Pre-diagnosis technology for short-circuit withstand capability of distribution transformer based on big data

2.1 Typical process classification for distribution transformers

This paper counts the most common S11∼S15 oil-immersed distribution transformers at present, and selects different processes under the four typical capacities of 100, 200, 400 and 630 kVA. There are six typical processes including block material, the winding compression ring structure, lead wire clamp, winding impregnation or winding varnishing, lead insulation, and core clamp ribs, as shown in Figure 1.

Figure 1:

Typical process map.

2.2 Typical process analysis of distribution transformers

(1). Block material: The block material acts as an insulation and mechanical support in the distribution transformer, and is distributed on the upper and lower sides of the winding to form an integral support structure with the clamp member. When the block is subjected to short-circuit impact force, it has a certain elastic buffering effect. The better material is laminated wood, and the poor one is insulated paperboard. (2). Lead insulation: Most of the lead insulation is insulated with cardboard or insulator to separate the low voltage winding lead wire from the neutral point lead wire, in order to prevent them discharging to each other when the transformer runs short circuit. (3). The winding compression ring structure: The winding compression ring structure mainly has an integral pull screw structure and a separate nail structure. The former tightly grips and clamps the entire winding by connecting a long screw in the middle of the clamp, and the latter independently holds a part of the winding by the upper and lower clamps with screws. (4). Lead wire clamp: The lead wire clamp member is used for fixing the lead wire end of the winding, and is generally fixed on the core clip by the lead wire clamp of the epoxy material, so as to avoid the fault caused by the excessive swing of the lead wire during the short circuit. (5). Winding impregnation or Winding varnishing: Winding impregnation or Winding varnishing process mainly adopts two methods. One is to dip the windings and the materials other than the windings as a whole, and the other is to paint only the windings. Winding impregnation or Winding varnishing process not only strengthens the winding insulation, but also enhances the mechanical properties of the winding, making it less prone to misalignment and enhancing short-circuit withstand capability. (6). Core clamp ribs: The iron core clamp rib is generally welded to the joint between the web and the limb of the core clamp to enhance mechanical stability.

3.1 Priority evaluation model

According to the hanging photos or design drawings, the different processes used for different capacity transformers are determined, we introduce the test parameter probability density fi and the process parameter weight density ρn, establish the total probability function P=∑n−16ρn•fn and the superior evaluation model (as shown in Table 1). Divide the priority level (as shown in Table 2), and judge whether the distribution transformer has short-circuit capability through the superior grade.

The establishment of the superior evaluation model adopts the expert diagnosis method based on fuzzy mathematics: by collecting and counting the hanging photos and type test data before and after the short-circuit test of 308 distribution transformers of the center in the past three years, attribution analysis was performed on typical processes of distribution transformers and short-circuit test pass rates. In the case of the unknown short-circuit test results, the experts in the field of distribution transformer design and inspection scored the short-circuit-proof design of the corresponding transformer from the perspective of six typical processes according to the hanging photos. After collecting and summarizing the scores, the distribution transformers are classified into superior, qualified and inferior products according to the level of each process. According to the value of Table 1, the six typical processes of a single distribution transformer form a lateral quantity fi. The process values of multiple distribution transformers of the same capacity are arranged in a certain order to form a matrix Fn. Fn is called the process matrix, which is shown in formula (1).

The short-circuit test pass rate (p(0≤p<1)) of a single distribution transformer is calculated by the set algorithm according to the actual short-circuit test results and test data. The short-circuit test pass rate of a single distribution transformer is divided into five levels according to Table 2. The short-circuit test pass rate (p) and the process lateral quantity of multiple distribution transformers of the same capacity are in the same order, and one-to-one correspondence to formed the column vector (P). The correspondence between the process matrix (Fn) and the short-circuit test pass rate column vector (P) is as shown in Eqs. (2) and (3).

which is

From this, the weight coefficients (ρ1∼ρ6) of six typical processes under the same capacity can be calculated. According to the idea of regression analysis, a linear multiple regression equation is established and the credibility of the regression equation is analyzed. Gradually eliminate the process in which the short-circuit test pass rate is not significant under this capacity, and finally establish a regression equation with higher reliability. For the single distribution transformer of the capacity applicable to the regression equation, the regression equation can be used to directly calculate the short-circuit test pass rate and determine the priority level. For the distribution transformers with the capacity not involved in the regression equation, the model of the adjacent capacity can be combined with the short-circuit test pass rate interval division map to determine the interval of the short-circuit test pass rate, and the priority level is determined.

3.2 Model derivation

Taking a distribution transformer with a capacity of 200 kVA as an example, regression analysis is performed with Matlab to establish a basic model p=ρ1f1+ρ2f2+ρ3f3+ρ4f4+ρ5f5+ρ6f6, Among them, f1∼f6 are the values of the six processes which are blind scored by the experts, p is short-circuit test pass rate which is converted by the actual short-circuit test data (based on the phase reactance change rate before and after the short-circuit test), and the corresponding relationship between p and the priority grades is shown in Table 3.

