) could be expressed as follows:(6) {diLdt=−1LVout+uLVdc+Γ(t)d2Voutdt2=uLCVdc−1LCVout−1RLoadCdVoutdt+Γ(t)

in which, Γ(t) shows a bounded lumped variable representing the uncertainties from environment condition alterations, changes in variables, and the DC-AC inverter modeling error.

3 Controller design

The DGUs in SIMG operate as a voltage/frequency control status (master unit), and also as a current control mode (slave unit) in a master-slave organized [11,23]. Hence, the voltage/frequency control mode has been designed for application in the master unit; after that, the current control status has been designed for application in the slave units according to the loads' current. Specifically designated active and reactive power amounts are to be generated and handed over by the slave units to the remainder of the system. The study uses load current as a measurable parameter, while the entire information of all units, such as voltage, frequency, current, and on/off states of relays, are transmitted to the cloud layer for determining master-slave SIMG organizations and control modes.

The following section introduces HBSMCs that use DO for controlling the master unit (voltage and frequency). Also, in the suggested smart island power grid, slave units are controlled by an HBSMC to control the current of slaves.

3.1 Voltage/frequency controller in master unit

The first step here is to design a disturbance observer, and after that, a proposed controller in charge of controlling the voltage/frequency in the master unit has been described.

3.1.1 DO

As discussed in section 2, the inverter might encounter unknown disturbances, hence these nonlinearities are compensated by designing a DO.

The uncertainties in the system for the expressed inverter model in Eq. (6) could be defined as below:(7) Γ(t)=d2Voutdt2−uLCVdc+1LCVout+1RLoadCdVoutdt

Assuming Γˆ is the observer's output, therefore the observation value is updated with the error among Γ and Γˆ according to Eq. (7) [26]:(8) ddtΓˆ=ρ(Γ−Γˆ)=ρ(d2Voutdt2−uLCVdc+1LCVout+1RLoadCdVoutdt−Γˆ)

in which, ddtΓˆ shows the derivative of Γˆ which represents the changing trend of Γˆ. ρ shows a constant positive.

Eq. (7) illustrates a simple observer, but the details of the second derivative of the voltage at the AC bus are required. In practical applications, obtaining the acceleration signal by differentiating the velocity signal can be challenging due to observation noises. As a result, Λ=Γˆ−ρ.ddtVout has been introduced as an instrumental parameter to establish a new observer, and its derivative can be given by Eq. (8):(9) ddtΛ=ddtΓˆ−ρ.d2Voutdt2=ρ(−uLCVdc+1LCVout+1RLoadCdVoutdt−Γˆ)

Afterward, a DO was achieved by Eq. (10) as below:(10) {ddtΛ=ρ(1LCVout+1RLoadCdVoutdt−uLCVdc−Γˆ)Γˆ=Λ+ρ.ddtVout

According to Eq. (10), the second derivative of Vout is not required in the suggested observer, meaning that the suggested observer has the practicable applications. Also, the error of the suggested observer could converge exponentially.Remark 1 In general, when the disturbances are constant or slow, ddtΓ could be supposed equal to zero. The observation error is defined as Γ˜=Γ−Γˆ, then we have:

(11) ddtΓ˜=ddtΓ−ddtΓˆ=−ddtΓˆ=−ρ.Γ˜→ddtΓ˜+ρ.Γ˜=0

So, the following is deduced:(12) Γ˜(t)=Γ˜(t0)e−ρt

in which, Γ˜(t0) shows the primary error. Eq. (12) shows that Γ(t) is exponentially convergent and that ρ can be adjusted to achieve convergent speed.

