A Real-Time and Online Dynamic Reconfiguration against Cyber-Attacks to Enhance Security and Cost-Efficiency in Smart Power Microgrids Using Deep Learning

Abstract

Ensuring the secure and cost-effective operation of smart power microgrids has become a significant concern for managers and operators due to the escalating damage caused by natural phenomena and cyber-attacks. This paper presents a novel framework focused on the dynamic reconfiguration of multi-microgrids to enhance system’s security index, including stability, reliability, and operation costs. The framework incorporates distributed generation (DG) to address cyber-attacks that can lead to line outages or generation failures within the network. Additionally, this work considers the uncertainties and accessibility factors of power networks through a modified point prediction method, which was previously overlooked. To achieve the secure and cost-effective operation of smart power multi-microgrids, an optimization framework is developed as a multi-objective problem, where the states of switches and DG serve as independent parameters, while the dependent parameters consist of the operation cost and techno-security indexes. The multi-objective problem employs deep learning (DL) techniques, specifically based on long short-term memory (LSTM) and prediction intervals, to effectively detect false data injection attacks (FDIAs) on advanced metering infrastructures (AMIs). By incorporating a modified point prediction method, LSTM-based deep learning, and consideration of technical indexes and FDIA cyber-attacks, this framework aims to advance the security and reliability of smart power multi-microgrids. The effectiveness of this method was validated on a network of 118 buses. The results of the proposed approach demonstrate remarkable improvements over PSO, MOGA, ICA, and HHO algorithms in both technical and economic indicators.

1. Introduction

In the past few years, intelligent digital communications and hierarchical controllers have evolved to facilitate advanced microgrids (MGs), together with smart generation units (SGUs) and smart dynamic reconfiguration (SDR), enabling the development of complex physical–cyber systems (CPSs). Modern power MGs are more vulnerable due to increasing populations of smart devices, rising load demand, and dependence on critical infrastructure [1]. Even though contemporary power systems have robust protection mechanisms in place, some kinds of cyber-attacks can harm physical components [2]. Coordinated cyber-attacks, for example, that target control systems, have the ability to interfere with regular operations and, if not quickly addressed, could result in physical harm or a chain reaction of failures [3]. It is crucial to make clear that sophisticated cyber-attacks and natural disasters are the main topics of this research. One important protection strategy to stop the harm from growing during these attacks is dynamic reconfiguration [4].

Nevertheless, cyber-physical failures have always inflicted severe impacts and disturbances on smart power MGs. Over the last few years, both the frequency and magnitude of man-made disasters and natural disasters like hurricanes, floods, and earthquakes have been on an upward trend. Therefore, the commonplace effects of power grid blackouts highly recommend the need for paying attention to CPS security and increasing resilience against low-probability but high-impact events [5]. Hence, the techno-economic online and real-time response to CPSs and cyber-attacks aimed at preserving and saving MGs is one of the most critical concerns and challenges faced by the managers and decision-makers of these modern networks. In this regard, past research and studies have shown the dynamic reconfiguration of power networks for improving system resiliency [6], reliability [7], stability [8], and other critical parameters of power MGs through changes in the power flow path and utilization of generation units. However, the response of dynamic reconfiguration against a cyber-attack has to be fast, economical, and technical, which will be discussed in the present paper. Integrating MGs with smart grid (SG) concepts is becoming important as the call for more efficient and resilient power systems grows. Advanced communication technologies and real-time monitoring are utilized in the SGs to optimize power distribution, improve reliability, and integrate renewable energy sources [9,10]. The proposed strategy is to leverage these SG concepts in the proposed microgrid framework, leading to heightened resilience and efficiency of power systems. One main goal of the proposed model is to use SG technologies such as real-time monitoring, dynamic reconfiguration, and intelligent control systems to address the challenges CPSs pose. This integration makes sure that the suggested framework is in line with the larger idea of a contemporary, interconnected power network, in addition to addressing current technological and financial issues. The following section will examine some of the studies and research carried out within this area.

Table 1. List of abbreviations.

DG	Distributed Generation	MOGA	Multi-Objective Genetic Algorithm
FDIA	False Data Injection Attacks	PSO	Particle Swarm Optimization
AMIs	Advanced Metering Infrastructures	ICA	Independent Component Analysis
FC	Fuel Cell	HHO	Harris Hawks Optimization
MT	Micro Turbine	PM	Proposed Method
ESS	Energy Storage System	EENS	Expected Energy Not Served

presents some key tools for readers, providing the necessary terminology used in this article.

1.1. Literature Review

The development of MGs has been notably influenced by technological progress in SGs. Real-time data analytics and adaptive control strategies make it possible to improve the response of MGs to dynamic cases and cyber risks [11,12,13]. Analysis has indicated that incorporating SGs enhances dependability, efficacy, and ability to withstand outages. Energy management systems (EMSs) are vital in monitoring and controlling power flow in MGs. These systems utilize real-time data to optimize the operation of energy resources, manage energy storage systems (ESSs), and maintain a balanced interconnection between the microgrid and the power grid, improving efficiency and reliability and reducing energy costs [14]. Optimal network reconfiguration (NR) in the EMS is an accepted practice that minimizes power loss and improves the voltage profile in electrical distribution networks [15]. NR is a control strategy that optimizes the distribution network’s configuration in response to changing power demand or system conditions. Utilities can use NR capabilities within an EMS to reduce power losses and enhance the efficiency of their systems, thereby achieving cost savings and reliability for utilities and their customers. Dynamic reconfiguration in MGs means that the microgrid can track changes in configuration while operating, ensuring a stable and efficient power supply [16]. The authors of [17] propose a comprehensive approach to optimizing energy management in MGs, considering factors such as renewable resources, pollution reduction, economic objectives, and uncertainty. They present the water cycle algorithm as a novel method for intelligent energy optimization in this context. Reference [18] presents active defense strategies to increase system security and detect FDI attacks in MGs by applying dynamic reconfiguration and distributed energy resources that improve security and allow the possibility of improving attack detection accuracy. The purpose of actively adapting the system’s configuration is to enhance security and the possibility of attack detection against the defense strategy’s passiveness limitations. The authors in [19] focus on the challenges of renewable energy sources (RESs) in remote areas with low transmission capacity. In that paper, it is proposed that ESSs be used as a way to store energy and compensate for the intermittent nature of RESs. Moreover, it introduces the concept of NR as a proactive and corrective action to enhance transmission flexibility during day-ahead scheduling. In reference [20], the authors proposed the distributed control strategy for multiple energy storage systems in islanded MGs to enhance their stability and security under faults and cyber-attacks. The methods involved adaptive techniques and resilient control methods validated using test systems. Reference [21] presented a methodology for optimizing system resilience and recovery scheduling in a multimode project with cascading failures and various resources. The research used a modified simulated annealing algorithm and a compound Poisson process to measure resilience. Reference [22] suggests a SMILP model of resilient distribution systems with line hardening, distributed generators, and energy storage. In that paper, the authors reduce the load-shedding cost by adopting two-stage stochastic optimization with a master-slave control method to improve resilience during the planning and emergency stages. Another study [5] introduces a reaction framework for distribution system operators to counter cyber-attacks in smart distribution networks. Real-time smart distribution network reconfiguration can prevent blackouts by reconfiguring the system topology, reducing dependence on the attacked retailers. Another study [23] considers a preventive–corrective resilient energy management strategy for CPSs with preventive and corrective actions. It utilizes pre-scheduled energy storage and NR to minimize energy curtailment costs and it evaluates the model using resistance, recovery, and resilience indices. In reference [24], a framework for evaluation is developed to assess the feasibility of distribution feeders in multiple inverter-based, dynamic MGs. It proposes solutions for restorations by cross-layer network reconfiguration and develops distributed controllers to manage topology changes and coordinative regulation. The framework and controllers are validated in real time using hardware-in-the-loop testing. Another article [25] presents a novel approach to enhancing energy performance and reducing gas emissions in microgrids using virtual power plants (VPPs) and DERs. It optimizes the scheduling and takes into consideration electric vehicles (EVs) and responsive loads in load-side management. Paper [26] introduced a multi-objective model for feeder reconfiguration, economic dispatching, and capacitor switching optimization, considering the operational costs, active power losses, voltage stability, reduction in emission, non-dispatchable DERs, ESS, and the stochastic behavior of generation, loads, and EVs. The multi-objective hybrid Big Bang Big Crunch algorithm finds the optimum solutions. The authors in [27] identify three relevant challenges in energy resource management for active buildings with RESs: stochastic modeling, reliability-based optimization, and uncertainty categorization. They present a probabilistic-based optimization approach that considers the uncertainties of photovoltaic generation and energy demand. Reference [28] outlines a hybrid grey wolf equilibrium optimizer (HGW-EO) algorithm that seeks to tackle the difficulties associated with fluctuating renewable energy sources (RESs) and the non-convexity and non-linearity of optimal power flow (OPF) formulations. The algorithm models the stochastic behavior of wind and solar power using relevant probability density functions. In this respect, it enhances the efficiency of hybrid power plant operations, considering factors such as fuel prices, fines, and uncertainties related to both excess and deficit estimations of RES generation. A new approach is proposed in [29] that combines secure data transfer using blockchain technology with the point estimate method (PEM), which optimizes scheduling and creates an algorithm to achieve optimal operation in interlinked microgrid scheduling. By adopting switching within the framework, it is possible to integrate renewable energy sources, dispatchable units, energy storage systems, and socioeconomic policies, which could help minimize costs while maximizing social benefits. In [30], a new ternary Markovian model was put forward to evaluate the influence of cyber-physical interactions on security in power systems. The research assesses the effect of DERs on energy management in power distribution systems as described in the article [31]. For instance, it introduces two metrics called energy management success rate and reliability index success rate, which are utilized to evaluate effectively how well energy management is performed and also how voltage is controlled. The research in [32] presents a new way of solving the dynamic distribution feeder reconfiguration problem, considering several objectives, including EENS, power loss, and operational cost. A time-of-use service demand response program, ESS, DGs, and solar photovoltaic arrays are incorporated into the optimization of the reconfiguration process by an improved particle swarm optimization algorithm.

