Download - Reliability centered asset management toolkth.diva-portal.org/smash/get/diva2:750131/FULLTEXT01.pdf · Reliability centered asset management tool The development of RACalc Claes Böös

Degree project in

Reliability centered asset managementtool

The development of RACalc

Claes Böös and Richard Göransson

Stockholm, Sweden 2009

XR-EE-ETK 2009:003

Electromagnetic EngineeringSecond Level, 30.0 HEC

I

Abstract Electrical distribution with high delivery quality is crucial for the society. The need for high quality power supply grows as people put more trust in electrical devices. However there are no perfect electrical distribution systems and interruptions occur randomly. To reduce the risk of outage, actions can be taken by the distribution system operator in the form of preventive maintenance. This report presents some of the methods for analysis that are available for the asset manager. The methods are all connected to the area of reliability centered asset management and have been implemented in RACalc, a software tool. RACalc is able to analyze the provided electrical distribution system and point out on which components maintenance should be placed to enhance the total system performance. Depending on what properties the distribution system operator wants to enhance, different components need to be maintained. RACalc provides the answer in relation to the system performance indices SAIFI, SAIDI, CAIDI, ASAI and AENS. The calculations have been validated by building small scale systems in RACalc and comparing results with hand made calculations.

As illustrated in this report a significant theoretical improvement of the overall reliability can be achieved. By using RACalc to categorize the importance of the components in the electrical distribution system a better placement of the assets can be achieved. In the report, the results of the component importance calculation have been restricted to the twenty most significant components of the analyzed distribution systems. Furthermore, an investigation of the theoretical improvement of the overall system availability is conducted. It is shown that by reducing the failure rate on the twenty most important components found by RACalc with ten percent, the total system performance is improved by almost eight percent in average.

III

Acknowledgements We want to thank our examiner at the Royal institute of Technology Patrik Hilber for support and friendship during the project. He has been a supreme source of knowledge, tossing challenging questions and donating great ideas to the project.

Furthermore we really appreciate the support and friendship given by Carl Johan Wallnerström and Johan Setréus, both co‐supervisors at the Royal Institute of Technology for letting us disturb them in their mental blacksmith –Time after time after time.

Special thanks go to Hans Reidemar and Mikael Eriksson, supervisors at the distribution company, Sandviken Energi Elnät AB. They both gave information which enabled us to conduct a pre study that gave data for simulations made by the developed tool.

Finally, deepest appreciation to both of our families for support, love and encouragement during demanding times.

Claes Böös & Richard Göransson Stockholm, February 2009

Table of contents 1 Introduction..................................................................................................................................... 1

1.1 Background.............................................................................................................................. 1

1.2 Problem ................................................................................................................................... 3

1.3 Assumptions and delimitations ............................................................................................... 5

1.4 Definitions ............................................................................................................................... 6

2 Theory............................................................................................................................................ 10

2.1 Basic factors........................................................................................................................... 10

2.2 Sustained interruption indices .............................................................................................. 10

3 Logics of RACalc............................................................................................................................. 20

3.1 Introduction........................................................................................................................... 20

3.2 Finding the critical structure paths ....................................................................................... 21

3.3 Categorization of components .............................................................................................. 25

3.4 Implementation of system reliability indices in RACalc ........................................................ 30

3.5 Implemented simulations...................................................................................................... 32

4 Analysis.......................................................................................................................................... 38

4.1 Pre study................................................................................................................................ 38

4.2 Using RACalc to optimize asset management...........................Error! Bookmark not defined.

4.3 Using RACalc to improve asset management ....................................................................... 46

4.4 Validation of RACalc .............................................................................................................. 61

5 Case study ..................................................................................................................................... 62

5.1 Introduction........................................................................................................................... 62

5.2 Analyzed systems in case study............................................................................................. 63

6 Closure........................................................................................................................................... 74

6.1 Conclusion ............................................................................................................................. 74

6.2 Future work ........................................................................................................................... 74

References............................................................................................................................................. 76

Appendix................................................................................................................................................ 77

A. Basis for block diagram (ÄT34), taken from pre study. ................................................................................ 77

B. Components to be maintained according to RACalc (ÄT34) ........................................................................ 77

C. Basis for block diagram (MT8), taken from pre study. ................................................................................. 77

D. Components to be maintained according to RACalc (MT8) ......................................................................... 77

E. Basis for block diagram (MT10), taken from pre study. ............................................................................... 77

F. Components to be maintained according to RACalc (MT10) ....................................................................... 77

G. Graphs obtained from calculations .............................................................................................................. 77

1. Introduction Page 1

1 Introduction Electrical distribution with high delivery quality is crucial for the society. The need for a high quality power supply grows as people put more trust in electrical devices. However there are no perfect electrical distribution systems and interrupts occur randomly. Interruptions can be caused by falling trees that short circuit two phases of an overhead line or by interference from for example constructions sites. To reduce the risk of outage, maintenance actions can be taken by the distribution system operator (DSO). This thesis will provide a tool to ease the decision where to take action. The tool is based on the theory of reliability centered asset management.

1.1 Background To understand the term “Reliability Centered Asset Management” the reader should start by getting familiar with the concept of what electrical distribution system maintenance is and why it is the subject to so many thoughts and calculations.

A electrical distribution system is dependent of its components. Components such as cables, transformers and breakers. All the components in a pre‐specified area belong to a single DSO. In Sweden there are many DSO, but there is always only one acting locally. This means that there is a sort of local monopoly for the DSO. The customers living in this area cannot choose on what distribution system the power should be delivered on. This decision lies on the company owning the concession right in that area [1]. This means that the responsibility of ensuring the power supply rests on one company for each area. Hence, the customers must pay that one company for ensuring the distribution of electricity and in here lays the question; “How much compensation can a legally monopolistic company claim for their services and who are to make that decision?”

That task lands on an authority called Energy Markets Incorporate [2]. EI used until January 2009 a tool to evaluate the theoretical reliability of a company’s system. And by studying different reliability indices EI decides what rates the DSO is allowed to collect from customers [10].

The DSO can invest for example in new equipment with higher reliability or changing the medium the power is transmitted by. This is usually done by replacing overhead lines with underground cables. Another good plan for maintenance is to reduce the risk of error. Maintenance provides a tool for the DSO to manage the risk for errors or faults by making preventive maintenance or, in other cases, corrective maintenance. This has led to the consequence that the DSO needs a cost efficient maintenance plan. An optimal maintenance plan is a plan that gives the accepted delivering quality to the lowest cost. To visualize the maintenance strategy has been one of the common maintenance problems for the DSO.


Figure 1 source: [3]

This is where the asset management comes into the picture. By choosing what component should be maintained and when, different properties can be given to the power system. The costs of these operations however are not to be forgotten. Each operation has its own costs which is not always economical. Costs could also refer to factors such as interruption time, unsatisfied customers and bad publicity. How can these maintenance operations be chosen so that most values are to be gained? Depending on what system properties the DSO wants to enhance different maintenance operations should be initialized.

When the DSO orders maintenance, the company does of course want the best return of the investments made. This since a profit‐driven company is always trying to cut losses. The question is, where should the maintenance be placed to get that most value? This is one of the questions this report will try to provide an answer to. The DSO uses different kinds of reliability indices; these indices are more thoroughly described in chapter 2.2. By changing specific component data and then study the variation of the different reliability indices, a method can be developed to evaluate how each component contributes to different system properties. Doing this by hand is a time consuming task, and it is not interesting from a DSO´s point of view. By programming a computer to run different simulations for whole systems, the total analysis process will dramatically speed up.

The report has been divided between the authors in the following way; R.Goransson focused on describing the logics of the tool RACalc and described the assumptions and delimitations of the project. C.Boos focused on describing theories in the field of reliability calculations, performed the analyses of the systems and validated the results of RACalc. Both authors cooperated in writing abstract and closure. The programming of RACalc was divided so that C.Boos enabled the save/load‐function, parts of the calculation modules and the result presentation. R.Goransson has more experience of programming and saw through that the interface was functioning, the logics of algorithm was performing as it should and ensuring a flexible code.


1.2 Problem The main problems this report will revolve around are “On which components shall a DSO place maintenance efforts to maximize the return of the investment?” and “How do distribution system managers find these components?”

This master thesis presents practical methods to provide answers to both questions. As illustrated in Figure 2 there are a few more common ways to manage maintenance. Today most electrical distribution managers follow a periodic‐based maintenance schedule which means that the maintenance is ordered on regular time basis [3]. A second way of planning maintenance is by assessing the condition of a component. This means that the electricians performing the maintenance operations appreciate when the next one should be recommended. The last method which will be described in this report is based on statistics for each type of component. The method is called reliability centered maintenance and the concept revolves around preventing the most common faults at the most risk exposed components. This is expected to be an increasingly more popular method [3].

