Power system state estimation is an essential component of the modern power system energy management system (EMS), and accurate state estimation is an indispensable basis for subsequent work. However, the attacker can inject biases into measurements to launch false data injection attacks (FDIAs) in smart grids, which ultimately cause state estimates to deviate from security values. This paper proposed the joint use of static state estimation and dynamic state estimation to detect the FDIA, i.e. the joint use of weighted least squares (WLS) and extended Kalman filter (EKF) with exponential weighting function (WEKF), which improves the robustness of state estimation. Since the WLS estimation considers only the measurements at the current moment, the recursive feature of the WEKF enables the estimation process to involve both historical state and current measurements. Therefore, consistency tests and residual tests were performed using the estimations of WLS and WEKF to effectively detect FDIA. In addition, a cluster partitioning approach with approximate equal redundancy of subsystems is proposed to locate the FDIA. The detection of FDIA triggers the partitioning of the network system, and then the chi-square test is used separately in each sub-network to determine the location of FDIA. Finally, the experimental results in the IEEE-14 bus system and the IEEE-30 bus system demonstrate that the approach can effectively detect and locate FDIAs.

An accurate power state is the basis of the normal functioning of the smart grid. However, false data injection attacks (FDIAs) take advantage of the vulnerability in the bad data detection mechanism of the power system to manipulate the process of state estimation. By attacking the measurements, then affecting the estimated state, FDIAs have become a serious hidden danger that affects the security and stable operation of the power system. To address the bad data detection vulnerability, in this paper, a false data attack detection method based on weighted least squares (WLS) and an adaptive interpolation extended Kalman filter (AIEKF) is proposed. On the basis of applying WLS and AIEKF, the Euclidean distance is used to calculate the deviation values of the two-state estimations to determine whether the current moment is subjected to a false data injection attack in the power system. Extensive experiments were conducted to simulate an IEEE-14-bus power system, showing that the adaptive interpolation extended Kalman filter can compensate for the deficiency in the bad data detection mechanism and successfully detect FDIAs.

The secure operation of smart grids is closely linked to state estimates that accurately reflect the physical characteristics of the grid. However, well-designed false data injection attacks (FDIAs) can manipulate the process of state estimation by injecting malicious data into the measurement data while bypassing the detection of the security system, ultimately causing the results of state estimation to deviate from secure values. Since FDIAs tampering with the measurement data of some buses will lead to error offset, this paper proposes an attack-detection algorithm based on statistical learning according to the different characteristic parameters of measurement error before and after tampering. In order to detect and classify false data from the measurement data, in this paper, we report the model establishment and estimation of error parameters for the tampered measurement data by combining the the k-means++ algorithm with the expectation maximization (EM) algorithm. At the same time, we located and recorded the bus that the attacker attempted to tamper with. In order to verify the feasibility of the algorithm proposed in this paper, the IEEE 5-bus standard test system and the IEEE 14-bus standard test system were used for simulation analysis. Numerical examples demonstrate that the combined use of the two algorithms can decrease the detection time to less than 0.011883 s and correctly locate the false data with a probability of more than 95%.

In a practical multichannel magnetocardiography (MCG) system based on superconducting quantum interference device (SQUID) magnetometers, the Tesla/Volt coefficient must be precisely calibrated for accurate analysis of heart diseases. In this article, we utilize the biplanar coil to calibrate the SQUID magnetometers in an MCG system for the first time. The coil design theory is discussed in detail, including the target-field theory and the Tikhonov regularization method. Also, the coil winding patterns can be obtained after discretization of the stream function, which is related to the current density. By defining the parameter of calibration uncertainty, the performance of the biplanar coil is analyzed and compared with a rectangular Helmholtz coil based on the COMSOL simulation method and experimental measurement. The measurement results are well in coincidence with the simulation ones, indicating that the biplanar coil has remarkable advantages over the Helmholtz coil. Also, Tesla/Volt coefficient calibrations of four SQUID magnetometers in an MCG system are conducted inside a magnetically shielded room (MSR) depending on these two coils. The final results show the superiority of the biplanar coil method in MCG system calibration.

The smart grid is built on an integrated and high-speed communication network, which renders it more vulnerable to cyber attacks. False data injection attacks (FDIAs) and sudden load changes (SLC) can bias state estimates (SE), causing the system to make incorrect decisions or provide incorrect outputs. For this reason, this paper proposes a novel outlier detection and state correction strategy. To detect outliers, we propose an extended Kalman filter (EKF) based on forecast assisted SE (FASE) to generate estimations. By modifying the prediction step in FASE into the form of adaptively adjusting the smoothing parameters, the accuracy of the state estimation can be improved. Then, outliers are detected using the deviation of the state estimate between the EKF and the weighted least squares (WLS) compared to a detection threshold determined offline at a specific false alarm rate. In addition, to recover the measurements and correction states in time, this paper proposes a data compensation strategy with a sliding window to compensate the measurements. Then, the compensated measurements are used to reconstruct the state equation and the measurement equation of the system. The IEEE 14-bus system and the IEEE 30-bus system are simulated to demonstrate the performance of the proposed algorithm in anomaly detection and state correction. Numerical examples show that our algorithm can accurately detect and correct states when anomalies are present.

This paper introduces a novel hybrid filtering algorithm that leverages the advantages of Phasor Measurement Units (PMU) to address state estimation challenges in power systems. The primary objective is to integrate the benefits of PMU measurements into the design of traditional power system dynamic estimators. It is noteworthy that PMUs and Supervisory Control and Data Acquisition (SCADA) systems typically operate at different sampling rates in power system estimation, necessitating synchronization during the filtering process. To address this issue, the paper employs a predictive interpolation method for SCADA measurements within the framework of the Extended Kalman Filter (EKF) algorithm. This approach achieves more accurate estimates, closer to real observation data, by averaging the KL distribution. The algorithm is particularly well-suited for state estimation tasks in power systems that combine traditional and PMU measurements. Extensive simulations were conducted on the IEEE-14 and IEEE-30 test systems, and the results demonstrate that the fused estimator outperforms individual estimators in terms of estimation accuracy.