The relationship between p and the phase reactance change rate ΔX is expressed by a piecewise function as shown in Eq. (4).

The results of the basic model regression test are shown in Table 4.

In the saliency verification of multiple regression, the linear relationship test (F-test) and the regression coefficient test (t-test) are no longer equivalent. The linear relationship test is mainly to verify whether the overall linear relationship between the short-circuit test pass rate p and the six typical processes is significant (at least one of ρ1∼ρ6 is not 0). In the six typical processes, as long as there is a significant linear relationship between the typical process and the short-circuit test pass rate, the F-test is significant, but this does not mean that each process in the six typical processes is significantly correlated with the short-circuit test pass rate. The regression coefficient test is to perform a separate test for each regression coefficient (ρi≠0, i = 1∼6) to determine whether the impact of each process on the pass rate of the short circuit test is significant. Due to the large number of processes, there may be a significant correlation between each process. We make significant verification of the basic model, and the t-test results are shown in Figure 2: t1 = 1.1863, t2 = 9.0315, t3 = −1.0290, t4 = 1.9300, t5 = −1.5761, t6 = 1.3667. The corresponding levels of significance (p value) are 0.2425, 0.000, 0.3097, 0.0607, 0.1229 and 0.1794. Only the significance level corresponding to ρ2 is less than 0.05, the significance of ρ4 is slightly larger than 0.05, and the significance of the other four regression coefficients is much larger than 0.05. From the confidence intervals of ρ, the confidence intervals of ρ1, ρ3, ρ5 and ρ6 are all contain 0, which obviously does not satisfy the requirement of regression coefficient test. It can be seen from F = 37.3507 that the F-test of the basic model is significant, and the t-test of five regression coefficients among the six regression coefficients is not significant.

Figure 2:

T-test of stepwise regression.

In general, the following conditions imply that the model has multiple collinearity:

1. There is a significant correlation between the respective variables in the model;

2. When the F-test of the model is significant, the t-test of almost all regression coefficients is not significant;

3. The sign of the regression coefficient is opposite to what is expected.

It is known from the significance verification that the 200 kVA distribution transformer’s basic model may have multiple collinearity, and for further confirmation, the correlation between the respective variables can be verified. The correlation between the respective variables can be calculated from the correlation coefficient as shown in Eq. (5).

In the formula, Cov(X,Y) is the covariance of X and Y, Var[X] is the variance of X, Var[Y] is the variance of Y. After calculation, the column vectors f1 to f6 have a large correlation coefficient between twos, indicating that the six processes are related to each other in the distribution transformer with a capacity of 200 kVA. Moreover, the regression coefficients of ρ3 and ρ5 are negative, which is obviously unreasonable. According to the foregoing, the resistance levels of the six processes and distribution transformers are positively correlated. Thus, it can be determined that the model has multiple collinearity.

To avoid multiple collinearity in the regression model, we use stepwise regression to combine the forward selection with the backward elimination to filter the independent variables. After adding a new independent variable, it will re-examine all the variables in the model to determine whether it is necessary to eliminate an independent variable (If a new independent variable is added, the contribution of the previous independent variable to the model becomes insignificant, and the previous variable will be removed). In this way, the variables are continuously increased and the insignificant variables are considered to be eliminated, until the increase of the variables has not been able to significantly reduce the sum of squared residuals Q (this process can be achieved by the F-test). By stepwise regression analysis, the independent variables f1, f3 and f5 are eliminated, and the regression equation of the 200 kVA distribution transformer is obtained as follows:

Similarly, regression equations for distribution transformers with capacities of 100, 400, and 630 kVA can be obtained. The model is summarized as Tables 5–8.

The regression equation is

The regression equation is

The regression equation is

The regression equation is

3.3 Data distribution analysis

When the number of samples is limited, a simple analysis using a box plot can visually observe the data distribution and determine if abnormal data exists. Box plots, alias boxes, boxes and so on, are statistical methods invented by John Wilder Tukey, which visually represent the overall distribution of data and eliminate abnormalities that are far from the overall data. The specific way is that all the data are arranged in order from small to large, and one number (two averages) in the middle of the data is the median. The numbers at the 75 and 25% positions in the permutation data are respectively defined as the upper quartile (Q3) and the lower quartile (Q1). The interquartile range is obtained from the upper and lower quartiles, is IQR = Q3 − Q1, and the upper and lower limits are respectively obtained according to Q3 + 1.5IQR and Q1 − 1.5IQR, and the values outside the upper and lower limits are defined as outliers. The specific Fig. is shown in Figure 3.

Figure 3:

Box plot.

