Inspection frequency optimization and partial discharge monitoring for condition based maintenance of substations

Zhou, “Stochastic Model Based Optimal Maintenance Frequency Analysis for Industrial Equipment with Different Failure Patterns”, Proceedings of the 10th Naval Platform Technology Seminar

PARTIAL DISCHARGE MONITORING FOR

CONDITION BASED MAINTENANCE OF

SUBSTATIONS

ZHOU RONGCHANG

NATIONAL UNIVERSITY OF SINGAPORE

2006

PARTIAL DISCHARGE MONITORING FOR

CONDITION BASED MAINTENANCE OF

2006

It is in great appreciation that I would like to thank my supervisor, Associate Professor Chang Che Sau, for his invaluable guidance and advice throughout the course of this project Without his encouragement, it would have been an insurmountable task in completing the work

I would like to express my gratitude to Dr T Hoshino from TMT&D Corporation of Japan, for his contributions on the experimental part of this project, as well as to Mr

H C Seow of Power Systems Laboratory, for his help and cooperation throughout this research project

Sincere thanks and appreciation are also towards my colleagues in the Power Systems Laboratory, Dr Charles Chang, Mr Jin Jun, Mr Wang Zhenyu, and many other friends who have encouraged me and helped me in one way or another

Finally, I would like to take this opportunity to thank my parents and sister, for their love, patience, and continuous support along the way Without them, none of this would even be possible

1 C S Chang, R C Zhou and J Jin, “Identification of SF6 Partial Discharge Sources in Gas-Insulated Substations”, Proceedings of the Australasian Universities Power Engineering Conference (AUPEC), Australia, September 26-

29, 2004

2 C S Chang and R C Zhou, “Stochastic Model Based Optimal Maintenance Frequency Analysis for Industrial Equipment with Different Failure Patterns”, Proceedings of the 10th Naval Platform Technology Seminar (NPTS), Singapore, May 17-18, 2005

