# Prioritizing CBs Maintenance and Identifying Mandatory Maintenance at Higher Priorities

Authors: A. Aranizadeh; S. M. Shahrtash; A. Gholami
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Preventive maintenance (PM) based on condition monitoring of circuit breakers (CBs) provides proper and timely maintenance of CBs and reduces their failure rate as well as network costs. Condition monitoring of CB considers functional age (not natural age) of CB. This functional age depends on CB erosion. In this paper, CB condition assessment is obtained by monitoring the coil current and its duty cycles. Then, the maintenance priority between CBs of a power network is achieved using self-evaluation decision-making algorithm (SEDMA). This algorithm works in such a way that both the performance of CB is tracked by itself over time as well as compared to other CBs. First, this means the condition of the CB is measured by itself, and if the condition of the CB deteriorates over time, the CB will be given priority for repair. Second, the CB is compared offline with other CBs, and owing to the CB failures compared to other CBs, the priority of CB repair will be finalized. Then, using sensitivity analysis, it is determined whether the CB with the highest priority needs to be repaired or not, and the failure level of each CB will be specified. The case study in this paper concerns about two similar CBs. Also, the effect of improving the condition of the CB will be determined by performing maintenance operations. Eventually, it will be clear which CB has a higher priority for maintenance and whether this higher priority justifies the need for maintenance or not.


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## Body

## 1. Introduction

Recently, the life of power equipment is one of the most challenging issues in power systems. Equipment life has a significant contribution in power station reliability calculations and economic analysis of asset management. Circuit breakers (CBs) are one of the most important apparatuses of an electrical power transmission system, though their function seems to be simple, i.e., open or close as it is ordered. CBs have a fundamental role in the reliability of power systems in normal operation and protection of power system against abnormal conditions, such as faults [1].Similar to other apparatuses, CBs are not able to be in service at all times, and there are some downtimes due to failures [2]. CB failures are divided into major and minor failures. A major CB failure is that type of failure that causes one or more parts in the CB to have a malfunction. In this type of failure, the faulty part must be repaired/replaced quickly. Any other failure is considered as a minor failure [3].Increasing the life of any equipment or reducing its failure rate is the goal of maintenance activities. The maintenance strategy is generally divided into two modes of corrective maintenance (CM) and preventive maintenance (PM). In CM method, also known as the run-to-failure method, no part of the equipment is repaired until the equipment fails. This approach is useful when the cost of an equipment failure is low. Noting that failure in CB will impose a high cost on the power system, this approach cannot be used. On the contrary, in the PM method, the maintenance operation is used to prevent the occurrence of equipment failure [2, 4–6].The time-based maintenance (TBM) is one of the PM methods, which is costly but at the same time is a simple approach. In this method, monitoring and maintenance are performed at predefined and fixed time intervals. These fixed maintenance intervals are usually given by the manufacturer. Although this method reduces the failure rate of the CBs, it is not economical. This method will try to reduce the failure rate using periodic maintenance.The condition-based maintenance (CBM) is also one of the PM methods and is based on the information obtained from the equipment conditions. Compared to the TBM method, this method increases the inspection intervals of the equipment and thus reduces the cost of maintenance [7–11]. Karimabadi et al. [12] determined the smart inspection rate of equipment using condition monitoring effect on the CB. It is possible to measure the condition of the CBs and prioritize them in maintenance scheduling. For this prioritization, four groups of features have been introduced and employed including [7–9,13,14]:(i)
Electrical characteristics, such as contact resistance, closing critical voltage, and tripping critical voltage.(ii)
Mechanical characteristics, such as closing time, opening time, voltage jump of the auxiliary contacts, and spring charge time, all collected offline using existing testing devices. According to Zhang et al. [15], about 54% of major failures and 49% of minor failures are related to mechanical characteristics.(iii)
Insulation characteristics, such as insulation resistance (insulation dissipation factor), SF6 gas density for SF6 CBs, oil level and oil quality, partial discharge (using high-frequency current transformers (HFCTs) and estimating the intensity of the partial discharge [16]).(iv)
Miscellaneous, such as operating environment, maintenance data, and operating age.Most of the information obtained from the CB is offline. In recent years, online condition monitoring methods have been expanded. This achievement is based on the evaluation of the real-time performance of the CBs based on the measured parameters. Coil current of CB is one of the parameters that can be checked online. It should also be added that since there are many apparatuses in the power grid, it is not economically possible to equip all of them with online monitoring. Razi-Kazemi et al. [17] estimated the optimal number of online monitoring equipment using an optimization framework.As aforementioned, failures related to mechanical operation are one of the most common causes of CB failures. The mechanical performance of CB is monitored by calculating the wear-out of CBs [18]. The state of the secondary circuit is usually used to evaluate the performance of CBs. The coil current represents this secondary circuit, which is designed for short operating times in both open and close modes.Wang and Yang [19] examined the role of contact wear of the CB on CBM. Razi-Kazemi [3] has used this coil current to evaluate the condition of CBs using fuzzy-probabilistic. In this reference, using Pearson correlation coefficient (PCC) and scatter plot, the effective features are identified and then by fuzzy processing, the failure rate is obtained. Zhong et al. [18] also has used the coil current to measure the condition of CBs and finally found the functional age of each CB. According to this reference, by unifying the monitored parameters of the CB in relation to the upper and lower constraints of each parameter, wear of CB is obtained. It then obtains the functional age of CB using the history of this information. Razi-Kazemi et al. [20] also used this coil current for failure tracking in CBs. According to this reference, by obtaining the effect of each failure on the coil current waveform, the type of failure can be identified. In fact, failures and their causes are categorized and the impact of various failures on the coil current will be identified. In other words, by measuring the coil current in each of coil voltage variation, coil failure, latch malfunction, and auxiliary contacts malfunction, the effect of these failures on the CB is measured, and in this way, subsequent failures will be tracked. Razi-Kazemi et al. [21] and Razi-Kazemi [22] have also used this current and data mining for condition assessment. According to these references, with the aid of the history of this information, the health intervals of CB and relationship between features are measured, and with the entry of new data, the health status or defect in corresponding CB is obtained. Geng and Wang [23] also evaluated the CB conditions using the coil current and intrinsic characteristics and using back-propagation neural network. Razi-Kazemi and Niayesh [24] asset management using diagnostic signals, intelligent modeling, and monitoring data. It presents real-time assessment of the diagnostic signals.Table1 compares the proposed method and other published methods. According to this table, several different aspects are given.(i)
Being applicable in inspecting ageing: i.e. not only the procedure is applicable for comparing different CBs but also the condition of the CB can be compared with its previous data during the time and assess the gradual deterioration of the CB. This index can also be expressed by the probability of failure and measures the probability of CB being in an unhealthy condition, according to the failure rate obtained from the CB.(ii)
Employing reliability (important) index: this aspect evaluates the reliability index of CBs which have been evaluated in other references but have not been considered in this paper. The reliability index takes into account the location of CB in the network and the cost of its fault.(iii)
Employing history data: this aspect expresses the memory of the algorithm, i.e., in the final decision for giving the maintenance priorities, the data will be considered from the beginning to the end. By considering this aspect, changes in a CB and its health or failure will be observed over time.(iv)
Estimating severity of failures: in order to help in prioritizing maintenance.(v)
Estimating time to CB failure.(vi)
Online application.(vii)
Ease in measuring the input data.Table 1
Compare the proposed method and previous methods.
No.Aspect[3][4][5][20][21][22][18][25][26][27][28][29][23][24][17]Thispaper1Being applicable in inspecting ageing✓2Employing reliability (important) index✓✓✓✓3Employing history data✓✓✓✓✓✓4Estimating severity of failures✓5Determine time to failure✓6Online application✓✓✓✓✓✓7Ease in measurement of the input data✓✓✓✓✓While the proposed method is an offline method and requires measuring the coil current, which is not so much easy, the first, the fourth and the fifth aspects mentioned in Table1 are considered for the first time in this paper. Therefore, the innovations of this paper can be expressed as follows:(i)
Proposing a new evaluation algorithm (SEDMA) for integrating two aspects of comparison between two CBs as well as comparing CB with its own previous condition.(ii)
Introducing new wear out function which can model the severity of failures.(iii)
Employing sensitivity analysis to estimate time to CB failure as well as determining failure level.The rest of this paper is constructed as follows. In Section2, the conditions and coil current of a CB are identified and evaluated. Section 3 describes the proposed methodology, which includes homogenizing outlier data, data windowing, CB wear-out function, self-evaluation decision-making algorithm (SEDMA), and determines the failure level based on sensitivity analysis. In section 4, the results of a case study are analyzed. This case study consists of two CBs. First, these two CBs are compared with each other and the higher priority CB is identified, and then, using sensitivity analysis, the failure level and the requirement of higher priority CBs for maintenance are determined. Finally, the effect of healing CB conditions will be determined by performing maintenance operations.