The accuracy of these predictions can always be questioned and much relies on the extent of the fault reporting. By using the latter method, simulations can be made to predict when and where interruptions are likely to occur. These predictions are made by reliability calculations, often by hand. The goal for this project is to develop a simulation tool that performs reliability calculations and ranks the included components in relation to importance for system reliability. It all comes down to know what assets are available, how much that is allowed to be spent, how and when to spend it.

Assets can be broken down to the following six forms. [3]

• Capital

• Equipment

• Employees

• Customers

• Corporate structure

• Brands

Figure 2 shows the three most commonly used preventive maintenance strategies.


With these instruments presented, the asset manager has a couple of closely linked actions to choose from. [3]

• Acquire • Maintain • Dispose • Replace • Redesign/Rebuild

Depending on what instruments are available, different actions are to be considered. To enhance the asset manager’s ability to make informed decisions based on reliability calculations, this projects main goal is to aid the asset manager to visualize the maintenance strategy and envision the maintenance goal.


1.3 Assumptions and delimitations

1.3.1 Fuses Due to the majority of short circuits that occur, the calculation method has been designed for this type of errors. The consequence of this assumption is that the fuse will not break at a fault, instead the fault has to break at the nearest circuit breaker. Hence, the fuse is only contributing with failure rate while not providing any functionality.

1.3.2 Circuit breakers are ideal The circuit breakers are not modeled with a failure rate. These are assumed to be perfect. In the calculation method the circuit breakers are not taken into consideration.

1.3.3 Redundancy The system analysis method of RACalc does not support the whole concept of redundancy; this means that the effect of redundant buses or redundant cables will not be processed in the right way. Calculations on these types of distribution systems will result in a result that is not correct.

1.3.4 Costumer interruption cost The costumer interruption cost is based on the assumption that each of the costumers connected to the distribution system will receive the minimum interruption fee.

1.3.5 Generators excluded from the analysis A generator that is connected to the distribution system is considered as either a bus or a customer. Since there generally are no generators that can operate without a bus connected to the distribution system the generators are considered as a costumer and can therefore be modeled as a transformer.


1.4 Definitions Coherence: Logically structured and connected.

Line‐scheme: A schematic specification which describes the incorporated components of a distribution system.

Radial distribution system: A distribution system with only one connection to a larger distribution system.

Redundancy: Literally it means overflow. In this text it is used in a context of an extra connection that does nothing but increases the fault tolerance of the system.

Bus: A node supplying the underlying system with power.

Infinite bus: A perfect node that never fails to supply. A common simplification when conducting calculations on a power system is that the start node is perfect.

The definitions below have been quoted from the IEEE Std 1366‐2008 [4].

Connected load: The connected transformer kVA, peak load, or metered demand (to be clearly specified when reporting) on the circuit or portion of circuit that is interrupted. When reporting, the report should state whether it is based on an annual peak or on a reporting period peak.

Distribution system: That portion of an electric system that delivers electric energy from transformation points on the transmission system to the customer.

Note:

The distribution system is generally considered to be anything from the distribution substation fence to the customer meter. Often the initial overcurrent protection and voltage regulator are within the substation fence.

Duration interruption: The period (measured in seconds, or minutes, or hours, or days) from the initiation of an interruption to a customer or other facility until service has been restored to that customer or facility. An


interruption may require step‐restoration tracking to provide reliable index calculation. It may be desirable to record the duration of each interruption.

Forced interruption: An interruption caused by a forced outage.

Interrupting device: A device capable of being reclosed whose purpose is to interrupt faults and restore service or disconnect loads. These devices can be manual, automatic, or motor‐operated. Examples may include transmission breakers, feeder breakers, line reclosers, and motor‐operated switches.

Interruption: The loss of service to one or more customers.

Note:

It is the result of one or more component outages, depending on system configuration. See: outage.

Interruptions caused by events outside of distribution: For most utilities, this type of interruption is a small percentage of the total interruptions. It will be defined here to account for the cases where outside influences are a major occurrence. Three categories that may be helpful to monitor are: transmission, generation, and substations.

Lockout: The final operation of a recloser or circuit breaker in an attempt to clear a persistent fault. The overcurrent protective device locks open their contacts under these conditions.

Loss of service: The loss of electrical power, a complete loss of voltage, to one or more customers or meters. This does not include any of the power quality issues (sags, swells, impulses, or harmonics).

Major event: A catastrophic event that exceeds design limits of the electric power system and that is characterized by the following (as defined by the utility):

a) Extensive damage to the electric power system;

b) More than a specified percentage of customers simultaneously out of service;

c) Service restoration times longer than specified.

Some examples are extreme weather, such as a one in five year event, or earthquakes.

Momentary interruption:


Single operation of an interrupting device that results in a voltage zero. For example, two breaker or recloser operations equals two momentary interruptions.


Outage (electric power systems): The state of a component when it is not available to perform its intended function due to some event directly associated with that component.

Notes:

1. An outage may or may not cause an interruption of service to customers, depending on system configuration. 2. This definition derives from transmission and distribution applications and does not apply to generation outages.

Scheduled interruption (electric power systems): A loss of electric power that results when a component is deliberately taken out of service at a selected time, usually for the purposes of construction, preventative maintenance, or repair.

Notes:

1. This derives from transmission and distribution applications and does not apply to generation interruptions. 2. The key test to determine if an interruption should be classified as a forced or scheduled interruption is as follows. If it is possible to defer the interruption when such deferment is desirable, the interruption is a scheduled interruption; otherwise, the interruption is a forced interruption. Deferring an interruption may be desirable, for example, to prevent overload of facilities or interruption of service to customers.

Step restoration: The restoration of service to blocks of customers in an area until the entire area or feeder is restored.

Sustained interruption: Any interruption not classified as a momentary event. Any interruption longer than 5 min.

2. Theory Page 10

2 Theory This Master of Science project is built on Patrik Hilbers doctoral thesis. His thesis presents a method to optimize the asset management for a power system. To do this optimization, a necessary initial step has been to create a reliability model of the power distribution system that the asset manager wishes to study.

The following is recommended to be at hand when creating a reliability model:

• Line‐scheme of the system.

• Fault and interruption statistics.

• Information on how long time maintenance personal use to operate and repair different components included in the system.

• Information on consumption and number of customers in system load points.

2.1 Basic factors These basic factors specify the data needed to calculate some of the mentioned indices. i denotes an interruption event [4].

= Restoration time for each interruption event

= Number of interrupted customers for each sustained interruption event during the reporting

period. In this report is calculated by multiplying failure rate (λ) with number of customers in the i load point. This will more thoroughly be explained in chapter 4.2.1.

= Total number of customers served for the areas

2.2 Sustained interruption indices In this chapter how to measure the performance of an electrical distribution system and component importance indices will be presented. The importance of a component is dependent of where it’s found in a system and fault and repair intensities [4].

2. Theory Page 11

2.2.1 SAIFI, System average interruption frequency index The system average interruption frequency index indicates how often the average customer experiences a sustained interruption over a predefined period of time [4].

(1)

2.2.2 SAIDI, System average interruption duration index This index indicates the total duration of interruption for the average customer during a predefined period of time. It is commonly measured in customer minutes or customer hours of interruption [4].

(2)

2.2.3 CAIDI, Customer average interruption duration index CAIDI represents the average time required to restore service [4].

(3)

2.2.4 ASAI, Average service availability index The average service availability index represents the fraction of time (often in percentage) that a customer has received power during the defined reporting period [4].

(4)

In this report the number of hours per year is assumed to be 8760.

2. Theory Page 12

2.2.5 Minimal cuts theory There are different ways to model a distribution system. One way is to use the cuts for a system. A cut is a set of components which non‐function state causes the system to fail. There is a definition called a minimal cut, which is a set of components which cannot be further reduced and remain a cut. [5]

To realize a whole system using this method paths are created to each and every load point. A path is formed using the included components enabling the power supply to a specific point in the system, and is consistently called a minimal path if it cannot be reduced further and still be a path. This will briefly be demonstrated.

Figure 3 A simple system is used to explain the cut/mean cut and path/mean path theory.

As seen in Figure 3 we have a block system. Each block represents a component, but in this set, it does not matter what type of component the blocks represent. The different components enable the system to supply the load point with power. Hence, a path to the load point is for example {1, 2, 3, 4} and the minimal paths are {1, 2, 3} or {1, 2, 4}.