ACKNOWLEDGEMENTS ……… i

PAPERS WRITTEN ARISING FROM WORK IN THIS THESIS ……… ii

TABLE OF CONTENTS ……… iii

SUMMARY ……… vii

LIST OF FIGURES ……… x

LIST OF TABLES ……… xii

CHAPTER 1: INTRODUCTION……….1

1.1 BACKGROUND……… 2

1.1.1 Evolution of Maintenance Strategies for Asset Management ……… 2

1.1.2 Condition Based Maintenance for Substations……… 3

1.2 OVERVIEW OF THE PROPOSED TECHNIQUES FOR IMPROVING CBM OF SUBSTATIONS ……… 6

1.2.1 Inspection Frequency Optimization……… 6

1.2.2 Partial Discharge Monitoring……… 9

1.3 THESIS ORGANIZATION……….12

CHAPTER 2: ADAPTIVE RELIABILITY MODELING OF SINGLE SUBSTATION EQUIPMENT ………… 14

2.1 ADAPTIVE MODEL BASED INSPECTION FREQUENCY OPTIMIZATION FOR SINGLE COMPONENT ……… 15

2.2 ADAPTIVE RELIABILITY MODELING ………… 16

2.2.2 Variations of Reliabilities with Different Inspection Frequencies 17

2.2.3 Adaptive Mechanism for Reliability Parameters 22

2.3 INSPECTION FREQUENCY OPTIMIZATION FOR SINGLE COMPONENT……… 26

CHAPTER 3: INSPECTION FREQUENCY OPTIMIZATION FOR MULTI- COMPONENT SUBSTATIONS ……… 30

3.1 INSPECTION FREQUENCY OPTIMIZATION FOR MULTI-COMPONENT SUBSTATIONS ………… 31

3.2 MINIMAL CUT-SET ANALYSIS FOR SUBSTATION ……… 34

3.3 SUBSTATION OPERATING COSTS EVALUATION……… 37

3.4 COST-OPTIMAL INSPECTION FREQUENCY……… 40

3.4.1 DE Algorithm for Cost Optimization……… 40

3.4.2 Case Studies on Various Substation Configurations ……… 44

3.4.3 Results and Discussions……… 46

CHAPTER 4: PARTIAL DISCHARGE DETECTION AND SOURCE IDENTIFICATION IN GIS ……… 53

4.1 PARTIAL DISCHARGE MONITORING FOR GIS……… 54

4.1.1 Partial Discharge in GIS……… 54

4.1.2 Various Approaches for PD Detection in GIS……… 55

4.2 PD SOURCE IDENTIFICATION FOR GIS……… 56

4.3 SPECTRUM CHARACTERISTICS OF PD SIGNALS FROM DIFFERENT SOURCES………58

4.3.2 Spectrum Analysis for Various Types of Discharge Signals……… 60

4.3.3 Discriminative Information Contained in Frequency Spectrum…… 63

4.4 FEATURE EXTRACTION FROM FREQUENCY SPECTRUM………… 63

4.4.1 Feature Measurement……… 64

4.4.2 Feature Extraction……… 66

4.4.3 Propagation Characteristics of UHF PD Signals……… 67

4.4.4 Classification Results……… 68

4.5 NEURAL NETWORKS FOR PD SOURCE IDENTIFICATION………… 68

4.5.1 Review on Artificial Neural Network ……… 69

4.5.2 Neural Networks for PD Source Identification……… 70

4.5.3 Performance Analysis……… 72

4.6 ROBUSTNESS OF THE NEURAL NETWORK BASED PD SOURCE IDENTIFICATION ……….73

CHAPTER 5: PARTIAL DISCHARGE SOURCE LOCATION IN GIS…… 77

5.1 PD SOURCE LOCATION IN GIS……… 78

5.2 THE LOGIC OF PD SOURCE LOCATION BASED ON TIME DELAY ESTIMATION……… 79

5.3 PD SOURCE LOCATION BASED ON DIFFERENT TIME DELAY ESTIMATION METHODS……… 80

5.3.1 Location of PD Sources Based on First Peak Detection……… 83

5.3.2 Location of PD Sources Based on Power Energy Curve………… 86

5.3.3 Location of PD Sources Based on Cumulative Energy Curve…… 88

5.3.4 Location of PD Sources Based on Cross-correlation Curve………… 91

CHAPTER 6: CONCLUSIONS……… 97

6.1 CONTRIBUTIONS OF THE RESEARCH……… 98

6.2 RECOMMENDATIONS FOR FUTURE RESEARCH ……… 100

REFERENCES ……… 102

APPENDICES……… 106

As a result of economic pressures caused by the power market deregulation, there is

an urgent need for electric utilities to seek a cost-effective maintenance strategy to keep substations operating both reliably and economically Condition-based maintenance (CBM) is now replacing the traditional time-based maintenance program due to its potential economic benefits Therefore, this project aims to realize some of the potential advantages of CBM for asset management of substations

This project has two objectives The first one is focused on the inspection frequency optimization for open-type substations In recent years, many diagnostic techniques such as transformer oil analysis have been proposed to inspect conditions of substation equipment and necessitate appropriate maintenance The yield of each inspection can be measured by the reduction of resulted operating cost Several mathematical models were previously proposed to minimize the operating cost by optimizing the inspection frequency Parameters in these models are however preset based on historical data and do not reflect the actual operating conditions of equipment In addition, a substation can have different combinations of apparatus, and the optimal inspection frequencies for various apparatus should consider all connected components in totality Therefore, a systematical approach is required to analyze how the reliability of each individual apparatus contributes to the overall operating cost of

a multi-component substation

The second objective deals with the partial discharge (PD) monitoring of insulated substations (GIS) GIS are integrally constructed and the fault development

gas-failures cannot be identified effectively by periodic inspections As a result, monitoring of PD is indispensable, which necessitates maintenance when the deterioration of dielectric integrity is detected Although quite a few PD diagnostic techniques have been proposed in recent years, many of them are either not reliable or computationally intensive, and thus not effective enough for real-time GIS implementation

continual-Through the two above objectives, three contributions have been made on CBM for substations with different structures The first contribution is concerned with the development of an adaptive reliability model for single substation equipment, which

is used to evaluate quantitatively the effects of deterioration and maintenance on the equipment reliability With the aid of a fuzzy inference engine, the proposed model adapts to the changing operating conditions of equipment and optimizes single-component inspection frequencies according to the actual equipment state

The second contribution involves the development of optimal maintenance-scheduling for multi-component substations The adaptive-model inspection frequency optimization for single component proposed in the first contribution is extended to multi-component substation by considering the composite effects of all connected components on the overall operating cost The minimal cut-set analysis is developed

to identify all the sets of component failures leading to overall failure of the substation, and calculate the probability of occurrence of each set of component failures With the inspection frequencies of individual components as the control variables, the overall operating cost of the entire substation is evaluated by combining the operating cost of

occurrence The algorithm of differential evolution (DE) is developed to optimally search through all the feasible inspection frequencies for minimizing the operating cost of substation

The third contribution is the development of a neural-network based PD source classifier for enhancing the reliability of GIS Features extracted from different spectra of PD signals are fed into a multi-layer feedforward neural network, and the trained network then identifies various PD sources Compared to many other techniques, this proposed method is simple but accurate, and has the potential of on-line implementation in PD monitoring system for GIS Furthermore, various time delay estimation methods have been investigated for locating different PD sources inside GIS, with the most accurate approach identified

