Dynamic State Estimation of Smart Grid Based on UKF Under Denial of Service Attacks
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摘要: 针对连续拒绝服务（Denial of service，DoS）攻击导致量测数据丢失使得动态状态估计失效、进而破坏智能电网安全经济运行问题，本文提出了一种适用拒绝服务攻击的改进无迹卡尔曼滤波（Unscented Kalman filter，UKF）方法，以进行智能电网动态状态估计.首先，分析拒绝服务攻击引起数据丢包特性并设计了数据补偿策略，以重构电力系统动态模型；然后，结合Holt's双参数指数平滑和无迹卡尔曼滤波方法，构造了融合补偿信息的新状态估计方程，并进一步基于估计误差协方差矩阵推导了状态增益更新方法，从而得到了无迹卡尔曼滤波动态状态估计新方法.最后，针对IEEE 30和118节点系统进行仿真，验证了所提方法的可行性和有效性.Abstract: When continuous denial of service (DoS) attacks cause measurement data losses in smart grid, the traditional dynamic state estimation is useless, destroying the running safety of smart grid seriously. To solve the problem, an improved unscented Kalman filter (UKF) is proposed, which can estimate the dynamic state of smart grid under DoS attacks. Firstly, the characteristics of data packet losses resulting from DoS attacks are analyzed and data compensation strategy is designed to reconstruct the dynamic model of power system. Integrating Holt's two-parameter exponential smoothing and unscented Kalman filter algorithms, a new state estimation equation including the compensation information is then constructed. Furthermore, a state gain updating method is derived from the estimated error covariance matrix, which produces a new enhanced UKF dynamic state estimation algorithm. Finally, simulations on IEEE 30-bus and 118-bus system confirm the feasibility and effectiveness of the proposed method.1) 本文责任编委 吴立刚
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图 1 拒绝服务攻击下基于改进UKF动态状态估计流程图
Fig. 1 Flowchat of new-UKF dynamic state estimation algorithm under DoS attacks
图 3 IEEE30节点系统丢包时序图$(\rho=0.05)$
Fig. 3 Data packet loss sequence of IEEE 30-bus system $(\rho=0.05)$
图 4 DoS攻击下节点2的电压幅值和相角的估计值$\left( \rho = 0.05 \right)$
Fig. 4 Estimated voltage magnitude and phase angle at bus 2 under DoS attacks $\left( \rho = 0.05 \right)$
图 5 DoS攻击下系统状态估计误差和性能指标$\left( \rho = 0.05 \right)$
Fig. 5 State estimation error and performance index of the system under DoS attacks $\left( \rho = 0.05 \right)$
图 6 在DoS攻击下节点2的电压幅值和相角估计值$\left( \rho = 0.1 \right)$
Fig. 6 Estimated voltage magnitude and phase angle at bus 2 under DoS attacks $\left( \rho = 0.1 \right)$
图 7 DoS攻击下系统状态估计误差和性能指标$\left( \rho = 0.1 \right)$
Fig. 7 State estimation error and performance index of the system under DoS attacks $\left( \rho = 0.1 \right)$
图 8 DoS攻击导致4种不同数据丢包概率下IEEE 30节点系统的状态估计误差和性能指标
Fig. 8 State estimation error and performance index of IEEE30-bus system with four different $\rho$ values
