## 2 The Method of Typical Scenarios Partitioning and Load Distribution Matching
### The Method of Load Distribution Matching  
This paper proposed a load distribution matching method, which can quickly find out the load that has the similar distribution with the load to be optimized from massive historical data, and the corresponding control schemes are also selected out. While the power flow of time \(t\) in a certain day is to be reactive power optimized, the first step is to select out the samples that both have the same topology scenario and load distribution scenario with the load at time \(t\), and the samples form a set. Secondly, load distribution matching method is implemented with the sample set, and then a smaller sample set is formed, which contains the optimal scheme. Assume that there are \(N_{0}\) days in the historical database that has the same topology scenario and load scenario to the time \(t\); then match the load distribution at time \(t\) of the \(N_{0}\) days with the moment to be optimized in turn, and select out the load that has the similar distribution with the time \(t\). Suppose that there are \(N_{e}\) similar load distributions are selected out, then the corresponding historical optimal schemes form the alternative set. Figure 1: The typical daily load curves of different scenarios in a certain region: (**a**) weekdays in four seasons; and (**b**) weekends in four seasons. It is necessary to make a matching rule for the load distribution matching. If a load distribution obeys the rule, it can judge that the load distribution is similar to the moment to be optimized, and its corresponding historical optimal plan can be an alternative. In the Pauta criterion of statistics, while the amount of statistical data is large enough, the probability of the value of the random variable that subject to the normal distribution \(N\sim\)(\(\mu\sigma^{2}\)) beyond \(\mu\)\(\pm\)\(3\sigma\) is \(0.27\%\), which is considered a small probability event and almost impossible happened in mathematics. The Pauta criterion is applied to the load distribution matching in this paper. In a system with \(n\) nodes, generate two load intervals (\(\mathbf{P}-3\sigma_{\mathbf{P}},\mathbf{P}+3\sigma_{\mathbf{P}}\)) and (\(\mathbf{Q}-3\sigma_{\mathbf{Q}},\mathbf{Q}+3\sigma_{\mathbf{Q}}\)), where the mean values are the load to be optimized in each node \(\mathbf{P}=(P_{1},\ldots,P_{n})\) and \(\mathbf{Q}=(Q_{1},\ldots,Q_{n})\); the variance values are \(\sigma_{\mathbf{P}}{}^{2}\) and \(\sigma_{\mathbf{Q}}{}^{2}\); \(\sigma_{\mathbf{P}}=(\sigma_{\mathbf{P}1},\ldots,\sigma_{\mathbf{P}n})\) and \(\sigma_{\mathbf{Q}}=(\sigma_{\mathbf{Q}1},\ldots,\sigma_{\mathbf{Q}n})\) are empirical value, which can be calculated with large amount of historical load in different typical scenarios. Take the active power load as an example to illustrate the specific matching process, the active load is divided into three regions by the interval (\(\mathbf{P}-3\sigma_{\mathbf{P}},\mathbf{P}+3\sigma_{\mathbf{P}}\)), which is shown in Figure 2.  
Read load distributions in the typical scenario from the historical database in turn. And if a load distribution is completely within the interval (\(\mathbf{P}-3\sigma_{\mathbf{P}},\mathbf{P}+3\sigma_{\mathbf{P}}\)), that is, within the Region 1 in Figure 2, take the corresponding historical optimal plan as an alternative; otherwise, the corresponding historical plan cannot be used. After the active power load distribution matching is finished and \(N_{m}\) historical load are selected out, reactive power load distribution matching is also carried out with the \(N_{m}\) historical load. In summary, if the reactive load optimization is carried out for the load at time \(t\), the process of the load distribution matching is shown in Figure 3, and the final result is a set of alternative schemes composed of \(N_{e}\) historical reactive power control plans. As the method proposed in this paper is dependent on the historical data, it is suitable for the system that the load changes smoothly and the historical data accumulates enough.