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Resilient energy management incorporating energy storage system and network reconfiguration: A framework of cyber‐physical system

Resilient energy management incorporating energy storage system and network reconfiguration: A... INTRODUCTIONThanks to the growing advancement of power systems information, communication technology, and the integration of distributed energy resources (DERs), modern smart grids can be described as complex cyber‐physical systems (CPSs). The CPSs for smart grids include integrating physical power systems and cyber communication grids such as power flow and information flow. Increasing smart equipment, load demand, and dependence on critical infrastructure have made these CPSs more vulnerable. However, cyber‐physical faults have always led to extensive damages and outages on electricity grids. In recent years, the number and severity of man‐made disasters and natural phenomena like hurricanes, floods, and earthquakes have increased. Considering the numerous consequences of power grids blackouts, the significance of such issues as CPS security and resilience to low‐probability, high‐impact events is completely felt [1, 2].The smart grid CPS resilience can also be defined as the ability of the system to adapt to disorder and quick recovery after that [2]. With a climate phenomenon, some network equipment is damaged, and the system will not supply all loads. Therefore, proper preparation of energy grids is vital for low‐probability, high‐impact events. Network vulnerability assessment and selection of damaged grid components are conducted either according to the fragility curve, and historical data [3] or are assessed based on the worst‐case scenario selection [4]. The risk assessment can be very reliable through the combination of these two methods. The authors in [5] seek to improve the network resilience to worst‐case scenarios depending on historical data. In [6], the worst‐case scenario is found for damaged electricity and gas system components for resilient network optimisation. Due to studies in [7], 43.6% of natural hazards that cause power outages are predictable. Consequently, CPSs can be prepared in advance to reduce the vulnerability of these physical disasters.Since the approximate time of some climate phenomena is predictable, the system's resilience can be increased by dividing into various islands and networked microgrids (MGs) [8]. The strategies such as network reconfiguration (NR) and MG formation as the preventive actions increase the system's responsiveness for rapid recovery and consciousness of these events. Considering the system vulnerability analysis before the hurricane in [9], the distribution system (DS) has been reconfigured as a preventive action for worst‐case faults. Due to NR being a quick and inexpensive measure, it can be performed as a preventive NR (PNR) before a severe fault occurs. The predicted faults information on the grid lines is transmitted to the system operator via the communication network. In such circumstances, CPS loads should be supplied based on priority and need to be managed in order to improve the technical and economic performance of the energy network. Another strategy to prevent low‐probability, high‐impact events, is the physical system hardening and the cyber system updating [10]. However, the expenditures of this preventative measure can be enormous. Likewise, the authors in [11] have analysed the resilience in smart grids and pointed out the importance of critical load supply through PNR and preventive DERs scheduling as cost‐effective strategies.Thanks to recent innovations in the reconstruction of power grids, DERs have a significant role in supplying system demands and energy management. DERs such as wind turbines (WTs), photovoltaics, distributed generators (DGs), and energy storage systems (ESSs) are among significant elements of MGs in enhancing the network's technical performance. In [5], a model has been proposed for optimal placement of renewable energy sources in the power system to reduce the load shedding, in which uncertainty of WTs and demand have been considered. Due to the power system uncertainties, some reliability problems, including voltage drop and sudden load change, occur in the network. ESSs can balance the uncertainties and reduce the energy pre‐scheduled fault factor [12]. The ESSs have the pre‐scheduled charge capability and act as a backup to reduce the load shedding cost by energy discharge in the power outages [13]. If ESSs are appropriately scheduled, their use will increase the CPS resilience and improve optimal energy management [14]. Cloud energy storage (CES) is a novel model based on ESSs power‐sharing. CES is a virtual facility linked to actual ESSs and is operated by a centralised operator [15]. ESS based on the cloud can be very effective in the energy management of CPSs and information exchange in the network [16]. In [17], the electrical system is planned considering CES services. The program is sent to the management system of each ESS at specified intervals. In [18], the predicted electricity demand and wind speed for an optimisation problem to day‐ahead energy management have been included. The proposed model in [19] characterises the day‐ahead energy schedule as a preventive action to improve the system's resilience.After a physical disaster and damage to the system, the DS divides into several islands. In this case, the load should be recovered to improve the CPS resilience by corrective actions [20]. In [21], a theory‐based graph mechanism for NR and system recovery is proposed. It also determines the optimal form of the islands to feed the unserved critical loads and minimise load shedding. The corrective NR (CNR) is one of the appropriate approaches to dealing with modern grid problems, which has received much attention due to the low costs in changing the network topology. CNR has been implemented in real‐time through heuristic methods to improve the network technical performance [22]. In [23], both cyber and physical NR are considered to enhance the CPS resilience, but the proposed model is without renewable energy sources. The authors in [24] have presented a method for energy management of DSs under the influence of CNR in the presence of various DERs such as WTs and ESSs. In [25], CNR and DERs are used to change the network configuration hourly to improve the system resilience, while PNR was not considered. The classification of studies in terms of energy management strategies for enhancing the resilience of CPSs is given in Table 1.1TABLEThe taxonomy of studies compared to the proposed PC‐REMS modelDescriptionReference number[2][3][5][7][8][9][13][20][21][23][24]This paperCyber‐physical system✓✓✓✓Vulnerability analysis✓✓✓✓Preventive‐corrective approach✓✓Time‐dependent✓✓✓✓✓✓✓✓✓✓Pre‐scheduled ESSs✓✓✓✓Preventive network reconfiguration✓✓Corrective network reconfiguration✓✓✓✓✓✓Resilience evaluation index✓✓✓✓✓The previous studies on power systems resilience have not referred to the cyber system section. Besides, most of them have not included vulnerability analysis and even are time‐independent. They generally focus on the resilience of the power grid after severe faults. There are also some studies relating to network preparation before disasters, which need considerable investment. In the reviewed references, NR models are mainly presented as a preventive or corrective measure instead of benefiting from both. Also, DERs have been used only for network recovery, while ESSs are pre‐schedulable. They have mainly used reliability indices such as the value of lost load for evaluating the proposed strategies to improve the system resilience. Nevertheless, the reliability and resilience concepts are different. The reliability criteria are considered for transient and minor faults, while the resilience criteria are used for significant and unexpected outages caused by cyber‐physical attacks.We found a two‐stage for resilient optimal energy management (PC‐REMS hereafter) to fill the mentioned gap by reviewing this area's research. This paper proposes a new preventive‐corrective perspective that considers effective strategies to achieve the significant smart grid CPS resilience. The first stage, preventive actions, focuses on ESSs pre‐scheduling and PNR according to vulnerability assessment and contingency outages. It means the preparation of the network topology and energy to predictable severe physical faults. Vulnerability analysis is applied based on the fragility curve to find damageable distribution lines before the hurricane. Using Monte Carlo simulation, the failure probability of network lines has been calculated. Due to the daily weather forecast, the network vulnerability information to the natural hazard is updated. This data is sent to the physical power system through the cloud‐based communication network. These preventive strategies are exerted to minimise the expected energy curtailment cost (EECC). The second stage as a corrective strategy involves the network recovery through CNR to minimise energy curtailment cost (ECC) after the actual hurricane. CNR strategy tries to restore the critical load demand while prioritising in real‐time. The proposed NR model is based on the master‐slave DG control framework so that each formed MG must have at least one DG as a master control unit. The resistance, recovery, and resilience indices have also evaluated the implemented strategies. The main contributions of the proposed PC‐REMS model are as follows:Developing the preventive‐corrective strategies for optimal energy management.Introducing new PNR and CNR to cope with physical disasters.Proposing the preventive strategies through pre‐scheduling of ESSs by the CES operator.Introducing the efficient resistance, recovery, and resilience indices for evaluating the CPS resilience.Coping with extreme natural disasters through smart grids’ cyber and physical coordination.The rest of this paper is organised as follows. Section 2 presents the smart grid CPS structure and the preventive‐corrective framework. Section 3 proposes the formulations of the PC‐REMS model. Simulation and numerical results are studied in Section 4. Section 5 concludes this article with the significant findings.PROPOSED FRAMEWORKThis section presents the cyber and physical coordination of the smart grid for optimal energy management and the explanation of the NR method and the proposed model.Coordination in CPSThe energy management capabilities increase in a cyber‐physical smart grid as a dynamic infrastructure with intelligent resource control. As shown in Figure 1, these grids can include integrating a power system with an information network. The physical system consists of a power system with load consumers and DERs. In contrast, the cyber system consists of a control centre and communication architecture that is embedded in the smart grid. CPSs may be attacked by physical disasters or cyber‐attacks on the infrastructure of information [23, 26]. The collected information is sent to the physical power system through the communication network. By hampering the data process, operators may receive misleading feedback, leading to a power system blackout. The proposed model focuses on physical disasters such as hurricanes on the network.1FIGUREThe cyber and physical components in a cyber‐physical power systemIn the cloud‐based communication network, the operator collects information about predicting sudden disasters, consumers’ behaviour, and energy production to have optimal planning for the next day. Also, based on the information gathered by the CES operator, an optimal charge and discharge program can be created for the ESSs to minimise operating costs.NR methodWhile the physical disaster event and damage happens in the DS, the grid divides into several islands. In the disconnected island's viewpoint from the upstream grid, loads are supplied through the available DERs on each island. However, due to the lack of power supply in some islands, there are no other convenient ways of commitment, and operators are compelled to use load shedding. In the NR, the operators use tie lines as an efficient measure to improve power system performance. The line switching should minimise the load curtailment while maintaining the radial network structure [27]. In this paper, a virtual network similar to the main system in connections and structure terms is assumed for NR. In the virtual network, one bus in each island is selected as the root bus, used as the energy source. Moreover, the rest of the buses have a unit load demand. To guarantee the radial grid structure, there must be a path from the root bus to the unit load at other buses on each island. Also, the number of closed lines must equal the total system buses minus the island's number [21].This paper presents an NR with a master‐slave DG control framework for resilient MG formation. In this framework, the frequency and voltage of the MG are set by only one DG as the master unit, while the other DGs as slave units follow the set frequency and voltage [28]. Thus, the MG formation is based on DGs location and damaged lines. That means each formed MG must have at least