Power distribution systems (PDS) face increasing challenges due to rising power demand, the integration of distributed generation (DG), and voltage stability concerns. To address these issues, this study proposes a no...
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Power distribution systems (PDS) face increasing challenges due to rising power demand, the integration of distributed generation (DG), and voltage stability concerns. To address these issues, this study proposes a novel mixed-integerlinearprogramming (MILP) model for the optimal placement, sizing, and operation of D-STATCOMs in radial distribution systems. Unlike existing methods, the proposed approach incorporates multi-period optimization, considering daily active and reactive power demand curves to dynamically adjust reactive power support throughout the day. The model is implemented in AMPL and solved using the CPLEX solver, ensuring globally optimal solutions. Numerical validation is performed on three test systems: 33-bus, 69-bus, and a simplified 136-bus PDS from Presidente Prudente, Brazil. The results demonstrate that the MILP model achieves up to a 23% reduction in energy losses and provides economic benefits of up to 15%, while also enhancing voltage stability. Additionally, the study presents new results for the 136-bus test system, which had not been previously reported in the literature. The findings demonstrate the effectiveness and scalability of the proposed MILP model, making it a practical tool to optimize power distribution system performance. Future research may extend this approach to meshed networks and stochastic demand scenarios.
Based on the method of the H-representation of the convex hull, the linear inequalities of all possible differential patterns of 4-bit S-boxes in the mixintegerlinearprogramming (MILP) model can be generated easily...
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Based on the method of the H-representation of the convex hull, the linear inequalities of all possible differential patterns of 4-bit S-boxes in the mixintegerlinearprogramming (MILP) model can be generated easily by the SAGE software. Whereas this method cannot be apply to 8-bit S-boxes. In this study, the authors propose a new method to obtain the inequalities for large S-boxes with the coefficients belonging to integer. The relationship between the coefficients of the inequalities and the corresponding excluded impossible differential patterns is obtained. As a result, the number of inequalities can be lower than 4000 for the AES S-box. Then, the new method for finding the best probability of the differential characteristics of 4-15 rounds SM4 in the single-key setting is presented. Especially, the authors found that the 15-round SM4 exists four differential characteristics with 12 active S-boxes. The exact lower bound of the number of differentially active S-boxes of the 16-round SM4 is 15. The authors also found eight differential characteristics of the 19-round SM4 with the probability 2(-124).
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