## 2. CBS Condition Monitoring

CB performance mechanism consists of two important parts, the mechanical drive system and the secondary circuit including control and auxiliary circuits. Secondary circuit condition is usually used to evaluate CB condition assessment, due to the fact that overall CB conditions will have special effects on this circuit.Coil current waveforms of CB can be measured and analyzed for a short time (less than 100 ms), on both opening and closing operations. A DC supply (battery) that feeds the coil current, disconnects quickly after the coil has been operated.CBs secondary circuit operation for opening performance is shown in Figure1. Six stages have been illustrated, including:Stage 1. The control circuit starts working as soon as the coil is energized by receiving a command signal from the trip switch and the opening operation starts at t1 (shown in Figure 2).Stage 2. The plunger begins to move and the coil current increases at t2 (shown in Figure 2).Stage 3. The coil current has a sag at t3 (shown in Figure 2) due to saturation, indicating that the plunger strikes the latch, and its velocity decreases.Stage 4. The latch unlocks and the main contacts begin to open, making the coil current to increase again.Stages 5 and 6. When the spring is released, the main contacts open, and the status of auxiliary contacts changes. Owing to these changes, the trip circuit becomes open and the trip coil is de-energized. Then, the coil current decreases and reaches zero at t4 (shown in Figure 2). The changes in statuses of the auxiliary contacts a and b occur at t5 and t6, respectively (shown in Figure 3).Figure 1
CB secondary circuit operation.Figure 2
Coil current duty cycle.Figure 3
Voltage jump at auxiliary contacts.Also, there are five characteristics to evaluate CB’s conditions by analyzing the coil current and the voltage jump of the contacts.As an example, Table2 gives the lower and upper values of the times t2–t6 [25, 26]. These values are later used as history information for CBs, in assessing the performance of the proposed method.Table 2
Lower and upper values of t2–t6.
Parameter (ms)Lower valueUpper valuet20.005.50t39.8016.4t426.043.4t549.967.5t662.075.8


## 3. Proposed Methodology

In this section, the proposed methodology with a novel CB wear-out function, self-evaluation decision-making algorithm (SEDMA), and validation method based on sensitivity analysis are explained.


### 3.1. Homogenizing Outlier Data to Improve Inputs

Bad data or outlier data refer to observations that are farther away from a central point (such as the mean) in terms of a scatter index (e.g., standard deviation). According to this, if the data have a normal distribution, it is very unlikely that a value outside the distance is three times the standard deviation from the mean. As a result, encountering such an observation, i.e. an observation that exceeds the mean value ± 3 × standard deviation, it is considered as an abnormal observation and it is homogenized.Taking Figure4(a) as an example, it is clear that these data have an outlier. This outlier sample may be either due to the conditions of the tester or the conditions of the test or the test device.Figure 4
t2 of CB1 (a) actual data (b) improved data.
(a)(b)Accordingly, using the smoothing spline method to fit the curve makes having softer data. Based on the smoothing spline method, it will be determined that by selecting the smoothness index equal to 0.9743 (the larger this number is, the closer the output to the actual values, while the smaller the output will be smoother), the range of data changes, and it is limited exactly to the mean ± 3 × standard deviation. Figure4(b) shows the result, where there are no outlier data, observed.All the data (t2–t6 in two CBs) become smooth, based on the same fit of the spline curve with the index value of 0.9743. Finally, these values will be used as input to the SEDMA algorithm. Further attempts of the authors are through identifying and improving outlier data in power system equipment and will be presented in future reports.


### 3.2. Data Windowing

To analyze the input data, either all the previous data can be analyzed (expanding window) or only the last few data can be examined (moving window). The advantage of the moving window is that the algorithm will be faster in detecting faults or improving CB conditions due to maintenance operations. Note that, by entering the sixth data, the first data will be deleted and the last five data will be placed in the algorithm again (moving window), and so on.


### 3.3. CB Wear-Out Function

To have a quantitative measure of wearing out of CB, a wear-out index (function) is proposed that is applied for each of the parameters mentioned in Table2. The proposed index (function) takes small values as long as each time value corresponds to CB healthy condition and large values as the CB conditions tend towards faulty condition. The introduced wear out index is defined as follows and depicted in Figure 5:(1)WIj=et−Hj/Hj−Ljk,t>Mj,eLj−t/Hj−Ljk,t≤Mj,j=2,…,6,where Hj is the upper limit, Lj is the lower limit, and Mj is the mean time for jth time feature.Figure 5
Proposed Wear-out function.Moreover, Figure5 represents the proposed CB wear-out function for different values of k. As can be seen, the higher the value of k, the discrimination of healthy condition is easier and the priority of CB for maintenance can be more clearly shown. In other words, by increasing the value of k, more severe failures will appear and decisions about the priority of maintenance will be easier and more realistic.Each part of CB is examined by analyzing the wear-out indices of the times which are associated with or affected by that part. The corresponding wear-out indices are combined to make one index.According to what mentioned in Section2, Wear-out function of trip coil (TC) is a function of t2, t3, and t4 as follows:(2)WITC=WIt2,t3,t4.(i)
Wear-out function of latch mechanism (LM) is a function of t2 and t3 as follows:(3)WILM=WIt2,t3.(ii)
Wear-out function of auxiliary contacts (AUX) is a function of t5 and t6 as follows:(4)WIAUX=WIt5,t6.(iii)
Overall wear-out function of CB (OVR) is a function of t2–t6 as follows:(5)WIOVR=WIt2,t3,t4,t5,t6.