图 9 DoS攻击下IEEE 30节点系统采用改进UKF算法和传统UKF算法状态估计误差和性能指标比较$\left( \rho = 0.05 \right)$
Fig. 9 Comparison of state estimation error and performance index of IEEE 30-bus system by using new-UKF and UKF methods under DoS attacks $\left( \rho = 0.05 \right)$
图 11 DoS攻击导致4种不同数据丢包概率下IEEE 118节点系统的状态估计误差和性能指标
Fig. 11 State estimation error and performance index of IEEE118-bus system with four different $\rho$ values
图 12 DoS攻击下IEEE 118节点系统采用改进UKF算法和传统UKF算法状态估计误差和性能指标比较$\left( \rho = 0.05 \right)$
Fig. 12 Comparison of state estimation error and performance index of IEEE 118-bus system by using new-UKF and UKF methods under DoS attacks $\left( \rho = 0.05 \right)$
表 1 网络数据包传递表
Table 1 Data packet transmission in network
$k$ ${\lambda _k(1)}$ ${\lambda _k(2)}$ ${\lambda _k(3)}$ ${\phi _k}$ ${\tau _k}$ ${k - {\tau _k} + 1}$ ${\bar z_k}$ 1 1 0 1 1 ${z_1}$ 2 1 0 1 2 ${z_2}$ 3 0 1 1 2 2 ${z_2}$ 4 0 0 1 2 3 2 ${z_2}$ 5 1 0 1 5 ${z_5}$ 6 0 1 1 2 5 ${z_5}$ 7 1 0 1 7 ${z_7}$ 8 0 1 1 2 7 ${z_7}$ 9 1 0 1 9 ${z_9}$ 10 1 0 1 10 ${z_{10}}$ 
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表 2 IEEE 30节点系统动态状态估计结果
Table 2 Dynamic state estimation results of IEEE 30-bus system
k 25 50 75 100 状态真值 ${x_2}$ -0.1314 -0.1322 -0.1312 -0.1312 -0.1311 ${x_4}$ -0.2497 -0.2495 -0.2493 -0.2505 -0.2481 ${x_6}$ -0.2259 -0.2261 -0.2256 -0.2252 -0.2249 ${x_8}$ -0.2450 -0.2456 -0.2456 -0.2463 -0.2460 ${x_{10}}$ -0.2443 -0.2462 -0.2443 -0.2473 -0.2460 ${x_{12}}$ -0.2636 -0.2627 -0.2625 -0.2655 -0.2656 ${x_{14}}$ -0.2800 -0.2816 -0.2807 -0.2791 -0.2809 ${x_{16}}$ -0.2776 -0.2792 -0.2783 -0.2807 -0.2780 ${x_{18}}$ -0.2935 -0.2941 -0.2923 -0.2937 -0.2940 ${x_{20}}$ -0.2822 -0.2859 -0.2842 -0.2841 -0.2842 ${x_{22}}$ -0.2826 -0.2863 -0.2847 -0.2837 -0.2844 ${x_{24}}$ -0.2838 -0.2788 -0.2842 -0.2824 -0.2815 ${x_{26}}$ -0.2739 -0.2715 -0.2746 -0.2708 -0.2741 ${x_{28}}$ -0.2929 -0.2898 -0.2966 -0.2923 -0.2963 ${x_{30}}$ 1.0606 1.0603 1.0599 1.0595 1.0600 ${x_{32}}$ 1.0127 1.0150 1.0119 1.0132 1.0135 ${x_{34}}$ 0.9986 1.0012 1.0015 0.9973 1.0000 ${x_{36}}$ 0.9906 0.9935 0.9925 0.9900 0.9924 ${x_{38}}$ 1.0299 1.0327 1.0280 1.0309 1.0305 ${x_{40}}$ 1.0711 1.0718 1.0690 1.0747 1.0720 ${x_{42}}$ 1.0734 1.0743 1.0687 1.0718 1.0710 ${x_{44}}$ 1.0202 1.0214 1.0184 1.0208 1.0194 ${x_{46}}$ 1.0085 1.0140 1.0085 1.0136 1.0116 ${x_{48}}$ 0.9994 1.0019 0.9952 1.0031 0.9996 ${x_{50}}$ 1.0000 1.0020 0.9980 1.0005 1.0008 ${x_{52}}$ 1.0005 1.0025 0.9985 1.0013 1.0012 ${x_{54}}$ 0.9955 0.9961 0.9926 0.9919 0.9945 ${x_{56}}$ 1.0058 1.0086 1.0052 1.0037 1.0053 ${x_{58}}$ 0.9863 0.9889 0.9860 0.9845 0.9851
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