Degree project in
Investigating the benefit of condition measurements for critical components
in power transmission systems
Johanna Gunhardson
Stockholm, Sweden 2013
XR-EE-ETK 2013:003 Electromagnetic Engineering Second Level, 30.0 HEC
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BSTRACTThis master thesis project has been conducted as a collaboration between Svenska Kraftnät and the Royal Institute of Technology.
High demands are being put on all components in a transmission system to be available for operation, making the allowed component down-time the limiting factor in the maintenance budget for Svenska Kraftnät and other transmission system operators. By conducting condition measurements that can be performed on-line, excessive down-times could be avoided in a step towards an as efficient maintenance strategy as possible.
The approach of this thesis work has been to perform a case study for a population of transmission grid circuit breakers, creating a model of the CBs’ lifetime which has then been simulated with the aim of studying the benefit of periodic on-line condition measurements for power system components. The main potential benefit examined is the decrease in total down- time for the component population, in relation to the respective components’ criticality.
The conclusions of this thesis project are summarized below.
Replacing the periodic off-line preventive maintenance with on-line condition measurements for the most critical circuit breakers in a power transmission system, significantly diminishes the weighted overall down-time for all circuit breakers in the system.
It is most preferable to use frequent intervals for condition measurements for a large part of the circuit breaker population.
A maintenance strategy based on condition measurements is best motivated in cases where the randomness of circuit breaker condition deterioration is high, the failure rate is high, or condition measurements have low uncertainty, and least motivated in cases where the conditions are the opposite.
Severe transient effects in average age of the component population may appear in response to any changes in maintenance strategy (or the lack of it), having a harsh impact for power system owners.
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CKNOWLEDGEMENTSI would like to thank my supervisor at the RCAM research group at KTH, Patrik Hilber, for his constant support in my work, regarding matters small and large and everything in between. I would like to thank my supervisor at Svenska Kraftnät, Tommie Lindquist, for great direction and input along the course of the project.
A big thank you also to Per Westerlund in the RCAM group for great attention to detail and for helping me improve my methods.
Everyone in the RCAM group, that have become good friends to me, I would like to thank for reminding me to take well-needed breaks, and of course for many laughs. A special thank you to Johanna Rosenlind for exceptional brain-storming, helping me break through at some of the tough moments in the project.
Another special thank you to Jenny Paulinder and Emil Andersson at Göteborg Energi Nät AB for valuable insights into the challenges facing distribution system operators in questions regarding maintenance and power system asset management.
These past months have taught me a lot regarding power grids, probably more even than I realize, making me more and more impatient to start my career as a power system engineer. Thanks again to everyone!
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NGLISH-S
WEDISH DICTIONARYEnglish Swedish Description
3D simulation 3D-simulering The model varies the main variables according to the model settings, running the simulation for each of their possible combinations.
Availability Tillgänglighet The time a component is connected to the network and in operation/ available for operation.
Circuit breaker (CB) Effektbrytare A mechanical switching device that may conduct or break the current under normal operation and that also can conduct, for a specified time, and break currents under specified abnormal conditions such as short circuits.
Condition Tillstånd A measure of how worn a component is. The condition is good when the component is new, and deteriorates with time and wear.
Condition based maintenance
Tillståndsstyrt underhåll
Makes use of the component’s estimated condition [1] to determine when preventive maintenance should take place.
Condition measurement
Tillståndsmätning The estimation of a component’s condition through periodic measurements (diagnostic testing).
Condition monitoring
Tillståndsövervakning Continuous on-line measurements of primary equipment with the devices permanently installed.
[2]
Corrective maintenance
Avhjälpande underhåll
Carried out after a component failure in order to restore the component to its required function.[1]
Critical component Kritisk komponent Important component to the overall function of a system.
8 Critical transfer
sections
Kritiska
överföringssnitt,
“flaskhalsar”
“Bottle necks” in transmission system, limiting the power transfer capability in a certain direction.
Decision process Beslutsprocess In this thesis referring to the decision of when to schedule a replacement of a component.
Diagnostic testing Diagnostisk mätning/test
The estimation of a component’s condition through periodic measurements.
Down-time Tid ur drift Time when a component is not available for service, while undergoing maintenance.
Equivalent age Ekvivalent ålder A measure of age combining a CB’s age and number of performed operations.
Failure Fel, haveri A failed component is unable to perform all its required functions.
Failure mode A Feltyp A Replacement is required to restore the CB to its required function.
Failure mode B Feltyp B Repair to pre-fault condition is sufficient to restore the CB to its required function.
Failure rate Felfrekvens The probability of a component failing.
Hazard rate Risknivå The probability of a component failing.
Importance Viktighet A measure of how critical a component is to the overall system function.
Importance index Viktighetsindex A tool for determining a system’s components’
importance level in relation to each other.
Important CB Viktig brytare In this thesis a CB regarded as more critical to the system.
Main variables Huvudvariabler QICB and MIICB, see Abbreviations and notations below.
N-1 criterion N-1 kriteriet Deterministic criterion signifying that any single component failure will not interrupt the system function (delivering power to all load points)
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Off-line Ur drift Equipment de-energized and disconnected from network.[2]
On-line I drift Equipment energized and connected to network.[2]
Operation Manöver
Drift
Opening or closing a circuit.
For instance, ‘operating a grid’ or ‘a component being in operation’
Preventive maintenance
Förebyggande underhåll
Carried out with the aim of preventing component failure.
Primary equipment Primärutrustning Components in a power grid with the main function of transferring power, such as transformers or over-head lines.
Reliability Tillförlitlighet The probability of a component performing its required function during a specified amount of time.
Reliability centered maintenance
Funktionssäkerhets- inriktat underhåll
Qualitative methodology with the purpose of creating cost effective maintenance plans based on probabilities and consequences of failure.
Repair Reparation In this thesis referring to restoring a failed CB to its pre-fault condition.
Replacement Ersättning, utbyte Preventive repl. – in this thesis referring to the scheduled replacement of a CB, in order to avoid future failure.
Corrective repl. – In this thesis referring to the replacement of a CB after failure.
Secondary equipment
Sekundärutrustning Components in power systems that do not have power transfer as their main function, such as protection relays.
