To enhance the resilience of distribution systems (DSs), networked microgrids (MGs) can be employed to restore critical loads after a blackout. However, uncertainties of renewable energy sources (RESs) and loads bring challenges to load restoration. This paper proposes a distributed risk-limiting load restoration strategy for unbalanced DS with networked MGs. In the proposed strategy, the risk is represented by the conditional value-at-risk (CVaR), based on which a risk-limiting load restoration model is formulated considering renewable and load uncertainties. With the projection function-based alternating direction method of multipliers (P-ADMM) and sub-additivity of the CVaR, the proposed risk-limiting model is decoupled and solved in a distributed manner. This enables distributed risk limiting among MGs. Each MG can make load restoration decisions individually, while ensuring that the risk-limiting constraints of the overall system are satisfied. The modified IEEE 123-node system with networked MGs was used to conduct case studies. Simulation results show that the proposed strategy can restore loads efficiently with a smaller risk index and can provide distributed and flexible risk management. Moreover, the proposed distributed strategy can reduce the computation burden and is more robust against controller failures compared with the centralized strategy.

With the advent of Smart Grids and advanced communication technologies, self-healing has become an important function of operation of electrical distribution systems (EDSs). In the presence of a permanent fault, an optimized self-healing scheme minimizes the unsupplied demand while having the faulted section isolated. The service restoration of the self-healing scheme is a combinatorial optimization problem whose computational complexity grows exponentially with the number of binary variables. To resolve this issue, a distributed optimal service restoration strategy is developed based on the alternating direction method of multipliers (ADMM). The service restoration problem is formulated as a mixed-integer second-order cone programming (MISOCP) problem. The decision variables of the problem are the status of the remote-controlled switches, load zones and load shedding at each controllable demand. Operational constraints, such as current and voltage magnitude constraints, distributed generation (DG) capacity constraints and radial topology constraints, are respected in the optimization problem. Through the ADMM, the optimization problem is distributed among the zones of the EDS without requiring a central controller. Case studies were conducted on an unbalanced 44-node system and the IEEE 123-node system. Results show that the proposed method can provide optimal service restoration solutions in reasonable time without a central controller.

This paper proposes a comprehensive scheme for day-ahead congestion management of distribution networks with high penetration of distributed energy resources (DERs). In the proposed scheme, the dynamic tariff (DT), network reconfiguration and re-profiling products are integrated, which combines the advantages of these methods. In addition, the previously proposed DT model is relaxed in order to handle possible infeasibility of the DT problem and set a limit for the DT. With the utilization of the flexibilities from various types of DERs and the advantages of the three congestion management methods, the proposed comprehensive scheme can solve the congestion more effectively and at the same time ensures that the congestion management prices are within an acceptable level. Three case studies were conducted with the modified Roy Billinton Test System (RBTS) to validate the effectiveness and advantages of the proposed comprehensive scheme.

This paper proposes a new distributed risk-limiting load restoration scheme for wind power penetrated interconnected bulk systems. The conditional value-at-risk (CVaR) is used as the risk-limiting index. The projection function based alternating direction method of multipliers algorithm (P-ADMM) is used to de-couple the CVaR integrated load restoration model into a distributed form. With the proposed algorithm, the risk-limiting constraints are decomposed and the complex non-convex load restoration model with the CVaR is transformed into small-scale scenario-based QP problems. The distributed risk-limiting load restoration scheme respects the individual decision-making of regional grids and reduces the security violation risk of the inter-connected bulk system under uncertain conditions. The CVaR integrated P-ADMM method can efficiently reduce the computation complexity of the load restoration optimization for the uncertain bulk system without loss of optimality. The effectiveness of the proposed method was validated using the IEEE-118 bus system connected with ten IEEE-33 bus systems.

This paper proposes a new scheme for bulk system restoration considering the available black-start resources (BSRs) in the distribution system (DS). The DS assisted generator start-up sequence (D-GSS) scheme is realized in a decentralized way, so that it does not only benefit the bulk system GSS by utilizing available BSRs in the DS, but also respects the independent operation of the transmission system operator (TSO) and distribution system operators (DSOs). First, the decentralized D-GSS scheme is presented including the interaction of the TSO and DSOs and the corresponding compact models. The models of the decentralized D-GSS scheme are built with the bulk system GSS modeled as a mixed-integer quadratic program (MIQP), the DS multi-step operation modeled as mixed-integer second-order conic programs (MISOCPs) and reliable power supply assessments of renewable energy sources as linear programs (LPs). Finally, a projection function based analytical target cascading (P-ATC) method is developed to iteratively solve the decentralized models with model complexity reduction. The P-ATC algorithm can handle integer variables and improve the computational efficiency of the iterative calculation process. The effectiveness of the proposed method is validated using the small-scale T6D2 system and large-scale T118D5 system, showing good GSS performance and computation efficiency.

This paper proposes a decentralized Volt/Var control method based on variable gradient projection (VGP) for the permanent magnet synchronous generator (PMSG)-based wind farm (WF). The aim is to achieve a fast Var response of each wind turbine (WT) to depress voltage fluctuations inside the WF caused by the stochastic wind and voltage disturbance of external girds. The gradient projection (GP) method is used in the PMSG-based WF to regulate terminal bus voltage within a feasible range in a fully decentralized manner while the dynamic characteristics of the PMSGs and grid side converters (GSCs) are taken into consideration. Moreover, according to the difference of the available power distribution among the WTs inside the WF, the adaptive and variable gain method is designed for the GP method, which can achieve maximum Var margin of each local WTs during the real-time operation of the WF. With the proposed control method, the PMSG-based WTs are coordinated to achieve near-global optimal performance only with local measurements. The voltage fluctuations of buses are reduced while the Var margin of WT converters is maximized. The WF with $24 \times 5$ MW WTs is tested in Matlab/Simulink with the real-time fully nonlinear AC power flow environment.