Resilient Adaptive Event-Triggered Load Frequency Control of Network-Based Power Systems against Deception Attacks

This paper investigates the problem of networked load frequency control (LFC) of power systems (PSs) against deception attacks. To lighten the load of the communication network, a new adaptive event-triggered scheme (ETS) is developed on the premise of maintaining a certain control performance of LFC systems. Compared with the existing ETSs, the proposed adaptive ETS can adjust the number of triggering packets, along with the state changes in the presence of deception attacks, which can reduce the average data-releasing rate. In addition, sufficient conditions can be derived, providing a trade-off between the limited network communication resources and the desired control performance of PSs. Finally, an application case is presented for the PSs to demonstrate the advantages of the proposed approach.


Introduction
It is known that load frequency control (LFC) is a core component of PSs, which governs the system frequency and power exchange between regions in an optimally scheduled way [1][2][3]. Proportional-integral (PI) control has been widely utilized as a common control strategy in LFC [4][5][6]. For example, the authors in [6] studied the area LFC problem using fuzzy gain scheduling with a PI controller. With the development of the PSs, control signals are transmitted via a special power channel and an networked communication infrastructure, which brings new challenges to the PI controller design of LFC. Recently, a lot of the published literature [7][8][9][10][11] has concerned networked LFC. For instance, in [8], an active interference suppression control method was proposed for interconnected LFC systems.
Since the control signals of PSs are transmitted through the communication network, the potential risks of LFC systems increases, such as cyber attacks [12][13][14][15][16][17]. Cyber-attacks have receieved great attention in recent years [1,2]. Usually, cyber-attacks discussed in the literature include denial of service (DoS) attacks and deception attacks. The deception attackers launch a attack by destroying data integrity, such as tampering or replacing transmitted data. In [18], a new control method was proposed in distributed networks subject to deception attacks. The DoS attacks prevent data transmission by occupying the shared network channel, thereby degrading the system performance. A resilient ETS was well-designed in [19] for LFC systems under DoS attacks. In [14], the event-triggered control was studied for multi-agent systems under DoS attacks.
In NCS, the time-triggered scheme (TTS) is widely used to obtain the system information through the sampler, under which a fixed sampling interval can guarantee the desired performance even if there are uncertainties, time-delays, external disturbances, etc. [20,21]. However, too many "unnecessary" sampling signals are transmitted via the network, which leads to a waste of resources [22,23]. To deal with these shortcomings, an event-triggered scheme (ETS) has been widely applied to ease the network burden in recent decades. Compared to the TTS, the sampling data packets are released only when an event generated by some elaborate condition occurs, which can effectively improve resource utilization while ensuring a satisfied system performance [24][25][26][27]. However, due to the complexity of the system and the contradiction between better system performance and a lower data transmission rate, it is usually difficult to design the threshold of event-triggered conditions in the practical application system. Therefore, some state-of-the-art ETSs have been proposed, such as memory-based ETS and adaptive ETS. The authors in [28] proposed a memory-based ETS for T-S fuzzy systems, wherein some historical triggered data were utilized in the ETS so that the control performance can be ensured. The authors in [29,30] proposed an adaptive ETS for nonlinear systems, wherein the threshold can be adjusted with the system states. However, the problem of H ∞ -based LFC for network-based PSs under deception attacks by adopting adaptive ETS has not yet been reported, which prompted this study.
In sum, the goal of this work is to design an adaptive event-triggered controller for LFC systems subject to deception attacks. Differing from the existing ETS with a preset threshold, the improved adaptive ETS can adjust the number of triggering packets along with the state changes, under which the transmission rate can be cut down while maintaining the desired frequency performance of LFC systems under deception attacks. Figure 1 displays a block diagram of a single-area LFC power system, where the area control error is presumed to be transmitted to the PI controller via a shared communication network.