3.1.2 HBSMC in master unit

The error between the reference and output signals is commonly used to describe the system. Here, the voltage/frequency is controlled through the use of a reference signal that has been tracked, and the system's output represents the capacitor/output voltage estimation. Afterward, the error between output and reference signals is represented by δ1, and can be described in the following way:(13) δ1=Vref−Vout

in this case, δ1 must equal zero. Hence, δ1 derivative is calculated as:(14) ddtδ1=ddtVref−ddtVout

when ddtVout is substituted in Eq. (14), the result is:(15) ddtδ1=ddtVref−1CiL+1C.RLoadVout−Γ

For proving stability, the following Lyapunov candidate was selected:(16) V1=12δ12

Thus, its derivative would be:(17) ddtV1=δ1.ddtδ1=δ1(ddtVref−1CiL+1C.RLoadVout−Γ)

in which, the second-order would be:(18) δ2=φ−iL→iL=φ−δ2

Thus, its derivative would be:(19) ddtδ2=ddtφ−ddtiL=ddtφ−VdcLu+1LVout−Γ

The following can be written from Eq. (17) and Eq. (18):(20) ddtV1=δ1(ddtVref−1Cφ+1Cδ2+1C.RLoadVout−Γ)

For having V˙≪0, φ should be selected as follows:(21) φ=C(ddtVref+1C.RLoadVout−Γ+ζ1δ1)

in which ζ1>0, So:(22) ddtV1=δ1(ddtVref−ddtVref−1C.RLoadVout+Γ−ζ1δ1+1Cδ2+1C.RLoadVout−Γ)

(23) →ddtV1=δ1(−ζ1δ1+1Cδ2)

(24) →ddtV1=δ1.ddtδ1

So,(25) ddtδ1=1Cδ2+−ζ1δ1

The second Lyapunov candidate would be:(26) V2=V1+12δ22

and its derivate would be:(27) ddtV2=ddtV1+δ2.ddtδ2

With Eqs. (23), (27)), and ddtV2, the following results can be obtained:(28) ddtV2=−ζ1δ12+1Cδ1δ2+δ2.ddtδ2

(29) →ddtV2=−ζ1δ12+δ2(1Cδ1+ddtδ2)

Based on Eqs. (19), (29)), ddtV2 can be expressed as follows:(30) ddtV2=−ζ1δ12+δ2(1Cδ1+ddtφ−VdcLu+1LVout−Γ)

Based on Eq. (21), the derivative of δ is as follows:(31) ddtφ=C(d2dt2Vref+1C.RLoad.ddtVout−ddtΓ+ζ1.ddtδ1)

So, the final V˙2 would be:(32) ddtV2=−ζ1δ12+δ2(1Cδ1+Cd2dt2Vref+1RLoad.ddtVout+Cζ1.ddtδ1−VdcLu+1LVout)

To reach V˙2<0, the control law “u” on the inverter is selected according to Eq. (33), that ζ1>0:(33) ubc=LVdc(1Cδ1+Cd2dt2Vref+1RLoad.ddtVout+Cζ1.ddtδ1+1LVout+ζ2δ2)

The positive ζ1 and ζ2 must be chosen to ensure an acceptable stability of the BSC for the system, according to the Lyapunov theory (a positive Lyapunov function and a negative derivation of the Lyapunov function are required for stability of the controller).

It can be concluded from these convergences that control input Eq. (33) results in output Vout tracking reference Vref exponentially under disturbance Γ(t); nevertheless, as shown in Eq. (21), disturbance Γ(t) has been employed in φ, and the time-derivative of φ has been employed in the control signal uBC. Explicit differentiation sensitivity to input noise, and time-derivative of disturbance Γ(t) pose significant problems. Thus, the controller cannot be executed due to its not proper. Hence, this problem is solved using a combination of BSC and high-order SMCs. Initially, an introduction of high-order SMC is introduced as following:

High-order SMC is employed to eliminate the chattering problem associated with classic sliding-mode controllers. Actually, the high-order sliding mode adopts a local r-sliding controller instead of the relay controller to decrease the chattering [27].

The switching surface is considered as follows:(34) S=λδ1+ddtδ1

in which, λ shows a firm positive real value.Lemma 1 ifDtq0f(t)=1L(1−q)ddt∫0tf(L)(t−τ)qby having the fractional orderqmeeting0≤q<1and the sign function are considered, the result is as follows [28]

(35) Dtq0sgn(s(t)){>0,ifs(t)>0,t<0>0,ifs(t)<0,t<0

Based on Lemma 1, the switching control law needs to be robust to uncertainties and disturbances, so we have:(36) usl=−kS−lsgn(S)

in which, k, l would be non-zero positive constants.

