The discrete wavelet transforms based on Daubechis wavelet has been used to detect and classify the high transient inrush current [14]. Figure 3 shows the structure of the proposed techniques for the transient inrush current classifier. The structure is composed of the discrete wavelet transform, wavelet scale analysis, maximum scale selection and transient classification from the inrush current 6-difference cases of transient mitigation methods in order to investigate the possible cause of capacitor bank switching. The DWT is used to analyze the transient signal at scale selecting between 1 to 30 scales only. The mother wavelet, db4 is also used to analyze the transient disturbance owing to less time requirement to do the calculation and provide the classification more correctly than others [10]. The wavelet coefficient from each scale will be determined by Equation (1) [15, 16]. The discrete wavelet transforms (DWT) is used to analyze the transient signal at scale selecting from first scale to thirty scales only.

Figure 3 The structure of transient inrush current detection and classification system with DWT

$$\begin{array}{}{\displaystyle {E}_{\psi}\left(s\right)=\sum _{m=0}^{n}{\left|DWT\left(m,n\right)\right|}^{2}(1)}\end{array}$$(1)

The wavelet coefficient in each phase during capacitor switching will be conducted for detection the high transient inrush current by using an if-then statement which will be compared with the wavelet coefficient during capacitor rated current (threshold, steady state) as follows.

If (IA, max) > (1.3xThreshold),1,0),

If (IB, max) > (1.3xThreshold),1,0),

If (IC, max) > (1.3xThreshold),1,0),

If (Imax, positive) > (1.3xThreshold),1,0)

and

If (AND (Imax, positive) = 1,

SUM (IA:IB:IC, max) ≥ 2),“Abnormal”,“Normal”)

The above if-then statement is designed to match the high transient inrush current phenomena and the philosophy of the protective relay setting accordance with IEC 60871-1:2014, IEC 60871-3:2015, IEEE Std. 1036-2010 and IEEE Std. C37.99-2012. The capacitor units shall be suitable for continuous operation at an r.m.s. current of 1.30 times the normal rated current that occurs at rated sinusoidal voltage and rated frequency, excluding transients. Therefore, for banks with separate overload and short-circuit protection, the overload protection is normally set in the range of 1.3 and 1.4 times rated current. The operating delay time is set long enough to avoid false trips during switching. The short-circuit protection is set above 3In and a few cycles delay. Refer to the if-then statement as above, the 130% or 1.3 times is from the maximum of capacitor overloading condition. If current phase A, B, C and positive sequence current are higher than the 1.3 times. It is a risk for capacitor damage and exposure due to capacitor overloading. This criterion is the pick-up current setting for overcurrent relay protection. During capacitor switching to close state, the transient inrush current phase A, B, C and positive sequence current will be increased rapidly and higher than the threshold. Therefore, the result of a proposed algorithm is the abnormal condition. Moreover, if the summation of wavelet coefficient of the positive sequence current is higher than the threshold and the summation of wavelet coefficient in each phase can detect more than 2 phases. We can conclude that these signals are abnormal. The criteria of the summation of wavelet coefficient in phase A, B and C shall be used equally or more than 2-phase detection because some of the switching devices are closed nearly to 0 degrees. Thus, the inrush current is very low signal. However, we cannot judge the transient signal whether it is the inrush current switching or normal capacitor rated current. The algorithm of standard deviation will be performed in order to find the type of these transients.

In the section of classification algorithm, the standard deviation is very important features to distinguish the transient disturbance classification [9]. Therefore, the equation to calculate the standard deviation is shown in Equation (2).

$$\begin{array}{}{\displaystyle \sigma =\sqrt{\frac{1}{N}\sum _{s=1}^{N}{\left({E}_{\psi}(s\right)-\mu )}^{2}}\phantom{\rule{thinmathspace}{0ex}}(2)}\end{array}$$(2)

The standard deviation of the discrete wavelet scale analysis and the number of maximum scales to detect in wavelet scale analysis can be used to classify the possible cause and origin of transient inrush current both isolate and back-to-back capacitor switching by using the if-then statement. The flowchart diagram of the proposed algorithm can be shown in Figure 4.

Figure 4 Flowchart diagram for detection and classification by using the discrete wavelet transforms

IF (AND (STDEV, inrush, positive) > (1.3*STDEV, threshold, positive), Wavelet, scale max < (Wavelet, scale threshold), “Normal switching”,“Back-to-Back switching”)

As the above algorithm, the standard deviation must be multiplied with 1.30 times to be setting the pick-up current (threshold). The capacitor unit can withstand for continuous operation at an r.m.s. current of 1.30 times the normal rated current that occurs at rated sinusoidal voltage and rated frequency, excluding transients. The variable “STDEV, inrush, positive” is the standard deviation which is calculated from the wavelet coefficient of positive sequence current by using the equation (2). This variable will be calculated the standard deviation totally 30 scale wavelet analysis. The variable “STDEV, threshold, positive” is the standard deviation which is calculated from wavelet coefficient of positive sequence current during normal capacitor switching totally 30 scale wavelet analysis.

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