D-Distance Technique to Determine Failure Probability of Power Circuit Breaker

: In this paper, a new D-distance factor is proposed to determine the failure probability and to prioritize maintenance actions of power circuit breakers in high-voltage substations. The D-distance factor is calculated by using the condition index and renovation index of a high-voltage circuit breaker (HVCB). To facilitate effective decision-making on maintenance with a simple method and less computational effort, the proposed model incorporates the weighting–scoring method (WSM) and analytical hierarchy process (AHP) with the various diagnostic methods for condition index assessments as well as the operation requirements of HVCBs for renovation index assessments. Many signiﬁcant parameters from circuit breaker testing, such as insulation resistance, contact resistance, contact timing, SF6 gas measurements, gas leakage rate, visual inspection, etc., have been considered for condition index determination. In addition to these, other signiﬁcant parameters, such as age of the circuit breaker, age of the interrupter and mechanism, number of fault current interruptions, actual load current to rated current ratio, actual short circuit current to rated interrupting current ratio, maintenance ability, spare parts availability, maintenance expertise level, etc., are also considered for renovation index determination. To validate the proposed model, the practical test data of twenty 115 kV HVCBs in various substations of a distribution utility in Thailand were utilized and tested. By analyzing the actual condition and operation requirement of the circuit breaker, the output, as the condition index and renovation index using the proposed method, is discussed with HVCB experts in the utility to adjust the scores and weights of all criteria to obtain the most accurate and reliable model. The results show that the D-distance technique measured from the risk matrix, which is deﬁned as the failure probability, can be used to rank the maintenance schedule from urgent to normal maintenance tasks. In addition, various failure probabilities in the risk matrix of the circuit breaker can be used to determine the appropriate maintenance strategies for the power circuit breaker in each group. Finally, the proposed method could help the utility managers and maintenance engineers manage the maintenance planning effectively and easily for thousands of HVCBs in the grid, and it can be further applied with other high-voltage equipment in both transmission and distribution systems to facilitate the maintenance activities according to available costs and human resources.