Single-point simulation
Enpunktssimulering The model runs the simulation for one value each of the main variables.
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maintenance
Tidsstyrt underhåll Performed at periodic intervals.
Time out of service Tid ur drift Time when a component is not available for service, while undergoing maintenance.
Transient Transient Diminishing oscillations that appear in response to a step change, which in time settle.
Transmission system/grid
Transmissionsnät, stamnät
The back bone of a power grid, with the main function of transferring large amounts of power long distances.
Transmission system operator
Stamnätsoperatör Organization responsible for the operation of a transmission grid.
Unavailability Otillgänglighet The time a component is disconnected from the network and not available for operation.
Unprioritized CB Oprioriterad brytare In this thesis a CB regarded as less critical to the system.
Weighted […] Viktad […] In this thesis referred to results weighted according to component importance.
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BBREVIATIONS AND NOTATIONSAbbreviation/notation Description
ABAO As bad as old
af Age factor
AGAN As good as new
ageOps Age in operations
ageYears Age in years
CA Condition measurement (Condition assessment)
CB Circuit breaker
CBM Condition based maintenance
CM Corrective maintenance
cond Condition
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Correlation a-d, A-D Correlation between main variables and 3D simulation output. See section 6.2.
eqAge Equivalent age
ICB Important circuit breaker
ID Importance distribution, either
ID 1 – Importance unit
ID 2 – Importance ranking (1, 2, 3, 4, …) ID 3 – Equal ranking (no importance weighting)
mCond Measured CB condition at CA
mEqAge Equivalent age of CB when CA takes place
MIICB Measurement interval for important circuit breakers – The number of years between condition measurements for important breakers.
ops Operations
QICB Quota of important circuit breakers – The percentage of the total amount of circuit breakers in the population to be regarded as important
PM Preventive maintenance
RCAM Reliability centered asset management
RCM Reliability centered maintenance
RTF Run to failure (maintenance philosophy)
SvK Svenska Kraftnät, Swedish TSO
TBM Time based maintenance
TSO Transmission system operator
UCB Unprioritized circuit breaker
WRR Weighted replacement ratio = Ratio replacements due to failure divided by scheduled replacements
WU Weighted unavailability = Total weighted time out of service on a component level
yOps Yearly number of operations
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AMMANFATTNINGDetta examensarbetes svenska sammanfattning vänder sig främst till personer på Svenska Kraftnät och på andra svenska elnätsföretag samt övriga aktörer inom branschen med intresse för frågor om underhållsstrategier.
Examensarbetet har utförts i samarbete mellan Svenska Kraftnät och Kungliga Tekniska högskolan.
Med de höga krav på tillgänglighet som ställs på komponenter i transmissionsnät idag är det viktigt att ha en så effektiv underhållsstrategi som möjligt. Av den anledningen är det intressant att undersöka nyttan av att styra en större del av underhållsresurserna till de mest kritiska komponenterna i nätet.
För Svenska Kraftnät utgörs den begränsande faktorn av tiden ur drift som tillåts på komponentnivå för förebyggande underhåll. Med tillståndsmätningar som kan utföras på komponenter i drift kan denna tid minskas.
Syftet med examensarbetet har varit att undersöka nyttan av regelbundna tillståndsmätningar som kan utföras i drift för kritiska komponenter i transmissionsnät. Den potentiella nyttan som huvudsakligen studerats är en minskad total tid ur drift för komponentpopulationen, i förhållande till komponenternas respektive viktighet.
Tillvägagångssättet som använts i undersökningen har varit att utföra en fallstudie för kraftbrytarna i ett transmissionsnät gällande tillståndsmätningar. En modell skapades för brytarnas levnad, som sedan simulerades i syftet att iaktta påverkan av
intervallet med vilket mätningar utförs på kritiska brytare,
andelen av den totala mängden brytare som anses vara kritiska
på den totala viktade tiden ur drift.
Genom att utföra en känslighetsanalys för resultaten av simuleringarna kunde vilka faktorer som är kritiska för beslutsfattande gällande regelbundna tillståndsmätningar identifieras.
Rekommendationerna från projektet består i huvudsak av ett antal punkter som skulle behöva undersökas av nätoperatörer för att resultaten från studien ska vara fullt applicerbara.
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Inledningsvis behöver de mest kritiska komponenterna i nätet identifieras för att klargöra var underhållsresurser bör riktas i första hand. För att sedan tillståndsmätningar ska bli aktuella behöver specifika mätmetoder och deras förmåga att återspegla komponenters tillstånd undersökas. Utöver dessa punkter är det även rimligt att undersöka om det är lämpligt att helt utesluta komponenter från förebyggande underhållsåtgärder som utförs ur drift.
Följande slutsatser kunde nås inom ramen för examensarbetet, sammanfattade i punktform.
Att ersätta det regelbundna förebyggande underhållet där komponenterna är ur drift med tillståndsmätningar som utförs i drift för de mest kritiska kraftbrytarna i ett transmissionsnät, kan den totala viktade tiden ur drift för alla brytare i systemet minskas markant.
Exkluderas tiden ur drift för det förebyggande underhållet i den totala tiden ur drift för brytarna, framgår det att det är mest fördelaktigt att använda frekventa intervall mellan tillståndsmätningar för en stor andel av den totala mängden brytare, oavsett om resultaten viktas mot kriticiteten hos brytarna eller inte.
En underhållsstrategi baserad på tillståndsmätningar är bäst motiverad för fall där slumpmässigheten hos degraderingen av brytartillståndet är hög, felfrekvensen är hög, tillståndsmätningarna har låg osäkerhet eller där tiden ur drift för avhjälpande underhållsåtgärder är hög i förhållande till förebyggande underhållsåtgärder.
En underhållsstrategi baserad på tillståndsmätningar är mindre motiverad eller omotiverad för fall där slumpmässigheten av brytartillståndet är låg, felfrekvensen är låg eller där tillståndsmätningarna har hög osäkerhet.
Påtagliga transienter i komponentpopulationens medelålder kan uppstå som följd av förändringar i underhållsstrategi (eller avsaknaden av förändring). Dessa transienter kan leda till haveritoppar, samt därmed även toppar för kostnaderna för avhjälpande underhåll, med stark påverkan för elnätsägare.
