SUBSTATION BUS ARRANGEMENT PERFORMANCE ANALYSIS PROGRAM AND
METRICS
Trevor Martin Oneal
B.S., University of California Davis, 2008
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONIC ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
SPRING
2011
© 2011
Trevor Martin Oneal
ALL RIGHTS RESERVED
ii
SUBSTATION BUS ARRANGEMENT PERFORMANCE ANALYSIS PROGRAM AND
METRICS
A Project
by
Trevor Martin Oneal
Approved by:
__________________________________, Committee Chair
Mohammad Vaziri, Ph.D., P.E.
__________________________________, Committee Member
Fethi Belkhouche, Ph.D.
____________________________
Date
iii
Student: Trevor Martin Oneal
I certify that this student has met the requirements for format contained in the University format
manual, and that this project is suitable for shelving in the Library and credit is to be awarded for
the project.
__________________________, Graduate Coordinator
Preetham B. Kumar, Ph.D.
Department of Electrical and Electronic Engineering
iv
___________________
Date
Abstract
of
SUBSTATION BUS ARRANGEMENT PERFORMANCE ANALYSIS PROGRAM AND
METRICS
by
Trevor Martin Oneal
During preliminary substation design, only minimal information is available to the
designer. Substation bus arrangements have been defined in textbooks for their advantages and
disadvantages. However, the exact level of superiority/inferiority of one design as compared to
another is definitely unclear. In this project, a Visual Basic for Applications (VBA) program
imbedded in a Microsoft Excel Spreadsheet has been developed to give a user easily comparable
data. The program requires minimal user input and calculates three different metrics as well as an
approximate cost comparison between the different Substation Bus Arrangement. The results are
displayed numerically and on a graph for quick intuitive comparison. Although much of the
results coincide with historical data, dramatic differences can be seen when different bus
arrangements are compared. Tradeoffs between certain arrangements can be determined
immediately and decisions on the correct bus arrangement choice can be made more easily.
, Committee Chair
Mohammad Vaziri, Ph.D., P.E.
______________________
Date
v
ACKNOWLEDGMENTS
I would like to give thanks to all of the people I worked with during my Internship at
PG&E. I would like to acknowledge my supervisor Rao Sunkara for giving me the time and
freedom to work on this and several other interesting projects during my internship. I would like
to extend special thanks to Andeth Pen for exposing me to substations, help in identifying their
many components, exposure to the many duties of a substation project engineer, and the
opportunity to see the many facets of an indoor substation. I would like to express my great
appreciation to both Dave Solhtalab for giving me preliminary work exposing me to the different
substation bus arrangements and Chung Lam for his encouragement and guidance.
The idea and metrics originally suggested by Ronald Vance made his guidance and
mentoring invaluable from the start to completion of this project. In fact, this project would never
have materialized without his inspiring suggestion. The greatest thanks goes to Roberto
González-Ramos who gave me needed support and answers to the many questions that came up
during my periods of frustration and confusion during the creating of this program.
vi
TABLE OF CONTENTS
Page
Acknowledgments.................................................................................................................... vi
List of Tables ........................................................................................................................ viii
List of Figures .......................................................................................................................... ix
Software Specifications ............................................................................................................ x
Chapter
1.
INTRODUCTION ............................................................................................................ 1
2.
OVERVIEW OF METRICS AND BUS ARRANGEMENTS ......................................... 4
Metric Definitions ........................................................................................................ 4
Bus Arrangement Definitions ...................................................................................... 5
Bus Arrangement Characteristics ................................................................................ 7
3.
PROGRAM DESIGN ..................................................................................................... 23
4.
ALGORITHMS .............................................................................................................. 27
5.
DESCRIPTION OF CODE AND ALGORITHM IMPLEMENTATION...................... 43
6.
RESULTS AND ANALYSIS ......................................................................................... 53
7.
CONCLUSION ............................................................................................................... 63
Improvements and Future Research........................................................................... 66
References ............................................................................................................................... 67
vii
LIST OF TABLES
Page
1.
Table 1 Bus Arrangement Cost Comparison ............................................................. 25
2.
Table 2 SBSB3 Fault and Maintenance Calculations ................................................ 28
3.
Table 3 SBSB6 Fault and Maintenance Calculations ................................................ 29
4.
Table 4 MT Fault and Maintenance Calculations ...................................................... 29
5.
Table 5 DBSB Fault and Maintenance Calculations ................................................. 29
6.
Table 6 DBDB Fault and Maintenance Calculations ................................................. 30
7.
Table 7 BAAH Fault and Maintenance Calculations................................................. 30
8.
Table 8 Ring Fault and Maintenance Calculations .................................................... 31
9.
Table 9 DBDB Breaker Operability .......................................................................... 35
10.
Table 10 BAAH Bus Operability............................................................................... 36
11.
Table 11 BAAH Breaker Operability ........................................................................ 38
12.
Table 12 BAAH Transformer/Line Operability......................................................... 39
13.
Table 13 Four Breaker Ring, Bus & Transformer/Line Operability.......................... 40
14.
Table 14 Five Breaker Ring, Bus & Transformer/Line Operability .......................... 41
15.
Table 15 Five Breaker Ring, Breaker Operability ..................................................... 41
16.
Table 16 Six Breaker Ring, Bus & Transformer/Line Operability ............................ 41
17.
Table 17 Six Breaker Ring, Breaker Operability ....................................................... 42
18.
Table 18 Bus Type Arrangement Comparison Table ................................................ 54
viii
LIST OF FIGURES
Page
1.
Figure 1 Bus Arrangements; SBSB3, SBSB6, MT...................................................... 5
2.
Figure 2 Bus Arrangements; DBSB, DBDB, BAAH .................................................. 6
3.
Figure 3 Bus Arrangement; Ring Bus .......................................................................... 7
4.
Figure 4 Diagram Legend ............................................................................................ 7
5.
Figure 5 SBSB Normal Switch Position ...................................................................... 8
6.
Figure 6 SBSB Fault Conditions................................................................................ 10
7.
Figure 7 SBSB Maintenance Conditions ................................................................... 10
8.
Figure 8 MT Normal Switch Positions ...................................................................... 12
9.
Figure 9 MT Fault Conditions ................................................................................... 12
10.
Figure 10 MT Maintenance Conditions ..................................................................... 12
11.
Figure 11 DBSB Normal Switch Position ................................................................. 14
12.
Figure 12 DBSB Fault Conditions ............................................................................. 14
13.
Figure 13 DBSB Maintenance Conditions ................................................................ 15
14.
Figure 14 DBDB Normal Switch Position................................................................. 16
15.
Figure 15 DBDB Fault Conditions ............................................................................ 17
16.
Figure 16 DBDB Maintenance Conditions ................................................................ 17
17.
Figure 17 BAAH Normal Switch Position ................................................................ 19
18.
Figure 18 BAAH Fault Conditions ............................................................................ 19
19.
Figure 19 BAAH Maintenance Conditions................................................................ 19
20.
Figure 20 Ring Normal Switch Position .................................................................... 21
21.
Figure 21 Ring Fault Conditions................................................................................ 21
22.
Figure 22 Ring Maintenance Conditions ................................................................... 21
ix
23.
Figure 23 Bus Type Arrangement Comparison Spreadsheet ..................................... 53
24.
Figure 24 Bus Type Arrangement Comparison Graph .............................................. 54
x
SOFTWARE SPECIFICATIONS
For Windows:
Microsoft Office Excel 2007 or later with Visual Basic for Applications (VBA) Capabilities
For Mac:
Microsoft Office Excel 2010 or later with Visual Basic for Applications (VBA) Capabilities
xi
1
Chapter 1
INTRODUCTION
Bus arrangements are well documented in various technical literature, standards and
IEEE publications. The typical bus arrangements have been discussed, described, and
documented thoroughly. There are many typical bus arrangements currently used by the major
electric utilities. There is the single bus single breaker arrangement, main and transfer
arrangement, double bus single breaker arrangement, double bus double breaker arrangement,
breaker and a half arrangement, and the ring bus arrangement. These arrangements are used
throughout the utilities to protect and distribute power throughout the grid in every transmission
and distribution network throughout the world.
When analyzing these different systems to determine which system is the best for each
particular application, it was found that there was not a simple way to gain a fair comparison
between arrangements. Typically, the literature gives descriptions on cost, complexity, and other
properties of each bus arrangement but does not give any real concrete proof as to why and how
the conclusions are made. Additionally, when someone is designing or making improvements to a
substation, one must choose a bus arrangement that meets the requirements by inference and
previous engineering experience. Reliability studies can be performed for this purpose. However,
the reliability studies often require a large amount of data to perform the analysis and can give
results that prove difficult to compare. A typical reliability study on a substation may require the
following data; failure rate, outage frequency, failure probability, duration, repair time,
availability, and/or unavailability. In many instances, this data may be unavailable. For example,
the case of a new design, a company where departmental data sharing is limited, previous data
available on a particular substation is usually outdated. Therefore, a program that gives an
2
engineer the performance of each substation bus arrangement with minimal user input would be
beneficial.
This project aims to facilitate in the decision-making process by providing engineers with
calculated evidence on the performance of each bus arrangement using minimal user input. In
fact, the program created here will give an engineer instant results as to how each bus
arrangement will perform for their given situation. This information adds a significant value to
the decision making process especially when limited information is known about the system.
The software program was created using Visual Basic for Applications (VBA) combined
with Excel 2007 to accept information from a user on the number of inputs and the number of