Introduction
A power circuit breaker, a mechanical switching device, is one of the key elements in an electrical power system.Its function is to make, carry, and interrupt currents occurring in the circuit under normal conditions, and to carry for a specified time, to make, and to interrupt currents arising in the circuit under defined abnormal conditions, e.g., a short circuit.A power circuit breaker consists of an interrupting unit, supporting porcelain Energies 2023, 16, 847 2 of 17 column, operating mechanism, metallic frame and structure, and control unit.In general, it works together with an instrument transformer as a sensing device and protective relay, as a brain that decides the electrical system condition.Once power circuit breakers in a high-voltage substation have been installed and put into service, cumulative stresses, such as thermal, electrical, and mechanical stresses during normal operation as well as abnormal operating conditions, such as a fault, are imposed on the equipment for a period of time [1][2][3][4].These stresses and faults significantly accelerate degradation, adversely affect the condition, and reduce the performance of the equipment.Consequently, the high-voltage circuit breaker (HVCB) is gradually degraded, and its lifetime is shortened.Finally, the failure of a HVCB could occur, leading to power interruption, and the system reliability could be reduced.The guide to investigate, analyze, and report HVCB failures and causes were introduced [5].
Various diagnostic methods to investigate the causes of failure in HVCBs were developed and implemented, such as an active breaker incidence (ABI) matrix to capture the active failure of breakers leading to load-point failures [6], the relationship of subjective historical data and failure rate [7,8], the dynamic resistance measurement [9], coil current measurement [10], radiometric monitoring [11], contact erosion [12], and full mechanical and electrical test methods [13].Many of these were practically applied to prevent unpredictable failure and extend the end of life of HVCBs.Both on-line and off-line condition monitoring and various diagnostic testing methods were introduced, such as a hybrid model that determines reliability and uncertainty based on the prognostics of HVCBs [14], reliability assessment model using an aging failure model [15], condition monitoring model [16,17], and condition assessment of gas-insulated switchgear using health index and conditional factor methods to improve the calculation accuracy [18].Some circuit breaker failure prognosis methods and models were also mentioned to maintain system reliability [19,20].These effective monitoring and diagnostic methods have been continually developed for condition and performance assessment in forms, i.e., health index, condition index, risk index, and failure probability, for the most effective operation and maintenance management [21][22][23][24].Subsequently, the maintenance tasks could be prioritized while their relevant costs could be minimized for better technical and economic aspects [25][26][27].Some asset management strategies, such as the weighting-scoring method; Weibull estimation technique, based on actual historical testing results; and the technical information of equipment and systems, were implemented to predict the lifetime and the end of life of the HVCB [28,29].
The failure rate is the frequency in which a component failed, which is expressed in failures per period.It is a significant indicator for maintenance engineers to evaluate their maintenance strategy, planning, and management.A lower failure rate refers to better performance of a maintenance management program.In a distribution system, the practical failure rate and consequences of HVCB failure are higher than other switching devices and metering instruments, such as a disconnecting and ground switch, current transformer, and voltage transformer [30].Their failure causes are recorded and illustrated in Table 1.Therefore, the maintenance strategy for HVCBs should be intensively focused.
In the distribution system of a utility in Thailand, there are 317 substations and more than one thousand and five hundred units of active HV circuit breakers.With the limitation of manpower, material (spare parts), and annual budget (money), the maintenance action plan needs to be designed appropriately to manage the limited resource effectively.The failure probability determined from the risk matrix is an effective tool to facilitate the effective allocation of limited resources directly to the most urgent HV circuit breaker.Twenty pilot units of HV circuit breakers with diverse ages and conditions are selected from various substations and applied with the proposed failure probability model using the D-distance assessment of HVCBs from the risk matrix.The whole conceptual process of the proposed method is shown in Figure 1.The data of the HVCBs, including technical data, test results, and visual inspection results, are collected annually by the utility engineer and technician.Then, the collected data are cleaned to avoid human error, and primarily prepared and allocated to databases before being further applied to calculate the %CI and %RI.Both the %CI and %RI are plotted on the risk matrix to determine the %D, which is used to prioritize the maintenance requirement.In the distribution system of a utility in Thailand, there are 317 substations and more than one thousand and five hundred units of active HV circuit breakers.With the limitation of manpower, material (spare parts), and annual budget (money), the maintenance action plan needs to be designed appropriately to manage the limited resource effectively.The failure probability determined from the risk matrix is an effective tool to facilitate the effective allocation of limited resources directly to the most urgent HV circuit breaker.Twenty pilot units of HV circuit breakers with diverse ages and conditions are selected from various substations and applied with the proposed failure probability model using the D-distance assessment of HVCBs from the risk matrix.
