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The electric power distribution network (PDN) and the transportation network (TN) are generally operated/coordinated by different entities. However, they are coupled through electric vehicle charging stations (EVCSs). This paper proposes to coordinate the operation of the two systems via a fully decentralized framework where the PDN and TN operators solve their own operation problems independently, with only limited information exchange. Nevertheless, the operation problems of both systems are generally mixed-integer programs (MIP), for which mature algorithms like the alternating direction method of multipliers (ADMM) may not guarantee convergence. This paper applies a novel distributed optimization algorithm called the SD-GS-AL method, which is a combination of the simplicial decomposition, gauss-seidel, and augmented Lagrangian, which can guarantee convergence and optimality for MIPs. However, the original SD-GS-AL may be computationally inefficient for solving a complex engineering problem like the PDN-TN coordinated optimization investigated in this paper. To improve the computational efficiency, an enhanced SD-GS-AL method is proposed by redesigning the inner loop of the algorithm, which can automatically and intelligently determine the iteration number of the inner loop. Simulations on the test cases show the efficiency and efficacy of the proposed framework and algorithm. 

The electric power distribution system (PDS) and the water distribution system (WDS) are coupled with each other through electricity-driven water facilities (EdWFs), such as pumps, water desalination plants, and wastewater treatment facilities. However, they are generally owned and operated by different utilities, and there does not exist an operator that possesses full information of both systems. As a result, centralized methods are not applicable for coordinating the operation of the two systems. This paper proposes a decentralized framework where the PDS and WDS operators solve their own operation problems, respectively, by sharing only limited information. Nevertheless, the boundary variables (i.e., the variables shared between two systems) are discontinuous due to their dependence on the on/off nature of EdWFs. Unfortunately, mature decentralized/distributed optimization algorithms like the alternating direction method of multipliers (ADMM) cannot guarantee convergence and optimality for a case like this. Therefore, this paper develops a novel algorithm that can guarantee convergence and optimality for the decentralized optimization of PDS and WDS based on a recently developed algorithm called the SD-GS-AL method. The SD-GS-AL method is a combination of the simplicial decomposition (SD), gauss–seidel (GS), and augmented Lagrangian (AL) methods, which can guarantee convergence and optimality for mixed-integer programs (MIPs) with continuous boundary variables. Nonetheless, the original SD-GS-AL algorithm does not work for the PDS-WDS coordination problem where the boundary variables are discontinuous. This paper modifies and improves the original SD-GS-AL algorithm by introducing update rules to discontinuous boundary variables (called the Auxiliary Variables Update step). The proposed mixed-integer boundary compatible (MIBC) SD-GS-AL algorithm has the following benefits: (1) it is capable of handling cases whose boundary variables are discontinuous with convergence and optimality guaranteed for mild assumptions, and (2) it only requires limited information exchange between PDS and WDS operators, which will help preserve the privacy of the two utilities and reduce the investment in building additional communication channels. Simulations on two coupled PDS and WDS test cases (Case 1: IEEE-13 node PDS and 11-node WDS, and Case 2: IEEE-37 node PDS and 36-node WDS) show that the proposed MIBC algorithm converges to the optimal solutions while the original SD-GS-AL does not converge for both test cases. The ADMM does not converge for the first test case while it converges to a sub-optimal solution, 63 % more than the optimal solution for the second test case. 

Emergency response resources (ERRs) such as mobile energy resources (MERs) and repair crews (RCs) play a pivotal role in the efficient restoration of power distribution systems after disasters. This paper presents a computationally tractable approach to utilize ERRs and post-disaster available distributed energy resources (PDA-DERs) in the restoration of disaster-impacted distribution systems. The post-disaster restoration model is proposed to co-optimize the dispatch of pre-allocated ERRs and PDADERs to minimize the impact of high-impact low-frequency (HILF) events on customers, i.e., energy not served for the entire restoration window. Compared with existing restoration strategies using ERRs, the proposed approach is more tractable since, in the restoration model, a super-node approximation (SNA) of distribution networks and the convex hulls relaxation (CHR) of non-linear constraints are introduced to achieve the best trade-off between computational burden and accuracy. Tests of the proposed approach on IEEE test feeders demonstrated that a combination of SNA and CHR remarkably reduces the solution time of the post-disaster restoration model.