High-OrderObserver-Based SlidingModeControl for the Isolated Microgrid with Cyber Attacks and Physical Uncertainties

System security is essential for the operation of the island microgrid. However, the system security is generally threatened due to the presence of physical uncertainties and cyber attacks. In this article, a novel sliding mode load control strategy is proposed for the microgrid to mitigate cyber attacks and physical uncertainties. Firstly, a high-order disturbance observer (HODO) is designed to estimate the unmeasurable factors in the microgrid. Secondly, a HODO-based sliding mode control (SMC) strategy is proposed where the estimated value observed by the HODO is applied to the sliding mode surface and control law. It can better guarantee the security of the isolated microgrid. )en, the stability of the HODO-based SMC is demonstrated by Lyapunov stability theory. Finally, simulation results show that the proposed control strategy has excellent control performance.


Introduction
e power system is regarded as a critical factor for economic development. With the rapid development of communication equipment, power system application, and energy management system [1][2][3], power systems merging primary and secondary systems are promoted to transform into the cyber-physical system (CPS). Consequently, the security of the cyber-physical power system has received widespread attention.
CPS security includes the security of physical systems and cyber systems. Physical security is the security of the primary system, which can stabilize the system at scheduled operating point under physical uncertainties. Cyber security means the security of the secondary system which is vulnerable to cyber attacks [4][5][6].
e insecurity of the cyber-physical power system has a significant impact on the society. For example, in 2019, the primary system of Venezuelan power system became the target of an attack, resulting in a large-scale blackout. In 2003, the secondary system, computer network at the power plant, was hacked in Davis-Besse, USA. On the contrary, the security of the power grid can improve the utilization rate of clean energy power generation and enhance the reliability of the power grid [7,8].
Because of the integration of advanced measuring devices, application software, and renewable generations, the security of the power system is threatened by serious attacks [9][10][11][12]. Multitype intelligent analysis software relies on computers and communication networks, which make the system vulnerable to cyber attacks. Meanwhile, the parameters of physical equipment including generators, turbines, and transmission lines are uncertain. Currently, many critical techniques about cyber attacks, which are the major challenge in the CPS, were studied by scholars. ere are some advanced resilient control technologies for cyber attacks [13][14][15], such as data intrusion attacks [16,17], nontechnical loss fraud, time-delay attacks [18], and replay attacks. Liu and Li [19] proposed a load distribution attack model with the incomplete acquisition of power system information. In [20], a detection technique was studied for uncertain systems. When the power system was attacked, it can be detected and protected immediately. In [21], a control strategy to protect distributed time-delay power systems was proposed. e method of time-delay estimation was introduced to solve time-delay switch attacks. In recent years, the advanced SMC has been proposed to address the threat of cyber attacks and physical uncertainties [22][23][24]. In [25], SMC with the neural network observer was constructed, where the measured values were used for the control law, and it was proven to be superior in simulation. Mi et al. [26] proposed SMC based on the proportional-integral sliding mode surface, and this method proved that the microgrid can be immune to the attacks.
In this paper, a control strategy is investigated. Firstly, a transformed dynamics system is established combining cyber attacks and physical uncertainties as a lumped attack. Secondly, the attack is measured by a high-order nonlinear observer where the attack and its derivatives are observed.
en, compared to the linear sliding surface, an improved sliding surface including the estimation value is proposed. By employing the estimation value, system states are forced to move to the sliding mode surface with the control law. Finally, simulation results on the isolated microgrid are carried out to verify the performance of the controller. e main contributions of the article are as follows: (1) Considering the characteristic of the power system, the presented HODO can be used to measure the cyber attacks and physical uncertainties in the power system (2) We construct the sliding mode surface and the control law based on the output of the HODO in the corresponding state space of the microgrid (3) Using the proposed control strategy, the security of the microgrid will be significantly improved, especially the frequency index is paper is organized as follows: in Section 2, the system structure of the microgrid and the dynamic equations are proposed. In Section 3, conventional SMC is illustrated. In Section 4, the control strategy is proposed. Firstly, HODO-based SMC is designed. Secondly, the stability is theoretically proved for the proposed method. e experimental simulation results are demonstrated in Section 5, while the work of this paper is summarized in Section 6.

