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Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
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The maximum power flow for lossy transmission lines is derived using ABCD parameters in phasor form. These parameters create a matrix relationship between the sending-end and receiving-end voltages and currents, allowing the determination of the receiving-end current. This relationship facilitates calculating the complex power delivered to the receiving end, from which real and reactive power components are derived.
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Distributed loads are a common type of load that engineers and scientists encounter in various practical situations. Distributed loads often refer to a type of load spread over a surface or a structure and can be modeled as continuous force per unit area.
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Related Experiment Video

Updated: Oct 5, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Two-Layered Hierarchical Optimization Strategy With Distributed Potential Game for Interconnected Hybrid Energy

Huifeng Zhang, Dong Yue, Chunxia Dou

    IEEE Transactions on Cybernetics
    |January 25, 2022
    PubMed
    Summary

    This study introduces a game theory strategy for optimizing hybrid energy systems (HESs). The method effectively manages competitive stakeholders and uncertainties for efficient HES operation.

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    Area of Science:

    • Engineering
    • Optimization
    • Game Theory

    Background:

    • Hybrid energy systems (HESs) face operational challenges due to multiple stakeholders and the inherent complexity and uncertainty of distributed energy resources.
    • The competitive nature among stakeholders in HESs complicates achieving optimal system operation.
    • High-dimensional complexity and output uncertainty are significant hurdles in HES optimization.

    Purpose of the Study:

    • To propose a novel potential game-based two-layered hierarchical optimization strategy for HESs.
    • To address the competitive relationships among stakeholders and the uncertainty issues in HES operation.
    • To enhance the optimal operation of HESs by reducing computational complexity and improving robustness.

    Main Methods:

    • A two-layered hierarchical HES model was developed, comprising upper-level and lower-level components.
    • A multiagent system and a potential game with a distributed primal-dual perturbed algorithm were employed to manage stakeholder competition in the upper-level model.
    • Uncertainty and robustness analysis was performed, coordinating the lower and upper models to define a feasible robust uncertainty interval.
    • A gradient descent-based multiobjective differential evolution (GD-MODE) algorithm was utilized for the lower-level optimization.

    Main Results:

    • The convergence and optimality of the potential game approach were mathematically proven.
    • A feasible robust uncertainty interval was deduced for the lower-level model through coordinated analysis.
    • The GD-MODE algorithm successfully optimized economic cost and emission simultaneously, yielding Pareto-optimal solutions.
    • Simulation results validated the proposed strategy's effectiveness in reducing computational complexity and handling uncertainties.

    Conclusions:

    • The proposed potential game-based hierarchical optimization strategy effectively addresses the complexities of HES operation.
    • The method successfully manages stakeholder competition and system uncertainties, leading to improved optimal operation.
    • The approach offers a robust and computationally efficient solution for optimizing hybrid energy systems.