Description of the LFC Systems
As shown in Figure 1, the model of the LFC systems can be indicated as follows [31] where the symbols of the LFC system are listed in Table 1 [2].
By applying the inverse Laplace transform to (1), it can be obtained that (2)

Adaptive ETS Controller Design
Simular to [10], the PI control strategy of the LFC systems is designed as where K P denotes proportional gain and K I stands for integral gain. For convenience of obtaining the controller gains, we transform the above PI control form into the output feedback problem. Then, we redefine the output variables Define K = [K P K I ], and we can rewrite (4) as However, the sampled signal of ACE (t) of networked LFC systems will only be released to the PI controller via the network when the preset condition is satisfied [20]. To adjust the number of triggering packets in the LFC system, along with the state changes under deception attacks, an improved adaptive ETS is put forward, as follows: where h is the sampling period, φ is a positive symmetric matrix to be designed, t k h is the data-releasing instant, wherein α ∈ (0, 1) is the upper bound of σ(t), ι and α are given positive constants.

Remark 1.
It can be seen from (7) that σ(t) can adaptively adjusted to the system states by a arctangent function, which is different from the existing ETS with a constant threshold. When the system states fluctuate, σ(t) will be adaptively adjusted to a lower value, by which more packets with the system information can be released to the controller. When the system is stable, σ(t) will be automatically adjusted to a larger value to decrease the release rate of sampled packets.
Based on the condition (6), one can obtain that Since the communication network is vulnerable to cyber attacks, the transmission signal can be written asŷ where the Bernoulli variable ϕ(t) ∈ {0, 1} is introduced to characterize the behavior of random deception attacks, E{ϕ(t)} =φ, E{(ϕ(t) −φ) 2 } = ρ 2 and the nonlinear attack signal ð(t) satisfies where G is a known matrix with appropriate dimension.

Remark 2.
Cyber-attack has receieved great attention in recent years since it is one of the major threats to system stability [1,2,19]. Usually, cyber-attacks discussed in the literature include DoS attacks and deception attacks. The DoS attacks prevent data transmission by occupying the shared network channel, thereby degrading system performance. The deception attackers launch an attack by destroying data integrity, such as tampering with or replacing transmitted data. In this paper, we consider a kind of deception attack when investigating the LFC problem of PSs.

Remark 3.
When ϕ(t) = 1, the true measurement data are replaced with the data of deception attacks. Otherwise, the true measurement data can be transmitted to the controller.
Considering the deception attacks, the output of the controller in (5) can be rewritten as

Closed-Loop Control of LFC Systems
According to the adaptive ETS in (6), the current signal is maintained by the zeroorder holder (ZOH) until the next packet is transmitted. Therefore, we need to divide the interval Π = [m ,n) into ℘ + 1 pieces, wherem = t k h + λ t k ,n = t k+1 h + λ t k+1 . The network-induced delay at instant t k h is denoted by λ t k and the holding interval Π can be divided into where (4)-(13), the LFC systems (3) with an adaptive event-triggered PI controller against deception attacks can be formulated as The purpose of this article is to design the adaptive event-triggered PI controller subject to deception attacks, while ensuring that E{ y(t) } ≤ E{γ ω(t) } holds with zero initial state conditions when ω(t) = 0, and the LFC system (14) could achieve stability with ω(t) = 0.

Main Results
In this section, we use the Lyapunov-Krasovskii function method to derive the stability criteria of the LFC system. Then, the weight matrix of adaptive ETS and the controller gain will be calculated by LMIs. The statement of sufficient conditions for the LFC system are shown in the following. Theorem 1. For given scalarsλ > 0, α ∈ (0, 1),φ ∈ (0, 1), ρ, H ∞ norm bound γ, and matrix K, the system (14) is asymptotically stable, if there exist matrices P > 0, P 2 > 0, R > 0, Q > 0 W > 0 and a matrix U such that where Proof. Construct a Lyapunov-Krasovskii function in [31] for the system (14) as Define (t) =λ 2ẋT (t)Rẋ(t) +λ 2ẋT (t)Wẋ(t); then, the following results can be derived from (17), where From the adaptive ETS (6), one can obtain According to inequality (10), it has where P 2 is a positive symmetric matrix.
To solve the problem of equality (24) in Theorem 2, we use the optimization algorithm in [32], which can be expressed as where κ > 0 is a small enough constant. Furthermore, the controller gain could be calculated by (25), (26) and (28).