one DG as a master control unit. This NR model is utilised as a preventive‐corrective measure to minimise load shedding and network restoration, as shown in Figure 2.2FIGURENR example: (a) Initial grid after physical disasters, (b) post‐PNR state, (c) pre‐CNR state, (d) post‐CNR stateFigure 2a shows the initial DS without reconfiguration after the physical disaster. The network is divided into three islands that have to feed their loads. Load shedding is high in this case, so preventive and corrective actions must be taken. PNR is a preventative measure that changes the initial topology to cope with contingency faults. Figure 2b represents the post‐PNR state applied after detecting vulnerable lines. Technically, the vulnerable line switches are opened, and tie lines connect the islands.It should be noted that the damaged lines in real‐time may not be precisely the contingency lines. While the system, after the severe fault occurrence and in pre‐CNR state, has the lower load shedding because the tie lines (as robust lines) are connected rather than vulnerable lines. To prove this statement, Figure 2c and a can be compared, which the number of islands has decreased from 3 to 2 in real‐time. The system should now be reconfigured to reach an optimal operating point and the CPS recovery. Consequently, CNR is implemented to the system restoration as represented in Figure 2d.It should be noted that tie lines are used as support lines to provide critical loads in critical situations; they have high resistance and are not vulnerable to natural disasters [25, 27]. This means under any fault type, the resilience of DS is improved because, in the first stage, tie lines are connected instead of the vulnerable lines. Thus, the network is entirely ready for any fault in the second stage.The PC‐REMS modelThe proposed PC‐REMS model consists of two‐stage for optimal resilient energy management. The first and the second stage are related to the before and after the physical disaster, respectively. This model prepares the network for the predictable natural phenomena with the preventive practices and then recovers the damaged system with the corrective measures. Vulnerability analysis is performed daily and notified to the system operator through the communication network. The distribution lines that are most likely to be vulnerable are determined based on the atmospheric model and the fragility curve. The CPS is prepared for contingency physical disaster in the preventive stage through pre‐scheduled ESSs power based on the cloud and PNR. The objective of preventive actions is reducing network vulnerability and minimising the EECC. In the corrective phase, the vulnerability status of the CPS components is monitored after the hurricane. The information obtained from the lines outage in real‐time is immediately sent to the system operator for network recovery. The corrective action used in the second stage is CNR to optimal energy management and minimise ECC. The flowchart of the proposed preventive‐corrective model is given in Figure 3.3FIGUREFlowchart of the proposed PC‐REMS modelThe proposed sequential steps for implementing the PC‐REMS model are shown in Figure 4. The strategies standpoint to increase resilience can be divided into two groups of planning and operation. This means the resilient energy management in the CPS is done from two viewpoints of the system planner and operator. The vulnerability assessment and preventive strategies are categorised from the planning perspective. The network monitoring after the physical attack and its recovery are classified from the operational perspective.4FIGURETimeline diagram of the proposed PC‐REMS modelThus, in the two stages of prevention and correction, first, a massive load shedding is prevented, and then it will be easier to recover the interrupted loads. As shown in Figure 5a, in traditional power systems that do not have a cloud‐based communication network and cyber sector, the resilience curve consists of four parts: normal operation, disruption, preparation, and system recovery. After a physical disaster occurs and the performance index drops (tp), the personnel present at the site need to determine the outage location to restore the system, so it takes tr − tp time for the system to be prepared for recovery. While in the CPS, by applying the proposed PC‐REMS model, the level of performance index increases fromF(tr)$F({t_r})$toG(tr)$G({t_r})$(G(tr)>F(tr)$G({t_r}) &gt; F({t_r})$). Also, due to online network monitoring and fault detection, the preparation part is removed from the CPS conceptual resilience curve. Figure 5b illustrates that the smart grid CPS is recovered immediately after the severe fault, increasing network resilience. It should be noted that the recovery part includes two operations of CNR and repair of damaged lines.5FIGUREA conceptual resilience curve when a physical disaster occurs: (a) Traditional power systems, (b) CPS by applying the PC‐REMS modelPROBLEM FORMULATIONThis section introduces objective function, constraints, and the optimisation model details.Objective functionThe PC‐REMS model consists the two different strategies before and after the physical disaster. The operating grid aims to minimise the unserved load cost in the fault event. The objective function is formulated as follows:1OF=MinEECC;Preventive strategyECC;Corrective strategy$$\begin{equation}OF = {\rm{Min}}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {EECC;}&{{\text{Preventive strategy}}}\\[3pt] {ECC;}&{{\text{Corrective strategy}}} \end{array} } \right.\end{equation}$$The first part of the objective function minimises the EECC to cope with the predictable disaster, which is presented in Equation (2). As Equation (3), the second part minimises the ECC to recover the CPS after the fault occurs.2EECC=∑h∈ΩH∑i∈ΩBVOLLi.wi.EPi,hLS$$\begin{equation}EECC = \sum_{h \in {\Omega _{{\rm{ H}}}}} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {VOL{L_i}.{\rm{ }}{w_i}.{\rm{ }}EP_{i,h}^{LS}} } \end{equation}$$3ECC=∑h∈ΩH∑i∈ΩBVOLLi.wi.Pi,hLS$$\begin{equation}ECC = \sum_{h \in {\Omega _{{\rm{ H}}}}} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {VOL{L_i}.{\rm{ }}{w_i}.{\rm{ }}P_{i,h}^{LS}} } \end{equation}$$ConstraintsThe following sub‐sections include power flow constraints, DERs, load demand, voltage, line power, and network reconfiguration. It should be noted that all of the following constraints are related to the second stage, and the same constraints are used for the first stage, with the difference that all variables have an “expected” prefix (e.g., EPi,hLS$EP_{i,h}^{LS}$), and the CPS operation is based on the expected faults.Power flow constraintsThe problem power flow constraints in the DS are presented in Equations (4)–(10):4Pi,hsub+Pi,hWT+Pi,hDG+Pi,hLS+Pi,hdch−Pi,hch−Pi,hD=∑j∈ΩijiPij,h$$\begin{equation}P_{i,h}^{sub} + P_{i,h}^{WT} + P_{i,h}^{DG} + P_{i,h}^{LS} + P_{i,h}^{dch} - P_{i,h}^{ch} - P_{i,h}^D = \sum_{j \in \Omega _{{\rm{ }}ij}^i} {{P_{ij,h}}} \end{equation}$$5Qi,hsub+Qi,hWT+Qi,hDG+Qi,hLS−Qi,hD=∑j∈ΩijiQij,h$$\begin{equation}Q_{i,h}^{sub} + Q_{i,h}^{WT} + Q_{i,h}^{DG} + Q_{i,h}^{LS} - Q_{i,h}^D = \sum_{j \in \Omega _{{\rm{ }}ij}^i} {{Q_{ij,h}}} \end{equation}$$6Pij,h=Vi,h2Zijcos(φij)−Vi,hVj,hZijcos(θi,h−θj,h+φij)$$\begin{equation}{P_{ij,h}} = \frac{{V_{i,h}^2}}{{{{\rm{Z}}_{ij}}}}cos({\varphi _{ij}}) - \frac{{{V_{i,h}}{V_{j,h}}}}{{{{\rm{Z}}_{ij}}}}cos({\theta _{i,h}} - {\theta _{j,h}} + {\varphi _{ij}})\end{equation}$$7Qij,h=Vi,h2Zijsin(φij)−Vi,hVj,hZijsin(θi,h−θj,h+φij)−bVi,h22$$\begin{equation}{Q_{ij,h}} = \frac{{V_{i,h}^2}}{{{{\rm{Z}}_{ij}}}}\sin ({\varphi _{ij}}) - \frac{{{V_{i,h}}{V_{j,h}}}}{{{{\rm{Z}}_{ij}}}}\sin ({\theta _{i,h}} - {\theta _{j,h}} + {\varphi _{ij}}) - \frac{{bV_{i,h}^2}}{2}\end{equation}$$8Iij,h2=IRij,h2+IMij,h2$$\begin{equation}I_{ij,h}^2 = I_{{R_{ij}},h}^2 + I_{{M_{ij}},h}^2\end{equation}$$9IRij,h=Vi,hcos(θi,h−φij)−Vj,hcos(θj,h−φij)Zij−bVi,hsinθi,h2$$\begin{equation}{I_{{R_{ij}},h}} = \frac{{{V_{i,h}}\cos {\rm{(}}{\theta _{i,h}}\! - {\varphi _{ij}}{\rm{)}}\! - {V_{j,h}}cos{\rm{(}}{\theta _{j,h}}\! - {\varphi _{ij}}{\rm{)}}}}{{{{\rm{Z}}_{ij}}}}\! - \frac{{b{V_{i,h}}\sin {\theta _{i,h}}}}{2}\end{equation}$$10IMij,h=Vi,hsin(θi,h−φij)−Vj,hsin(θj,h−φij)Zij+bVi,hcosθi,h2$$\begin{equation}{I_{{M_{ij}},h}} = \frac{{{V_{i,h}}\sin {\rm{(}}{\theta _{i,h}}\! - {\varphi _{ij}}{\rm{)}}\! - {V_{j,h}}\sin {\rm{(}}{\theta _{j,h}}\! - {\varphi _{ij}}{\rm{)}}}}{{{Z_{ij}}}} +\! \frac{{b{V_{i,h}}\cos {\theta _{i,h}}}}{2}\end{equation}$$Equations (4) and (5) illustrate the balance of production and consumption of active and reactive power. The branches’ active and reactive power injections are given in Equations (6) and (7), respectively. Constraint (8) presents the branch current between bus i and j, which its active and reactive parts are obtained in Equations (9) and (10) [9].ESS constraintsThe EES charge and discharge equations and their constraints are modelled in Equations (11)–(15) [8]. Internal ESS partial discharge is omitted when not charging and discharging.11SoCi,h=SoCi,h−1+(Pi,hchηch−Pi,hdch/ηdch).Δh$$\begin{equation}So{C_{i,h}} = So{C_{i,h - 1}} + (P_{i,h}^{ch}{\eta _{ch}} - P_{i,h}^{dch}/{\eta _{dch}}).\Delta h\end{equation}$$12SoC̲≤SoCi,h≤SoC¯$$\begin{equation}\underline {SoC} \le So{C_{i,h}} \le \overline {SoC} \end{equation}$$130≤Pi,hch≤Pich¯(1−δi,h)$$\begin{equation}0 \le P_{i,h}^{ch} \le \overline {P_i^{ch}} (1 - \delta _{i,h})\end{equation}$$140≤Pi,hdch≤Pidch¯.δi,h$$\begin{equation}0 \le P_{i,h}^{dch} \le \overline {P_i^{dch}} .{\rm{ }}\delta _{i,h}\end{equation}$$15(Pi,hchηch−Pi,hdch/ηdch).Δh=SoCiReserve−SoCiInitial;ifh<hcritical−SoCiReserve+SoCi̲;ifh≥hcritical$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} (P_{i,h}^{ch}{\eta _{ch}} - P_{i,h}^{dch}/{\eta _{dch}})\\[6pt] \quad .\Delta h = {\rm{ }}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {SoC_i^{{\mathop{\rm Reserve}\nolimits} } - SoC_i^{Initial};}&{if{\rm{ h}} &lt; {h_{critical}}}\\[4pt] { - SoC_i^{{\mathop{\rm Reserve}\nolimits} } + \underline {So{C_i}} ;}&{if{\rm{ h}} \ge {h_{critical}}} \end{array} } \right. \end{array} \end{equation}$$where Δh$\Delta h$ represents the time interval, and its value is intended 1 h. The binary variable δi,h$\delta _{i,h}$ indicates the ESS charge and discharge status. The ESS's state of charge (SoC) is determined by (11), which is bounded by constraint (12). ESS charging and discharging power are limited by Equations (13) and (14). To control the repeated cycle of ESS's charge and discharge in the critical time (i.e., when the hurricane affects the physical DS), the stored energy at the beginning and end of each day is limited in constraint (15).DG and WT constraintsThe limitations of the active and reactive power of DGs and WTs are given in constraints (16), (17) and (18), (19), respectively [5].16PiDG̲≤Pi,hDG≤PiDG¯$$\begin{equation}\underline {P_i^{DG}} \le P_{i,h}^{DG} \le \overline {P_i^{DG}} \end{equation}$$17QiDG̲≤Qi,hDG≤QiDG¯$$\begin{equation}\underline {Q_i^{DG}} \le Q_{i,h}^{DG} \le \overline {Q_i^{DG}} \end{equation}$$180≤Pi,hWT≤Pi,hWT¯$$\begin{equation}0 \le P_{i,h}^{WT} \le \overline {P_{i,h}^{WT}} \end{equation}$$19Qi,hWT̲≤Qi,hWT≤Qi,hWT¯$$\begin{equation}\underline {Q_{i,h}^{WT}} \le Q_{i,h}^{WT} \le \overline {Q_{i,h}^{WT}} \end{equation}$$Lines power constraintsThe general connection or disconnection status of line ij is given by the binary variable qij${q_{ij}}$in Equation (20). The line's power capacity constraints are presented in Equations (21) and (22).20qij=υij.κij$$\begin{equation}{q_{ij}} = {\upsilon _{ij}}.{\rm{ }}{\kappa _{ij}}\end{equation}$$21Sij,h=(Vi,h∠θi,h)Iij,h∗$$\begin{equation}{S_{ij,h}} = ({V_{i,h}}\angle {\theta _{i,h}})I_{ij,h}^*\end{equation}$$22Sij̲.qij≤Sij,h≤Sij¯.qij$$\begin{equation}\underline {S_{ij}} .{\rm{ }}{q_{ij}} \le {S_{ij,h}} \le \overline {S_{ij}} .{\rm{ }}{q_{ij}}\end{equation}$$where the binary variable qij${q_{ij}}$ depends on the two binary variables υij${\upsilon _{ij}}$ and κij${\kappa _{ij}}$, which υij${\upsilon _{ij}}$ shows the lines damage status against the hurricane and κij${\kappa _{ij}}$ illustrates the line switching status during the NR. If line ij is damaged in the physical disaster υij=0${\upsilon _{ij}} = 0$, otherwise υij=1${\upsilon _{ij}} = 1$. Also, according to the NR, if line switch ij is disconnected κij=0${\kappa _{ij}} = 0$, otherwise κij=1.${\kappa _{ij}} = 1.$Voltage constraintThe problem voltage in bus i and time h is bounded as:23Vi̲≤Vi,h≤Vi¯$$\begin{equation}\underline {V_i} \le {V_{i,h}} \le \overline {V_i} \end{equation}$$Interrupted load constraintsAt the time of the disaster, if any load needs to be interrupted, it is clear that its value is equal to the amount of the main load. So the interrupted active and reactive load is limited by Equations (24) and (25) [9].24Pi,hLS=ai,h.Pi,hD$$\begin{equation}P_{i,h}^{LS} = {a_{i,h}}.P_{i,h}^D\end{equation}$$25Qi,hLS=ai,h.Qi,hD$$\begin{equation}Q_{i,h}^{LS} = {a_{i,h}}.Q_{i,h}^D\end{equation}$$The decision binary variableai,h${a_{i,h}}$indicates the unsupplied power of each load unit in the buses if there is sufficiently generated power to supply the bus load i ai,h=1${a_{i,h}} = 1$, otherwise ai,h=0${a_{i,h}} = 0$.Radiality constraintsDSs are operated radially, and to establish the radial condition of the network during operation, there must be no loops in the network that are modelled as follows:26∑(i,j)∈ΩBqij=Nb−∑i∈ΩBλi$$\begin{equation}\sum_{(i,j) \in {\Omega _{{\rm{ B}}}}} {{q_{ij}} = {N_b} - \sum_{i \in {\Omega _{{\rm{ B}}}}} {{\lambda _{{\rm{ }}i}}} } \end{equation}$$27∑j∈ΩijiYij≤M.