Due to the promising development of direct current (dc) distribution networks, we focus on the demand-side management (DSM) problems which aim at the minimization of operational costs in dc distribution networks. Based on the established voltage model of power electronic loads, we formulate a DSM optimization problem that coordinates the bus voltage by minimizing the system cost, and the underlying optimization problem is nonconvex. In order to solve this nonconvex problem, we first reformulate it as a difference of convex programming problem, and then propose a novel algorithm based on branch and bound to implement the optimal solution. It is shown that the system is guaranteed to converge to the global optimum under the proposed method. As demonstrated with numerical examples, we analyze the convergence and global optimality of the proposed method, and discuss the computational complexity and scalability with respect to the size of distribution networks. Moreover, in case each of individual loads can make its own decisions by itself, the underlying optimization problem is implemented in the context of the noncooperative game. The existence of the Nash equilibrium is verified and demonstrated through simulation results.

中文翻译：

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直流配电网中的负载控制问题：最优性，博弈均衡

由于直流配电网的发展前景可观，因此我们专注于需求侧管理（DSM）问题，旨在最大程度地降低直流配电网的运营成本。基于已建立的电力电子负载电压模型，我们制定了一种DSM优化问题，该问题可以通过最小化系统成本来协调母线电压，而潜在的优化问题是非凸的。为了解决这个非凸问题，我们首先将其重新设计为凸规划问题的差分，然后提出一种基于分支定界的新算法来实现最优解。结果表明，所提方法保证了系统收敛于全局最优。如数值示例所示，我们分析了所提出方法的收敛性和全局最优性，并讨论了有关配电网络规模的计算复杂性和可扩展性。此外，如果每个单独的负载都可以自己做出自己的决定，则潜在的优化问题是在非合作博弈的背景下实现的。通过模拟结果验证并证明了纳什均衡的存在。