The integrity of distribution network state estimation is critically challenged by false data injection attacks, whose detection is often hampered by the numerical instability of underlying estimators. Such instability introduces artifacts that can mask an attack’s signature. This article presents a unified framework that achieves robust detection by decoupling these estimator artifacts from malicious data patterns. The framework’s core is a numerically stabilized forecasting aided state estimation employing a U-D factorization cubature Kalman filter (UD-CKF). By ensuring covariance positive-definiteness, it generates high-fidelity state estimates and, crucially, a statistically consistent innovation covariance matrix. This stable foundation enables a novel geometric inconsistency detector (GID). Instead of analyzing temporal patterns, the GID evaluates the geometric alignment between the observed innovation vectors and their expected statistical distribution defined by the UD-CKF. By monitoring the evolution of the innovation subspace, it effectively distinguishes the random orientation of noise from the persistent directional signature of a stealthy attack. This approach is validated on IEEE test feeders, demonstrating exceptional capability in identifying subtle FDIAs that remain undetected by magnitude-based or purely temporal methods.

Time series anomaly detection is essential in various fields such as industrial monitoring, cybersecurity, and finance. Traditional supervised methods often face challenges due to the limited availability of labeled anomaly instances for training. Moreover, these methods struggle to deal with intricate systems that incorporate information about topological structures. In this paper, we propose a novel approach called the Partially-Supervised Graph Derivation Network with Meta Learning (PS-GDNML) for time series anomaly detection. PS-GDNML combines the power of graph-based representations, partially-supervised learning, and meta-learning to enhance the effectiveness and robustness of anomaly detection. The method represents time series data as a graph, where each data point is a node, and temporal relationships are captured through edges. By leveraging a graph attention neural network (GAT), the model effectively captures complex dependencies and relationships within the data. To address the scarcity of labeled anomaly instances, PS-GDNML adopts a partially-supervised learning framework. It utilizes both labeled and unlabeled data, enabling the model to learn from the available information and generalize to detect anomalies in unseen data. Additionally, to explore the underlying commonalities of data across different time periods and enhance the model’s adaptability, we adopted a new meta-learning method called Task Relation Meta-Learner (TRMLearner). The purpose of this project is to utilize task relationships to guide the meta-learning optimization process. We evaluated the performance of PS-GDNML on benchmark datasets and compared it with state-of-the-art anomaly detection methods. The experimental results demonstrate that, even with a restricted set of labeled instances, our method excels at accurately detecting anomalies. Furthermore, the meta-learning component enhances the model’s capacity to generalize to novel and evolving anomaly patterns.

Power distribution networks are evolving toward a modernized cyber-physical system that is vulnerable to mounting cybersecurity threats brought by false data injection attacks (FDIAs). To address the issue, this article innovatively proposes a multiarea probabilistic forecasting-aided interval state estimation (MPF-ISE) framework for FDIA identification in power distribution networks. The framework devises a novel probabilistic forecasting (PF) approach to achieve interval pseudo measurement modeling. A nonlinear programming-based training algorithm is formulated to minimize the interval width of forecasting error quantiles, which are analytically approximated by Cornish-Fisher expansion. Next, real-time interval measurements are constructed based on the unknown-but-bounded theory. By implementing interval measurement conversion, the local PF-ISE model is converted into rectangular coordinate forms and iteratively solved using a modified Krawczyk operator. Then, the local model is extended to a multiarea form and solved by considering the information exchange between adjacent subareas. Finally, the solution of MPF-ISE, which takes into account measurement uncertainties and line parameter variations, is regarded as the normal operating level, thus forming the proposed FDIA identification scheme. Case studies on the modified IEEE 123-node test feeder demonstrate the superiority of the proposed PF and the effectiveness of MPF-ISE in identifying FDIAs compared with existing ones.