λj+1$$\begin{equation}\sum_{j \in \Omega _{{\rm{ }}ij}^i} {{Y_{ij}} \le M.{\lambda _j} + 1} \end{equation}$$28−M.λj+1≤∑j∈ΩijiYij$$\begin{equation} - M.{\lambda _j} + 1 \le \sum_{j \in \Omega _{{\rm{ }}ij}^i} {{Y_{ij}}} \end{equation}$$29Yij=−Yji$$\begin{equation}{Y_{ij}} = - {Y_{ji}}\end{equation}$$30−M.qij≤Yij≤M.qij$$\begin{equation} - M.{q_{ij}} \le {Y_{ij}} \le M.{q_{ij}}\end{equation}$$Two conditions must be met to maintain the radial structure of DS [28]. The first condition is given in Equation (26). When the binary variable λi${\lambda _{{\rm{ }}i}}$is equal to 1, it indicates that bus i is selected as the root bus, and vice versa. The second condition is presented in constraints (27)–(29), which ensure that all the buses on the island are connected. The disconnection or connection state of virtual network lines is also expressed in constraint (30).Evaluation indicesTo evaluate CPSs performance from any perspective, indices must be calculated to describe that feature. The performance index can be the amount of load supplied or the number of healthy electrical equipment in the power grid. In the present paper, the following indicators have been used to evaluate the performance of the CPS against physical disasters.31Resistance=∑h∈T∑i∈ΩBwi.Pi,hD,Not-Intrrupted∑h∈T∑i∈ΩBwi.Pi,hD$$\begin{equation}{\rm{Resistance}} = \frac{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.} P_{i,h}^{D,{{\rm Not}\hbox{-}{\rm Intrrupted}}}} }}{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.P_{i,h}^D} } }}\end{equation}$$32Recovery=∑h∈T∑i∈ΩBwi.Pi,hD,Recovered∑h∈T∑i∈ΩBwi.Pi,hLS$$\begin{equation}{\rm{Recovery}} = \frac{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.} P_{i,h}^{D,{\rm{Recovered}}}} }}{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.P_{i,h}^{LS}} } }}\end{equation}$$33Resilience=∑h∈T∑i∈ΩBwi.Pi,hD,Not-Intrrupted+Pi,hD,Recovered∑h∈T∑i∈ΩBwi.Pi,hD$$\begin{equation}{\rm{Resilience}} = \frac{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {w_i}. \left({P_{i,h}^{D,{{\rm Not}\hbox{-}{\rm Intrrupted}}} + } P_{i,h}^{D,{\rm{Recovered}}}\right)} }}{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.P_{i,h}^D} } }}\end{equation}$$The resistance index is the ratio of the total not‐interrupted loads to the total network loads, which indicates the system's ability to resists the disaster and prevent its propagation based on Equation (31). The recovery index defined in (32) is obtained from the ratio of energy recovered from the interrupted loads to the total load curtailed during the study period. Also, the resilience index given in (33) is calculated from the ratio of the total loads supplied during the study period (i.e., full not‐interrupted loads and recovered loads) to the total network loads.NUMERICAL RESULTSIn this paper, the 33‐bus physical DS shown in Figure 6 is used to review the effect of the physical disaster and test the proposed PC‐REMS model on the CPS. This system consists of 32 sectionalising switches, five tie switches, and 32 load points. All switches can be controlled remotely by the cyber network. The base power and voltage of the system are 100 MVA and 12.66 kV, respectively. The active and reactive powers of the whole system are 3.715 MW and 2.3 MVAr, respectively. Also, the load value weights of buses 3, 5, 7, 9, 12, 14, 20, 22, 27, and 30 are considered 3, and the weight of other load buses is 1. The cost of load shedding in this system is estimated at $8/kWh.6FIGURE33‐bus radial physical DSAll DGs installed in the grid are controllable, and their maximum generating capacity is 0.4 MW, which are located at buses 10, 19, 23, and 30. The DGs installed at buses 19, 23, and 30 are capable of operating as a master unit, so the maximum number of the formable MGs will be 3. WTs are installed at buses 4, 17, and 27 with a maximum capacity of 0.6 MW. The estimated average wind speed of WT is shown in Figure 7. The ESSs are installed at buses 14, 25, and 32 with the size of 1 MWh and the discharge depth of 0.33. Their charge and discharge efficiencies are 95% and 90%, respectively.7FIGUREAverage wind speed per hour of the day [18]The network load demand for a sample day is presented in Figure 8. The electricity price in the upstream grid for purchasing power in the DS is given in [29].8FIGUREHourly load demand profile [29]The PDFs parameters for vulnerability analysis, the fragility curve of the DS components, and Monte Carlo simulation details are presented in [9]. The vulnerability results of the 32 DS lines in the order from the most resistant to the most vulnerable are shown in Figure 9.9FIGUREVulnerability colour spectrum of 33‐bus physical DS lines [9]The proposed optimisation model is mixed‐integer nonlinear programming (MINLP), which is simulated in general algebraic modelling system (GAMS) and solved by the BONMIN solver. The AD‐RP model has been executed in a PC with Intel Core i7 CPU @3.20 CPU and 4 GBs of RAM.Preventive strategyIn the first stage of the PC‐REMS model as a preventive measure, the CPS is prepared through pre‐scheduled ESSs power and PNR to deal with the predictable physical disaster. The operator qualifies the physical DS based on the vulnerability analysis result to minimise the EECC. To simulate the contingency hurricane, lines with greater vulnerability than the critical value are disconnected. Therefore, according to weather forecasts before the hurricane, the operator predicts that the fault occurs in lines 19, 12, 16, and 27, as shown in Figure 10. The probable time of disaster is 10 to 12 noon, and the repair team's reaction time to repair the damaged lines is considered three hours.10FIGURE33‐bus radial test system after the contingency hurricaneWhen the fault occurs, and the switches of four vulnerable lines are disconnected, the DS is divided into five islands. Part of the system still has access to the upstream grid, so no load shedding is expected. If the remaining four islands include DERs, the load curtailment will be prevented in proportion to the capacity of these resources; otherwise, the system will encounter forced load shedding. In this case, it is expected that 1.124, 1.181, and 1.106 MW load shedding will occur at hours 12, 13, and 14, respectively. The total load curtailment and the EECC will be 3.411 MWh and $27,288.Due to the predictability of the hurricane time, the operator must schedule the production resources available in the network to supply loads with minimum interruption. Thus, the CES operator takes preventive action and pre‐schedules the ESSs installed on buses 14, 25, and 32 for the interruption time to reduce load shedding. The scheduling for the ESSs should be such that sufficient power is available for discharging around the physical disaster time. As shown in Figure 11, the SoC of ESSs is fully charged before the probable hurricane time.11FIGURESoC of ESSs in pre‐scheduled modeBefore the hurricane, the operator opens the switches of four vulnerable lines that are expected to be damaged. Accordingly, the PNR is performed so that the EECC is minimised. Therefore, the network is configured by considering all the radial constraints, as shown in Figure 12. When the switches of tie lines are closed, lines switches 11 and 18 are opened. In this way, the system is prepared for the contingency hurricane and the second stage of the PC‐REMS model with a new configuration without any load shedding.12FIGUREOptimal PNR of 33‐bus radial test system after the contingency hurricaneCorrective strategyAfter preparing the CPS to probability hurricane, the operator performs optimal CNR to minimise the ECC and loads recovery in the second stage of the proposed model while the real hurricane occurrence. Given that the damaged lines caused by the actual hurricane may not be the same as the potentially vulnerable lines, the final status of the lines can be different from the predicted condition.In this section, corrective strategy is examined for two different cases of fault occurrence in the physical DS. In Case 1, lines 10, 16, 19, and 29 are damaged after the actual hurricane. Two of the mentioned damaged lines are among the lines with a high probability of vulnerability. In Case 2, lines 1, 16, 19, and 29 are assumed to be damaged. The severity of the hurricane and outages in Case 2 is higher than that in Case 1.Case 1After applying the preventive strategy in the previous stage, the system is prepared with a new configuration to cope with the real hurricane. The DS is divided into three islands when the hurricane occurs in Case 1. The network is reconfigured to system restoration and is turned into two islands. The system's final configuration after the actual hurricane until the damaged lines repair in Case 1 is shown in Figure 13. Total load shedding is 0.534 MWh, and 12.911 MWh of system loads are supplied, which reduces the ECC to $4.272. In this case, 0.187, 0.192, and 0.155 MW load interruption occurs at hours 12, 13, and 14, respectively. It should be noted that without applying the proposed PC‐REMS model in this case, 3.14 MWh load interruption occurs in the network, and the ECC would be $25,120, which $20,848 of this cost has been reduced by the preventive‐corrective measures.13FIGUREOptimal CNR of 33‐bus radial test system in Case1Case 2The CPS is prepared to deal with the contingency hurricane in the first stage, and the real hurricane occurs in the second stage. When branch 1–2 is damaged, the complete DS is separated from the upstream grid and operated as an island. After the hurricane occurs in Case 2, the system is divided into four islands. By implementing CNR to reduce the interrupted loads, 7.956 MWh of total system loads are fed at the severe fault time, and 5.489 MWh of system loads are interrupted. In this case, 1.824, 1.907, and 1.758 MW interruption of load occurs at hours 12, 13, and 14, respectively, and the total ECC will be $43,912. The system's final configuration after the actual hurricane until the repair of broken poles in DS lines in Case 2 is shown in Figure 14. If the hurricane had occurred in this case without applying the proposed preventive‐corrective measures, the ECC would have been $56,672, which would have saved $12,760 in cost by implementing the PC‐REMS model.14FIGUREOptimal CNR of 33‐bus radial test system in Case2The PC‐REMS model in Case 1 has recovered most of the interrupted loads, and the system has returned to normal operation. However, due to the higher severity of network vulnerability in Case 2, the proposed two‐stage model can recover 59% of interrupted loads. To show the efficiency of the proposed model, the results of the PC‐REMS model are compared with the presented model in [9]. It should be noted that the test system and DERs used in both articles are similar, and the results are compared under the same conditions. The difference between these two articles’ methods is in the preventive‐corrective strategies used. The proposed PC‐REMS model performs better in the optimal energy distribution between selected islands to reduce the ECC and network recovery. This comparison is illustrated based on the recovery index in Figure 15. By examining the sensitivity analysis in the following, the results and achievements of this research become more prominent.15FIGUREComparison of the proposed model results with the article [9]Sensitivity analysisThis section evaluates the effectiveness of DERs and NR in improving resilience and their limits and ability to recover loads. Sensitivity analysis of the CPS behaviour in the two different hurricane cases is investigated. Table 2 shows the resistance, recovery, and resilience indices for Case 1 and 2 at two different outage time duration. All tie line switches are used in the results of this table, and all DERs are operated at their maximum capacity. Due to the increase in the fault severity in Case 2, the indicator's values are smaller than those in Case 1. Also, the system evaluation indices decrease with the extension of the interruption time duration and increasing the ECC.2TABLEPerformance of the DS with increasing outage timeOutage time (T)Outage time (2T)Case 1Case 2Case 1Case 2ECC ($)4.27243.91213.09696.512Resistance0.6100.530Recovery0.890.590.860.52Resilience0.960.590.930.52The behaviour of DERs and power exchange with the upstream grid in Case 1 and Case 2 with 2T outage time duration are illustrated in Figure 16. The results indicate that even if the repair time of damaged lines is more extended, this proposed model can effectively improve system resilience. As shown in both cases, a significant amount of load is restored.16FIGUREBehaviour of DERs and power exchange with the main grid with 2T outage time duration in: (a) Cases 1, (b) Case 2In Table 3, for different capacities of the ESS installed in the system, the ECC and the resilience index are calculated for Case 2. It is clear that the greater capacity of ESS to store energy, the more the participation rates