### 3.4. Self-Evaluation Decision-Making Algorithm (SEDMA)

The details of the proposed method, or in other words, SEDMA method will be provided in sequel.There are two basic aspects to consider when considering CB failure and prioritizing maintenance:(1)
Assessment of CB condition against ageing.(2)
Assessment of CB condition in comparison with other CBs.Based on these two aspects, the self-evaluation decision-making algorithm is introduced as in Figure6:Figure 6
Proposed SEDMA.According to this procedure, after collecting the data and identifying outlier data, the condition of each CB will be determined according to the boundary conditions. Next, using two aforementioned aspects, the maintenance priority (MP) is evaluated using SEDMA. Finally, the MP of each CB will be obtained. In the sequel, SEDMA is introduced to find out the MP of CB1, CB2, CB3,…:Step #MP1: Initial self-wise comparison matrix will be calculated according to equation (6), where WIj,k,CB1 stands for WI of the time feature, tj, at the kth measurement (extracted from history data) of CB1:(6)CICB1=WI2,1,CB1WI2,1,CB1WI2,1,CB1WI3,1,CB1WI2,1,CB1WI4,1,CB1WI2,1,CB1WI5,1,CB1WI2,1,CB1WI6,1,CB1WI3,1,CB1WI2,1,CB1WI3,1,CB1WI3,1,CB1WI3,1,CB1WI4,1,CB1WI3,1,CB1WI5,1,CB1WI3,1,CB1WI6,1,CB1WI4,1,CB1WI2,1,CB1WI4,1,CB1WI3,1,CB1WI4,1,CB1WI4,1,CB1WI4,1,CB1WI5,1,CB1WI4,1,CB1WI6,1,CB1WI5,1,CB1WI2,1,CB1WI5,1,CB1WI3,1,CB1WI5,1,CB1WI4,1,CB1WI5,1,CB1WI5,1,CB1WI5,1,CB1WI6,1,CB1WI6,1,CB1WI2,1,CB1WI6,1,CB1WI3,1,CB1WI6,1,CB1WI4,1,CB1WI6,1,CB1WI5,1,CB1WI6,1,CB1WI6,1,CB1⋮⋮⋮⋮⋮WI2,n,CB1WI2,n,CB1WI2,n,CB1WI3,n,CB1WI2,n,CB1WI4,n,CB1WI2,n,CB1WI5,n,CB1WI2,n,CB1WI6,n,CB1WI3,n,CB1WI2,n,CB1WI3,n,CB1WI3,n,CB1WI3,n,CB1WI4,n,CB1WI3,n,CB1WI5,n,CB1WI3,n,CB1WI6,n,CB1WI4,n,CB1WI2,n,CB1WI4,n,CB1WI3,n,CB1WI4,n,CB1WI4,n,CB1WI4,n,CB1WI5,n,CB1WI4,n,CB1WI6,n,CB1WI5,n,CB1WI2,n,CB1WI5,n,CB1WI3,n,CB1WI5,n,CB1WI4,n,CB1WI5,n,CB1WI5,n,CB1WI5,n,CB1WI6,n,CB1WI6,n,CB1WI2,n,CB1WI6,n,CB1WI3,n,CB1WI6,n,CB1WI4,n,CB1WI6,n,CB1WI5,n,CB1WI6,n,CB1WI6,n,CB1.It should be noted that the larger value of each matrix element, the greater is the vulnerability of the time feature corresponding to the numerator rather than the one corresponding to the denominator (for example:WI6,n,CB1/WI2,n,CB1>1⇒WI6,n,CB1>WI2,n,CB1). The same process will be repeated for CB2, CB3, …, and consequently CICB2, CICB3,… are calculated.Step #MP2: Initial pairwise comparison matrices of criteria between CB1 and CB2 are constructed as in equation (7), where CIIj,CB1-CB2 stands for comparisons between WIj,k,CB1 and WIj,k,CB2:(7)CIIj,CB1−CB2=WIj,1,CB1WIj,1,CB1WIj,1,CB1WIj,1,CB2WIj,1,CB2WIj,1,CB1WIj,1,CB2WIj,1,CB2⋮⋮WIj,n,CB1WIj,n,CB1WIj,n,CB1WIj,n,CB2WIj,n,CB2WIj,n,CB1WIj,n,CB2WIj,n,CB2.Similarly, the initial pair comparison matrix will be repeated for CIIj,CB1-CB3,….Step #MP3: Final pairwise comparison matrix is introduced as in:(8)DICB1=WI2,CB1¯ΘWI2,CB1¯WI2,CB1¯ΘWI3,CB1¯WI2,CB1¯ΘWI4,CB1¯WI2,CB1¯ΘWI5,CB1¯WI2,CB1¯ΘWI6,CB1¯WI3,CB1¯ΘWI2,CB1¯WI3,CB1¯ΘWI3,CB1¯WI3,CB1¯ΘWI4,CB1¯WI3,CB1¯ΘWI5,CB1¯WI3,CB1¯ΘWI6,CB1¯WI4,CB1¯ΘWI2,CB1¯WI4,CB1¯ΘWI3,CB1¯WI4,CB1¯ΘWI4,CB1¯WI4,CB1¯ΘWI5,CB1¯WI4,CB1¯ΘWI6,CB1¯WI5,CB1¯ΘWI2,CB1¯WI5,CB1¯ΘWI3,CB1¯WI5,CB1¯ΘWI4,CB1¯WI5,CB1¯ΘWI5,CB1¯WI5,CB1¯ΘWI6,CB1¯WI6,CB1¯ΘWI2,CB1¯WI6,CB1¯ΘWI3,CB1¯WI6,CB1¯ΘWI4,CB1¯WI6,CB1¯ΘWI5,CB1¯WI6,CB1¯ΘWI6,CB1¯,where Θ (here and elsewhere) means each element of the first matrix is divided by the same element of the second matrix and finally, a 1×3 matrix will be formed. So, each element of this matrix has three fuzzy values (Least, Average, Max) or (L, A, M) found for the corresponding element of CICB1 among 1st to nth measurement. Thereupon the final pairwise comparison matrix between the criteria of CB1 will be obtained. The same process will be repeated for CB2, CB3,… and DICB2, DICB3,….Step #MP4: Final pairwise comparison matrix between CB1 and CB2 according to the time feature, tj, is constructed as:(9)DIIj,CB1−CB2=WIj,CB1¯ΘWIj,CB1¯WIj,CB1¯ΘWIj,CB2¯WIj,CB2¯ΘWIj,CB1¯WIj,CB2¯ΘWIj,CB2¯,where, again, each element of this matrix has three fuzzy values (Lower, Average, Max) or (L, A, M) found for the corresponding element of CIIj,CB1-CB2 among 1st to nth measurement.Step #MP5: Now, two fuzzy synthesis values are employed, which are triangular fuzzy number and are obtained as [30]:(10)SDI,p=∑q=26WIq,CB1¯ΘWIp,CB1¯⊗∑p=26∑q=26WIq,CB1¯ΘWIp,CB1¯−1,for DI,where p and q denote tj related to time feature according to (8); and(11)SDII,q,h=∑m=1kWIq,CBm¯ΘWIq,CBh¯⊗∑h=1k∑m=1kWIq,CBm¯ΘWIq,CBh¯−1,for DII,where q denotes time feature according to equation (9), m and h stands for CB number (or row and column numbers of (9)), k is the number of CB under consideration. All of the values in equations (10) and (11) are triangular fuzzy numbers (L, A, M) and ⊗ means each element of the first matrix is multiplied by the same element of the second matrix and finally, a 1 × 3 matrix will be formed. The notations in equations (10) and (11) stand for:(12)∑q=26WIq,CB1¯ΘWIp,CB1¯=∑q=26Lq,∑q=26Aq,∑q=26Mq1×3,for   DI,∑m=1kWIq,CBm¯ΘWIq,CBh¯=∑m=1kLm,∑m=1kAm,∑m=1kMm1×3,for   DII,∑p=26∑q=26WIq,CB1¯ΘWIp,CB1¯=∑p=26Lp,∑p=26Ap,∑p=26Mp1×3,for   DI,∑h=1k∑m=1kWIq,CBm¯ΘWIq,CBh¯=∑h=1kLh,∑h=1kAh,∑h=1kMh1×3,for   DII,Step #MP6: According to the multiplication rule of two fuzzy numbers (given in Appendix), following equations are used to calculate the failure severity of the criterion and alternatives. These weight vectors are normalized, according to the corresponding maximum value, to obtain the final weight vectors in the range of (0, 1).(13)EICBx,i=minVSDI,i≥SDI,k,k=2,3,…,6,k≠i.where EI is the evaluation index of each CB relative to itself; and(14)EIIi,CBx−CBy=minVSDII,i,x≥SDII,i,y.as the evaluation index of each CB relative to other CB.Step #MP7: The priority evaluation for CBX over CBY will be calculated as follows:(15)MPX=∏i=26EICBx,i×EIIi,CBx−CBy.Step #MP8: Finally, the cumulative priority evaluation for CBX over CBY will be calculated as follows:(16)CMPX=∑i=1NMPX,iN.where N is the number of samples measured (extracted from history data).MP DecisionStep: According to equation (15), by comparing CBs in pairs, the MP between two CBs can be found. The value of MPX in equation (15) is between 0 and 1 and the higher the value, the higher the priority in maintenance. By calculating the value of MPX, the value of MPY is also obtained as MPY = 1–MPX. When the value of equation (15) is more than 0.5, it means that CBX has worse condition rather than CBY, and vice versa. Finally, according to equation (16), by calculating the average of the MP from the beginning to the last data obtained, the priority of the CB under consideration can be determined.As mentioned, evaluating a CB in the two dimensions shows the advantage of the proposed comparison method, so that both the condition of the two CBs against each other and the condition of each CB according to itself is measured over time. Note that in this description, all wear-out WI2, WI3, WI4, WI5, and WI6 are considered. Obviously, in order to prioritize the overall condition index, all five indices must be taken into account. Moreover, if each of trip coil condition (WI2, WI3, WI4), or latch mechanism condition (WI2, WI3) or auxiliary contacts condition (WI5, WI6) are going to be evaluated independently, the same algorithm can be followed with the wear-out functions of each condition. Up to here, the MP of a CB among the others has been found.


