Degree project in
Claes Böös and Richard Göransson
Stockholm, Sweden 2009
XR-EE-ETK 2009:003 Electromagnetic Engineering
Second Level, 30.0 HEC
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.
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
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
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
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].
2.2.1 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.
2.2.5 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.
2.2.6 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.
Figure 4 source: [7]
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)
Figure 5 source: [7]
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]
Figure 6 source: [3]
(8) is a small change in failure rate, due to increased or decreased maintenance on a component i.
[1]
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]
Figure 7 source: [3]
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:
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
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: Null Counter:0
2 Comp: Circuit breaker 3
Sys.struct: Bus, 1,f12,2,f23,4,3,f45 Circuit breaker queue: Sw 1, Sw2 Counter:2
2 Comp: Circuit breaker1 Sys.struct:Bus,1
Circuit breaker queue: Null Counter:0
3 Comp: Circuit breaker 3
Sys.struct: Bus, 1,f12,2,f23,4,3,f45 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 Circuit breaker queue: Sw 1, Sw2,Sw3 Counter:3
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 Circuit breaker queue: Sw 1, Sw2,Sw3 Counter:3
2 Comp: 2
Sys.struct: Bus, 1,f12,2
Circuit breaker queue: Circuit breaker 1 Counter:1
2 Comp: Circuit breaker 4
Sys.struct: Bus, 1,f12,2,f23,4,3,f45,51,52 Circuit breaker queue: Sw 1, Sw2,Sw3 Counter:3
2 Comp: f23
Sys.struct: Bus, 1,f12,2,f23
3 Comp: Circuit breaker 4
Sys.struct: Bus, 1,f12,2,f23,4,3,f45,51,52
Circuit breaker queue: Circuit breaker 1 Counter:1
Circuit breaker queue: Sw 1, w2,Sw3,Sw4 Counter:4
2 Comp: 4
Sys.struct: Bus, 1,f12,2,f23,4
Circuit breaker queue: Circuit breaker 1 Counter:1
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
Circuit breaker queue: Sw1 Counter:1
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
Sys.struct: Bus, 1,f12,2,f23,4,3,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
2 Comp: Circuit breaker 2
Sys.struct: Bus, 1,f12,2,f23,4,3,f45 Circuit breaker queue: Sw1 Counter:1
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.
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.
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.
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.
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.
