Distributed Energy Management for Port Power System under False Data Injection Attacks

This paper investigates a distributed energy management strategy for the port power system under false data injection attacks. The attacker can tamper with the interaction information of energy equipment, penetrate the boundary between port information system and port power system, and cause serious operation failure of port energy equipment. Firstly, a hierarchical topology is proposed to allocate the security resources of the port power system. Secondly, by reconstructing the topological structure of the port information system, the robustness of the information system is improved, and the impact of false data injection attacks on the port power system is reduced, which realizes secure distributed energy management of the port power system. Finally, the simulation results show the eﬀectiveness of the proposed strategy, and the defense capability of the port power system is improved.


Introduction
With the development of the shipping industry [1], the types and quantities of energy equipment in port are increasing, and the port has become an energy-intensive region that relies on fossil energy; pollutant emissions are also increasing year by year [2]. In order to achieve effective pollution control, the interaction of multiple stakeholders in the maritime shore power system is required [3]. Port enterprises should speed up the realization of the strategy of "implementing shore power," and the government should actively supervise pollution emissions and encourage the use of clean energy [4]. Optimizing the utilization rate of renewable energy is the breakthrough point to solve the problem of high energy consumption and high emission in ports, but as the penetration rate of renewable energy becomes higher and higher, its randomness and volatility bring uncertainty to the port power system [5,6]. More noteworthy, the Port of Barcelona was the target of a cyberattack that affected some of its servers and systems on the morning of September 20, 2018, forcing the organization to launch the contingency plan designed specifically for these incidents [7]. An Israeli cyber attack on the Iranian port setup caused serious chaos in the port's waterways and roads according to the Washington Post reported in May 2020 [8]. A study by Lloyd's of London showed that a cyberattack affecting major ports in the Asia-Pacific could cost $110 billion [9]. erefore, how to carry out port energy management has become a key issue in order to make full use of the renewable energy of the port, reduce the environmental pollution caused by the redundant power supply, and ensure the normal run of the port power system.
At present, the energy management of port mainly draws on the experience and methods of the distribution grid, and it is actually an optimization problem of the complex system considering various practical constraints [10]. It aims to realize the balance of supply and demand and to maximize the operation benefit of the port power system when meeting the physical constraints of energy equipment [11,12]. At the same time, the ports that implement wind power generation and photovoltaic power generation have the characteristics of distribution and uncertainty, which brings difficulties to the traditional centralized energy management strategy [13,14]. Port energy management is gradually transformed into a distributed management method with the advantages of flexibility, high reliability, and scalability [15][16][17]. A number of studies concerned about energy management have been proposed for power systems, including hierarchical decentralized energy management, multiagent system-based coordinated operation strategy, and hybrid energy management [18][19][20]. To solve the energy management problem of the energy Internet, the work in [18] proposed a completely distributed algorithm, in which each participant can realize the estimation of the optimal energy price and the calculation of the optimal energy output by only interacting with the neighbors. e largescale connected inverter (CI) networks increase the reliability and resilience for the power grid, which may also cause grievous adventure to the reliable and stable operation of the main grid if the control of multiple CIs could not enable good cooperation [21,22]. Lu et al. proposed a master-slave cluster cooperation strategy over the twolayer switching cyber network topologies to realize the economic distribution among multiple clusters [23]. ere have been many studies on ports in different directions. e literature [24][25][26] reduces the peak load in the port by excavating the peak cutting and valley filling capacity of port freezers, terminal cranes, and electric vehicles. In reference [27], aiming at the problem that a large number of flexible loads such as reefers, ships, and electric vehicles are difficult to be highly coordinated, the port load management optimization is realized by using multiagent system with electricity price as the regulation signal. A novel decentralized power management method for a large port-based multiagent system (MAS) is proposed in [28].
It is specially mentioned that the information interaction process is vulnerable to malicious network attacks among the calculation and analysis of energy supply equipment due to the strong distributed characteristics of the current port power system [29]. In the next place, owing to the rapid development of information technology, there is a strong coupling characteristic between port cyber system and its power system [30,31], which determines that the secure operation of information communication network is a basic foundation for the normal operation of its power system obviously [32]. Considering the increasing degree of dependence between information flow and power flow, the threat on information communication flow within the port power system will influence the normal operation of the power system, which will penetrate the boundary between the above two systems and have several negative impacts on disturbance, system instability, and collapse of the energy system [33,34]. us, in order to ensure the reliable operation of the port power system under the above situations, it is necessary to strengthen the security defense of its information and communication system, so as to ensure the normal operation of its internal equipment [35][36][37]. It is noted that the operations security and efficiency of energy utilization are the most significant requirements within the port cyber-physical system [38]. erefore, ports must make cyber security a top priority to ensure its security, compliance, and commercial competitiveness. e direct target of network attacks is the information flow in the information layer. It is common that cyberattacks include denial of service attacks, packet loss attacks, false data injection attacks (FDIAs), malicious software viruses, and so on [39]. Among them, the false data injection attack approach is easy to implement and has the characteristics of strong concealment and interference, which have attracted widespread attention from researchers in related fields. Literature [40] mainly treats the perturbation term in FDI attacks as a constant. In Literature [41], to verify the robustness of the proposed technique, four cases of FDI attacks across attacker injection signals were considered that are non-periodic attack, non-periodic replacement attack, periodic attack, and simultaneous attack. All of the above attack types will be within our consideration. In the next place, we need to focus on existing ways to resist attacks, a method for detecting FDIA in DC microgrid current measurement based on distributed control strategy control is introduced in [42]. e authors study fault identification using SVM, decision trees, and random forests in [43,44]. e detection method of FDIA was studied in the above literature. e work in [45] proposes an antioffensive cooperative control strategy, which can adjust the power of the virtual power plant under a specific scheduling command. References [46,47] proposed a trust-based antiattack resilient cooperative distributed control method and designed a resilient synchronization protocol to solve the problem of sensor attacks and reduce the adverse effects of attacks on communication links and hijacking of controllers. e author analyzed the relationship of the maximum amount of tolerable attacks and the number of total agents, and connected number has been provided for consensus under adversarial attacks, and a sequence of resilient consensus algorithms were developed in [48,49].
However, the existing defense mechanisms rely mainly on the means of detecting attacks, and the effectiveness of those is still restricted by the maximum amount of tolerable attacks. To actively defend and relax the assumption on the maximum amount of tolerable attacks, this article was completed inspired by [50]. is paper proposes a distributed energy management strategy for the port power system based on hierarchical topology reconstruction of communication networks in order to reduce the impact of false data injection attacks on port energy management within limited defense resources to ensure the safe run of the system with lower security defense cost. e main contributions of this paper are summarized as follows: (1) is paper investigates the problem of distributed port energy management when the network of the port power system is under attack, where the tolerable number of attack nodes is unknown and can be arbitrarily large.
(2) To increase the security capacity of the port power system under false data injection attacks, this paper proposes a hierarchical topology reconstruction method of the port information system, which can reduce the impact of false data injection attacks on the port power system during the whole operation condition.
2 Complexity e rest of the paper is organized in the following. Section 2 presents the main types of port power facilities and energy management. e secure distributed energy management under FDIAs is detailed given in Section 3. In Section 4, the proposed method is simulated for port power system, and the obtained results are presented and evaluated. Finally, Section 5 draws a general conclusion.

