No Arabic abstract
When a major outage occurs on a distribution system due to extreme events, microgrids, distributed generators, and other local resources can be used to restore critical loads and enhance resiliency. This paper proposes a decision-making method to determine the optimal restoration strategy coordinating multiple sources to serve critical loads after blackouts. The critical load restoration problem is solved by a two-stage method with the first stage deciding the post-restoration topology and the second stage determining the set of loads to be restored and the outputs of sources. In the second stage, the problem is formulated as a mixed-integer semidefinite program. The objective is maximizing the number of loads restored, weighted by their priority. The unbalanced three-phase power flow constraint and operational constraints are considered. An iterative algorithm is proposed to deal with integer variables and can attain the global optimum of the critical load restoration problem by solving a few semidefinite programs under two conditions. The effectiveness of the proposed method is validated by numerical simulation with the modified IEEE 13-node test feeder and the modified IEEE 123-node test feeder under plenty of scenarios. The results indicate that the optimal restoration strategy can be determined efficiently in most scenarios.
Repair crews (RCs) and mobile power sources (MPSs) are critical resources for distribution system (DS) outage management after a natural disaster. However, their logistics is not well investigated. We propose a resilient scheme for disaster recovery logistics to co-optimize DS restoration with dispatch of RCs and MPSs. A novel co-optimization model is formulated to route RCs and MPSs in the transportation network, schedule them in the DS, and reconfigure the DS for microgrid formation coordinately, etc. The model incorporates different timescales of DS restoration and RC/MPS dispatch, the coupling of transportation and power networks, etc. To ensure radiality of the DS with variable physical structure and MPS allocation, we also model topology constraints based on the concept of spanning forest. The model is convexified equivalently and linearized into a mixed-integer linear programming. To reduce its computation time, preprocessing methods are proposed to pre-assign a minimal set of repair tasks to depots and reduce the number of candidate nodes for MPS connection. Resilient recovery strategies thus are generated to enhance service restoration, especially by dynamic formation of microgrids that are powered by MPSs and topologized by repair actions of RCs and network reconfiguration of the DS. Case studies demonstrate the proposed methodology.
Self-healing capability is one of the most critical factors for a resilient distribution system, which requires intelligent agents to automatically perform restorative actions online, including network reconfiguration and reactive power dispatch. These agents should be equipped with a predesigned decision policy to meet real-time requirements and handle highly complex $N-k$ scenarios. The disturbance randomness hampers the application of exploration-dominant algorithms like traditional reinforcement learning (RL), and the agent training problem under $N-k$ scenarios has not been thoroughly solved. In this paper, we propose the imitation learning (IL) framework to train such policies, where the agent will interact with an expert to learn its optimal policy, and therefore significantly improve the training efficiency compared with the RL methods. To handle tie-line operations and reactive power dispatch simultaneously, we design a hybrid policy network for such a discrete-continuous hybrid action space. We employ the 33-node system under $N-k$ disturbances to verify the proposed framework.
Mobile energy storage systems (MESSs) provide promising solutions to enhance distribution system resilience in terms of mobility and flexibility. This paper proposes a rolling integrated service restoration strategy to minimize the total system cost by coordinating the scheduling of MESS fleets, resource dispatching of microgrids and network reconfiguration of distribution systems. The integrated strategy takes into account damage and repair to both the roads in transportation networks and the branches in distribution systems. The uncertainties in load consumption and the status of roads and branches are modeled as scenario trees using Monte Carlo simulation method. The operation strategy of MESSs is modeled by a stochastic multi-layer time-space network technique. A rolling optimization framework is adopted to dynamically update system damage, and the coordinated scheduling at each time interval over the prediction horizon is formulated as a two-stage stochastic mixed-integer linear program with temporal-spatial and operation constraints. The proposed model is verified on two integrated test systems, one is with Sioux Falls transportation network and four 33-bus distribution systems, and the other is the Singapore transportation network-based test system connecting six 33-bus distribution systems. The results demonstrate the effectiveness of MESS mobility to enhance distribution system resilience due to the coordination of mobile and stationary resources.
Because failures in distribution systems caused by extreme weather events directly result in consumers outages, this paper proposes a state-based decision-making model with the objective of mitigating loss of load to improve the distribution system resilience throughout the unfolding events. The sequentially uncertain system states, e.g., feeder line on/off states, driven by the unfolding events are modeled as Markov states, and the probabilities from one Markov state to another Markov state throughout the unfolding events are determined by the component failure caused by the unfolding events. A recursive optimization model based on Markov decision processes (MDP) is developed to make state-based actions, i.e., system reconfiguration, at each decision time. To overcome the curse of dimensionality caused by enormous states and actions, an approximate dynamic programming (ADP) approach based on post-decision states and iteration is used to solve the proposed MDP-based model. IEEE 33-bus system and IEEE 123-bus system are used to validate the proposed model.
The resilience of cyberphysical systems to denial-of-service (DoS) and integrity attacks is studied in this paper. The cyberphysical system is modeled as a linear structured system, and its resilience to an attack is interpreted in a graph theoretical framework. The structural resilience of the system is characterized in terms of unmatched vertices in maximum matchings of the bipartite graph and connected components of directed graph representations of the system under attack. We first present conditions for the system to be resilient to DoS attacks when an adversary may block access or turn off certain inputs to the system. We extend this analysis to characterize resilience of the system when an adversary might additionally have the ability to affect the implementation of state-feedback control strategies. This is termed an integrity attack. We establish conditions under which a system that is structurally resilient to a DoS attack will also be resilient to a certain class of integrity attacks. Finally, we formulate an extension to the case of switched linear systems, and derive conditions for such systems to be structurally resilient to a DoS attack.