Since the short-circuit test is a destructive test, 308 distribution transformers for short-circuit test contain four capacities of 100, 200, 400, and 630 kVA, and the number of samples of the same capacity is relatively small. For the four capacity distribution transformers, the distribution of the short-circuit test pass rate p was analyzed by using the box plot function in Minitab software. The box shape of the short-circuit test pass rate p of the four-capacity distribution transformer is shown in Figure 4. From the neutral line connection, it can be seen that the short-circuit test pass rate p of the distribution transformer has a tendency to decrease as the capacity of the distribution transformer increases. This is in line with our experience. As the capacity of the distribution transformer increases, the short-circuit inrush current increases, and the short-circuit electric power increases squarely as the short-circuit inrush current increases. The fastening measures that can achieve better results in small-capacity distribution transformers. But when it used on large-capacity distribution transformers, the results are often not ideal. This is also an important reason for the low short-circuit rate of large-capacity distribution transformers.

Figure 4:

Box plot of four capacity distribution transformer test pass rate.

On the box plot of the short-circuit pass rate of the distribution transformers of 100, 200, 400, and 630 kVA, the upper limit, the lower limit, the first quartile, and the third quartile are respectively taken. By performing piecewise linear interpolation on other uncovered capacities, the short-pass rate distribution map of the following Fig. can be obtained. The green part in Figure 5 is the most likely short-circuit test pass rate p for a single transformer under the corresponding capacity.

Figure 5:

Short-circuit pass rate interval division map.

4.1 Case 1 (typical capacity)

In April 2018, the center received an S13-M-630/10 oil-immersed distribution transformer commissioned by a power grid company. After the routine test was completed, the hanging core inspection before the short-circuit test was performed on the distribution transformer, and the state of the typical process of internal use of the distribution transformer was photographed from a plurality of angles. The photo of the hanging core inspection is shown in Figure 6.

Figure 6:

Hanging core of 630 kVA distribution transformer.

It can be seen from Figure 6 that the distribution transformer does not use the winding compression ring structure of the pressing nail or the pulling screw to compress the winding to prevent the winding from being axially moved by the electric power. The low voltage lead-out soft row is also not fixed, and is separated from the core clip only by the insulating cardboard. The surface of the winding is painted, but not the overall dipping. No reinforcing ribs are used on the core clamp. That is to say, except the winding painting process is used, the other five typical processes are not used. Therefore, the winding impregnation or winding. Varnishing f4 has a value of 0.5, but the other three typical processes block materials f1, winding compression ring structure f2, and lead wire clamp f3 which have a significant influence on the distribution transformers of 630 kVA are all 0. The short-circuit passing rate of the distribution transformer conforms to table (4) model.

Substituting the value of f1∼f4 into Eq. (4) and obtaining p = 0.11225, corresponding to the priority classification of Table 2, the short-circuit withstand capability of the distribution transformer is extremely poor, so it is the subject of key inspection. After testing, the phase reactance change after the short-circuit test of the distribution transformer was 38.6%, far exceeding the phase reactance change rate of 7.5% within the standard requirement.

4.2 Case 2 (atypical capacity)

In May 2018, the center received an S13-M-315/10 oil-immersed distribution transformer commissioned by a power grid company. After the routine test was completed, the hanging core inspection before the short-circuit test was performed on the distribution transformer, and the state of the typical process of internal use of the distribution transformer was photographed from a plurality of angles. The photo of the hanging core inspection is shown in Figure 7.

Figure 7:

Hanging core of 315 kVA distribution transformer.

It can be seen from Figure 7 that the distribution transformer adopts a laminated wood integral block and is pressed by a pull screw pressing ring structure. The low-voltage lead wire is fixed on the core clip with a laminated wood clip. The winding is immersed and the webs and ribs of the core clamp are reinforced with ribs. That is to say, six typical processes are used on the distribution transformer, and the structure is compact. The neutral line with no current passing under the symmetrical load is also tied and fixed. The distribution transformer obviously adopts strengthening measures in the short-circuit withstand capability improvement. Therefore, the values of the six typical processes are all 1. There is no ready-made regression equation that can directly apply the short-circuit through rate of a distribution transformer with a capacity of 315 kVA. Thus, the regression equations of 200 and 400 kVA and the short-circuit pass rate interval division map are combined to judge. Substituting the regression equation of 200 kVA, the short-circuit passing rate p1 is 0.9519, and the regression equation of 400 kVA is substituted to calculate the short-circuit passing rate p2 of 0.6799. Therefore, as shown in Figure 8, the short-circuit test pass rate p3 of the transformer is more likely to appear in the upper yellow area or the red areas, the corresponding interval is [0.60 0.85]. At this time, the priority level of the corresponding Table 2 is divided, and the level of the short-circuit withstand capability of the transformer is between general and excellent. After verification by the real short-circuit test, the phase reactance change after the short-circuit test was 1.68%, and its’ short-circuit withstand capability was excellent, which was in good agreement with the pre-diagnosis.

Figure 8:

Short-circuit pass rate interval division map.