If component 1 or 2 should fail; the path to the load point would be interrupted, causing the system to fail. If component 3 fails, there is still a path to the load point via component 4 and vice versa. This means that a cut for this system would be {2, 3} and the minimal cuts are thus {1}, {2} or {3, 4}. An analogy could be that each block represents a bridge crossing a river. If there are no bridges to cross, the road is interrupted.

A benefit with this way of building reliability models is that redundancy is fairly easy to model. However, minimal paths and minimal cuts are increasingly complex to find for larger systems.

2. Theory Page 13

2.2.6 Birnbaum’s importance index The first index that will be presented is Birnbaum’s reliability index.

(5)

, where is the non‐fault probability for component i, [6].

is the system non‐fault probability and can be calculated from the system structure function.


When Birnbaum’s importance measure is used on a coherent system , the two state model

probability can only enact the values 1 or 0.

With this measure, the components with the highest availability that are the most critical in a series system. For parallel systems, the most important components are the ones with lowest availability. When using Birnbaum’s importance index to determine a components importance, one should take into consideration that a components Birnbaum value is independent of its own non‐fault probability. Hence, its value is only depending on system structure and relation to other components [8].

2.2.7 Critical importance index The critical importance index is related to Birnbaum’s importance index as can be seen in equation (6).

(6)

2. Theory Page 14


This measure is useful to asset managers, when planning preventive maintenance operations.

2.2.8 The interruption cost based importance index

The interruption cost based importance index is an importance measure based on reliabilities, the expected total yearly interruption cost for each component. As will be shown, this index depends

on reliabilities indirectly, due to expected yearly interruption costs. The index is expressed in equation (7).

(7)

is the expected total yearly interruption cost for system and is the failure rate for component i. [6]


(8)

is a small change in failure rate, due to increased or decreased maintenance on a component i. [1]

2. Theory Page 15

The following relation is only valid for changes in one component at the time, which could be seen as a limitation. [9]

However, that limitation is true for the other importance indices presented in this report as well. [9]

2.2.9 Maintenance potential index The last index that will be presented is the maintenance potential importance index. It is closely

linked to the interruption cost based importance index . The mathematical expression is found in equation (9).

(9)

Where all included parameters have been defined earlier in the report. [9]

In [2], the following approximation has been noted

(10)

However, the approximation only seems valid with linear interruption costs. [9]


2. Theory Page 16

2.2.10 Example of theory To visualize the component importance indices that were described in the previous subchapters, a small system will be analyzed with each and every one of the indices. All values will be specified as thoroughly as possible.

Figure 8 shows the block diagram of a simple system used for applying theories to practice.

To perform an initial calculation of this simple system, resolve the structure formula .

The following input data is specified for the example system, shown in Table 1:

Table 1 shows the input of the reliability calculations

Name of component

Failure rate [int./year, km or pcs]

Length [km]

λ [Expected int./year]

Repair time [h]

Fault location time [h]

Total time [h]

C1 0,01 * length 2 0,0200 0,25 1,5 1,75 C2 0,001* length 0,5 0,0005 6 6 12 C3 0,009 * # pieces ‐ 0,0090 2 4 6 C4 0,009 * # pieces ‐ 0,0090 2 4 6 C5 0,001* length 0,2 0,0002 6 6 12 C6 0,01* length 1,5 0,0150 0,25 1,5 1,75

The components that is critical for each load point is shown in Table 2.

Table 2 shows the critical components for each load point.

Load point Critical components Load point 1 C1, C2 and C3 Load point 2 C1, C2, C3, C4, C5 and C6

For Load point 1 the non‐fault probability is:

2. Theory Page 17

For Load point 2 the non‐fault probability is:

Indices may be calculated, shown in Table 3.

Table 3 shows calculated importance indices for the included components.

Index C1 C2 C3 C4 C5 C6 IB for LP1 0,999993 0,999990 0,999995 N/A N/A N/A IB for LP2 0,999984 0,999980 0,999986 0,999986 0,999980 0,999983

ICR for LP1 0,36842 0,063160 0,568420 N/A N/A N/A ICR for LP2 0,19701 0,033770 0,303960 0,197010 0,197010 0,197010

When introducing costs for each load point, see Table 4, one can start making calculations on costs depending on what component that fails.

Table 4 shows specifications for the load points.

Name of component

# of Customers Average consumption [kW]

Fixed cost for interruption [SEK/f,kW]

Cost for energy not supplied [SEK/kWh]

Load point 1 (LP1) 100 500 34 169 Load point 2 (LP2) 3000 3000 2 4

The cost, in case of interruption, for the different components per hour is presented in Table 5.

Table 5 shows the cost for an interruption with the duration of one hour for each component.

Index C1 C2 C3 C4 C5 C6

Initial failure cost 500*34+3000*2 500*34+3000*2 500*34+3000*2 3000*2 3000*2 3000*2

Hourly cost 169*500+3000*4 169*500+3000*4 169*500+3000*4 3000*4 3000*4 3000*4

Fault duration 1 hour 1 hour 1 hour 1 hour 1 hour 1 hour

Total cost 23000+96500 23000+96500 23000+96500 6000+12000 6000 +12000 6000+12000

IH ∑ 119500 [SEK] ∑ 119500 [SEK] ∑ 119500 [SEK] ∑ 18000 [SEK] ∑ 18000 [SEK] ∑ 18000 [SEK]

Calculating the system reliability indices SAIFI, SAIDI, ASAI, and AENS is described in chapter 2.2 and will only be presented as values in this chapter. The studied system receives the following reliability indices, see Table 6.

Table 6 shows the results of the handmade reliability calculations.

SAIFI [int./y] SAIDI [h/y] AENS [kWh]0,0529 0,1750 0,1872

2. Theory Page 18

2. Theory Page 19

3. Logics of RACalc Page 20

3 Logics of RACalc RACalc is a computer software that has been developed to simplify the analyses that can provide a better understanding of a distribution system behavior.

3.1 Introduction RACalc was developed with the aim to simplify the large data processing which is needed when implementing the reliability analysis. The benefit is present when the distribution system is composed of many components. This software also minimizes the potential risk that exists due to human error. Although, the risk with the software is its logics that governs the calculations. A great challenge has been to try to validate the methods accuracy. The problem is to be able to guarantee the methods correctness on a general level. All methods that are of an interest for the accuracy of the calculations will be explained later on in this chapter.

RACalc has built‐in features that make construction of large system fast and easy. There is an option that forces all failure‐rates to a certain value after all components have been placed. This feature was developed during the thesis due to all components of same type, had the same failure rates and realizing that this option, of setting all failure rates afterwards, would reduce the model time. Also, much effort has been put in RACalc to make it easy to use. Only a few inputs are needed and the theory of reliability calculations is unnecessary for the user to know.

Another reason for the development of this calculation tool is that there are few available tools at present day, which can derive a prioritized list of components based on their importance for the total distribution system. This is a feature which comes in handy when dealing with a maintenance scheduling.

The benefits of RACalc are that it provides a better understanding of where the greatest improvements for the total distribution system can be made. In this case it is the prioritized list of components which is the indicator. These optimizations of the maintenance scheduling are based on a comparison of the impact a change in the failure rate has for the system reliability indices.

The purpose of RACalc is to be an easy tool for economic as well as technical analyzes of radial distribution systems. One drawback is the ability to only handle radial electrical distribution systems and the dependability of graph handling software such as Excel.


3.2 Finding the critical structure paths RACalc is based on load point‐driven reliability calculations. This means that each load point is analyzed by its dependency of each and every component. The more components the load point is relying on, the more vulnerable it becomes. One way to minimize the number of critical components is by dividing the distribution system into smaller subsystems. The circuit breaker is the component that makes this breakdown of the distribution system possible. It is automatic and so fast that the error does not spread to higher subsystems. However, a fault can affect other subsystems if the component which is in a state of fault is critical for the power flow.

The distribution system seen in Figure 9 is divided by circuit breakers (crosses) into five separate subsystem. Each subsystem except for number 1 affects none of the other subsystems. This is explained by the fact that each of the components in subsystem 1 is critical for the power flow for at least one of the other subsystems.

Figure 9 shows a distribution system and the five subsystems.

The difference between a circuit breaker and a load disconnector is that the load disconnector is not automatic and therefore not isolating the fault until manually disconnected. This means that a fault will affect the system during a shorter period of time compared to the total reparation time for the component. These components are categorized as subcritical.

The behavior of a distribution system is the fundamentals for the distribution system analysis module in RACalc. A general method taking into account all the different compositions a distribution system may consist of must be applied. The method that has been developed to meet these design criteria is shown in Figure 10.


Figure 10 shows the simplified workflow of the method for finding the critical structure paths.

The simplification of the actual workflow that is made in Figure 10 due to the complexity of the method is quite extensive.