transformers connected to a bus arrangement and use that information to calculate how each
arrangement reacts to faults, maintenance, and a combination of the two. The program was
developed for the following specific reasons;
1. to give a user instant and easy comparison between many different arrangements,
2. to require minimal user input and easily understandable results,
3. to calculate and produce results using readily available software,
4. to evaluate existing substations, analyze the increased improvement made by
substation upgrades, and
5. to give new engineers insight into the advantages and limitations of each
arrangement.
In a global sense, with this program, a user can make an educated decision about a
specific bus arrangement based on a comparative analysis with relatively limited user input.
In addition to this introductory chapter, the project is presented in 6 more chapters as
briefly described in the following;
3
Metric definitions, bus arrangement definitions and bus arrangement characteristics are
outlined in Chapter 2. The program design is described in Chapter 3. In Chapter 4, the algorithms
used to calculate each given metric is discussed in great detail. A description of each module in
the actual code is explored in Chapter 5. The results of running the program is presented and
analyzed in Chapter 6. Finally, the overall conclusion made by using the program is stated in
Chapter 7.
4
Chapter 2
OVERVIEW OF METRICS AND BUS ARRANGEMENTS
This chapter introduces both the metrics and bus arrangements being analyzed. First, the
metrics are defined to give the user of the program an intuitive way of analyzing bus
arrangements. Second, the bus arrangements are defined to introduce the specific Transmission
Substation bus arrangements used within this project. Third, the bus arrangement characteristics
are reviewed to give the reader a background on each bus arrangement. The background consists
of characteristics such as cost, flexibility, complexity, number of breakers used to isolate specific
faults, number of breakers used to isolate a component for maintenance, number of disconnects,
and number of breakers per line. The bus arrangements introduced are typical bus arrangements
used within substations throughout the world.
Metric Definitions
Each substation bus arrangement is evaluated based on three metrics. When lines are
mentioned, this refers to both input lines into the bus and output lines tied to the transformers.
The assumption for this version of the program is that transformer and line faults or maintenance
have the same probability and are combined as a “transformer/line” event. A fault accounts for a
bus fault, breaker failure, and transformer/line fault. Maintenance accounts for all three
components also. All three components are weighted equally giving each the same percentage of
failure or maintenance. The metrics are defined as follows.
1. Robustness – The number of lines remaining in service after a fault occurs
2. Maintainability – The number of lines remaining in service when a component is
down for maintenance
5
3. Operability – The number of lines remaining in service when a component is down
for maintenance and then a fault occurs
The final piece of data presented in the final results is the breaker to input/output ratio or
breaker IO ratio. This ratio is a rough estimation of the cost based on the number of breakers
divided by the number of inputs and outputs.
Bus Arrangement Definitions
The most common Transmission Substation bus arrangements were chosen for use in this
program. Automatic reclosers and sectionalizers are not used in this version of the program. The
following one-line diagrams assume the top three lines are inputs into the substation and the
bottom three lines are tied to step down transformer banks.
Figure 1: Bus Arrangements; SBSB3, SBSB6, MT
Single Bus Single Breaker Three (SBSB3): Refers to a configuration with 3 breakers tied
directly to the inputs of the substation bus without additional breakers between the bus and
transformers. See Figure 1.
6
Single Bus Single Breaker Six (SBSB6): Refers to a configuration with 3 breakers tied
directly to the inputs into the substation bus and 3 breakers between the bus and transformers. See
Figure 1.
Main and Transfer (MT): Refers to a configuration that has one breaker per input and
transformer. There are two busses in this configuration and an additional bus-tie breaker between
the two. The bus-tie breaker, which is usually used during maintenance, can substitute for any
breaker tied to the bus. See Figure 1.
Figure 2: Bus Arrangements; DBSB, DBDB, BAAH
Double Bus Single Breaker (DBSB): Refers to a configuration that has one breaker per
input and transformer. Similar to the MT, there is a bus-tie breaker between the two busses. The
difference between the DBSB and MT configurations is that the DBSB can be sectionalized
where half of the breakers are connect to one bus with the other half connect to the other bus.
This is not possible with the MT scheme. As in the MT, the bus-tie breaker can substitute for any
breaker tied to the bus. See Figure 2.
7
Double Bus Double Breaker (DBDB): Refers to a configuration that has two breakers per
input and transformer. The breaker is connected to the first bus, which is connected to a feeder
and the feeder is connected to a second breaker tied to a second bus. See Figure 2.
Breaker and a Half (BAAH): Refers to a configuration that has a breaker between one
bus and a feeder, in series with another breaker connected to another feeder, in series with a third
breaker tied to a second bus as shown. See Figure 2.
Figure 3: Bus Arrangement; Ring Bus
Ring Bus (Ring): Refers to a configuration that has a breaker between every incoming
and outgoing line forming a ring configuration. There is no specific “Bus” for this configuration.
See Figure 3.
Bus Arrangement Characteristics
It is assumed, as in the definition section that the top three lines are inputs into the
substation and the bottom three lines are tied to step down transformer banks. “Isolate” refers to
the number of fuses or breakers that operate to isolate a fault or maintenance condition. “Loss”
refers to the number of lines lost, input, output or both (I/O).
-Normal Failures
8
• Substation Transformer – gassing, internal arcs, winding short
• Breaker – insulation breakdown
• Bus
• Maintenance
Figure 4: Diagram Legend
-Single Bus Arrangement
This system has a feeder into a single bus with no breaker protection. The transformers
are usually protected by fuses. Main characteristics of this arrangement are:
• Simple and economical.
• Transformers are only protected by fuses,
• Transformer/line fault causes a fuse to blow resulting in the loss of downstream circuit
until the cause of fault has been investigated and the fuse is replaced.
• Transformer: Isolate-1, Loss-1 input or output line (I/O)
• Usually, there are no local Bus Protection schemes used for this configuration.
Therefore, bus faults must be cleared from remote terminals serving the transmission
9
lines supplying this bus. Automatic and/or manual switching must be used to isolate the
fault, perform maintenance, and restore power
• Bus: Isolate-3, Loss-6 I/O
• Switches must be opened for transformer maintenance
• Depends on switch arrangement
• Breaker Disconnects = depends
• Breakers = 0
-Single Bus, Single Breaker Arrangement (SBSB)
This system has transmission lines tied to a breaker, which is then tied to the bus. This
system could also have breakers between the bus and step down transformers. See Figure 5.
Switch Positions
Figure 5: SBSB Normal Switch Position
10
Bus Fault
Breaker Failure
Transformer Fault
Figure 6: SBSB Fault Conditions
Bus Maintenance
Breaker
Maintenance
Transformer
Maintenance
Figure 7: SBSB Maintenance Conditions
Main characteristics of this arrangement are:
• Simple
• Relatively inexpensive
• A bus or breaker fault causes the loss of the entire substation
• For a 3-breaker arrangement with breakers on the transmission line side only, a fault
anywhere on the bus or beyond (up to any fuses) causes all three breakers to trip.
Switches can be used to isolate the faulted section and to restore healthy sections.
• Bus, Breaker, Transformer: Isolate-3, Loss-6 I/O
11
• For the 6-breaker arrangement, a fault on the bus or any breaker failure will cause all
remaining breakers to trip depending on the protection scheme
• Bus, Breaker: Isolate-6, Loss-6 I/O
• Transformer/line fault trips one breaker isolating the fault
• Transformer: Isolate-1, Loss-1 I/O
• Bus maintenance causes the loss of all I/O lines
• Bus: Isolate-3 or 6, Loss-6 I/O
• Breaker maintenance causes the loss of one I/O line if breaker bypasses are not installed
• Breaker: Isolate-1, Loss-1 I/O, Isolation: 2 Switches
• Transformer maintenance isolated using one breaker in the 6-breaker system, lose only
maintenance line
• Transformer: Isolate-1, Loss-1 I/O
• Transformer maintenance isolated using all breakers in the 3-breaker system, switches
isolate Transformer, power restored, temporary loss of all Transformers
• Transformer: Isolate-3, Loss-6 I/O, Isolation: 1 Switch isolates line
• Breaker Disconnects = 2 per line
• Breakers = 3 to 6, 0.5 to 1.0 breakers per line or breakers/line
- Main and Transfer Arrangement (MT)
This system has a switch to select the main or transfer bus and one breaker per I/O line.
Typically, there is one breaker between the input and bus, also one breaker between the bus and
output. During normal operation, all breakers are tied to the lower bus with the bus-tie breaker
open. See Figure 8.
12
Switch Positions
Figure 8: MT Normal Switch Position
Bus Fault Main
Bus Fault Transfer
Breaker Failure
Transformer Fault
Figure 9: MT Fault Conditions
Bus Maintenance Condition 1
Bus Maintenance Condition 2
Breaker Maintenance
Transformer Maintenance
Figure 10: MT Maintenance Conditions
13
Main characteristics of this arrangement are:
• Low initial cost
• Breakers can be serviced using the bus-tie breaker and transfer bus for protection
• Extra breaker is needed for the bus-tie breaker
• Complicated switching for breaker removal
• Complicated relay protection for the tie breaker, must substitute for any breaker
• Main Bus or breaker fault causes the loss of the entire substation, until fault isolation
• Bus, Breaker: Isolate-6, Loss-6 I/O
• Secondary Bus fault trips nothing unless the bus-tie breaker is active
• Bus: Isolate-1, Loss-0 I/O
• Transformer/line fault trips one breaker isolating effected line
• Transformer: Isolate-1, Loss-1 I/O
• Breakers can be serviced using the bus-tie breaker and transfer bus for protection
• Breaker: Isolate-1, Loss-0 I/O, Isolation: 5 Switches
• Transformer is serviced using 1 breaker for switching and isolation
• Transformer: Isolate-1, Loss-1 I/O
• Breaker Disconnects = 3 per line
• Breakers = 7, 1.167 breakers/line
-Double Bus, Single Breaker Arrangement (DBSB)
This system has switches to select the bus and a single breaker to protect any input and
any output tied to the bus. Typically, there is a breaker between the input (e.g. source
transmission line) and the bus and another breaker between the bus and the output (e.g. a
14
substation transformer). There is also a bus-tie breaker, which can be substituted for any other
breaker in the system. See Figure 11.
Switch Positions
Figure 11: DBSB Normal Switch Position
Bus Fault Condition 1
Bus Fault Condition 2
Breaker Failure
Transformer Fault
Figure 12: DBSB Fault Conditions
15
Bus Maintenance Condition 1
Bus Maintenance Condition 2
Breaker Maintenance
Transformer Maintenance
Figure 13: DBSB Maintenance Conditions
Main characteristics of this arrangement are:
• Very flexible arrangement
• Complicated switching to isolate breaker for maintenance
• Complicated relay protection for bus-tie breaker, must substitute for any breaker
• Complicated bus protection scheme
• Bus or breaker fault could trip all breakers, yet the fault and entire bus or breaker can be
isolated using switches with full power restoration
• Bus, Breaker: Isolate-7, Loss-6 I/O’s
16
• Transformer/line fault trips one breaker isolating the fault
• Transformer: Isolate-1, Loss-1 I/O
• Breaker bypass switches for breaker maintenance
• Breaker: Isolate-1, Loss-0 I/O, Isolation: 3 Switches
• Breakers can be serviced at any time using the bus-tie breaker for protection
• Transformer is serviced using 1 breaker for switching and isolation
• Transformer: Isolate-1, Loss-1 I/O
• Either main bus can be isolated for maintenance
• Bus: Isolate-1, Loss-0 I/O, Isolation: 6 Switches, 1 Breaker
• Extra breaker needed for the bus-tie breaker
• Breaker Disconnects = 5 per line
• Breakers = 7, 1.167 breakers/line
-Double Bus, Double Breaker Arrangement (DBDB)
This system has two breakers connecting a single I/O line to both buses. Typically, both
busses are hot and all breakers are normally closed. See Figure 14.
