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Combining risk and uncertainty in technical systems
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering. (RCAM)ORCID iD: 0000-0002-2462-8340
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering. (RCAM)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The risk matrix is tool for making decision about technical system such as prioritising of maintenance. It is used in methods such as FMEA (failure mode and effect analysis) and it is based on the definition of risk as the product of the probability of a certain failure and its consequence.

The problem with the standard formulation is that the probability is not always completely known. The uncertainty of the probability can be estimated by its variance. %We suggest that the the mean value plus the standard deviation times a factor could be used instead of just the mean value.

Instead of a specific value for the probability of failure, a beta distribution is used for the probability. The main point is to find a trade-off between mean and variance. In this case we want to avoid probabilities larger than the mean. We use a loss function taking into account only the right tail starting at a factor times the mean. The exponent of the deviation is 0. We have calculated how much a decreasing variance should compensate for an increasing mean. We get an approximate relation between the quotient of variances and the quotient of means.

The conclusion is that this model should be investigated further.

Keywords [en]
risk analysis, decision making, reliability, risk matrix, beta distribution
National Category
Probability Theory and Statistics
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-214982OAI: oai:DiVA.org:kth-214982DiVA, id: diva2:1145077
Projects
RCAM
Funder
SweGRIDS - Swedish Centre for Smart Grids and Energy Storage
Note

QC 20170928

Available from: 2017-09-27 Created: 2017-09-27 Last updated: 2022-06-27
In thesis
1. Condition measuring and lifetime modelling of disconnectors, circuit breakers and other electrical power transmission equipment
Open this publication in new window or tab >>Condition measuring and lifetime modelling of disconnectors, circuit breakers and other electrical power transmission equipment
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The supply of electricity is important in modern society, so the outages of the electric grid should be few and short, especially for the transmission grid. A summary of the history of the Swedish electrical system is presented. The objective is to be able to plan the maintenance better by following the condition of the equipment.

The risk matrix can be used to choose which component to be maintained. The risk matrix is improved by adding a dimension, the uncertainty of the probability. The risk can be reduced along any dimension: better measurements, preventive maintenance or more redundancy. The number of dimensions can be reduced to two by following iso-risk lines calculated for the beta distribution.

This thesis lists twenty surveys about circuit breakers and disconnectors, with statistics about the failures and the lifetime. It also presents about forty condition-measuring methods for circuit breakers and disconnectors, mostly applicable to the electric contacts and the mechanical parts.

A method for scheduling thermography based on analysis of variance of the current is tried. Its aim is to reduce the uncertainty of thermography and it is able to explain two thirds of the variation using the time of the day, the day of the week and the week number as explanatory variables. However, the main problem remains as the current is in general too low.

A system with IR sensors has been installed at the nine contacts of six disconnectors with the purpose of avoiding outages for maintenance if the contacts are in a good condition. The measured temperatures are sent by radio and regressed against the square of the current, the best exponent found. The coefficient of determination $R^2$ is high, greater than 0.9. The higher the regression coefficient is, the more heat is produced at the contact. So this ranks the different contacts.

Finally a framework for lifetime modelling and condition measuring is presented. Lifetime modelling consists in associating a distribution of time to failure with each subpopulation. Condition measuring means measuring a parameter and estimating its value in the future. If it exceeds a threshold, maintenance should be carried out. The effect of maintenance of the contacts is shown for four disconnectors.

An extension of the risk matrix with uncertainty, a survey of statistics and condition monitoring methods, a system with IR sensors at contacts, a thermography scheduling method and a framework for lifetime modelling and condition measuring are presented. They can improve the planning of outages for maintenance.

Finally a framework for lifetime modelling and condition measuring is presented. Lifetime modelling consists in associating a distribution of time to failure with each subpopulation. Condition measuring means measuring a parameter and estimating its value in the future. If it exceeds a threshold, maintenance should be carried out. The effect of maintenance of the contacts is shown for four disconnectors.

An extension of the risk matrix with uncertainty, a survey of statistics and condition monitoring methods, a system with IR sensors at contacts, a thermography scheduling method and a framework for lifetime modelling and condition measuring are presented. They can improve the planning of outages for maintenance.

Abstract [sv]

Elförsörjningen är viktig i det moderna samhället, så avbrotten bör vara få och korta, särskilt i stamnätet. En kortfattad historik över det svenska elsystemet presenteras. Målet är att kunna planera avbrotten för underhåll bättre genom att veta mera om apparaternas skick.

Det är svårt att planera avbrott för underhåll och utbyggnad. Riskmatrisen är verktyg för att välja vad som ska underhållas och den kan förbättras genom att lägga till en dimension, sannolikhetens osäkerhet. Risken kan minskas längs med varje dimension: bättre mätningar, förebyggande underhåll och mer redundans. Antalet dimensioner kan igen bli två genom att följa linjer med samma risk, som är beräknade för betafördelningen.