Figure 1.1 CBM for different types of substations ……… 4

Figure 1.2 Inspection frequency optimization ……… 7

Figure 1.3 Partial discharge monitoring for GIS ……… 10

Figure 2.1 Adaptive reliability modeling for inspection frequency optimization 15

Figure 2.2 The basic multi-phase stochastic model ……… 17

Figure 2.3 Sensitivity analysis of inspection frequency in the first phase ……… 20

Figure 2.4 Sensitivity analysis of inspection frequency in the second phase …… 21

Figure 2.5 Sensitivity analysis of inspection frequency in the third phase ……… 21

Figure 2.6 Update of model parameters using fuzzy inference engine … 23

Figure 2.7 Membership functions used in the fuzzy inference process 24

Figure 2.8 Update of membership function ……… 25

Figure 3.1 Flowchart of the inspection frequency optimization for multi-component substations ……… 32

Figure 3.2 Two simple substation arrangements ……… 33

Figure 3.3 Flowchart of minimal cut sets analysis for substation ……… 35

Figure 3.4 Flowchart of the DE optimization ……… 41

Figure 3.5 Effects of different F on the DE optimization ……… 43

Figure 3.6 Effects of different CR on the DE optimization ……… 43

Figure 3.7 Typical substation configurations ……… 44

Figure 4.1 Flowchart of proposed PD source identification ……… 58

Figure 4.2 Typical waveforms of measured UHF signals ……… 60

Figure 4.3 Thresholds for selecting starting points of discharge signals ………… 62

Figure 4.4 Typical spectra of the four different types of PD (5000 samples) …… 62

Figure 4.6 Classification of various types of PD based on energy ratios ……… 68 Figure 4.7 Structure of the SOM network for PD source identification ……… 71 Figure 4.8 Structure of the MLP network for PD source identification ……… 71 Figure 5.1 PD source location based on TDE ……… 80 Figure 5.2 Typical waveforms of PD from particle on conductor (7.8/2.5) …… 81 Figure 5.3 Typical waveforms of PD from particles on conductor (4.3/6.0) … 82 Figure 5.4 Typical waveforms of PD from free particles on enclosure (7.8/2.5)… 82 Figure 5.5 Typical waveforms of PD from free particles on enclosure (4.3/6.0)… 83 Figure 5.6 First-peak detection of the two UHF PD waveforms ……… 84 Figure 5.7 Power energy curve for illustrating time delay estimation ……… 86 Figure 5.8 Cumulative energy curve for illustrating time delay estimation … 89 Figure 5.9 Cross-correlation curve for illustrating time delay estimation ……… 93 Figure A.1 Structure of fuzzy inference system ……… 107 Figure A.2 Sample membership function indicating different ages ……… 108 Figure C.1 An SOM neural network with n-inputs and m-output neurons ………115 Figure C.2 An MLP neural network with two hidden layers ……… 117 Figure D.1 Layout of the test setup with a compartment of an 800kV GIS …… 119Figure D.2 Layout of the dual-channel PD measurement ……… 121

Table 2.1 Model parameters for the sensitivity analysis of inspection

frequencies ……… 19

Table 2.2 Historical records of maintenance events ……… 22

Table 2.3 Parameters used in the four case studies……… 28

Table 2.4 Optimization results of the four case studies……… 29

Table 3.1 Model parameters for power transformers and circuit breakers 45

Table 3.2 Parameters for the cost-optimal inspection frequency analysis 46

Table 3.3 Optimization results for different substation configurations ………… 51

Table 3.4 Comparisons of optimal inspection frequencies for single and multiple substation components ……… 52

Table 4.1 Summary information of measurement data for various PD sources ……… 59

Table 4.2 Energy ratio ranges of various PD sources in four frequency bands ……… 66

Table 4.3 Performance comparison of SOM and MLP on PD source identification ……… 73

Table 4.4 Summary information of measurement data for various PD types with different PD-to-sensor distance ……… 74

Table 4.5 Summary of optimization results for different study cases …… 76

Table 5.1 Sensor locations of the two measurement channels …… 80

Table 5.2 Location errors based on the first peak detection for PD from particle on conductor ……… 84

Table 5.3 Location errors based on the first peak detection for PD from free particle on enclosure……… 85

Table 5.4 Location errors based on the power energy curve for PD from particle on conductor ……… 87

Table 5.5 Location errors based on the power energy curve for PD from free particle on enclosure ……… 88