Model of the Cyber-Physical Power System
In this paper, a typical cyber-physical system composed of the power system and controller is considered. e matrix form of the cyber-physical power system is expressed as follows: where x(t) is the system state vector; A n , B n , and F n are system matrices; Δf(t), ΔP g (t), and ΔX g (t) are the deviations of frequency, power output, and governor valve position, respectively; T p , T T , and T g are the time constants of the power system, turbine, and governor, respectively; K p denotes the power system, R is speed drop; and u(t) and ΔP d (t) denote the control vector and the cyber attacks, respectively. e formulated cyber-physical power system is similar to that of the literature [25].
Considering the physical uncertainties of the system dynamic model, equation (1) is written as where A ′ , B ′ , and F ′ are the determined physical system and ΔA, ΔB, and ΔF denote the uncertainties of the physical system. Equation (4) is the detailed representation of system dynamics (3): where k mn denotes physical uncertainties. e system dynamic model with cyber attacks and physical uncertainties can be represented as follows: where e matrix form of system dynamic model (5) is where A � A n , B � B n , F d �

Assumption 1. Pair A is observable.
In order to design the observer conveniently, let us transform system dynamics (5) using the transformation matrix. e structure is e aforementioned system is represented as For the transformed dynamic equation (9), the following assumption is necessary.
e attacks d 1i are continuous, and their higher-order derivative with respect to time satisfies where χ is a positive number.
Remark 2. Using a linear nonsingular transformation, system dynamic model (5) can be transformed into system (9). It should be noted that system (9) facilitates the design of HODO-based SMC. Meanwhile, η is equivalent to x(t) in simulation analysis.

Conventional SMC Design
In the microgrid, the conventional SMC was proposed to ensure system security through secondary frequency regulation of the generator, which adjusts the system to the normal working range with the attacks. e design of the SMC is composed of two processes: firstly, to design a sliding surface; secondly, to design the control law. e designed sliding surface drives system states to the desired equilibrium asymptotically and remain on it.
e system state can be driven to the sliding surface by the designed control law after sufficient time. (8), the linear SMC is designed as

Linear SMC. Based on system dynamic
where are constants, and c 3 � 1. c i meets that the polynomial c 1 + c 2 p + c 3 p 2 , which is Hurwitz, such that the eigenvalues of the polynomial are less than zero.
According to the literature [27], the reaching condition is chosen as s 1 · _ s 1 < 0. e equality reaching condition is selected as follows: where k d1 and k ε1 are positive numbers and sign(·) is the sign function. e control law is designed based on (8), (11), and (12), which drives the system state to the sliding surface:

Proportional-Integral SMC.
e proportional-integral SMC is presented in this section. e proportional-integral sliding surface is selected as where matrix K is designed as λ( e control law is designed as follows: However, there are two obvious drawbacks including large overshoot and the lack of estimation for the attack.

High-Order Observer for Cyber Attacks and Physical
Uncertainties. In this section, an observer is proposed to estimate the attack [28]. In Figure 1, physical attacks k mn appear in the governing system, turbine, and power system. Meanwhile, cyber attacks ΔP d (t) corrupt the power system. When the system is attacked, the boundaries of the undetectable attack will be directly used in SMC without the HODO.
us, the control is conservative. e proposed control strategy where the HODO can accomplish the detection of unknown attacks compensates this shortcoming to make the controller output more accurate.
e HODO can estimate the attacks for system (9) as follows: where L q � 1r , respectively, and p 1iq are auxiliary variables e estimation errors are defined as 1i , i � 1, 2, 3; q � 3, 4, 5, . . . , n, and d is the error in the estimation of d (q− 1) 1i . From (8), (17), and (18), it follows that From (19) and (20) Differentiating (25) and using (26) give Since [(d where In equation (28), the estimation error vector e is illuminated in (21). e derivatives of all vectors in the estimation error vector can be calculated from (25) and (26). From (28), obviously, we can choose appropriate matrix L q (q � 1, 2, 3, . . . , r) such that the eigenvalues of D r can be placed arbitrarily. Assume that L q are designed to guarantee the eigenvalues of D r less than zero. A positive symmetric matrix can be selected as follows: Define a Lyapunov functional, and λ min is the smallest eigenvalue; then, (31) Consequently, for (8), (25), and (26), after sufficiently long time, the norm of the estimation error is ultimately bounded by When the error state trajectory enters into the closed ball centered at e � 0 with radius φ and the smallest eigenvalue λ min > 0, the Lyapunov function satisfies _ V(e) < 0. It implies that the estimation error system is stable. e bound of the estimation error can be lowered by the appropriate choice of the parameter L q (q � 1, 2, 3, . . . , r).