The whole conceptual process of the proposed method is shown in Figure 1.The data of the HVCBs, including technical data, test results, and visual inspection results, are collected annually by the utility engineer and technician.Then, the collected data are cleaned to avoid human error, and primarily prepared and allocated to databases before being further applied to calculate the %CI and %RI.Both the %CI and %RI are plotted on the risk matrix to determine the %D, which is used to prioritize the maintenance requirement.The D-distance factor is calculated by using the percentage of the condition index (%CI) and the percentage of the renovation index (%RI).To obtain the %CI and %RI, actual data, including technical data, routine and special test results, and visual inspections, are applied in the assessment model as shown in Figure 2. The weighting-scoring method or WSM is a numerical technique used to calculate the condition and renovation indexes from various evaluation criteria.A scoring technique is used to transform the raw inspection and testing results from each test method to a quantitative value known as a score, The D-distance factor is calculated by using the percentage of the condition index (%CI) and the percentage of the renovation index (%RI).To obtain the %CI and %RI, actual data, including technical data, routine and special test results, and visual inspections, are applied in the assessment model as shown in Figure 2. The weighting-scoring method or WSM is a numerical technique used to calculate the condition and renovation indexes from various evaluation criteria.A scoring technique is used to transform the raw inspection and testing results from each test method to a quantitative value known as a score, while Energies 2023, 16, 847 a weighting technique is used to assign the numerical value representing the importance of each test method as well as the significance of each component in a HVCB unit, known as the weighting value [31].The importance of the weight setting is arranged regarding the importance and effectiveness of each concerned item.Hence, criteria or sub-criteria weights need to be determined appropriately and logically.The score is classified based on international standards and expert experiences.The opinions of the experts are brainstormed along with the application of the analytical hierarchy process (AHP), which is a mathematical tool using pairwise-comparing opinion and expertise from experts to each criterion to obtain the numerical weight.The large number of weights implies the significance of that criterion and its effect on the overall index variation.Subsequently, the final weighting and scoring values can be assigned to each criterion.
Energies 2023, 16, x FOR PEER REVIEW 4 of 17 while a weighting technique is used to assign the numerical value representing the importance of each test method as well as the significance of each component in a HVCB unit, known as the weighting value [31].The importance of the weight setting is arranged regarding the importance and effectiveness of each concerned item.Hence, criteria or subcriteria weights need to be determined appropriately and logically.The score is classified based on international standards and expert experiences.The opinions of the experts are brainstormed along with the application of the analytical hierarchy process (AHP), which is a mathematical tool using pairwise-comparing opinion and expertise from experts to each criterion to obtain the numerical weight.The large number of weights implies the significance of that criterion and its effect on the overall index variation.Subsequently, the final weighting and scoring values can be assigned to each criterion.After successful validation of the proposed D-distance risk factor with the pilot HVCBs of the 20 units, this method can be further applied with the rest of the HVCBs in the transmission and distribution substations in the grid.The proposed method can also be adapted to implement with other high-voltage equipment or HVCBs in other voltage ratings, such as a medium-voltage switchgear, a power transformer, an instrument transformer, a disconnecting switch, and a lightning arrester, by adjusting some evaluation criteria and scoring details according to the physical behavior and operating principle of those devices.With this proposed method, the huge amount of maintenance tasks regarding HVCBs and other high-voltage equipment in an electrical system can be logically prioritized according to the known failure probability of those devices.For HVCBs with a high %CI, the servicing, repairing of defected components, or replacement of the defective components by a new one should be executed to lower the %CI, while for HVCBs with a high %RI, the planned replacement or relocation should be appropriate.Therefore, with After successful validation of the proposed D-distance risk factor with the pilot HVCBs of the 20 units, this method can be further applied with the rest of the HVCBs in the transmission and distribution substations in the grid.The proposed method can also be adapted to implement with other high-voltage equipment or HVCBs in other voltage ratings, such as a medium-voltage switchgear, a power transformer, an instrument transformer, a disconnecting switch, and a lightning arrester, by adjusting some evaluation criteria and scoring details according to the physical behavior and operating principle of those devices.With this proposed method, the huge amount of maintenance tasks regarding HVCBs and other high-voltage equipment in an electrical system can be logically prioritized according to the known failure probability of those devices.For HVCBs with a high %CI, the servicing, repairing of defected components, or replacement of the defective components by a new one should be executed to lower the %CI, while for HVCBs with a high %RI, the planned replacement or relocation should be appropriate.Therefore, with the known %CI, %RI, and failure probability, the appropriate maintenance strategy can be effectively planned and managed based on limited resources according to the criticality level of HVCBs in these three aspects.With a clear strategic action plan, high performance of maintenance actions as well as a better asset management strategy could be achieved, and the failure rate of HVCBs could be reduced, resulting in better reliability of the electrical transmission and distribution system.