Simulation Examples
An application example of LFC systems in [33,34] is given to verify the efficacy of the method, whose nominal values are listed in Table 2. Select the attack function ð(t) = −tanh (Gy(t)) [2] and G = diag{0.8, 0.1}. The mathematic expectation of the deception attack is given asφ = 0.5. The disturbance is chosen as otherwise.
Next, two cases are utilized to manifest the proposed method for LFC systems. It is assumed that the initial condition of system is The results are obtained in Figures 2-5. The state responses of the LFC system in Case 1 are shown in Figure 2, which indicates that the LFC system is stable after 60 s. Figure 3 illustrates the responses of control input. The adaptive law σ(t) is shown in Figure 4, where the curve finally converges to the upper bound α = 0.8, which indicates that the amount of transmitted signals is greatly reduced when the system is stable. Figure 5 illustrates the deception attack signals of simulation.    Figure 6 depicts the system state trajectories, from which one can see that the state response curves of the turbine output power ∆H m and frequency deviation ∆a of the closed-loop system subjected to changes in load demand. Compared to Figure 2 in Case 1, the turbine output power ∆H m and the system frequency deviation ∆a approach zero in a shorter time, which indicates the use of controller in Case 2 can better mitigate the impact of deception attacks and suppress the fluctuations in system frequency and restore the stability of the system. The control input of the LFC system based on adaptive ETS are displayed in Figure 7. Figure 8 exhibits the threshold σ(t) of the system with adaptive ETS, where the triggering threshold is automatically adjusted even if the system suffers from the disturbance. When the system is stable, the adaptive threshold converges to a constant.  To reflect the merits of the proposed method in saving the network bandwidth, we compare the adaptive ETS with the conventional ETS as follows: (i) Consider σ(t) in adaptive ETS (6) with the parameters α = 0.8, ι = 1.
(ii) The ETS in (6) with a fixed thresholdσ is considered, which is reduced to a conventional ETS. Without loss of generality, the threshold is selected to be an average value that can be calculated byσ where ν ∈ N, σ ν denotes the ν-th the triggering threshold in adaptive ETS (6) at the ν-th sampling instant, and NDS is the number of data samplings. Using LMIs, one can obtain the controller gains of two ETSs, which are listed in Table 3. The event-triggered constantσ = 0.7 is calculated by (29) within 60 s. Figures 9 and 10 plot the triggering and releasing intervals of the discussed system under two schemes, in which fewer sampling packets are released over the network under the adaptive ETS. For better analysis, the statistical results of the NDS, and the packetreleasing (NPR) and data-releasing rate (DRR) for two ETSs are written in Table 4, wherein DRR = NPR NDS .   As shown in Table 4, the number of sampling data is 1200 within 60 s. Under the adaptive ETS (6) proposed in this paper, the number of released packets is 31, and the DRR is 2.58%. Compared to the DRR = 3.58% of the conventional ETS, the proposed adaptive ETS can significantly reduce the transmission of unnecessary packets. This indicates that more communication resources can be saved by utilizing our developed adaptive ETS.

Conclusions
The problem of H ∞ LFC has been addressed for LFC systems under deception attacks by applying the developed adaptive ETS in this paper. To solve the issues of limited communication resources and deception attacks, a new adaptive ETS has been proposed, by which the thresholds for event-triggered conditions could be adapted to the changes in the system state under deception attacks. Based on the adaptive ETS, the average data released are lower than under the conventional ETS, and the perfomance of LFC systems subject to deception attacks can be guaranteed. Finally, the simulation results demonstrate the reliability of our proposed scheme. In future research, actuator saturation for LFC systems under cyber attacks will be worth consideration under the proposed adaptive ETS.
Author Contributions: All of the authors contributed substantially to this work: Conceptualization, X.Z. and X.S.; Methodology, F.Y. and X.Z.; Software, X.Z. and X.S.; Formal Analysis, X.Z.; Investigation, F.Y. and X.S.; Resources, F.Y.; Data Curation, X.Z.; Writing-Original Draft Preparation, Review and Editing, X.Z., F.Y. and X.S.; Project Administration, F.Y.; Funding Acquisition, F.Y. and X.S. All authors have read and agreed to the published version of the manuscript.