Dynamic State Estimation of Distribution Network by Integrating High-degree Cubature Kalman Filter and LSTM Under FDIA

XU Daxing; SU Lei; HAN Heqiao; WANG Hailun; ZHANG Heng; CHEN Bo

doi:10.11999/JEIT250805

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XU Daxing, SU Lei, HAN Heqiao, WANG Hailun, ZHANG Heng, CHEN Bo. Dynamic State Estimation of Distribution Network by Integrating High-degree Cubature Kalman Filter and LSTM Under FDIA[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250805

Citation:

XU Daxing, SU Lei, HAN Heqiao, WANG Hailun, ZHANG Heng, CHEN Bo. Dynamic State Estimation of Distribution Network by Integrating High-degree Cubature Kalman Filter and LSTM Under FDIA[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250805

Citation:

XU Daxing, SU Lei, HAN Heqiao, WANG Hailun, ZHANG Heng, CHEN Bo. Dynamic State Estimation of Distribution Network by Integrating High-degree Cubature Kalman Filter and LSTM Under FDIA[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250805

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Dynamic State Estimation of Distribution Network by Integrating High-degree Cubature Kalman Filter and LSTM Under FDIA

doi: 10.11999/JEIT250805 cstr: 32379.14.JEIT250805

1.
School of Electrical and Information Engineering, Quzhou University, Quzhou 324000, China
2.
School of Automation, Hangzhou University of Electronic Science and Technology, Hangzhou 310018, China
3.
School of Computer Engineering, Jiangsu Ocean University, Lianyungang 222000, China
4.
School of Information Engineering, Zhejiang University of Technology, Hangzhou 310024, China

Funds: The National Natural Science Foundation of China (62441311), Quzhou Science and Technology Plan Project (2025K206)

Accepted Date: 2025-12-01
Rev Recd Date: 2025-12-01

Available Online: 2025-12-05

Abstract

Abstract

Objective Dynamic state estimation of distribution networks is a key technology for the safe and stable operation of cyber-physical power systems, but its accuracy and security are constrained by the system's strong nonlinearity, high-dimensional characteristics, and false data injection attacks (FDIA). This paper proposes a dynamic state estimation method fusing high-degree cubature Kalman filter (HCKF) and long short-term memory network (LSTM): first, HCKF is used to improve the estimation accuracy of nonlinear high-dimensional systems; second, the estimation results of HCKF and weighted least squares (WLS) are combined to achieve rapid FDIA detection based on residual analysis; finally, the LSTM model is adopted to reconstruct the measured data of attacked nodes and correct the state estimation results. The effectiveness of the proposed algorithm is verified on the IEEE 33-bus distribution system. Methods Due to the strong nonlinearity of the distribution system, the dynamic estimation method based on Cubature Kalman Filter (CKF) has limited state estimation accuracy. To this end, a hybrid measurement state estimation model based on Phasor Measurement Unit (PMU) and Supervisory Control and Data Acquisition (SCADA) is established. HCKF is used to improve the state estimation accuracy of strongly nonlinear and high-dimensional distribution networks through a high-degree cubature point generation strategy. In the face of FDIA launched by malicious attackers, the state estimation values of WLS and HCKF are combined, and rapid detection of FDIA is realized based on residual analysis and state consistency check. When FDIA is detected, the LSTM model is used for time-series prediction and reconstruction of the measurement data of the attacked nodes. Then, abnormal data is replaced and the state estimation results are corrected. Results and Discussions Experiments on the IEEE 33-bus distribution system show that in the absence of FDIA, the estimation accuracy of HCKF for voltage amplitude and phase angle is significantly better than that of CKF. The Average Voltage Relative Error (ARE) of voltage amplitude is reduced by 57.9%, and the ARE of voltage phase angle is reduced by 28.9%. These verify the advantage of the proposed algorithm in handling strongly nonlinear and high-dimensional systems. In the FDIA scenario, the detection method based on residual analysis can effectively identify cyber attacks and avoid false positives and false negatives. The prediction error of LSTM for the measurement data of attacked nodes and associated branches is on the order of 10^-⁶, indicating that the reconstructed data is reliable. The method combining HCKF and LSTM can still stably track the real state after the attack. The performance of the proposed algorithm is better than that of WLS, adaptive Unscented Kalman Filter. Conclusions The dynamic state estimation method combining HCKF and LSTM proposed in this paper improves the adaptability to the strong nonlinearity and high-dimensional characteristics of the distribution network through HCKF. Rapid and accurate detection of FDIA is realized based on residual analysis. The measurement data of attacked nodes is effectively reconstructed by means of LSTM. The proposed method can provide high-precision estimation in the absence of attacks. In the FDIA scenario, it can resist attack interference and maintain estimation stability and accuracy. It provides key technical support for the safe and stable operation of the distribution network in the environment of cyber attacks.
- State estimation,
- Distribution network,
- Kalman filter,
- False data injection attack (FDIA)

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References(15)

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