Switch Positions
Figure 14: DBDB Normal Switch Position
17
Bus Fault
Breaker Failure
Transformer Fault
Figure 15: DBDB Fault Conditions
Bus Maintenance
Breaker Maintenance
Transformer Maintenance
Figure 16: DBDB Maintenance Conditions
18
Main characteristics of this arrangement are:
• High Cost
• Best reliability
• Flexible operation
• All switching is done with breakers
• Bus fault trips half of the breakers, all circuits remain in operation
• Bus: Isolate-6, Loss-0 I/O
• Transformer/line fault trips 2 breakers, no other line loss
• Transformer: Isolate-2, Loss-1 I/O
• Breaker failure trips 6 breakers, 1 line lost
• Breaker: Isolate-7, Loss-1 I/O
• Either main bus can be isolated for maintenance
• Bus: Isolate-6, Loss-0 I/O
• Breakers can be serviced at any time using the complementary breaker for protection
• Breaker: Isolate-1, Loss-0 I/O, Isolation: 2 Switches
• Transformer is serviced using 2 breakers for switching and isolation
• Transformer: Isolate-2, Loss-1 I/O
• 2 breakers for each line provides high reliability
• Successful clearing of the fault depends on 2 breakers increasing probability of failure
• Breaker Disconnects = 4 per line
• Breakers = 12, 2 breakers/line
-Breaker and a Half Arrangement (BAAH)
19
This system has a breaker between one bus and a feeder, in series with another breaker
connected to another feeder, in series with a third breaker tied to a second bus. See Figure 17.
Switch Positions
Figure 17: BAAH Normal Switch Position
Bus Fault
Center Breaker
Fault
End Breaker
Fault
Transformer
Fault
Figure 18: BAAH Fault Conditions
Bus
Maintenance
Breaker
Maintenance
Transformer
Maintenance
Figure 19: BAAH Maintenance Conditions
20
Main characteristics of this arrangement are:
• Flexible operation
• High reliability
• All switching is done with breakers
• Bus fault trips 3 breakers, all circuits remain in operation
• Bus: Isolate-3, Loss-0 I/O
• Transformer/line fault trips 2 breakers, all other circuits remain in operation
• Transformer: Isolate-2, Loss-1 I/O
• Center breaker failure trips 2 breakers, removes 2 I/O lines from service
• Center Breaker: Isolate-3, Loss-2 I/O
• End breaker failure trips 3 breakers, removes 1 I/O line
• End Breaker: Isolate-4, Loss-1 I/O
• Either bus or breaker can be isolated for maintenance, no line loss
• Bus: Isolate-3, Loss-0 I/O
• Breaker: Isolate-1, Loss-0 I/O, Isolation: 2 Switches
• Transformer is serviced using 2 breakers for switching and isolation
• Transformer: Isolate-2, Loss-1 I/O
• Complicated protection relaying for center breaker to respond to either circuit
• Breaker Disconnects = 6 per 2 lines, 3 per line
• Breakers = 9, 1.5 breakers/line
-Ring Bus Arrangement
This system has a breaker between every incoming and outgoing line, forming a ring
configuration. See Figure 20.
21
Switch Positions
Figure 20: Ring Normal Switch Position
Bus Fault
Breaker Fault
Transformer Fault
Figure 21: Ring Fault Conditions
Bus Maintenance
Breaker Maintenance
Transformer Maintenance
Figure 22: Ring Maintenance Conditions
Main characteristics of this arrangement are:
• Low initial and final cost
• Uncomplicated bus protection
22
• Typically limited to 6 breakers, although I have observed 8 breakers in practice
• Breaker failure trips 2 breakers, 2 I/O lines lost
• Breaker: Isolate-3, Loss-2 I/O
• Bus, line, or Transformer failure trips 2 breakers, only affected line lost
• Bus, Transformer: Isolate-2, Loss-1 I/O
• Bus, line, or Transformer failure when 1 breaker is open can cause ring bus separation
• Breaker can be isolated for maintenance, no I/O line loss, easy switching
• Breaker: Isolate-1, Loss-0 I/O, Isolation: 2 Switches
• Transformer is serviced using 2 breakers for switching and isolation
• Transformer: Isolate-2, Loss-1 I/O
• All switching is performed by breakers
• Requires voltage devices on all circuits
• Breaker Disconnects = 2 per line
• Breakers = 6, 1 breaker/line
23
Chapter 3
PROGRAM DESIGN
The following is a brief overview of the program design. The description includes many
of the assumptions made during the design. An explanation on how a user operates the program is
given. Also discussed is a brief summary on the metric calculations performed by the program, as
well as, an analysis of the breaker IO ratio metric and its validity.
Several variations of the code have been developed to serve different purposes.
However, the focus of this project is the Bus Type Arrangement Comparison Spreadsheet. The
full code description and algorithms can be found in later sections of the report.
The program was created to give engineers a quick reference to the robustness,
maintainability, operability, and breaker IO ratio of all following substation bus types. The bus
types focused on are the single bus single breaker (SBSB3 and SBSB6), main and transfer (MT),
double bus single breaker (DBSB), double bus double breaker (DBDB), breaker and a half
(BAAH), and the ring bus (Ring) as described in Chapter 2.
In this program, the user provides as input the number of incoming transmission lines
connected to the substation and the number of outputs from the bus arrangement to the step down
transformers. Invoking the “Run” command, the program then calculates the number of breakers
needed in each type of bus arrangement. Once the program has the numbers of inputs,
transformers, breakers and the bus type the substation metrics can be calculated. Refer to the
Algorithm section for the exact calculations used to find the substation metrics. The program then
calculates the robustness, maintainability, operability, and breaker IO ratio for each substation
type.
24
The robustness is the percentage of lines lost due to a fault. Lines lost include both inputs
and outputs to the bus arrangement. Within this calculation bus faults, breaker failures, and
transformer faults are considered. The numbers of lines lost due to a bus fault, breaker failure and
transformer fault are calculated separately. A transformer fault may be slightly misleading in this
case, for this program, a transformer fault includes faults on all input and output lines. This means
that a fault on the input transmission line and the output line to the step down transformer are
both being included in this calculation. Therefore, this fault is referred to as a transformer/line
fault. Once all of the lines lost values are known they are turned into percentage of lines lost and
the average of the three are taken. After the percent average lines lost due to the three fault types
mentioned above is calculated the value is converted into the percentage of remaining lines. This
value is the resulting robustness of that particular bus arrangement.
The maintainability is the percentage of lines lost due to a component being serviced. As
with the robustness metric, the maintainability metric considers lines lost due to bus maintenance,
breaker maintenance, and transformer/line maintenance. Again similar to the robustness
calculations, the transformer maintenance includes maintenance of the input transmission lines
and the outputs to the step down transformers. Once the lines lost due to maintenance are known
then the values are converted into percentages. Those percentages for bus, breaker, and
transformer/line maintenance are then averaged to find the overall percentage of average lines
lost due to maintenance. Finally, the percentage of lines lost is converted to percentage of lines
remaining in service due to maintenance and that value is the maintainability metric.
The operability metric is similar to both the robustness and maintainability metrics but in
order to calculate this metric, quite complex algorithms must be used to take into account all of
the possible situations that can occur. See the algorithm portion of the code for a full description
of the mathematics behind these calculations. The operability metric is basically the number of
25
lines remaining in service when a component is down for maintenance and a fault on some other
component occurs. The calculation takes into account any component being down for service and
then any type of fault occurring while that component is down for service. So this includes a
breaker being serviced and there is a bus, breaker, or transformer/line fault. Also included is the
condition when the bus is down for maintenance and a bus, breaker, or transformer/line fault
occurs. Likewise, if a transformer/line is being serviced and there is a bus, breaker, or
transformer/line fault, all conditions are considered. Once the numbers of lines lost are calculated
for all of these conditions they are combined to find the total average percentage of lines lost
under all of the conditions above. Finally, the percentage of lines lost is converted into the
percentage of lines remaining and this is the operability metric.
The final metric is the breaker IO ratio metric. This is the ratio of breakers to the number
of inputs and outputs connected to the bus. This ratio gives a very general estimate of the cost of
each bus arrangement. The US Department of Agriculture has a report presenting data on
Approximate Relative Cost Comparison between bus arrangements. When comparing this data
with the calculated breaker IO ratio the results are relatively similar, as seen below in Table 1.
The ratio provides a useful comparison between of the cost of one bus arrangement to another.
This is by no means a complete view of the actual costs. Variations due to the labor costs,
material costs, land costs, must be taken into account. Due to these other considerations, costs can
vary greatly and will deviate from the breaker IO ratio calculation.
Bus Arrangement
SBSB6
MT
DBDB
BAAH
Ring
Approximate Relative Cost
Comparison [3]
100%
143%
214%
158%
114%
Ratio of
100%
117%
200%
150%
100%
Table 1: Bus Arrangement Cost Comparison
Breakers
Input/Output lines
26
The metrics are calculated for every bus type and those values are filled back into the
excel spreadsheet. The values associated with each metric are also graphed below the excel
spreadsheet. The graph gives the user a rough estimate and comparison of each bus type and the
metrics associated with them. The spreadsheet provides the detail and exact numbers of percent
lines remaining in service for each metric. Each metric is highlighted in a specific color in both
the spreadsheet and the graph for quick and easy viewing. With this program, the user can gain a
large amount of knowledge about the different substations arrangements and choose the best one
for each particular situation.
27
Chapter 4
ALGORITHMS
Within this chapter, the main algorithms for calculating the metrics are presented and
discussed. The algorithms in this section were intuitively created based on the description and
operation of the protection systems for specific bus arrangements. The algorithms are relatively
simple despite the many different calculations that take place throughout the program. Several
improvements can be made and are described throughout the document. These calculations are
described in great detail throughout this chapter. To aid in the understanding of the algorithms
please refer to the figures in Chapter 2. Some variables are used in additional versions of the
program and may go unutilized here. Finally, these calculations are scalable and work for any
sized system with any number of inputs and transformers connected to the bus arrangement. For
simplicity the arrangements being analyzed will have 3 lines or inputs into the arrangement and 3
transformers or outputs connected to the arrangement giving a total of 6 input and output lines. It
is also assumed that these are transmission side substation arrangements and sectionalizers either
do not exist or are in the closed position.
First, simplified variables must be identified to make the equations easier to follow.
In= the number of breakers that trip isolating a component during fault or maintenance.
Ln= the number of lines lost when a component is isolated during a fault or maintenance.
In-1= the number of breakers that previously tripped isolating a component for maintenance.
Ln-1= previous lines lost when a component was isolated for maintenance.
ba= the number of breakers that are available to trip or active breakers remaining in the system.
la= the number of active input/output lines that remain connected to the system.
bT= breakers total in the entire bus arrangement.
28
lT= total number of input/output lines connected to the bus arrangement.
t= number of transformers.
i= number of inputs.
SBSB3
Bus Fault
Tripped Breakers (In)
I n  ba  I n 1  bT
Lines Lost (Ln)
Ln  la  Ln 1  lT
Breaker Failure
I n  ba  I n 1  bT
Ln  la  Ln 1  lT
Transformer/Line
Fault
Bus Maint.
In 
I n  ba  I n 1  bT
Ln  la  Ln 1  lT
Breaker Maint.
I n  1  I n 1
Ln  1  Ln 1
Transformer/Line
Maint.
In 
  b
t
la
a
  b
t
la
a
 I n 1  
 I n 1  
  1  I
i
la
  1  I
i
la
n 1
n 1