A more detailed explanation of the method is seen below. This explanation is written to give a better insight in how the method is programmed.

1. The infinite bus must be found and enqueued in a queue which holds the next starting component.

2. The first element in the queue for the next starting component is dequeued and is set as starting component.

3. Check for a connected component.

4. If the found component is a circuit breaker, put it in the queue for circuit breakers.

5. If the found component is a disconnector, put it in the queue for disconnectors.

6. If none of 4 or 5, put the found component in the queue for the next starting component and put it in the list for the critical path.


7. Repeat from 3, until there are no more connected components to the starting component

that has not been handled.

8. Save the critical path in a queue for critical paths and enqueue it as many times as there are disconnectors in the queue for disconnectors. Clear the critical structure path and load the critical structure path by dequeuing the queue for critical paths.

9. Try to repeat from 2, if there are no components in the queue for next starting components try to dequeue the queue for disconnectors and put it in the queue for starting components.

10. If there are no components in the queue for next starting components and the trial to dequeue the queue for disconnectors failed. Try to dequeue the queue for the circuit breakers and put it in the queue for starting components.

11. Repeat from 2 until all components have been handled.

12. When done return the system list.


3.2.1 Example of critical structure path search method The purpose of this method is to achieve the critical components for each load point. An example is demonstrated below.

Figure 11 shows the system with the components names

These are the results which are achieved when applying the method that has been described on the distribution system that is shown in Figure 11. Each of the structures represent a substructure and the list from a to h represent the system list which contains the critical structure paths for the system. There are conclusions that can be made when analyzing the results below. The number of components in a substructure is not relative to the substructures place in the system list. To that, there are substructures that does not contain any transformer or load point. This however is not a negative aspect of the analysis method or the distinction of a substructure. These substructures will later be searched for transformers in the other calculation methods.

a. Bus, 1, f12

b. Bus, 1, f12, 2, 4, f23, f45

c. Bus, 1, f12, 2, 4, f23, f45, 3

d. Bus, 1, f12, 2, 4, f23, f45, 51, 52

e. Bus, 1, f12, n2722

f. Bus, 1, f12, 2, 4, f23, f45, n2789

g. Bus, 1, f12, 2, 4, f23, f45, 3, n2783


h. Bus, 1, f12, 2, 4, f23, f45, 51, 52, n2791

3.3 Categorization of components When the critical paths are at hand the next analysis will try to achieve the subcritical components for each load point. This is quite easy since a component only has three categorizes; Critical, subcritical and non critical. Non critical components are the ones that never cause a disturbance for the specified load point. Ideal components can still be critical or subcritical although they never cause a fault.

Subcritical components have a smaller impact for the availability of the load point, whilst the critical components affect the load point for the longest period of time. Typically the subcritical components will cause a fault duration that is determined by the disconnecting time for the specified component.

The assumption that has been made in this study is that the total time is only the disconnection time and not the sum of the disconnection time and the fault location time. This assumption originates from the reasoning that the fault location time can be neglected when the locating is restricted to which substructure the fault is eminent. The major part of the fault location time is imposed when locating which component in the substructure is in error state.

The method for determining the subsystems for each load point is presented below in Figure 12.

Figure 12 shows the workflow for the component categorization


A more detailed explanation of the method is seen below. This explanation is written to give a better understanding how the method is programmed.

1. Find the infinite bus and add it to a list.

2. Find the connecting component. Add it to the list if it is not a circuit breaker and repeat from step 2.

3. If the component is a circuit breaker the counter should be increased by one. The circuit breakers are then added to a queue and then try finding other connected components to the starting component (repeat from step 2).

4. If there are no more components that are not a circuit breaker. Enqueue the achieved list for the number of times described in the counter and save the list in a list at the consecutive element. Reset the counter.

5. Clear the list and load it by dequeuing the queue holding the components. Start with the first circuit breaker in the queue for the circuit breakers.

6. Repeat from step 2 until all components have been handled.

This method has a major resemblance with the method for achieving the critical structure paths. The only difference is that the division is determined by fewer components and conditions. Hence this method is a lighter version of the critical structure path analysis method.


Figure 13 shows the test system that the example analyze.


When following the detailed method description the first two substructures will be found according to Table 7. The table should be read from top to bottom and right to left.

Table 7 shows iteration with the intention to clarify the method.

1 Comp: Bus

Sys.struct :Bus

Circuit breaker queue: Null Counter:0

3 Comp: Circuit breaker 2

Sys.struct: Bus, 1,f12,2,f23,4,3,f45

Circuit breaker queue: Sw 1, Sw2 Counter:2

2 Comp:1

Sys.struct: Bus, 1




Circuit breaker queue: Sw 1, Sw2 Counter:2

2 Comp: Circuit breaker1

Sys.struct:Bus,1




Circuit breaker queue: Sw 1, Sw2,Sw3 Counter:3

3 Comp: Sw1

Sys.struct: Bus, 1

Circuit breaker queue: Sw 1 Counter:1

2 Comp: 51

Sys.struct: Bus, 1,f12,2,f23,4,3,f45,51


2 Comp: f12

Sys.struct: Bus, 1,f12

Circuit breaker queue: Sw1 Counter:1

2 Comp: 52

Sys.struct: Bus, 1,f12,2,f23,4,3,f45,51,52


2 Comp: 2

Sys.struct: Bus, 1,f12,2

Circuit breaker queue: Circuit breaker 1 Counter:1




2 Comp: f23

Sys.struct: Bus, 1,f12,2,f23





Circuit breaker queue: Sw 1, w2,Sw3,Sw4

Counter:4

2 Comp: 4

Sys.struct: Bus, 1,f12,2,f23,4


4 Structure queue: {Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52}

System list: {Bus, 1,f12,2,f23,4,3,f45,51,52}

Counter: 0

2 Comp: 3

Sys.struct: Bus, 1,f12,2,f23,4,3


5 Structure queue: {Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52

System list: {Bus,1,f12,2,f23,4,3,f45,51,52}

Circuit breaker queue: Sw2,Sw3,Sw4

Counter: 0

Comp: Circuit breaker1

2 Comp: f45


Circuit breaker queue: Sw 1 Counter:1

2 Comp: N2722

Sys.struct: Bus, 1,f12,2,f23,4,3,f45,51,52,N2722

Circuit breaker queue: Sw2,Sw3,Sw4 Counter:0




4 Structure queue: {Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52},{Bus, 1,f12,2,f23,4,3,f45,51,52

System list: {Bus, 1,f12,2,f23,4,3,f45,51,52},{ Bus, 1,f12,2,f23,4,3,f45,51,52,N2722}

Counter: 0


3.4 Implementation of system reliability indices in RACalc The different indices that are commonly used are SAIFI, SAIDI, CAIDI, ASAI and AENS. Their meaning is presented in chapter 2.2. The calculation of each index in RACalc will be presented later on in this chapter. As mentioned earlier on in the previous chapter RACalc uses a LP‐driven (load point driven) calculation method. To solve the different obstacles, which are involved at the attempt to automate a sophisticated analysis of a complex system, a fragmentation of the calculations has been applied. That means that a part of the index calculation are performed independently of each other and combined at a later instruction.

To clarify the implementation of the calculation method, an example is given. In the example it is assumed that the system analysis described in the previous chapter has been performed and the system data is at hand.

Figure 14 shows the workflow for the calculation of the systems reliability indices


A more detailed explanation of the method is seen below. This explanation is written to give a better insight in how the method is programmed.

1. Search the critical structure path for the first transformer that has not been handled. Set a pointer at the first element in the critical structure path list. Summarize the contribution of total number of clients that are connected to the selected transformer.

2. For the component at the specified element in the critical structure path list calculate the failure rate and the unavailability. Here the unavailability is the failure rate multiplied with the sum of the reparation time and the fault location time.

3. Summarize the contribution from the component to the total load point unavailability and summarize the contribution from the component to the total load point failure rate.

4. Increase the pointer for the critical structure path list.

5. Repeat from step 2 until there are no more components in the critical structure path.

6. Find the first element in the list with all the system structures which holds the specified transformer. Set a pointer at the first element in the specified system list.

7. Search for the component at the specified element in the selected system list in the critical structure path that was found in step 1.

8. If there is no hit in the search in step 7 proceed to step 9. Otherwise the pointer should be increased to the next element in the selected system list and then step 7 should be repeated.

9. Calculate the failure rate and the unavailability for the specified component. Here the unavailability is the failure rate multiplied with the disconnecting time.

10. Summarize the contribution from the component to the total load point unavailability and summarize the contribution from the component to the total load point failure rate.