Distributed Energy Management of Port
Power System

Port Power System Configuration.
In the port information energy system, there are multiple energy supply, energy demand, and energy storage entities [51]. In terms of energy supply, the port is particularly suitable for converting natural resources such as wind energy, tidal energy, and solar energy into electrical energy; in terms of energy use, the port uses a large number of cranes, gantry cranes, bridge cranes, plug-in electric vehicles, and so on [52]. In terms of energy storage, it is necessary to alleviate the uncertainty of port load and absorb intermittent and fluctuating renewable energy; energy storage equipment needs to be considered in the port power system.

Renewable
Generator. Solar and wind energy are the main renewable energy sources. Considering the intermittency and volatility of renewable energy, it is unable to participate in the energy management process of the port, so according to the dispatch forecast curve before the day, the average value is used as a reference. Taking renewable power generation equipment as an example, its power generation can be expressed as follows: where p i is the power generation predicted by the renewable energy equipment i according to the day-ahead dispatch period T. Assuming that the prediction error described by the probability density function obeys the Gaussian distribution, it can be expressed as follows: Choose an appropriate confidence level to get the confidence interval of the prediction error [ΔP min i , ΔP max i ]. us, the power generation of renewable energy equipment i can be expressed as follows: To sum up, considering the actual operation effect, the operation cost function of renewable energy equipment i can be expressed as follows: where b i and c i are the coefficients of the operating cost function; the optimality and possibility of renewable energy equipment operation can be balanced to take renewable energy into energy management.

