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Active resilient defense control against false data injection attacks in smart grids

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Abstract

The emerging of false data injection attacks (FDIAs) can fool the traditional detection methods by injecting false data, which has brought huge risks to the security of smart grids. For this reason, a resilient active defense control scheme based on interval observer detection is proposed in this paper to protect smart grids. The proposed active defense highlights the integration of detection and defense against FDIAs in smart girds. First, a dynamic physical grid model under FDIAs is modeled, in which model uncertainty and parameter uncertainty are taken into account. Then, an interval observer-based detection method against FDIAs is proposed, where a detection criteria using interval residual is put forward. Corresponding to the detection results, the resilient defense controller is triggered to defense the FDIAs if the system states are affected by FDIAs. Linear matrix inequality (LMI) approach is applied to design the resilient controller with H\(_{{\infty }}\) performance. The system with the resilient defense controller can be robust to FDIAs and the gain of the resilient controller has a certain gain margin. Our active resilient defense approach can be built in real time and show accurate and quick respond to the injected FDIAs. The effectiveness of the proposed defense scheme is verified by the simulation results on an IEEE 30-bus grid system.

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Abbreviations

a :

Attack vector

\(B_{ij}\) :

The susceptance of the power line

c :

State change caused by attack

\(D_{i}\) :

The damping coefficient of the ith generator

\(E_{qi}^{^{\prime }}\) :

The transient voltage in quadrature

\(\varkappa _{i}\) :

The inertia coefficient of the ith generator

H :

Jacobian matrix

\(K^{k}\) :

Gain of controller

\(\delta _{i}\) :

The phase angle of the ith generator

\(\omega _{i}\) :

The relative speed of the ith generator

\(\omega _{0}\) :

The synchronous machine speed

\(P_{mi}\) :

The mechanical input power

\(H_{i}\) :

The inertia coefficient of the ith generator

\(X_{ei}\) :

The steam valve opening of the ith generator

\(T_{mi}\) :

The time constant of the ith machine’s turbine

\(K_{mi}\) :

The gain of the ith machine’s turbine

\(T_{ei}\) :

The time constant of the ith machine’s speed governor

\(K_{ei}\) :

The gain of the ith machine’s speed governor

\(R_{i}\) :

The regulation constant of the ith machine

r :

State residual

\(r_{a}\) :

State residual under FDIAs

\(\tau \) :

Precomputed threshold

\(f^{k}\left( t\right) \) :

Attack vector

\(\varDelta A^{k}\) :

The matrix function representing time-varying parameter uncertainty

\(x^{k}\) :

The state vector of the kth interval observer

\({\underline{x}}^{k}\) :

The lower bounds of \(x^{k}\)

\({\bar{x}}^{k}\) :

The upper bounds of \(x^{k}\)

\(y^{k}\) :

The output vector of the kth interval observer

\({\underline{y}}^{k}\) :

The lower bounds of \(y^{k}\)

\({\bar{y}}^{k}\) :

The upper bounds of \(y^{k}\)

\(L^{k}\) :

The gain of the kth interval observer

\({\underline{r}}^{k}\) :

The lower bound of \(r^{k}\) respectively

\({\bar{r}}^{k}\) :

The upper bound of \(r^{k}\) respectively

\(x=\left( x_{1},x_{2},\cdots ,x_{n}\right) ^{\textrm{T}}\) :

State vector

\(z=\left( z_{1},z_{2},\cdots ,z_{n}\right) ^{\textrm{T}}\) :

Measurement vector

\(F^{k}\) :

A known real matrix with appropriate dimension

BDD:

Bad data detection

FDIAs:

False data injection attacks

DoS:

Denial of service attack

PMUs:

Phasor measurement units

WLS:

Weighted least squares

LMI:

Linear matrix inequality

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Author notes

  1. Xiaoyuan Luo, Lingjie Hou, Ruiyang Gao, Shuzheng Wang and Xinping Guan contributed equally to this work.

Authors and Affiliations

  1. School of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, Hebei, China

    Xiaoyuan Luo, Lingjie Hou, Xinyu Wang & Ruiyang Gao

  2. School of Electrical Engineering, Jiangsu Collaborative Innovation Center for Smart Distribution Network, Nanjing, 636600, Jiangsu, China

    Xinyu Wang & Shuzheng Wang

  3. School of Electronic and Electric Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Xinping Guan

Authors
  1. Xiaoyuan Luo
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Correspondence to Xinyu Wang.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

This work was supported by the National Nature Science Foundation of China (Nos. 62103357, 62203376), the Science and Technology Plan of Hebei Education Department (No. QN2021139), the Nature Science Foundation of Hebei Province (Nos. F2021203043, F2022203074) and the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network, Nanjing Institute of Technology (No. XTCX202203).

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Luo, X., Hou, L., Wang, X. et al. Active resilient defense control against false data injection attacks in smart grids. Control Theory Technol. 21, 515–529 (2023). https://doi.org/10.1007/s11768-023-00141-2

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