### 3.5. Determining Failure Level Based on Sensitivity Analysis

Now that the priority of a CB for maintenance has been determined, the failure level should be realized. For this purpose, the sensitivity analysis of t2–t6 values and sensitivity analysis of TC, LM, AUX, and OVR (introduced in section 3.3) for health (H), minor deterioration (mD), major deterioration (MD), and fault (F) condition will be examined.According to Table2, two prerequisites are needed in order to proceed in this section:(1)
The closer the data (corresponding to TC, LM, AUX, and OVR) to the middle of the intervals between lower and upper values, the more probable that the corresponding part(s) is healthy, and by deviating from the midpoint of the intervals, they indicate some failure [3].(2)
The middle half of each interval indicates healthy condition and the rest belongs to mD and MD conditions, respectively. Finally, outliers indicate faulty conditions [3].Step #FL1: Defining wear out intervals for each parameter of Table2.For example, according to the lower and upper values given in the first row of Table2, the sensitivity of t2 can be defined as in Figure 7 and Table 3. For t3 to t6, the same procedure may be followed according to their lower and upper values, where similar sensitivity intervals will be found as for t2 in Table 3. The sensitivity index of each of conditions (H, mD, MD, and F) is adjusted on the vertical axis, where these values are obtained by the relations given in Table 3. According to those relations, the sensitivity of each condition are equal for t > Mj and t < Mj.Step #FL2: Defining an artificial CB (with the three parts of trip coil, latch mechanism, auxiliary contacts, and the overall performance) to be as a reference for failure evaluation of CB (with the highest MP among all the CBs under consideration).The artificial CB (in the four aspects) can take each of the following characteristics, accordingly:(i)
CBHealth, with all corresponding WIs equal to 0.6065.(ii)
CBmD, with all corresponding WIs equal to 0.7788.(iii)
CBMD, with all corresponding WIs equal to 0.8825.(iv)
CBFault, with all corresponding WIs equal to 1.Step #FL3: Comparing the CB under consideration (CBX) with the artificial CB which has taken the characteristics from the previous step (i.e. CBFault, CBMD, CBmD, and CBHealth) according to SEDMA, as in Figure 6.FL DecisionStep: Reaching to equations (15) and (16) in SEDMA, the following rules will be used to find out the failure level of the CB under consideration:(i)
The CB under consideration will be in failure condition, if(a)
Its MP is greater than or equal to 0.5 in comparison with CBFault,;(ii)
The CB under consideration will be in major deterioration condition, if(a)
Its MP is less than 0.5 in comparison with CBFault, and(b)
Its MP is greater than or equal to 0.5 in comparison with CBMD,(iii)
The CB under consideration will be in minor deterioration condition, if(a)
Its MP is less than 0.5 in comparison with CBMD, and(b)
Its MP is greater than or equal to 0.5 in comparison with CBmD,(iv)
The CB under consideration will be in Healthy condition, if(a)
Its MP is less than 0.5 in comparison with CBmD.Figure 7
Sensitivity value for each condition.Table 3
Sensitivity intervals of each condition.
ConditionRelations for t2Sensitivity intervalHealth Condition Sensitivity rangeet−Hj/Hj−Lj=e2.75−5.5/5.5−0=0.60650.60650.7787mD Condition Sensitivity rangeet−Hj/Hj−Lj=e4.125−5.5/5.5−0=0.77880.77880.8824MD Condition Sensitivity rangeet−Hj/Hj−Lj=e4.8125−5.5/5.5−0=0.88250.88250.9999Fault Condition Sensitivity rangeet−Hj/Hj−Lj=e5.5−5.5/5.5−0=11.000upperIt is worth to mention that in comparison with CBHealth, MP of the CB under consideration will never take a value less than 0.5, as CBHealth represents the best condition.


## 3.1. Homogenizing Outlier Data to Improve Inputs

Bad data or outlier data refer to observations that are farther away from a central point (such as the mean) in terms of a scatter index (e.g., standard deviation). According to this, if the data have a normal distribution, it is very unlikely that a value outside the distance is three times the standard deviation from the mean. As a result, encountering such an observation, i.e. an observation that exceeds the mean value ± 3 × standard deviation, it is considered as an abnormal observation and it is homogenized.Taking Figure4(a) as an example, it is clear that these data have an outlier. This outlier sample may be either due to the conditions of the tester or the conditions of the test or the test device.Figure 4
t2 of CB1 (a) actual data (b) improved data.
(a)(b)Accordingly, using the smoothing spline method to fit the curve makes having softer data. Based on the smoothing spline method, it will be determined that by selecting the smoothness index equal to 0.9743 (the larger this number is, the closer the output to the actual values, while the smaller the output will be smoother), the range of data changes, and it is limited exactly to the mean ± 3 × standard deviation. Figure4(b) shows the result, where there are no outlier data, observed.All the data (t2–t6 in two CBs) become smooth, based on the same fit of the spline curve with the index value of 0.9743. Finally, these values will be used as input to the SEDMA algorithm. Further attempts of the authors are through identifying and improving outlier data in power system equipment and will be presented in future reports.


## 3.2. Data Windowing

To analyze the input data, either all the previous data can be analyzed (expanding window) or only the last few data can be examined (moving window). The advantage of the moving window is that the algorithm will be faster in detecting faults or improving CB conditions due to maintenance operations. Note that, by entering the sixth data, the first data will be deleted and the last five data will be placed in the algorithm again (moving window), and so on.


## 3.3. CB Wear-Out Function

To have a quantitative measure of wearing out of CB, a wear-out index (function) is proposed that is applied for each of the parameters mentioned in Table2. The proposed index (function) takes small values as long as each time value corresponds to CB healthy condition and large values as the CB conditions tend towards faulty condition. The introduced wear out index is defined as follows and depicted in Figure 5:(1)WIj=et−Hj/Hj−Ljk,t>Mj,eLj−t/Hj−Ljk,t≤Mj,j=2,…,6,where Hj is the upper limit, Lj is the lower limit, and Mj is the mean time for jth time feature.Figure 5
Proposed Wear-out function.Moreover, Figure5 represents the proposed CB wear-out function for different values of k. As can be seen, the higher the value of k, the discrimination of healthy condition is easier and the priority of CB for maintenance can be more clearly shown. In other words, by increasing the value of k, more severe failures will appear and decisions about the priority of maintenance will be easier and more realistic.Each part of CB is examined by analyzing the wear-out indices of the times which are associated with or affected by that part. The corresponding wear-out indices are combined to make one index.According to what mentioned in Section2, Wear-out function of trip coil (TC) is a function of t2, t3, and t4 as follows:(2)WITC=WIt2,t3,t4.(i)
Wear-out function of latch mechanism (LM) is a function of t2 and t3 as follows:(3)WILM=WIt2,t3.(ii)
Wear-out function of auxiliary contacts (AUX) is a function of t5 and t6 as follows:(4)WIAUX=WIt5,t6.(iii)
Overall wear-out function of CB (OVR) is a function of t2–t6 as follows:(5)WIOVR=WIt2,t3,t4,t5,t6.