Table 2. Comparison of the features of the proposed method and recent previous methods.

Factors	[7]	[11]	[12]	[13]	[14]	[15]	[16]	[18]	[19]	[20]	[21]	This Paper
Energy Management	✓	✓	✓	✓	✓	✓	✓	✓	✗	✓	✓	✓
Uncertainty	✓	✓	✓	✗	✗	✓	✓	✓	✗	✗	✗	✓
Power Loss	✓	✓	✓	✓	✗	✓	✗	✓	✗	✓	✓	✓
Voltage Profile	✓	✗	✗	✓	✗	✓	✗	✗	✗	✓	✗	✓
Network Reconfiguration	✓	✗	✓	✓	✗	✗	✗	✗	✗	✗	✓	✓
Cost of Load	✗	✗	✗	✗	✗	✓	✗	✗	✗	✓	✓	✓
Pollution Reduction	✗	✓	✗	✗	✓	✓	✗	✓	✗	✓	✗	✓
Optimal Switching	✗	✗	✗	✗	✗	✗	✗	✓	✗	✗	✓	✓
EENS	✗	✓	✗	✓	✗	✗	✓	✗	✗	✓	✓	✓
Operation Cost of the MGs	✓	✓	✗	✓	✓	✓	✗	✗	✗	✓	✓	✓
Voltage Deviation	✓	✓	✗	✓	✗	✗	✗	✗	✗	✓	✓	✓
Real-Time or Fast Online	✓	✗	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓
Dynamic Reconfiguration	✗	✗	✗	✓	✗	✓	✗	✗	✗	✗	✓	✓
Cyber-Attacks	✓	✗	✗	✓	✗	✗	✗	✓	✓	✗	✗	✓
Stability and Reliability Indexes	✓	✗	✓	✓	✗	✓	✓	✓	✗	✗	✗	✓
Dynamic Reconfiguration with Three Types of Switching	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✓

reports the limitations of previous research and studies regarding parameters of economic objectives and technical indicators such as losses, voltage deviation, and reliability indicators such as EENS and DR with three types of switching, real-time or fast online.

1.2. Contribution

Following the discussion of the above-mentioned limitations of previous works, this paper presents an online and real-time framework for DR of power multi-MGs based on hierarchical control in order to mitigate damages from cyber-attacks. The framework covers economic, technical, and network reliability objectives. Articulation of the goals mentioned below distinguishes this paper from other previous studies:

• Proposing an online and real-time framework for SG reconfiguration against CPSs using neural networks and conventional recurrent neural networks based on the long short-term memory (LSTM) approach.
• Evaluating technical indicators of MGs such as voltage deviation and avoiding changes in short-circuit levels (to prevent disruption of protective settings) along with economic objectives in determining optimal dynamic reconfiguration.
• Assessing reliability indicators such as the expected energy not served (EENS) and load ability limit (LAL) of the system along with economic objectives after the CPS.
• Considering three different types of switching in the problem of dynamic reconfiguration:

• Switching of coupled lines in the main distribution network (regular reconfigurations).
• Switching of the lines between the MGs connected to the upstream network.
• Switching of the connection lines of MGs to the upstream distribution network.

1.3. Organization

The structure of the present paper will be as follows: Section 2 is dedicated to the conceptual model. Section 3 presents the mathematical formulation of the proposed method. Also, Section 4 addresses the modeling of the suggested method within the framework of a multi-objective optimization method with a flowchart. Section 5 will focus on fast decision-making by the LSTM neural network. Section 6 deals with simulation and discusses the results obtained from the simulation. The main conclusion of this article is given in Section 7.

2. Proposed Framework

Figure 1 illustrates the proposed conceptual model of dynamic network reconfiguration against cyber-physical attacks. As seen in this figure, a holistic model should be able to dynamically use all potentials available in the network, such as changing the state of network switches and optimizing resource generation and consumption control optimization in a real-time and online manner within a hierarchical control scheme. With respect to that, reliability goals—like expected energy not served (EENS) and load ability limit (LAL) and other technical parameters of the network, such as losses, voltage deviations (VDs), and short-circuit levels (SCLs), should be integrated with economic objectives.

The proposed dynamic reconfiguration methodology is designed to respond to cyber-attacks such as false data injection, which can disrupt normal operations and potentially cause physical damage to power system components. These types of cyber-attacks can bypass robust protection mechanisms by corrupting control data, leading to unintended physical consequences like component overloads or voltage deviations. The system minimizes the risk of such harmful effects by quickly detecting these anomalies and adjusting the network configuration in real-time. This method protects the network from threats that can jeopardize its physical infrastructure and operational integrity.

3. Mathematical Problem Formulations

The mathematical formulation is conducted in this section for the proposed method (PM) of optimal dynamic reconfiguration within the limits of distribution networks and their associated MGs. It includes considerations of optimal and secure energy management scheduling, improvement of technical indices, and system reliability according to the PM process outlined in Algorithm 1. Therefore, a developed multi-objective optimization algorithm is used to optimize the multi-objective mathematical function that will be introduced later and detailed in the fourth section. Accordingly, cost functions for DGs and other technical index modeling and network reliability modeling are presented.

Algorithm 1: Real-time dynamic reconfigurations against the physical–cyberattacks.