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ONTENTS1. INTRODUCTION ... 19
1.1. Background ... 19
1.2. Purpose ... 19
1.3. Approach ... 19
1.4. Outline ... 20
2. POWER SYSTEM MAINTENANCE ... 21
2.1. Types of maintenance ... 21
2.1.1 Maintenance philosophies... 21
2.2. Condition monitoring and condition measurements ... 23
2.2.1. Condition monitoring... 23
2.2.2. Periodic condition measurements ... 24
3. IMPORTANCE INDICES FOR POWER SYSTEM COMPONENTS... 25
3.1. Importance indices in general ... 25
3.2. Importance index with regard to system stability ... 26
4. THE SIMULATED SYSTEM ... 27
4.1. Circuit breaker population ... 27
4.1.1. Distribution of main kind of service ... 27
4.1.2. Distribution of circuit breaker importance ... 27
4.2. Modes of ageing ... 30
4.2.1. Equivalent age ... 30
4.2.2. Condition ... 31
5. MODEL ... 33
5.1. Model settings ... 35
5.2. Start of model ... 36
5.3. Break-downs ... 36
5.3.1. Hazard function ... 36
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5.3.2. Two types of failures... 36
5.4. Condition measurements ... 38
5.4.1. Decision process ... 39
5.5. Replacements ... 45
5.6. Repairs ... 45
5.7. Ageing... 45
5.7.1. Equivalent age ... 46
5.7.2. Condition ... 46
5.8. End of model ... 46
6. RESULTS ... 47
6.1. Results of base case simulations ... 47
6.1.1. CA time out of service for UCBs = 36 hours ... 48
6.1.2. CA time out of service for UCBs = 0 hours ... 51
6.1.3. Results of single-point simulation ... 53
6.2. Results of sensitivity analysis ... 60
6.2.1. Base case for sensitivity analyses ... 61
6.2.2. Varying the time out of service... 66
6.2.3. Varying the stress factor ... 73
6.2.4. Varying the age factor ... 77
6.2.5. Varying the hazard function ... 80
6.2.6. Varying the measurement uncertainty ... 87
6.2.7. Varying the measurement uncertainty combined with an increased hazard rate ... 91
6.2.8. Comments... 94
7. CLOSURE ... 97
7.1. Discussion ... 97
7.2. Conclusions ... 100
7.3. Future work ... 101
REFERENCES ... 103
APPENDIX 1: Derivation of the hazard function ... 105
APPENDIX 2: Settings for QICB, MIICB and number of iterations for each simulation ... 109
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APPENDIX 3: Calculating the RR ... 111 APPENDIX 4: Select graphs from the sensitivity analysis ... 113 APPENDIX 5: Number of iterations versus variance reduction ... 117
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1. I
NTRODUCTION 1.1. BackgroundIn power transmission systems, such as the Swedish transmission grid operated by Svenska Kraftnät (SvK), the “N-1 criterion” is universally applied. The criterion signifies that should any single component in the grid fail, the failure will not cause any disruption in power delivery to any customers. This puts a high demand on all components in the system to be available for operation, making the allowed component down-time the limiting factor in the maintenance budget for SvK and other transmission system operators.
In the light of this, it is essential to have an as efficient maintenance strategy as possible. In the interest of avoiding excessive down-time, alternative strategies to the time based maintenance widely used today such as condition based maintenance with on-line methods are being investigated as viable options.
1.2. Purpose
The aim of this thesis has been to study the benefit of periodic on-line condition measurements as a replacement for off-line preventive maintenance of critical transmission system components.
Due to the N-1 criterion, the main potential benefit studied is a decrease in total down-time for the component population, in relation to the respective components’ criticality. In this way the effects of channeling maintenance resources toward the most critical components is investigated.
1.3. Approach
The approach of this thesis work has been to perform a case study for the population of transmission grid circuit breakers of National Grid in Great Britain, regarding the potential benefits of condition measurements.
The case study is carried out by the creation of a model of the CB’s lifetime and the behavior of the CB condition. The model is then simulated with component importance index values applied, to observe the impact of
the intervals with which measurements are carried out for critical CBs
The percentage of the complete CB population to be regarded as critical
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By conducting a sensitivity analysis for the results of the simulations, factors critical for decision making regarding periodic condition measurements are identified.
1.4. Outline
Chapter 2 describes various types of maintenance strategies in general terms, and specifically the ideas behind condition based maintenance.
Chapter 3 explains the general theory of determining component criticality and more specifically how this is done with respect to the system stability in systems where the N-1 criterion is applied.
Chapter 4 outlines the specifics of the system of circuit breakers simulated in the case study, in particular which importance index distributions are considered and how they are assumed to age.
Chapter 5 provides an overview of the structure of the simulated model, an overview as well as insights into the workings of each part of the model.
Chapter 6 presents the results of the base case simulations as well as the results of the sensitivity analysis.
Chapter 7 concludes the thesis by a discussion, conclusions and suggestions for future work.
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2. P
OWER SYSTEM MAINTENANCE 2.1. Types of maintenanceFigure 1. Schematic depiction of the sub-categories of maintenance.
There are in general two parts to maintenance, corrective and preventive maintenance. Corrective maintenance is carried out after a component failure in order to restore the component to its required function[1]. For instance, corrective maintenance could comprise bringing the component’s condition back to its pre-fault state, making it as bad as old (ABAO), or replacing the component altogether, bringing the component to the state as good as new (AGAN).
Preventive maintenance is, as the name implies, carried out in order to prevent component failure. Preventive maintenance actions range from smaller tasks such as inspections or cleaning [3] to larger tasks such as replacing the component ahead of failure with a new one.[1]
2.1.1 Maintenance philosophies
Preventive maintenance can be divided into time based maintenance and condition based maintenance.[1] Time based maintenance is performed at periodic intervals, in the case of circuit breakers intervals of for instance time or number of CB operations.
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Condition based maintenance makes use of the component’s estimated condition [1] to determine when preventive maintenance should take place. As mentioned in [1], a basic form of condition based maintenance is to delay the time period until the first periodic maintenance, thus assuming that its condition is better than the condition of older components. More advanced forms of condition monitoring and diagnostic techniques are described in section 2.2.
