This article is aimed at optimizing the operation of the integrated electrical and natural‐gas systems (IENGS) with combined cooling, heating, and power (CCHP) considering demand response (DR) under uncertain conditions. First, the deterministic optimization model of IENGS is established. Then, considering the uncertainty of light intensities, the uncertain optimization model of IENGS is proposed by interval mathematics. Next, the interval optimization model is solved by the improved interval linear programming method, in which affine arithmetic is applied in the solving progress to get less conservative results. In the numerous cases, the proposed method is compared with the Monte‐Carlo simulation and interval linear method without affine mathematics to verify its correctness and effectiveness. The influence of the uncertainty brought by light intensities is analyzed. Four scenarios are designed to testify the economy of electrical and natural‐gas DR programs. The results lead to the conclusion that high uncertain level of light intensities will make operation cost of the IENGS fall in a wider interval and the lower cost can be obtained when the electrical and natural‐gas DR programs are implemented simultaneously.

中文翻译：

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考虑到需求响应，结合了冷却，加热和功率的集成式电气和天然气系统的间隔优化

本文旨在考虑不确定条件下的需求响应（DR），以结合了制冷，制热和电力（CCHP）的方式优化集成的电气和天然气系统（IENGS）的运行。首先，建立了IENGS的确定性优化模型。然后，考虑到光强度的不确定性，通过区间数学方法提出了IENGS的不确定性优化模型。接下来，通过改进的区间线性规划方法求解区间优化模型，该方法在求解过程中采用仿射算法来获得较不保守的结果。在许多情况下，将所提出的方法与没有仿射数学的蒙特卡罗模拟和区间线性方法进行比较，以验证其正确性和有效性。分析了光强度带来的不确定性的影响。设计了四种方案来证明电气和天然气DR计划的经济性。结果得出的结论是，高不确定性的光强度将使IENGS的运行成本落在更宽的区间内，同时实施电气和天然气DR程序可以降低成本。