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スマートグリッドの情報セキュリティシステム

智能电网信息安全系统

基本信息

批准号：
12J01935
负责人：
傅愛玲
金额：
$ 1.15万
依托单位：
The University of Tokyo (2013)Meiji University (2012)
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2012
资助国家：
日本
起止时间：
2012 至 2013
项目状态：
已结题

项目摘要

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

能源消耗的变异性是总变化对总平均消耗的分数。实际数据显示了聚合变异性与客户数量的收敛。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。我们表明，在实际数据上的收敛结果与简单的随机相关变量和的预测是一致的。15分钟消费数据的数据粒度：每天获取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，对于具有均值μ和方差σ^2的随机变量(或向量)x，随机变量αx，其中α&gt；0具有均值αμ、方差α^2σ^2和变异性σ/μ。我们看到，变异性与和中项的数量成平方根反比为零，v_&lt；sum&gt；(k)=(σ_&lt；sum&gt；(k))/(μ_&lt；sum&gt；(k))=1/(√&lt；k&gt；)σ/μ.在真实数据上，我们没有看到这种行为，…更多可能是因为数据集较小，其中1/(√&lt；k&gt；)=0.1.然而，这种趋同于变异值的非零值也可能是因为消费者不是独立的。例如，对于1个消费者的10个副本，我们得到与集群大小无关的常量非零变异性。居住在同一城镇的客户和一年中同一时间采集的数据意味着数据中的许多相关性。因此，在分析聚类变异性之前，必须找到这种相关性并用协方差矩阵来表征。C_&lt；ij&gt；=&lt；(x_i-μ_j)(x_j-μ_i)&gt；我们得出结论：对于每个时刻t，都会收敛到一个窄范围内。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”，并且收敛不同于乘性因子。总之，我们看到可变性确实是一个很好的参数来编码真实数据的许多属性，并且需要相对较小的数据集大小来忠实地描述更大的图景，因为它收敛到一个恒定值。较少