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This paper proposes a novel spatial branch-and-cut approach for fast resilience analysis of integrated electricity-gas systems. The proposed method makes two improvements to the traditional branch-and-cut algorithms to accelerate the solution process of the scenario-based post-contingency load restoration. First, a new cone-specific spatial branching strategy is developed to handle the non-convex nature of the integrated electricity-gas flow. Compared with the existing branching strategies which can only handle bilinear equality constraints, the scale of branching variables is reduced by two-thirds without affecting the accuracy of solutions. Second, a combinatorial cut generation strategy is proposed to convert the traversal of all failure scenarios into a guided generation of single branch-and-cut search tree. The key idea is to equate the solution process of each failure scenario to a subset of the search tree, so that the load restoration problem only needs to be solved once. The performance of the proposed approach is tested on three integrated electricity-gas systems of different sizes. The comparison against seven alternative solution methods further verifies the superiority of the proposed method in terms of accuracy and efficiency.

In the present letter, a vortex phase imaging method is proposed to improve the lateral resolution of a millimeter-wave (MMW) focal plane imaging system. For the efficient transmission of vortex beams carrying different orbital angular momentum (OAM), the spiral phase plates processed by 3-D printing technology are designed to be loaded onto the front of horn antenna. Then, the reflection spectra of the object are analyzed for discussion. A specific OAM mode carrying more azimuth information is found to be dominant under a vortex incidence, and a sharper image can theoretically be obtained using the vortex phase. In addition, a concise reflective vortex imaging system is developed to collect the information about OAM phase. According to the experimental results, the vortex phase imaging method proposed in this study is effective in significantly improving the outcome of imaging at 80 GHz, with a lateral -resolution of 0.42λ0 achieved. This method is applicable to other MMW imaging systems, which may contribute to an in-depth understanding and utilization of scattering vortex spectrum.

A growing number of microgrid (MG) systems ipate in market trading as prosumers to improve their own operation profits, as well as the flexibility of power supply. To handle the MG dispatch problem with uncertainties in both load demands and electricity prices, this paper provides a data-driven robust optimization (RO) approach. Firstly, the correlations between the uncertainties of demands and prices are verified via the analysis of historical monitoring data from a real-world case. Based on the data-fitting for the rectangular and ellipsoidal intervals, a new data-driven demand-price uncertainty set with correlations is built to eliminate these unreasonable scenarios effectively. Secondly, a two-stage RO dispatch model is established considering multiple uncertainties of renewable-load power and prices in MGs. The bilinear objective term brings huge obstacles to the solution of the RO model, therefore a novel nested iterative algorithm is further exploited. The bilinear terms of power and price in the objective function are linearized by a binary expansion approach. Besides, to avoid the enumerations of numerous binary recourses in problem solving, the block coordinate descent (BCD) theory is adopted to co-optimize different types of variables, thereby enhancing the computational tractability. Numerical simulations indicate the validity and superiority of the developed RO model and the solution algorithm.