Ln 
Ln 
  l
t
la
  l
t
la
a
a
 Ln 1  
 Ln 1  
  1  L

  1  L

i
la
i
la
n 1
n 1
Table 2: SBSB3 Fault and Maintenance Calculations
With the simplified variables identified, the logical starting point is the SBSB3 module
due to its simplicity to understand. From this point, greater complexity will be encountered.
Please refer to Figure 1 for the SBSB3 arrangement. The equation for the number of breakers to
isolate a bus fault is I n  ba  I n1  bT . As seen in the figure, a bus fault causes all breakers (bT)
to trip isolating the fault. Therefore, the number of active breakers (ba) trip and the number of
inactive breakers (In-1) are added resulting in the total number of breakers that trip ( I n  bT  3 )
isolating the bus fault. Next, the number of lines lost during a bus fault in the SBSB3 arrangement
is, Ln  la  Ln 1  lT . The equation shows the number of active lines (la) and the number of
inactive lines (Ln-1) are added resulting in the number of lines lost (Ln) which in this case is also
the total number of lines ( lT  Ln  6 ). The transformer/line fault and maintenance equations are
slightly more complex due to the unbalance in the bus arrangement. If the fault or maintenance is
on the transformer then all breakers trip to isolate the fault. If the fault is on the input lines only
one breaker trips isolating that single line. This is why the transformer/line equations are split into
29
two parts, as seen in Table 2. Finally, for breaker maintenance only one breaker trips and only
one line is lost plus any previous conditions. From this point on all equations are displayed in a
table for each arrangement with only an explanation for the most complex calculation.
SBSB6
Bus Fault
Tripped Breakers (In)
Lines Lost (Ln)
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Breaker Failure
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Transformer/Line Fault
I n  1  I n 1
Ln  1  Ln1
Bus Maint.
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Breaker Maint.
I n  1  I n 1
Ln  1  Ln1
Transformer/Line Maint.
I n  1  I n 1
Ln  1  Ln1
Table 3: SBSB6 Fault and Maintenance Calculations
MT
Bus Fault
Tripped Breakers (In)
Lines Lost (Ln)
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Breaker Failure
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Transformer/Line Fault
I n  1  I n 1
Ln  1  Ln1
Bus Maint.
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Breaker Maint.
I n  1  I n 1
Ln  0  Ln1
I n  1  I n 1
Ln  1  Ln1
Transformer/Line Maint.
Table 4: MT Fault and Maintenance Calculations
DBSB
Bus Fault
Tripped Breakers (In)
Lines Lost (Ln)
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Breaker Failure
I n  ba  I n1  bT
Ln  la  Ln 1  lT
Transformer/Line Fault
I n  1  I n 1
Ln  1  Ln1
Bus Maint.
I n  1  I n 1
Ln  0  Ln1
Breaker Maint.
I n  1  I n 1
Ln  0  Ln1
Transformer/Line Maint.
I n  1  I n 1
Ln  1  Ln1
Table 5: DBSB Fault and Maintenance Calculations
30
DBDB
Bus Fault
Tripped Breakers (In)
Lines Lost (Ln)
In 
Ln  0  Ln1
Breaker Failure
I n  b2a  1  I n1
Ln  1  Ln1
Transformer/Line Fault
I n  2  I n1
Ln  1  Ln1
Bus Maint.
In 
Ln  0  Ln1
Breaker Maint.
I n  1  I n 1
Ln  0  Ln1
Transformer/Line Maint.
I n  2  I n1
Ln  1  Ln1
ba
2
ba
2
 I n1
 I n1
Table 6: DBDB Fault and Maintenance Calculations
A few additional variables must be introduced for the following calculations.
Ic= number of breakers that trip during a center breaker failure.
Lc= number of lines lost during a center breaker failure. Is=number of breakers that trip during a
side breaker failure.
Ls= number of lines lost during a side breaker failure.
These are combined into the single breaker failure results with an equal probability of failure for
each breaker position.
BAAH
Bus Fault
Tripped Breakers (In)
Lines Lost (Ln)
In 
 I n1
Ln  0  Ln1
Breaker Failure Center
I c  3  I n1
Lc  2  Ln1
Breaker Failure Side
Is 
Ls  1  Ln1
ba
3
ba
3
 1  I n1
Breaker Failure
I n   13  I c   23  I s
Ln   13  Lc   32  Ls
Transformer/Line Fault
I n  2  I n1
Ln  1  Ln1
Bus Maint.
I n  b3a  I n1
Ln  0  Ln1
Breaker Maint.
I n  1  I n 1
Ln  0  Ln1
Transformer/Line Maint.
I n  2  I n1
Ln  1  Ln1
Table 7: BAAH Fault and Maintenance Calculations
31
Ring
Bus Fault
Tripped Breakers (In)
Lines Lost (Ln)
I n  2  I n1
Ln  1  Ln1
Breaker Failure
I n  3  I n1
Ln  2  Ln1
Transformer/Line Fault
I n  2  I n1
Ln  1  Ln1
Bus Maint.
I n  2  I n1
Ln  1  Ln1
Breaker Maint.
I n  1  I n 1
Ln  0  Ln1
I n  2  I n1
Ln  1  Ln1
Transformer/Line Maint.
Table 8: Ring Fault and Maintenance Calculations
These equations result in the numbers of lines lost and breakers needed to trip isolating
components during faults and maintenance for each type of bus arrangement. After these numbers
are calculated, the percent values are determined. This calculation finds the average of the results
above. For example, only looking at lines lost during fault, the three values used are bus, breaker,
and transformer/line fault calculated values for lines lost. Each value is separately turned into a
percentage by bus _ pcnt 
  100% . That is lines lost due to bus fault divided by lines total
Ln
LT
and multiplied by 100 creating a percentage. Once the bus, breaker, and transformer/line lines lost
percentage is found then the average is taken. Simply, the addition of all three values divided by
three gives the average. Mathematically the average in this case is
ave 
 bus_pcnt+bkr_pcnt+bnk_pcnt  . The average values are calculated for lines lost due to
3
fault as shown, lines lost due to maintenance, breakers tripped to isolate a fault and breakers
tripped to isolate a component for maintenance. Once all of average values are calculated the
metrics are found.
The three simple metrics are robustness, maintainability, and cost. Operability will be
discussed next. As defined in chapter 2, “Robustness” is simply the number of lines remaining in
32
service after a fault. The average number of lines remaining in service is calculated under all
three fault cases bus, breaker, and transformer/line faults. The robustness is found by subtracting
the average percentage of lines lost during faults from 100 resulting in the average percentage of
lines left in service during faults. Maintainability is similar, being 100 minus the average
percentage of lines lost during maintenance resulting in the percentage of lines left in service
during maintenance. The equation used is Lines Remaining= 100 -  Lines Lost  . Finally, the
breaker IO ratio is calculated. This function gives an approximation of each bus arrangement cost
and is discussed in more detail in Chapter 3. The cost here is the number of breakers divided by
the number of lines and multiplied by 100. This results in a percentage as compared to the SBSB6
arrangement, which is 100. The cost function is solely based on the numbers of breakers and does
 Breakers 
  100 .
 Lines 
not take into account labor, structure costs and so on. The function is Cost= 
The final metric is now calculated. Operability is by far the most complex metric to
calculate due to the fact that first the maintenance condition is analyzed then fault values are
calculated during each maintenance condition. So this is similar to a n-1 situation, maintenance
then fault. The operability of SBSB3 is basically 0 and is set as such. For SBSB6 and all other
bus arrangements, the information from earlier maintenance calculations is used for each
maintenance condition. Each bus arrangement is analyzed under bus maintenance then all fault
types, breaker maintenance then all fault types, and transformer/line maintenance then all fault
types.
Starting with SBSB6 the previous maintenance results are used to calculate the
operability. First, simple bookkeeping of previously calculated values must be done.
I n1  I n  Bus Maintenance 
33
Ln1  Ln  Bus Maintenance 
ba  bT  I n 1
la  lT  Ln 1
These equations result in the numbers of breakers used to isolate the bus during
maintenance, lines lost during bus maintenance, breakers available during bus maintenance and
remaining active or connected input/output lines during maintenance. If la is zero then the number
of lines remaining in service is zero, robust1 is set to zero and the program moves on to breaker
maintenance. Although if la is not equal to zero, the previous values stored during the
bookkeeping procedure are used. The module SBSB6 is called again to calculate all three fault
values. Then the average percent values are calculated and the resulting number of lines lost from
the three fault types is subtracted from 100. The result of these calculations is labeled as robust1
and stands for the number of lines remaining in service during bus maintenance then a fault
occurs.
For this case the breaker and transformer/line operability procedure is exactly the same.
The previous breaker and transformer/line maintenance result, bookkeeping is done. If the active
input/output lines remain and la is not zero then SBSB6 is called to calculate fault values and
robust2 is calculated giving the lines remaining in service during breaker maintenance then a
fault. The same procedure is followed resulting in robust3, the number of lines remaining in
service during transformer/line maintenance then a fault. Finally the operability of SBSB6 is the
average number of lines remaining in service and is calculated as follows,
 robust1+robust2+robust3 
Operability= 
.
3


34
The calculations begin to get more interesting as bus arrangement complexity is
increased. The operability for MT is similar to SBSB6. For simplicity the following explanation
is broken into steps. The three items to be calculated is operability for bus, breaker, and
transformer/line and then those three are combined into the one single operability metric for that
specific bus arrangement. In each of the three item operability calculations, there are basically
three steps. Step one is the bookkeeping of previous value as described. Step two is if the number
of input/output lines remaining is greater than 0 an additional bus arrangement module is run to
find the fault values after maintenance, percent values are calculated and the lines remaining in
service are assigned to robust1, 2, or 3 depending on the component being analyzed. Step three is
if the number of input/output lines is 0 then robust1, 2, or 3 is set to 0 depending on the
component being analyzed. Step three is intuitive and will be eliminated from this point on.
For MT item 1 bus operability is calculated. Step one, previous maintenance value
bookkeeping is done. Step two, the metric SBSB6 is called resulting in robust1 being the lines
remaining in service when the bus is under maintenance then a fault occurs. The reason SBSB6 is
called during the analysis for MT is because when the bus is down for maintenance the bus
arrangement is reduced to a SBSB6 arrangement.
MT item 2 breaker operability begins with step one, previous value bookkeeping. The
module SBSB6 is run resulting in lines remaining in service or robust2. During breaker
maintenance, the MT arrangement reduces to SBSB6 as seen with bus maintenance. Item 3
transformer/line maintenance, step one, bookkeeping is performed. Step two, MT is called and
the resulting robust3 is calculated. It is clear in this case that transformer/line maintenance does
not result in the reduction from MT to SBSB6 and this can be easily seen in Figure 10 under the
35
transformer maintenance diagram. Finally, the operability is calculated,
 robust1+robust2+robust3 
Operability= 
.
3


The next arrangement analyzed for operability is DBSB. For items 1 and 2 bus and
breaker operability step one, previous value bookkeeping is performed. Step two is the same as
MT for items 1 and 2, where the module SBSB6 is run resulting in robust1 and 2. For item 3,
transformer/line operability step one and step two is performed where module DBSB is used to
calculate robust3. Finally, the operability is calculated.
DBDB operability is now calculated. Item 1, bus operability is calculated as in previous
arrangements, step one, then step two calls the SBSB6 module. Item 3, transformer/line
operability is calculated by performing step one then step two calling the DBDB module. Item 2,
breaker operability is calculated differently than previous calculations. Step one is the same. Step
two starts with the following calculations in Table 9.
Breaker Operability
Bus Fault
Tripped Breakers (In)



