In the present study, a new mixed-integer linear programming is presented for a reliability-oriented power network. The reliability approach is conducted using the Average Energy Not Supplied (AENS) index and System Average Interruption Duration Index (SAIDI) based on the feeder’s failure rate. In this formulation, the constraints include standard ranges for electric power and current magnitude, acceptable voltage drop, power law, and power balance considering loss power. Moreover, the relation between feeder failure rate and electric power level and subsequently SAIDI for outage duration control is added in constraints to improve network reliability. The model is studied on a real case study in Iran in two scenarios with or without considering DG. The obtained results indicate that optimization for DG location and its capacity in the power system decrease AENS cost. Furthermore, DG incorporation in the grid reduces load congestion in substations and system’ total cost. Augmented Epsilon Constraint (AEC) method is utilized to solve two-objective mixed-integer linear programming. To overcome the uncertain environment, the robust optimization is applied, and the effect of $\mathrm{\Gamma }$ parameters is investigated on Pareto sets and system’s total costs. As confirmed by numerical results, by increasing demand constraint conservative level, the objective function gets away from the nominal value, requiring that Decision-Makers create an appropriate balance between conservative levels and system costs. The obtained results reveal the efficiency and effectiveness of the proposed mathematical model in the real world.

在本研究中，针对面向可靠性的电网提出了一种新的混合整数线性规划方法。可靠性方法是根据馈线的故障率，使用平均未供应能量（AENS）指数和系统平均中断持续时间指数（SAIDI）进行的。在此公式中，约束条件包括电功率和电流大小的标准范围，可接受的压降，功率定律以及考虑损耗功率的功率平衡。此外，在约束中添加了馈线故障率和电功率水平之间的关系，以及随后用于中断持续时间控制的SAIDI之间的关系，以提高网络可靠性。在有或没有考虑危险品的两种情况下，在伊朗的一个真实案例研究中对该模型进行了研究。获得的结果表明，对DG位置及其在电力系统中的容量的优化降低了AENS成本。此外，将DG并入电网可减少变电站的负荷拥塞和系统的总成本。利用增强的Epsilon约束（AEC）方法求解两目标混合整数线性规划。为了克服不确定的环境，应用了稳健的优化方法，并且$\mathrm{\Gamma }$对Pareto集和系统的总成本调查参数。数值结果证实，通过提高需求约束的保守水平，目标函数偏离了名义价值，要求决策者在保守水平和系统成本之间建立适当的平衡。获得的结果揭示了所提出的数学模型在现实世界中的效率和有效性。