Resilient Event-triggered Control of Grid Cyber-physical Systems Against Cyber Attack
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摘要: 本文将电动汽车（Electric vehicles，EVs）引入到典型的信息物理系统（Cyber-physical systems，CPS）智能电网中，采用负荷频率控制（Load frequency control，LFC）方法，能够快速抑制系统扰动所引发的频率变化.在考虑拒绝服务（Denial-of-Service，DoS）攻击的情况下，提出了一种弹性事件触发机制，使系统能够容忍攻击所造成的数据丢失.与此同时，PI型静态输出反馈控制器的输入按需更新，减少了通信负担.对于建立的闭环时滞系统模型，构造新型李亚普诺夫泛函，对系统进行稳定性分析，推导出系统所能承受的最大DoS攻击持续时间，并对控制器增益和弹性事件触发矩阵进行协同设计.最后，通过多域电力系统仿真，验证了所提出方法的有效性.Abstract: In this paper, the electric vehicles (EVs) are integrated into the smart grid, a class of representative cyber-physical systems (CPS), and can participate into the load frequency control (LFC) to promptly suppress the variations of system disturbances. In the case of denial-of-service (DoS) attacks, a resilient event-triggering scheme is proposed to allow the system to tolerate data loss caused by the attacks. At the same time, the PI-type static output feedback controller input is updated only when necessary so that the communication burden is reduced. For the established closed-loop time-delay system model, the new Lyapunov functional is constructed to analyze the stability and derive the maximum DoS attack duration, meanwhile the controller gain and the resilient event-triggering matrix are jointly designed. Finally, the effectiveness of the proposed method is verified through multi-area power system simulation.1) 本文责任编委 邓方
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图 1 基于弹性事件触发机制的电力CPS负载频率控制模型
Fig. 1 Grid CPS LFC model with a resilient event-triggered
表 1 带EVs电力CPS负载频率控制模型参数($i=1, 2, \cdots, n$)
Table 1 Parameters of power CPS LFC model including EV aggregators ($i=1, 2, \cdots, n$)
参数符号Parameter notations 物理含义Physical meanings $M_i$ 惯性常数 Inertia constant $D_i$ 负载阻尼常数 Load-damping constant $T_{gi}$ 调速器时间常数 Time constant of governor $T_{ci}$ 涡轮机时间常数 Time constant of turbine $T_{ri}$ 再热时间常数 Time constant of reheat $F_{pi}$ 总涡轮功率分数 Fraction of total turbine power $R_i$ 转速 Speed droop $\beta_i$ 频率偏差系数 Frequency bias factor $K_{EVi}$ 电池系数 Battery coefficient $T_{EVi}$ 电池时间常数 Time constant of battery $T_{ij}$ 联络线同步系数 Synchronizing coefficient of tie-line $\Delta f_i$ 频率偏差 Deviation of frequency $\Delta P_{tie-i}$ 联络线的功率交换 Power transfer of tie-line 
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表 2 带EVs三域LFC模型参数($i=1, 2, 3$)
Table 2 Parameters of three-area LFC model including EV aggregators ($i=1, 2, 3$)
参数 取值 $M_i$ 10 $D_i$ 1.0 $T_{gi}$ 0.1 $T_{ci}$ 0.3 $T_{ri}$ 10 $F_{pi}$ 0.05 $R_i$ 0.05 $\beta_i$ 21 $K_{EVi}$ 1 $T_{EVi}$ 1 $T_{ij}$ 0.026
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表 3 给定不同的$\sigma$和$\sigma_r$, 最大连续丢包量$\tau_M$和攻击持续时间$\tau_{{\rm dos}}$的值
Table 3 $\tau_M$ and $\tau_{{\rm dos}}$ for different $\sigma$ and $\sigma_r$
$\sigma$ 0.1 0.1 0.3 0.3 0.5 0.5 0.5 $\sigma_r$ 0.01 0.03 0.01 0.03 0.01 0.03 0.05 $\tau_M$ 2 1 4 2 5 3 2 $\tau_{{\rm dos}}$ 0.02 0.01 0.04 0.02 0.05 0.03 0.02
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