Lastly, according to Eq. (33) and Eq. (36), the control signal is:(37) u=ubc+usl

3.2 Current controller in slave unit

3.2.1 DO

The system uncertainties of the inverter model expressed in Eq. (6) are as follows:(38) Γ(t)=diLdt+1LVout−uLVdc

For simplifying the disturbance design, Γ(t) should be bounded and satisfied, so, we have:(39) ddtΓ=0

Γˆ is defined as the observer output, the observation amount is updated through the use of error among Γˆ and Γ as depicted in Eq. (7) [26](40) ddtΓˆ=ρ(Γ−Γˆ)=ρ(diLdt−uLVdc+1LVout−Γˆ)

in which, ddtΓˆ shows the derivative of Γˆ, depicting the changing trend of Γˆ, ρ shows a constant positive value.

The observation error is defined as Γ˜=Γ−Γˆ, and as shown in Eq. (38), we have:(41) ddtΓ˜=ddtΓ−ddtΓˆ=−ddtΓˆ=−ρ.Γ˜→ddtΓ˜+ρ.Γ˜=0

The following is deduced:(42) Γ˜(t)=Γ˜(t0)e−ρt

in which, Γ˜(t0) shows the primary error. Eq. (41) shows that Γ(t) is exponentially convergent and that ρ can be adjusted to achieve convergent speed

3.2.2 HBSMC in slave unit

An error among reference and output signals is commonly used to describe a system model. A reference signal from the cloud is used here for controlling the output and estimating the output current. After calculating the error among the reference and output signals, the tracking error can be expressed in the following way:(43) δ=iref−iout

Eq. (43) derivative is calculated and then Eq. (6) is applied, we have:(44) ddtδ=ddtiref−ddtiout=ddtiref−(ddtiL−ddtic),ic=CdVoutdt

The following can be obtained from Eq. (44) and Eq. (6):(45) ddtδ=ddtiref+Cd2Voutdt2+1LVout−VdcLu+Γ

The selected Lyapunov candidate function is defined:(46) V=12δ2

Eq. (46) derivative is calculated and applied Eq. (45), then the following results can be obtained:(47) ddtV=δddtδ=δ(ddtiref+Cd2Voutdt2+1LVout−VdcLu+Γ)

The system stability is guaranteed by defining the δ derivative as Eq. (48):(48) ddtδ=−ϱδ

in which, ϱ shows a positive constant. Eq. (49) determines the control law “ubc” according to Eq. (47) and Eq. (48):(49) ubc=LVdc(ddtiref+Cd2Voutdt2+1LVout+Γ+ϱδ)

The slave unit dynamic for controlling current is first order, hence the switching surface resembles Eq. (43). With a first-order system, based on Lemma 1, the switching control law would be:(50) usl=−ςsgn(δ)

in which, ς shows non-zero positive constant.

Lastly, according to Eq. (49) and Eq. (50), the control signal would be:(51) u=ubc+usl

4 Cloud-fog computing

In the suggested consensus-based technique, the data must be exchanged among agents. A leader must additionally be selected to facilitate the convergence process. Therefore, the study suggests the neighbor virtualization approach to be used in the cloud-fog-device architecture [29,30]. The technique involves agents exchanging data with each other's virtual neighbors instead of their actual neighbors. The study describes a virtualization unit (which is a service in the fog layer) responsible for determining the MG's virtual topology. Once the unit has collected all the necessary data from each agent, the unit transmits every agent's data to its virtual neighbors, in all iterations. Because of this, the agents will receive information unaware of whose data it is.

A structure that the suggested approach can be implemented on requires the following: 1) Monitor the system in real-time to determine agent status and the load demand; 2) Protect the units' privacy from neighbors; 3) Enabling real-time data exchange between units sans direct communication with the aim of increasing security and protecting exchanged data; 4) Choosing the leader and analyzing convergence factors along with the system's topology.