them in improving network resilience. By discharging energy at the disaster time, ESSs get the supporting role for critical loads considering the priority in load supply.3TABLEImpact of ESS capacity on the network performanceESS capacity (%)ECC ($)Resilience065.5520.392560.1360.445054.7360.497549.3360.5410043.9120.59To better observe the role of NR, DERs, and the effect of the proposed PC‐REMS model on improving resilience, six modes of different sizes of DERs and with/without tie lines in DS have been investigated. Table 4 shows the proposed two‐stage model performance for six different strategies in Case 1.4TABLEPerformance of the proposed PC‐REMS model in six different strategies for Case 1With tie and 100% DERsWith tie and 50% DERsWith tie and 0% DERsNo tie and 100% DERsNo tie and 50% DERsNo tie and 0% DERsECC ($)4.27213.28022.28829.36030.78441.840Resistance0.610.610.610.610.610.61Recovery0.890.680.460.290.260Resilience0.960.870.790.720.710.61According to the obtained results, network resilience can be improved to an acceptable level by using DERs and NR. Given that in Case 2, the severity of the network vulnerability is higher and the DS is completely disconnected from the upstream grid, the system resistance is zero. The performance of the proposed two‐stage model based on six different strategies in Case 2 is reviewed in Table 5. Due to the severity of the network vulnerability, in this case, NR alone cannot improve the system resilience without DERs to feed the interrupted loads. This means the role of tie lines in load recovery is diminished, and DERs play an essential role in load supply. Therefore, the superiority of the proposed PC‐REMS model in the presence of DERs in Case 2 compared to the bi‐level model presented in [9] is quite obvious.5TABLEPerformance of the proposed PC‐REMS model in six different strategies for Case 2With tie and 100% DERsWith tie and 50% DERsWith tie and 0% DERsNo tie and 100% DERsNo tie and 50% DERsNo tie and 0% DERsECC ($)43.91275.760107.56043.92075.728107.560Resistance000000Recovery0.590.2900.590.290Resilience0.590.2900.590.290Due to the vulnerability curve, the network lines are resistant to wind speeds below 50 m/s, which the system lines outage increases by rising wind speeds. The capability and importance of the proposed model for recovering interrupted loads at hurricane speeds above 50 m/s are pretty obvious and it reduce the ECC significantly. In Figure 17, the ECC and the evaluation indices are calculated to increase the wind speed and severity of system components’ vulnerability. It is clear that as the wind speed increases, the number of damaged lines increases, and the model performance in improving resilience will decrease slightly. The load recovery through line switching and NR will not cost much for the system operator, while it can be very efficient and economical. It is worth mentioning the intensity of line vulnerability at low speeds is lower than higher speeds, so NR is more useful in recovering interrupted loads. However, with the increasing severity of the system components damaged, the NR strategy alone cannot recover loads, so the role of DERs in supplying network loads will be much greater. The proposed PC‐REMS model using two supplements, DERs and NR, is very effective in improving the system resilience against weak and normal hurricanes. In severe hurricanes, it is needed to reduce the vulnerability of physical systems by hardening power grid infrastructure, which will be considered as a future research study of the authors.17FIGUREThe evaluation indices and the ECC relative to increased wind speedModel analysis in a large‐scale test systemTo further investigate and conclude from the proposed model, this section examines the impact of physical disasters on a larger CPS. The 118‐bus radial DS, including three feeders and 15 tie lines, is intended as a test system. The base power and voltage of the system are 100 MVA and 11 kV, respectively. This test system's total active and reactive power loads are 22.71 MW and 17.04 MVAr, respectively. Data related to line parameters and loads of the test system are given in [30]. The location of WTs, ESSs, and DGs are listed in Table 6, as well as the ability to perform as a master unit. The capacity of the DERs installed in the network is the same as their capacity in the 33‐bus test system.6TABLEThe location of DGs, WTs, and ESSs in the 118‐bus systemDG unitBusMaster unit capabilityWT unitBusESS unitBus17✓114112217227226324✓342340433453448543555572651✓674680759✓784790867✓8938106976✓99910881011011103✓1211313117After preparing the network and taking preventive actions, corrective measures are taken to recover the grid against the real hurricane. As shown in Figure 18, the 12 distribution lines are damaged by the physical disaster at 12 noon, and the network is expected to take at least 3 hours to repair. By applying the proposed PC‐REMS model for network restoration, the system is divided into 4 MGs. The load shedding at hours 12, 13, and 14 are 11.360, 11.880, and 10.972 MW, respectively, and the total ECC is $273,696. Without the PC‐REMS model, the ECC would have been $479,016. In other words, now $205,320 has been saved after network recovery and implementing the preventive‐corrective measures.18FIGURE118‐bus radial test system restoration by implementing the PC‐REMS modelAs mentioned above, both NR and DERs play an influential role in medium and weak physical disasters. For severe faults, because more switches are damaged, or access to the upstream grid is lost, DERs are more successful in supplying critical loads. When the DS is wholly disconnected from the upstream grid (such as Case 2), the role of NR in system recovery diminishes. This means that there will be no way to feed the loads without power limitation, so the system must be powered by optimal energy management of DERs. The performance of the proposed PC‐REMS model in six different strategies for the 118‐bus radial network is presented in Table 7. Since the 118‐bus test network consists of three feeders, and not all have been disconnected from the upstream grid after the real hurricane, line switching is very effective in network restoration. Due to the high severity of the physical disaster and the failure of 12 lines, DERs and NR can recover 50% of the interrupted loads and bring the resilience index to 0.58.7TABLEPerformance of the proposed PC‐REMS model in six different strategies for the 118‐bus radial physical DSWith tie and 100% DERsWith tie and 50% DERsWith tie and 0% DERsNo tie and 100% DERsNo tie and 50% DERsNo tie and 0% DERsECC ($)273,696344,176395,664435,840517,112599,672Resistance0.080.080.080.080.080.08Recovery0.500.390.310.250.120Resilience0.580.470.400.330.210.08DiscussionThe execution time for the 118‐bus radial test system and in Case 2 and Case 1 for the 33‐bus radial test system are 628, 252 and 174 s, respectively. The obtained execution times confirm the computational efficiency of the proposed model in large‐scale CPSs. However, the execution times have increased by raising the number of variables and problem constraints in the large‐scale test system and the severity of the disaster in the medium‐scale test system. It should be noted that based on the scale of the studied CPSs and the simultaneous consideration of different capabilities in the evaluation process, these execution times are pretty reasonable, and the proposed PC‐REMS model for use in real distribution networks is also applicable.The proposed model for both test systems has a compelling performance in improving the CPS resilience. The main findings of this paper based on the investigated cases are summarised as follows:The cyber system part, through online network monitoring and immediate decision, can improve the speed restoration of the physical system part.Optimal pre‐scheduling of ESSs is a critical part of preventive strategies to enhance system resilience.The PNR and CNR as two complementary approaches can be quite fruitful in boosting the CPS resilience.The NR play the most crucial role in a moderate disruption, while DERs are more critical in a severe disorder.The specialised indices used to analyse the model performance are much more effective than the reliability indicators.CONCLUSIONThis paper presented a preventive‐corrective optimisation model for improving the CPS resilience in the face of predictable physical disasters such as a hurricane. The distribution lines that are most likely to be damageable are determined based on the vulnerability assessment. The CPS is prepared for contingency faults in the preventive stage through pre‐scheduled ESSs power based on the cloud and PNR to minimise the EECC. In the corrective stage, the vulnerability status of the CPS components is monitored after the severe physical faults, and the information obtained in real‐time is immediately sent to the system operator for the network restoration. The corrective action used in the second stage is CNR to optimal energy management and minimise ECC. The effects of EESs and NR on resilience features are also examined through evaluation indices. The simulation results demonstrate the efficiency of the proposed PC‐REMS model in optimal energy management and improving the CPS resilience.In the future and the continuation of this research, the benefits of different strategies can be compared, and a compromise between the various resilience improvement strategies can be established by cost‐benefit analysis. Thus, future research could include the optimal distribution lines hardening and cost‐benefit analysis for affordable response to low‐probability, high‐impact events in CPSs.CONFLICT OF INTERESTThe 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.FUNDING INFORMATIONFunding information is not available for this article.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.NOMENCLATUREIndices and symbolshIndex of time periodsi,j$i,j$Index of system buses¯/̲$\overline {{\rm{ }}} /\underline {{\rm{ }}} $Upper and lower limits’ symbolsSetsΩBSet of system busesΩHSet of time periodsΩiji$\Omega _{{\rm{ }}ij}^i$Set of buses connected to bus iParametershcritical${h_{critical}}$Time of hurricane impact on the physical DSMLarge valueNb${N_b}$The number of system busesSoCiInitial/Reserve$SoC_i^{Initial{\rm{/}}{\mathop{\rm Reserve}\nolimits} }$Initial/reservation state of charge of the ESS in bus iPi,hD/Qi,hD$P_{i,h}^D{\rm{/}}Q_{i,h}^D$Active/reactive load demand of bus i at time hVOLLi$VOL{L_i}$Value of lost load in bus iwi${w_i}$Priority of the load weight at bus iZij/φij${{\rm{Z}}_{ij}}/{\varphi _{ij}}$Magnitude/angle of line impedance ijηch/dch${\eta _{ch/dch}}$Charging/discharging efficiency of ESSΔh$\Delta h$Time intervalsVariablesai,h${a_{i,h}}$Binary variable for unsupplied power state of each unit load at bus i and time hEECCExpected energy curtailment costECCEnergy curtailment costEPi,hLS$EP_{i,h}^{LS}$Expected active load shedding of bus i at time hIij,h$I_{ij,h}$Magnitude of line current ij at time hIRij,h/IMij,h$I_{{R_{ij}},h}{\rm{/}}I_{{M_{ij}},h}$Real/imaginary part of line current ij at time hPij,h/Qij,h${P_{ij,h}}{\rm{/}}{Q_{ij,h}}$Active/reactive power flow of line ij at time hPi,hch/dch$P_{i,h}^{ch/dch}$Charging/discharging ESS power of bus i at time hPi,hDG/Qi,hDG$P_{i,h}^{DG}{\rm{/}}Q_{i,h}^{DG}$Active/reactive power generated by DG of bus i at time hPi,hLS/Qi,hLS$P_{i,h}^{LS}{\rm{/}}Q_{i,h}^{LS}$Active/reactive load shedding of bus i at time hPi,hsub/Qi,hsub$P_{i,h}^{sub}{\rm{/}}Q_{i,h}^{sub}$Active/reactive power injection of substation to bus i at time hPi,hWT/Qi,hWT$P_{i,h}^{WT}{\rm{/}}Q_{i,h}^{WT}$Active/reactive power generated by WT of bus i at time hqij${q_{ij}}$Binary variable for final status of line connection ijSij,h${S_{ij,h}}$Apparent power flow of line ij at time hSoCi,h$So{C_{i,h}}$ESS's state of charge of bus i at time hTFault time intervalYij${Y_{ij}}$Power flow of line ij of virtual gridVi,h/θi,h${V_{i,h}}/{\theta _{i,h}}$Voltage magnitude/angle of bus i at time hδi,h$\delta _{i,h}$Binary variable for status of ESS charge and discharge of bus i at time hυij${\upsilon _{ij}}$Binary variable for status of line damage ij against physical disasterκij${\kappa _{ij}}$Binary variable for status of line switching ij during the NRλj${\lambda _j}$Binary variable to determine the root busAbbreviationsCESCloud energy storageCNRCorrective NRCPSCyber‐physical systemDERDistributed energy resourceDGDistributed generatorDSDistribution systemEECCExpected energy curtailment costECCEnergy curtailment costESSEnergy storage systemsGAMSGeneral algebraic modelling systemMGMicrogridMINLPMixed‐integer non‐linear programmingNRNetwork reconfigurationPC‐REMSPreventive‐corrective resilient energy management strategyPDFProbability density functionPNRPreventive NRSoCState of chargeWTWind turbineREFERENCESHaque, M.A., Shetty, S., Gold, K., Krishnappa, B.: Realising cyber‐physical systems resilience frameworks and security practices. 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Resilient energy management incorporating energy storage system and network reconfiguration: A framework of cyber‐physical system

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© 2023 The Institution of Engineering and Technology.