Start 1. Calculate Required Parameters for Optimal Dynamic Reconfiguration:   Input Data:   ● Load Profile   ● Electricity Price   ● Initial Reconfiguration   ● Initial DG Generation 2. Hierarchical Control System:   Gather Required Data:   ▪ Gather Required Data:   ▪ Initial Losses Index   ▪ Initial VD Index   ▪ Initial EENS Index   ▪ Initial SCL Index   ▪ Initial LAL Index   ▪ Initial SOC of ESS   ▪ Initial DG Limits 3. Prepare Data for Optimization Algorithm   For Each Parameter:   ● Collect relevant data points   ● Format data for the optimization algorithm   End 4. Optimize Proposed Objective Function For Each Optimization Iteration:   ● Apply the optimization algorithm to minimize/maximize the objective function   ● Evaluate performance metrics (e.g., cost, losses)   End 5. Train LSTM Neural Network for Optimal DR   If Training Data is Sufficient:   ● Use the optimized data to train the LSTM neural network   ● Perform back-propagation and adjust weights   Else:   ● Collect additional data and retry training   End 6. Select Optimal DR Using LSTM Neural Network   For Each Real-Time Input:   ● Utilize the trained LSTM neural network to predict the optimal DR based on current conditions   End 7. Receive Real-Time Input Data from Online DMU:   Input Data:   ▪ Voltages Magnitude of Each Bus   ▪ Voltage Angle of Each Bus   ● Update the system state with the latest input data   End Stop

3.1. Cost Modelling of the Solar and Wind Generation Units

The power output of photovoltaic plants is directly related to solar radiation. The cell temperature and solar radiation intensity at the maximum power point determine the output power of photovoltaic arrays, which can be determined using Equations (1) and (2) [33,34,35].

$$P_{PV}(t)=\left[P_{PV,STC}\times {\displaystyle \frac{G_T(t)}{1000}}\times \left[1-\gamma (T_j-25)\right]\right]\times N_{PVs}\times N_{PVp}$$

(1)

$$T_j=T_{amp}+{\displaystyle \frac{G_T}{G_{T,STC}}}\times \left(NOCT-20\right)$$

(2)

where in Equations (1) and (2), $P_{PV}$, $P_{PV,STC}$, $G_T$, $\gamma$, $T_j$, $N_{PVs}$, $N_{PVp}$, and $NOCT$ represent the rated power of the photovoltaic system at the maximum power point and standard conditions, the amount of radiation under standard conditions, the temperature coefficient of power at the maximum power point, the temperature of solar cells, the nominal operating cell temperature, and the number of modules in series and parallel, respectively. Furthermore, the output power of wind turbines depends on wind speed. The wind speed variations can occur on an instantaneous, hourly, daily, and seasonal basis. Therefore, Equation (3) is used to model the actual power generated by a wind turbine [36].

$$P_{wt}(\nu )=\left\{\begin{array}{l}0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}if\nu <V_{ci}\\ P_R(A+B\nu +C{\nu }^2)\hspace{1em}if\hspace{0.33em}{V}_{ci}<\nu <V_r\\ P_R\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}if\hspace{0.33em}{V}_r<\nu <V_{co}\\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.33em}\hspace{0.33em}if\hspace{0.33em}{V}_{co}<\nu \end{array}\right.$$

(3)

where in Equation (3), $V_{ci}$, $V_{co}$, $V_r$, $P_R$, A, B, and C represent the cut-in, cut out, and rated wind speeds, rated power of the wind turbine, and coefficients associated with the turbine, respectively.

3.2. Cost Modelling of the Traditional Generation Units

Equation (4) models the cost of operating traditional distributed generation units such as microturbines and diesel generators, including operational costs and pollution costs [36].

$$C_{DG,t}=C_{DG,t}^{OP}+C_{DG,t}^{EMI}$$

(4)

where in Equation (4), $C_{DG,t}^{OP}$ presents the cost of operating and $C_{DG,t}^{EMI}$ is the cost associated with the pollution of the units in each time interval t.

3.3. Battery Energy Storage Unit Modeling

Maintaining frequency within the allowed limits in the present hybrid systems has become very challenging because of the increasing penetration of renewables and electric vehicles. Supplementing energy units always strive to balance supply and demand and never allow the frequency to deviate from its nominal value in real-time. An energy storage system (ESS) can act as standby power and immediately compensate for frequency deviations when there are generation fluctuations in renewable generation. The operating constraints of such an ESS are determined by factors such as the arrangement of the battery unit, duration of backup, temperature, life expectancy of battery units, discharge depth, needs of power reserve, and generation of RESs within the grid. The charge/discharge program for such an ESS unit can be defined as [37]:

$$P_{ESS}(t)=P_{ch}(t)\hspace{1em}if\hspace{0.33em}\left\{\begin{array}{l}{P}_{PV}(t)+P_{WT}(t)+P_{DG}(t)\\ +P_{FC}(t)+P_{MT}(t)\\ +P_g(t)-P_D(t)\end{array}\right\}\ge 0$$

(5)

$$P_{ESS}(t)=P_{dch}(t)\hspace{1em}if\hspace{0.33em}\left\{\begin{array}{l}{P}_{PV}(t)+P_{WT}(t)+P_{DG}(t)\\ +P_{FC}(t)+P_{MT}(t)\\ +P_g(t)-P_D(t)\end{array}\right\}<0$$

(6)

where $P_{ESS}(t)$, $P_{DG}(t)$, $P_{FC}(t)$, $P_g(t)$, and $P_D(t)$ are the power of the ESS, DG, FC, MT, grid, and load demand, respectively. Also, $P_{ch}(t)$ and $P_{dch}(t)$ are the charging and discharging power of the ESS.

ESS power for charge or discharge conditions is calculated as follows:

Charging state:

$$E_{ch}(t)=\left({\displaystyle \frac{P_{DG}(t)+P_{WT}(t)+P_{FC}(t)+P_{MT}(t)-P_D(t)}{{\eta }_{Conv}}}+P_{PV}(t)\right)\times \Delta t\times {\eta }_{ch}$$

(7)

$$SOC(t)=SOC(t-1)(1-\sigma )+E_{ch}(t)$$

(8)

Discharging state:

$$E_{dch}(t)=\left({\displaystyle \frac{-P_{DG}(t)-P_{WT}(t)-P_{FC}(t)-P_{MT}(t)+P_D(t)}{{\eta }_{Conv}}}-P_{PV}(t)\right)\times \Delta t\times {\eta }_{ch}$$

(9)

$$SOC(t)=SOC(t-1)(1-\sigma )-E_{ch}(t)$$

(10)

where $SOC(t)$, $E_{ch}(t)$, $E_{dch}(t)$, $\sigma$, ${\eta }_{ch}$, and ${\eta }_{Conv}$ denote the battery charge state, charging energy, discharging energy, self-discharge rate, charging/ discharging efficiency, and converter efficiency, respectively.

There are two main factors involved in the life expectancy of a battery unit: throughput of lifetime (Qlifetime) and storage float life (Rbatt, f). The MGO is responsible for determining the battery lifetime limiting factor by time, throughput, or both. The lifetime expectancy of an ESS unit can be achieved by the following relationship:

$$R_{batt}=\left\{\begin{array}{l}{\displaystyle \frac{N_{batt}{Q}_{lifetime}}{Q_{thrpt}}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.33em}\hspace{0.33em}if\hspace{0.33em}\mathrm{limited}\hspace{0.33em}\mathrm{by}\hspace{0.33em}\mathrm{throughput}\\ R_{batt,\hspace{0.33em}f}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.33em}\hspace{0.33em}if\hspace{0.33em}\mathrm{limited}\hspace{0.33em}\mathrm{by}\hspace{0.33em}\mathrm{time}\\ \min \left[{\displaystyle \frac{N_{batt}{Q}_{lifetime}}{Q_{thrpt}}},R_{batt,\hspace{0.33em}f}\right]\hspace{1em}if\hspace{0.33em}\mathrm{limited}\hspace{0.33em}\mathrm{by}\hspace{0.33em}\mathrm{throughput}\hspace{0.33em}\mathrm{and}\hspace{0.33em}\mathrm{time}\end{array}\right.$$

(11)

where $N_{batt}$ and $Q_{thrpt}$ are number of batteries and the annual throughput of storage, respectively.

The storage float life is defined as the time interval an ESS unit can operate before needing to be replaced. Note that the float life is only applicable in case the battery life expectancy is selected to be characterized by time, and thus cannot be used for the condition where only the throughput is selected. The wear cost of the ESS ($C_{bw}$) unit can be described as:

$$C_{bw}={\displaystyle \frac{C_{rep,\hspace{0.33em}batt}}{N_{batt}{Q}_{lifetime}\sqrt{\eta rt}}}$$

(12)

where $C_{rep,\hspace{0.33em}batt}$ and $\eta rt$ are storage replacement cost and the roundtrip efficiency of storage, respectively.