For this purpose, a three-layer cloud-fog-device scheme consisting of the below layers is suggested:

Device layer: This layer contains MG physical components such as RERs, smart meters, sensors, batteries, and plug-and-play devices. This equipment is worked according to the received information from the fog which is the upper layer, and also have exchanged data with the virtual neighbors.

Fog layer: Local servers and decentralized computation are included in this layer which consists of the network devices. In this layer, short-term information storage and real-time analysis are made easier because cloud computing is extended near the devices. Neighbors' virtual topology in MGs is determined by this layer. The real-time condition of every agent is pursued and the agents' attendance status is investigated in every iteration. After gathering data from each agent, a randomly selected leader has been chosen at every interval.

Cloud layer: An enormous storage space is provided by the cloud layer along with the ability to compute. A summary of information is received from the fog layer and stored in the cloud's storage for an extended period. This layer sets policies and enforces punishments for malicious agents. Also, this layer performs communications between fog layers or amongst fog layers and the utility. Fig. 3 shows an overview of the suggested structure.Fig. 3 Overview of the cloud-fog structure-based SIMG with multiple layers.

Fig. 3

5 Proposed process and outcomes

5.1 Proposed approach

This paper proposes a smart MG in island mode consisting of three production units with various local loads including linear and non-linear, and smart sensors. The control of this system is in the master-slave architecture, which means that one of the production units is in the master mode, in which the voltage/frequency of the system is controlled, and the slave units are responsible for controlling the output current of generation units.

In the desired smart island, each production unit with local loads is considered a fog layer, where each fog contains several device layers such as smart load and converter layers. In each device layer, for example, a smart home layer, home management optimization calculations are computed in the device layer, and then the results, which include the required power amount, are sent to the relevant fog layer. Then, each fog sends sensor information, generated power, and required power to the cloud layer for long-term planning of the entire network. Also, the cloud sends the information related to the required power of each production unit for production, along with the control mode of each unit (Master or Slave control mode) to the production units. Fig. 4 shows the proposed process of CFC in a smart grid. As in this paper, the main goal is to design a controller, so we only consider the control section in CFC architecture, and other aspects will be considered in future works.Fig. 4 The proposed process of CFC.

Fig. 4

Fig. 5 shows the suggested system, which includes 3 production units. To consider the suggested layout, the proposed hybrid controller in master-slave architecture to control the DC/AC inverters has been evaluated. Also, the inverter input is renewable resources that are modeled with a UPS source because the main goal is designing the controllers for the master-slave organization.Fig. 5 Cyber-physical smart-island based on CFC.

Fig. 5

Various case studies have been investigated to evaluate the efficiency of the suggested controller comprehensively. Table 1 presents the controller variables, loads' details, and system's information. Firstly, the suggested controller in the Master unit is evaluated for controlling the system's voltage/frequency in response to sudden load variations.Table 1 The controller variables, loads' details, and system information of master-slave units.

Table 1Symbol	Quantity	Amount	
Master Unit	
Vdc	DC input voltage	400	
f	Frequency	60	
Vref	Reference signal of grid's voltage	110sin(2πft)	
L	Filter inductive	250 μH	
C	Capacitor filter	100 μF	
fs	Switching frequency	15 kHZ	
ζ1	Control variables	25000	
ζ2	30000	
λ	15000	
k	0.001	
l		0.8	
Slave Units	
Vdc	DC input voltage	400	
L	Filter inductive	250 μH	
C	Capacitor filter	100 μF	
fs	Switching frequency	15 kHz	
ϱ	Control variables	25000	
ς	0.7	

5.2 Efficiency of controller in master unit in response to load changes in islanded mode

Here, the performance of the controller has been evaluated in comparison to other control methods in the same situation with a variety of load changes, including resistive, inductive, and nonlinear loads [10,22,23]. The initial load is 20(Ω) and the secondary loads consist of resistive, inductive, and nonlinear loads whose values are [1.5(Ω)], [10(Ω),20(mH)], and [Rdc=18(Ω),Cdc=8200(μF),Rs=1.5(Ω)] respectively. Also, the scheme of nonlinear load is depicted in Fig. 6. The control block diagram for the master unit can be seen in Fig. 3.Fig. 6 Schematic of the nonlinear load.