SMC Based on the HODO.
When the system is attacked, SMC is an effective control strategy to guarantee the security of the system. However, the shortcoming is that the conventional SMC method would bring some adverse effects such as introducing overshoot. In this section, a HODObased SMC is presented. It should be noted that SMC and HODO are designed, respectively.
To be immune to attacks, a linear sliding surface based on the HODO is applied to improve the stability of the power system. e sliding surface is selected as follows: Theorem 1. Using HODO (17)- (20) and the designed controller law (35), all the states of (9) are ultimately bounded; therefore, the closed-loop system is asymptotically stable around equilibrium with the following control law: where ς � k d s * + k ε sign s * , and k d and θ are positive constants.
Proof. Construct a Lyapunov candidate function as It obviously elicits From (9) and (34), it follows that Inserting (35) into (39), we obtain _ s * � c 1 + c 2 l 111 + l 112 d 11 + c 2 + l 121 d 12 According to (24), we have en, substituting (41) to (40), we have Substituting (42) into (38), it follows that According to (21), is bounded as follows: is completes the proof. It should be noted that CA 2 B is invertible. e control block diagram of the proposed HODO-based SMC is shown in Figure 2. Figure 2 briefly illuminates the steps of the HODObased SMC. Firstly, the system dynamics is obtained, and coordinate transformation is performed. Secondly, the transformed coordinate is applied in the HODO. irdly, the estimated values calculated by the HODO work on the sliding mode surface. Finally, the calculated control law obtained from the sliding mode surface has an effect on the power system and the HODO.

Simulation Results with SMC
In this section, the proposed control strategy is analyzed by several numerical simulations. As we all know, in the cyberphysical power system, frequency deviation is the most important security index. Consequently, the frequency deviation is mainly discussed in the simulation.
In order to verify the effectiveness of the studied control strategy for the CPS, comparative results between the HODO-based SMC and the conventional SMC are simulated and analyzed. e system parameters for simulation are listed in Table 1 [23]. In this simulation, the second-and the third-order observer are analyzed for the effect of this control strategy.
By using the HODO based on equations (17)- (20), the second-and third-order disturbance observers are expressed as follows.
e second-order disturbance observer: e third-order disturbance observer: e control parameters and the initial variables are selected as

5.1.
Step Cyber Attack. In this case, a step cyber attack is applied without physical uncertainties. Cyber attack is executed to the microgrid, which is 0.1 pu. And the cyber attack is added at the initial time and ends at 5 s. Power system dynamic mode equation (5) Transformed system equation (7) Sliding surface equation (30) Control law equation (31) Equation (14) (q = 1) Equation (17 Figure 2: Block diagram of the system with the proposed SMC.  We can see that the proposed SMC can ensure system security (especially, frequency deviation). e simulation result is presented in Figure 3. Moreover, it has a small overshoot compared with the conventional SMC at the initial time.
An evaluation index based on frequency deviation is employed to demonstrate HODO's control performance, which is (48) Table 2 shows the evaluation index of frequency deviation between the conventional SMC and the second-order disturbance observer with different parameters. It can be concluded from Table 2 that the adjustment ability of the second-order disturbance observer is superior to the conventional SMC. Furthermore, the selection of the parameter in the second-order disturbance observer has an improvement on the overshoot.

Random Cyber Attacks.
In this case, the designed SMC with the second-order disturbance observer and third-order disturbance observer is tested in the microgrid. e random external attack is injected into the microgrid, which is ΔP d (t) � 0.2 sin(t) and ends at 15 s. e parameters of the disturbance observer are as follows: (a) e second-order disturbance observer: where f D2 and f D3 represent the evaluation index of the second-and third-order disturbance observer. It can be concluded that it quickly converges to 0 with the third-order disturbance observer, compared with the effect of the second-order disturbance observer.

Physical Uncertainties with Cyber Attacks.
e stochastic step attack is executed to the microgrid (see Figure 6). Adjust the uncertainty time constant T T , the governor time constant T g , and the speed drop R to 0.38, 0.08, and 2.5 in 20 s, respectively. System uncertainties and cyber attacks occur simultaneously between 15 and 20 seconds. When physical uncertainties appear in the secondary system, the system variables of the microgrid are gradually stable within the limited time by using HODObased SMC, which are shown in Figure 7.

Conclusion
In this paper, a HODO-based SMC is employed to guarantee the security of the cyber-physical power system. Firstly, HODO is applied to measure cyber attacks and physical uncertainties with matching and unmatching. Secondly, the SMC with the estimated value obtained by the HODO effectively stabilizes the system, furthermore, as compared with the conventional SMC and the proposed control strategy, and the advantage of the HODO-based SMC is small overshoot. In future, further research will be extended to the power-interconnected and time-delay system.

Data Availability
e data used in the research of this article are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.