3.4. Demand Response Implementation

Network operators can reduce the network demand burden economically and reliably by involving customers in energy management programs with incentive plans. Demand response (DR) is achieved by persuading the customer to adjust their consumption in accordance with the operator’s instructions [38].

Consumption Management through Time-Based Rate and Incentive-DR Scheme

The objective of this scheme is to adjust the consumer demands according to the service pricing enforced. The modified consumption pattern under a time-based rate DR strategy during the i-th and j-th hour is calculated by the following relationship [39].

$$d(i)=d_0(i)\left\{1+{\displaystyle \frac{E(i)\left[\rho (i)-{\rho }_0(i)\right]}{{\rho }_0(i)}}+{\displaystyle {\sum }_{j=1,j\ne i}^{24}E(i,j)\frac{\left[\rho (j)-{\rho }_0(j)\right]}{{\rho }_0(j)}}\right\}$$

(13)

The cross-elasticity between variables is denoted by $E(i,j)$, while $E(i)$ presents the self-elasticity. The initial electricity price is represented by ${\rho }_0(i)$, and $A(i)$ denotes the incentive amount at the i-th hour. The spot electricity price is indicated by $\rho (i)$. The modified load demand, measured in kW, reflects the changes resulting from the demand response.

This strategy tries to modify the customer consumption pattern by defining a reward and penalty system. The adjusted power demand under the incentive-based DR scheme is calculated according to the following equation:

$$\begin{array}{l}d(i)=d_0(i)\left\{1+{\displaystyle \frac{E(i)\left[\rho (i)-{\rho }_0(i)-A(i)+pen(i)\right]}{{\rho }_0(i)}}\right.\\ \left.+{\displaystyle {\sum }_{j=1,j\ne i}^{24}E(i,j)\frac{\left[\rho (j)-{\rho }_0(j)-A(j)+pen(j)\right]}{{\rho }_0(j)}}\right\}\end{array}$$

(14)

where $pen(i)$ is the penalty amount at the i-th hour and $pen(j)$ is the penalty amount at the j-th hour.

3.5. Modelling the Uncertainty in Loads and Renewable Energy Sources

The load and RES uncertainties are included based on forecasting using historical records. The forecast quantities are calculated based on the point prediction method [40], using long-term observations during a specific time course in a particular area. However, the forecasts based on the point value method are erroneous in response to uncertainties such as wind speed, solar radiation, and load demand [41]. Therefore, forecast errors are essential to consider in practice. In this study, these factors are considered with the help of the interval prediction technique [42], which estimates the lower/upper bounds of the uncertain quantities based on the confidence level at each forecast point. Considering a point forecast value equal to $L$, corresponding to the forecast error Probability Density Function (PDF) of ($\varphi$), the set for general forecast quantities $U_D$ can be characterized as:

$$U_D=\left[L(t)+f^{-1}(\tilde{\varphi }),L(t)+f^{-1}(\widehat{\varphi })\right]$$

(15)

with $\tilde{\varphi }$ and $\widehat{\varphi }$ denoting the parameters indicated by the confidence level of $\lambda$.

Based on the interval prediction theory, and according to Equation (15), the lower/upper bounds of the renewable power generation can be calculated for the base point forecast for renewable power generation ${\overline{P}}_R$ and the forecast error PDF selected $f(\Delta P_R)$ as follows:

$${\tilde{P}}_R^{*}={\overline{P}}_R+f^{-1}(\tilde{\varphi })$$

(16)

$${\widehat{P}}_R^{*}={\overline{P}}_R+f^{-1}(\widehat{\varphi })$$

(17)

Nevertheless, renewable power generation units have limited output, so the boundaries calculated in Equations (16) and (17) must be corrected:

$${\tilde{P}}_R=\max \left[{\tilde{P}}_R^{*},P_R^{\min }\right]$$

(18)

$${\widehat{P}}_R=\min \left[{\widehat{P}}_R^{*},P_R^{\max }\right]$$

(19)

The renewable power generation forecast with uncertainty considerations is obtained as:

$$U_{P_R}=\left\{P_R:\hspace{0.33em}{\tilde{P}}_R\le P_R\le {\widehat{P}}_R\right\}$$

(20)

For the load, the forecast error PDF, $f(\Delta P_L)$, can be considered as a normal distribution, and thus, according to (15), the uncertain forecast set for the load can be obtained based on the point forecast for load demand ${\overline{P}}_L$ as:

$$\begin{array}{l}{U}_{P_L}=\{P_L:\hspace{0.33em}{\tilde{P}}_L\le P_L\le {\widehat{P}}_L\\ {\tilde{P}}_L={\overline{P}}_L+f^{-1}(\tilde{\varphi }),{\widehat{P}}_L={\overline{P}}_L+f^{-1}(\widehat{\varphi })\}\end{array}$$

(21)

3.6. Power Losses Formulation

In this article, the overall losses in the distribution networks are considered as one of the objective function factors, which is obtained using Equation (22) [43]:

$$\begin{array}{l}Active\hspace{0.33em}Losses={\left({\displaystyle \frac{{\left|V\right|}^2}{R_{Z_i}}}\right)}_{end}-{\left({\displaystyle \frac{{\left|V\right|}^2}{R_{Z_j}}}\right)}_{start}\\ \mathrm{Re}active\hspace{0.33em}Losses={\left({\displaystyle \frac{{\left|V\right|}^2}{X_{Z_i}}}\right)}_{end}-{\left({\displaystyle \frac{{\left|V\right|}^2}{X_{Z_j}}}\right)}_{start}\end{array}$$

(22)

$R_{Z_i}$ and $R_{Z_j}$ are the resistances of the respective components $X_{Z_i}$ and $X_{Z_j}$ in the system. The subscripts (end) and (start) indicate the state of the system at the end and start of a particular event or time period. $X_{Z_i}$ and $X_{Z_j}$ are the reactance of the respective components $Z_j$ and $Z_i$ in the system.

3.7. Voltage Deviation Formulations

Another objective of the present paper is to reduce voltage deviation in the distribution network during the response to a cyber–physical attack. The voltage deviation can be obtained according to Equation (23) [43]:

$$VD=\sqrt{{\displaystyle \sum _{i=1}^{Nb}{\left(\frac{V_{S\tan dard}}{V_{Base}}-\frac{V_i}{V_{Base}}\right)}^2}}$$

(23)

Voltage deviation ($VD$) represents the measure of the difference between the actual voltage levels $V_i$ at bus (from i = 1 to $Nb$) and the standard voltage levels $V_{S\tan dard}$ in the system. $Nb$ represents the total number of buses in the electrical system. The $V_{Base}$ is the base voltage level against which other voltages are compared.

3.8. Dynamic Reconfiguration Modeling

As seen in Figure 2, the components of a distribution network, along with the MGs connected to it, are interconnected by power distribution lines. In this regard, the dynamic reconfiguration of the distribution network and the connected MGs change through the opening and closing of the breakers present in the network. Therefore, the MGs can operate optimally and safely in two modes: (1) connected to the main network, and (2) isolated from the main network (islanded), where energy exchange takes place between the microgrid and the main network in the connected mode. Additionally, other coupling switches present in the network can modify the power distribution path throughout the network through opening and closing actions. In order to model the open or closed states of the switches in the network, a binary formulation is used, with 0 representing the open state and 1 representing the closed state, as described in Equation (24):

$$S_i=\left\{\begin{array}{l}1\hspace{1em}\hspace{1em}if\hspace{0.33em}Switch\hspace{0.33em}is\hspace{0.33em}connected\\ 0\hspace{1em}\hspace{1em}if\hspace{0.33em}Switch\hspace{0.33em}is\hspace{0.33em}not\hspace{0.33em}connected\end{array}\right.$$

(24)

3.9. Short-Circuit Level Criteria Modeling

This paper has emphasized that dynamic network reconfiguration in response to a cyber-attack needs to consider the short-circuit level (SCL). The SCL is a critical parameter that guides the security of the network and must be kept as stable as possible to avoid potential damage due to improper performance of protection systems. The SCL index can be defined as follows:

$$SCLI=({\displaystyle \sum _{k=1}^{nb}\left(1-\frac{I_k^{*}(F)}{I_k(F)}\right)})$$

(25)

$$I_k(F)={\displaystyle \frac{V_k}{Z_{kk}+Z_f}}$$

(26)

$$I_k^{*}(F)={\displaystyle \frac{V_k^{*}}{Z_{kk}+Z_f}}$$

(27)

In the above equations, $V_k$ and $V_k^{*}$ represent the voltage of each bus in the network before and after any changes in the network. $Z_{kk}$ and $Z_f$ represent the impedance of the bus and the impedance of the fault that occurred at the bus in the network, respectively.