Table 5.7 Location errors based on the cumulative energy curve for PD from free

TDE methods ……… 96

of substations Following that, the third section outlines the organization of this thesis

1.1 BACKGROUND

1.1.1 Evolution of Maintenance Strategies for Asset Management

Over the past century, maintenance strategies for asset management have evolved tremendously along with the technological revolution of the industries In those days when industry was not highly mechanized, maintenance problems received little attention and apparatus were simply repaired or replaced after they failed [1] With system configurations becoming more complicated, this approach was found to be neither economical nor efficient as it could result in catastrophic failure Therefore, the so-called time-based preventive maintenance (PM) became widely adopted to increase the reliability of industrial systems [2-4] Although being easy to implement, intervals between time-based maintenance must be carefully adjusted according to each apparatus’s operating environment and condition, as over-maintenance can lead

to wastes in time and/ or resource [4] To secure the maximum return on the investment, many industries have moved from the time-based to the condition-based maintenance (CBM) program [5]

Unlike the time-based maintenance routine, apparatus under CBM can be maintained based on their working conditions, which are evaluated by continuous on-line monitoring or periodic inspections [6] Appropriate maintenance actions will be triggered only when a predictable failure pattern of equipment is recognized, and thus lots of unnecessary maintenance activities can be avoided The resulting operating cost reduces significantly without sacrificing the reliability

1.1.2 Condition Based Maintenance for Substations

Substations provide continuity of power supply to industries and link between electric power transmission and distribution As a result of economic pressures caused by the power market deregulation starting from the 1990s, there is an urgent need for electric utilities to seek a cost-effective maintenance strategy to keep substations operating both reliably and economically [7] Therefore, this research is set out to realize some

of the potential advantages of CBM for substations In this part, problems associated with CBM of substations are discussed An overview of the proposed approaches to deal with these problems is presented in the next section

In general, substations can be divided into two categories: the open-type substations and the gas-insulated substations (GIS) [8] The study of CBM for substations in this thesis is based on these two different structures, as shown in Figure 1.1 The reliability of open-type substations mainly depends on the primary equipment such as power transformers and circuit breakers Under CBM, appropriate maintenance activities are implemented on these apparatus based on periodic inspection of equipment conditions Unlike open-type substations, GIS is integrally constructed and most of its live equipment (circuit breakers, disconnect switches, current and voltage transformers, etc.) are isolated from air in grounded metal tanks sealed and filled with compressed SF6 gas [9] Because of the short development time of faults in GIS, potential failures cannot be identified effectively by periodic inspections [10] As a result, continual-monitoring based CBM is required by GIS, which necessitates maintenance when the deterioration of dielectric integrity is detected

Figure 1.1 CBM for different types of substations

As shown in Figure 1.1, effective diagnostic techniques for each apparatus are required in an open-type substation for supporting periodic-inspection based CBM In recent years, many such techniques have been developed for substation equipment such as power transformers to inspect their conditions and necessitate appropriate maintenance [11-13] The yield of each inspection can be measured by the reduction

of resulting operating cost There is therefore the need for minimizing the total cost by optimizing the inspection frequency To carry out optimizations, mathematical models are needed which can evaluate quantitatively the impact of deterioration and maintenance on the resulted equipment reliability [14] Quite a few mathematical models representing the deterioration process of apparatus have been proposed to optimize the inspection frequency of industrial equipment [15-22] Several of them

were also applied to the reliability analysis of power apparatus such as transformer and circuit breaker [23-26] Parameters in many of these models are however preset based on historical data and do not reflect the deterioration and operating conditions

of equipment In addition, a substation can have different combinations of apparatus,

so the optimal inspection frequencies for various apparatus should consider all connected components in totality Therefore, a systematical approach is required to analyze how the reliability of each individual apparatus contributes to the overall operating cost of a multi-component substation

The breakdown of GIS caused by insulation faults is invariably preceded by partial discharge (PD) activities inside the GIS chamber [27] Therefore, PD monitoring is widely adopted in CBM of GIS Among the various PD diagnostic techniques applied

to GIS, the detection of ultra-high frequency (UHF) resonance signals caused by PD current pulse is most widely used due to its high sensitivity to detect even small PD activities [28] Based on the UHF measurement technique, many approaches have been proposed to predict potential breakdown risk of GIS through recognizing the PD defects [29-38] Fundamentally, all these PD diagnostic techniques are based on feature extraction in the time-, frequency- or time-frequency-domain Most of the time-domain approaches monitor PD activities by analyzing the phase-resolved PD patterns [29-34] These phase-resolved methods require continuous monitoring of PD activities over long periods to collect plenty of data for PD pattern analysis, but PD can progress very quickly from initiation to breakdown in GIS In addition, more than one type of PD activity can take place during the long measurement time, which results in inaccurate phase-resolved PD patterns and leads to misclassification [29] For spectrum analysis in the frequency domain, a few methods were previously