eISSN
1751-8695
DOI
10.1049/gtd2.12478
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Abstract

INTRODUCTIONThanks to the growing advancement of power systems information, communication technology, and the integration of distributed energy resources (DERs), modern smart grids can be described as complex cyber‐physical systems (CPSs). The CPSs for smart grids include integrating physical power systems and cyber communication grids such as power flow and information flow. Increasing smart equipment, load demand, and dependence on critical infrastructure have made these CPSs more vulnerable. However, cyber‐physical faults have always led to extensive damages and outages on electricity grids. In recent years, the number and severity of man‐made disasters and natural phenomena like hurricanes, floods, and earthquakes have increased. Considering the numerous consequences of power grids blackouts, the significance of such issues as CPS security and resilience to low‐probability, high‐impact events is completely felt [1, 2].The smart grid CPS resilience can also be defined as the ability of the system to adapt to disorder and quick recovery after that [2]. With a climate phenomenon, some network equipment is damaged, and the system will not supply all loads. Therefore, proper preparation of energy grids is vital for low‐probability, high‐impact events. Network vulnerability assessment and selection of damaged grid components are conducted either according to the fragility curve, and historical data [3] or are assessed based on the worst‐case scenario selection [4]. The risk assessment can be very reliable through the combination of these two methods. The authors in [5] seek to improve the network resilience to worst‐case scenarios depending on historical data. In [6], the worst‐case scenario is found for damaged electricity and gas system components for resilient network optimisation. Due to studies in [7], 43.6% of natural hazards that cause power outages are predictable. Consequently, CPSs can be prepared in advance to reduce the vulnerability of these physical disasters.Since the approximate time of some climate phenomena is predictable, the system's resilience can be increased by dividing into various islands and networked microgrids (MGs) [8]. The strategies such as network reconfiguration (NR) and MG formation as the preventive actions increase the system's responsiveness for rapid recovery and consciousness of these events. Considering the system vulnerability analysis before the hurricane in [9], the distribution system (DS) has been reconfigured as a preventive action for worst‐case faults. Due to NR being a quick and inexpensive measure, it can be performed as a preventive NR (PNR) before a severe fault occurs. The predicted faults information on the grid lines is transmitted to the system operator via the communication network. In such circumstances, CPS loads should be supplied based on priority and need to be managed in order to improve the technical and economic performance of the energy network. Another strategy to prevent low‐probability, high‐impact events, is the physical system hardening and the cyber system updating [10]. However, the expenditures of this preventative measure can be enormous. Likewise, the authors in [11] have analysed the resilience in smart grids and pointed out the importance of critical load supply through PNR and preventive DERs scheduling as cost‐effective strategies.Thanks to recent innovations in the reconstruction of power grids, DERs have a significant role in supplying system demands and energy management. DERs such as wind turbines (WTs), photovoltaics, distributed generators (DGs), and energy storage systems (ESSs) are among significant elements of MGs in enhancing the network's technical performance. In [5], a model has been proposed for optimal placement of renewable energy sources in the power system to reduce the load shedding, in which uncertainty of WTs and demand have been considered. Due to the power system uncertainties, some reliability problems, including voltage drop and sudden load change, occur in the network. ESSs can balance the uncertainties and reduce the energy pre‐scheduled fault factor [12]. The ESSs have the pre‐scheduled charge capability and act as a backup to reduce the load shedding cost by energy discharge in the power outages [13]. If ESSs are appropriately scheduled, their use will increase the CPS resilience and improve optimal energy management [14]. Cloud energy storage (CES) is a novel model based on ESSs power‐sharing. CES is a virtual facility linked to actual ESSs and is operated by a centralised operator [15]. ESS based on the cloud can be very effective in the energy management of CPSs and information exchange in the network [16]. In [17], the electrical system is planned considering CES services. The program is sent to the management system of each ESS at specified intervals. In [18], the predicted electricity demand and wind speed for an optimisation problem to day‐ahead energy management have been included. The proposed model in [19] characterises the day‐ahead energy schedule as a preventive action to improve the system's resilience.After a physical disaster and damage to the system, the DS divides into several islands. In this case, the load should be recovered to improve the CPS resilience by corrective actions [20]. In [21], a theory‐based graph mechanism for NR and system recovery is proposed. It also determines the optimal form of the islands to feed the unserved critical loads and minimise load shedding. The corrective NR (CNR) is one of the appropriate approaches to dealing with modern grid problems, which has received much attention due to the low costs in changing the network topology. CNR has been implemented in real‐time through heuristic methods to improve the network technical performance [22]. In [23], both cyber and physical NR are considered to enhance the CPS resilience, but the proposed model is without renewable energy sources. The authors in [24] have presented a method for energy management of DSs under the influence of CNR in the presence of various DERs such as WTs and ESSs. In [25], CNR and DERs are used to change the network configuration hourly to improve the system resilience, while PNR was not considered. The classification of studies in terms of energy management strategies for enhancing the resilience of CPSs is given in Table 1.1TABLEThe taxonomy of studies compared to the proposed PC‐REMS modelDescriptionReference number[2][3][5][7][8][9][13][20][21][23][24]This paperCyber‐physical system✓✓✓✓Vulnerability analysis✓✓✓✓Preventive‐corrective approach✓✓Time‐dependent✓✓✓✓✓✓✓✓✓✓Pre‐scheduled ESSs✓✓✓✓Preventive network reconfiguration✓✓Corrective network reconfiguration✓✓✓✓✓✓Resilience evaluation index✓✓✓✓✓The previous studies on power systems resilience have not referred to the cyber system section. Besides, most of them have not included vulnerability analysis and even are time‐independent. They generally focus on the resilience of the power grid after severe faults. There are also some studies relating to network preparation before disasters, which need considerable investment. In the reviewed references, NR models are mainly presented as a preventive or corrective measure instead of benefiting from both. Also, DERs have been used only for network recovery, while ESSs are pre‐schedulable. They have mainly used reliability indices such as the value of lost load for evaluating the proposed strategies to improve the system resilience. Nevertheless, the reliability and resilience concepts are different. The reliability criteria are considered for transient and minor faults, while the resilience criteria are used for significant and unexpected outages caused by cyber‐physical attacks.We found a two‐stage for resilient optimal energy management (PC‐REMS hereafter) to fill the mentioned gap by reviewing this area's research. This paper proposes a new preventive‐corrective perspective that considers effective strategies to achieve the significant smart grid CPS resilience. The first stage, preventive actions, focuses on ESSs pre‐scheduling and PNR according to vulnerability assessment and contingency outages. It means the preparation of the network topology and energy to predictable severe physical faults. Vulnerability analysis is applied based on the fragility curve to find damageable distribution lines before the hurricane. Using Monte Carlo simulation, the failure probability of network lines has been calculated. Due to the daily weather forecast, the network vulnerability information to the natural hazard is updated. This data is sent to the physical power system through the cloud‐based communication network. These preventive strategies are exerted to minimise the expected energy curtailment cost (EECC). The second stage as a corrective strategy involves the network recovery through CNR to minimise energy curtailment cost (ECC) after the actual hurricane. CNR strategy tries to restore the critical load demand while prioritising in real‐time. The proposed NR model is based on the master‐slave DG control framework so that each formed MG must have at least one DG as a master control unit. The resistance, recovery, and resilience indices have also evaluated the implemented strategies. The main contributions of the proposed PC‐REMS model are as follows:Developing the preventive‐corrective strategies for optimal energy management.Introducing new PNR and CNR to cope with physical disasters.Proposing the preventive strategies through pre‐scheduling of ESSs by the CES operator.Introducing the efficient resistance, recovery, and resilience indices for evaluating the CPS resilience.Coping with extreme natural disasters through smart grids’ cyber and physical coordination.The rest of this paper is organised as follows. Section 2 presents the smart grid CPS structure and the preventive‐corrective framework. Section 3 proposes the formulations of the PC‐REMS model. Simulation and numerical results are studied in Section 4. Section 5 concludes this article with the significant findings.PROPOSED FRAMEWORKThis section presents the cyber and physical coordination of the smart grid for optimal energy management and the explanation of the NR method and the proposed model.Coordination in CPSThe energy management capabilities increase in a cyber‐physical smart grid as a dynamic infrastructure with intelligent resource control. As shown in Figure 1, these grids can include integrating a power system with an information network. The physical system consists of a power system with load consumers and DERs. In contrast, the cyber system consists of a control centre and communication architecture that is embedded in the smart grid. CPSs may be attacked by physical disasters or cyber‐attacks on the infrastructure of information [23, 26]. The collected information is sent to the physical power system through the communication network. By hampering the data process, operators may receive misleading feedback, leading to a power system blackout. The proposed model focuses on physical disasters such as hurricanes on the network.1FIGUREThe cyber and physical components in a cyber‐physical power systemIn the cloud‐based communication network, the operator collects information about predicting sudden disasters, consumers’ behaviour, and energy production to have optimal planning for the next day. Also, based on the information gathered by the CES operator, an optimal charge and discharge program can be created for the ESSs to minimise operating costs.NR methodWhile the physical disaster event and damage happens in the DS, the grid divides into several islands. In the disconnected island's viewpoint from the upstream grid, loads are supplied through the available DERs on each island. However, due to the lack of power supply in some islands, there are no other convenient ways of commitment, and operators are compelled to use load shedding. In the NR, the operators use tie lines as an efficient measure to improve power system performance. The line switching should minimise the load curtailment while maintaining the radial network structure [27]. In this paper, a virtual network similar to the main system in connections and structure terms is assumed for NR. In the virtual network, one bus in each island is selected as the root bus, used as the energy source. Moreover, the rest of the buses have a unit load demand. To guarantee the radial grid structure, there must be a path from the root bus to the unit load at other buses on each island. Also, the number of closed lines must equal the total system buses minus the island's number [21].This paper presents an NR with a master‐slave DG control framework for resilient MG formation. In this framework, the frequency and voltage of the MG are set by only one DG as the master unit, while the other DGs as slave units follow the set frequency and voltage [28]. Thus, the MG formation is based on DGs location and damaged lines. That means each formed MG must have at least one DG as a master control unit. This NR model is utilised as a preventive‐corrective measure to minimise load