Mobile emergency generators (MEGs) can effec-tively restore critical loads as flexible backup resources after power network disturbance from extreme events, thereby boost-ing the distribution system resilience. Therefore, MEGs are re-quired to be optimally allocated and utilized. For this purpose, a novel three-stage stochastic planning model is proposed for MEG allocation of resilient distribution systems in consideration of planning stage (PLS), preventive response stage (PRS) and emergency response stage (ERS). Moreover, the nonanticipativity constraints are proposed to guarantee that the MEG allocation decisions are dependent on the stage-based uncertainties. Specif-ically, in the PLS, the intensity uncertainty (IU) of disasters and the outage uncertainty (OU) incurred by a given disaster are considered with probability-weighted scenarios for the effective MEG allocation. Then, with the IU that can be observed in the PRS, the MEGs are pre-positioned in the consideration of OU. It is noted that the pre-position decisions should only correspond to the IU realizations, according to nonanticipativity constraints. Last, with the further realization of OU in the ERS, the MEGs are re-routed from the pre-position to the target location, so that the provisional microgrids can be formed to restore critical loads. The proposed planning model can be large-scale due to multiple sce-narios. Therefore, the progressive hedging algorithm (PHA) is customized to reduce the computational burden. The simulation results in 13 and 123 node distribution systems show the effec-tiveness and superiority of the proposed three-stage MEG plan-ning model over the traditional two-stage model.

Traditional simulation-based method for resilience assessment of distribution systems is very time consuming since the network topology is characterized with a large number of scenario-specific optimization models. In this paper, we propose a methodology for fast resilience assessment of distribution systems with a non-simulation-based, which can significantly improve the assessment accuracy and computational efficiency. First, a probabilistic metric is proposed to assess the system resilience against extreme events, which quantifies the system performance starting from the pre-event stage to the post-event stage. Then, a mixed-integer linear programming (MILP) is proposed to model the energization paths (EPs) with binary decision variables. Subsequently, the resilience metric-related probability events are built using the EPs. Last, the probabilistic resilience metric is explicitly expressed based on the total probability formula, conditional probability formula and EP-topology simplification methods. In the proposed method, the topology evolution along with the system degradation, restoration (part healed) and recovery (all healed) is characterized with a non-simulation-based method, rather than the multiple scenarios in traditional methods. The numerical tests validate the effectiveness of the proposed method and superiority over the simulation-based approach

Multiple wind farms (WFs) should be spatially and temporally coordinated during inertial control to avoid the under- or over-power supply. For this purpose, we propose a second-order cone predictive model to exploit the optimal inertial control scheme (ICS) of multiple WFs for under-frequency and over-frequency events. Specifically, we firstly build the nonlinear predictive model including the predictive models of synchronous generators and wind turbines (WTs), power flow model and the stable operating constraints. In this nonlinear model, multiple WFs can be properly coordinated to achieve the optimal ICS. Then, the approximation methods are proposed to recast the above nonlinear model as a second-order cone programming (SOCP), and a sequential SOCP algorithm (SSA) is presented for the optimal solution. The SOCP model is offline executed to generate the optimal power references of WFs, and power references are further fitted with 5-parameter piecewise curves to reduce the communication burden. Lastly, the fitted curves can be distributed to WF controllers to be online tracked after detecting the disturbance. Numerical tests are conducted based on the 5 WFs integrated IEEE 39-bus system to validate the effectiveness and superiority of the proposed method.

For wind farm clusters, the overall performance of reactive power optimization can be further improved via optimal network switching. The problem can be precisely formulated as a mixed integer nonlinear programming (MINP) model, which is intractable since its non-convexity and nonlinearity. In this paper, a deep reinforcement learning (DRL) based algorithm is proposed to improve the real-time performance. There are two stages in this solution, the first stage is to train the agent. The second stage is online application using the trained agent and the MINP model can be efficiently solved. Considering the operational constraints, a learning framework containing over-limit behavior penalty and model-guided control is introduced. Furthermore, a weighted sampling method and asymptotic convergence strategy are applied to enhance the training efficiency. Numerical tests show that the proposed algorithm can solve this problem with acceptable computation time and the optimal network switching strategies can further improve the wind farms’ safety and economic level.