Time based and condition based maintenance can be combined to form other maintenance philosophies, such as reliability centered maintenance.[4] Reliability centered maintenance is a structured qualitative methodology with the purpose of creating cost effective maintenance schemes based on the probabilities and the consequences of failure.[4]
A separate maintenance strategy is to avoid preventive maintenance, letting all components run to failure before taking any measures. In a comprehensive international survey conducted by Cigré [5], it was shown that while run to failure may be feasible for non-critical functions or subcomponents, no transmission or distribution system operators found it appropriate as an overall maintenance philosophy.
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2.2. Condition monitoring and condition measurements
Advanced versions of condition based maintenance aim to detect, through either continuous or periodic measurements, both deterioration and wear due to age and normal usage as well as faults and defects.[4]
Figure 2. Schematic depiction of sub-categories within the scope of condition based maintenance.
2.2.1. Condition monitoring
Condition monitoring signifies continuous on-line measurements of primary equipment for chosen parameters with the devices permanently installed.[2] The measuring devices are either be attached onto old equipment or built-in from fabrication, the latter being less costly.[4]
A few examples of parameters that can be measured by condition monitoring of circuit breakers are presented in Table 1 [4].
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Table 1. A few parameters that can be measured using condition monitoring.[4]
Subcomponent of CB Parameter
Insulating medium Gas pressure, gas density
Arcing contacts Summation of interrupted currents Operating mechanism Number of operating cycles Control/auxiliary circuits Trip and closing coils
The equipment necessary for continuous on-line monitoring does need maintenance in itself, and may have as little as half the life expectancy of the circuit breaker it surveils.[4] These non-ideal aspects of condition monitoring are the reasons why this thesis instead focuses on periodic diagnostic testing.
2.2.2. Periodic condition measurements
Periodic diagnostic testing, in this thesis work referred to as simply condition measurements or CAs, signifies recurring measurements of primary or secondary functions, either on-line or off-line.
Costs for measurement equipment of this type are distributed over a larger part of a component population than condition monitoring equipment, making these measurements easier than condition monitoring to motivate economically.[4]
Examples of parameters that can be measured by diagnostic testing of circuit breakers are presented in Table 2 [4].
Table 2. A few parameters that can be measured using diagnostic testing.[4]
Subcomponent of CB Parameter
Insulating medium Insulation resistance
Arcing contacts Co-ordination with main contacts Operating mechanism Force, damping
Control/auxiliary circuits Operating time
In agreement with [4], these types of measurements are used in the simulations in this thesis with the purpose of determining when a circuit breaker needs to be replaced with a new one.
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3. I
MPORTANCE INDICES FOR POWER SYSTEM COMPONENTS 3.1. Importance indices in generalThe general idea behind importance indices is that they provide a means of assessing how important components in a specified system are to the overall system reliability.[6] Each studied component thus receives a quantitative measure of how critical it is to a specific system function.[6] Based on the provided importance data the components can then be ranked in accordance with their criticality to the system function, yielding an order in which to prioritize components in for instance matters regarding maintenance of the system.[6]
The basis of computing the importance of each component is the probability of the component failing to perform its required function, in the form of component reliability, as well as the consequence of the component failing, in the form of its location in the network topology and load demands.[6]
When applying traditional importance index calculations to power systems, some difficulties arise.
As discussed in [6] and [1], this is mainly due to the fact that a power system has numerous states besides fully functional or non-functional. Within the RCAM research group at KTH, several importance indices for power systems have been developed.[6] In [1] for instance, a means of calculating the component importance based on the cost of the interruption caused by the component failing is provided.
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3.2. Importance index with regard to system stability
Methods of determining component importance for distribution systems cannot be straight- forwardly applied for transmission systems, as they are often based on the consequence, either cost or energy not delivered [1], of the supply to certain load points being interrupted.[6] For transmission systems, where a single component failure does not cause an interruption in power delivery to any load points, alternative methods are required.
Setréus [6] presents three different importance indices based on the performance of transmission systems. They are as follows:
Reduced transmission system security margin, of which one measure is the previously mentioned deterministic N-1 criterion, which is of importance for transmission system operators.
Interrupted load supply, importance from the point-of-view of a distribution company.
Disconnected generating units, importance from the stand point of a generating company.
In [6], the reduced system security margin is studied specifically for the critical transfer sections1. A critical transfer section, if overloaded or close to its transfer capability limits, gives an indication of the system security margin and so the risk of system collapse.[6]
In this thesis the importance index and ranking in regard to reduced system security margin are applied for the system simulated in [6], as they are of interest for the transmission system operators such as Svenska Kraftnät.
1”Bottle necks” in transmission systems, limiting the power transfer capability in a certain direction across the system.
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4. T
HE SIMULATED SYSTEMFor the case study in this thesis a specific population of components were chosen, namely transmission system circuit breakers (CBs). Section 4.1 describes the CB population, which in the model described in chapter 5 are simulated according to the various modes of aging described in section 4.2.
4.1. Circuit breaker population
The CB population in the case study and their respective component importance values used are taken from Setréus [6], in which critical components of the power transmission system of National Grid in Great Britain were identified, according to the method described in section 3.2.
4.1.1. Distribution of main kind of service
In the CB population the CBs have six different main kinds of service, i.e. different positions in the transmission system, as displayed in Table 3.
Table 3. Number of CBs per main kind of service.
Main kind of service Number of CBs
Line2 926
Transformer 420
Shunt reactor 42
Capacitor 82
Bus-coupler 420
Other3 20
Total 1910
4.1.2. Distribution of circuit breaker importance
In the simulation the importance index values of the CBs have been applied in three different manners. In the first instance the importance values are as given in [6]. Ordered from the highest component importance to the lowest, the importance is distributed as shown in Figure 3.
2 Overhead line or cable
3 Series reactors or static VAR compensators
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Figure 3. Distribution of component importance sorted by size.
The 152 CBs with the lowest component importance are not displayed in Figure 3, as they are equal to 0 and cannot be displayed in a diagram with a logarithmic scale.