shedding and network restoration, as shown in Figure 2.2FIGURENR example: (a) Initial grid after physical disasters, (b) post‐PNR state, (c) pre‐CNR state, (d) post‐CNR stateFigure 2a shows the initial DS without reconfiguration after the physical disaster. The network is divided into three islands that have to feed their loads. Load shedding is high in this case, so preventive and corrective actions must be taken. PNR is a preventative measure that changes the initial topology to cope with contingency faults. Figure 2b represents the post‐PNR state applied after detecting vulnerable lines. Technically, the vulnerable line switches are opened, and tie lines connect the islands.It should be noted that the damaged lines in real‐time may not be precisely the contingency lines. While the system, after the severe fault occurrence and in pre‐CNR state, has the lower load shedding because the tie lines (as robust lines) are connected rather than vulnerable lines. To prove this statement, Figure 2c and a can be compared, which the number of islands has decreased from 3 to 2 in real‐time. The system should now be reconfigured to reach an optimal operating point and the CPS recovery. Consequently, CNR is implemented to the system restoration as represented in Figure 2d.It should be noted that tie lines are used as support lines to provide critical loads in critical situations; they have high resistance and are not vulnerable to natural disasters [25, 27]. This means under any fault type, the resilience of DS is improved because, in the first stage, tie lines are connected instead of the vulnerable lines. Thus, the network is entirely ready for any fault in the second stage.The PC‐REMS modelThe proposed PC‐REMS model consists of two‐stage for optimal resilient energy management. The first and the second stage are related to the before and after the physical disaster, respectively. This model prepares the network for the predictable natural phenomena with the preventive practices and then recovers the damaged system with the corrective measures. Vulnerability analysis is performed daily and notified to the system operator through the communication network. The distribution lines that are most likely to be vulnerable are determined based on the atmospheric model and the fragility curve. The CPS is prepared for contingency physical disaster in the preventive stage through pre‐scheduled ESSs power based on the cloud and PNR. The objective of preventive actions is reducing network vulnerability and minimising the EECC. In the corrective phase, the vulnerability status of the CPS components is monitored after the hurricane. The information obtained from the lines outage in real‐time is immediately sent to the system operator for network recovery. The corrective action used in the second stage is CNR to optimal energy management and minimise ECC. The flowchart of the proposed preventive‐corrective model is given in Figure 3.3FIGUREFlowchart of the proposed PC‐REMS modelThe proposed sequential steps for implementing the PC‐REMS model are shown in Figure 4. The strategies standpoint to increase resilience can be divided into two groups of planning and operation. This means the resilient energy management in the CPS is done from two viewpoints of the system planner and operator. The vulnerability assessment and preventive strategies are categorised from the planning perspective. The network monitoring after the physical attack and its recovery are classified from the operational perspective.4FIGURETimeline diagram of the proposed PC‐REMS modelThus, in the two stages of prevention and correction, first, a massive load shedding is prevented, and then it will be easier to recover the interrupted loads. As shown in Figure 5a, in traditional power systems that do not have a cloud‐based communication network and cyber sector, the resilience curve consists of four parts: normal operation, disruption, preparation, and system recovery. After a physical disaster occurs and the performance index drops (tp), the personnel present at the site need to determine the outage location to restore the system, so it takes tr − tp time for the system to be prepared for recovery. While in the CPS, by applying the proposed PC‐REMS model, the level of performance index increases fromF(tr)$F({t_r})$toG(tr)$G({t_r})$(G(tr)>F(tr)$G({t_r}) &gt; F({t_r})$). Also, due to online network monitoring and fault detection, the preparation part is removed from the CPS conceptual resilience curve. Figure 5b illustrates that the smart grid CPS is recovered immediately after the severe fault, increasing network resilience. It should be noted that the recovery part includes two operations of CNR and repair of damaged lines.5FIGUREA conceptual resilience curve when a physical disaster occurs: (a) Traditional power systems, (b) CPS by applying the PC‐REMS modelPROBLEM FORMULATIONThis section introduces objective function, constraints, and the optimisation model details.Objective functionThe PC‐REMS model consists the two different strategies before and after the physical disaster. The operating grid aims to minimise the unserved load cost in the fault event. The objective function is formulated as follows:1OF=MinEECC;Preventive strategyECC;Corrective strategy$$\begin{equation}OF = {\rm{Min}}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {EECC;}&{{\text{Preventive strategy}}}\\[3pt] {ECC;}&{{\text{Corrective strategy}}} \end{array} } \right.\end{equation}$$The first part of the objective function minimises the EECC to cope with the predictable disaster, which is presented in Equation (2). As Equation (3), the second part minimises the ECC to recover the CPS after the fault occurs.2EECC=∑h∈ΩH∑i∈ΩBVOLLi.wi.EPi,hLS$$\begin{equation}EECC = \sum_{h \in {\Omega _{{\rm{ H}}}}} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {VOL{L_i}.{\rm{ }}{w_i}.{\rm{ }}EP_{i,h}^{LS}} } \end{equation}$$3ECC=∑h∈ΩH∑i∈ΩBVOLLi.wi.Pi,hLS$$\begin{equation}ECC = \sum_{h \in {\Omega _{{\rm{ H}}}}} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {VOL{L_i}.{\rm{ }}{w_i}.{\rm{ }}P_{i,h}^{LS}} } \end{equation}$$ConstraintsThe following sub‐sections include power flow constraints, DERs, load demand, voltage, line power, and network reconfiguration. It should be noted that all of the following constraints are related to the second stage, and the same constraints are used for the first stage, with the difference that all variables have an “expected” prefix (e.g., EPi,hLS$EP_{i,h}^{LS}$), and the CPS operation is based on the expected faults.Power flow constraintsThe problem power flow constraints in the DS are presented in Equations (4)–(10):4Pi,hsub+Pi,hWT+Pi,hDG+Pi,hLS+Pi,hdch−Pi,hch−Pi,hD=∑j∈ΩijiPij,h$$\begin{equation}P_{i,h}^{sub} + P_{i,h}^{WT} + P_{i,h}^{DG} + P_{i,h}^{LS} + P_{i,h}^{dch} - P_{i,h}^{ch} - P_{i,h}^D = \sum_{j \in \Omega _{{\rm{ }}ij}^i} {{P_{ij,h}}} \end{equation}$$5Qi,hsub+Qi,hWT+Qi,hDG+Qi,hLS−Qi,hD=∑j∈ΩijiQij,h$$\begin{equation}Q_{i,h}^{sub} + Q_{i,h}^{WT} + Q_{i,h}^{DG} + Q_{i,h}^{LS} - Q_{i,h}^D = \sum_{j \in \Omega _{{\rm{ }}ij}^i} {{Q_{ij,h}}} \end{equation}$$6Pij,h=Vi,h2Zijcos(φij)−Vi,hVj,hZijcos(θi,h−θj,h+φij)$$\begin{equation}{P_{ij,h}} = \frac{{V_{i,h}^2}}{{{{\rm{Z}}_{ij}}}}cos({\varphi _{ij}}) - \frac{{{V_{i,h}}{V_{j,h}}}}{{{{\rm{Z}}_{ij}}}}cos({\theta _{i,h}} - {\theta _{j,h}} + {\varphi _{ij}})\end{equation}$$7Qij,h=Vi,h2Zijsin(φij)−Vi,hVj,hZijsin(θi,h−θj,h+φij)−bVi,h22$$\begin{equation}{Q_{ij,h}} = \frac{{V_{i,h}^2}}{{{{\rm{Z}}_{ij}}}}\sin ({\varphi _{ij}}) - \frac{{{V_{i,h}}{V_{j,h}}}}{{{{\rm{Z}}_{ij}}}}\sin ({\theta _{i,h}} - {\theta _{j,h}} + {\varphi _{ij}}) - \frac{{bV_{i,h}^2}}{2}\end{equation}$$8Iij,h2=IRij,h2+IMij,h2$$\begin{equation}I_{ij,h}^2 = I_{{R_{ij}},h}^2 + I_{{M_{ij}},h}^2\end{equation}$$9IRij,h=Vi,hcos(θi,h−φij)−Vj,hcos(θj,h−φij)Zij−bVi,hsinθi,h2$$\begin{equation}{I_{{R_{ij}},h}} = \frac{{{V_{i,h}}\cos {\rm{(}}{\theta _{i,h}}\! - {\varphi _{ij}}{\rm{)}}\! - {V_{j,h}}cos{\rm{(}}{\theta _{j,h}}\! - {\varphi _{ij}}{\rm{)}}}}{{{{\rm{Z}}_{ij}}}}\! - \frac{{b{V_{i,h}}\sin {\theta _{i,h}}}}{2}\end{equation}$$10IMij,h=Vi,hsin(θi,h−φij)−Vj,hsin(θj,h−φij)Zij+bVi,hcosθi,h2$$\begin{equation}{I_{{M_{ij}},h}} = \frac{{{V_{i,h}}\sin {\rm{(}}{\theta _{i,h}}\! - {\varphi _{ij}}{\rm{)}}\! - {V_{j,h}}\sin {\rm{(}}{\theta _{j,h}}\! - {\varphi _{ij}}{\rm{)}}}}{{{Z_{ij}}}} +\! \frac{{b{V_{i,h}}\cos {\theta _{i,h}}}}{2}\end{equation}$$Equations (4) and (5) illustrate the balance of production and consumption of active and reactive power. The branches’ active and reactive power injections are given in Equations (6) and (7), respectively. Constraint (8) presents the branch current between bus i and j, which its active and reactive parts are obtained in Equations (9) and (10) [9].ESS constraintsThe EES charge and discharge equations and their constraints are modelled in Equations (11)–(15) [8]. Internal ESS partial discharge is omitted when not charging and discharging.11SoCi,h=SoCi,h−1+(Pi,hchηch−Pi,hdch/ηdch).Δh$$\begin{equation}So{C_{i,h}} = So{C_{i,h - 1}} + (P_{i,h}^{ch}{\eta _{ch}} - P_{i,h}^{dch}/{\eta _{dch}}).\Delta h\end{equation}$$12SoC̲≤SoCi,h≤SoC¯$$\begin{equation}\underline {SoC} \le So{C_{i,h}} \le \overline {SoC} \end{equation}$$130≤Pi,hch≤Pich¯(1−δi,h)$$\begin{equation}0 \le P_{i,h}^{ch} \le \overline {P_i^{ch}} (1 - \delta _{i,h})\end{equation}$$140≤Pi,hdch≤Pidch¯.δi,h$$\begin{equation}0 \le P_{i,h}^{dch} \le \overline {P_i^{dch}} .{\rm{ }}\delta _{i,h}\end{equation}$$15(Pi,hchηch−Pi,hdch/ηdch).Δh=SoCiReserve−SoCiInitial;ifh<hcritical−SoCiReserve+SoCi̲;ifh≥hcritical$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} (P_{i,h}^{ch}{\eta _{ch}} - P_{i,h}^{dch}/{\eta _{dch}})\\[6pt] \quad .\Delta h = {\rm{ }}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {SoC_i^{{\mathop{\rm Reserve}\nolimits} } - SoC_i^{Initial};}&{if{\rm{ h}} &lt; {h_{critical}}}\\[4pt] { - SoC_i^{{\mathop{\rm Reserve}\nolimits} } + \underline {So{C_i}} ;}&{if{\rm{ h}} \ge {h_{critical}}} \end{array} } \right. \end{array} \end{equation}$$where Δh$\Delta h$ represents the time interval, and its value is intended 1 h. The binary variable δi,h$\delta _{i,h}$ indicates the ESS charge and discharge status. The ESS's state of charge (SoC) is determined by (11), which is bounded by constraint (12). ESS charging and discharging power are limited by Equations (13) and (14). To control the repeated cycle of ESS's charge and discharge in the critical time (i.e., when the hurricane affects the physical DS), the stored energy at the beginning and end of each day is limited in constraint (15).DG and WT constraintsThe limitations of the active and reactive power of DGs and WTs are given in constraints (16), (17) and (18), (19), respectively [5].16PiDG̲≤Pi,hDG≤PiDG¯$$\begin{equation}\underline {P_i^{DG}} \le P_{i,h}^{DG} \le \overline {P_i^{DG}} \end{equation}$$17QiDG̲≤Qi,hDG≤QiDG¯$$\begin{equation}\underline {Q_i^{DG}} \le Q_{i,h}^{DG} \le \overline {Q_i^{DG}} \end{equation}$$180≤Pi,hWT≤Pi,hWT¯$$\begin{equation}0 \le P_{i,h}^{WT} \le \overline {P_{i,h}^{WT}} \end{equation}$$19Qi,hWT̲≤Qi,hWT≤Qi,hWT¯$$\begin{equation}\underline {Q_{i,h}^{WT}} \le Q_{i,h}^{WT} \le \overline {Q_{i,h}^{WT}} \end{equation}$$Lines power constraintsThe general connection or disconnection status of line ij is given by the binary variable qij${q_{ij}}$in Equation (20). The line's power capacity constraints are presented in Equations (21) and (22).20qij=υij.κij$$\begin{equation}{q_{ij}} = {\upsilon _{ij}}.{\rm{ }}{\kappa _{ij}}\end{equation}$$21Sij,h=(Vi,h∠θi,h)Iij,h∗$$\begin{equation}{S_{ij,h}} = ({V_{i,h}}\angle {\theta _{i,h}})I_{ij,h}^*\end{equation}$$22Sij̲.qij≤Sij,h≤Sij¯.qij$$\begin{equation}\underline {S_{ij}} .{\rm{ }}{q_{ij}} \le {S_{ij,h}} \le \overline {S_{ij}} .{\rm{ }}{q_{ij}}\end{equation}$$where the binary variable qij${q_{ij}}$ depends on the two binary variables υij${\upsilon _{ij}}$ and κij${\kappa _{ij}}$, which υij${\upsilon _{ij}}$ shows the lines damage status against the hurricane and κij${\kappa _{ij}}$ illustrates the line switching status during the NR. If line ij is damaged in the physical disaster υij=0${\upsilon _{ij}} = 0$, otherwise υij=1${\upsilon _{ij}} = 1$. Also, according to the NR, if line switch ij is disconnected κij=0${\kappa _{ij}} = 0$, otherwise κij=1.${\kappa _{ij}} = 1.$Voltage constraintThe problem voltage in bus i and time h is bounded as:23Vi̲≤Vi,h≤Vi¯$$\begin{equation}\underline {V_i} \le {V_{i,h}} \le \overline {V_i} \end{equation}$$Interrupted load constraintsAt the time of the disaster, if any load needs to be interrupted, it is clear that its value is equal to the amount of the main load. So the interrupted active and reactive load is limited by Equations (24) and (25) [9].24Pi,hLS=ai,h.Pi,hD$$\begin{equation}P_{i,h}^{LS} = {a_{i,h}}.P_{i,h}^D\end{equation}$$25Qi,hLS=ai,h.Qi,hD$$\begin{equation}Q_{i,h}^{LS} = {a_{i,h}}.Q_{i,h}^D\end{equation}$$The decision binary variableai,h${a_{i,h}}$indicates the unsupplied power of each load unit in the buses if there is sufficiently generated power to supply the bus load i ai,h=1${a_{i,h}} = 1$, otherwise ai,h=0${a_{i,h}} = 0$.Radiality constraintsDSs are operated radially, and to establish the radial condition of the network during operation, there must be no loops in the network that are modelled as follows:26∑(i,j)∈ΩBqij=Nb−∑i∈ΩBλi$$\begin{equation}\sum_{(i,j) \in {\Omega _{{\rm{ B}}}}} {{q_{ij}} = {N_b} - \sum_{i \in {\Omega _{{\rm{ B}}}}} {{\lambda _{{\rm{ }}i}}} } \end{equation}$$27∑j∈ΩijiYij≤M.