Denna avhandling tar upp tjugo studier av fel i brytare och frånskiljare med data om felorsak och livslängd. Den har också en översikt av ett fyrtiotal olika metoder för tillståndsmätningar för brytare och frånskiljare, som huvudsakligen rör de elektriska kontakterna och de mekaniska delarna.

Ett system med IR sensorer har installerats på de nio kontakterna på sex frånskiljare. Målet är att minska antalet avbrott för underhåll genom att skatta skicket när frånskiljarna är i drift. De uppmätta temperaturerna tas emot genom radio och behandlas genom regression mot kvadraten av strömmen, då den bästa exponenten för strömmen visade sig vara 2,0. Förklaringsfaktorn $R^2$ är hög, över 0,9. För varje kontakt ger det en regressionskoefficient. Ju högre koefficienten är, desto mer värme utvecklas det i kontakten, vilket kan leda till skador på materialet. Koefficienterna ger en rangordning av frånskiljarna. Systemet kan också användas för att minska eller öka den tillåtna strömmen baserat på skicket.

Slutligen förklaras ett ramverk för livslängdsmodellering och tillståndsmätning. Livslängdsmodellering innebär att koppla en fördelning för tiden till fel med varje delpopulation. Med tillståndsmätning avses att mäta en parameter och skatta dess värde i framtiden. Om den överskrider en tröskel, måste apparaten underhållas. Effekten av underhåll visas för fyra frånskiljare.

En utveckling av riskmatrisen med osäkerheten, en sammanställning av statistik och metoder för tillståndsövervakning, ett system med IR-sensor vid kontakerna, en metod för termografiplanering och ett ramverk för livslängdsmodellering och tillståndsmätningar presenteras. De kan förbättra avbrottsplaneringen.

Abstract [es]

El suministro de energía eléctrica es importante en la sociedad moderna. Por eso los cortes eléctricos deben ser poco frecuentes y de poca duración, sobre todo en la red de transmisión. Esta tesis resume la historia del sistema eléctrico sueco. El objetivo es planificar los cortes mejor siguiendo la condición de los aparatos.

La matriz de riesgo se utiliza muchas veces para escoger en qué aparatos debería realizarse mantenimiento. Esta matriz se puede mejorar añadiendo una dimensión: la incertidumbre de la probabilidad. El riesgo puede ser disminuido siguiendo cada una de las tres dimensiones: mejores mediciones, mantenimiento preventivo y mayor redundancia. El número de dimensiones puede reducirse siguiendo líneas del mismo riesgo calculadas para la distribución beta.

Esta tesis presenta veinte estudios de fallos en interruptores y seccionadores con datos sobre la causa y el tiempo hasta la avería. Contiene también una visión general de cuarenta métodos para medir la condición de seccionadores e interruptores, aplicables en su mayoría a los contactos eléctricos y los componentes mecánicos.

Se ha instalado un sistema con sensores infrarrojos en los seis contactos de nueve seccionadores. El objetivo es disminuir los cortes de servicio para mantenimiento, estimando la condición con el seccionador en servicio. Las temperaturas son transmitidas por radio y se hace una regresión con el cuadrado de la corriente, ya que el mejor exponente de la corriente resultó ser 2,0. $R^2$ alcanza un valor de 0,9 indicando un buen ajuste de los datos por parte del modelo. Existe un coeficiente de regresión para cada contacto y este sirve para ordenar los contactos según la necesidad de mantenimiento, ya que cuanto mayor sea el coeficiente más calor se produce en el contacto.

Finalmente se explica que el modelado de tiempo hasta la avería consiste en asignar una distribución estadística a cada equipo. La monitorización del estado consiste en medir y estimar un parámetro y luego predecir su valor en el futuro. Si va a sobrepasar un cierto límite, el equipo necesitará de mantenimiento. Se presenta el efecto de mantenimiento de cuatro seccionadores.

Un desarrollo de la matriz de riesgo, un conjunto de estadísticas y métodos de monitoreo de condición, un sistema de sensores IR situados cerca de los contactos, en método de planificación de termografía y un concepto para explicar la modelización de tiempo hasta la avería y de la monitorización de la condición han sido presentados y hace posible una mejor planificación de los cortes de servicio.

Place, publisher, year, edition, pages
Stockholm: Kungliga Tekniska högskolan, 2017. p. 78
Series
TRITA-EE, ISSN 1653-5146 ; 2017:134
Keywords
reliability, maintenance, condition monitoring, disconnector, circuit breaker, Weibull distribution, prediction, risk analysis, decision making, beta distribution
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-214984 (URN)978-91-7729-543-3 (ISBN)
Public defence
2017-10-23, Kollegiesalen, Brinellvägen 8, Stockholm, 13:15 (English)
Opponent
Supervisors
Funder
SweGRIDS - Swedish Centre for Smart Grids and Energy Storage
Note

QC 20170928

Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2022-06-27Bibliographically approved

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