proposed to identify PD sources [35, 36] However, these methods do not fully classify the patterns of different PD sources As for the time-frequency approach, some wavelet analysis based approaches have been proposed to detect the UHF PD signals in GIS [37, 38] However, wavelet analysis tends to be computational intensive [39], which is an obstacle for real-time GIS implementation As a result, a more efficient PD monitoring technique for GIS is proposed here to give prompt warning messages before the breakdown occurs

1.2 OVERVIEW OF THE PROPOSED TECHNIQUES FOR IMPROVING CBM OF SUBSTATIONS

From the background review in the previous section, it is seen that there are some drawbacks in the traditional approaches for CBM of substations, and further improvements are needed Therefore, this research aims to improve the existing techniques There are two objectives for this project The first one is focused on the design of adaptive-reliability-model based inspection frequency optimization for open-type substations The second objective deals with the development of a reliable and efficient PD monitoring technique for GIS An overview of the approaches proposed to accomplish these two objectives is presented in this section

1.2.1 Inspection Frequency Optimization

The cost-optimal inspection frequency analysis developed for single as well as multiple components within a substation is illustrated in Figure 1.2 It is seen that the multi-phase reliability model for each substation component is the basis of all the

other analyses, because it provides a quantitative connection between maintenance and reliability Unlike the traditional reliability models, the proposed model is adaptive in nature Initial model parameters are established by historical operating records of equipment Actual operating conditions of equipment are fed into a fuzzy inference engine [40], the outputs of which are used to adjust the model parameters

As a result, the proposed model adapts to changing operating conditions of equipment and thus ensures reliability Detailed description of the adaptive reliability model will

be given in Chapter 2

Figure 1.2 Inspection frequency optimization

Using the adaptive model, effects of deterioration and maintenance on the reliability and operating cost of each substation component are evaluated As shown in Figure 1.2, if a substation component is unconnected to other equipment, only cost related to

maintenance and repair actions of this single component needs to be determined This cost can be minimized by exhaustively searching over feasible inspection frequencies for the optimal frequency in each phase of equipment life-span, as there are only few variables involved The adaptive-model based inspection frequency optimization for

single component will be discussed in Chapter 2

The single-component based inspection frequency optimization however does not guarantee the overall cost minimization of the entire substation with different combinations of components Therefore, it is extended by considering the composite effects of all components on the overall operating cost of multi-component substation

As shown in Figure 1.2, the cost analysis for connected substation components is configuration-dependent The minimal cut-set analysis method [41] is adopted to identify all the possible combinations of component failure events resulting in the load interruption and evaluate the probability of each load-point failure Based on the estimated failure probabilities, cost due to load-point interruptions is calculated using the reliability models Through combining this cost with the other part of cost related

to maintenance and repair actions, the overall operating cost of the entire substation is determined, as illustrated in Figure 1.2

To minimize the overall operating cost of substation, the number of control variables (inspection frequency) involved will be far greater than that for the single-component optimization More powerful technique beyond the exhaustive search such as differential evolution (DE) [42] is developed for handling all components in different substation configurations As shown in Figure 1.2, DE evaluates all the feasible

inspection frequencies for the optimal frequency with minimum operating cost for each configuration

The evaluation of operating cost based on minimal cut-set analysis and reliability model of multi-component substation, as well as the implementation of DE optimization algorithm for 6 substation configurations, will be discussed in detail in

Chapter 3

1.2.2 Partial Discharge Monitoring

The block diagram of the proposed PD monitoring technique is shown in Figure 1.3

It can be seen that UHF couplers are mounted on the GIS chamber, and the signals detected by these sensors are continuously monitored The signal processing procedure of PD monitoring can be divided into three steps: detection, identification, and location

Figure 1.3 Partial discharge monitoring for GIS

To detect the UHF resonance signals radiated from PD Signals, a threshold is set based on the background noise level A partial discharge is considered to occur when the amplitude of a detected signal exceeds the threshold value It has been found that the proposed PD source identification and location technique only requires analyzing

a segment of data containing the initial surge of a discharge signal This can reduce the storage memory and accelerate the processing speed, which is beneficial to on-line GIS implementation

After a discharge signal has been detected, the next step is to classify between the harmful PD activities in SF6 gas and the not-so-harmful air corona from outside GIS