λj+1$$\begin{equation}\sum_{j \in \Omega _{{\rm{ }}ij}^i} {{Y_{ij}} \le M.{\lambda _j} + 1} \end{equation}$$28−M.λj+1≤∑j∈ΩijiYij$$\begin{equation} - M.{\lambda _j} + 1 \le \sum_{j \in \Omega _{{\rm{ }}ij}^i} {{Y_{ij}}} \end{equation}$$29Yij=−Yji$$\begin{equation}{Y_{ij}} = - {Y_{ji}}\end{equation}$$30−M.qij≤Yij≤M.qij$$\begin{equation} - M.{q_{ij}} \le {Y_{ij}} \le M.{q_{ij}}\end{equation}$$Two conditions must be met to maintain the radial structure of DS [28]. The first condition is given in Equation (26). When the binary variable λi${\lambda _{{\rm{ }}i}}$is equal to 1, it indicates that bus i is selected as the root bus, and vice versa. The second condition is presented in constraints (27)–(29), which ensure that all the buses on the island are connected. The disconnection or connection state of virtual network lines is also expressed in constraint (30).Evaluation indicesTo evaluate CPSs performance from any perspective, indices must be calculated to describe that feature. The performance index can be the amount of load supplied or the number of healthy electrical equipment in the power grid. In the present paper, the following indicators have been used to evaluate the performance of the CPS against physical disasters.31Resistance=∑h∈T∑i∈ΩBwi.Pi,hD,Not-Intrrupted∑h∈T∑i∈ΩBwi.Pi,hD$$\begin{equation}{\rm{Resistance}} = \frac{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.} P_{i,h}^{D,{{\rm Not}\hbox{-}{\rm Intrrupted}}}} }}{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.P_{i,h}^D} } }}\end{equation}$$32Recovery=∑h∈T∑i∈ΩBwi.Pi,hD,Recovered∑h∈T∑i∈ΩBwi.Pi,hLS$$\begin{equation}{\rm{Recovery}} = \frac{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.} P_{i,h}^{D,{\rm{Recovered}}}} }}{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.P_{i,h}^{LS}} } }}\end{equation}$$33Resilience=∑h∈T∑i∈ΩBwi.Pi,hD,Not-Intrrupted+Pi,hD,Recovered∑h∈T∑i∈ΩBwi.Pi,hD$$\begin{equation}{\rm{Resilience}} = \frac{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {w_i}. \left({P_{i,h}^{D,{{\rm Not}\hbox{-}{\rm Intrrupted}}} + } P_{i,h}^{D,{\rm{Recovered}}}\right)} }}{{\sum_{h \in T} {\sum_{i \in {\Omega _{{\rm{ B}}}}} {{w_i}.P_{i,h}^D} } }}\end{equation}$$The resistance index is the ratio of the total not‐interrupted loads to the total network loads, which indicates the system's ability to resists the disaster and prevent its propagation based on Equation (31). The recovery index defined in (32) is obtained from the ratio of energy recovered from the interrupted loads to the total load curtailed during the study period. Also, the resilience index given in (33) is calculated from the ratio of the total loads supplied during the study period (i.e., full not‐interrupted loads and recovered loads) to the total network loads.NUMERICAL RESULTSIn this paper, the 33‐bus physical DS shown in Figure 6 is used to review the effect of the physical disaster and test the proposed PC‐REMS model on the CPS. This system consists of 32 sectionalising switches, five tie switches, and 32 load points. All switches can be controlled remotely by the cyber network. The base power and voltage of the system are 100 MVA and 12.66 kV, respectively. The active and reactive powers of the whole system are 3.715 MW and 2.3 MVAr, respectively. Also, the load value weights of buses 3, 5, 7, 9, 12, 14, 20, 22, 27, and 30 are considered 3, and the weight of other load buses is 1. The cost of load shedding in this system is estimated at $8/kWh.6FIGURE33‐bus radial physical DSAll DGs installed in the grid are controllable, and their maximum generating capacity is 0.4 MW, which are located at buses 10, 19, 23, and 30. The DGs installed at buses 19, 23, and 30 are capable of operating as a master unit, so the maximum number of the formable MGs will be 3. WTs are installed at buses 4, 17, and 27 with a maximum capacity of 0.6 MW. The estimated average wind speed of WT is shown in Figure 7. The ESSs are installed at buses 14, 25, and 32 with the size of 1 MWh and the discharge depth of 0.33. Their charge and discharge efficiencies are 95% and 90%, respectively.7FIGUREAverage wind speed per hour of the day [18]The network load demand for a sample day is presented in Figure 8. The electricity price in the upstream grid for purchasing power in the DS is given in [29].8FIGUREHourly load demand profile [29]The PDFs parameters for vulnerability analysis, the fragility curve of the DS components, and Monte Carlo simulation details are presented in [9]. The vulnerability results of the 32 DS lines in the order from the most resistant to the most vulnerable are shown in Figure 9.9FIGUREVulnerability colour spectrum of 33‐bus physical DS lines [9]The proposed optimisation model is mixed‐integer nonlinear programming (MINLP), which is simulated in general algebraic modelling system (GAMS) and solved by the BONMIN solver. The AD‐RP model has been executed in a PC with Intel Core i7 CPU @3.20 CPU and 4 GBs of RAM.Preventive strategyIn the first stage of the PC‐REMS model as a preventive measure, the CPS is prepared through pre‐scheduled ESSs power and PNR to deal with the predictable physical disaster. The operator qualifies the physical DS based on the vulnerability analysis result to minimise the EECC. To simulate the contingency hurricane, lines with greater vulnerability than the critical value are disconnected. Therefore, according to weather forecasts before the hurricane, the operator predicts that the fault occurs in lines 19, 12, 16, and 27, as shown in Figure 10. The probable time of disaster is 10 to 12 noon, and the repair team's reaction time to repair the damaged lines is considered three hours.10FIGURE33‐bus radial test system after the contingency hurricaneWhen the fault occurs, and the switches of four vulnerable lines are disconnected, the DS is divided into five islands. Part of the system still has access to the upstream grid, so no load shedding is expected. If the remaining four islands include DERs, the load curtailment will be prevented in proportion to the capacity of these resources; otherwise, the system will encounter forced load shedding. In this case, it is expected that 1.124, 1.181, and 1.106 MW load shedding will occur at hours 12, 13, and 14, respectively. The total load curtailment and the EECC will be 3.411 MWh and $27,288.Due to the predictability of the hurricane time, the operator must schedule the production resources available in the network to supply loads with minimum interruption. Thus, the CES operator takes preventive action and pre‐schedules the ESSs installed on buses 14, 25, and 32 for the interruption time to reduce load shedding. The scheduling for the ESSs should be such that sufficient power is available for discharging around the physical disaster time. As shown in Figure 11, the SoC of ESSs is fully charged before the probable hurricane time.11FIGURESoC of ESSs in pre‐scheduled modeBefore the hurricane, the operator opens the switches of four vulnerable lines that are expected to be damaged. Accordingly, the PNR is performed so that the EECC is minimised. Therefore, the network is configured by considering all the radial constraints, as shown in Figure 12. When the switches of tie lines are closed, lines switches 11 and 18 are opened. In this way, the system is prepared for the contingency hurricane and the second stage of the PC‐REMS model with a new configuration without any load shedding.12FIGUREOptimal PNR of 33‐bus radial test system after the contingency hurricaneCorrective strategyAfter preparing the CPS to probability hurricane, the operator performs optimal CNR to minimise the ECC and loads recovery in the second stage of the proposed model while the real hurricane occurrence. Given that the damaged lines caused by the actual hurricane may not be the same as the potentially vulnerable lines, the final status of the lines can be different from the predicted condition.In this section, corrective strategy is examined for two different cases of fault occurrence in the physical DS. In Case 1, lines 10, 16, 19, and 29 are damaged after the actual hurricane. Two of the mentioned damaged lines are among the lines with a high probability of vulnerability. In Case 2, lines 1, 16, 19, and 29 are assumed to be damaged. The severity of the hurricane and outages in Case 2 is higher than that in Case 1.Case 1After applying the preventive strategy in the previous stage, the system is prepared with a new configuration to cope with the real hurricane. The DS is divided into three islands when the hurricane occurs in Case 1. The network is reconfigured to system restoration and is turned into two islands. The system's final configuration after the actual hurricane until the damaged lines repair in Case 1 is shown in Figure 13. Total load shedding is 0.534 MWh, and 12.911 MWh of system loads are supplied, which reduces the ECC to $4.272. In this case, 0.187, 0.192, and 0.155 MW load interruption occurs at hours 12, 13, and 14, respectively. It should be noted that without applying the proposed PC‐REMS model in this case, 3.14 MWh load interruption occurs in the network, and the ECC would be $25,120, which $20,848 of this cost has been reduced by the preventive‐corrective measures.13FIGUREOptimal CNR of 33‐bus radial test system in Case1Case 2The CPS is prepared to deal with the contingency hurricane in the first stage, and the real hurricane occurs in the second stage. When branch 1–2 is damaged, the complete DS is separated from the upstream grid and operated as an island. After the hurricane occurs in Case 2, the system is divided into four islands. By implementing CNR to reduce the interrupted loads, 7.956 MWh of total system loads are fed at the severe fault time, and 5.489 MWh of system loads are interrupted. In this case, 1.824, 1.907, and 1.758 MW interruption of load occurs at hours 12, 13, and 14, respectively, and the total ECC will be $43,912. The system's final configuration after the actual hurricane until the repair of broken poles in DS lines in Case 2 is shown in Figure 14. If the hurricane had occurred in this case without applying the proposed preventive‐corrective measures, the ECC would have been $56,672, which would have saved $12,760 in cost by implementing the PC‐REMS model.14FIGUREOptimal CNR of 33‐bus radial test system in Case2The PC‐REMS model in Case 1 has recovered most of the interrupted loads, and the system has returned to normal operation. However, due to the higher severity of network vulnerability in Case 2, the proposed two‐stage model can recover 59% of interrupted loads. To show the efficiency of the proposed model, the results of the PC‐REMS model are compared with the presented model in [9]. It should be noted that the test system and DERs used in both articles are similar, and the results are compared under the same conditions. The difference between these two articles’ methods is in the preventive‐corrective strategies used. The proposed PC‐REMS model performs better in the optimal energy distribution between selected islands to reduce the ECC and network recovery. This comparison is illustrated based on the recovery index in Figure 15. By examining the sensitivity analysis in the following, the results and achievements of this research become more prominent.15FIGUREComparison of the proposed model results with the article [9]Sensitivity analysisThis section evaluates the effectiveness of DERs and NR in improving resilience and their limits and ability to recover loads. Sensitivity analysis of the CPS behaviour in the two different hurricane cases is investigated. Table 2 shows the resistance, recovery, and resilience indices for Case 1 and 2 at two different outage time duration. All tie line switches are used in the results of this table, and all DERs are operated at their maximum capacity. Due to the increase in the fault severity in Case 2, the indicator's values are smaller than those in Case 1. Also, the system evaluation indices decrease with the extension of the interruption time duration and increasing the ECC.2TABLEPerformance of the DS with increasing outage timeOutage time (T)Outage time (2T)Case 1Case 2Case 1Case 2ECC ($)4.27243.91213.09696.512Resistance0.6100.530Recovery0.890.590.860.52Resilience0.960.590.930.52The behaviour of DERs and power exchange with the upstream grid in Case 1 and Case 2 with 2T outage time duration are illustrated in Figure 16. The results indicate that even if the repair time of damaged lines is more extended, this proposed model can effectively improve system resilience. As shown in both cases, a significant amount of load is restored.16FIGUREBehaviour of DERs and power exchange with the main grid with 2T outage time duration in: (a) Cases 1, (b) Case 2In Table 3, for different capacities of the ESS installed in the system, the ECC and the resilience index are calculated for Case 2. It is clear that the greater capacity of ESS to store