## 3.4. Self-Evaluation Decision-Making Algorithm (SEDMA)

The details of the proposed method, or in other words, SEDMA method will be provided in sequel.There are two basic aspects to consider when considering CB failure and prioritizing maintenance:(1)
Assessment of CB condition against ageing.(2)
Assessment of CB condition in comparison with other CBs.Based on these two aspects, the self-evaluation decision-making algorithm is introduced as in Figure6:Figure 6
Proposed SEDMA.According to this procedure, after collecting the data and identifying outlier data, the condition of each CB will be determined according to the boundary conditions. Next, using two aforementioned aspects, the maintenance priority (MP) is evaluated using SEDMA. Finally, the MP of each CB will be obtained. In the sequel, SEDMA is introduced to find out the MP of CB1, CB2, CB3,…:Step #MP1: Initial self-wise comparison matrix will be calculated according to equation (6), where WIj,k,CB1 stands for WI of the time feature, tj, at the kth measurement (extracted from history data) of CB1:(6)CICB1=WI2,1,CB1WI2,1,CB1WI2,1,CB1WI3,1,CB1WI2,1,CB1WI4,1,CB1WI2,1,CB1WI5,1,CB1WI2,1,CB1WI6,1,CB1WI3,1,CB1WI2,1,CB1WI3,1,CB1WI3,1,CB1WI3,1,CB1WI4,1,CB1WI3,1,CB1WI5,1,CB1WI3,1,CB1WI6,1,CB1WI4,1,CB1WI2,1,CB1WI4,1,CB1WI3,1,CB1WI4,1,CB1WI4,1,CB1WI4,1,CB1WI5,1,CB1WI4,1,CB1WI6,1,CB1WI5,1,CB1WI2,1,CB1WI5,1,CB1WI3,1,CB1WI5,1,CB1WI4,1,CB1WI5,1,CB1WI5,1,CB1WI5,1,CB1WI6,1,CB1WI6,1,CB1WI2,1,CB1WI6,1,CB1WI3,1,CB1WI6,1,CB1WI4,1,CB1WI6,1,CB1WI5,1,CB1WI6,1,CB1WI6,1,CB1⋮⋮⋮⋮⋮WI2,n,CB1WI2,n,CB1WI2,n,CB1WI3,n,CB1WI2,n,CB1WI4,n,CB1WI2,n,CB1WI5,n,CB1WI2,n,CB1WI6,n,CB1WI3,n,CB1WI2,n,CB1WI3,n,CB1WI3,n,CB1WI3,n,CB1WI4,n,CB1WI3,n,CB1WI5,n,CB1WI3,n,CB1WI6,n,CB1WI4,n,CB1WI2,n,CB1WI4,n,CB1WI3,n,CB1WI4,n,CB1WI4,n,CB1WI4,n,CB1WI5,n,CB1WI4,n,CB1WI6,n,CB1WI5,n,CB1WI2,n,CB1WI5,n,CB1WI3,n,CB1WI5,n,CB1WI4,n,CB1WI5,n,CB1WI5,n,CB1WI5,n,CB1WI6,n,CB1WI6,n,CB1WI2,n,CB1WI6,n,CB1WI3,n,CB1WI6,n,CB1WI4,n,CB1WI6,n,CB1WI5,n,CB1WI6,n,CB1WI6,n,CB1.It should be noted that the larger value of each matrix element, the greater is the vulnerability of the time feature corresponding to the numerator rather than the one corresponding to the denominator (for example:WI6,n,CB1/WI2,n,CB1>1⇒WI6,n,CB1>WI2,n,CB1). The same process will be repeated for CB2, CB3, …, and consequently CICB2, CICB3,… are calculated.Step #MP2: Initial pairwise comparison matrices of criteria between CB1 and CB2 are constructed as in equation (7), where CIIj,CB1-CB2 stands for comparisons between WIj,k,CB1 and WIj,k,CB2:(7)CIIj,CB1−CB2=WIj,1,CB1WIj,1,CB1WIj,1,CB1WIj,1,CB2WIj,1,CB2WIj,1,CB1WIj,1,CB2WIj,1,CB2⋮⋮WIj,n,CB1WIj,n,CB1WIj,n,CB1WIj,n,CB2WIj,n,CB2WIj,n,CB1WIj,n,CB2WIj,n,CB2.Similarly, the initial pair comparison matrix will be repeated for CIIj,CB1-CB3,….Step #MP3: Final pairwise comparison matrix is introduced as in:(8)DICB1=WI2,CB1¯ΘWI2,CB1¯WI2,CB1¯ΘWI3,CB1¯WI2,CB1¯ΘWI4,CB1¯WI2,CB1¯ΘWI5,CB1¯WI2,CB1¯ΘWI6,CB1¯WI3,CB1¯ΘWI2,CB1¯WI3,CB1¯ΘWI3,CB1¯WI3,CB1¯ΘWI4,CB1¯WI3,CB1¯ΘWI5,CB1¯WI3,CB1¯ΘWI6,CB1¯WI4,CB1¯ΘWI2,CB1¯WI4,CB1¯ΘWI3,CB1¯WI4,CB1¯ΘWI4,CB1¯WI4,CB1¯ΘWI5,CB1¯WI4,CB1¯ΘWI6,CB1¯WI5,CB1¯ΘWI2,CB1¯WI5,CB1¯ΘWI3,CB1¯WI5,CB1¯ΘWI4,CB1¯WI5,CB1¯ΘWI5,CB1¯WI5,CB1¯ΘWI6,CB1¯WI6,CB1¯ΘWI2,CB1¯WI6,CB1¯ΘWI3,CB1¯WI6,CB1¯ΘWI4,CB1¯WI6,CB1¯ΘWI5,CB1¯WI6,CB1¯ΘWI6,CB1¯,where Θ (here and elsewhere) means each element of the first matrix is divided by the same element of the second matrix and finally, a 1×3 matrix will be formed. So, each element of this matrix has three fuzzy values (Least, Average, Max) or (L, A, M) found for the corresponding element of CICB1 among 1st to nth measurement. Thereupon the final pairwise comparison matrix between the criteria of CB1 will be obtained. The same process will be repeated for CB2, CB3,… and DICB2, DICB3,….Step #MP4: Final pairwise comparison matrix between CB1 and CB2 according to the time feature, tj, is constructed as:(9)DIIj,CB1−CB2=WIj,CB1¯ΘWIj,CB1¯WIj,CB1¯ΘWIj,CB2¯WIj,CB2¯ΘWIj,CB1¯WIj,CB2¯ΘWIj,CB2¯,where, again, each element of this matrix has three fuzzy values (Lower, Average, Max) or (L, A, M) found for the corresponding element of CIIj,CB1-CB2 among 1st to nth measurement.Step #MP5: Now, two fuzzy synthesis values are employed, which are triangular fuzzy number and are obtained as [30]:(10)SDI,p=∑q=26WIq,CB1¯ΘWIp,CB1¯⊗∑p=26∑q=26WIq,CB1¯ΘWIp,CB1¯−1,for DI,where p and q denote tj related to time feature according to (8); and(11)SDII,q,h=∑m=1kWIq,CBm¯ΘWIq,CBh¯⊗∑h=1k∑m=1kWIq,CBm¯ΘWIq,CBh¯−1,for DII,where q denotes time feature according to equation (9), m and h stands for CB number (or row and column numbers of (9)), k is the number of CB under consideration. All of the values in equations (10) and (11) are triangular fuzzy numbers (L, A, M) and ⊗ means each element of the first matrix is multiplied by the same element of the second matrix and finally, a 1 × 3 matrix will be formed. The notations in equations (10) and (11) stand for:(12)∑q=26WIq,CB1¯ΘWIp,CB1¯=∑q=26Lq,∑q=26Aq,∑q=26Mq1×3,for   DI,∑m=1kWIq,CBm¯ΘWIq,CBh¯=∑m=1kLm,∑m=1kAm,∑m=1kMm1×3,for   DII,∑p=26∑q=26WIq,CB1¯ΘWIp,CB1¯=∑p=26Lp,∑p=26Ap,∑p=26Mp1×3,for   DI,∑h=1k∑m=1kWIq,CBm¯ΘWIq,CBh¯=∑h=1kLh,∑h=1kAh,∑h=1kMh1×3,for   DII,Step #MP6: According to the multiplication rule of two fuzzy numbers (given in Appendix), following equations are used to calculate the failure severity of the criterion and alternatives. These weight vectors are normalized, according to the corresponding maximum value, to obtain the final weight vectors in the range of (0, 1).(13)EICBx,i=minVSDI,i≥SDI,k,k=2,3,…,6,k≠i.where EI is the evaluation index of each CB relative to itself; and(14)EIIi,CBx−CBy=minVSDII,i,x≥SDII,i,y.as the evaluation index of each CB relative to other CB.Step #MP7: The priority evaluation for CBX over CBY will be calculated as follows:(15)MPX=∏i=26EICBx,i×EIIi,CBx−CBy.Step #MP8: Finally, the cumulative priority evaluation for CBX over CBY will be calculated as follows:(16)CMPX=∑i=1NMPX,iN.where N is the number of samples measured (extracted from history data).MP DecisionStep: According to equation (15), by comparing CBs in pairs, the MP between two CBs can be found. The value of MPX in equation (15) is between 0 and 1 and the higher the value, the higher the priority in maintenance. By calculating the value of MPX, the value of MPY is also obtained as MPY = 1–MPX. When the value of equation (15) is more than 0.5, it means that CBX has worse condition rather than CBY, and vice versa. Finally, according to equation (16), by calculating the average of the MP from the beginning to the last data obtained, the priority of the CB under consideration can be determined.As mentioned, evaluating a CB in the two dimensions shows the advantage of the proposed comparison method, so that both the condition of the two CBs against each other and the condition of each CB according to itself is measured over time. Note that in this description, all wear-out WI2, WI3, WI4, WI5, and WI6 are considered. Obviously, in order to prioritize the overall condition index, all five indices must be taken into account. Moreover, if each of trip coil condition (WI2, WI3, WI4), or latch mechanism condition (WI2, WI3) or auxiliary contacts condition (WI5, WI6) are going to be evaluated independently, the same algorithm can be followed with the wear-out functions of each condition. Up to here, the MP of a CB among the others has been found.