11. Increase the pointer for the specified system list.

12. Repeat from step 7 until there are no more unhandled components in the specified system list.

13. Calculate the partial system reliability indices.

14. Repeat from step 2 with the next occurring transformer in the critical structure path list. Set a pointer at the first element in the specified critical structure path list. Summarize the contribution of total number of clients that are connected to the selected transformer.

15. Complete the system reliability indices calculations for the whole system.


3.5 Implemented simulations Simulations are a great help to expand the understanding of the dynamics of a distribution system. This chapter will give an insight in the simulations that have been implemented in RACalc.

3.5.1 Introduction In addition to the traditional reliability calculations that have been described earlier in this report a couple of simulation methods have been implemented as well. There are a total of four different simulation methods which can be performed to extend the analysis of the distribution systems reliability. The simulations are designed to target possible weaknesses in the distribution systems structure.

The storm simulation performs a calculation with altered failure rates for all overhead lines. Thus, an insight in the distribution systems possible reliability during such a condition can be reached. If the distribution systems dependency of underground cables is the main interest the cold simulation is most suitable. The cold simulation only increases the reparation time as an attempt to simulate the prolonging that occurs due to frost. This reasoning is due to the idea that maintenance is more demanding when working under cold circumstances.

There is also a simulation method that tries to describe the variations that exist during a year. This simulation is called 12‐month simulation and here all components failure rates is altered in such way that it corresponds to the environmental variations.


3.5.2 Storm simulation The storm simulation method is designed to measure the analyzed distribution systems dependency of overhead lines functionality. A storm simulation will result in an increase of the system reliability indices (except for the availability), which is a negative consequence. The amount of the increase is dependent of the percentage of overhead line and overhead cable in the distribution system that is being analyzed.

Figure 15 shows the workflow for storm simulation

As seen in Figure 15 the storm simulation method is just a reliability calculation where the failure rates for the overhead lines and overhead cables have been scaled by the factors that are shown in Table 8.

Table 8 shows the factors that scales the failure rates

Component type: Failure rate scale factor:

Transformer 1

Overhead line 10

Overhead cable 3

Disconnector 1

Circuit breaker 1

Underground cable 1

The scale factors that are shown in Table 8 have been derived only by assumptions and discussions. They have been set so that there is a well defined difference between the overhead lines and cables and the other components. Therefore the exact achieved system reliability indices are not at any interest, only the percentage of change that was imposed is relevant.


3.5.3 Cold simulation The frost simulation method has the purpose to show how much an increase of the reparation time embosses to the total unavailability of the distribution system that is being analyzed. Here, like in the storm simulation the simulation is nothing more than a reliability analysis with parameters changed to reflect the conditions that exist during frost. Unlike the storm simulation the frost simulation only scales the reparation time and not the failure rates. This approach is based on the reasoning that the failure rate of the underground cables is not affected by a decrease of temperature.

Figure 16 shows the workflow for frost simulation

The reparation time scale factors that are shown in Table 9 are not based on any scientific report or research. The scale parameters have been derived by discussions and reasoning that a good distinction is needed to reflect the difference between the components reparation time that is embossed by the frost.

Table 9 shows the scale factors used in the frost simulation

Component type: Reparation time scale factor:

Transformer 1

Overhead line 1,5

Overhead cable 1

Disconnector 1

Circuit breaker 1

Underground cable 10


3.5.4 12month simulation The 12‐month simulation method has its background in the desire to understand how a distribution system is affected by variations in the environmental conditions that exist during a year. This method is not fully perfected because of the manipulations that are introduced to the original distribution system. The only parameter that is scaled is the failure rate. This is however not the only parameter that change during a year. During a year the reparation time is absolutely changing.

In this study it is decided that the failure rate will be the only parameter that will be scaled in this simulation. This due to the fact that the scaling factors are derived by Patrik Hilber in his research [8]. Hence, a higher reliability in the accuracy of the method is achieved by not implementing the variations of the reparation time.

Figure 17 shows the workflow for the 12-month simulation

As mentioned earlier, the failure rate scale factors for the months in a year are presented in Table 10 and in Figure 18 shows the scale factors in a diagram.Error! Reference source not found.. The failure rate scale factors have a behavior that, at first glance, is not obvious. When calculating the medium value of the scale factors. It will be found to be equal to one. This is an important condition. If the medium value is not equal to one the overall failure rate during a year has also been changed.


Table 10 shows the scale factors that is used in the 12-month simulation

Month: Failure rate scale factor: Month: Failure rate scale factor:

January 1.11 July 1.07

February 1.05 August 0.95

March 1.12 September 0.81

April 0.93 October 0.93

May 0.83 November 1.02

June 0.93 December 1.19

Figure 18 shows the scale factors in a diagram.


3.5.5 Component importance calculation To be able to determine the most efficient maintenance schedule one must have a method to distinguish which of the components that has the greatest impact on the reliability for the system. This is a task that can be performed in many ways. Birnbaum´s index is one method that can be used to quantify the importance of the specific component. RACalc uses another method to prioritize the components. This method is easier in its implementation but yet as effective. The method uses an iterative structure where the selected component that is to be studied has had its failure rate set to zero. Thereafter a reliability calculation is executed and the results are saved. The components failure rate is reset to the previous value and the process is repeated for each of the components in the distribution system. Figure 19 show the described workflow.

Figure 19 shows the workflow of the component importance method

The results that the method provides are thereby a set of calculated system reliability indices. Each of them represents the distribution system when the referred component is ideal. To assume that a component can become ideal by increased maintenance is not relevant. Although the assumption that the improvement of the availability of the system is relative to the improvement of the availability of the component. The proportion of these improvements can be deemed as the importance of the component.

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4 Analysis This chapter will give an explanation to the process of analysis and the information that is needed when performing an analysis.

4.1 Pre study To give a real coupling of the theories to actual distribution systems a pre study has been performed. The pre study is used as a source of information giving the required input data as well as system structures. It was performed in 2008 at Sandviken Energi AB (SE).

4.1.1 Empirical method The basic premise for a pre study to be considered reliable is the degree of reliability and validity a pre study investigation meets. In other words critically examine the procedure which has been applied in the data collection.

4.1.2 Trustworthiness of study The definition of trustworthiness is assessing the degree of repeatability of the study when it is carried out under the same conditions. An important factor to achieve repeatability is by maintaining a careful documentation throughout the whole process. By continuously reviewing the documentation, high reliability is achieved. Other important factors for high trustworthiness are that measurements are carried out correctly and accurately, so that the same results can be achieved several times. Deficiencies in the trustworthiness that may arise are mainly due to the subjective assessment of the size and decisiveness on the analyzed risk. This aspect directly affects the accuracy of the index that assesses and describes the distribution system's properties.

4.1.3 Validation of study The purpose of the validation study is to get an idea of whether the study examines the elements meant to research. The approach in this study to maintaining high validity includes clear clarification on what should be studied and how the pre study proceeds. In addition, the study describes the methods and assessment tools that have been applied so that the study can be repeated. In order to ensure the validity a big effort has been to implement theories that are rooted in the theoretical frame of reference. Furthermore, re‐connection with the operating staff at SE has been a step to strengthen the validity.

4.1.4 Describing the statistical basis The system analysis included in the reliability calculations requires some type quantity that can represent the behavior of different components. The failure rate is a widely used measure. Failure rate gives an estimate of how often a component fails during a specified period of time. The standard is one year.

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Since this measure is based on statistical data the estimated failure rate can in some cases be misleading. This problem is often present due to the substandard in the available information. The credibility of the statistical value increases by the time for which the value corresponds to. However, this requires that the same type of component is studied over the period.

4.1.5 GIS Meldis The GIS system MELDIS provides an error‐reporting feature that has been used in recent years. A report describing when and where the error occurred is posted for each error. This will in the long run serve as a good source of information for future analyzes. Of course, the creditability would have been better if the statistics had stretched further back in time. Although when comparing the estimated failure rates and those handed by Elforsk the calculated failure rates were deemed as a probable estimates and will be used for the pre studies.

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4.2 Handmade calculations To assess the developed tool, a small distribution system is studied to facilitate an overview of incorporated components. The analyzed test distribution system has been retrieved from RCAM research group at Royal Institute of Technology. The line‐scheme is seen in Figure 20.

Figure 20 shows the line scheme of the test system.

In the line‐scheme the larger components and the components which properties enable the ability to maneuver the system is shown. In addition to the information provided in the line‐scheme, it has been given that faults that occur in one load point do not affect the remaining distribution system. To satisfy this condition the model could be complemented with a circuit breaker between all load points and power lines. Finally the dotted lines are, in this case, non‐isolated over head lines. The block diagram is illustrated in Figure 21. This example is retrieved from the course TillfE’s, held at KTH, example collection. TRITA‐EE_2007_067.