energy, the more the participation rates them in improving network resilience. By discharging energy at the disaster time, ESSs get the supporting role for critical loads considering the priority in load supply.3TABLEImpact of ESS capacity on the network performanceESS capacity (%)ECC ($)Resilience065.5520.392560.1360.445054.7360.497549.3360.5410043.9120.59To better observe the role of NR, DERs, and the effect of the proposed PC‐REMS model on improving resilience, six modes of different sizes of DERs and with/without tie lines in DS have been investigated. Table 4 shows the proposed two‐stage model performance for six different strategies in Case 1.4TABLEPerformance of the proposed PC‐REMS model in six different strategies for Case 1With tie and 100% DERsWith tie and 50% DERsWith tie and 0% DERsNo tie and 100% DERsNo tie and 50% DERsNo tie and 0% DERsECC ($)4.27213.28022.28829.36030.78441.840Resistance0.610.610.610.610.610.61Recovery0.890.680.460.290.260Resilience0.960.870.790.720.710.61According to the obtained results, network resilience can be improved to an acceptable level by using DERs and NR. Given that in Case 2, the severity of the network vulnerability is higher and the DS is completely disconnected from the upstream grid, the system resistance is zero. The performance of the proposed two‐stage model based on six different strategies in Case 2 is reviewed in Table 5. Due to the severity of the network vulnerability, in this case, NR alone cannot improve the system resilience without DERs to feed the interrupted loads. This means the role of tie lines in load recovery is diminished, and DERs play an essential role in load supply. Therefore, the superiority of the proposed PC‐REMS model in the presence of DERs in Case 2 compared to the bi‐level model presented in [9] is quite obvious.5TABLEPerformance of the proposed PC‐REMS model in six different strategies for Case 2With tie and 100% DERsWith tie and 50% DERsWith tie and 0% DERsNo tie and 100% DERsNo tie and 50% DERsNo tie and 0% DERsECC ($)43.91275.760107.56043.92075.728107.560Resistance000000Recovery0.590.2900.590.290Resilience0.590.2900.590.290Due to the vulnerability curve, the network lines are resistant to wind speeds below 50 m/s, which the system lines outage increases by rising wind speeds. The capability and importance of the proposed model for recovering interrupted loads at hurricane speeds above 50 m/s are pretty obvious and it reduce the ECC significantly. In Figure 17, the ECC and the evaluation indices are calculated to increase the wind speed and severity of system components’ vulnerability. It is clear that as the wind speed increases, the number of damaged lines increases, and the model performance in improving resilience will decrease slightly. The load recovery through line switching and NR will not cost much for the system operator, while it can be very efficient and economical. It is worth mentioning the intensity of line vulnerability at low speeds is lower than higher speeds, so NR is more useful in recovering interrupted loads. However, with the increasing severity of the system components damaged, the NR strategy alone cannot recover loads, so the role of DERs in supplying network loads will be much greater. The proposed PC‐REMS model using two supplements, DERs and NR, is very effective in improving the system resilience against weak and normal hurricanes. In severe hurricanes, it is needed to reduce the vulnerability of physical systems by hardening power grid infrastructure, which will be considered as a future research study of the authors.17FIGUREThe evaluation indices and the ECC relative to increased wind speedModel analysis in a large‐scale test systemTo further investigate and conclude from the proposed model, this section examines the impact of physical disasters on a larger CPS. The 118‐bus radial DS, including three feeders and 15 tie lines, is intended as a test system. The base power and voltage of the system are 100 MVA and 11 kV, respectively. This test system's total active and reactive power loads are 22.71 MW and 17.04 MVAr, respectively. Data related to line parameters and loads of the test system are given in [30]. The location of WTs, ESSs, and DGs are listed in Table 6, as well as the ability to perform as a master unit. The capacity of the DERs installed in the network is the same as their capacity in the 33‐bus test system.6TABLEThe location of DGs, WTs, and ESSs in the 118‐bus systemDG unitBusMaster unit capabilityWT unitBusESS unitBus17✓114112217227226324✓342340433453448543555572651✓674680759✓784790867✓8938106976✓99910881011011103✓1211313117After preparing the network and taking preventive actions, corrective measures are taken to recover the grid against the real hurricane. As shown in Figure 18, the 12 distribution lines are damaged by the physical disaster at 12 noon, and the network is expected to take at least 3 hours to repair. By applying the proposed PC‐REMS model for network restoration, the system is divided into 4 MGs. The load shedding at hours 12, 13, and 14 are 11.360, 11.880, and 10.972 MW, respectively, and the total ECC is $273,696. Without the PC‐REMS model, the ECC would have been $479,016. In other words, now $205,320 has been saved after network recovery and implementing the preventive‐corrective measures.18FIGURE118‐bus radial test system restoration by implementing the PC‐REMS modelAs mentioned above, both NR and DERs play an influential role in medium and weak physical disasters. For severe faults, because more switches are damaged, or access to the upstream grid is lost, DERs are more successful in supplying critical loads. When the DS is wholly disconnected from the upstream grid (such as Case 2), the role of NR in system recovery diminishes. This means that there will be no way to feed the loads without power limitation, so the system must be powered by optimal energy management of DERs. The performance of the proposed PC‐REMS model in six different strategies for the 118‐bus radial network is presented in Table 7. Since the 118‐bus test network consists of three feeders, and not all have been disconnected from the upstream grid after the real hurricane, line switching is very effective in network restoration. Due to the high severity of the physical disaster and the failure of 12 lines, DERs and NR can recover 50% of the interrupted loads and bring the resilience index to 0.58.7TABLEPerformance of the proposed PC‐REMS model in six different strategies for the 118‐bus radial physical DSWith tie and 100% DERsWith tie and 50% DERsWith tie and 0% DERsNo tie and 100% DERsNo tie and 50% DERsNo tie and 0% DERsECC ($)273,696344,176395,664435,840517,112599,672Resistance0.080.080.080.080.080.08Recovery0.500.390.310.250.120Resilience0.580.470.400.330.210.08DiscussionThe execution time for the 118‐bus radial test system and in Case 2 and Case 1 for the 33‐bus radial test system are 628, 252 and 174 s, respectively. The obtained execution times confirm the computational efficiency of the proposed model in large‐scale CPSs. However, the execution times have increased by raising the number of variables and problem constraints in the large‐scale test system and the severity of the disaster in the medium‐scale test system. It should be noted that based on the scale of the studied CPSs and the simultaneous consideration of different capabilities in the evaluation process, these execution times are pretty reasonable, and the proposed PC‐REMS model for use in real distribution networks is also applicable.The proposed model for both test systems has a compelling performance in improving the CPS resilience. The main findings of this paper based on the investigated cases are summarised as follows:The cyber system part, through online network monitoring and immediate decision, can improve the speed restoration of the physical system part.Optimal pre‐scheduling of ESSs is a critical part of preventive strategies to enhance system resilience.The PNR and CNR as two complementary approaches can be quite fruitful in boosting the CPS resilience.The NR play the most crucial role in a moderate disruption, while DERs are more critical in a severe disorder.The specialised indices used to analyse the model performance are much more effective than the reliability indicators.CONCLUSIONThis paper presented a preventive‐corrective optimisation model for improving the CPS resilience in the face of predictable physical disasters such as a hurricane. The distribution lines that are most likely to be damageable are determined based on the vulnerability assessment. The CPS is prepared for contingency faults in the preventive stage through pre‐scheduled ESSs power based on the cloud and PNR to minimise the EECC. In the corrective stage, the vulnerability status of the CPS components is monitored after the severe physical faults, and the information obtained in real‐time is immediately sent to the system operator for the network restoration. The corrective action used in the second stage is CNR to optimal energy management and minimise ECC. The effects of EESs and NR on resilience features are also examined through evaluation indices. The simulation results demonstrate the efficiency of the proposed PC‐REMS model in optimal energy management and improving the CPS resilience.In the future and the continuation of this research, the benefits of different strategies can be compared, and a compromise between the various resilience improvement strategies can be established by cost‐benefit analysis. Thus, future research could include the optimal distribution lines hardening and cost‐benefit analysis for affordable response to low‐probability, high‐impact events in CPSs.CONFLICT OF INTERESTThe 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.FUNDING INFORMATIONFunding information is not available for this article.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.NOMENCLATUREIndices and symbolshIndex of time periodsi,j$i,j$Index of system buses¯/̲$\overline {{\rm{ }}} /\underline {{\rm{ }}} $Upper and lower limits’ symbolsSetsΩBSet of system busesΩHSet of time periodsΩiji$\Omega _{{\rm{ }}ij}^i$Set of buses connected to bus iParametershcritical${h_{critical}}$Time of hurricane impact on the physical DSMLarge valueNb${N_b}$The number of system busesSoCiInitial/Reserve$SoC_i^{Initial{\rm{/}}{\mathop{\rm Reserve}\nolimits} }$Initial/reservation state of charge of the ESS in bus iPi,hD/Qi,hD$P_{i,h}^D{\rm{/}}Q_{i,h}^D$Active/reactive load demand of bus i at time hVOLLi$VOL{L_i}$Value of lost load in bus iwi${w_i}$Priority of the load weight at bus iZij/φij${{\rm{Z}}_{ij}}/{\varphi _{ij}}$Magnitude/angle of line impedance ijηch/dch${\eta _{ch/dch}}$Charging/discharging efficiency of ESSΔh$\Delta h$Time intervalsVariablesai,h${a_{i,h}}$Binary variable for unsupplied power state of each unit load at bus i and time hEECCExpected energy curtailment costECCEnergy curtailment costEPi,hLS$EP_{i,h}^{LS}$Expected active load shedding of bus i at time hIij,h$I_{ij,h}$Magnitude of line current ij at time hIRij,h/IMij,h$I_{{R_{ij}},h}{\rm{/}}I_{{M_{ij}},h}$Real/imaginary part of line current ij at time hPij,h/Qij,h${P_{ij,h}}{\rm{/}}{Q_{ij,h}}$Active/reactive power flow of line ij at time hPi,hch/dch$P_{i,h}^{ch/dch}$Charging/discharging ESS power of bus i at time hPi,hDG/Qi,hDG$P_{i,h}^{DG}{\rm{/}}Q_{i,h}^{DG}$Active/reactive power generated by DG of bus i at time hPi,hLS/Qi,hLS$P_{i,h}^{LS}{\rm{/}}Q_{i,h}^{LS}$Active/reactive load shedding of bus i at time hPi,hsub/Qi,hsub$P_{i,h}^{sub}{\rm{/}}Q_{i,h}^{sub}$Active/reactive power injection of substation to bus i at time hPi,hWT/Qi,hWT$P_{i,h}^{WT}{\rm{/}}Q_{i,h}^{WT}$Active/reactive power generated by WT of bus i at time hqij${q_{ij}}$Binary variable for final status of line connection ijSij,h${S_{ij,h}}$Apparent power flow of line ij at time hSoCi,h$So{C_{i,h}}$ESS's state of charge of bus i at time hTFault time intervalYij${Y_{ij}}$Power flow of line ij of virtual gridVi,h/θi,h${V_{i,h}}/{\theta _{i,h}}$Voltage magnitude/angle of bus i at time hδi,h$\delta _{i,h}$Binary variable for status of ESS charge and discharge of bus i at time hυij${\upsilon _{ij}}$Binary variable for status of line damage ij against physical disasterκij${\kappa _{ij}}$Binary variable for status of line switching ij during the NRλj${\lambda _j}$Binary variable to determine the root busAbbreviationsCESCloud energy storageCNRCorrective NRCPSCyber‐physical systemDERDistributed energy resourceDGDistributed generatorDSDistribution systemEECCExpected energy curtailment costECCEnergy curtailment costESSEnergy storage systemsGAMSGeneral algebraic modelling systemMGMicrogridMINLPMixed‐integer non‐linear programmingNRNetwork reconfigurationPC‐REMSPreventive‐corrective resilient energy management strategyPDFProbability density functionPNRPreventive NRSoCState of chargeWTWind turbineREFERENCESHaque, M.A., Shetty, S., Gold, K., Krishnappa, B.: Realising cyber‐physical systems resilience frameworks and security practices. 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IET Generation Transmission & Distribution – Wiley

Published: Apr 1, 2023

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