The data point in Figure 3 at importance 0.00001 represents the two most critical CBs in the population. Their respective component importance are about 100 times larger than the component importance for the third most critical CB. As these 2 out of 1 910 CBs would significantly determine the outcome of the model, they have been adapted in the model to equal the same component importance as the third most critical CB. Seen from a TSO perspective, such superiorly critical CBs would need to be treated separately in a risk and vulnerability analysis.
In the second instance, the component importance values have been converted to importance ranking, i.e. the CB with the highest component importance will get importance ranking 1910 (as there are 1910 CBs in total in the population), the second highest will get importance ranking 1909, etc. See Figure 4.
1E-19 1E-17 1E-15 1E-13 1E-11 1E-09 0,0000001 0,00001 0,001
0,1 0 500 1000 1500
Component importance
Circuit breaker number
Importance distribution 1
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Figure 4. Distribution of importance ranking, ordered by size.
In the third instance, no component importance or ranking has been applied. The CBs all have the component importance equal to 1, thus all CBs for this third case are regarded as equally critical.
See Figure 5.
Figure 5. Distribution at equal ranking, with no component importance or ranking applied.
0 400 800 1200 1600 2000
0 500 1000 1500
Importance ranking
Circuit breaker number
Importance distribution 2
0 1 2
0 500 1000 1500
No importance index
Circuit breaker number
Importance distribution 3
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Several factors influence how fast the condition of a CB deteriorates, such as age, number of operations (closing and opening circuits), and other types of stress such as fault currents.
For each calendar year run through in the simulation, one year will be added to the calendar age (age in years) of each CB. In the same way, a number of yearly operations will each year add to each CBs age in operations. The average yearly number of operations for a CB with a certain main kind of service can be seen in Table 4 [5].
Table 4. Number of yearly operations per main kind of service.
Main kind of service Number of yearly operations [5]
Line4 375
Transformer 38
Shunt reactor 279
Capacitor 114
Bus-coupler 22
Other6 173
Total 457
For the simulations, the number of yearly operations for each breaker is randomly generated in a uniform distribution in an interval of +/- 30% of the average number of operations given in Table 4.
4.2.1. Equivalent age
The age in years and in operations for each CB can be combined into an equivalent age, according to Equation 1. What Equation 1 represents is that 1 equivalent year, the least expected life-span of a CB, corresponds to either 30 calendar years [7] or 10 000 operations [7],[8], or a combination of these two as displayed in Figure 6.
4 Overhead line or cable
5 According to [9] these values are much lower for the line breakers SvK operates.
6 Series reactors or static VAR compensators
7 Weighted average over the number of CBs of each kind of service.
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Eq. 1
Figure 6. Correlation between CB age, number of operations and equivalent age.
4.2.2. Condition
The condition of a CB is a measure of how worn the CB is. It takes into account both calendar age and age in operations through the equivalent age as well as the impact of stress. The condition of a brand new CB is 1 in the simulation, and with time it is reduced to lower values. Equation 2 shows the relationship between equivalent age, stress and CB condition in the general case.8
Eq. 2
How each CB’s condition is affected by an increased equivalent age varies somewhat in the simulations. This is to say that the age factor af in Equation 2 differs for each CB, representing a difference in durability for the breakers. The age factor is randomly generated with a normal
8 The numerator 0.5 is arbitrarily chosen. With an af of 1 and stress factor of 0, this would mean that the CB condition is 0.5 at the equivalent age of 1.
32
distribution of mean value 1 and the standard deviation 0.15 for each CB. These values were chosen so as to give some variation within reasonable limits.
The impact of stress on the CB condition is randomly generated according to a normal distribution of mean value 0 and standard deviation 0.03. Positive values for stress represent stress such as high fault currents for a real life CB. Negative values for stress represent a lack of the normal stress affecting a real life CB. The negative values for stress are not to be interpreted as the CB condition actually regressing, but rather as a mathematical mechanism for slowing or halting the deterioration for a period of time.
33
5. M
ODELWhat the model mainly seeks to imitate, is a maintenance scheme where the CB population is divided into two parts and subsequently treated according to which group they adhere to:
important CBs (ICBs) or unprioritized CBs (UCBs). UCBs will continue to receive preventive maintenance off-line in a time based manner, while ICBs will receive off-line preventive maintenance only when the periodic on-line condition measurements (CAs) deem it necessary.
See Table 5 for a structured picture of the difference in maintenance between the two groups.
Table 5. Differences in preventive maintenance between the two groups of CBs: ICBs and UCBs.
Preventive maintenance ICBs UCBs
On/Off-line On-line Off-line
Condition measurement Yes Yes
Other maintenance actions None Yes, such as lubricating the operating mechanism and exercising the CB. [3]
Maintenance interval 1 – 15 years 15 years [7]
As the UCBs are off-line during maintenance, it is assumed that the same information can be procured from this more extensive type of maintenance as from the on-line CAs. The principal differences are the maintenance intervals and that the preventive maintenance for the UCBs requires a certain amount of component down-time. The potential positive effects from the other maintenance actions performed, as presented in Table 5, are disregarded in the model due to the difficulty of determining how significant these effects are.
The model written in Mathworks Matlab simulates a number of years in the life of a CB population, as described in chapter 4. The purpose of the model is to identify how the unavailability9 of the CBs on a component level is affected by changing two main variables. The variables being changed are:
9 Total time out of service.
34
The quota of important CBs (QICB) – The percentage of the total amount of CBs in the population that are to be regarded as important.
The measurement interval for important CBs (MIICB) – The interval with which the important CBs undergo condition measurements.
A schematic depiction of the model is displayed in Figure 7, and the various model blocks are described in sections 5.1-8.
Figure 7. Schematic depiction of the model for the CB population.
35 5.1. Model settings
The behavior of the model is determined by a series of settings, described in Table 6.
Table 6. Settings for the simulation of the model.
Setting Value used Description
Length of model 40 years The number of fictive years the model runs through and records before presenting the model output.
Length of start-up period 30 years The number of years the model runs through before it starts recording data, in order to allow the model to settle.
See more in section 6.2.8.
Measurement interval for CA of UCBs
15 years [7] The interval with which the UCBs undergo CAs.
