A Novel Detection and Identification Mechanism for Malicious Injection Attacks in Power Systems
Abstract
:1. Introduction
2. Related Works
 How to address the limitation caused by precomputed threshold;
 How to cut down the effect of model error and external disturbance.
 A novel detection model is developed based on the UIOs and cosine similarity theorem. By designing the UIOs to handle the effect of model error and external disturbance, the accuracy of state estimation can be improved. By using the principle of cosine similarity matching, the limitation caused by the precomputed detection threshold can be addressed.
 An observer combinationbased attack identification framework is proposed. By introducing the observer combination strategy, the influence caused by the injected FDI attacks can quickly be identified and eliminated.
3. Problem Description
3.1. ThreePhase VoltageBased Power State Model
3.2. Problem Formulation
4. Detection and Identification Mechanism for FDI Attacks
4.1. UIOBased State Estimation
4.2. Cosine Similarity TheoremBased Detection Method
Algorithm 1: Cosine similarity theorembased detection algorithm against FDI attacks 
1. $GCM\to \mathrm{Grid}\text{}\mathrm{state}\text{}\mathrm{model}$; 2. $UIOs\to \mathrm{Unknown}\text{}\mathrm{input}\text{}\mathrm{observers}$; 3. $ES\to Estimation\text{}\mathrm{state}$; 4. $CSV\to cosine\text{}similarity\text{}value$ 5. $UIOs\leftarrow GCM$; 6. $ES\leftarrow UIOs$; 7. $CSV\leftarrow ES$ 8. $IF\text{}0\leftarrow CSV,\text{}\mathrm{No}\text{}\mathrm{attacks}$ 9. $ELSEIF\text{}\mathrm{attacks}$ 
4.3. Observer CombinationBased Identification Method
Algorithm 2: Observer combinationbased attack identification 
1. ${y}_{1}\cdots {y}_{N}\to All\text{}\mathrm{outputs}$ 2. $RIFEH\to repeated\text{}iteratively\text{}for\text{}each\text{}half\text{}of\text{}the\text{}attacked\text{}ouputs$ 3. $UIOs\to \mathrm{Unknown}\text{}\mathrm{input}\text{}\mathrm{observers}$; 4. $CSV\to cosine\text{}similarity\text{}value$ 5. $UIOs\leftarrow {y}_{1}\cdots {y}_{N}$ 6. $IF\text{}1\leftarrow CSV,\text{}\mathrm{attacks}$; 7. $RIFEH\leftarrow {y}_{1}\cdots {y}_{\raisebox{1ex}{$N$}\!\left/ \!\raisebox{1ex}{$2$}\right.}\text{}\mathrm{and}\text{}RIFEH\leftarrow {y}_{\raisebox{1ex}{$N$}\!\left/ \!\raisebox{1ex}{$2$}\right.}\cdots {y}_{N}$ 8. Else no attacks; 9. Repeat steps 5–7; 10. Output: the attacked nodes. 
5. Results
5.1. Case 1: Detection of One FDI Attack on an IEEE 6Bus Power System
5.2. Case 2: Detection and Identification of Multiple FDI Attacks on an IEEE 39Bus Power System
5.3. Case 3: Detection and Identification of Multiple FDI Attacks on IEEE 118Bus Power System
6. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Definition of all parameters  
${A}_{\iota}$  amplitude of the threephase voltage 
$\omega t$  angular frequency 
$\theta $  angular phase 
${V}_{1}\left(k\right)$  voltage signal of the 1st generator 
${V}_{2}\left(k\right)$  voltage signal of the 2nd generator 
${V}_{3}\left(k\right)$  voltage signal of the 3rd generator 
${\Delta}_{k}$  model error and external disturbance, which is normbounded 
$C$  observation matrix of appropriate dimensions 
$B$  constant matrix of appropriate dimensions 
${\lambda}_{k}$  output residual 
${\mathit{z}}_{k}$  measurement output 
$\tau $  the precomputed detection threshold 
${\hslash}_{k}^{f}$  output residual under FDI attacks 
${\mathit{z}}_{k}^{f}$  measurement output under FDI attacks 
${\hat{\mathit{x}}}_{k}^{a}$  state estimation under FDI attacks 
$\mathcal{l}$  increment of state caused by the attack 
$F$  attackselected matrix of appropriate dimensions 
${\tilde{A}}^{l}$  constant matrix of appropriate dimensions 
${K}^{l}$  constant matrix of appropriate dimensions 
${z}_{k+1}^{l}$  state vector of UIO 
${\hat{x}}_{k}^{l}$  estimation value of ${x}_{k}^{l}$ 
${H}^{l}$${G}^{l}$${U}^{l}$${K}^{l}$  designed system parameter matrix 
${P}_{6}^{l}$  constant matrix of appropriate dimensions 
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Category  Approach  Advantages  Disadvantages 

Datadriven methods  [11,12,13,14,15,16,17,18] 


Modelbased methods  [19,20,21,22,23,24,25] 

System  Detection Time (s)  Identification Time (s) 

6bus  0.8  1.2 
39bus  1.5  3.8 
118bus  2.2  4.5 
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Zhang, H.; Wang, X.; Ban, L.; Sun, M. A Novel Detection and Identification Mechanism for Malicious Injection Attacks in Power Systems. Symmetry 2023, 15, 2104. https://doi.org/10.3390/sym15122104
Zhang H, Wang X, Ban L, Sun M. A Novel Detection and Identification Mechanism for Malicious Injection Attacks in Power Systems. Symmetry. 2023; 15(12):2104. https://doi.org/10.3390/sym15122104
Chicago/Turabian StyleZhang, Hongfeng, Xinyu Wang, Lan Ban, and Molin Sun. 2023. "A Novel Detection and Identification Mechanism for Malicious Injection Attacks in Power Systems" Symmetry 15, no. 12: 2104. https://doi.org/10.3390/sym15122104