With the advance in communication facilities and information technologies, the state estimation (SE) of distribution networks is subject to intensified cybersecurity threats caused by false data injection attacks (FDIAs). To address the issues, this paper proposes a novel FDIA detection strategy for unbalanced distribution networks. The SE model and corresponding general imperfect FDIA are introduced first to emulate the attacking behavior in practice. To achieve FDIA detection, we propose a square-root unscented Kalman filter (SR-UKF) based forecasting-aided SE (FASE) to generate estimation results. By modifying the filtering step of the proposed FASE into a redundant linear regression form, random outliers can be effectively detected and suppressed by leveraging the projection statistics (PS). Afterward, based on the acquired SE results, a generalized likelihood ratio test (GLRT) is designed to detect FDIAs on consecutive snapshots. In the GLRT, the dynamic time warping (DTW) distance between two innovation sequences is set as the test variable, which is compared with the offline determined detection threshold under a specific false alarm rate. The feasibility of the proposed general imperfect FDIA and the effectiveness of the proposed FDIA detection strategy are validated through extensive numerical simulations.

An enormous challenge for state estimation (SE) in power distribution networks with high penetration of photovoltaic generators lies in how to deal with measurement uncertainty. Driven by this motivation, an interval arithmetic (IA) based SE is proposed in this paper, which considers interval modeling for measurement uncertainty. The proposed SE is formulated as two interval optimization models based on the unknown-but-bounded theory, and solution bounds of state variables are obtained using a two-stage linear programming approach. In particular, the proposed SE is extended to realistic power distribution networks with mixed microphasor measurement units (μPMU), voltage magnitude, smart meters and feeder terminal units. Case studies and results are illustrated and discussed to demonstrate the performance of the proposed IA-based SE. It could provide the operators intuitive and effective bounds of system states for advanced power industrial applications under consideration of uncertainty.

Distribution networks with high penetration of distributed generation (DG) yield complicated and uncertain power flow, which make 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 a HSE for power distribution networks using power flow measurements (PFM) mixed phasor measurement units (PMU). Then, a 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 co-simulation platform), where two typical three-phase power distribution networks are considered to simulate with its hybrid measurement system.

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.

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 ( μ PMU) 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 paper 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 Distflows 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 bi-level 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.