Fuel
Generator. e use of alternative clean energy in port equipment and buildings can effectively reduce environmental pollution and greenhouse gas emissions in the port area, which is in line with the development concept of green port [48]. e choice of alternative clean energy fuels plays an important role in the sustainable development of ports and the improvement of the port environment. e local optimization problem of fuel energy equipment can be transformed into

Shore-Ship Power Supply.
In order to effectively promote the development of energy-saving and low-carbon emission reduction, the use of shore-based power supply by ships calling at ports is one of the key tasks of the port industry for energy conservation and emission reduction. When the ship is at the berth, the ship's auxiliary generator runs in parallel with the shore power source to ensure the ship's reliable operation. e operating cost of the auxiliary engine (only fuel is considered) is approximated by the second-order polynomial of the power generated by the generator [28]:

Plugged in Electric
Vehicle. Electronic transportation in the port improves energy efficiency and reduces greenhouse gas emissions. e use of electric vehicles instead of port internal combustion engine operating vehicles (such as automobiles, forklifts, etc.) will effectively reduce carbon emissions in the port. In the future, large ports can charge and discharge electric vehicles through charging piles, thereby increasing the flexibility of providing port energy requirements. e cost function of PEV can be modeled as follows [27]: Electric vehicles are constrained by battery charging efficiency and battery capacity as follows: Complexity

Distributed Power Storage
Device. Distributed renewable energy generation has the characteristics of intermittent and volatility. Large-scale access to distributed power generation equipment increases the adjustment difficulty of the grid and is likely to cause a lot of waste of resources such as abandoning light and wind; When a large number of short-cycle loads are connected, it will cause large fluctuations in the frequency or voltage of the grid, which will affect the stability of other electrical equipment. e addition of energy storage system in the power grid will not only help to reduce the abandonment of new energy and make up for the instability of new energy power generation but also reduce the demand pressure at the peak of power consumption by releasing the stored energy. On the energy-consuming side, it meets the rapid response requirements of frequency and voltage regulation and provides high-quality electric energy. e cost of energy storage equipment i can be defined as follows: where p i represents the charge and discharge power of the energy storage device i, and its symbol represents the state of charge and discharge (the discharge state is positive, and the charge state is negative). Energy storage equipment cannot work in charging and discharging at the same time and needs to meet multiple restricted operating conditions: where P i should be between the maximum charging power P ch, max i and the maximum discharging power P ds, max i , ς ch and ς ds are positive numbers between 0 and 1, and represents the energy loss during the charging and discharging process of the energy storage device i.

Distributed Energy Management Scheme of Port Power System
e goal of energy management of the port power system is to maximize the operation benefit or minimize the operation cost on the basis of ensuring the safe operation of port power equipment and the balance of supply and demand of the port power system.
We assume that the port power system can be represented by an undirected graph G � (V, E, A), where V � v 1 , v 2 , . . . , v n is a vertex set, E⊆V × V is the set of undirected edges, and A is weighted and non-negative adjacency matrix [50]. It assumed that there are n power devices in the port power system, whose cost function of device i can be denoted by C i (P i ), where P i is the output power of device i. e energy management problem can be expressed as follows: subject to the following constraints: (a) Device constrains where P min i , P max i are the minimum and maximum power output of the device i, respectively, and P ramp i is the ramp rate constraint of the power facility.
where d i is load. It is assumed that the energy management problem is solvable; the following conditions are satisfied: Assumption 1. For each i ∈ 1, 2, . . . , N { }, the cost function C i (P i ): R + ⟶ R + is strictly convex and continuously differentiable, where R + denotes the set of non-negative real numbers.
e Lagrangian function of problem (14) and constraints (15) is as follows: where λ is the dual variable. By decoupling P i from L(P, λ), we get Assumption 2. e Lagrangian function L(P, λ) has a saddle point, that is, there exists an optimal solution (P * , λ * ) such that holds for all P i ∈ Ω, λ ∈ R + . With Assumption 2, problem (14) is a convex optimization problem, and the duality gap is 0; it can be transformed into its dual problem, which can be expressed as follows: 4 Complexity Using the gradient descent method to solve, the update of λ(k) can be described as follows: where α > 0 is a constant that represents the step size. e energy management based on the gradient descent method can be expressed as follows: It is worth noting that the above energy management method is centralized and λ(k) is a global variable, which requires the centralized control center to collect the information of all devices in the system and greatly increases the computing burden and communication burden of the control center. In this case, once the control center fails, the energy management process of the port power system will collapse, and the safe operation of the system will be seriously threatened. In [54], a distributed estimator λ i (k) is introduced to evaluate global variables λ(k), and a distributed energy management algorithm is designed through a finite number of consensus protocol calculations, which alleviates the communication burden and computing burden of the scheduling center (Algorithm 1).
Here, w ij > 0 is the weight assigned by node i to node j.
Assumption 3. e existence of a double random matrix W � [w ij ] n×n which satisfies W � W T and for