Failure Probability Assessment and Maintenance Strategy
In this paper, a failure probability assessment of HVCBs is presented.The failure probability is identified in terms of the D-distance factor, which is calculated by using the percentage of the condition index (%CI) and the percentage of the renovation index (%RI).To obtain the %CI and %RI, actual data, including technical data, routine and special test results, and visual inspections, are applied in the assessment model.Then, twenty HVCBs in various substations are applied with the assessment program, and the results are satisfied.The technical data sets, including age, serial number, manufacturer, model, mechanism type, rated current, rated voltage, and related international standards and recommendations, as well as the commissioning test record, are segregated into the individual data of the equipment, while some common data, which is similar for a particular model, are also set up as model data, such as spare part availability, maintenance effort, time consumed, etc.In the condition index evaluation, both individual and model data are simultaneously retrieved from the database and further calculated according to the above procedure.

Condition Index Calculation
The Condition Index (%CI) represents the equipment's condition in numeric form, which is determined by using the WSM technique.First, the score (S i ) of various routine and special tests as well as a visual inspection of the circuit breaker must be determined to transform the physical condition to a numerical value.To achieve that, the test results are compared and justified based on the recommendation in the international standards, commissioning record, and instruction manual from the manufacturer, as well as the knowledge in engineering, operation, and maintenance.The special tests include the contact timing test together with SF 6 pressure, dew point, percentage and purity, amount of SO2, gas leakage rate measurement, as well as counter and operating checks.In addition, the routine tests consist of tests on insulation and contact resistance, undamaged, clean, fastening terminal, and function checks.Visual inspection records have been designed with sufficient guidelines to observe and to consistently gather the general condition of HVCB components, such as undamaged parts, cleanness, fastening, operating, counter, drive mechanism condition, lubrication, rusty, construction condition, interlocking system operation, vacuum test, and spout test.The criteria and scores of all tests are detailed in Table 2.The %CI is calculated by using Equation ( 1) according to the WSM technique.However, the worst score (S i, worst ) from all tests in each major criteria is applied in the %CI calculation to make the model sensitive in early warning whether to repair or to replace any equipment.
where %CI is the percentage condition index of any circuit breaker, S i, worst is the worst score of all tests in each criteria, and S i, max is the maximum score of all criteria.A higher %CI implies a poorer condition of the equipment, which means a large deviation from the instruction manual or international standard recommendation and commissioning record, whereas a smaller %CI represents a better condition.The judgement of condition index is presented in Table 3.The evaluated result is displayed as a traffic light color of green, orange, or red for good (%CI is lower than 40), moderate (%CI is between 40 to 80), and poor condition (%CI is greater than 80), respectively.The numerical boundary of %CI is determined from sensitivity analysis by first simulating the possible defective parts found and recorded in the utility's failure record forms according to the test methods described in Table 2 and observing the obtained %CI, then fine tuning the weighting value by combining more defective parts as much as possible and observing their impacts on the %CI.Once the rough boundary values are determined by simulated test cases, it is further tested with the actual data by comparing the actual condition of the equipment, historical failure rate, maintenance record, as well as the historical test results with the calculated results of the proposed method.This sensitivity analysis is performed by the brainstorming of utility experts with their expertise in engineering, operation, and maintenance of HVCBs from various departments to share their opinions on the %CI values obtained from various simulated and actual cases together with statistical methods and variance of distribution from evaluated populations.By this means, the boundary values between good to acceptable and acceptable to poor conditions can be determined, but it needs to be reconsidered for adjustment to improve the accuracy of this evaluation procedure when a greater number of HVCB populations have been evaluated.

Renovation Index Calculation
The Renovation Index (%RI) has been developed to notify the necessity level of renovation tasks to upkeep the reliability of an electrical system.%RI is evaluated by analyzing age, number of interruptions, inadequate rating, technology obsolescence, maintain ability, and symptom level as shown in Table 4.In the %RI evaluation, the equipment symptom and model failure rate are determined by analyzing the historical failure records.The required data sets include defects in major components, defects in minor components, failure mode, environmental effect, failure situation, root cause, down time, up time, outage duration, and solution.Moreover, the symptom level of the equipment is also determined by considering the defects in major components, minor components, and failure mode.Therefore, a major defect is defined as the equipment has a major failure with an urgent shutdown for repair or replacement and a high cost and high effort to repair.Conversely, a minor defect means that the defect in the equipment does not result in an immediate failure and has a low cost and low effort to repair.The scores and weights of all criteria in Table 4 are applied with the WSM technique to calculate the %RI by using Equation (2).The %RI is classified and displayed as a traffic light color of green, orange, or red for long-term, medium-term, and urgent requirements for renovation or replacement.
where %RI is the percentage renovation index, S j is the score of the sub-criterion j, W j is the weight of the sub-criterion j, and S j, max is the maximum score in all sub-criteria.The judgement of the renovation index is presented in Table 5.The evaluated result is displayed as a traffic light of green, orange, or red for long-term (%RI is lower than 24), medium-term (%RI is between 24 to 43), and urgent situation (%RI is greater than 43), respectively.Similar to the %CI boundary determination, the numerical boundary of %RI is determined from sensitivity analysis by first simulating the possible renovation criteria described in Table 4 and observing the obtained %RI, then fine tuning the weighting value by combining more renovation criteria as much as possible and observing their impacts on the %RI.Once the rough boundary values are determined by simulated test cases, it is further tested with the actual data by comparing the actual information of the equipment and historical minor and major refurbishment frequency with the calculated result.This sensitivity analysis is performed by the brainstorming of utility experts with their expertise on HVCBs from various departments to share their opinions on the %RI values obtained from various simulated and actual cases together with statistical methods and variance of distribution from evaluated populations.By this means, the boundary values can be determined, but it also needs to be reconsidered for adjustment to improve the accuracy of this evaluation procedure when a greater number of HVCB populations have been evaluated.