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Figure 21 shows a general block diagram made of the test system.

In the example it has been given how many customers that are connected to each load point and how much the total power consumption per year is at each load point. Information about what kind of cable or power line the distribution is conducted on and the length of them has been provided. To apprehend this information a search in the geographic information system (GIS) could prove to be a satisfying source. Thereafter components as underground cables, lines and load points can be modeled in a block diagram.

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When the block diagram has been created, the translation to RACalc is relatively simple. The calculations are conducted and the calculation process is fairly time efficient. Finally, the block diagram in RACalc will look something like Figure 22. Other information that is necessary is failure rates for each component type. The failure rates can be calculated by collecting data from interruption reports.

Figure 22 shows the test system’s block diagram in RACalc.

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4.2.1 Manual reliability calculations The hand‐made reliability calculations are presented in Table 11, Table 12, Table 13 and Table 14

Table 11 shows manual reliability calculations made for load point N2722.

Load point name: Komponent id

Failure rate [int./year]

Repair time [h/int.]

Fault location time [h/int.]

Total time [h/int.]

Length [km or #]

Unavailability [h/year]

N2722 Infinite bus 0 0 0 0 0 0 Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,034000 51 Disconnector 1 0 0 0 0 1 0 Consumption: N2722 0,050000 1,5 1,5 3 1 0,150000 349532 kWh Underground cable 2 0,009816 1 1,5 1 0,818 0,009816 Underground cable 3 0,004140 1 1,5 1 0,345 0,004140 Disconnector 2 0 0 0 1 1 0 Disconnector 3 0 0 0 1 1 0 Over head line 1 0,066960 0,5 0,5 1 0,558 0,066960 Over head line 2 0,111960 0,5 0,5 1 0,933 0,111960

Underground cable 4 0,000096 1 1,5 1 0,008 0,000096

∑ = 0,25657 ∑ =0,37697






Total time [h/int.]

Length [km or #]


N2789 Infinite bus 0 0 0 0 0 0 Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,034000 10 Disconnector 1 0 0 0 0 1 0 Consumption: Underground cable 2 0,009816 1 1,5 2,5 0,818 0,024540 142837 kWh Underground cable 3 0,004140 1 1,5 2,5 0,345 0,010350 Disconnector 2 0 0 0 0 1 0 Disconnector 3 0 0 0 0 1 0 N2789 0,050000 1,5 1,5 3 1 0,150000 Over head line 1 0,066960 0,5 0,5 1 0,558 0,066960 Over head line 2 0,111960 0,5 0,5 1 0,933 0,111960


∑ = 0,25657 ∑ = 0,39791

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Total time [h/int.]

Length [km or #]


N2783 Infinite bus 0 0 0 0 0 0 Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,034000 33 Disconnector 1 0 0 0 0 1 0 Consumption: Underground cable 2 0,009816 1 1,5 2,5 0,818 0,024540 183009 kWh Underground cable 3 0,004140 1 1,5 2,5 0,345 0,010350 Disconnector 2 0 0 0 0 1 0 Disconnector 3 0 0 0 0 1 0 Over head line 1 0,066960 0,5 0,5 1 0,558 0,066960 N2783 0,050000 1,5 1,5 3 1 0,150000 Over head line 2 0,111960 0,5 0,5 1 0,933 0,111960


∑ = 0,25657 ∑ = 0,39791






Total time [h/int.]

Length [km or #]


N2791 Infinite bus 0 0 0 0 0 0 Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,03400 13 Disconnector 1 0 0 0 0 1 0 Consumption: Underground cable 2 0,009816 1 1,5 2,5 0,818 0,02454 74220 kWh Underground cable 3 0,004140 1 1,5 2,5 0,345 0,01035 Disconnector 2 0 0 0 0 1 0 Disconnector 3 0 0 0 0 1 0 Over head line 2 0,111960 0,5 0,5 1 1 0,11196 Underground cable 4 0,000096 1 1,5 2,5 0,558 0,00024 N2791 0,05 1,5 1,5 3 0,933 0,15000

Over head line 1 0,066960 0,5 0,5 1

0,008

0,06696

∑ = 0,25657 ∑ = 0,39805

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By using the formulas from chapter 2.2 the calculation of the reliability indices were performed. The following values were derived.

These manual calculations will form the basis of quality control of the developed tool. As will be shown in chapter 4.4, the calculations where performed with good accuracy by RACalc.

When the DSO wants to see what component in the example system that provides the desired improvement when maintained, the asset manager can use the “Component sensitivity analysis” which is one of the available calculation alternatives. By doing this, RACalc will perform the calculation explained in chapter 3.3. The results will be the different reliability indices and presenting new values to these indices based on the “perfect behavior” of the optimized component.

RACalc is based on analytical reliability calculation methods [7].

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4.3 Using RACalc to improve asset management To explain how to use the software RACalc, images taken when using RACalc and a systematic description of the usage will be provided.

First, start the program by clicking the icon. Thereafter should the information specified in chapter 0 be present so that necessary data can be collected and extracted. When this fundamental information is in place, the system can be modeled.

For the system to be realized in the software there must be an infinite bus which represent the strong transmission system. In RACalc, the infinite bus is a perfect component that never fails, and can be found in the component list at the top of the screen. The infinite bus is orange and can be seen in Figure 23. Unfortunatly, the analysis tool cannot handle redundant systems therefore only radial electrical distribution systems are possible to study.

Start by adding an infinite bus on the workspace. Press the orange icon and click on the white area called workspace. The infinite bus can be put anywhere on the workspace.

Figure 23 shows the available components in the upper left corner. From the left there are transformer, ground cable, over head line, disconnector, isolated over head line, fuse, radio-controlled disconnector, infinite bus and breaker.

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Then the components that are part of the system are to be modeled. This is done, by looking at the information of the system, the line‐scheme or the data found in the GIS. In this example, the first component is a ground cable with a length of 300 meters. The underground cable is red in RACalc. It can be found at the same place as the infinite bus. Deploy it in the system the same way as with the infinite bus. First press the red icon and click somewhere close to the infinite bus. When the underground cable has been placed on the workspace, one wants to change its properties. To alter the properties of a component, right‐click on the placed underground cable and choose “Ändra komponentegenskaper”. This is shown in Figure 24. What happens next is that a window will appear and show that specific components properties. This underground cable has a failure rate of 0,02 faults per year and a total fault time of 4 hours.

Name of the component can be chosen freely, in this case the name has been chosen to Underground cable 1. When the correct values are set, press “Ok” and the settings will be saved. This window is shown in Figure 25.

Figure 24 shows the workspace and two components. The user is in this case about to change the properties of a ground cable.

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Connected to the first Underground cable there is a load point called N2722. Given in the example specification is that faults that occur in one load point does not affect other load points. This implies that a breaker is added in front of the load point. A breaker is in line‐schemes usually described as a cross, which it also is in RACalc. This component is found in the list among the rest of the components. To connect two components, the user must press the “c”‐button. To easier remember this, c can stand for connect. First press “c” then click at the two components that are supposed to be connected.

A load point has in data such as name, failure rate, fault location time, repair time, number of customers and yearly consumption. A load point is yellow in RACalc.

After that, there is supposed to be a disconnector. It has been given that the disconnectors are maneuvered in one hour. In the same fashion as described earlier, the user choose a disconnector to be placed, the blue icon, places it on the workspace, alter the properties and connects it to the other modeled components.

Hereafter it is just to model the remaining system in the same way as earlier described.

When the user considers him or her to be finished with the model, it is recommended to save the system. This is done by clicking at the file‐menu and choosing the “Spara som” alternative. By doing this, RACalc will save a survey picture of the modeled system and of course all the incorporated components coordinates, component types, properties etcetera.

Figure 25 shows the window for component information input.

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Finally, when the model is finished; all wanted components are incorporated and their properties are set, the user can press the “Action”‐menu and choose calculate. A window will appear, see Figure 26, and show different calculation options. First option is the ordinary reliability calculation. These calculations are the ones described in chapter 4.2.1.

Next is the component sensitivity analysis, which is described in chapter 0. Finally there are different scenarios which can be simulated. The ones chosen is a representation over a 12 month period, based on Patrik Hilber’s research [3], “Storm” and “Extreme cold” based on discussions with Sandviken Energi Elnät AB and supervisors on Royal Institute of Technology.

Figure 26 shows the window where the user chooses what calculations are to be made.

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Figure 27 shows the window in RACalc that displays the output-data.

When desired calculations have been chosen, the user press ”Ok”‐button and RACalc will start analyzing the system with algorithms described in chapter 3.2 and in the end a window with results will be shown, Figure 27.