Remark 1.
e above algorithm does not need centralized scheduling and decentralize the computation burden of the scheduling center. Each node only needs to exchange information with its neighbors to alleviate the communication burden of the central nodes. In this case, distributed scheduling method assumes that the network environment is benign, and if there are intruders in the information network, it is very likely that the consensus between nodes cannot be achieved.

Distributed Energy Management under FDIAs
With the deep fusion of information flow and energy flow in the port power system, the safe operation of the port power system is facing many challenges. More and more energy devices with communication abilities are connected to the port power system, and the information transmitted by energy equipment is threatened by network attacks [55].

Energy Management Problem under FDIAs.
Considering the features of concealment and interference, false data injection attacks (FDIAs) have been regarded as one of the most popular attacks of the communication system in the port power system [56]. Furthermore, the attacker can track the configuration of the port power system, tamper with the sensing data of the sensor or tamper with the command signal sent by the controller, which will lead to the error of the state estimation process, and finally make the power system unable to operate normally [57]. As mentioned above, the false data injection attack model is as follows: where λ i (k) denotes the information of device i exchanged with other devices and ζ i (λ i (k)) represents arbitrary update function.
Without losing generality, we assume that node i � 1, 2, . . . , n 0 is not attacked by false data injection attacks and node i � n 0 + 1, n 0 + 2, . . . n is attacked by false data injection attacks. e interaction of λ i (k) in information layer can be rewritten as follows: Complexity λ 1 (k + 1) e goal of energy management of the port power system under FDIAs is to maximize the operation benefit of nonattacked devices. e energy management problem can be expressed as follows: subject to the following constraints: (a) Device constrains where P min i , P max i are the minimum and maximum power output of the device i, respectively, and P ramp i is the ramp rate constraint of the power facility. (b) Supply-demand imbalance constraints where P im thres is the constant threshold of power mismatch under false data injection attacks.

Secure Distributed Energy Management Based on Topology Reconfiguration.
e topology of the information Initialization: Each node i initializes λ i (0), step size α and calculation times σ Iteration: (k ≥ 0) (1) Each node i updates P i (k) according to (24) (2) Each node i updates v 0 i (k + 1) based on the gradient descent method, v 0 ALGORITHM 1: Distributed energy management scheme. 6 Complexity network is the key factor to realize the coordinated operation of port power devices and energy management of port power systems [53]. It is noted that the reliable transmission of information is a necessary condition to ensure the safe, stable, and economic operation of the port energy system. Information networks can provide different services and guarantees for energy equipment in different regions. In order to build a safe information network environment, we consider changing the port information network from a flat topology to a hierarchical topology. e hierarchical topology is as Figure 1.
Hierarchical topology divides n nodes into m layers and marks the layers as 1 to m from top to bottom. e nodes in the first layer only send information to the second layer, and the nodes in the i layer at least send messages to one node in the i + 1 layer. In each layer, the information interaction between nodes can be bidirectional. Using hierarchical topology, it is realized that when false data injection attacks occur in the port information network, we should divide the attacked node and the non-attacked node into different topology layers and reduce the weight of the non-attacked node assigned to the attacked node, so as to reduce the impact of network attacks on the port information network.
Inspired by the literature [50], we protect some nodes in the port power system from being invaded by attack nodes. By expanding the influence of these protected nodes in the network, to suppress the impact of false data injection attacks on the port information and energy system, the protection measures include: (1) improving the firewall security level of the protected nodes, and make redundant resources of the protected nodes to ensure that the protected nodes get real and reliable information; (2) Using the digital signature and data encryption technology, to the protected nodes the real information sent cannot be tampered. Before introducing a secure distributed energy management strategy, we introduce the following definitions and assumptions.
For the convenience of description, we regard the vertex set T � v i |i � 1, 2, . . . n 1 as the set of protected nodes, and the vertex set A � v i |i � n 0 + 1, n 0 + 2, . . . , n as the set of attacked nodes. e other vertex is ordinary nodes.