D-Distance Factor Calculation
In this session, the failure probability of HVCB usage is determined in terms of the D-distance factor (%D), which can be calculated by using Equation (3) and further plotted in the risk matrix as shown in Figure 3.The previously calculated %CI and %RI of each device are further substituted into the calculation.In the risk matrix, the %CI and %RI are considered of equal importance, which is determined by the 45 • line at the origin of the risk matrix.Thus, both angles θ 1 and θ 2 are equal to 45 of this evaluation procedure when a greater number of HVCB populations have been evaluated.
Table 5. Renovation judgement from the %RI assessment result.

D-Distance Factor Calculation
In this session, the failure probability of HVCB usage is determined in terms of the D-distance factor (%D), which can be calculated by using Equation (3) and further plotted in the risk matrix as shown in Figure 3.The previously calculated %CI and %RI of each device are further substituted into the calculation.In the risk matrix, the %CI and %RI are considered of equal importance, which is determined by the 45° line at the origin of the risk matrix.Thus, both angles θ1 and θ2 are equal to 45°.

Risk Matrix with Proper Maintenance Action
After obtaining the %CI, %RI, and %D from the above calculation procedures, those indexes are used to build the risk matrix as shown in Figure 3. From the risk matrix, the green rectangular zone means that the device is in good condition with a long-term renovation requirement resulting in a very low failure probability zone or very low failure probability.On the contrary, the top right red rectangular zone means that the device is in poor condition with an urgent renovation requirement leading to a very high failure probability zone or very high failure probability.Therefore, in Figure 3, there are 5 levels of failure probability in the risk matrix ranging from "very low", "low", "moderate", "high", and "very high" failure probability represented by the green, light green, yellow, orange, brown, and red color, respectively.Then, different maintenance strategies can be identified as presented in Table 6.Then, with this information, the utility can effectively plan an appropriate maintenance action, such as a short-term repair, planned renovation, or refurbishment.Moreover, an urgent risk can be determined by normalizing as %D and classified into 3 zones as shown in Table 7.

Risk Matrix with Proper Maintenance Action
After obtaining the %CI, %RI, and %D from the above calculation procedures, those indexes are used to build the risk matrix as shown in Figure 3. From the risk matrix, the green rectangular zone means that the device is in good condition with a long-term renovation requirement resulting in a very low failure probability zone or very low failure probability.On the contrary, the top right red rectangular zone means that the device is in poor condition with an urgent renovation requirement leading to a very high failure probability zone or very high failure probability.Therefore, in Figure 3, there are 5 levels of failure probability in the risk matrix ranging from "very low", "low", "moderate", "high", and "very high" failure probability represented by the green, light green, yellow, orange, brown, and red color, respectively.Then, different maintenance strategies can be identified as presented in Table 6.Then, with this information, the utility can effectively plan an appropriate maintenance action, such as a short-term repair, planned renovation, or refurbishment.Moreover, an urgent risk can be determined by normalizing as %D and classified into 3 zones as shown in Table 7.

