Optimization algorithms are tools used in the planning and operations of renewable energy-based distributed power systems. Mixed integer linear programming as a classical optimization method is considered in the literature for sizing nanogrid systems due to simplicity and speed. However, the method has limited capabilities in implementing multi-configurational analysis and requires large formulations. In this paper, nested integer linear programming is proposed to decompose the large formulations and simplify the multi-configurational sizing of residential nanogrid in a semiarid zone. The proposed method is aimed at optimal sizing for energy cost reduction and increased supply availability. The method is implemented in multi-stage hybridization of relaxation and integer methods of linear programming to achieve optimal sizes of the nanogrid components using photovoltaics, wind turbines, and battery. The method realizes $72,343 net present cost and 0.3755 $/kWh levelized cost of energy indicating 33% and 11% reductions compared to mixed integer linear programming and particle swarm optimization. System availability of 99.97% is envisaged to achieve 6677–7782 kWh per capita electricity consumption in residential buildings against the existing 150 kWh. Three configurations analyzed indicated the robustness of the proposed method and the multi-configurational designs clarify options against factors such as space, logistics, or policies.

优化算法是用于规划和运营基于可再生能源的分布式电力系统的工具。由于简单和速度，混合整数线性规划作为经典优化方法在文献中被认为用于确定纳米网格系统的大小。然而，该方法在实现多构型分析方面的能力有限，并且需要大量的公式。在本文中，提出了嵌套整数线性规划来分解大型公式并简化半干旱地区住宅纳米网格的多配置尺寸。所提出的方法旨在优化尺寸以降低能源成本和增加供应可用性。该方法在松弛和整数线性规划方法的多阶段混合中实施，以使用光伏、风力涡轮机和电池实现纳米网格组件的最佳尺寸。该方法实现了 72,343 美元的净当前成本和 0.3755 美元/千瓦时的平准化能源成本，与混合整数线性规划和粒子群优化相比，分别降低了 33% 和 11%。预计 99.97% 的系统可用性将使住宅建筑的人均电力消耗达到 6677-7782 千瓦时，而现有的 150 千瓦时。分析的三种配置表明所提出方法的稳健性，多配置设计阐明了针对空间、物流或政策等因素的选项。3755 美元/千瓦时的能源平准化成本表明与混合整数线性规划和粒子群优化相比降低了 33% 和 11%。预计 99.97% 的系统可用性将使住宅建筑的人均电力消耗达到 6677-7782 千瓦时，而现有的 150 千瓦时。分析的三种配置表明所提出方法的稳健性，多配置设计阐明了针对空间、物流或政策等因素的选项。3755 美元/千瓦时的能源平准化成本表明与混合整数线性规划和粒子群优化相比降低了 33% 和 11%。预计 99.97% 的系统可用性将使住宅建筑的人均电力消耗达到 6677-7782 千瓦时，而现有的 150 千瓦时。分析的三种配置表明所提出方法的稳健性，多配置设计阐明了针对空间、物流或政策等因素的选项。