Remark 2.
Topology reconstruction from communication network due to attack does not mean that the operation of the attacked node stops completely. e isolated node does not mean that its corresponding unit stops power output. It will continue to supply local load demand because the attack action of an isolated node only occurs at the communication layer. e physical layer topology of the actual power supply unit will not change due to the occurrence of a network attack.
e Lagrangian function of problem (28) and constraints (31) is as follows: where λ is the dual variable. By decoupling P i from L(P, λ), we get: Remark 3. e above Lagrange function assumes that the supply is in short demand in the port power system. It can also assume that the supply exceeds the demand in the port power system. Owing to the port power system containing energy storage equipment, it can provide or store electric energy in time to reduce the negative pressure of power imbalance in case of emergency.

Assumption 4.
e Lagrangian function L(P, λ) has a saddle point, that is, there exists an optimal solution (P holds for all P i ∈ Ω, λ ∈ R + . With Assumption 4, problem (14) is a convex optimization problem, and the duality gap is 0; it can be transformed into its dual problem, which can be expressed as follows: Before introducing a secure distributed energy management strategy, we introduce the following definitions and assumptions. Definition 1. G d is a connected dominating set of G � (V, E, A) if each node i, which does not belong to the subset G d , has at least one neighbor in the subset G d and all nodes in G d can form a connected graph.

Assumption 5.
e protected nodes induce a connected dominating set of G � (V, E, A).
According to the secure distributed energy management scheme under FDIAs, each node i determines the maximum threshold χ M i (k) and minimum threshold χ m i (k). And then, the set R i (k) can be obtained by threshold filtering. During the k iteration of node i, R i (k) can be divided into three Complexity 7 types: from the set of protected nodes R T i (k), itself χ i (k), and the set of the other nodes R T i (k). Equation in Algorithm 2, can be rewritten as follows where ∀χ j (k) ∈ R T i (k); it can be expressed as us, equation in Algorithm 2, can be further rewritten as follows: Initialization: Each node i initializes λ i (0) Iteration: (k ≥ 0) (1) Each node i updates P i (k) according to (24) (2) Each node i updates χ i (k) based on the gradient descent method, 4) Node i identifies the information of the protected node, compares with its own information, and then determines the maximum threshold χ M i (k) and minimum threshold χ m i (k) (5) Node i filters information between χ m i (k) and χ M i (k) and then formulates the set Each node i estimates λ i (k + 1) and λ i (k + 1) � χ i (k + 1) Let k � k + 1, until |λ i (k) − λ j (k)| < ε, j � 1, 2, . . . , n 1 ALGORITHM 2: Secure distributed energy management scheme under FDIAs. 8 Complexity en, we have ⋮ ⋱ ⋮ · · · ⋮ m n 1 1 · · · m n 1 n 1 · · · 0 ⋮ · · · ⋮ ⋱ ⋮ m n 0 1 · · · m n 0 n 1 · · · m n 0 n 0 Compared with (27a), after topology reconstruction, the links from ordinary nodes to protected nodes and the links from attacked nodes to protected nodes are weakened, and the connection between attacking node and common node is also weakened. Equation (38) can be expressed as: where M n 1 ×n 1 is the interaction between protected nodes, M n 2 ×n 1 denotes the interaction between protected node and ordinary nodes, and M n 2 ×n 2 is the interaction of itself. e nodes of the communication network can be divided into three layers by hierarchical topology reconstruction algorithm: layer 1 of trusted nodes, layer 2 of common nodes, and layer 3 containing attack nodes. Furthermore, equation (38) can be written as follows: Under Assumption 5 and Algorithm 2, Ψ(k, t) have the following property: for any fixed t, n 2 non-zero entries in ψ(t) are lower bounded by φ d .
To estimate λ(k), define the set as follows: and define the solution set as follows: By choosing μ � φ d and η � n 1 , it is easy to obtain Y(μ, η) is a convex set. According to reference [38], when α(k) meets lim k⟶∞ α(k) � 0, the λ i (k) of all protected nodes and ordinary nodes is convergent from (40), and converges to the set Y(μ, η) of optimal solutions of a weighted average of local cost functions g i (λ) belonging to all protected nodes and ordinary nodes.
Remark 4. Compared with literature [50], this paper focuses on secure energy management under FDIAs, which is a constrained optimization problem with coupling characteristics. By decoupling P i from L(P, λ), the dual problem is simplified, which make λ can achieve consensus.