Fig. 6

Fig. 7 shows the suggested controller's efficiency for a resistive load and the transient responses to instantaneous changes in the load.Fig. 7 Simulation results for DO-based HBSMC with instantaneous change in resistance load: a) reference and output voltage waveforms; b) Consumption current of loads; c) Tracking error of voltage; and d) Harmonic spectrum of voltage.

Fig. 7

The performance of the offered hybrid controller with DO is depicted in Fig. 7 under instantaneous change by resistive load connection. As can be seen in Fig. 7b, the resistive secondary load is connected to the AC link at 1.0042 s after the simulation starts. Fig. 7a shows the reference and output voltage waveforms, as shown in this figure, the output voltage is controlled well, and it responds quickly to instantaneous changes in resistive load to regulate the voltage/frequency of the system and tracks the reference signal with a low tracking error (See Fig. 7c). Harmonic spectrum of output voltage is shown in Fig. 7d, and the fundamental amplitude and THD of output voltage are 108.9 V, and 0.29 %, respectively.

The performance of the suggested hybrid controller with DO under instantaneous changes by inductive and nonlinear loads connection are shown in Fig. 8, Fig. 9, respectively. As can be seen in Fig. 8b and 8c, the inductive and nonlinear secondary loads are connected to the AC link at 1.0042 s after the simulation starts. Fig. 8, Fig. 9a show the reference and output voltage waveforms, as shown in these figures, the output voltage is controlled well, and the controllers respond quickly to instantaneous changes in inductive, and nonlinear loads to regulate the voltage/frequency of the system and track the reference signal with a low tracking error (See Fig. 8, Fig. 9c). The harmonic spectrum of the output voltage is shown in Fig. 8, Fig. 9d, and the fundamental amplitude of inductive and nonlinear loads is 108.9 V. Also, the THD of the output voltage of inductive and nonlinear loads are 0.33 and 0.30 %, respectively. Therefore, the proposed controller is clearly capable of reacting quickly to load variations and tracking the voltage reference signal.Fig. 8 Simulation results for DO-based HBSMC with instantaneous change by inductive load connection: a) reference and output voltage waveforms; b) Consumption current of loads; c) Tracking error of voltage; and d) Harmonic spectrum of voltage.

Fig. 8

Fig. 9 Simulation results for DO-based HBSMC with instantaneous change by nonlinear load connection: a) reference and output voltage waveforms; b) Consumption current of loads; c) Tracking error of voltage; and d) Harmonic spectrum of voltage.

Fig. 9

Simulation is performed under the changing DC input voltage link condition. The suggested controller demonstrates its robustness towards varying energy of renewable energy resources that fed the DC input voltage link. The DC input voltage is changed from 400 V to 350 V, 350 V–450 V, and 450 V into 425 V at time [0.3s], [0.5s], and [0.7s], respectively. The simulation outcomes of changes in the DC input voltage link are shown in Fig. 10. The DC input voltage link, output voltage of the system, and tracking error of voltage are illustrated in Fig. 10 (a), (b), and (c), respectively. Fig. 10 illustrates how the proposed controller performs robustly in varying DC input voltage links when it is fed in an acceptable range.Fig. 10 Variable DC input voltage link. a) DC input voltage, b) Grid's voltage. c) Tracking error of voltage.

Fig. 10

Table 2 illustrates the steady-state outcomes and comparison of the DO-based HBSMC performance with other control methods [10,22,23]. Different types of loads are examined to conduct a comprehensive analysis. According to the suggested approach, output peak voltage, root-mean-square (RMS) of the voltage, and THD are modified well with a low SSE. As can be seen in Table 2, the offered control scheme has improved the efficiency and performance by increasing peak and RMS output voltage amounts, decreasing THD, and higher robustness in comparison to previously reported control methods [10,22,23].Table 2 Steady-state outcomes of the output voltage.