    1 

I n  12  b2T  12 
Breaker Failure
In

bT
2
bT
2
 I n1

bT
2
2

   2 
lT 1
lT
In  3
Bus Fault
Lines Lost (Ln)
Ln  0   12   1  12 
Transformer/Line
Fault

1  

ba  
 
bT
2
Transformer/Line
Fault
Breaker Failure


Ln  1 


Ln  1




1  

ba  

bT
2
1
lT

1  
2
ba  
 
bT
2


1   1 
  1  
ba   ba 

bT
2
Table 9: DBDB Breaker Operability

bT
2

1 
1

ba 
36
After these calculations are performed, the percent values are calculated as before and finally
robust2 is calculated as before where the lines lost due to fault are subtracted from 100, resulting
in the lines remaining in service during maintenance on a breaker and then a fault occurs. Now
that robust1, 2, and 3 are known the overall operability is calculated as before,
 robust1+robust2+robust3 
Operability= 
.
3


Next, BAAH operability is calculated. In this case, each operability calculation must have
the fault portion calculated separately. Starting with item 1, bus operability, step one is performed
followed by the fault calculations as seen in Table 10. These equations can easily be figured out
by referring to Figure 19 and looking at the various faults during each maintenance condition.
The equations given can also be confirmed by plugging in values to confirm the expected
outcome.
Bus Operability-BAAH
Bus Fault
Tripped Breakers (In)
I n  b3T
Breaker Failure
I n  12   I n1  2  12 
Transformer/Line Fault
Bus Fault
I n  12  1  I n1   12   2  I n1 
Lines Lost (Ln)
Ln  lT
Breaker Failure
Ln  12  2  12  lT
Transformer/Line Fault
Ln  12 1  12  2
   1 I 
bT
3
n 1
Table 10: BAAH Bus Operability
After the calculations for bus operability are performed the percent values are calculated and
robust1 is calculated as before.
The breaker operability is by far the most complicated operability calculations performed
due to the fact that the breaker down for maintenance could be a center breaker or side breaker in
37
the arrangement. Therefore, each condition must be analyzed during the breaker operability
calculations for the BAAH arrangement. As seen in Table 11, the calculations are done for each
component fault first looking at the side breaker down for maintenance then looking at the
situation with the center breaker down for maintenance and finally both are combined to give the
results of each component under fault. The process works as before starting with step one, the
bookkeeping of past values and then step two continues where each fault after the breaker is
down for maintenance is calculated.
38
Breaker
OperabilityBAAH
Bus Fault (side)
Tripped Breakers (In)
I S ,n  12 
bT
3
 I n1  12 
Bus Fault (center)
I C ,n
bT
3
 I n 1
Bus Fault (total)
I n  23  I S ,n  13  I C ,n
Breaker Failure
(side)
I S ,n 

 1 

bT
3

1
2
bT
3
 I n 1
ba


I C ,n  5 
Breaker Failure
(total)
Transformer/Line
Fault (side)
I S ,n   2  I n 1 
Transformer/Line
Fault (center)
I C ,n
bT
LC ,n  1  1
Bus Fault (total)
Ln  23  LS ,n  13  LC ,n
Breaker Failure
(side)
LS ,n  1
Transformer/Line
Fault (total)
b
bT
3
  3  I n 1 
a
bT
3
1
ba
  2  I n 1 
bT
3
I n  23  I S ,n  13  I C ,n
Bus Fault (center)
Transformer/Line
Fault (center)
2
lT  2
1
1
  2  I n 1   1  I n 1 
lT
lT
lT
l 2
2
  2  I n 1  T
 1  I n 1 
lT
lT
Bus Fault (side)
Breaker Failure
(total)
Transformer/Line
Fault (side)
3
bT
3
bT
3
Lines Lost (Ln)
LS ,n  12   lT  2  12  0
Breaker Failure
(center)
 
 2  I n 1
1
2  I n1
 4
  3  I n 1 
ba
ba
ba
2
1
I n  3  I S ,n  3  I C ,n
Breaker Failure
(center)
Transformer/Line
Fault (total)


bT
3
bT
bT
 I n 1
1
1
I
I
3 3
 2 n 1  2 3
 2 n 1
ba
ba
ba
ba
ba
bT
2  b3T  2  I n 1
1
2  I n 1
LC ,n  3
1
2 3
ba
ba
ba
2
1
Ln  3  LS ,n  3  LC ,n
lT  2
1
1
 2 1
lT
lT
lT
l 2
2
1 T
1
lT
lT
LS ,n  1
LC ,n
Ln  23  LS ,n  13  LC ,n
Table 11: BAAH Breaker Operability
I n 1
ba
39
As seen, the final results are numbers for bus, breaker, and transformer/line faults which are the
same as all previous calculations. From these results, the percent values are calculated and
robust2 is calculated.
The last step is the calculation of BAAH transformer/line operability. Step one is
performed, step two is calculated using the formulas in Table 12 and robust3 is found. Finally, the
total operability for BAAH is found using the operability formula.
Transformer/line
Operability-BAAH
Bus Fault
Tripped Breakers (In)
Breaker Failure
bT
 1 bT
1
 3 3 3

ba
ba
l 2
1
I n   2  I n 1  T
 1  I n 1 
la
la
Lines Lost (Ln)
Ln  12 1  12  2
I n  12
In 
Transformer/Line Fault
Bus Fault
Breaker Failure


bT
3
 
 1  12
2

bT
3
bT
3
2




bT
3
2
 b1  5
a
1
ba
bT
3
bT
bT
1
1
1
1
3 3
2 3 3
ba
ba
ba
ba
l 2
1
Ln  2 T
2
la
la
Ln  2
Transformer/Line Fault
bT
3
bT
3
Table 12: BAAH Transformer/Line Operability
The ring bus is difficult because the size of the ring and fault placement can change the
problem significantly. One thing to keep in mind is that maintenance and then a fault can cause
islanding where part of the system is cut off from another although current may still flow in the
two separate sections. For this reason, the result turns red in the spreadsheet to bring attention to
this problem. Another important thing about the ring bus arrangement is that a ring should only
be expanded to 6 breakers. In practice, a ring arrangement should never go beyond 6 breakers
therefore the calculations stop at the 6 breaker system. In addition, in a ring arrangement there
40
really is not a bus as in conventional systems. For that reason, bus and transformer/line
calculations are combined because they are connected to the same point in the system.
Unfortunately, this doubles the probability of a fault at this point in the calculations and this will
be remedied in future versions.
First is a ring arrangement of 3 breakers. In this case, the results are 0 for all three
operability cases giving an overall operability of 0.
Second is the ring arrangement of 4 breakers. The bus and transformer/line operability
are the same. Step one is performed pulling the maintenance data from the previous calculations.
Step two is calculated using the formulas in Table 13 where bus and transformer/line faults are
combined. The percent values are calculated and robust1 & 3 are found.
Bus & Transformer Operability-Ring 4
Bus & Transformer Fault
Tripped Breakers (In)
I n  23 1  I n1   13  2  I n1 
Breaker Failure
Bus & Transformer Fault
I n  bT
Lines Lost (Ln)
Ln  23  2  13  lT
Breaker Failure
Ln  lT
Table 13: Four Breaker Ring, Bus & Transformer/Line Operability
Next, the breaker operability is calculated. In this case all lines are lost resulting in a value of 0
for robust2.
If the ring bus is a 5 breaker arrangement then all of the steps followed in the previous
arrangement are followed again with the substitution of the equations used in Table 14. In
addition, the breaker operability is calculated using the equations in Table 15 and robust2 will be
a number and not 0 as calculated previously.
41
Bus & Transformer Operability-Ring 5
Bus & Transformer Fault
Tripped Breakers (In)
I n  12 1  I n1   12  2  I n1 
Breaker Failure
Bus & Transformer Fault
I n  23  2  I n1   13 bT
Lines Lost (Ln)
Ln  12  2  12  3
Breaker Failure
Ln  23  3  13  lT
Table 14: Five Breaker Ring, Bus & Transformer/Line Operability
Breaker Operability-Ring 5
Bus & Transformer Fault
Tripped Breakers (In)
I n  23 1  I n1   13 bT
Breaker Failure
Bus & Transformer Fault
I n  bT
Lines Lost (Ln)
Ln  23  3  13  lT
Breaker Failure
Ln  lT
Table 15: Five Breaker Ring, Breaker Operability
The 6-breaker Ring bus arrangement is now calculated following the processes used in
arrangements 4 and 5. Remember islanding can easily occur in this arrangement during n-1 or
multiple contingencies. Those contingencies could be maintenance and a fault or dual faults in
different places. As in previous arrangements, the final results are robust1, 2, and 3.
Bus & Transformer Operability-Ring 6
Bus & Transformer Fault
Tripped Breakers (In)
I n  52 1  I n1   52  2  I n1   15  2  I n1 
Breaker Failure
Bus & Transformer Fault
I n  12  2  I n1   12  3  I n1 
Lines Lost (Ln)
Ln  52  2  52  3  15  4
Breaker Failure
Ln  12  3  12  4
Table 16: Six Breaker Ring, Bus & Transformer/Line Operability
42
Breaker Operability-Ring 6
Bus & Transformer Fault
Tripped Breakers (In)
I n  12 1  I n1   12  2  I n1 
Breaker Failure
Bus & Transformer Fault
I n  23  2  I n1   13 bT
Lines Lost (Ln)
Ln  12  3  12  4
Breaker Failure
Ln  23  4  13  lT
Table 17: Six Breaker Ring, Breaker Operability
Once the ring bus calculations are finished the robust results are used to calculate the
overall operability of the ring bus arrangement using the formula,
 robust1+robust2+robust3 
Operability= 
.
3