3.10. Load Ability Limit Criteria

In this paper, the load ability limit (LAL) of the power distribution network is defined as a target for improving network security. The LAL is designed so that it decreases as the system load increases, approaching zero near the network collapse and maximum tolerable system load [44].

$$VS{I}_m={\left|V_1\right|}^4-4{\left|V_1\right|}^2(R_{eq}{P}_{Lm}+X_{eq}{Q}_{Lm})-4{(X_{eq}{P}_{Lm}-R_{eq}{Q}_{Lm})}^2$$

(28)

In Equation (28), $\left|V_1\right|$ represents the voltage magnitude at the bus, $R_{eq}$ and $X_{eq}$ are the equivalent resistance and reactance of the line, and $P_{Lm}$ and $Q_{Lm}$ represent the total active and reactive power of all nodes, respectively.

3.11. Expected Energy Not Served Criteria

This study assesses network reliability through the EENS index. The EENS is calculated by taking into account forced outage probabilities of generating units, power distribution lines, and a virtual power generator at each bus. A deterministic model is employed to generate continuous events and their associated probabilities, excluding events with probabilities less than 0.000001. The EENS index is then calculated using the following equation [45].

$$\begin{array}{l}{F}_i=EENS=EEN{S}_G+EEN{S}_L\\ subject\hspace{0.33em}to:\\ EEN{S}_G={\displaystyle \sum _{i=1}^{NG}{\rho }_i^G{E}_{i,P_{G_i}^{Outage}}^G}\\ EEN{S}_L={\displaystyle \sum _{j=1}^{NL}{\rho }_j^L{E}_{i,L_i^{Outage}}^L}\end{array}$$

(29)

3.12. Objective Function Formulation

The optimization model proposed in this paper is formulated as a multi-objective problem consisting of several conflicting objectives. Unlike traditional optimization problems, it lacks a unique solution. In this regard, any solution that does not violate the defined constraints can be chosen as an optimal solution and trained on the desired artificial neural network. To achieve the specified objectives of secure and optimal dynamic rearrangement while satisfying the defined constraints, various types of information such as unit commitment and controllable distributed generation unit capacities, as well as power exchange with the upstream network, need to be determined for each hour of a day in advance. The ultimate goal of this comprehensive planning is to achieve optimal and safe operation considering all technical parameters of the network in response to a cyber-attack. Therefore, to achieve this goal, a mixed-integer linear programming formulation is used for the multi-objective optimization problem. In this regard, the proposed planning problem is formulated with a multi-objective function according to Equation (30).

$$\min \left\{F_i(P_{D{G}_i},S_i,{P_{DR}}_i)\right\}$$

(30)

In Equation (30), $F_i$ represents the objective functions in the planning problem mentioned, which are dependent on the independent variables $P_{D{G}_i}$ (generation values) and $S_i$ (switch states). Therefore, the desired objective functions in this problem can be formulated as follows:

$$F_1(P_{D{G}_i},S_i,P_{DR})=Total\hspace{0.33em}\mathrm{Cos}t=\left\{\begin{array}{l}\underset{PV\hspace{0.33em}\mathrm{Cos}t}{\underbrace{C_{PV}(P_{PV})}}+\underset{wind\hspace{0.33em}turbine\hspace{0.33em}\cos t}{\underbrace{C_{wt}(P_{wt})}}+\underset{microturbine\hspace{0.33em}\cos t}{\underbrace{C_{MT}(P_{MT})}}+\underset{Deidel\hspace{0.33em}\cos t}{\underbrace{C_{Dg}(P_{Dg})}}\\ +\underset{utility\hspace{0.33em}\cos t}{\underbrace{C_{utility}(P_{utility})}}+\underset{Demand\hspace{0.33em}\mathrm{Re}sponse\hspace{0.33em}\cos t}{\underbrace{C_{DR}(P_{DR})}}+\underset{Battery\hspace{0.33em}\mathrm{Cos}t}{\underbrace{C_{battery}(P_{Battery})}}\end{array}\right\}$$

(31)

$$F_2(P_{D{G}_i},S_i,{P_{DR}}_i)=Losses=\underset{Active\hspace{0.33em}Losses}{\underbrace{{\left({\displaystyle \frac{{\left|V\right|}^2}{R_{Z_i}}}\right)}_{end}-{\left({\displaystyle \frac{{\left|V\right|}^2}{R_{Z_j}}}\right)}_{start}}}+\underset{\mathrm{Re}active\hspace{0.33em}Losses}{\underbrace{{\left({\displaystyle \frac{{\left|V\right|}^2}{X_{Z_i}}}\right)}_{end}-{\left({\displaystyle \frac{{\left|V\right|}^2}{X_{Z_j}}}\right)}_{start}}}$$

(32)

$$F_3(P_{D{G}_i},S_i,P_{D{R}_i})=VD=\sqrt{{\displaystyle \sum _{i=1}^{Nb}{\left(\frac{V_{s\tan dard}}{V_{Base}}-\frac{V_i}{V_{Base}}\right)}^2}}$$

(33)

$$F_4(P_{D{G}_i},S_i,P_{D{R}_i})=VS{I}_m$$

(34)

$$F_5(P_{D{G}_i},S_i,P_{D{R}_i})=(1-{\displaystyle \sum _{k=1}^{nb}\frac{I_k^{*}(F)}{I_k(F)}})$$

(35)

$$F_6(P_{D{G}_i},S_i,P_{D{R}_i})=EENS$$

(36)

In a distribution network with interconnected MGs, bidirectional energy exchange is possible among the network, MGs, and generation/consumption sources. Each existing objective function aims to maximize its benefit under multi-objective conditions. Considering different operational states for the MGs, the multi-objective function for optimal and safe energy management of the entire network can be mathematically expressed as follows:

$$\min \left\{O{F}_{Total}\right\}=\left[{\chi }_{12}\hspace{1em}{\chi }_{12}\hspace{0.33em}\dots \hspace{1em}{\chi }_{pk}\right]\left[\begin{array}{c}O{F}_1\\ O{F}_2\\ ⋮\\ O{F}_k\end{array}\right]$$

(37)

In Equation (37), ${\chi }_{pk}$ represents the weight coefficient of the objective functions. The weight adjustment for each objective function should consider specific events and system characteristics such as different system states during maintenance, replacement time, probability of element failure, and various error events (based on their persistence and location) in the system that each result in separate system performance conditions. The weights are adjusted to appropriately reflect the importance of these events and characteristics in the overall optimization. The weight adjustment process involves careful consideration of each event and system feature to ensure an optimal and balanced solution for the multi-objective optimization problem.

4. Multi-Objective Optimization Method

Optimization problems with multiple objectives can be in mathematical form:

$$min,F={\left[f_1\left(\chi \right),f_2\left(\chi \right),f_3\left(\chi \right),\dots ,f_p\left(\chi \right)\right]}^T$$

(38)

$$Subject\_to:\left\{\begin{array}{l}{g}_i\left(x\right)\prec 0,\\ h_i\left(x\right)\prec 0,\end{array}\right.\left.\begin{array}{l}i=1,2,3,\dots ,N_{ueq}\\ i=1,2,3,\dots ,N_{eq}\end{array}\right\}$$

(39)

In [46], other details of the proposed multi-objective method are comprehensively explained.

