A novel affine arithmetic (AA) method with missed triangular domain (remaining area is convex polygons) is proposed in this paper for solving interval power flow (IPF) problem with uncertainties. An interval correlation model of random variables is established, and the original correlated interval variables are transformed into the standard space using interval arithmetic (IA) to reduce overestimation problem because of interval operation. To alleviate the errors caused by inaccurate enveloping of different intervals, an interval model with missed triangular domain is proposed and integrated into optimization model of IPF in form of additional constraints, which is developed in this paper through AA. IPF results, i.e., voltage magnitude, voltage angles and line flows are much narrower because it enhances restriction of correlated variables. Case studies on various test systems, i.e., IEEE 33-bus, 69-bus, and 118-bus system, indicate effectiveness of proposed technique compared with the other methods.

中文翻译：

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不确定三角域的新型仿射算法。

为了解决不确定的区间潮流（IPF）问题，提出了一种缺失三角形区域（剩余区域为凸多边形）的新型仿射算法（AA）。建立了随机变量的区间相关模型，并使用区间算术（IA）将原始的相关区间变量转换为标准空间，以减少因区间运算而引起的高估问题。为了缓解不同间隔包络的误差，提出了一种带有三角形缺失域的间隔模型，并以附加约束的形式集成到IPF的优化模型中。IPF结果，即电压幅度，电压角度和线路流量要窄得多，因为它增强了对相关变量的限制。