Now that the operability is calculated the cells in the spreadsheet can be filled and the
graph can be created giving one a feel for the performance of each bus arrangement compared to
one and other with the same number of inputs and outputs. All algorithms in this section are kept
in their expanded form in order for readers to understand their derivation. All algorithms could be
simplified and reduced although the origin would be hidden.
43
Chapter 5
DESCRIPTION OF CODE AND ALGORITHM IMPLEMENTATION
The overall code and algorithm for this project is quite complex and will be described in
detail using the code for the bus type arrangement comparison spreadsheet. The programming
language used is VBA or Visual Basic for Applications, which interfaces directly with Microsoft
Excel 2007. Initially all of the public global variables are declared. From this point, the code is
sectionalized into sub sections or standard modules each of which perform specific functions.
From this point on, the sub sections or standard modules are referred to using the generic term
modules. The modules are described in the order as they appear in the code.
Master Module
The Master module is the main code and is what runs to perform the calculations, data
population and graph creation; it is what executes within the spreadsheet when the run button is
pressed. First, the Clear_cells module is run to clear the cells of the calculated data from the
previous execution of the code. Second, an If statement is encountered to check whether the user
input cells contain data, if they do the program continues in the If statement. Third, the
Populate_variables module is encountered which pulls data from the user inputs and places them
into variables used in further calculations. Fourth, the Num_bkr module runs to calculate the
number of breakers needed for each specific substation bus arrangement depending on the
number of inputs and transformers specified by the user. Fifth, “r” and “c” are set to the row and
column of the first cell that will be populated by the program, the Breakers cell. Sixth, a Do
While loop is encountered which runs through each cell until an empty cell is reached. This loop
looks for data in the Breakers cell and continues looping until each bus type metrics has been
44
calculated. Seventh, the bus_type and brks_total variables are populated from the data in the excel
spreadsheet under columns Bus Type and Breakers. The variable bkrs is also populated with the
number of total breakers for a particular bus type which is used for later calculations. Eighth, the
Populate_variables module is run again to populate the variables from the user inputted data for
every iteration of the Do While loop. Ninth, the cell colors are reset because certain cell colors
are changed to indicate sectionalization of the bus during component maintenance and a fault.
Tenth, the Bus_select module is run to perform the main bulk of the calculations and direct the
code to specific modules for each specific bus type. Eleventh, “r” is increased by one to move to
the next row and the Do While loop is repeated until a blank cell is reached. Once the Do While
loop is completed the If statement also ends. Twelfth, the Data_Chart module runs to take all of
the calculated data and populate the graph with that data for easy comparison. This ends the
Master module.
Num_bkr Module
This module calculates the number of breakers needed for a particular bus type
depending on the number of inputs and transformers declared by the user. First, the column
number “c” is set to 4. Second, a For loop runs for each row 2 through 8. Third, the Select Case
command runs on the variable “r” which is different for each row and each row in this
spreadsheet is a different bus type.
Case 2 is the SBSB3 bus type arrangement. For SBSB3 the total number of breakers
(bkrs_total) is equal to the number of inputs (inpts) as defined by the user. Next, the previously
calculated value of the total number of breakers is entered into the spreadsheet under the Breakers
column in the first cell in row 2 column 4. After that, the bus type string (bus_type) is set to
SBSB3 and the bus type is entered into the cell in row 2 column 5.
45
Case 3 is the SBSB6 bus type arrangement. For SBSB6 the total number of breakers
(bkrs_total) is equal to the number of inputs (inpts) plus the number of transformers (trfs) input
by the user. The equation is (inpts+trfs). Next, the previously calculated value of the total number
of breakers is entered into the spreadsheet under the Breakers column in the first cell in row 3
column 4. After that, the bus type string (bus_type) is set to SBSB6 and the bus type is entered
into the cell in row 3 column 5.
Case 4 is the MT bus type arrangement. For MT the total number of breakers (bkrs_total)
is equal to the number of inputs (inpts) plus the number of transformers (trfs) + 1. The equation is
(inpts+trfs)+1. Next, the previously calculated value of the total number of breakers is entered
into the spreadsheet under the Breakers column in the first cell in row 4 column 4. After that, the
bus type string (bus_type) is set to MT and the bus type is entered into the cell in row 4 column 5.
Case 5 is the DBSB bus type arrangement. For DBSB the total number of breakers
(bkrs_total) is equal to the number of inputs (inpts) plus the number of transformers (trfs) + 1.
The equation is (inpts+trfs)+1. Next, the previously calculated value of the total number of
breakers is entered into the spreadsheet under the Breakers column in the first cell in row 5
column 4. After that, the bus type string (bus_type) is set to DBSB and the bus type is entered
into the cell in row 5 column 5.
Case 6 is the DBDB bus type arrangement. For DBDB the total number of breakers
(bkrs_total) is equal to the number of inputs (inpts) plus the number of transformers (trfs) and that
entire quantity is multiplied by 2 because this bus type has twice as many breakers as inputs and
outputs to the bus. The equation is (inpts+trfs)*(2). Next, the previously calculated value of the
total number of breakers is entered into the spreadsheet under the Breakers column in the first cell
in row 6 column 4. After that, the bus type string (bus_type) is set to DBDB and the bus type is
entered into the cell in row 6 column 5.
46
Case 7 is the BAAH bus type configuration. For BAAH the total number of breakers
(bkrs_total) is equal to the number of inputs (inpts) plus the number of transformers (trfs). That
entire quantity is multiplied by 3/2 and then ¼ is added to that quantity. The equation is
((inpts+trfs)*(3/2))+(1/4). This equation takes advantage of the fact that the bkrs_total variable is
defined as an integer. For example, if there are 3 inputs and 3 transformers the result should be 9
breakers. Using the above equation the result is 9 and ¼ which automatically rounds to 9. If there
are 2 inputs and 3 transformers the result should be 8. In this case, the equation result is 7 and ¾
which automatically rounds to 8 resulting in the correct number of breakers. Next, the previously
calculated value of the total number of breakers is entered into the spreadsheet under the Breakers
column in the first cell in row 7 column 4. After that, the bus type string (bus_type) is set to
BAAH and the bus type is entered into the cell in row 7 column 5.
Case 8 is the Ring bus type configuration. For the Ring Bus the total number of breakers
(bkrs_total) is equal to the number of inputs (inpts) plus the number of transformers (trfs). The
equation is (inpts+trfs). Next, the previously calculated value of the total number of breakers is
entered into the spreadsheet under the Breakers column in the first cell in row 8 column 4. After
that, the bus type string (bus_type) is set to Ring and the bus type is entered into the cell in row 8
column 5.
After Case 8 is completed the case statement ends and the for loop ends resulting in the
completion of this module.
47
Bus_select Module
This module selects which calculations should be done depending on the bus type
configuration. The module starts with a Select Case command based on bus type. Using the same
bus type order as the previous module, the first Case starts with the bus type SBSB3. Within the
Case statement, the module SBSB3 is called which calculates the numbers of breakers for
isolation and lines lost for both fault conditions and maintenance conditions. Next, the
Calc_pcnt_values module uses the values calculated in the module SBSB3 to calculate the
percentage of breakers that trip to isolate a fault or isolate components for maintenance. The
Calc_pcnt_values module also calculates the percentage of lines lost due to a fault or component
down for maintenance. The Calc_metrics module calculates the metrics for robustness,
maintainability, and the breaker IO ratio whose variable is labeled cost within the code. Next, the
Calc_operability runs calculating the operability metric. To finish the Case statement, the
Fill_cells module is called filling the cells in the spreadsheet with the calculated metrics data.
The following Case statements are similar to the first with some minor changes. One of
the differences is that each Case statement starts with the module of the same name as the bus
type in the Case statement. This is due to the differences in calculations to find the numbers of
breakers for isolation and lines lost for both fault conditions and maintenance conditions when
different bus types are considered. All of the following Case statements are the same up to the
Fill_cells module and those Case statements are SBSB6, MT, DBSB, DBDB, BAAH, and Ring.
The BAAH Case includes one command following fill cells that makes the operability cell red to
indicate sectionalization occurs. The Ring Case includes an If statement so if there are 6 breakers
in the ring then sectionalization can occur and the cell will be turned red. The final Case is the
Case Else and this Case only occurs if the cell containing the bus type is labeled incorrectly. In
this particular spreadsheet, this case will never happen but if the code is used on some other
48
spreadsheet then it can occur. When the Case Else is activated a message appears to the user that
says “Incorrect Bus Type Label,” shows what the cell was labeled “in cell,” and then the cell
position is given so the user can easily find and correct the mistake. This ends the case and
module.
SBSB3 Module, SBSB6 Module, MT Module, DBSB Module, DBDB Module, BAAH
Module, and Ring Module
These modules are all mathematical algorithms used to calculate the numbers of lines lost
and breakers needed to isolate specific portions of the system under certain conditions. Those
conditions are fault conditions, and maintenance conditions on the bus, breaker, and
transformer/line. The addition of lines_lost and bkr_iso in these formulas are needed for the
operability function. The additional variables allow modules to be called recursively after the first
maintenance calculation has been performed in the operability section. These modules are all
described in detail in the algorithm section of the report, Chapter 4.
Calc_operability Module
This is the most complex module of the entire program. The operability as described
before is the system when one item is down for maintenance and a fault occurs. Due to the
complexity of the algorithms in this module, they are described in detail in the algorithms section
of the report, Chapter 4. This module is basically a case statement where each case is a different
bus arrangement.
Within each case statement for specific arrangements, bus maintenance is calculated
followed by the calculation of a fault on the bus, breaker, and transformer/line. Next, the
49
Calc_pcnt_values module is called returning the average lines lost for all three fault types. The
100 is subtracted from the lines lost value resulting in the number of lines left in service when bus
maintenance is being performed and a fault occurs.
The previously described calculations are performed again for breaker maintenance and
transformer/line maintenance. Finally, the results of all three maintenance conditions with faults
included are combined and averaged resulting in the operability of that specific bus arrangement.
The procedure is repeated using different algorithms for each type of bus arrangement.
Please see the algorithms section for details of the algorithms used, Chapter 4.
Calc_pcnt_values Module
This module calculates the percentage of breakers needed to isolate a fault, percentage of
lines lost due to a fault, the percentage of breakers to isolate components for maintenance, and
percentage of lines lost due to maintenance. The first module encountered is the Pcnt_ave_calc
module used to calculate the percent average of three different values. In this case the
Pcnt_ave_calc module receives the number of breakers needed to isolate a fault for a bus fault,
breaker failure, and transformer fault. The module is also given the total number of breakers. The
module returns the average percentage of those three pieces of data or the total percent average
number of breakers needed to isolate a problem due to a fault. It is important to realize that all of
the faults are given equal probability. Next, the data received from the previous module is input
into the bkr_iso_flt variable for later use. This two step process is repeated several times to
calculate the percentage of lines lost from a fault (lines_lost_flt), the percentage of breakers
needed to isolate components for maintenance (bkr_iso_mnt), and the percentage of lines lost due
to maintenance (lines_lost_mnt). That completes this module.
50
Calc_metrics Module
The Calc_metrics module calculates robustness, maintainability, and the breaker IO ratio
also known as cost in this program. The robustness is just 100 – lines_lost_flt and is therefore a
measure of the average percentage of lines remaining in operation due to all fault conditions.
Next, maintainability is calculated using the formula 100 – lines_lost_mnt resulting in the average
percentage of lines still in operation under all maintenance conditions. Finally, the cost function
or breaker IO ratio is calculated using the formula (bkrs/i_o)*100 and this formula gives a very
general percentage of the cost of each bus arrangement based solely on the varying number of
breakers in each system. That concludes this module.
Pcnt_ave_calc Module
This module takes in three variables and a denominator to calculate the percent average