Multi-objective optimization uses variables and label notations such as p (number of objective functions), $N_{ueq}$ (number of inequality constraints), $N_{eq}$ (number of equality constraints), and $\chi$ (decision vector).

$$\begin{array}{l}{e}_{2,n2}=f_2^{SN}-\left({\displaystyle \frac{f_2^{SN}-f_2^U}{q_2}}\right)\times n2,\hspace{1em}n2=0,1,\dots ,q_2\\ e_{2,n2}=f_p^{SN}-\left({\displaystyle \frac{f_p^{SN}-f_p^U}{q_p}}\right)\times np,\hspace{1em}np=0,1,\dots ,q_p\end{array}$$

(40)

Solving subproblems with the Equation (40) constraints and main problem constraints yields Pareto front, eliminating infeasible solutions and transforming objective function constraints to equalities.

$$\left\{\begin{array}{l}min,\left(f_1\left(\stackrel{-}{\chi }\right)-r_1{\displaystyle \sum _{i=2}^P\left(\frac{s_i}{r_i}\right)}\right)\\ Subject to\\ f_i\left(\stackrel{-}{\chi }\right)+s_i,n_i=e_i,n_i,\to i=2,\dots ,p\&s_i,n_i\in R^{+}\\ \stackrel{-}{\chi }\in \Omega \end{array}\right.$$

(41)

The method $s_2,\dots ,s_p$ addresses scaling issues by introducing slack variables based on the Equation (41) formula and includes $r_1({\displaystyle \frac{s_i}{r_i}})$, a term in the objective function to handle objective scale discrepancies, while the ranges of objective functions are determined using the payoff matrix $\left(r_i=f_i^{SN}-f_i^U\right)$. The augmented epsilon-constraint method with fuzzy satisfying finds the most desirable solution.

$${\mu }_{Fi}\left(\chi \right)=\left\{\begin{array}{cc}1& F_i\left(\chi \right)\le F_i^{\min }\\ {\displaystyle \frac{F_i^{\max }-F_i\left(\chi \right)}{F_i^{\max }-F_i^{\min }}}& F_i^{\min }\le F_i\left(\chi \right)\le F_i^{\max }\\ 0& F_i\left(\chi \right)\ge F_i^{\max }\end{array}\right.$$

(42)

It states that the value of the objective function $F_i$ evaluated at the current values of $\chi$ should be less than or equal to a specified minimum value $F_i^{\min }$ or maximum value $F_i^{\max }$. The membership function evaluates the satisfaction level of the objective function condition, with 1 indicating satisfaction and 0 representing no satisfaction; $F_i^k$ represents the value of each objective function; and ${\mu }_i^k$ is the membership value in the Pareto solution k. This membership function is designed for minimizing objective functions. The overall membership value ${\mu }^k$ determines the most compromised solution.

$${\mu }^k={\displaystyle \frac{{\displaystyle \sum _{i=1}^P{w}_i·{\mu }_i^k}}{{\displaystyle \sum _{k=1}^M{\displaystyle \sum _{i=1}^P{w}_i·{\mu }_i^k}}}}$$

(43)

The weighting factor $w_i$ determines the importance of each objective function i as the decision maker selects the optimal expansion plan based on system requirements, with the solution having the highest ${\mu }^k$ value chosen as the most compromised solution considering the weighted membership values.

5. Fast Decision-Making Using LSTM Neural Network

This section provides a clear explanation of how the suggested framework applies SGs. SGs benefit from adaptive control techniques and real-time data processing. By including these functions in the MG control system, the suggested framework improves the system’s capacity to react to dynamic changes and cyber-attacks. The system can now make judgments more quickly and optimally thanks to this integration. The utilization of the LSTM neural network is presented to estimate the best state of dynamic switches in power distribution systems and interconnected MGs in real time, mostly when faced with physical–cyber-attacks. By utilizing its distinct memory cell structure, the LSTM is specially designed to overcome the drawbacks of conventional recurrent neural networks, such as the vanishing gradient issue.

5.1. Inputs and Outputs of the LSTM Network

The voltage magnitude and angle at each bus in the power network are the inputs of the LSTM network, and the binary states (0 or 1) of all the dynamic switches in the network are the outputs. Based on current circumstances, the dynamic switches decide whether to open or close a specific connection in the distribution network [47]. The relationship between these inputs and outputs is graphically shown in Figure 3, highlighting the importance of the LSTM in quickly reaching data-driven judgments.

5.2. Optimization and Training Process

The LSTM network is trained using an optimization method to ensure that the performance criteria related to the objective function are met optimally. The goal is to minimize disruptions and maintain stability during cyber-attacks by quickly adjusting switch states. The training process involves backpropagation through time, ensuring that the network learns the correct switching patterns based on historical and real-time data [48].

5.3. LSTM Architecture and Functionality

The components of the LSTM architecture are as follows, as depicted in Figure 3:

• The cell state section formulation:

$$C{ℂ}_t=f_t\times C{ℂ}_{t+1}+i_t\times C\underset{t}{\overset{-}{ℂ}}$$

(44)

$f_t$ is the “forget gate” and it resets the cell variable so the stored input in $C{ℂ}_t$ will be forgotten. Also, $i_t$ is the input value. The old cell state $C_{t-1}$ is updated to the new cell state $C{ℂ}_t$.

2.

The Input Gate section formulation:

$$\left\{\begin{array}{l}{i}_t=\sigma \left(W_i\cdot \left[{\hslash }_{t-1},\left.{\chi }_t\right]+b_i\right.\right)\\ C\stackrel{-}{{\displaystyle {ℂ}_t}}=\tanh \left({W_{ℂ}}_C\cdot \left[{\hslash }_{t-1},\left.{\chi }_t\right]+b_f\right.\right)\end{array}\right.$$

(45)

$i_t$ represent the value of the input and $C\stackrel{-}{{\displaystyle {ℂ}_t}}$ is the expected value of the memory cell and t is the time step. Meanwhile, the input gate reads the inputs from ${\chi }_t$ vector and the output gate writes the output in ${\hslash }_t$ vector [47]. Also, $W\left[{\hslash }_{t-1},{\chi }_t\right]$ and $b$ represent the weight matrices and bias, respectively. Both $\sigma$ and $\hslash$ are point-wise nonlinear activation functions [49].

3.

The Forget Gate section formulation:

$$f_t=\sigma \left(W_f\cdot \left[{\hslash }_{t-1},{\chi }_t\right]+b_f\right)$$

(46)

The Output Gate section formulation:

$$\left\{\begin{array}{l}{o}_t=\sigma \left(W_{\circ }\cdot \left[{\hslash }_{t-1},{\chi }_t\right]+b_{\circ }\right)\\ {\hslash }_t=o_t\times \tanh \left(C_t\right)\end{array}\right.$$

(47)

6. Simulation Results and Discussion

In this section, the proposed method for the comprehensive evaluation and assessment of optimal dynamic reconfiguration in intelligent distribution networks and their connected subnetworks is examined based on the MATLAB software 2023a toolbox. This evaluation was conducted over a 24-hour period, aiming to combat cyber-attacks. In this regard, according to Figure 4, a 118-bus distribution network along with its connected MGs was utilized to test and validate the proposed method, comparing it with other recent previous methods. The details of the load data and network lines mentioned above are explained in detail in the reference [50].