## 3.5. Determining Failure Level Based on Sensitivity Analysis

Now that the priority of a CB for maintenance has been determined, the failure level should be realized. For this purpose, the sensitivity analysis of t2–t6 values and sensitivity analysis of TC, LM, AUX, and OVR (introduced in section 3.3) for health (H), minor deterioration (mD), major deterioration (MD), and fault (F) condition will be examined.According to Table2, two prerequisites are needed in order to proceed in this section:(1)
The closer the data (corresponding to TC, LM, AUX, and OVR) to the middle of the intervals between lower and upper values, the more probable that the corresponding part(s) is healthy, and by deviating from the midpoint of the intervals, they indicate some failure [3].(2)
The middle half of each interval indicates healthy condition and the rest belongs to mD and MD conditions, respectively. Finally, outliers indicate faulty conditions [3].Step #FL1: Defining wear out intervals for each parameter of Table2.For example, according to the lower and upper values given in the first row of Table2, the sensitivity of t2 can be defined as in Figure 7 and Table 3. For t3 to t6, the same procedure may be followed according to their lower and upper values, where similar sensitivity intervals will be found as for t2 in Table 3. The sensitivity index of each of conditions (H, mD, MD, and F) is adjusted on the vertical axis, where these values are obtained by the relations given in Table 3. According to those relations, the sensitivity of each condition are equal for t > Mj and t < Mj.Step #FL2: Defining an artificial CB (with the three parts of trip coil, latch mechanism, auxiliary contacts, and the overall performance) to be as a reference for failure evaluation of CB (with the highest MP among all the CBs under consideration).The artificial CB (in the four aspects) can take each of the following characteristics, accordingly:(i)
CBHealth, with all corresponding WIs equal to 0.6065.(ii)
CBmD, with all corresponding WIs equal to 0.7788.(iii)
CBMD, with all corresponding WIs equal to 0.8825.(iv)
CBFault, with all corresponding WIs equal to 1.Step #FL3: Comparing the CB under consideration (CBX) with the artificial CB which has taken the characteristics from the previous step (i.e. CBFault, CBMD, CBmD, and CBHealth) according to SEDMA, as in Figure 6.FL DecisionStep: Reaching to equations (15) and (16) in SEDMA, the following rules will be used to find out the failure level of the CB under consideration:(i)
The CB under consideration will be in failure condition, if(a)
Its MP is greater than or equal to 0.5 in comparison with CBFault,;(ii)
The CB under consideration will be in major deterioration condition, if(a)
Its MP is less than 0.5 in comparison with CBFault, and(b)
Its MP is greater than or equal to 0.5 in comparison with CBMD,(iii)
The CB under consideration will be in minor deterioration condition, if(a)
Its MP is less than 0.5 in comparison with CBMD, and(b)
Its MP is greater than or equal to 0.5 in comparison with CBmD,(iv)
The CB under consideration will be in Healthy condition, if(a)
Its MP is less than 0.5 in comparison with CBmD.Figure 7
Sensitivity value for each condition.Table 3
Sensitivity intervals of each condition.
ConditionRelations for t2Sensitivity intervalHealth Condition Sensitivity rangeet−Hj/Hj−Lj=e2.75−5.5/5.5−0=0.60650.60650.7787mD Condition Sensitivity rangeet−Hj/Hj−Lj=e4.125−5.5/5.5−0=0.77880.77880.8824MD Condition Sensitivity rangeet−Hj/Hj−Lj=e4.8125−5.5/5.5−0=0.88250.88250.9999Fault Condition Sensitivity rangeet−Hj/Hj−Lj=e5.5−5.5/5.5−0=11.000upperIt is worth to mention that in comparison with CBHealth, MP of the CB under consideration will never take a value less than 0.5, as CBHealth represents the best condition.


## 4. Results of Case Study

In this section, the proposed algorithm will be analyzed and implemented on the previously mentioned data. There are 20 data t2–t6 for two similar CBs, which will produce 20 wear-out values WI2–WI6 for both CBs. Initially, the first five data will be considered as SEDMA input data, and the calculation for the first five data will be done (n = 5).In this step, the priority assessment will be obtained for two CBs in the following three states applied to the wear-out function introduced in equation (1):(1)
Weakened wear-out function: assuming k = 0.5.(2)
Base wear-out function: assuming k = 1.(3)
Boosted wear-out function: assuming k = 3.By increasing the value of k, severe failures will become highlighted. Accordingly, three aforementioned states are evaluated to show all severe and moderate failures and observe different conditions.So far, CB condition assessments have been carried out with the first five data. Then, by entering the sixth data into SEDMA, all the values will be updated and the priority assessment for two CBs will be repeated in all aforementioned situations. In this case, the values of EI and EII will be updated according to the new input value (see Figure6).This procedure will be performed for all four tests of CBs: trip coil mechanism, latch mechanism, auxiliary contacts mechanism, and overall CBs mechanism. Accordingly, in Section4.1, a comparison between two CBs is performed and maintenance planning is prioritized and the SEDMA algorithm is implemented for these two CBs. Then, in Section 4.2, the sensitivity analysis is performed to determine the degree of CB failure, where eventually it is determined whether or not the CB selected needs maintenance, and if so, which part of CB should be repaired/replaced. Finally, in Section 4.3, assuming maintenance operation on a CB, the effect of this repair on maintenance prioritization is checked.