Time out of service for CA of UCB
36 hours [3]/ 0 hours
The down-time of a UCB undergoing CA.
Time out of service for CA of ICB 0 hours The down-time of an ICB undergoing CA.
Time out of service for repair of failed CB
24 hours [10] The down-time of a CB for a failure requiring repair of the CB.
Time out of service for planned replacement of CB
24 hours [10] The down-time of a CB being replaced according to schedule.
Time out of service for replacement of failed CB
48 hours [10] The down-time of a CB for a failure requiring replacement of the CB.
Measurement interval for CA of ICBs (MIICB)
Variable, 1 - 15 years
The interval with which the ICBs undergo CAs.
Quota of ICBs (QICB) Variable, 0 - 100 % The percentage of the total amount of CBs in the population to be regarded as important.
Number of iterations 5 - 1000 The number of iterations performed for each set of main variables.
36 5.2. Start of model
The main task of the Start block of the model is to distinguish and separate which of the CBs are to be regarded as important, using the QICB variable. For example, if QICB is set to 10 % the 191 CBs with the highest component importance will be chosen from the total population of 1 910 CBs.
5.3. Break-downs
The Break-down block of the model determines whether a CB fails or not during a certain year, and what type of maintenance measure that will be required to regain the CB function.
5.3.1. Hazard function
Equation 3 represents the hazard function that determines the risk of the CB failing in the model.
The input is the CB condition.
Eq. 3
For information on how the hazard function was derived, see Appendix 1.
5.3.2. Two types of failures
In the simulations there are two types of failures with different resulting consequences. For failure mode A a replacement is required to restore the CB to its original function, and it is therefore as good as new (AGAN) after the required maintenance. For failure mode B a repair is sufficient, bringing the CB back to the pre-fault condition, that is as bad as old (ABAO).
The risk of failure mode B is, as expressed in Equations 5 and 7 and Figure 8, the largest part of the total risk of failure for brand new breakers, and then decreases linearly to 0 at the equivalent age equal to 1. The risk of failure mode A increases linearly with increasing equivalent age, becoming all-encompassing at the equivalent age equal to and above 1, shown in Equations 4 and 6.
37
Figure 8. The risk of failure mode A and B occurring in relation to the total risk of failure.
For
o Risk of failure mode A: Eq. 4 o Risk of failure mode B: Eq. 5
For
o Risk of failure mode A: Eq. 6 o Risk of failure mode B: Eq. 7
0 20 40 60 80 100
0 0,5 1 1,5 …
Percentage of total risk of fauílure [%]
Equivalent age of CB
Failure modes
Failure mode A Failure mode B
38 5.4. Condition measurements
In the model, condition measurements are made with the aim of obtaining a basis for decision- making regarding when to replace the CB. Ideally the time at which to replace the CB is as late as possible, however the risk of failure increases with CB age (see section 5.3.1), and so considering this trade-off the replacement should not be scheduled for a too high CB age.
Figure 9 shows the general outline of the CA block of the model. The decision process uses the measured value of the CB condition and the CB age at the measurement as input, and results in the calendar age at which to replace the CB.
Figure 9. Schematic depiction of the CA block of the model.
Condition measurements are made for both important and unprioritized CBs, with the difference that the interval between measurements are always 15 years for UCBs and for ICBs the interval is changeable between 1 and 15 years.
There is also a period of down-time for the UCB CAs, equal to 36 hours, as specified in Table 6. The real life CAs for the UCBs would occur at the preventive maintenance recurring for the CB every 15th year [7].
There is a measurement uncertainty incorporated in the model, causing the resulting measured condition value to be somewhere within the interval of +/- 0.02 from the true value. It was set to this relatively low value to create near-ideal conditions. In the sensitivity analysis in section 6.2, the measurement uncertainty is removed and increased respectively for some of the cases.
Measured condition and
age at measurement
Decision process
Replacement scheduled at a
certain CB calendar age
39 5.4.1. Decision process
The decision process in the model consists of two main steps. Step A estimates the expected future development of the CB’s condition and risk of failure based upon the information of the CBs measured condition and its current equivalent age. Step B weighs the consequence of a planned replacement against the probability and consequence of CB failure for each CB calendar age p. The replacement is then planned to the age at which the compounded consequence, distributed over the CB lifetime, is the lowest.
Step A
Based upon the measured condition, mCond, and the equivalent age at the measurement, mEqAge, the following equations are used to estimate future development of the CB. p represents the calendar age of the CB, and the factors below are calculated for each p of the breaker from its current age until 100 years of age10.
i. Equivalent age:
ii. Condition:
iii. For , (see section 5.3.2)
a. Risk of failure and replacement :
b. Risk of failure and repair to ABAO:
iv. For , (see section 5.3.2)
a. Risk of failure and replacement : b. Risk of failure and repair to ABAO:
10 This restriction was set to reduce the run time of the model.
Eq. 8 Eq. 9
Eq. 13 Eq. 11
Eq. 12 Eq. 10
40 Step B
Figure 10. Probability tree for CB lifetime.
For every calendar age of a CB, there are three possible outcomes, in accordance with Figure 10. In Table 7 and Equations 14 to 25 x represents the calendar age of the CB at the time of the CA.
41
Table 7. Description of notations used in step B of the decision process.
Notation Description
r(q) The probability that the CB fails and is repaired to ABAO year 11
s(q) The probability that the CB fails and is replaced year v(q) The probability that the CB does not fail year
v’(q) The probability that the CB has not been replaced year
R(q) Summarized probability consequence of corrective repair S(q) Summarized probability consequence of corrective replacement V(q) Summarized probability consequence of a planned replacement
Eq. 14
Eq. 15
Eq. 16
Eq. 17
Eq. 18
Eq. 19
Eq. 20
Eq. 21
11 p = x + q : q represents the difference between the examined calendar age p and the CB’s current calendar age x.
42
Step B then summarizes the probability consequence for each outcome, distributed over the CB lifetime, for each p from x+1 to 100.
Planned replacement of CB year p
CB failure and repair to ABAO from year x+1 to year p
This factor is somewhat underestimated, as the possibility of a CB failing and being repaired to ABAO, then later on failing and being replaced, is not taken into account.