As illustrated in Figure 4, the main distribution network comprises 118 buses. MG1, MG2, and MG3 are connected to 26, 79, and 117 buses of the main distribution network through 119, 123, and 126 MG buses, respectively. These MGs can dynamically connect or disconnect from each other and the upstream network through the switch breakers indicated. Additionally, MG1 is connected to MG2 and MG3 through switch breakers on the line between buses 122 and 125 and on the line between buses 122 and 129, respectively. Conversely, MG2 and MG3 are connected via switch breakers between 125 and 129 buses. In this network configuration, the lines between buses 11–12, 68–69, and 105–106 are coupled with the lines between buses 17–27, 80–99, and 91–115, respectively. Furthermore, the distributed generation resources in the MGs consist of a combination of wind turbines, photovoltaic systems, microturbines, and diesel generators to provide operational power, while batteries serve as energy storage sources. The proposed method underwent evaluation against recent methods, both with and without consideration of network security and reliability indicators. Additionally, a developed multi-objective differential evolution optimization algorithm was employed to optimize the multi-objective function, and its outputs were compared with other optimization algorithms.

6.1. Input Parameters of the System

Figure 4 graphically represents the relationship between the inputs and outputs of the LSTM network, emphasizing its role in facilitating rapid, data-driven decisions. Specifically, it shows how the advanced distribution network, including the connected MGs, incorporates distributed generation sources such as wind and photovoltaic systems. The LSTM processes real-time data from these sources to optimize the dynamic switches in response to cyber-attacks or other network disruptions. Figure 5a,b provides further context by illustrating the solar radiation and ambient temperature over a 24 h period, which are crucial inputs for the performance of photovoltaic systems. These environmental factors directly influence power generation, and the LSTM network takes these variations into account when making fast decisions regarding power distribution. In addition, Figure 6a,b provides key insights into the wind speed profile and the consumption load profile within the network over a 24 h period. These factors are critical inputs for the LSTM network, as the wind speed directly impacts the power generation from wind turbines, while the load profile reflects the varying demand across the distribution network. By considering these inputs, the LSTM network can accurately estimate the optimal state of the dynamic switches in real time, ensuring efficient power distribution and maintaining system stability, even under fluctuating environmental conditions and consumption demands. This highlights the LSTM’s ability to adapt to the continuous changes in the network, further reinforcing its role in fast decision-making.

6.2. Results Analysis

This section comprehensively examines optimal dynamic reconfiguration in the distribution network and connected subnetworks using the proposed approach and other recent approaches. Specifically, a study was conducted where the line between buses 2 and 10 was subjected to a physical–cyber-attack, and a hierarchical neural network-based control system, with the capability of selecting optimal connection states for the subnetworks and the main distribution network, as well as determining the overall optimal dynamic reconfiguration, is proposed. The focus is on achieving real-time optimal reconfiguration of the distribution network to respond to the attack and ensure seamless operation. In this regard, the performance of the proposed method is compared with previous methods over 24 h. In

Table 3. Comparison of the proposed optimization algorithm with other optimization methods over 24 h.

Optimization Method	Best O.F.	Number of Iterations	CPU Times(s)	Operating Cost ($)	Power Losses (KW)	VD (pu)	EENS (kWh)	Load Ability Limit (KW)	Sum of SCL Changes (pu)
(PM)	380.4826	15	19	27,557,510.40	10.46	5.0	58.62	2,079,887.87	0.0027
(PSO)	392.5123	21	22	2,796,6581.51	11.12	5.31	55.46	2,091,957.19	0.0045
(MOGA)	384.7896	18	21	27,855,164.43	10.74	5.21	54.82	2,088,287.52	0.0039
(ICA)	383.4212	19	23	27,697,412.74	10.46	5.01	50.18	2,088,254.54	0.0029
(HHO)	382.5893	17	20	27,594,718.87	10.48	5.0	58.62	2,080,917.73	0.0028

, the performance of the proposed optimization method (PM) is compared with several other techniques, including Particle Swarm Optimization (PSO), Multi-Objective Genetic Algorithm (MOGA), Imperialist Competitive Algorithm (ICA), and Harris Hawk Optimization (HHO). The comparison is based on key performance indicators such as the objective function value, number of iterations, CPU time, operating cost, power losses, VD, EENS, load ability limit, and the sum of SCL over a 24 h period. It is observed that the proposed optimization method consistently outperforms the other methods in all metrics, highlighting its superior capability in optimizing dynamic reconfiguration.

As discussed in the problem formulation of the proposed approach, a multi-objective function with six objectives (six dimensions) is employed for the current framework. At this stage, it has not been possible to plot the Pareto optimization convergence curve, which is commonly used in multi-objective optimization problems. However, we have provided the convergence curve for the total objective function, where all objectives have been combined with equal weights, as shown in Figure 7. As can be observed from the figure, the proposed method demonstrates superior performance in terms of optimization accuracy and iteration efficiency compared to other optimization methods.

In the verification stage, the suggested LSTM network’s functionality was carefully examined in relation to an independent validation dataset made up of signals the network had never seen before. This made it possible to assess its diagnostic skills objectively. The outcomes demonstrated how well the LSTM network defends against different cyber–physical threats. All things considered, the training and validation procedures confirmed the LSTM network’s resilience and dependability in managing cyber–physical disruptions, making it an important instrument for improving power system monitoring and protection. In this investigation, experiments were carried out utilizing data from model tests comprising 1500 cases, each of which represented a distinct fault type, using MATLAB 2024a. Using the suggested method, the vibration time-series data were gathered and then divided into tiny intervals of 0.01 s, with 60 consecutive sample points at a constant 1.5 kHz sampling rate contained in each segment. A validation set of 25% of the observations was put aside, and the data were shuffled appropriately, to guarantee the precision of the model selection. In order to decrease prediction errors during training, the LSTM network modifies its weights and biases to identify patterns and temporal relationships in the input sequences.

The distinct LSTM architecture, which combines gating functions and cell state mechanisms, makes this learning process possible. The network is trained to produce precise numerical predictions, which are the model’s outputs.

The learning rate was set at 0.01 and progressively decreased throughout the course of 200 epochs of training. The percentage of predictions within an acceptable error margin and the root-mean-square error (RMSE) of the forecasts were used to continuously assess the accuracy of the model. The suggested LSTM network was trained and analyzed using the Sgdm optimizer, as shown in Figure 8.

Table 4. A range of assessment criteria applied to the LSTM network when it was trained on a single CPU.

Epoch	Iteration	Time Elapsed (hh:mm:ss)	Mini-Batch RMSE	Mini-Batch Loss	Base Learning Rate
1	1	00:00:04	1.96	1.9	0.01
50	50	00:00:06	0.05	1.4 × 10⁻3	0.01
100	100	00:00:07	0.04	1.0 × 10⁻3	0.01
150	150	00:00:08	0.03	5.3 × 10⁻⁴	0.001
200	200	00:00:09	0.01	5.2 × 10⁻⁵	0.001

gives information on the learning rate, related losses, and mini-batch accuracy for both the training and validation stages. The model demonstrated its accuracy and resilience by achieving an RMSE accuracy of 0.01 and a loss accuracy of 5.2 × 10⁻⁵ by the end of the training session. It should be noted that the measurements on the training data are represented by darker colors, while the metrics on the validation data are represented by lighter colors.

In addition, Figure 9 shows the root-mean-square error (RMSE) comparison between the actual signal and the predicted signal produced by the LSTM network, allowing for an assessment of the network’s performance using actual data. Even with a small number of samples, the suggested method demonstrated remarkable accuracy in forecasting each output, as seen in the image. This demonstrates the LSTM network’s dependability and resilience in processing noisy input and precisely identifying fault conditions.

Continuing further, after sending the voltage magnitude and angle data of buses through measurement devices and executing the multi-objective optimization algorithm on the neural network, the optimal generation status of distributed generation sources, connection states of subnetworks to each other and to the main distribution network, optimal configuration of the distribution network, and other objective function indicators defined in Equations (31)–(36) are determined by the hierarchical control system. Figure 10 displays the power generation status of each source during a 24 h day. Additionally, Figure 11 and Figure 12 illustrate the connection and disconnection states of the subnetworks to the main distribution network and each other throughout the 24 h day, respectively. Finally, Figure 13 depicts the various states of the coupled switch breakers for determining the optimal configuration of the main distribution network.

Table 5. Comparison of the proposed method with other recent past methods over 24 h.