### 4.1. Maintenance Priority Determination

As mentioned, trip coil, latch mechanism, auxiliary contacts, and overall condition of CB depends on (WI2, WI3, WI4), (WI2, WI3), (WI5, WI6), and (WI2, WI3, WI4, WI5, WI6), respectively. After implementation of SEDMA, first, the priority assessment of each CB against other CBs will be achieved, according to equations (15) and (16). Figure 8 shows the results of assessment for trip coil, latch mechanism, auxiliary contacts and overall condition of CB. The vertical axis indicates priority assessment of CBs for different tests and the horizontal axis indicates the results for the last five samples in the moving data window, that is, the first set represents the results for the data window containing the first to the fifth sample; and the three bars are the results of calculating the MP with k = 0.5, 1, and 3 in creating WI, in equation (1), respectively. The black line also shows the cumulative MP (CMP) for CB1 (considering K = 3), where being higher than 0.5, CB1 is in priority, else, CB2 is in the MP.Figure 8
Comparison of two CBs (a) TC comparison of two CBs (b) LM comparison of two CBs (c) AUX comparison of two CBs (d) OVR comparison of two CBs.
(a)(b)(c)(d)As aforementioned, values higher than 0.5 are in the higher priority of maintenance. It can be seen that in trip coil (Figure8(a)) and latch mechanism (Figure 8(b)), CB1 has larger MP values rather than CB2, but in auxiliary contacts mechanism (Figure 8(c)), is vice versa. If any of these mechanisms are significant, maintenance decisions should be made based on these results. Otherwise, the overall condition of CB must be exploited. According to the overall conditions of two CBs (Figure 8(d)), it is observed that overall condition is more affected by TC and LM rather than AUX mechanism. It can be also seen that with entry observed data 9, TC and LM conditions have worsened, and this factor (data entry 9) has an impact on the overall condition of CB1, which is clearly seen in Figure 8. So, in this overall mechanism, CB1 is worse than CB2 and has the first priority for maintenance.Also, by increasing the value of k, the condition of CB1 moves away from CB2, and this factor becomes more apparent with entry observed data 9. Therefore, in addition to the fact that CB1 has worse condition, the greater the importance of CB wear-out (increasing the value of k), the worse the condition of CB1 will be. Also note that in samples where the MP for two CBs is changing, low values of k do not indicate this change correctly, while high values of k indicate this change well.


### 4.2. Sensitivity Analysis to Determine Failure Level

In this section, sensitivity analysis is implemented to determine the failure level of CB (according to Section3.5) and the results are presented. Figure 9 shows the results of this case study.Figure 9
Sensitivity analysis of CB1 (a) TC Sensitivity (b) TC CMP (c) LM Sensitivity (d) LM CMP (e) AUX Sensitivity (f) AUX CMP (g) OVR Sensitivity (h) OVR CMP.
(a)(b)(c)(d)(e)(f)(g)(h)Before proceeding to inspection of Figure9, it should be reminded that according to Figure 8, the following comparisons can be made:(i)
(According to Figure8(a)) the TC condition of CB1 is worse than the TC condition of CB2.(ii)
(According to Figure8(b)), the LM condition of CB1 is worse than the LM condition of CB2.(iii)
(As shown in Figure8(c)), the AUX condition of CB2 is worse than the AUX condition of CB1.(iv)
(As shown in Figure8(d)), the overall condition of CB1 is worse than CB2.Although these comparisons are informative, they do not give the details of failure level of each of the CBs under consideration. Based on the aforementioned, as it was found that CB1 has a higher priority of maintenance, it will be evaluated for failure level to determine whether it justifies the need for maintenance or not.The evaluation of failure levels of CB1 has been shown in Figure 9. On the left side of this figure, there are sets of three bars in each subplot, where (from left to right) the first one depicts the comparison of CB behavior with CBmD; the secondbar shows the comparison of CB behavior with CBMD, and the last shows the comparison of CB behavior with CBFault. Also, on the right side of this figure, the diagrams show the CMP for the CB under consideration in comparison with CBmD (solid line), CBMD (dash-dotted line), and CBFault (dashed line), i.e., they represent the failure level of the corresponding CB. Then, the following remarks may be expressed:(i)
According to Figures9(a) and 9(b), for the samples measured and processed, the condition of TC of CB under consideration starts from minor deterioration (as the corresponding MP and CMP are solely greater than 0.5) and then becomes worse (as the corresponding CMP increases) and even worst as the CMP in comparison with CBMD becomes larger and exceeds 0.5, i.e., this indicates that at last TC mechanism of the CB under consideration is in major deterioration condition.(ii)
Moreover, according to Figures9(c) and 9(d), for the samples measured and processed, the condition of LM of CB under consideration starts in major deterioration (as the corresponding MP and CMP are greater than 0.5) and remains in this condition.(iii)
Furthermore, it can be seen from Figures9(e) and 9(f), for the samples measured and processed, the condition of AUX of CB under consideration starts in healthy condition (as none of the CMP values in comparison with CBmD, CBMD, and CBFault, respectively, are greater than 0.5) and remains in this condition.(iv)
Finally, according to Figures9(g) and 9(h), for the samples measured and processed, overall condition of CB under consideration starts in minor deterioration (as the corresponding MP and CMP are greater than 0.5) and remains in this condition.(v)
It can be deduced that the minor deterioration of overall condition is due to the aggregation of unhealthy conditions of trip coil and latch mechanisms and healthy condition of auxiliary contacts of the CB under consideration.(vi)
The last but not the least is that the proposed decision algorithm (SEDMA) can give a quantitative comparison among CBs in taking MP as well as determining the failure level of different parts of CBs, which makes the corresponding decisions more clearly and accurately.


### 4.3. Maintenance Priority Analysis of Repaired CB

In this section, a situation is considered in which the condition of a CB is healed after maintenance. It is shown, by applying the proposed algorithm, the considered CB in this situation loses the priority for maintenance.For this purpose, all WI values of the considered CB are put in healthy condition (equal to 0.6065 according to Table3) from a measurement onwards. The considered CB is named CB1 and repair is assumed to happen between the 10th and 11th measurement. Figure 10 shows a comparison of two CBs, where the first one has gone through maintenance, while the other one is remained as it goes. In this case, according to SEDMA, the condition of CB1 should be continuously improved from the 11th sample, onwards. Three bars of Figure 10(a) are the results of calculating the MP with k = 0.5, 1, and 3 in creating WI, in (1), respectively. Also, in Figure 10(b), the diagrams show the CMP for the CB1 with respect to CB2 for k = 0.5 (dashed line), k = 1 (dash-dotted line), and k = 3 (solid line). The following remarks can be deduced (note that where these lines are above 0.5, CB1 is in priority, else, CB2 is in the MP):(i)
The MP index (regardless of k value) changes rapidly for CB1 as soon as the repair has been assumed.(ii)
The CMP value for CB1 has been later changed from the greater values than 0.5 to smaller values indicating that this CB can be put out of repair list, in comparison with CB2.(iii)
The delay in changeover of CMP is due to the cumulative nature of this index.(iv)
As k takes larger values, wear-out function also takes larger values for failure conditions; therefore, by applying these values SEDMA will show much difference in the corresponding index values for the CBs in the priority list.Figure 10
OVR Comparison of improved CB1 and CB2(a) MP for two CBs (b) CMP for two CBs.
(a)(b)