of those values. This module was added due to the number of times this calculation needs to be
performed. First, three variables are declared for use in the calculations. Second, an If statement
is encountered which makes sure the following equations do not divide by zero causing an error.
Third, the bus percentage (bus_pcnt) is calculated using the formula (bus/denom)*100. Similarly,
the breaker percentage (bkr_pcnt) is calculated using the formula (bkr/denom)*100. Likewise, the
transformer percent (bnk_pcnt) average is calculated using the formula (bnk/denom)*100. Once
each percentage is obtained the total percent average is calculated by adding the three and
dividing by three, (bus_pcnt + bkr_pcnt + bnk_pcnt) / 3. If the denominator is zero the Else
portion of the If statement activates returning a percent average value of 0. That is the end of the
If statement and the module.
51
Populate_variables Module
This module pulls data from the excel spreadsheet and puts the data into variables for use
throughout the program. First, data is pulled from the cell in row 2, column 1 where the user input
the number of inputs for the system, this data is stored in the variable “inpts.” Second, data is
pulled from the cell in row 2, column 2 where the user input the number of transformers, this data
is stored in the variable “trfs.” Third, the number of transformers and inputs are added together to
find the total number of inputs and outputs connected to the bus arrangement, i_o_total = inpts +
trfs. Fourth, the input-output variable (i_o) is populated with the input-output total value
(i_o_total) because the i_o value may be changed by the code at some point. Finally, the bkr_iso
and lines_lost variables are set to zero due to the fact that these variables are used later for
recursive iterations of the same code. The variables are needed to take into account the previously
known values for lines lost and breakers needed to isolate a situation. It is important that these
variables start out at zero. The module has been completed.
Fill_cells Module
This module runs at the end of the main code to fill cells in the spreadsheet with the data
calculated in the program. First, the robustness cell is filled, then the maintainability cell is filled,
then the operability cell is filled, and finally the breaker IO ratio is filled using the cost variable.
This code is run over and over proceeding row to row filling the cells with data. That completes
the module.
52
Data_Chart Module
This module uses the calculated data to create a chart giving the user a good, simple
graphical representation of the data calculated. The first command in this module activates the
chart on the first sheet of the spreadsheet. Second, the command sets the range of the data to be
used from the spreadsheet to create the chart. Third, this command tells excel what type of chart
to create. Fourth, the chart title is enabled. Fifth, the chart title is declared “Bus Type
Arrangement Comparison.” Finally, a cell is selected to be active so the program doesn’t end with
the chart selected which is just an inconvenience not allowing the user to hit the run button
multiple times. This finishes the Data_Chart module.
Clear_cells Module
This module clears the cells that were populated by the previous run of the program. This
is to make sure extraneous data does not hang around. This code declares its own “r” and “c”
variables for rows and columns because it can also work as a standalone module. First, a For loop
is encountered which runs through rows 2 through 8. Second, another For loop is encountered
which runs through columns 4 through 9. Third, an If statement is reached which checks to see if
the cell is empty, if the cell is not empty then it proceeds to clear the contents of the cell. After
looping through all of the For loops this module is finished.
53
Chapter 6
RESULTS AND ANALYSIS
In this chapter, the program results are displayed and analyzed to gain maximum
information about each of the bus arrangements.. In addition, comparisons are made between
arrangements to show the advantages and disadvantages of choosing specific substation bus
arrangements. Figure 23 is the entire spreadsheet results. Figure 24 shows the graphical results
and Table 18 shows the exact tabulated results.
Figure 23: Bus Type Arrangement Comparison Spreadsheet
54
Figure 24: Bus Type Arrangement Comparison Graph
Table 18: Bus Type Arrangement Comparison Table
The program gives some expected and interesting results. As seen in Figure 23, the
program provides the user with a single page of results including the exact metric numbers, Table
18, and a graphical representation of those results, Figure 24. All metrics are highlighted in a
specific color for both the table and graph for quick analysis. In this case, the number of inputs is
set to 3 and the number of transformers is set to 3. As one can see, the single bus single breaker
case one (SBSB3) calculated the number of breakers needed as 3. The single bus single breaker
case two (SBSB6) calculated the number of breakers as 6. The main and transfer (MT) calculated
55
the number of breakers as 7. The double bus single breaker (DBSB) calculated the number of
breakers needed as 7. The double bus double breaker (DBDB) calculated the number of breakers
needed as 12. The breaker and a half (BAAH) calculated the number of breakers as 9. And the
Ring bus calculated the number of breakers needed as 6. These results are correct and can be
compared to the diagrams and bus arrangement characteristics in Chapter 2.
First, the robustness is analyzed. The robustness is the percentage of lines remaining in
service when a fault occurs. For the SBSB3 arrangement, the robustness is 14%. This is an
expected result. During both a bus fault and breaker failure, all of the lines are lost. Although,
during a transformer/line fault the results are slightly different, in fact two results are possible.
First, if the fault is on the transformer then every breaker trips and all of the lines are lost. Second,
if the fault is on the incoming transmission line then only a single breaker trips and only one line
is lost. The final case is what results in a 14% robustness.
The SBSB6 arrangement results in a robustness of 28%. As with the first case, during a
bus fault or breaker failure all lines are lost. During a transformer/line fault only a single line is
lost resulting in a robustness of 28%. Refer to Figure 6 for details.
During normal operation, the MT arrangement operates as a SBSB6 arrangement. All
fault scenarios are the same resulting in the same robustness of 28%. Compare Figure 9 to Figure
6 to confirm the similarity to the SBSB6 arrangement.
During normal operation, the DBSB arrangement also resembles the SBSB6 arrangement
and the results are the same, robustness is 28%. The bus connections can be modified slightly to
improve the robustness by sectionalizing half of the connections to one side of the bus and the
other half to the other but this is not typical. Please refer to Figure 12 for details on the different
fault conditions.
56
The DBDB arrangement gives the best results for robustness with a value of 89% lines
remaining due to a fault. This arrangement has significant improvement over the previous
arrangements. By examining the fault diagrams in Figure 15, it is found that under most faulted
conditions, only one line is lost and on a bus fault, zero lines are lost. This proves that the DBDB
arrangement is the most robust; being able to withstand minimal loss during a fault condition and
the program shows that fact instantly.
The BAAH arrangement is very robust with 87% of lines remaining in service due to any
fault condition. This type of bus arrangement is very hard to analyze due to differing fault
conditions needing to be considered as seen in Figure 18. It is easily seen that this arrangement is
slightly less robust then the DBDB arrangement due to the one condition when the center breaker
fails and two lines are lost. Other than that, the BAAH arrangement is a highly robust system.
The final arrangement is the Ring arrangement with a resulting robustness of 78%. In
practice, the Ring arrangement is limited to 6 breakers, therefore this is the largest ring bus that
should be built. The Ring arrangement looses only one line during bus or transformer/line faults
and looses two lines during a breaker fault as seen in Figure 21.
Second, the maintainability is analyzed. For the SBSB3 arrangement, the maintainability
is found to be 42%. For bus maintenance, all of the lines are lost. For breaker maintenance, only
one line is lost. For transformer maintenance, all of the lines are lost. And for input transmission
line maintenance only one line is lost. Therefore, the maintainability is an accurate measurement
of the percentage of lines remaining in service during maintenance conditions.
The analysis of the SBSB6 arrangement results in a maintainability of 55%. In this case,
bus maintenance removes all lines from service. Although breaker, transformer or transmission
line maintenance only removes one line from service. This results in an average of 55% of the
lines remaining in service. The maintenance conditions can be seen in Figure 7.
57
The MT arrangement has a maintainability of 61%. Maintenance of the main bus results
in the loss of all lines, although the transfer bus can be serviced at any time during normal
operation because the bus-tie breakers connected switches remain open. During breaker
maintenance, the bus-tie breaker is used and the breaker is serviced without losing any lines.
Moreover, during transformer or transmission line maintenance only the effected line is lost.
These maintenance scenarios can be seen in Figure 10. The combination of maintenance
scenarios result in an average percentage of lines remaining in service as 61% during
maintenance of any portion of the substation.
The DBSB arrangement has a maintainability of 94%. This shows that the DBSB
arrangement is highly maintainable with minimum lines lost during all maintenance conditions.
Referring to Figure 13, it can be seen that either bus can be serviced without any loss of lines. In
addition, any breaker can be serviced by using the bus-tie breaker resulting in no lines lost. And
finally the transformer or transmission lines can be serviced losing only the line being serviced.
This shows a significant advantage over the MT design.
The system regarded as the best, shown in Figure 16. The system is the DBDB
arrangement, which has a maintainability of 94%. The results are the same as the DBSB
arrangement because the only time a line is lost for maintenance is when the transformer or
transmission line is being serviced. Therefore, the line lost is the line being serviced. This bus
arrangement is highly serviceable.
The BAAH arrangement also has a maintainability of 94%. As in the previous two
arrangements, the only time a line is lost is when that line is being serviced, see Figure 19. This is
also a highly maintainable system.
Finally, the Ring arrangement has a maintainability of 89%. The maintainability is very
high for this arrangement also. During bus, transformer or transmission line maintenance a line is
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lost, as seen in Figure 22. The only reason the maintainability for the Ring arrangement is less the
previous three arrangements is due to the inclusion of bus faults in which this system has either
six busses or no busses at all. The bus was included into the analysis due to some discussion with
several senior engineers who refer to this arrangement as a 6 bus arrangement, otherwise its
maintenance characteristics are quite similar to the previous three arrangements discussed.
Third, the operability is analyzed. The operability is a measurement of the percentage of
lines that remain in service when one component is down for service and then a fault occurs.
These are extreme cases and result in many complex scenarios all of which must be analyzed
individually. Due to the number of scenarios being considered figures of each scenario was not
drawn. To do a self-analysis of every potential scenario one can look at the maintenance figures
and then analyze those for different fault conditions. The algorithm and analysis of this portion of
the program is quite complex for certain bus arrangements.
The operability for the SBSB3 arrangement was found to be 0%. One specific case exists
in which not all lines would be lost. Although, that case is very improbable and most likely would
not be allowed to happen due to the protection scheme being used. The case mentioned is when a
breaker is down for service and then one of the transmission lines has a fault. The fault would trip
the breaker leaving one transmission line in service. In this case, the one transmission line would
be feeding the three remaining transformers. Most likely, the one line would not be able to supply
the load of those three transformers and the protection would trip that final breaker. Therefore,
this remote case was not considered and under the operability conditions, the percentage of lines
remaining in service is 0%.
The SBSB6 arrangement has an operability of 15%. During bus maintenance, all lines are
lost. During both breaker and transformer/line maintenance, one line is lost and then the
arrangement is analyzed for faults as a SBSB6 arrangement minus one line. This analysis results
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in the average percentage of lines remaining in service at 15% under all fault conditions after one
item has been removed for maintenance.
The MT arrangement has an operability of 17%. In this case the during main bus
maintenance all lines are lost. During breaker maintenance, one breaker is taken out of service
and the bus is analyzed for faults using the SBSB6 model. And for the transformer/line
maintenance condition one breaker and line are removed and the system is analyzed for faults
using the MT condition minus one line and one breaker. This analysis results in an average
percentage of lines remaining in service at 17%.
The DBSB arrangement has an operability of 26%. When either bus is removed for
maintenance, the system is analyzed for faults using the SBSB6 model. When a breaker is down
for maintenance, the bus-tie breaker is used and the system is analyzed for faults using the
SBSB6 model. Finally, when the transformer/line is being serviced one line and one breaker is
lost and the system is analyzed for faults using the DBSB model minus one line and breaker.