As can be seen in Figure 1.3, air corona and three types of SF6 PD from different sources namely spacer, conductor, and enclosure are considered in this thesis An effective PD source classification technique has been developed Features extracted from different spectra of PD signals are used to train a multi-layer perceptron (MLP) neural network [43] Various PD sources can then be identified with high accuracy by

the trained network Chapter 4 will give the details of this neural-network based PD

source classifier

Further effort is required to precisely locate the PD sources, which have been identified from particle on enclosure or conductor, for necessary maintenance and repair Generally, for each PD event, two sets of UHF resonance signals can be detected by the two sensors mounted on both sides of the GIS chamber containing the defect Through calculating the arrival time difference between the UHF signals detected by these two different sensors, the distances between the PD source and the sensors can be estimated based on the propagation characteristics of UHF signals inside GIS Therefore, the time delay estimation (TDE) approach is adopted to locate these two PD sources inside the GIS chamber Various TDE approaches and their corresponding estimation accuracy in locating different PD sources have been investigated, and it has been found from the analysis results that different TDE approaches should be adopted for different PD sources to achieve the best location accuracy More details regarding the TDE based PD source location approach will be

given in Chapter 5

1.3 THESIS ORGANIZATION

This thesis comprises six chapters, which are briefly described as follows:

Chapter 1 introduces the different maintenance approaches for asset management of

industrial systems, as well as condition-based maintenance for different kinds of substations Some problems in the traditional approaches for CBM of substations are discussed, and an overview of the proposed techniques to improve the CBM of substations is also presented

Chapter 2 proposes an adaptive model to study the effects of changing operating

conditions on the resulted optimal inspection frequencies for single substation equipment The model structure as well as updating process of model parameters is described, and the single-component cost optimization approach is given Results of optimal inspection frequencies for single apparatus are also presented based on four typical cases of operating conditions

Chapter 3 extends adaptive-model based inspection frequency optimization from

single component to the entire substation with different kinds of apparatus The evaluation process of the overall operating cost for a multi-component substation is discussed based on the minimal cut-set analysis and the reliability model The implementation of differential evolution in deriving the cost-optimal inspection frequencies for various substation components is also described To this end, the proposed inspection frequency optimization is implemented on six typical substation configurations and corresponding results are presented

Chapter 4 develops an effective PD detection and source identification technique for

GIS based on spectrum analysis of discharge signals The feature extraction procedure

as well as the implementation of neural network in PD source identification is discussed in detail Moreover, the robustness of the proposed PD source classifier has also been studied and verified using large volume of laboratory-measured data

Chapter 5 investigates the different time delay estimation approaches for PD source

location in GIS Performance of these methods has been compared based on the laboratory data and the selection of appropriate time delay estimation methods based

on the identified PD sources is also discussed

Chapter 6 summarizes the main achievements of this research and its improvements

over the previous works Some recommendations for future work on condition-based maintenance of substations are also presented

CHAPTER 2

_

To overcome the drawbacks of traditional reliability models as identified in Chapter 1,

an adaptive model is proposed for single substation equipment This chapter begins with an introduction to adaptive-model based inspection frequency optimization for single component The updating process of parameters of the basic reliability model is then presented, and the inspection frequency optimization for single component is also described

Results from 4 case studies of operating conditions demonstrate the reliability of the adaptive model With the aid of a fuzzy inference engine, the proposed model adjusts its parameters according to changing operating conditions of apparatus Therefore, optimization for the inspection frequencies of single equipment is guaranteed

2.1 ADAPTIVE-MODEL BASED INSPECTION FREQUENCY OPTIMIZATION FOR SINGLE COMPONENT

As identified in the background review of Chapter 1, parameters for many of the previous proposed reliability models are set beforehand and unable to best fit the actual state of equipment Therefore, an adaptive reliability model has been developed

to optimize the inspection frequencies of single substation equipment, as shown in Figure 2.1

Figure 2.1 Adaptive reliability modeling for inspection frequency optimization

The single-component inspection frequency optimization consists of two parts, namely the adaptive modeling and exhaustive search for single apparatus The former updates parameters of the basic reliability model according to operating conditions and new maintenance records of equipment Based on the adaptive model, the latter searches exhaustively over feasible inspection frequencies for the optimal inspection frequency that minimizes the cost associated with single component

2.2 ADAPTIVE RELIABILITY MODELING

2.2.1 Basic Reliability Model

Although the deterioration of equipment is a continuous process [20], discrete phases are usually used in many of the previously proposed reliability models for the ease of modeling [21-26] Moreover, most of them are stochastic models since the time spent

on various phases of the equipment decay process is random in nature Therefore, a basic multi-phase stochastic model is developed here