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4.3.1 Results from RACalc The result of the example will according to RACalc be as presented in

Table 15.

Table 15 shows the output from RACalc for test system, transferred to an Excel-table.

KomponentnamnFelfrekvens[fel/år,km]

Felsökningstid[h]

Reparations‐tid [h]

Total tid [h]

Längd[km]

Otillgänglighet[h/år]

Lastpunkts namn: N2722 Infinite bus 0 0 0 0 0 0

Antal kunder: 51 st Underground

cable 1 0,0136 1 1,5 2,5 0,68 0,034

Effektförbrukning: 349532 kWh Disconnector 1 0 0 0 0 1 0

Avbrottskostnad (12<t<24 [h]): 45900 kr N2722 0,05 1,5 1,5 3 1 0,15

Avbrottskostnad (24<t<48 [h]): 91800 kr




ENS i lastpunkten: 15,04 Disconnector 2 0 0 0 1 1 0

Del‐SAIFI: 13,085172 Disconnector 3 0 0 0 1 1 0

Del‐SAIDI: 19,225572 Over head line

1 0,06696 0,5 0,5 1 0,558 0,06696

h(p(i)): 0,9999927397348887637872438023

Over head line 2 0,11196 0,5 0,5 1 0,933 0,11196

Underground

cable 4 0,000096 1 1,5 1 0,008 0,000096

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Felsökningstid[h]


Total tid [h]

Längd[km]




cable 1 0,0136 1 1,5 2,5 0,68 0,034



Underground cable 2 0,009816 1 1,5 2,5 0,818 0,02454



Avbrottskostnad (48<t<72 [h]): 27000 kr Disconnector 2 0 0 0 0 1 0


Del‐SAIFI: 2,565720 N2789 0,05 1,5 1,5 3 1 0,15

Del‐SAIDI: 3,9790600 Over head line

1 0,06696 0,5 0,5 1 0,558 0,06696

h(p(i)): 0,9999911465963000987991954165

Over head line 2 0,11196 0,5 0,5 1 0,933 0,11196

Underground

cable 4 0,000096 1 1,5 1 0,008 0,000096

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Felsökningstid[h]


Total tid [h]

Längd[km]




cable 1 0,0136 1 1,5 2,5 0,68 0,034



Underground cable 2

0,009816 1 1,5 2,5 0,818 0,02454


Underground cable 3

0,00414 1 1,5 2,5 0,345 0,01035


Disconnector 2 0 0 0 0 1 0


Del‐SAIFI: 8,466876 Over head line

1 0,06696 0,5 0,5 1 0,558 0,06696

Del‐SAIDI: 13,1308980 N2783 0,05 1,5 1,5 3 1 0,15

h(p(i)): 0,9999835028283576229710429514

Over head line 2

0,11196 0,5 0,5 1 0,933 0,11196

Underground

cable 4 0,000096 1 1,5 1 0,008 0,000096

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Felsökningstid[h]


Total tid [h]

Längd[km]




cable 1 0,0136 1 1,5 2,5 0,68 0,034






Avbrottskostnad (48<t<72 [h]): 35100 kr Disconnector 2 0 0 0 0 1 0


Del‐SAIFI: 3,335436 Over head line

2 0,11196 0,5 0,5 1 0,933 0,11196

Del‐SAIDI: 5,1746500 Underground

cable 4 0,000096 1 1,5 2,5 0,008 0,00024

h(p(i)): 0,9999783549288690432098661979 N2791 0,05 1,5 1,5 3 1 0,15

Over head line

1 0,06696 0,5 0,5 1 0,558 0,06696

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As can be seen, the values presented in

Table 15,

Table 16,

Table 17 and

Table 18 is a perfect match of the handmade calculations made in chapter 4.2.1.

The reliability indices acquired from the test distribution system are according to RACalc shown in Table 19.

Table 19 shows the reliability indices for test system, calculated by RACalc.

SAIFI [int./y] SAIDI [h/y] CAIDI [h/int.] ASAI ENS [kWh] AENS [kWh] 0,25657 0,38794 1,51203 0,999955 33,21 0,31042

If the user copies the values given from RACalc to a table managing software, for example Microsoft Excel, graphs can be created to easier grasp the results.

Here are examples of results extracted from RACalc. Interruption costs for each load point during different time intervals t, shown in Graph 1.

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Graph 1 shows the most significant components affecting SAIFI for test system.

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Component importance results

In this chapter the results of the component importance analysis will be presented. In this small system all components are shown in the graphs which lead to the fact that some components do not contribute to a better reliability of the system, when they are optimized. This is due to the fact that they, from the beginning, are considered to never fail.

Graph 2 shows the most significant components affecting SAIFI for test system.

From Graph 2 it can be seen that the components affecting SAIFI are the over head lines in the system. By securing these components the number of faults will decrease dramatically leading to a better availability of the system.

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Graph 3 shows the most significant components affecting SAIDI for test system.

In Graph 3 it is evident that the component affecting SAIDI the most is one of the over head lines. When studying Graph 4 it is also giving an indication for the importance of maintaining the over head line.

Graph 4 shows the most significant components affecting CAIDI for test system.

CAIDI is a measure depending on the earlier mentioned measures SAIFI and SAIDI. Even if the reliability of the system generally has been better, it is not obvious that this measure is lower. CAIDI is a measure that reflects how long each outage lasts. Even if there are fewer faults, the faults occurring may last longer. As seen in Graph 4 all reliability measures are not comparable. This is

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easiest explained by a small example. If a system consist of two components were both components fail one time each year. The first component, C1, has a total time of one hour while the other component, C2, has a total time of 100 hours. The mathematical explanation is that if a load point with one customer is connected to these components and C1 becomes optimized the new CAIDI will increase with almost 100 %, despite a total improvement of the system reliability.

The resemblance can be seen in Table 20.

Table 20 shows an example of the CAIDI index and how an outcome can be if a component is set to be perfect.

With explained, it is realized that CAIDI is not a measure that necessary describes the reliability of the system as SAIFI and SAIDI, only how long a fault is averaged to last when it occurs.

Graph 5 shows the most significant components affecting ASAI for test system.

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To improve the ASAI index at a big scale is difficult when dealing with single components. In this measure, components with high failure rate and long total time stand out if there is a bigger change. In Graph 5 one can see that the over head line has biggest impact on the ASAI index.

Graph 6 shows the most significant components affecting AENS for test system.

Another of measures that can be extracted from RACalc is AENS. This measure declares the delivering quality of the system and the components affecting it. For this distribution system, once again it is the over head line that clearly has biggest impact on the AENS index.

By studying these graphs, the DSO can allocate the maintenance depending on what reliability measure that is needed to be improved.

12‐month simulation results

One of the simulation alternatives is the 12‐months simulation. This calculation takes in consideration an altered failure rate for each month of the year.

The scale factors are based on Patrik Hilber’s research of time based failure rates and how they are distributed over a year. The distribution can be seen in Graph 7. [3].

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Graph 7 shows the 12-month distribution of the different reliability indices for the test system.

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4.4 Validation of RACalc To be able to guarantee the correctness of the reliability indices and other results that RACalc produces a comparison with results that have been calculated by hand has been performed. The distribution system that will be evaluated is illustrated in Figure 28.

Figure 28 illustrates the distribution system used for validation.

To validate the results acquired from RACalc, this chapter will present a comparison between the hand‐made calculations performed in chapter 4.2.1 and the output from RACalc presented in chapter 4.3.1. The results are presented in Table 21, Table 22.

Table 21 Results acquired from hand-made calculations.


Table 22 Results acquired from RACalc.


The results are the same andvalidates RACalc and the algorithm that perform the calculations.

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5 Case study Case studies have been performed on some parts of the electrical distribution system that is owned by SEEAB. The calculations and results are all achieved by using RACalc.

5.1 Introduction To ease the survey of these systems, information from the pre study is shown. The analyzed distribution systems are classified and therefore not official. Hence, the case study chapter will be censured when this report are published.

The areas that are to be analyzed with RACalc are situated in the vicinity of Sandviken. In Figure 29, Figure 30 and Figure 31 a survey view of each area is provided. In Figure 32, Figure 33 and Figure 34 the line schemas that were obtained during the pre study is illustrated. These systems are also presented as block schemes from RACalc in Figure 35, Figure 36 and Figure 37.

There are two result chapters for the case study. The purpose of this is to distinguish the result that has been derived by using RACalc and those not derived by RACalc. The results derived by RACalc are presented as charts which were composed by using Excel. An interesting result for this case study is that by decreasing the failure rate of the twenty most important components by 10% a total system improvement were obtained which is illustrated in Table 23, Table 24 and Table 25.

