**4. Case Analysis**

In order to verify the advantages of the SLCVA*k*NN method in the power transmission system disturbance detection, this section gives the case study on the real industrial data collected from the actual power transmission system. For method comparison, four methods, including the proposed SLCVAkNN method and three other methods of PCA, PCA*k*NN, and CVA*k*NN, are all applied to build the monitoring models for disturbance detection. The PCA method has two monitoring statistics *T*<sup>2</sup> and *Q*, while the other three methods are with the *k*NN-based statistics *DT*<sup>2</sup> and *DQ*. When these methods are used, they indicate the system status by the monitoring charts, where the monitoring indices of normal and faulty samples are given by black and blue solid lines, respectively, while the detection threshold, that is the 95% confidence limit of the monitoring index, is plotted by the red dashed line. One evaluation index, called the disturbance detection rate (DDR), is used to evaluate the different monitoring methods. DDR is the percentage of the abnormal samples exceeding the detection threshold over all the abnormal samples.

The used real industrial data are collected from the seven transmission lines in a power supply station in August 2018. These lines are radially connected. Their data are collected because all of them involve the ground fault. The data acquisition units, designed by Qingdao Topscomm Communication CO. LTD, are used to collect the electric field intensity and current. Here, the real line voltage is up to 110 KV so that the existing equipment can not directly measure it. Therefore, the electric field intensity is applied to reflect the voltage trend. For each transmission line, one corresponding data set is recorded that involves the normal state and the abnormal state. The data set has the length of about 1300 samples, where the disturbance starting time (DST) is different in different transmission lines. The detailed information about the acquired data sets are listed in Table 1, where DST data record the sample number corresponding to the disturbance starting time. A demonstration of the collected data for the DATA-A is given in Figure 2, where six measured variables, including the electric field intensities of phase A, B, and C, and the currents of phase A, B, and C, are involved. Due to the existence of the harmonic load, the current sine wave distortion can be seen in these curves.

**Table 1.** The collected industrial data sets.


**Figure 2.** Data waveform collected from 904 line exit. (**a**) Three-phase electric field intensity; (**b**) Three-phase current.

Taking the data set DATA-2 as one example, it is collected from the pole 116-3 of the line 906. This data set includes 1312 samples. To investigate it with the help of on-site engineers, it is known that the disturbance occurs from the 456th sample. Although engineers can find this disturbance by careful analysis, this manual way is very time-consuming and inefficient, so it is difficult to implement in large-scale transmission system monitoring. Therefore, building an automatic multivariate data analysis tool is very necessary. In

this section, we apply four MSA methods, which are PCA, PCA*k*NN, CVA*k*NN, and SLCVA*k*NN, to perform the automatic fault detection. When the statistical models are developed, the model parameters are set as follows: *k* = 3, *L* = 10, *l* = 2, *w* = 20. For the data set DATA-2, the first 320 sampling point are considered to be in a normal operating state, they can be utilized as the training data set for model development, while monitoring charts of PCA, PCA*k*NN, CVA*k*NN, and SLCVA*k*NN are demonstrated in the Figures 3–6, respectively. By the PCA monitoring results shown in Figure 3, it can be seen that the disturbance cannot be detected very effectively. The DDR of PCA *T*<sup>2</sup> is 4.43%, while the *Q* is a little better with the DDR of 29.52%. When PCA*k*NN is used, the *DT*<sup>2</sup> has a similarly poor detection rate, but the *DQ* statistic achieves clear improvement with the DDR of 57.76%. These results demonstrate that the PCA*k*NN method proposed by Cai et al. [20] can deal with the power system data with oscillation characteristic effectively. However, from these figures, the monitoring statistics do not exceed the confidence limits significantly. This may lead to the uncertain judgement on the occurrence of disturbance. When the CVA*k*NN is applied in Figure 5, the *DQ* statistic performs a little better with the DDR of 49.71%. However, its *DT*<sup>2</sup> indicator clearly improves the DDR to 92.51%, which means a significant detection rate improvement of about 70% in contrast with the PCA*k*NN's *DQ* index. The best monitoring results on this data set is provided by SLCVAkNN, which are shown in Figure 6. By this figure, it is observed that the disturbance is detected very clearly with the DDRs of 97.25% and 96.80% for *DT*<sup>2</sup> and *DQ*, respectively. This case gives a comprehensive comparison on the four methods of PCA, PCA*k*NN, CVA*k*NN, and SLCVA*k*NN. The applications show that PCA*k*NN does better than PCA due to the use of *k*NN, while SLCVA*k*NN further prompts the disturbance detection performance with the integration of CVA and SLA.