The DBDB arrangement has an operability of 61%. This arrangement has the highest
operability proving why it is regarded as the overall best bus arrangement. During bus
maintenance, the DBDB is downgraded to the SBSB6 model for fault analysis. For
transformer/line maintenance, two breakers and one line are lost resulting in a DBDB model
minus the one line lost and two breakers lost, and then fault analysis is performed. During breaker
maintenance, there are many different conditions, which must be considered, and they are fully
explored and explained in the algorithm section of the report. After all of the analysis is
performed, the average percentage of lines remaining in service is 61%, which is very high and
shows the advantage of using the DBDB arrangement.
The BAAH arrangement has an operability of 55%. The BAAH arrangement is one of the
most complex systems to analyze for operability because there are so many different scenarios
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that can take place. The scenarios that must be considered are any one item being down for
maintenance and any type of fault happening at any given point in the system. This system does
not default to some other type of arrangement under any condition. In addition, the protection
scheme is quite complex for the center breaker because it must protect against faults from both
sides. One important thing to remember is that when an item is down for maintenance there are
maintenance and operations personnel on site to handle any fault conditions, which may occur.
One of the conditions of concern about this setup occurs during bus maintenance when there is a
fault on the other bus. In that, special case the bus will sectionalize and island the center breakers.
During any islanding condition, the code assumes that all of the islanded lines are lost, although
in actual practice this is not true. During this island situation, a transmission line can provide
current through the islanded breaker to the step down transformer load or another transmission
line. Luckily, this situation has a low probability and personnel are on site with contingency plans
to address such a situation. Islanding can occur in other situations using this bus type, the code
assumes those lines are lost, in addition, the operability cell in the spreadsheet is flagged red to
alert the user to this condition. With all of those situations considered, an overall average
percentage of lines remaining in service of 55% is very good and with operators on site most of
the issues mentioned can be addressed and hopefully rectified quickly.
Finally, the Ring arrangement has an operability rating of 44%. In this arrangement, the
code assumes that if sectionalization occurs the section with the minimum number of lines is lost.
For this very reason, in practice, the ring bus is limited to a total of 6 breakers. Sectionalization or
islanding can occur in all three conditions of maintenance, bus, breaker, and transformer/line.
During these maintenance conditions, if a transformer/line fault occurs two lines away from the
item in maintenance then islanding occurs and the bus is broken into separate sections. As in the
previous arrangement, operations personnel will be on site during maintenance with a
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contingency plan for any potential problem which may arise. With all of these situations taken
into account, the overall average percentage of lines remaining in service is 44%.
Fourth, the breaker IO ratio is analyzed. The breaker IO ratio is just the number of
breakers divided by the number of input and output lines connected to the bus arrangement
multiplied by 100 to get a percentage. Therefore, a 100% breaker IO ratio means there is exactly
the same number of breakers as there are lines connected to the bus arrangement. Moreover, a
200% breaker IO ratio means there are twice as many breakers then lines connected to the bus
arrangement. This metric gives a rough estimate of cost if it is assumed that cost is based on the
number of breakers in the arrangement. The ratio found for SBSB3 is 50%, SBSB6 is 100%, MT
is 117%, DBSB is 117%, DBDB is 200%, BAAH is 150%, and the Ring bus arrangement is
100%. Of course, for actual cost, bus, switch, labor, land, and more costs must be taken into
account, see Chapter 3 for more details.
When doing a full analysis of all of the metrics combined, several conclusions can be
made. In the SBSB3 arrangement one finds that the cost is cheap and if breaker protection is
needed but loosing lines is not a concern then this is a viable option. For the SBSB6, MT, and
DBSB arrangements, the robustness is low and equal to each other. The main difference between
these three is maintainability. The DBDB arrangement is significantly more maintainable when
compared to the SBSB6 arrangement. This gives the user a choice as to whether a slightly larger
investment should be made so that maintenance can be performed without losing a significant
amount of lines, this maintenance mainly pertains to bus maintenance. As expected, the DBDB
arrangement performs the best for all metrics although the cost is much greater also. The BAAH
arrangement metrics are very close in value to the DBDB arrangement for a reduced cost, which
is why it is implemented in almost every 500kV transmission substation in the PG&E grid. In
addition, both BAAH and DBDB arrangements can be expanded to accommodate more and more
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lines, which is a major limitation to the Ring arrangement. The advantage to the Ring
arrangement is that for small systems the metrics are very good, the cost is low, and this
arrangement gives a major improvement over all of the other designs with similar costs.
Therefore, the program gives real results and comparisons between many different types
of bus arrangements making it easy for a user to get a quick feel for how each arrangement
compares when a fault, maintenance, or both situations occur. It also gives the user a rough
estimate for the cost comparison between arrangements. Finally, it give the user another tool to
use when making, justifying, or just solidifying the reasons for making a specific bus arrangement
choice.
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Chapter 7
CONCLUSION
Engineers in the field make substation design decisions based on research, experience,
previous design implementations, current standards, future models, performance and reliability
data. Many decisions are based on past experience and standards put in place without considering
any numeric analyses that compare performance differences between the various substation bus
arrangements. The goal of this effort was to develop a tool to be used by engineers that gives
them immediate feedback on the performance of each substation bus arrangement with relatively
little input data. The fact is engineers rarely have access to reliability studies, future growth
studies or other data needed to make sound decisions about the optimal choice of the bus
arrangement for their current design needs. The program gives them instant access to valuable
calculated information giving them the information needed to make informed design decisions.
It was found that with minimal data such as; the number of source line inputs into the
substation and the number of transformers connected to the bus, a large amount of information
can be generated for many different substation bus arrangement designs. In fact, if only the
numbers of source line inputs and transformers are known, the number of breakers for each bus
type can be calculated. Subsequently, from that information the robustness, maintainability,
operability, and breaker IO ratio of each bus arrangement can also be calculated. The robustness,
maintainability, and operability are metrics that were created to give the user knowledge on the
performance of differing substation bus arrangements. They take into account the substations
performance under fault conditions, maintenance conditions, and a combination of the two. These
metrics give the user an instant measurement on the performance of each bus arrangement
resulting in more data from limited information to make a more informed design decision.
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For a three input, three transformer substation, the robustness was found to be greatest in
the DBDB, BAAH, and Ring bus arrangements. This tells the designer that if this substation is
critical, supplies large numbers customers, and/or supplies industrial customers who demand
power with minimal outages, one of these three arrangements would be the best choice.
The maintainability was found to be the highest for the DBSB, DBDB, BAAH, and the
Ring bus arrangements. This metric tells the designer that if frequent maintenance is expected in
the future, then a substation design with a high maintainability rating must be used. Circuit
breaker replacements maintenance, transformer replacement/maintenance, or bus section
replacement/maintenance are examples of events that increase the frequency of maintenance in a
substation. The ring bus is not expandable beyond 6 breakers so this would not be a good choice
if bus expansion was expected in the future. Also, the DBSB arrangement has a low robustness
rating and should not be used in critical systems where excessive down times due to faults maybe
unacceptable.
The operability metric being the combination of a component down for maintenance
followed by a fault gives the designer a view of the flexibility of each system. Operability tells
the designer if the bus arrangement can continue to provide power in some capacity if multiple
problems arise at the same time. This is also an important metric if a significant amount of
maintenance is going to be performed on a particular bus type. The DBDB arrangement is by far
the best performing substation design when it comes to operability. The BAAH and Ring bus
arrangements both have good operability numbers. However, they also have the potential to
sectionalize, breaking into multiple sections under specific conditions. This is a potential hazard
and must be considered in the engineers design.
The breaker IO ratio gives the user an approximation of the cost of a particular substation
design, as well as, the size of the footprint for the bus arrangement. The DBDB is by far the most
65
expensive and has twice as many breakers as the SBSB6 arrangement. The MT and DBSB
arrangements have the same numbers of breakers, are comparable in cost with slight performance
increases for the DBSB arrangement. The most economical arrangement is the SBSB3
arrangement with breakers only connected to the incoming transmission lines. The breaker IO
ratios give an engineer another useful piece of information to help make an informed engineering
decision.
The summary of what was found using the program is that the DBDB arrangement is the
best performing bus arrangement out of all bus arrangements tested. The DBDB arrangement is
also the most expensive making it an infeasible option for certain applications. The BAAH and
Ring bus arrangements both have great performance characteristics although the ring bus is
limited in its ability to be expanded. The DBSB is a good compromise option with a high
maintainability metric, which is desirable in certain cases. The MT and SBSB6 arrangements are
almost comparable in performance characteristics. The main difference between the two is during
specific maintenance or fault conditions, the bus-tie breaker in MT configuration can be used to
reduce the number of line outages in certain instances. And finally, the SBSB3 arrangement with
breakers tied only to the input transmission lines is the most economical, with least number of
breakers, and lowest performance. However in rural areas where down time is more tolerable, this
system provides an adequate design option.
Finally, the program provides significant numeric results on the performance of different
substation bus arrangements based on several metrics. The user of the program receives
understandable information in both exact numbers and in graphical formats for easy comparison.
The algorithms used consider all situations and provide a true measurement of the performance of
different bus arrangements. The results can verify many of the assumptions made in the past
design choices, hence lending justification as to why specific arrangement had been chosen. This
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program is a simple tool that engineers can use to gain a feel for the actual performance of
different substation designs.
Improvements and Future Research
Many improvements are foreseeable for this program. The first improvement would be to
add weighting factors to the probability of a fault occurring on specific components. The
weighting factor could also be applied to the items in need of maintenance. In addition, actual
probability numbers from specific substations could be implemented into the calculations. A
second page could be added to show the percent of breakers used to isolate faults or components
for maintenance. A more accurate cost function could be implemented. Additions could be made
to calculate metrics of additional and non-standard substation arrangements not addressed in this
report. Also, the program could be modified to include distribution substations as well as
switchyards, and generation substations. Modifications could be made to take into account other
types of substation equipment such as; fuses, switches, reclosers etc. Finally, this program could
be adapted and applied to other systems in addition to substation design.
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REFERENCES
P.M. Anderson, Power System Protection. New York, NY: IEEE Press, 1999, pp. 160-166.
T. Gönen, Electric Power Distribution System Engineering. Boca Raton, FL: CRC Press, 2008,
pp. 176-180.
“Design Guild for Rural Substations,” Rural Utilities Service, United States Department of
Agriculture, June 2001
J. Green, S. Bullen, R. Bovey, M. Alexander, Excel 2007 VBA. Indianapolis, IN: Wiley
Publishing, 2007
B. Jelen, T. Syrstad, VBA and Macros for Microsoft Office Excel 2007. Indianapolis, IN:
Que Publishing, 2008
D. Nack, “Reliability of Substation Configurations,” Iowa State University, IA, 2005.
Web. 13 April 2011. [Online]. Available:
http://www.ee.iastate.edu/~jdm/ee653/SubstationReliability.pdf