## 4.1. Maintenance Priority Determination

As mentioned, trip coil, latch mechanism, auxiliary contacts, and overall condition of CB depends on (WI2, WI3, WI4), (WI2, WI3), (WI5, WI6), and (WI2, WI3, WI4, WI5, WI6), respectively. After implementation of SEDMA, first, the priority assessment of each CB against other CBs will be achieved, according to equations (15) and (16). Figure 8 shows the results of assessment for trip coil, latch mechanism, auxiliary contacts and overall condition of CB. The vertical axis indicates priority assessment of CBs for different tests and the horizontal axis indicates the results for the last five samples in the moving data window, that is, the first set represents the results for the data window containing the first to the fifth sample; and the three bars are the results of calculating the MP with k = 0.5, 1, and 3 in creating WI, in equation (1), respectively. The black line also shows the cumulative MP (CMP) for CB1 (considering K = 3), where being higher than 0.5, CB1 is in priority, else, CB2 is in the MP.Figure 8
Comparison of two CBs (a) TC comparison of two CBs (b) LM comparison of two CBs (c) AUX comparison of two CBs (d) OVR comparison of two CBs.
(a)(b)(c)(d)As aforementioned, values higher than 0.5 are in the higher priority of maintenance. It can be seen that in trip coil (Figure8(a)) and latch mechanism (Figure 8(b)), CB1 has larger MP values rather than CB2, but in auxiliary contacts mechanism (Figure 8(c)), is vice versa. If any of these mechanisms are significant, maintenance decisions should be made based on these results. Otherwise, the overall condition of CB must be exploited. According to the overall conditions of two CBs (Figure 8(d)), it is observed that overall condition is more affected by TC and LM rather than AUX mechanism. It can be also seen that with entry observed data 9, TC and LM conditions have worsened, and this factor (data entry 9) has an impact on the overall condition of CB1, which is clearly seen in Figure 8. So, in this overall mechanism, CB1 is worse than CB2 and has the first priority for maintenance.Also, by increasing the value of k, the condition of CB1 moves away from CB2, and this factor becomes more apparent with entry observed data 9. Therefore, in addition to the fact that CB1 has worse condition, the greater the importance of CB wear-out (increasing the value of k), the worse the condition of CB1 will be. Also note that in samples where the MP for two CBs is changing, low values of k do not indicate this change correctly, while high values of k indicate this change well.


## 4.2. Sensitivity Analysis to Determine Failure Level

In this section, sensitivity analysis is implemented to determine the failure level of CB (according to Section3.5) and the results are presented. Figure 9 shows the results of this case study.Figure 9
Sensitivity analysis of CB1 (a) TC Sensitivity (b) TC CMP (c) LM Sensitivity (d) LM CMP (e) AUX Sensitivity (f) AUX CMP (g) OVR Sensitivity (h) OVR CMP.
(a)(b)(c)(d)(e)(f)(g)(h)Before proceeding to inspection of Figure9, it should be reminded that according to Figure 8, the following comparisons can be made:(i)
(According to Figure8(a)) the TC condition of CB1 is worse than the TC condition of CB2.(ii)
(According to Figure8(b)), the LM condition of CB1 is worse than the LM condition of CB2.(iii)
(As shown in Figure8(c)), the AUX condition of CB2 is worse than the AUX condition of CB1.(iv)
(As shown in Figure8(d)), the overall condition of CB1 is worse than CB2.Although these comparisons are informative, they do not give the details of failure level of each of the CBs under consideration. Based on the aforementioned, as it was found that CB1 has a higher priority of maintenance, it will be evaluated for failure level to determine whether it justifies the need for maintenance or not.The evaluation of failure levels of CB1 has been shown in Figure 9. On the left side of this figure, there are sets of three bars in each subplot, where (from left to right) the first one depicts the comparison of CB behavior with CBmD; the secondbar shows the comparison of CB behavior with CBMD, and the last shows the comparison of CB behavior with CBFault. Also, on the right side of this figure, the diagrams show the CMP for the CB under consideration in comparison with CBmD (solid line), CBMD (dash-dotted line), and CBFault (dashed line), i.e., they represent the failure level of the corresponding CB. Then, the following remarks may be expressed:(i)
According to Figures9(a) and 9(b), for the samples measured and processed, the condition of TC of CB under consideration starts from minor deterioration (as the corresponding MP and CMP are solely greater than 0.5) and then becomes worse (as the corresponding CMP increases) and even worst as the CMP in comparison with CBMD becomes larger and exceeds 0.5, i.e., this indicates that at last TC mechanism of the CB under consideration is in major deterioration condition.(ii)
Moreover, according to Figures9(c) and 9(d), for the samples measured and processed, the condition of LM of CB under consideration starts in major deterioration (as the corresponding MP and CMP are greater than 0.5) and remains in this condition.(iii)
Furthermore, it can be seen from Figures9(e) and 9(f), for the samples measured and processed, the condition of AUX of CB under consideration starts in healthy condition (as none of the CMP values in comparison with CBmD, CBMD, and CBFault, respectively, are greater than 0.5) and remains in this condition.(iv)
Finally, according to Figures9(g) and 9(h), for the samples measured and processed, overall condition of CB under consideration starts in minor deterioration (as the corresponding MP and CMP are greater than 0.5) and remains in this condition.(v)
It can be deduced that the minor deterioration of overall condition is due to the aggregation of unhealthy conditions of trip coil and latch mechanisms and healthy condition of auxiliary contacts of the CB under consideration.(vi)
The last but not the least is that the proposed decision algorithm (SEDMA) can give a quantitative comparison among CBs in taking MP as well as determining the failure level of different parts of CBs, which makes the corresponding decisions more clearly and accurately.


## 4.3. Maintenance Priority Analysis of Repaired CB

In this section, a situation is considered in which the condition of a CB is healed after maintenance. It is shown, by applying the proposed algorithm, the considered CB in this situation loses the priority for maintenance.For this purpose, all WI values of the considered CB are put in healthy condition (equal to 0.6065 according to Table3) from a measurement onwards. The considered CB is named CB1 and repair is assumed to happen between the 10th and 11th measurement. Figure 10 shows a comparison of two CBs, where the first one has gone through maintenance, while the other one is remained as it goes. In this case, according to SEDMA, the condition of CB1 should be continuously improved from the 11th sample, onwards. Three bars of Figure 10(a) are the results of calculating the MP with k = 0.5, 1, and 3 in creating WI, in (1), respectively. Also, in Figure 10(b), the diagrams show the CMP for the CB1 with respect to CB2 for k = 0.5 (dashed line), k = 1 (dash-dotted line), and k = 3 (solid line). The following remarks can be deduced (note that where these lines are above 0.5, CB1 is in priority, else, CB2 is in the MP):(i)
The MP index (regardless of k value) changes rapidly for CB1 as soon as the repair has been assumed.(ii)
The CMP value for CB1 has been later changed from the greater values than 0.5 to smaller values indicating that this CB can be put out of repair list, in comparison with CB2.(iii)
The delay in changeover of CMP is due to the cumulative nature of this index.(iv)
As k takes larger values, wear-out function also takes larger values for failure conditions; therefore, by applying these values SEDMA will show much difference in the corresponding index values for the CBs in the priority list.Figure 10
OVR Comparison of improved CB1 and CB2(a) MP for two CBs (b) CMP for two CBs.
(a)(b)


## 5. Conclusion

In this paper, using the coil current monitoring of CB and using the proposed SEDMA method, MP of CBs is obtained. CB prioritization is determined by comparing conditions of each pair of CBs, as well as the performance of each CB with itself over time. The comparison is made from different aspects of TC, LM, AUX, and OVR. The CB that has a higher rank for maintenance is examined by sensitivity analysis to determine failure level, as well. So, according to the proposed process, higher CB maintenance priorities can be found, and it can also be seen whether the selected CBs are required to be put in the maintenance list or not. Finally, it can be seen that with the condition improvement, CB was removed from the MP.



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*Source: 5008166-2022-08-18.xml*