The use of bi-directional converters (BDCs) is crucial for enhancing power exchange in hybrid AC/DC networked microgrids (NMGs). However, the dynamic nature of their conversion efficiency and the non-convex conversion direction expression of BDC models result in a highly non-convex programming problem, which leads to significant computational challenges. This paper proposes a least squares approximation approach to simplify the complex trigonometric function that characterizes the dynamic changes in BDC conversion efficiency with power. The simplified expression transforms the original non-convex relationship into a computationally efficient convex form. Subsequently, we systematically explore and validate the sufficient conditions to achieve non-simultaneous rectification and inversion behaviors of BDCs in a convex form. These explored conditions are further customized and extended to various practical application scenarios. Case studies are conducted on a hybrid AC/DC NMG with 66 nodes. The results demonstrate that our proposed least squares approximation method transforms the computationally intractable model into one that is solvable. Additionally, the explored conditions contribute to a substantial reduction in solution time by more than two orders of magnitude. These results verify the superiority of our proposed method, and showcase its applicability in practical scenarios.

Previous robust transmission expansion planning (RTEP) studies have rarely considered the important question of how large the uncertainty set should be, and hence, how the uncertainty budget can be determined objectively. This study addresses this issue by proposing a novel adaptive optimization method that optimizes the value of the uncertainty budget to minimize the size of the uncertainty set while considering the underlying risk for wind power generation (WPG) fluctuations residing outside of the proposed uncertainty set. As such, the proposed method ensures a good tradeoff between the robustness and costs of RTEP solutions. In addition, the proposed method optimizes investment strategies under forecasted WPG scenarios, while providing a security guarantee under extreme WPG scenarios. The variable-limit integral terms introduced by the proposed method are addressed in the solution process by applying the piecewise linearization approximation method combined with the quadratic Newton-Gregory interpolating polynomial technique, which allows the solution process to be cast as a mixed integer linear programming problem. The good performance and effectiveness of the proposed adaptive uncertainty set optimization method are verified by numerical results.

Hybrid ac/dc microgrids (HMGs) have emerged as a promising paradigm for integrating large numbers of inherently uncertain and correlated renewable energy sources (RESs). To address the uncertainty introduced by extensive RES integration, a quad-level energy management model is proposed for HMGs, incorporating a novel data-driven uncertainty set. Specifically, a pair convex hull uncertainty set (PCHUS) is developed with adjustable size, which utilizes a graph neural network to identify and exclude outliers in RES data. This approach provides trustworthy RES data at any given confidence level. Then, a quad-level energy management model is designed to determine the minimal-size PCHUS among all possible options, ensuring the least conservative solution, while maintaining robustness against RES fluctuations. Furthermore, a modified version of Taguchi’s orthogonal array testing (TOAT) method, termed quasi-TOAT, enhances the proposed solution algorithm. This modification enables parallel processing capabilities, significantly improving both the global optimum-seeking process and computational efficiency. To validate the proposed approach, the proposed uncertainty set and enhanced algorithm are compared against existing methods using a practical HMG case study. The results demonstrate the effectiveness and superiority of the proposed methodology in managing uncertainty within HMGs.

This paper focuses on the interchange and generation scheduling problem of multi-area power systems, where decentralized decision procedure is preferred and the uncertainties of nodal injections should be considered. The problem is formulated as a multi-area robust security constrained unit commitment model, with a novel uncertainty set specified by the variance of system net load. We prove that such an uncertainty set can provide a more precise probabilistic guarantee than conventional budgeted sets. To solve the problem in decentralized manner, an upper-level robust convex optimization model is proposed to optimize the tie-line power flow and derive a generation interval for each area. Then through the coordinated uncertainty requirement decided by the generation interval, each regional system operator can solve a decoupled robust unit commitment problem independently. Besides, a modified outer approximation algorithm is developed to obtain higher-quality solution of the bilinear programming involved in the process. Simulation results on a two-area system demonstrate the effectiveness of the uncertainty set, and show the economic efficiencies of unit commitment solutions acquired from the hierarchical method.

Bi-directional converters (BDCs) facilitate the high efficiency of hybrid AC/DC microgrids (HMs). However, the HM operation is rather challenging due to the non-convex system model. This letter develops a data-driven convex model for HM operation involving BDCs. First, a least squares approximation method with data-driven weight functions is proposed to linearize BDC efficiency behavior. Then, the convex linear HM model is formulated by combining this linearized model with an analysis of the conditions ensuring non-simultaneous BDC inverting and rectifying operations. The low approximation error and high computational efficiency of the proposed model are demonstrated based on an analysis of numerical studies.