As shown in Figure 2.2, the decay process of an apparatus before failure is represented by N discrete phases with the degree of deterioration increases from D1 to

Dn The number of phases to be used and the mean time spent on each phase depend

on the apparatus to be modeled The following assumptions are made on this model: 1) If no maintenance, the equipment condition deteriorates gradually from one phase to the next, with a transition rate λi,i+1 (from Di to Di+1) Transition rates

λi,f (1 ≤ i ≤ N-1) are included in this model due to the competing risks caused

by some undetected failures [18] The apparatus will be fixed immediately once

it fails, and it will then start working from phase D1 with a transition rate μf,1 2) During each inspection, the current phase of equipment is determined by diagnostic testing results Based on the equipment state, appropriate maintenance action Mi will then be taken with the probability of Pij

(maintenance action Mj taken in phase Di) After being maintained (M2 or M3), the apparatus can transit to other phases with the probability of Pijk (transit to phase Dk after maintenance action Mj taken in phase Di) The apparatus is then assumed to start working from the beginning of the new phase If no

maintenance (M1) is implemented, the equipment will just remain in the same phase, which means Pi1i always equals to one

3) The transition rates among various phases are assumed to be exponentially distributed That is, the probability density function of λi,j is with the form of

, where C is a constant value and t is the time index

)exp( C t

Figure 2.2 The basic multi-phase stochastic model

2.2.2 Variations of Reliabilities with Different Inspection Frequencies

As illustrated in Figure 2.1, the single-component operating cost is minimized by exhaustively searching for the best inspection frequency in each phase of equipment life-span To investigate the range of feasible inspection frequencies in various phases, variations of reliabilities with different inspection frequencies are studied As usual, the mean time to failure (MTTF) of an apparatus is used to indicate its reliability

during the entire life-span [44] For an apparatus represented by a three-phase

stochastic model (with N=3 in Figure 2.2), its MTTF from phase Di can be calculated

based on the discrete-time Markov chains analysis [45], and is given by:

j

j i P

where P(i, j) is the ith row, jth column element of the square matrix:

1

, 3 2 , 3 1 , 3 2

, 3 1

, 3

3 , 2 ,

2 3 , 2 1 , 2 1

, 2

3 , 1 2

, 1 ,

1 3

−

−

−+

+

−

−

−+

+

=

f f

f P

λμμμ

μ

λλ

λμμ

λλ

λλ

λ

(2.2)

and µi,j is given by:

)2

exp(

1

)2

exp(

1

3 1

3

1 ,

k ikj ij i

j

P P I

P P I

where I i is the inspection frequency of phase Di

Using equations (2.1)-(2.3), impact of different inspection frequencies in various

phases of the apparatus on its reliability is evaluated Parameters of the three-phase

reliability model (D1 with no deterioration, D2 with minor deterioration and D3 with

major deterioration) used in the sensitivity analysis of this section are tabulated as

shown in Table 2.1

Table 2.1 Model parameters for the sensitivity analysis of inspection frequencies

Parameters λ12 λ23 λ3f λ1f λ2f P11 P12

Values 1/5 1/3 ½ 1/30 1/15 0.80 0.15 Parameters P13 P21 P22 P23 P31 P32 P33

Values 0.05 0.10 0.80 0.10 0.05 0.15 0.80 Parameters P111 P112 P113 P121 P122 P123 P131

Values 1.00 0.00 0.00 0.99 0.01 0.00 0.97 Parameters P132 P133 P211 P212 P213 P221 P222

Values 0.02 0.01 0.00 1.00 0.00 0.25 0.65 Parameters P223 P231 P232 P233 P311 P312 P313

Values 0.10 0.55 0.25 0.20 0.00 0.00 1.00 Parameters P321 P322 P323 P331 P332 P333 µf,1

Values 0.05 0.25 0.70 0.10 0.55 0.35 52

Figure 2.3 to Figure 2.5 show the different MTTF values obtained from varying the inspection frequency in various phases of the equipment The following observations are made:

1) No maintenance is required in the first phase (D1), and increasing the inspection frequency of D1 would result in shorter instead of longer MTTF, as shown in Figure 2.3 This is because phase D1 is assumed to have no deterioration and any maintenance implemented in D1 can only keep the equipment in the same phase,

or even deteriorate its condition when disassembling the equipment for inspection

2) Appropriate inspection frequency of D2 can extend the MTTF, but too high a frequency would not benefit the equipment, as illustrated in Figure 2.4 This is because maintenance implemented in D2 can increase the probability (μ2,1) of improving the equipment condition back to D1, which results in a higher MTTF value However, the probability (λ2,3) of deteriorating the equipment state into