Table 2Controller	Load kind	Output
Voltage
Peak (Volt)	Output voltage
RMS (Volt)	THD (%)	Robustness	
Proposed HBSMC with DO	Resistive	108.9	76.99	0.29	Excellent	
Inductive	108.9	76.99	0.33	
Nonlinear	108.9	76.99	0.30	
Adaptive back
-stepping controller [23]	Resistive	108.5	76.75	0.37	Very good	
Inductive	108.5	76.74	0.35	
Nonlinear	108.5	76.74	0.37	
Classic back
-stepping controller [23]	Resistive	102.7	72.6	0.55	Good	
Inductive	102.6	72.57	0.52	
Nonlinear	102.6	72.55	0.55	
Classic SMC [2,23]	Resistive	106.8	75.55	0.68	Good	
Inductive	106.8	75.52	0.72	
Nonlinear	106.8	75.52	0.74	

5.3 Controller's efficiency for master--slave units

Fig. 5 depicts the system consisting of 3 islanded fog units. This system has a master-slave configuration, with one unit acting as the master to maintain voltage/frequency (The generation unit in fog-A acts as the master mode, and the other units in fog-B and fog-C operate in slave mode).

Fig. 11 depicts the DO-based HBSMC performance for linear loads such as inductive and resistive loads which are connected to the AC link at 1.0042 s after the simulation starts. In addition, Fog-B and Fog-C are in charge of fed loads and generate the consumption current of loads. Also, Fog-A is the master unit that is in charge of voltage/frequency regulation. The simulation outcomes are illustrated in Fig. 11.Fig. 11 Simulation results for DO-based HBSMC with instantaneous changes by linear loads with master-slave organized: a) SIMG voltage, b) Consumption current of loads, c) Production current of Fog-A (Master unit), d) Reference signal and production current of Fog-B (slave unit), e) Reference signal and production current of Fog-C (slave unit), f) ZSSE of voltage, g) ZSSE of current in Fog-B, h) ZSSE of current in Fog-C, i) Harmonic spectrum of current of Fog-B, j) Harmonic spectrum of current of Fog-C.

Fig. 11

Fig. 11a shows the output voltage waveforms, as shown in this figure, the output voltage is controlled well, and it responds quickly to instantaneous changes in linear loads to regulate the voltage/frequency of the system and tracks the reference signal with a low tracking error (See Fig. 11f).

The consumption current of loads is shown in Fig. 11b, that initial loads of Fogs-B and Fog-C are [40(Ω)]. Also, the secondary loads include resistive and inductive loads which the value are [1.5(Ω)], and [10(Ω),20(mH)], respectively. Here, it is assumed that the cloud layer determines the slave unit reference signals (Fog-B and Fog-C) accordingly: (i) Fog-B feds its initial load (40(Ω) and the secondary resistive load (1.5(Ω); (ii) Fog-C feds its initial load (40(Ω)) and the secondary inductive load (10(Ω),20(mH));

The production currents and reference signals of Fog-B and Fog-C (slave units) are shown in Fig. 11d and 11e, respectively. Current ZSSEs of Fog-B and Fog-C are shown in Fig. 11g and h, respectively. As can be seen in Fig. 11d and e, the suggested hybrid controller effectively tracks the reference signal with a low SSE. It is shown in Fig. 11c that the output current of Fog-A (master unit) nearly reaches zero since slave units are feeding the entire loads. Therefore, the robustness of the suggested controller against linear loads is shown in Fig. 11. Fig.s. 11i and j show the harmonic spectrum of current of Fog-B and Fog-C respectively, as can be seen, the THD of Fog-B and Fog-C are 0.57 % and 1.26 %, respectively.