Results and Discussions
After the evaluation procedure for the 115 kV HVCB was established, the detailed calculation of the %CI, %RI, and %D was determined and implemented in the developed failure probability assessment program for the HV circuit breaker.It is presently used by a distribution system utility in Thailand to record the technical data of all 115 kV HVCBs installed in the electrical system as well as the testing and visual inspection results.First, the %CI and %RI were evaluated by applying the WSM and AHP technique, and then, the results were further used to calculate the %D.Consequently, the failure probability can be determined, and the proper maintenance tasks can be suggested.All technical and maintenance data as well as maintenance costs are systematically recorded in a central database.Hence, the actual technical and testing data of the HVCB can be quickly retrieved from the database and further used in the analysis.With the developed software program, the evaluation results can be quickly performed and shown in this section.To illustrate the proposed method and evaluation process, pilot 115 HVCB#2 was selected as an example.In Table 8, the condition index of HVCB#2 was determined by starting from the raw data of the visual inspection and test results in the second column.In Table 8, this raw data is transformed to the numerical scoring value by using the criteria determined in Table 2.With the weighting-scoring method, the %CI of HVCB#2 is 50%, which is an acceptable condition due to the minor problems regarding insulation resistance, SF6 quality, and abnormal operating counter found from the visual inspection.In Table 9, the renovation index of HVCB#2 was determined by starting from the raw data in the third column.Then, this raw data is transformed to the numerical scoring value by using the criteria determined in Table 4.With the weighting-scoring method, the %RI of HVCB#2 is 30.36%, which is a medium-term renovation requirement due to the increasing problems regarding age, number of fault current interruptions, lack of spare parts, maintenance expertise, and after-sale quality.Finally, the D-distance factor of this HVCB can be determined as 40.18%, which is a moderate-failure probability as shown in Table 10.To facilitate such tedious work, the proposed method has been further developed by using the Microsoft Excel program with a Visual Basic Application for automatic data retrieval from the database and evaluation as shown in Figure 4.The criteria for scoring and weighting values can be set in the Excel sheet.To quickly recognize the abnormal results from testing and inspection results or raw data exceeding the pre-determined criteria, the traffic light color is set as orange or red to provide a pre-warning or alert actuation to the users, respectively.From the developed program, similar results for the %CI and %RI can be obtained as shown in Figure 4.
To facilitate such tedious work, the proposed method has been further developed by using the Microsoft Excel program with a Visual Basic Application for automatic data retrieval from the database and evaluation as shown in Figure 4.The criteria for scoring and weighting values can be set in the Excel sheet.To quickly recognize the abnormal results from testing and inspection results or raw data exceeding the pre-determined criteria, the traffic light color is set as orange or red to provide a pre-warning or alert actuation to the users, respectively.From the developed program, similar results for the %CI and %RI can be obtained as shown in Figure 4. Subsequently, twenty of the existing 115 kV HVCBs installed in several substations in a distribution utility were analyzed with this method using the developed software.The actual HVCB data required for the %CI and %RI assessments are collected and presented in Tables 11 and 12. Similarly, with HVCB#2 in the above example, the actual test data and physical condition of the component's degradation, shown in Tables 11 and 12, are transformed into the numerical scores by using the criteria mentioned in Tables 2 and  4. The raw score and evaluation results of the %CI, %RI, and %D of the twenty 115 kV HV circuit breakers are presented in Table 13.Subsequently, twenty of the existing 115 kV HVCBs installed in several substations in a distribution utility were analyzed with this method using the developed software.The actual HVCB data required for the %CI and %RI assessments are collected and presented in Tables 11 and 12. Similarly, with HVCB#2 in the above example, the actual test data and physical condition of the component's degradation, shown in Tables 11 and 12, are transformed into the numerical scores by using the criteria mentioned in Tables 2 and 4. The raw score and evaluation results of the %CI, %RI, and %D of the twenty 115 kV HV circuit breakers are presented in Table 13.To make it better for result understanding and easier to interpret the failure probability assessment result, the risk matrix is employed, and the values of the %CI and %RI are plotted in the risk matrix as shown in Figure 5. Two HVCBs, HVCB#14 and HVCB#15, lie in the high-failure probability zone, while HVCB#1 lies in the low-failure probability zone.The other 17 HVCBs are in the moderate-failure probability zone.Moreover, when considering the %RI, it is found that seventeen HVCBs need urgent renovation action as their ages are approaching the end of life.However, HVCB#16 with 16 years in operation is also in the urgent renovation requirement zone due to a lack of spare parts and maintenance expertise.Two HVCBs need medium-term renovation action with the ages of 13 and 17 years in service, while only HVCB#1 needs long-term renovation action because it is only 8 years in service.Regarding the condition index, eighteen HVCBs are in good condition, but two HVCBs are in moderate condition, HVCB#2 and HVCB#13, because of the problems regarding insulation resistance, SF6 quality, and abnormal items found by the visual inspection.With the above results, the maintenance tasks of thousands of HVCBs in the grid can be easily prioritized with the known causes.This could effectively improve the performance of HVCB maintenance with less cost and effort.To make it better for result understanding and easier to interpret the failure probability assessment result, the risk matrix is employed, and the values of the %CI and %RI are plotted in the risk matrix as shown in Figure 5. Two HVCBs, HVCB#14 and HVCB#15, lie in the high-failure probability zone, while HVCB#1 lies in the low-failure probability zone.The other 17 HVCBs are in the moderate-failure probability zone.Moreover, when considering the %RI, it is found that seventeen HVCBs need urgent renovation action as their ages are approaching the end of life.However, HVCB#16 with 16 years in operation is also in the urgent renovation requirement zone due to a lack of spare parts and maintenance expertise.Two HVCBs need medium-term renovation action with the ages of 13 and 17 years in service, while only HVCB#1 needs long-term renovation action because it is only 8 years in service.Regarding the condition index, eighteen HVCBs are in good condition, but two HVCBs are in moderate condition, HVCB#2 and HVCB#13, because of the problems regarding insulation resistance, SF6 quality, and abnormal items found by the visual inspection.With the above results, the maintenance tasks of thousands of HVCBs in the grid can be easily prioritized with the known causes.This could effectively improve the performance of HVCB maintenance with less cost and effort.