D3 will also increase simultaneously, and this effect can offset the benefit from the increasing μ2,1 if the inspection frequency is getting very high Therefore, the

inspection frequency of D2 which best extends the equipment life-span is the result of a compromise between the simultaneous increasing μ2,1 and λ2,3

3) A higher inspection frequency is always beneficial to enhance the equipment reliability, as can be observed in Figure 2.5 This is due to the fact that maintenance implemented in D3 can improve the equipment condition back to the previous phases (D1 or D2), or remain in the same phase in the worst case Therefore, the resulted MTTF would not be shorter than that without any maintenance Due to the existence of some undetectable breakdown risks in various phases, however, the MTTF value tend to stabilize when the inspection frequency keeps on increasing

Figure 2.3 Sensitivity analysis of inspection frequency in the first phase

Figure 2.4 Sensitivity analysis of inspection frequency in the second phase

Figure 2.5 Sensitivity analysis of inspection frequency in the third phase

2.2.3 Adaptive Mechanism for Reliability Parameters

Reliability model parameters are initially taken from manufacturer specifications and

historical operating data of equipment As shown in Figure 2.1, these parameters are

adjusted in two parallel ways with either new maintenance records or changing

operating conditions

During each inspection, the maintenance expert conducts the diagnostic tests (such as

dissolved gas analysis for oil-immersed transformer), decides upon and conducts

subsequent maintenance, and creates the maintenance record afterwards Table 2.2

shows some typical maintenance records, using which reliability parameters Piq and

Pijq are obtained The new maintenance record generated from a recent inspection

activity is added into the original records, based on which parameters Piq and Pijq are

also updated Suppose the equipment phase before maintenance is Di and the phase

after maintenance is Dk with the maintenance action Mj, then parameters Piq and Pijq

of the basic reliability model are adjusted as follows:

×

=+

+

×

=

j q for N

P

N

j q for N

)1(

×

=+

+

×

=

k q for N

P

N

k q for N

),1/(

)(

),1/(

)1(

(2.5)

where N is the sets of data in the original maintenance records

Table 2.2 Historical records of maintenance events Historical Records

Phase Before Maintenance D1 D2 D2 … D3

Maintenance Action Taken M1 M3 M2 … M2

Phase After Maintenance D1 D1 D2 … D3

(B) Adjustment of Reliability Parameters Using Changing Equipment

Operating Conditions

This is carried out using a fuzzy inference engine as illustrated in Figure 2.6 Fuzzy membership functions used in the fuzzy inference engine are shown in Figure 2.7 The flexible structure of these membership functions allows their parameters to be set

up hypothetically, and modified subsequently Typically, each input has a range from

0 to 100, indicating the degree of its membership For example, if the value of working environment is 50, then the environmental condition can be regarded as average or poor to some extent (50%) The output of the fuzzy inference engine is ranged from -1 to +1, which indicates the extent of a parameter to be changed For example, if the output value of mean time in each phase is -0.25, then the corresponding model parameter 1/λi,j as indicated in Figure 2.6 will reduce 25% The parameter remains unchanged if the output is zero

Figure 2.6 Update of model parameters using fuzzy inference engine

Figure 2.7 Membership functions used in the fuzzy inference process

The shapes of membership functions used in the fuzzy inference system are based on historical data as well as experience gained from maintenance experts All membership functions can be tuned according to new statistical data of equipment operations For example, if new technology is adopted in the manufacturing of a certain type of equipment to improve its reliability, the corresponding membership function of equipment age may be modified as shown in Figure 2.8 The updated membership function can thus reflect the fact that the equipment has been manufactured to be able to operate for a longer time

Figure 2.8 Update of membership function

Inputs and outputs of a fuzzy inference engine are linked by inference rules, which can be created and maintained in the following way:

ƒ Some of the rules are generated directly from the historical data (i.e data taken from the equipment operating database)

ƒ Experts formalize their experience on equipment maintenance and convert their knowledge into rules of the fuzzy inference system

ƒ The above two steps can be merged and the domain experts can also modify those rules generated by the statistical data When new data or technology becomes available, new rules should be created to ensure the reliability of the inference system

Typically, the fuzzy inference rules are in the following format:

ƒ If equipment age is new or working environment is good, then the breakdown risk is lower;

ƒ If working environment is good and load factor is low, then the mean time in each phase is longer;

ƒ If equipment age is old, and working environment is poor or load factor is high, then the breakdown risk is higher

The rules for the same output parameter can be with different weights in the inference process, depending on their importance to the output value Detailed information on the fuzzy inference process is given in Appendix A