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能源消耗的可变性是总方差除以总平均消耗的分数。实际数据显示，总变异性随客户数量的增加而收敛。我们研究了这种现象的数学原因，以及收敛速度的微妙之处。我们证明了对实际数据的收敛结果与随机相关变量的简单和的预测是一致的。15分钟消费数据的数据粒度：每天获得96个数据点，计算总消费的变异性。当消费分布归一化时，可变性不变。也就是说，对于均值μ和方差σ^2的随机变量（或向量）x，随机变量αx（其中α>0）具有均值αμ，方差α^2σ^2和可变性σ/μ。我们看到，变异性与总和中项数的平方根倒数为零，v_<sum>(k)=(σ_<sum>(k))/(μ_<sum>(k))=1/(√<k>)σ/μ。在实际数据中，我们没有看到这种行为，这可能是因为数据集规模较小，其中1/(√<k>)=0.1。然而，这种收敛到变异性的非零值也可能是由于消费者不是独立的事实。例如，对于一个消费者的10个副本，我们得到独立于集群大小的恒定非零可变性。居住在同一个城镇的客户和在一年中的同一时间采集的数据意味着数据中有很多相关性。因此，在分析聚类变异性之前，应该先找出这种相关性，并用协方差矩阵来表征。c_<ij>=<(x_i-μ_j)(x_j-μ_i)>我们得出，对于每一次t，都会收敛到一个很小的范围内。我们还得出结论，有一种方法可以计算/估计变异性的“收敛速度”，并且收敛速度因乘法因子而不同。总之，我们看到可变性确实是编码真实数据的许多属性的一个很好的参数，并且需要相对较小的数据集大小来忠实地描述更大的图像，因为它收敛到一个常数值。少

A variability of energy consumption is the fraction of total variance over total mean consumption. Real data shows convergence of aggregated variability ith number of customers. We investigate the mathematical reasons of this phenomenon, as well as the subtleties of convergence rate. We show that the results for convergence on real data are consistent with the prediction of a simple sum of random correlated variables. Data granularity of 15-min consumption data : 96 data points per day were obtained to calculate the variability of aggregate consumption. Variability is unchanged when consumption distributions are normalized. That is, for a random variable (or vector) x with mean μ and variance σ^2, the random variable αx, where α>0, has mean αμ, variance α^2σ^2, and variability σ/μ. We see that the variability falls to zero as inverse square root with the number of the terms in the sum, v_<sum>(k)=(σ_<sum>(k))/(μ_<sum>(k))=1/(√<k>)σ/μ. on the real data, we don't see this behavior, which … More is maybe because of small data set size, where 1/(√<k>)=0.1. However, this convergence to nonzero value of variability can also be due to the fact that consumer are not independent. For example, for 10 copies of 1 consumer we get constant nonzero variability independent of cluster size. Customers living in the same town and the data taken in the same time of the year means a lot of correlations in the data. So this correlation should be found and characterized by covariance matrix before analyzing the cluster variability. c_<ij>=<(x_i-μ_j)(x_j-μ_i)>We conclude that for each time t, will converge to lie within a narrow range. We also conclude that there is a way to calculate/estimate "convergence rate" of variability and the convergence differs by a multiplicative Factor. In conclusion, we see that variability is indeed a good parameter to encode a lot of properties of the real data, and relatively small dataset size are required to faithfully describe the bigger picture, as it converges to a constant value. Less