This paper proposes a distribution system restoration model which is in response to multiple outages caused by natural disasters. The proposed restoration model includes the coordination of routing repair crews (RRCs), mobile battery-carried vehicles (MBCVs), and networked microgrids (NMGs) formed by soft open points (SOPs). The travel and repair time constraints are modeled for each RRC; travel path and charging strategy are modeled for each MBCV; and the network reconfiguration is developed considering the optimal operation of SOP-based NMGs. The proposed model is presented as a mixed-integer linear program which is solved by an auxiliary induce function based algorithm to reduce the computational complexity. The modified IEEE 33-bus and 69-bus distribution systems are tested with multiple outages. The presented results demonstrate the effectiveness of the proposed model.

A novel multi-stage stochastic programming model is proposed for the expansion co-planning of gas and power net-works considering the uncertainties in net load demand. Mean-while, the nonanticipativity constraints are taken into account to guarantee the decisions should only depend on the information of realized uncertainties up to the present stage. Compared with the traditional two-stage stochastic programming model, the proposed multi-stage stochastic programming model yields se-quential investment decisions with the uncertainties revealed gradually over time, such that the investment decisions are ca-pable of keeping future options open and can shift from “never be changed” decisions to a flexible “wait and see” decisions. The test on three systems shows the effectiveness of the proposed multi-stage stochastic programming model.

To address the uncertain renewable energy in the day-ahead op-timal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to characterize the uncertainties over the multiple stages by a scenario tree. Most importantly, to deal with the “Curse of Dimensionality” of sto-chastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a lin-ear piecewise function. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.

Electric vehicles (EVs) have rapidly developed in recent years and their penetration has also significantly increased, which, however, brings new challenges to power systems. Due to their stochastic behaviors, the improper charging strategies for EVs may violate the voltage security region. To address this problem, an optimal EV charging strategy in a distribution network is proposed to max-imize the profit of the distribution system operators while satisfying all the physical constraints. When dealing with the uncertainties from EVs, a Markov decision process (MDP) model is built to characterize the time series of the uncertainties and then the deep deterministic policy gradient based reinforcement learning tech-nique is utilized to analyze the impact of uncertainties on the charging strategy. Finally, numerical results verify the effectiveness of the proposed method.

The reliability evaluation of integrated power-gas systems (IPGS) becomes critical due to the high dependency of the two energy systems. Once a contingent incident happens in one system, the other system will accordingly be affected. In this paper, a detailed model for the IPGS is presented with the consideration of the power-to-gas devices and gas storages. Furthermore, a Sequential Monte Carlo (SMC) simulation is utilized to evaluate the reliability of the IPGS. Finally, the proposed model is tested on an integrated IEEE 24-bus power system and 20-node gas system. The results show the effectiveness of the proposed model.