Conclusions
In the distribution system of a utility in Thailand, there are more than three hundred substations and more than one thousand five hundred units of active HV circuit breakers.With the limitations of manpower, material in terms of spare part availability and testing devices, as well as annual budget, the action maintenance plan needs to be designed appropriately to manage the limited resources effectively.The proposed failure probability determined from the risk matrix is an effective tool to facilitate the effective allocation of limited resources to the most urgent HV circuit breakers.The pilot circuit breakers of

Conclusions
In the distribution system of a utility in Thailand, there are more than three hundred substations and more than one thousand five hundred units of active HV circuit breakers.With the limitations of manpower, material in terms of spare part availability and testing devices, as well as annual budget, the action maintenance plan needs to be designed appropriately to manage the limited resources effectively.The proposed failure probability determined from the risk matrix is an effective tool to facilitate the effective allocation of limited resources to the most urgent HV circuit breakers.The pilot circuit breakers of twenty units with diverse ages and conditions selected from various substation were applied with

Figure 1 .
Figure 1.The overview diagram of the proposed method.

Figure 1 .
Figure 1.The overview diagram of the proposed method.

Figure 2 .
Figure 2. The overall procedure of the assessment model.

Figure 2 .
Figure 2. The overall procedure of the assessment model.

Figure 3 .
Figure 3. Measurement of the D-distance factor for the failure probability assessment.

Figure 3 .
Figure 3. Measurement of the D-distance factor for the failure probability assessment.

Figure 4 .
Figure 4. Example of the developed software for evaluating the condition and renovation index with the weighting-scoring technique.

Figure 4 .
Figure 4. Example of the developed software for evaluating the condition and renovation index with the weighting-scoring technique.

Figure 5 .
Figure 5. Failure probability evaluation of twenty 115 kV HVCBs using the risk matrix.

Figure 5 .
Figure 5. Failure probability evaluation of twenty 115 kV HVCBs using the risk matrix.

Table 1 .
Power circuit breaker failure detail.

Table 2 .
Weighting-scoring method for the condition assessment of HVCB.

Table 3 .
Condition judgement from the %CI assessment result.

Table 4 .
Criteria and weighting-scoring method for the %RI evaluation of HVCBs.

Table 5 .
Renovation judgement from the %RI assessment result.

Table 6 .
Failure probability zone and recommended maintenance action in the risk matrix.

Table 7 .
D-Distance factor for failure probability assessment and maintenance actions.

Table 8 .
Condition index determination of HVCB#2 by using its actual data and test results.

Table 9 .
Renovation index determination of HVCB#2 by using actual data and test results.

Table 10 .
D-distance calculation of HVCB#2 by using the evaluated %CI and %RI.

Table 11 .
Technical specification, test result, and operation information of twenty 115 kV HV circuit breakers.

Table 12 .
Practical visual inspection results of twenty 115 kV HV circuit breakers.

Table 13 .
Scores and evaluation results of the %CI, %RI, and D-distance of twenty 115 kV HV circuit breakers.