The state estimation method is troubled by heavy computational tasks and poor estimation tracking capability for the large-scale active distribution network. Given the aforementioned difficulty, in this article, we proposed a novel multiarea forecasting-aided state estimation (FASE) strategy to perceive the state of the system effectively. The proposed strategy begins with the implementation of an improved multiarea FASE model. The processing of multisource measurement data, such as microphasor measurement units and supervisory control and data acquisition, and equivalent load-based information interaction reliably complete the FASE of multiareas. Especially, a third degree dimensionality reduction square root cubature Kalman filter (SR-CKF) algorithm is designed for local FASE model considering the influence of large-scale distribution networks data on the numerical stability of the estimator. The case study shows the advantages of the proposed strategy in estimation accuracy, efficiency, and numerical stability compared with the existing ones.

Due to the rapid growth of distribution systems in urban areas, the increasing complexity of these distribution systems brings challenges to accurate topology identification. The collected voltage data from smart meters have been proven effective in topology identification applications. However, when multiple feeders are connected to the same bus, the accuracy of existing voltage-correlation-based topology identification can be degraded significantly. To address this challenge, a comprehensive inference method is proposed in this article to identify theon/offswitch state in the distribution system considering the same-bus-different-feeder condition. The voltage-power-dependence principle among connected nodes is revealed. Based on this theory, a physical probabilistic network model is proposed to represent the causal relationships between the switch states and the voltage-power dependence in a distribution network. The belief propagation algorithm is introduced to deduce the topology identification model, which can reduce the time consumption of the inference. The performance of the proposed method and its advantage over the existing methods are verified in case studies.

A grand challenge for the state estimation (SE) method in large-scale distribution networks lies in how to deal with the increasing computational tasks. This article addresses the issue and proposes a novel multiarea architecture for the unbalanced distribution network SE method. The first step of the method is to introduce an innovative multiarea state estimation (MASE) model using microphasor measurement units (μPMU) mixed with conventional supervisory control and data acquisition (SCADA) systems, with both the coordinate tensions and synchronization issues considered. The proposed model contains a SCADA measurement delay estimator and a MASE algorithm. Then, the hybrid state estimation (HSE) model is solved in a distributed way. In each subarea, the HSE problem is solved locally with minimal data exchanges among neighbor subareas. Case studies show the accuracy and efficiency enhancements obtainable of the proposed MASE method with respect to existing ones.

The increasing penetration of photovoltaic (PV) generators has led to a reduction in the effectiveness of existing strategies for restoring the power distribution network. This article proposes a dynamic robust restoration (DRR) framework for the recovery of outage power considering uncertain PV outputs and demands. This framework is presented in two subsequent steps. In the first step, optimal decisions regarding the network configurations are generated. The second step then computes the modified dynamic Distflow equations and constraints under consideration of the worst operating conditions over the associated uncertainty sets with the aim of maximizing the recovery of outage power. The DRR model is formulated as a bilevel mixed-integer linear programming problem. A decomposition algorithm in a master-sub structure is used to solve the resulting system. The results of case studies show that the proposed DRR model yields obvious advantages over the existing deterministic dynamic restoration model in terms of robustness against system uncertainties.

Distribution networks with high penetration of distributed generation yield complicated and uncertain power flow, which makes most existing faulted line identification methods not adaptable for industrial applications. Driven by this motivation, a novel single-phase-to-ground (SPTG) faulted line identification method is proposed based on hybrid state estimator (HSE). The first step of the method is to present an HSE for power distribution networks using power flow measurements mixed phasor measurement units. Then, an SPTG fault on a power line is treated as an event that suddenly increases one virtual bus in the monitored network, so as to form the extended bus admittance matrix and augmented HSE based on the specific network topology. In this way, the faulted line identification could be obtained by computing parallel estimated results transversally. Robustness and effectiveness of the proposed HSE and the HSE-based SPTG faulted line identification method are validated by means of a cyber-physical system (a cosimulation platform), where two typical three-phase power distribution networks are considered to simulate with its hybrid measurement system.