Fig. 12 depicts the DO-based HBSMC performance for nonlinear load, which is connected to the AC link at 1.0042 s after the simulation starts. In addition, Fog-B and Fog-C are in charge of fed loads and generate the consumption current of loads. Also, Fog-A is the master unit that is in charge of voltage/frequency regulation in the Smart Island. The simulation outcomes are illustrated in Fig. 12. Fig. 12a shows the output voltage waveforms, as shown in this figure, the output voltage is controlled well, and it responds quickly to instantaneous changes in nonlinear loads to regulate the voltage/frequency of the system and tracks the reference signal with a low tracking error (See Fig. 12f).Fig. 12 Simulation results for DO-based HBSMC with instantaneous changes by nonlinear loads with master-slave organized: a) SIMG voltage, b) Consumption current of loads, c) Production current of Fog-A (Master unit), d) Reference signal and production current of Fog-B (slave unit), e) Reference signal and production current of Fog-C (slave unit), f) ZSSE of voltage, g) ZSSE of current in Fog-B, h) ZSSE of current in Fog-C.

Fig. 12

The consumption current of loads is shown in Fig. 12b, the initial loads of Fogs-B and Fog-C are [40 (Ω)]. Also, the secondary load includes nonlinear load in which the value is [Rdc=18(Ω),Cdc=8200(μF),Rs=1.5(Ω))]. Here, it is assumed that the cloud layer determines the slave unit reference signals (Fog-B and Fog-C) accordingly: (i) Fog-B feds 40 % of the loads; Fog-C feds 60 % of the loads.

The production currents and reference signals of Fog-B and Fog-C (slave units) are shown in Fig. 12d and 12e, respectively. Current ZSSEs of Fog-B and Fog-C are shown in Fig. 12g and h, respectively. As can be seen in Fig. 12d and e, the suggested hybrid controller effectively tracks the reference signal with a low SSE. It is shown in Fig. 12c that the output current of Fog-A (master unit) nearly reaches zero since slave units are feeding the entire loads. Therefore, the robustness of the suggested controller versus nonlinear loads is shown in Fig. 12.

6 Conclusion

A new distributed consensus-driven strategy with a DO-based HBSMC for controlling the master-slave architecture of DG units in smart islands with cloud-fog computing is proposed in the study. A model based on cloud-fog computing that uses different device layers was examined for implementing distributed controllers with a multi-agent system. In the suggested model, smart sensors, smart loads, and the converter controller communicate with each other and the RERs. The stability of the system is achieved, as the data is exchanged constantly between agents that are in different layers (cloud, fog, and device layers) of SIMG.

The DO-based HBSMC is suggested for controlling the voltage/frequency and current within the SIMG's control section. The robustness of the suggested control method is guaranteed, and also it is sufficient robustness versus sudden disturbances and uncertainties in the system, which includes diverse load kinds such as linear (inductive, and resistive) and nonlinear loads. The suggested voltage control mode and current control mode are proposed as the master, and slave units, respectively, in the master-slave organized in the SIMG. Simulations are carried out in MATLAB/Simulink environment, and also simulations indicated that the suggested control approach can track the reference current signal in the slave unit and regulate the voltage/frequency in SIMG effectively and efficiently. In addition, the reference signal has been pursued very well with a small steady-state error in different load connections. As compared to the other controllers such as adaptive back-stepping controller, classic back-stepping controller, and classic SMC, the suggested DO-based HBSMC performs better and is capable of improving steady-state results, such as peak output voltage, THD, and SSE. For future works, the suggested controller will be implemented on DSP board for voltage/frequency control and power control in islanded MG, and then the blockchain technology will be implemented on this system to improve the security of the exchanged data between units in a smart island. Furthermore, the energy management program based on deep machine learning will be performed on the suggested cloud-fog architecture to show the performance of this structure in reducing the computational burden clearly.

Data availability statement

Data is contained within the article.

Funding information

The authors received no funding for this work.

CRediT authorship contribution statement

Mohammad Ali Azizi: Writing – original draft, Software, Resources, Investigation, Formal analysis, Data curation. Taher Niknam: Writing – review & editing, Visualization, Validation, Supervision, Project administration, Conceptualization. Moslem Dehghani: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Formal analysis, Data curation, Conceptualization. Hossein Jokar: Writing – review & editing, Validation, Resources, Investigation, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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