Table 23 show the improvements for ÄT34:s reliability indices when decreasing the failure rate by 10% of the twenty most important components according to RACalc.

SAIFI [int./y] SAIDI [h/y] CAIDI [h/int.] ASAI AENS [kWh] 8,11% 8,27% 0,18% 0,0015% 8,22%

Table 24 show the improvements for MT8:s reliability indices when decreasing the failure rate by 10% of the twenty most important components according to RACalc.

SAIFI [int./y] SAIDI [h/y] CAIDI [h/int.] ASAI AENS [kWh] 7,32% 7,10% ‐0,24% 0,0016% 7,21%

Table 25 show the improvements for MT10:s reliability indices when decreasing the failure rate by 10% of the twenty most important components according to RACalc.


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5.2 Analyzed systems in case study The systems analyzed in this thesis are geographically represented in figure 29, figure 30 and figure 31

Figure 29 shows a geographical view of the system departing from ÄT34.

Figure 30 shows a geographical view of the system departing from MT8.

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Figure 31 shows a geographical view of the system departing from MT10.

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When gathering information about the system, the line scheme posses a great deal of information. The following line schemes were apprehended at Sandviken Energi AB for the systems to be analyzed.

Figure 32 shows the line scheme of ÄT34. Altered figure due to classified contents.

Figure 33 shows the line scheme of MT8. Altered figure due to classified contents.

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Figure 34 shows the line scheme of MT10. Altered figure due to classified contents.

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When modeling the systems in RACalc, the following graphical representation of the systems is shown in figure 35, figure 36 and figure 37.

Figure 35 shows the block diagram of ÄT34, modeled in RACalc.

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Figure 36 shows the block diagram of MT8, modeled in RACalc.

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Figure 37 shows the block diagram of MT10, modeled in RACalc.

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5.2.1 Results from RACalc

Table 26 shows the reliability indices of ÄT34, calculated in RACalc.

SAIFI [int./y] SAIDI [h/y] CAIDI [h/int.] ASAI AENS [kWh] 1,594 1,615 1,013 0,99981 1,486

Table 27 shows the reliability indices of MT8, calculated in RACalc.


Table 28 shows the reliability indices of MT10, calculated in RACalc.


5.2.2 Results after improvements Due to the fact that some components have a big impact on one reliability index, for example SAIFI, while other components contributes more to an improvement in another index, for example SAIDI. A method to determine the overall importance has been developed.

By summarizing the improvements of SAIFI, SAIDI, ASAI and AENS for each component that were calculated by the component importance calculation method in RACalc a categorization can be made. The formula for determining the total improvement is shown below.

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Graph 8 shows the sum of improvements for each component, SAIFI, SAIDI, ASAI, AENS.


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The components that have been determined to be the twenty most significant components for the total improvements of the systems are displayed in Appendix B, Appendix D and Appendix F. The numbers in the blocks represents the importance were 1 has highest total improvement capability.

If the DSO were to maintain the twenty most influential components and by doing so decreasing the failure rate of those components by 10 % a total improvement of the reliability indices would be achieved as stated in Graph 9, Graph 10 and Graph 8.

Table 29 show the improvements for ÄT34:s reliability indices when decreasing the failure rate by 10% on the twenty most important components according to RACalc.


Table 30 show the improvements for MT8:s reliability indices when decreasing the failure rate by 10% on the twenty most important components according to RACalc.

SAIFI [int./y] SAIDI [h/y] CAIDI [h/int.] ASAI AENS [kWh] 7,32% 7,10% ‐0,24% 0,0016% 7,21%

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Table 31 show the improvements for MT10:s reliability indices when decreasing the failure rate by 10% on the twenty most important components according to RACalc.


Figure 38 shows the total improvement in percent for the different reliability indices at each system.

6. Closure Page 75

6 Closure

6.1 Conclusion The thesis presents a tool, RACalc. RACalc is able to analyze the provided electrical distribution system and point out on which components maintenance should be placed on in order to enhance the total system performance. There is a need for this type of tool; due to there might be money to be saved when acquiring a more efficient maintenance plan. In addition to component sensitivity analysis, the scenarios included in the tool can be helpful to point out potential weaknesses in the system. This is useful support when performing risk analysis of electrical distribution systems. Depending on what properties the DSO wants to enhance, different components need to be maintained. RACalc provides the answer in relation to the performance indices SAIFI, SAIDI, CAIDI, ASAI and AENS.

The major advantages with RACalc are that it makes reliability calculations easy and fast. This is achieved by:

• Limiting the demand of the end‐user’s reliability calculation skills.

• Enabling a graphical interface that eases the survey of the system.

• Using a fast algorithm that represent how an electrical distribution system responds to different interruptions.

• Requiring few inputs.

• Performing component sensitivity analysis and presenting where in the system maintenance should be placed to enhance the performance of the system.

• Presenting results directly when calculation is complete.

The calculations have been validated by building small scale systems in RACalc and comparing results with hand made calculations. Discussions have also been held with supervisors and examiner to ensure the quality of the calculations.

6.2 Future work RACalc is depending on a table handling software, for example Microsoft Excel. Without the ability to transform the values to graphs, the results are hard to interpret.

The fact that fuses so far not respond to an interruption in the algorithm is important. This fact has a big impact on the system model since the fuse does not contribute with any real function in the model except for introducing another possible failure position. They are modeled to support future work with this software and have been set as ideal. In this way the fuse does not affect the overall availability of the system.

A future feature in RACalc which is fairly easy implemented is a present value analysis. There is already an option available to choose component type. For example overhead line can be chosen as

6. Closure Page 76

five different FEAL, with different dimensions. An application can be added that correlate the specific component type to an acquisition value, date of construction and calculates a present value for the specific component.

In addition there is a vision of implementing redundancy capability in RACalc. The absence of possibility for redundancy calculations has not posed as a problem for the case studies since none of the analyzed distribution systems have a second feeding bus.

A more complex way to model a system is explained in chapter 2.2.5. An even more advanced method is presented in [8], where an algorithm for searching all multi‐state minimal cuts is presented. The authors see great potential in the algorithm. Using this methodology, the redundancy issue is solved although the code to the tool RACalc would be forced to be significantly modified. The implementation of the algorithm presented in [8] not only solves the redundant feed calculation problem but also the more complex redundant cable calculation. This would add further usefulness of the tool RACalc by making it more agile.

References Page 77

References [1]. Hans Olander. Energimarknadsinspektionen. http://www.energimarknadsinspektionen.se. [Online] [retrieved: 16 02 2009.] http://www.energimarknadsinspektionen.se/upload/Enheter/N%C3%A4t/Koncessioner%20f%C3%B6r%20kraftledningar.pdf.

[2]. Energimarknadsinspektionen. [Online] [retrieved: 12 1 2009.] http://www.energimarknadsinspektionen.se/For‐Energiforetag/El/Inrapportering‐for‐elnatsforetag/Natnyttomodellen/.

[3]. Hilber, Patrik. Maintenance Optimization for Power Distribution Systems. Stockholm : KTH, 2008 TRITA‐EE_2008_012.

[4]. Bertling, Lina. Reliability‐centred maintenance for electric power distribution systems. Stockholm : KTH, 2002.

[5]. Hilber, Patrik. A Method for Extracting Reliability Importance Indices from Reliability Simulations of Electrical Networks. Stockholm : Royal Instititute of Technology, 2005.

[6]. Bertling, Lina. http://www.etk.ee.kth.se. [Online] [retrieved: 16 2 2009.] http://www.etk.ee.kth.se/courses/EI2450/A‐ETS‐EEK‐0501.pdf.

[7]. Patrik Hilber, Lina Bertling. Monetary Importance of Component Reliability in Electrical Networks for Maintenance Optimization. IEEE, 2004. 8th lnternational Conference on Probabilistic Methods Applied to Power System.

[8]. Wei‐Chang Yeh IEEE. A Fast Algorithm for Searching All Multi‐State Minimal Cuts Member. Taiwan : IEEE, 2008.

[9]. Guide for Electric Power Distribution Reliability Indices., IEEE Power Engineering Society. IEEE. SS95193.

[10]. Wallnerström, Carl Johan. On Risk Management of Electrical Distribution Systems and the Impact of Regulations. Stockholm : KTH, 2008. ISBN 978‐91‐7178‐954‐9.

Appendix Page 78

Appendix

A. Basis for block diagram (ÄT34), taken from pre study.

B. Components to be maintained according to RACalc (ÄT34)

C. Basis for block diagram (MT8), taken from pre study.

D. Components to be maintained according to RACalc (MT8)

E. Basis for block diagram (MT10), taken from pre study.

F. Components to be maintained according to RACalc (MT10)

G. Graphs obtained from calculations

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