CB failure and replacement from year x+1 to year p
Lastly, step B finds the CB age p for which the sum of these factors has its minimum value:
Eq. 25 Example
For a CB that has the calendar age of 18 years, equivalent age of 0.75, a measured condition of 0.50, and the number of yearly operations equal to 250, the decision process is performed as follows.
43 Step A
Based upon age and the measured CB condition, step A projects the future development of the CB.
Figure 11. Projected future development of the example CB.
Table 8. Projected development of the example CB.
p eqAge(p) Cond(p) hazA(p) hazB(p)
0 0.0000 1.0000 0.0000 0.0023
1 0.0417 0.9722 0.0001 0.0024
2 0.0833 0.9444 0.0002 0.0025
… … … … …
17 0.7083 0.5278 0.0076 0.0031
18 0.7500 0.5000 0.0088 0.0029
19 0.7917 0.4722 0.0102 0.0027
… … … … …
66 2.7500 -0.8333 0.9233 0.0000
67 2.7917 -0.8611 1.0000 0.0000
The projection stops at the age of 67 in this case, as the risk of failure mode A occurring is 100 %.
44 Step B
Based on the information in Step A, Step B determines the probabilities of the CB failing or not failing in the future years, as described earlier in this section.
Table 9. Projected probabilities of the example CB failing or not.
q s(q) r(q) v(q) v'(q)
1 0.0088 0.0029 0.9882 0.9912
2 0.0101 0.0027 0.9783 0.9810
3 0.0116 0.0023 0.9671 0.9694
… … … … …
24 0.0392 0 0.3718 0.3718
25 0.0388 0 0.3330 0.3330
26 0.0381 0 0.2949 0.2949
… … … … …
48 6.29E-06 0 1.17E-06 1.17E-06
49 1.08E-06 0 8.98E-08 8.98E-08
The probabilities are determined up until
As the final step in the decision process, the minimum of Equation 25 is found, the minimum of the sum of all probabilities multiplied by their respective consequences.
45
Table 10. Sum of the probabilities multiplied by the consequences.
q V(q) R(q) S(q) Sum(q)
1 1,2520 0,0037 0,4247 1,6804
2 1,1772 0,0067 0,4490 1,6330
3 1,1079 0,0091 0,4755 1,5925
… … … … …
9 0,7208 0,0102 0,7201 1,4511
10 0,6756 0,0098 0,7608 1,4463 11 0,6322 0,0095 0,8027 1,4444 12 0,5903 0,0092 0,8456 1,4451
The minimum is found at , indicating that the year of replacement should be scheduled to the CB’s calendar age
5.5. Replacements
In the Replacement block of the model, CBs are replaced for two reasons:
Preventive replacement – The CB in question has reached the calendar age at which it was planned to be replaced at its latest CA. The scheduled replacement takes 24 hours.
Corrective replacement at failure mode A – The CB has failed and needs to be replaced to be restored to its required function. The corrective replacement takes 48 hours.
At replacement the CB’s age is restored to 0, its condition restored to 1, and a new age factor is generated.
5.6. Repairs
The process in the Repair block of the model restores the CB to pre-fault function and condition should failure mode B occur. The corrective repair takes 24 hours.
5.7. Ageing
All CBs that have not been replaced, either by scheduled or corrective replacement, pass through the Ageing block of the model. Both the equivalent age and the CB’s condition is updated at this point.
46 5.7.1. Equivalent age
The equivalent age is updated by one calendar year and one set of the individual CB’s yearly operations.
5.7.2. Condition
The condition of the CB is updated according to its new equivalent age, and the impact of stress.
Eq. 26
The stress affecting the CB at the end of each loop of the simulation in the Ageing block, is randomly generated according to a normal distribution of mean value 0 and standard deviation 0.03. In comparison the average condition deterioration from increased equivalent age equals
5.8. End of model
At the end of the simulation, the output is summed up and displayed. There are two sets of output to be obtained, depending on what type of run mode the model is assigned to perform.
3D simulation – The model varies the main variables QICB and MIICB according to the model settings, and runs the simulation for each of their possible combinations. The output is the sum of the weighted time out of service for each CB, here called the weighted unavailability, for each case.
Single-point simulation – The model runs through the simulation for one fixed value each of QICB and MIICB. This type of run gives a more detailed insight into the workings of the model as output. For instance it is possible to see how the average age over the CB population develops over the length of the simulation, how many ICBs and UCBs are replaced either by schedule or failure each year, and what age they were at the replacement.
47
6. R
ESULTSThe results of the simulation in the form of 3D-graphs over the total weighted component unavailability as well as the results of a single-point simulation are displayed below in section 6.1.
In section 6.2 these results and a few additional simulation outputs are compared with simulations for which various parameters were changed in a sensitivity analysis.
Throughout the results, the numbers 1, 2 and 3 in tables and 3D-graph headings refer to the various importance distributions as described in section 4.1.2.
Table 11. Notation regarding importance distributions for the results.
Notation Importance distribution (ID)
WU 1 Unavailability weighted against component importance
WU 2 Unavailability weighted against component importance ranking
WU 3 Non-weighted unavailability
Simulation resolution and number of iterations per simulation for every simulation are catalogued in Appendix 2.
6.1. Results of base case simulations
In studying the output from the simulations, it became obvious early on that the 36 hours it takes to perform the CA for the UCBs was significantly larger than any other down-times. From that output it was difficult to draw any conclusions as to whether the MIICB had any significant influence on the time out of service resulting from repairs and replacements. For this reason, the results below for the base case are presented in two parts, one for which the simulations have been performed with the CA time out of service for UCBs being 36 hours, and the second with this factor being 0 hours.
48 6.1.1. CA time out of service for UCBs = 36 hours
Figure 12. WU 1 (with ID 1) for the base case, with CA down-time for UCBs being 36 hours.
49
Figure 13. WU 2 (with ID 2) for the base case, with CA down-time for UCBs being 36 hours.
Figure 14. WU 3 (with ID 3) for the base case, with CA down-time for UCBs being 36 hours.
50
As previously mentioned in section 6.1, the only factor having a visible impact on the Figures 12-14 is the 36 hours CA time out of service for UCBs. The portion of the component population making out the UCBs decreases as the QICB increases, hence the weighted unavailability of the components decrease with an increasing QICB.
