The use of bi-directional converters (BDCs) is crucial for enhancing power exchange in hybrid AC/DC networked microgrids (NMGs). However, the dynamic nature of their conversion efficiency and the non-convex conversion direction expression of BDC models result in a highly non-convex programming problem, which leads to significant computational challenges. This paper proposes a least squares approximation approach to simplify the complex trigonometric function that characterizes the dynamic changes in BDC conversion efficiency with power. The simplified expression transforms the original non-convex relationship into a computationally efficient convex form. Subsequently, we systematically explore and validate the sufficient conditions to achieve non-simultaneous rectification and inversion behaviors of BDCs in a convex form. These explored conditions are further customized and extended to various practical application scenarios. Case studies are conducted on a hybrid AC/DC NMG with 66 nodes. The results demonstrate that our proposed least squares approximation method transforms the computationally intractable model into one that is solvable. Additionally, the explored conditions contribute to a substantial reduction in solution time by more than two orders of magnitude. These results verify the superiority of our proposed method, and showcase its applicability in practical scenarios.

This paper proposes a post-disaster cyber-physical interdependent restoration scheduling (CPIRS) framework for active distribution networks (ADN) where the simultaneous damages on cyber and physical networks are considered. The ad hoc wireless device-to-device (D2D) communication is leveraged, for the first time, to establish cyber networks instantly after the disaster to support ADN restoration. The repair and operation crew dispatching, the remote-controlled network reconfiguration and the system operation with DERs can be effectively coordinated under the cyber-physical interactions. The uncertain outputs of renewable energy resources (RESs) are represented by budget-constrained polyhedral uncertainty sets. Through implementing linearization techniques on disjunctive expressions, a monolithic mixed-integer linear programming (MILP) based two-stage robust optimization model is formulated and subsequently solved by a customized column-and-constraint generation (C&CG) algorithm. Numerical results on the IEEE 123-node distribution system demonstrate the effectiveness and superiorities of the proposed CPIRS method for ADN.

This paper proposes a two-stage method for the robust design of resilient active distribution networks (ADNs) against high-impact and low-probability (HILP) events. The line hardening and the deployment of remote-controlled switches (RCSs) are considered as two powerful measures for resilience enhancement. Especially, the hardening of tie lines and the deployment of bilateral tie switches are emphasized as part of the resilient design. A novel progressive detection mechanism (PDM) is devised to estimate the potential propagation of outages and identify surviving nodes outside of the minimum outage area after intentional islanding. The proposed PDM method considers potential RCS locations among regular lines and tie lines on outage to calculate the global optimal design scheme. The two-stage robust design model is formulated as a mixed-integer linear programming (MILP). The nested column-and-constraint generation (nested C&CG) algorithm is customized to solve the proposed model. Numerical results on a modified IEEE 33-node distribution system demonstrate the effectiveness and the superiority of the proposed resilience enhancement method.

The post-disruption microgrid (MG) formation and the subsequent scheduling are resilience-enhancing measures for active distribution networks (ADNs) against disastrous events. This article proposes an integrated MG formation and scheduling solution, considering stochastic loads and distributed generators (DGs). Specifically, a first-stage MG formation model and a second-stage MG scheduling model are proposed to flexibly identify MG boundaries and restore as many critical loads as possible. The MG formation problem is formulated over multiple time steps to address time-varying generation outputs of intermittent DGs. Moreover, in the MG scheduling problem, the stochasticity of load demands and DG outputs is modeled as joint chance constraints (JCCs) to describe the possibility of security violations in the overall system. An efficient approximation method is next developed to convexify the JCCs into solvable second-order cones. The interaction between the MG formation and scheduling by the model predictive control implementation achieves a responsive solution for enhancing the emergency support capability of ADNs by incorporating power forecasts and real-time scheduling. The performance of the proposed method is verified in a modified real-world 136-node test feeder under catastrophic failures.

This article presents a dynamic restoration strategy for active distribution networks (ADNs) by coordinating repair crew dispatch and frequency-constrained cold load pickup. To incorporate the stochastic repair time, the repair crew dispatch is formulated as “event-driven” with the implementation of model predictive control (MPC). The stochastic repair time is estimated, convexified, and updated dynamically with each MPC execution. The finish of a repair task triggers the subsequent cold load pickup model, where the frequency dynamics are computed and linearly constrained with the help of a uniform frequency response model for low-inertia systems. Next, a co-optimization framework of the two models is developed to coordinate the repair crew dispatch and cold load pickup under a unified time scale. Numerical results on a modified IEEE 33-node test feeder and a real-world 136-node distribution system have verified the effectiveness of the proposed model.

With a rapid growth in the deployment of renewable and distributed energy resources (DERs) in active power distribution networks, especially the inverter-interfaced distributed generators (IIDGs), existing fault section estimation methods are facing additional challenges. This paper proposes an optimization model for fault diagnoses in active power distribution systems, which aims at simultaneous identifications of suspected fault line sections and potential false alarms sent by remote fault indicators (RFIs). First, mathematical expressions of expected and false alarms of oriented RFIs (ORFIs) and non-oriented RFIs (NRFIs) are formulated to construct a basic fault diagnosis model. Minimizing the number of false alarms is chosen as the objective function to find the most credible one from all possible fault hypotheses which represent different combinations of elements in the outage area. Next, considering IIDGs, a modified fault diagnosis model is established by eliminating misleading components from the objective function which are produced by incompetent RFIs and have failed to detect weak currents. The monitoring data provided by distribution level phasor measurement units (D-PMUs) for weak IIDG fault currents are leveraged to construct the equivalent RFI current, which is compared with the trigger threshold to find incompetent sensors. The proposed problem is formulated as a mixed-integer linear programming (MILP) model, which is solved by off-the-shelf commercial solvers. The effectiveness of the proposed fault diagnosis model is validated by test cases representing several DERs and false alarms applied to a utility feeder.