Continuity of supply plays a significant role in modern distribution system planning and operational studies. Accordingly, various techniques have been developed for reliability assessment of distribution networks. However, owing to the complexities and restrictions of these methods, many researchers have resorted to several heuristic optimization algorithms for solving reliability-constrained optimization problems. Therefore, solution quality and convergence to global optimality cannot be guaranteed. Aiming to address this issue, two salient mathematical models are introduced in this paper for topology-variable-based reliability evaluation of both radial and radially-operated meshed distribution networks. Cast as a set of linear expressions, the first model is suitable for radial networks. The second model relies on mixed-integer linear programming and allows handling not only radial networks but also radially-operated meshed distribution grids. Therefore, the proposed formulations can be readily incorporated into various mathematical programming models for distribution system planning and operation. Numerical results from several case studies back the scalability of the developed models, which is promising for their further application in distribution system optimization studies. Moreover, the benefits of the proposed formulations in terms of solution quality are empirically evidenced.

中文翻译：

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考虑切换中断的基于拓扑变量的配电系统可靠性评估的线性公式

供应的连续性在现代配电系统规划和运营研究中起着重要作用。因此，已经开发了各种技术用于配电网络的可靠性评估。然而，由于这些方法的复杂性和局限性，许多研究人员已采用几种启发式优化算法来解决可靠性受限的优化问题。因此，不能保证解决方案的质量和收敛到全局最优性。为了解决这个问题，本文介绍了两个显着的数学模型，用于径向和径向操作的网状配电网的基于拓扑变量的可靠性评估。转换为一组线性表达式后，第一个模型适用于径向网络。第二个模型依赖于混合整数线性规划，不仅允许处理径向网络，而且还允许处理径向操作的网格化配电网。因此，提出的公式可以很容易地纳入各种数学规划模型中，用于配电系统的规划和运行。几个案例研究的数值结果支持了已开发模型的可扩展性，这对于将其进一步应用于配电系统优化研究具有希望。而且，经验上证明了所提出的制剂在溶液质量方面的益处。所提出的公式可以很容易地并入各种数学规划模型中，以进行配电系统的规划和运行。几个案例研究的数值结果支持了已开发模型的可扩展性，这对于将其进一步应用于配电系统优化研究具有希望。而且，经验上证明了所提出的制剂在溶液质量方面的益处。所提出的公式可以很容易地并入各种数学规划模型中，以进行配电系统的规划和运行。几个案例研究的数值结果支持了已开发模型的可伸缩性，这对于将其进一步应用于配电系统优化研究具有希望。而且，经验上证明了所提出的制剂在溶液质量方面的益处。