Consideration Statues	Operating Cost ($)	Power Losses (kW)	VD (pu)	EENS (kWh)	Load Ability Limit (kW)	Sum of SCL Changes (pu)
PM	27,557,510.4	10.46	5.0	50.07	2,079,887.87	0.007
[23,51]	31,956,594.76	13.34	5.45	334.91	24,750.58	0.23
[52]	29,165,841.21	11.34	6.28	448.51	31,252.61	0.12
[53,54]	243,116,712.42	-	-	-	-	-

presents the results of comparing the performance of the proposed method with previous methods on various economic, reliability, and network security indicators in the context of implementing the optimal energy management program during a 24 h study period. To ensure fairness and consistency, reliance was not placed on the optimal values reported in other papers. Instead, the methods from previous studies were re-implemented using our own setup, ensuring that the same objective functions, input parameters, and computational resources were uniformly applied across all methods. Our investigation aimed for equitable comparisons by focusing on a more intricate 118-bus distribution system that incorporated three microgrids. Although notable differences in system size and configuration existed, we meticulously accounted for all relevant complexities related to the distribution network and microgrid interconnections. Each method was allocated a fixed number of problem evaluations to control for variations in computational costs, allowing for a more accurate and meaningful comparison. All methods were tested on the same optimization problem, enabling a fair assessment of their effectiveness under similar conditions. This approach allowed for an objective comparison of each method’s strengths and weaknesses in a controlled, directly comparable environment.

As shown in Table 5, the proposed approach outperforms previous methods in various economic and technical network indicators despite considering reliability and network security indicators that were neglected in previous studies. The PM shows significant improvements over other methods in several key metrics. The PM is 3200% lower in the sum of SCL changes compared to [23,51] and 1700% lower than [52]. Regarding LAL, the PM is 98.8% higher than [23,51] and 98.5% higher than [52]. The EENS of PM is 568% lower than [23,51] and 797% lower than [52]. Moreover, the PM performs 9% better in VD than [23,51] and 25.6% better than [52]. The power losses of the PM are 27.6% lower than [23,51] and 8.4% higher than [52]. Lastly, the operating cost of the PM is 16% lower than [23,51], 5.9% lower than [52], and approximately 88.7% lower than [53,54].

The proposed approach utilizes the full potential of distributed control in the distribution network and intelligent MGs, such as different states of connection and disconnection between MGs and the main distribution network, to achieve optimal operation. For example, as observed in Figure 11, the energy storage installed in MG3 is charged during hours 5 and 7, resulting in the disconnection of MG3 from the main distribution network (Figure 12) and MG3 connection to MG1 and MG2 (Figure 13). This allows the energy stored in MG3 to be efficiently used to store the low-cost energy generated by other MGs. During these hours (Figure 11), the system operates under low-load conditions, and the energy obtained from the power company through the bus connected to the upper-level network is zero. Therefore, to ensure safe and economical network operation, the loads in MG should be supplied by local distributed generation.

Furthermore, the dynamic line between buses 104 and 105 is open during hours 5:00 and 7:00 (Figure 13), and the coupled line between buses 91 and 115 is closed. This arrangement allows the energy of loads near bus 117, from which MG3 has been disconnected during these hours, to be supplied through a shorter path, resulting in improved indices such as losses, short-circuit level, voltage deviation, and network capacity. While the load increases from 9:00, the energy storage of MG3 enters the discharging mode, and MG3 remains connected to the upper-level network to directly inject the energy generated by distributed sources into the network through bus 117, supplying the loads near it. The dynamic line between buses 104 and 105 is closed from 9:00–24:00 (Figure 11). Still, the coupled line between buses 91 and 115 is open, allowing it to power supply 117-bus loads as much as possible from MG3, which is closer to the loads, improving both technical and economic indices. In this regard, the switches between MG1 to MG3 are opened and closed at different hours (Figure 12), to facilitate the energy flow and power exchange that align with the objectives of the comprehensive energy management program.

Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19 illustrate the voltage profile, losses, production and operation costs, short-circuit level index, energy shortfall, and load profile variations during 24 h with and without considering the dynamic reconfiguration.

In Figure 14 and Figure 15, the voltage deviation and power losses exhibit lower values with dynamic reconfiguration capability in the distribution network considering the main grid and MGs. However, in the case of utilizing the dynamic reconfiguration capability of the network, other indicators such as reliability and short-circuit level are also taken into account, which introduces additional constraints in finding the optimal solution. On the other hand, as shown in Figure 15, the voltage deviation is higher only at 9:00 and 19:00 h with dynamic reconfiguration compared to without dynamic reconfiguration. This is due to the disconnection of MG1 and MG3 from the main grid and each other. Furthermore, in these hours, as depicted in Figure 14, the dynamic coupling lines (1) and (3) change their configuration to redirect power flow in a way that optimizes all the objective function indicators.

Figure 16 shows that the total operating cost of the network is lower with dynamic reconfiguration than without it, especially during peak consumption hours. One of the most critical indicators that should be considered in the optimal energy management planning of distribution networks is the short-circuit level variation index. This index is crucial because changes in the short-circuit level due to production and topology variations in the network can disrupt the protection system settings, leading to significant damages and costs to the system. As observed in Figure 17, the short-circuit level variation index approaches zero when considering the dynamic reconfiguration capability, which prevents disruptions in the protection system settings.

Figure 18 exhibits the reliability status of the network based on the EENS index for the network, which has a significantly lower value in all hours except for hour 19:00, which was discussed according to the loss’s indicator. However, in general, considering Table 5, it can be said that when utilizing the dynamic reconfiguration capability of the network, the total energy not supplied to the entire system has a much lower value compared to the case where the dynamic reconfiguration capability is not considered. By examining the load curve in Figure 19, it can be observed that in the case of utilizing the dynamic reconfiguration capability of the network, consumers have less tendency to reduce their consumption. This is because, with the reduction in operation and generation costs, consumers have less incentive to decrease their consumption. Therefore, since, as shown in Figure 16, the total costs of electricity generation and operation are lower in the proposed approach compared to conventional methods in all hours, consumers have less inclination to reduce their consumption.

7. Conclusions

Today, smart distribution microgrids consist of independent units that act as both consumers and generators, playing a significant role in economic efficiency and the safe operation of smart distribution networks. The dynamic capability of connecting and disconnecting these microgrid networks to each other and the upstream distribution network, along with the dynamic reconfiguration of the network, can transform these units into nodes of an intelligent network. A substantial portion of the energy is locally generated, and all generators and consumers are managed intelligently. Consequently, these networks are susceptible to various physical–cyber-attacks. If immediate action is not taken to mitigate the effects of these attacks, the network can incur irreparable damage. Hence, this article proposes a solution for optimal dynamic reconfiguration planning of the distribution network and the connected MGs based on LSTM neural networks. This solution, in addition to controlling resource generation, utilizes the control capabilities of the connection and disconnection states of the microgrid networks, along with the dynamic reconfiguration of the distribution network. By utilizing the capacity created in energy transfer and transformation paths within the network, it aims to reduce the damage caused by cyber-attacks while ensuring real-time operation. In this regard, when formulating the objective function in a comprehensive dynamic reconfiguration program for the network, it is necessary to consider not only economic indicators but also indicators of reliability and network security. Neglecting these indicators can sometimes overshadow all the benefits of optimal distribution generation. Therefore, the present paper provides a framework that incorporates not only economic indicators but also other reliability and security indicators, such as the EENS, load ability limit, and the absence of changes in the level of short-circuit connection, in the formulation of a multi-objective optimization algorithm for optimal management of dynamic reconfiguration. This ensures that concerns arising from expected energy not served and disruptions in protection settings are largely addressed during the economic operation of the distribution network and the connected MGs in the event of cyber-attacks. This can be achieved through the capabilities created in the connection and disconnection states of the microgrid networks, along with the dynamic reconfiguration. In this case, by comparing the results of the proposed method with previous methods, it is observed that despite considering reliability and security indicators in the formulation of the dynamic reconfiguration problem, the proposed method consistently shows significant improvements over previous studies in terms of both technical and economic indicators.