Despite it is essential to distribution network economics, computing energy loss for most major networks is still a tough task due to the absence of full monitoring. Assume the line current follows a normal distribution, the sum of its square is a linear combination of independent chi-square variables, which follows a generalized noncentral chi-square distribution. Based on this finding, we develop a new probability-based analytical method to estimate distribution network energy losses efficiently. The proposed analytical method requires merely the knowledge of mean and variance of line current as well as the line resistance while provides a closed-form formula of the probability characteristics of energy loss. The method is demonstrated on a three-feeder radial network.

中文翻译：

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一种使用最小线路电流信息估计能量损失的新概率方法

尽管它对配电网络经济学至关重要，但由于缺乏全面监控，计算大多数主要网络的能量损失仍然是一项艰巨的任务。假设线路电流服从正态分布，其平方和是独立卡方变量的线性组合，服从广义非中心卡方分布。基于这一发现，我们开发了一种新的基于概率的分析方法来有效地估计配电网络能量损失。所提出的分析方法只需要知道线电流的均值和方差以及线电阻，同时提供能量损失概率特性的封闭式公式。该方法在三馈线径向网络上进行了演示。