**Figure 3.** PCA monitoring results on the DATA-2 case.

**Figure 4.** PCA*k*NN monitoring results on the DATA-2 case.

**Figure 5.** CVA*k*NN monitoring results on the DATA-2 case.

**Figure 6.** SLCVAkNN monitoring results on the DATA-2 case.

Another example on the data set DATA-6 is illustrated, which corresponds to the line 906 exit. The modeling procedure is similar to the above case. Here we only give the monitoring charts of CVA*k*NN and SLCVA*k*NN, as shown in the Figures 7 and 8. With the consideration of system dynamics, the CVA*k*NN *DT*<sup>2</sup> monitoring chart gives a higher DDR of 88.51%. Compared with the CVA*k*NN method, which has only one effective monitoring statistic, SLCVA*k*NN has two well-behaved monitoring statistics. The *DT*<sup>2</sup> and *DQ* have the DDRs of 97.37% and 97.25%, respectively. The testing results on DATA-6 further verify the advantage of the proposed method over the CVA*k*NN method.

**Figure 7.** CVA*k*NN monitoring results on the DATA-6 case.

The summary of disturbance detection rates for all seven data sets are shown in Table 2. From this table, it is shown that the faults in DATA-2 and DATA-4 are difficult to detect by PCA, whose DDRs are all lower than 30%. By the use of PCA*k*NN, these two faults are detected with higher DDRs, which are 57.76% and 26.78%, respectively. By contrast, CVA*k*NN does better on the two faults. In particular, its *DT*<sup>2</sup> statistic gives the DDR higher than 90%. When SLCVAkNN is used, its two monitoring statistics have the higher DDRs than 95%. For the sets of DATA-1, DATA-3, DATA-6, and DATA-7, PCA can detect these faults with about 70-80% DDR on one statistic. That means PCA can alarm these faults, but

the alarm degree is not very sufficient. The PCA*k*NN and CVA*k*NN improve the DDR to about 90%. Further combining the SLA technique, SLCVA*k*NN achieves higher DDR than CVA*k*NN on these four sets. As to DATA-5, all these four methods give a similarly good performance with the DDRs higher than 95%. Considering all seven of these data sets, we observe that the average detection rates of CVA*k*NN outperforms the PCA and PCA*k*NN method, while the ones of SLCVA*k*NN statistics can reach 97.46% and 96.29%, which are the highest among these four methods.

**Figure 8.** SLCVAkNN monitoring results on the DATA-6 case.


**Table 2.** The disturbance detection rate of PCA, PCA*k*NN, CVA*k*NN, and SLCVA*k*NN for the tested data sets.

To sum up, the applications on real industrial data verify the effectiveness of the proposed SLCVA*k*NN in the power transmission system monitoring. All the tested faults are about the ground faults. Although this paper does not provide the results on the other disturbances such as 1,3-phase short circuits, overvoltages, the presented algorithm is also suitable for these cases because they similarly lead to the changes of voltage and current. However, one related issue should be noted. In this article, this method detects all the occurred disturbances, including normal disturbances such as load power variations. To judge whether the disturbance is a fault or a normal disturbance is a further job. In fact, as to this issue, one solution is to enrich the modeling data with different normal changes. As the *k*NN used in this method can deal with the multimodal data case, the trained model can distinguish the faults and normal disturbances effectively when the normal changing data are considered in the model training procedure.