Numerical Results
Consider port power system shown in Figure 2 and network topology under FDIAs shown in Figure 3; there are eight nodes in the port information network; the set of attacked nodes is v 6 , v 7 , v 8 .
e FDIA models are formed as Complexity λ 6 (k + 1) � 8 sin(0 · 0025πλ 2 (k + 1)) + 35, λ 7 (k + 1) � (k/ 100) 2 , and λ 8 (k + 1) � 40. We set cost function C i (P i ) � a i P i 2 + b i P i + c i of devices i, with different parameters shown in Table 1. e loads are set as 85 MW, 50 MW, 105 MW, 85 MW, 77 MW, 30 MW, 33 MW, and 40 MW. According to Algorithm 1, set the initial value of the dual variable be 0, and the number of calculations is 40. Figure 4(a) shows that when the nodes in the information network are attacked, the existing distributed energy management cannot guarantee the asymptotic consistency of the dual variable, and it leads to the outputs of power equipment fluctuating significantly, and the safe operation of the equipment is not realized as shown in Figure 4(b). As a result, the power mismatch of distributed energy management strategy cannot converge, and the imbalance constraint between supply and demand cannot be satisfied shown in Figure 4(c). It can be seen that the distributed energy management strategy loses effectiveness under FDIAs.
ere are a total of eight nodes in the network of the information energy system: v 1 , v 2 , v 3 are protected nodes, v 4 , v 5 are ordinary nodes, and v 6 , v 7 , v 8 are the nodes that are attacked. e network after topology reconstruction is shown in Figure 5, which divided nodes into two layers: the protected nodes are in the first layer and the other nodes are in the second layer. e information transfer from the first layer to the second layer in the topology is directed.
In the case of a network attack, the dual variables of nodes 1-5 are asymptotically consistent by topology reconstruction shown in Figure 6(a). Furthermore, Figure 6(b) shows that the output of all energy equipment tends to be safe run with small fluctuations, indicating that the energy strategy after topology reconstruction basically guarantees the safe run of the system. e energy management solution is given by P * 1 � 73.8660 MW, P * 2 � 40.0000 MW, P * 3 � 62.9363 MW, P * 4 � 40.0000 MW, and P * 5 � 73.8660 MW. Power mismatches for secure distributed energy management fluctuate around −20 as shown in Figure 6(c), which greatly reduces the degree of energy mismatch compared with before the topology reconstruction. Although the energy mismatch still fluctuates to a small extent due to the direct transmission of information between nodes of the layered network after topology reconstruction, it is acceptable because it is safer than before topology reconstruction. In summary, the distributed optimization scheduling strategy has been topologically restructured to increase the robustness of the network and strengthen the active defense capability of the network.

Conclusions
In this paper, a distributed energy management strategy for the port power system has been proposed under false data injection attacks. First of all, we proposed a hierarchical topology to allocate the security resources of the port power system. en, by reconstructing the topological structure of the port information network, the robustness of the information network is improved; the impact of false data injection attacks on the port power system is reduced; and thus, the secure distributed energy management of the port energy system is realized. We have relaxed the assumption of the maximum tolerable number of attack nodes (F) while increasing the maximum number of tolerable attack nodes in the network. By protecting a portion of the nodes in the network, the normal operation of all the attacked nodes is ensured. Finally, the effectiveness of the proposed energy management was investigated by simulation results, and the defense capability of the port power system has been improved. It is important to note that our study still has some limitations. e method of topological reconstruction using the threshold changes the interactions between agents; although it is safer after topological reconstruction, there are still small fluctuations leading to energy mismatch, and it is acceptable. So the topological reconstruction algorithm still needs to be improved; is paper only studies the FDIA attacks; more types of attacks and attacks with a wider range can be considered in future work.  e interaction between protected nodes M n 2 ×n 1 : e interaction between protected node and ordinary nodes M n 2 ×n 2 : e interaction of itself.

Data Availability
e data used to support this study are obtained by contacting the first author.

Conflicts of Interest
e authors declare that they have no conflicts of interest.