For these results, it becomes apparent what impact the different ways of taking component importance into account makes. Figure 12 suggests that the impact of viewing up to 10 % of the component population as important is sufficient, if the aim is to significantly decrease the weighted time out of service by simply not performing the standard preventive maintenance requiring 36 hours time out of service.
Figure 15 represents a similar simulation to the one represented in Figure 12, with the only difference that QICB ranges from 0 to 0.1 instead of from 0 to 1.
Figure 15. WU 1 for the base case (QICB 0-10%), with CA down-time for UCBs being 36 hours.
This way zooming in on the steep increase in Figure 12, it is noticeable that the 3-4 % most critical components stand for most of the decrease in WU.
51 6.1.2. CA time out of service for UCBs = 0 hours
Figure 16. WU 1 (with ID 1) for the base case, with CA down-time for UCBs being 0 hours.
52
Figure 17. WU 2 (with ID 2) for the base case, with CA down-time for UCBs being 0 hours.
Figure 18. WU 3 (with ID 3) for the base case, with CA down-time for UCBs being 0 hours.
53
With the CA time out of service for UCBs set to 0 hours, what the figures show is the WU from corrective maintenance and scheduled replacements of CBs resulting from the various combinations of QICB and MIICB. While WU in Figure 16 has seemingly no cohesive correlation (or a very weak one) with the main variables, Figures 17 and 18 show that more frequent CAs and a higher percentage of ICBs result in lower values for WU.
6.1.3. Results of single-point simulation
The results of a standard single-point simulation is displayed below, highlighting the inner workings of the simulation. For a standard single-point simulation, the QICB is set to 10% and the MIICB set to 5 years.
Time out of service
Total time and total weighted time out of service, due to corrective maintenance and scheduled replacements of CBs are presented in Figures 19 and 20.
Figure 19. Total time out of service for the CB population.
0 500 1000 1500 2000 2500
1 4 7 10 13 16 19 22 25 28 31 34 37 40
Time [h]
Year
Total time out of service [h]
54
Figure 20. Total weighted (ID 1) time out of service for the CB population.
In Figure 20 the times out of service are weighted against the component importance (ID 1).
Number of measurements
The number of condition measurements for UCBs and ICBs respectively are shown in Figure 21.
Figure 21. Number of CAs for the CB population.
0,00 0,50 1,00 1,50 2,00 2,50 3,00
1 4 7 10 13 16 19 22 25 28 31 34 37 40
Time [weighted hours]
Year
Total weighted time out of service [weight.h]
0 20 40 60 80 100 120
1 4 7 10 13 16 19 22 25 28 31 34 37 40
No. of measurements
Year
No. of measurements
No. of CMs for UCBs
No. of CMs for ICBs
55 Number of replacements and repairs
The number of replacements due to failure and scheduling, as well as repairs due to failure.
Figure 22. Number of replacements and repairs for the CB population.
0 5 10 15 20 25 30 35 40 45 50
1 4 7 10 13 16 19 22 25 28 31 34 37 40
No. of maintenance measures
Year
No. of replacements & repairs
Sch.
replacements Fail.
replacements Fail. repairs
56 Age for scheduled replacement
Figure 23 represents the ages that are scheduled for planned replacements of CBs. That is, every time a CB goes through the CA block of the model and the decision process delivers an age at which a CB should be replaced, that specific age is registered for the data in Figure 23.
Figure 23. Age scheduled for planned replacement of CBs.
The bars at ages 45 and 60 are of high values, due to the fact that UCBs are measured with an interval of 15 years. For a part of the UCBs, the decision is to replace the component right away, basically because it already should have been replaced because of rapid deterioration of late.
The bar at age 100 represents all ages including and above 10012, as well as the ages that could not be determined due to CB condition being above 1 at the time for the particular CA13, see Figure 11 for reference.
12 This restriction was set to reduce the run time of the model.
13 Possible due to negative stress (see Equation 29).
0 50 100 150 200 250
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
No. of schedulings
Age sch. for planned replacement of CB
Calendar age for sch. repl.
ICBs UCBs
57 Calendar age at replacement
Calendar age at the actual replacements of the CBs, as well as the numbers of replacements of each category during the time horizon of the simulation are presented in Figures 24 and 25.
Figure 24. Age at replacement of CBs.
Figure 25. Number of replacements of CBs.
0 20 40 60 80 100 120 140
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
No. of CBs
Calendar age at replacement
Calendar age at replacement
Fail. Repl.
Sch. Repl.
0 200 400 600 800 1000 1200 1400 1600
0 1 2 3 4 5 6 7 8 9 10
No. of CBs
No. of replacements
No. of replacements
Fail. Repl.
Sch. Repl.
58 Average age at replacement
The average calendar and equivalent age respectively at replacement for each category of CBs.
Table 12. Average age at replacement for CB population.
CBs Calendar age Equivalent age
All CBs 40.7 1.38
Important CBs 43.3 1.45
Line CBs 41.4 1.39
Transformer CBs 41.8 1.40
Shunt reactor CBs 33.6 1.49
Capacitor CBs 39.7 1.40
Bus-coupler CBs 39.6 1.32
Other CBs 33.8 1.27
Average calendar age of CB population
The average calendar age of the CB population through the simulation is show-cased in Figure 26.
Figure 26. Average age of the CB population.
10 15 20 25 30
1 4 7 10 13 16 19 22 25 28 31 34 37 40
Calendar age
Year
Average calendar age [years]
ICBs All CBs
59 Five CBs’ conditions
The condition of 5 of the 1911 CBs in the population, throughout the simulation. The near-vertical sections represent a replacement of the CB. The purpose of this plot is to show examples of how CB condition may develop through the years.
Figure 27. The condition through the simulation of 5 breakers.
After replacement, breaker 1 and 3 clearly display the impact of the possibility of differing age factors, as defined in Equation 2.
0 0,2 0,4 0,6 0,8 1 1,2
1 4 7 10 13 16 19 22 25 28 31 34 37 40
CB condition
Year
Five CBs' conditions
1 2 3 4 5
