SECONDARY DISTRIBUTION SYSTEM OPTIMIZATION METHODOLOGY
AND MATLAB PROGRAM
A Project
Presented to the faculty of the Department of Electrical and Electronic Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Electrical and Electronic Engineering
by
Steve Ghadiri
Majid Hosseini
FALL
2013
© 2013
Steve Ghadiri
Majid Hosseini
ALL RIGHTS RESERVED
ii
SECONDARY DISTRIBUTION SYSTEM OPTIMIZATION METHODOLOGY
AND MATLAB PROGRAM
A Project
by
Steve Ghadiri
Majid Hosseini
Approved by:
_________________________________, Committee Chair
Turan Gönen, Ph.D.
_________________________________, Second Reader
Salah Yousif, Ph.D.
_________________________
Date
iii
Student: Steve Ghadiri
Majid Hosseini
I certify that these students have 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.
_________________________
Date
Department of Electrical and Electronic Engineering
iv
ACKNOWLEDGMENTS
The authors would like to acknowledge Dr. Turan Gonen, Professor of Electrical
Engineering at California State University, Sacramento, for his guidance, supervision,
patience, and care in recommending and evaluating this project in the area of Power
Engineering at California State University, Sacramento.
The authors are also appreciative of Dr. Salah Yousif, Professor of Electrical Engineering
at California State University, Sacramento, for his excellent instruction in the area of
Power Engineering at California State University, Sacramento, as well as being a reader
of this project.
The author would also like to acknowledge Dr. Preetham Kumar, Graduate Coordinator,
and Professor of Electrical Engineering at California State University, Sacramento, for his
guidance and direction in completion of this project.
v
Abstract
of
SECONDARY DISTRIBUTION SYSTEM OPTIMIZATION METHODOLOGY
AND MATLAB PROGRAM
by
Steve Ghadiri
Majid Hosseini
The goal of many utilities is to provide an economically balanced energy delivery
system that will provide customers with safe, reliable, and efficient means of power while
not subjecting them to over-designs with unjustifiable cost. In achieving that goal, the
utility company must rely on system designers to optimize several key parts of their
delivery system. The distribution system secondary, e.g., is one of these subsystems, and
therefore, it can pose optimization type challenge for the distribution system designers.
Arriving at optimal solutions, serves the best interests of the utility and the long-term
objectives of the customers and ratepayers.
In this paper, the authors analyze many alternative intelligent choices when considering a
simplified distribution system selection and show, thru the formulation and Matlab
computer programming, how a simple optimization technique can arrive at a standard
selection of the system components. Total Annual Cost (TAC) is the reviewed concept,
vi
and essentially, it reduces to a sum of initial capital investment, maintenance, and
operating costs including the costs of system losses. The optimization process is pivotal
in minimization of the TAC. Customer loadings are a key part of this selection and have
been considered in the program formulation, as well. Matlab program provides the ease
in selection of the components and speed in calculation performance to arrive at a most
feasible answer among optimized choices. Voltage drop is the constraint in this
optimization process, which is usually limited by the utility company’s requirement.
_________________________________, Committee Chair
Turan Gönen, Ph.D.
_________________________
Date
vii
DEDICATION
We dedicate this paper to our family for supporting and inspiring us in this journey.
viii
TABLE OF CONTENTS
Page
Acknowledgement ...............................................................................................................v
Dedication ....................................................................................................................... viii
List of Tables ......................................................................................................................x
List of Figures ................................................................................................................... xi
Chapter
1. INTRODUCTION ..........................................................................................................1
2. DISTRIBUTION SYSTEM DESCRIPTION .................................................................5
2.1 Distribution System Design Requirement ..............................................................5
2.2 Distribution System Planning Methodology ........................................................7
3. LITERATURE REVIEW .............................................................................................10
3.1 Design Criteria .....................................................................................................10
3.2 Components of Secondary Distribution System .................................................15
3.3 Voltage and Load Criteria ...................................................................................16
3.4 Main Factors ........................................................................................................17
3.5 Changing Paradigm of the Power Distribution System .......................................19
4. OPTIMIZATION METHODOLOGY ..........................................................................24
5. ECONOMIC ESTIMATION AND ANALYSIS .........................................................43
6. NUMERICAL RESULTS ...........................................................................................49
7. CONCLUSIONS ..........................................................................................................64
Appendix A: Matlab Optimization Program for Secondary Distribution System ............68
Appendix B: Instruction for Matlab TAC Program in Distribution System ....................79
Appendix C: Secondary Distribution System Voltage Drop Program ............................83
Appendix D: Distribution System Component Information Background ........................91
Bibliography .....................................................................................................................96
ix
LIST OF TABLES
Table
Page
4.1 Load Data for Book Example 6.1 ...............................................................................39
6.1 Summary of the Runs .................................................................................................53
x
LIST OF FIGURES
Figures
Page
1.1 One Line Diagram of Typical Primary Distribution Feeders .......................................2
3.1 Radial-type Primary Feeders .......................................................................................11
3.2 One Line Diagram of a Typical Distribution System .................................................14
4.1 Flow Chart of Safigianni’s Optimization Process ......................................................25
4.2 Matlab Program Flow Chart .......................................................................................30
4.3 One Line Diagram of Multiple Primary System for JHC ...........................................32
4.4 Typical Residential Area Lot Layout and Service Arrangement ................................33
4.5 Illustration of a Typical Residential Secondary Pattern ..............................................33
5.1 Current Transformer Cost ............................................................................................45
5.2 Historic Cost of Transformers ....................................................................................45
5.3 Current Cable Cost .......................................................................................................47
5.4 Historic Cable Cost ......................................................................................................48
6.1 Transformer Cost Fit into Third Order Model ............................................................51
6.2 Cable Cost Fit into Second Order Model ....................................................................52
6.3 Cable Cost For Different Sizes ...................................................................................52
xi
1
Chapter 1
INTRODUCTION
1. Introduction
The power distribution systems, which carry electric energy to even far-flung
customers utilizing the most appropriate voltage level, are divided into primary and
secondary. The part of the electric utility system, which is between the distribution
substation and the distribution transformers, is the primary feeders or primary
distribution feeders. The secondary power distribution systems include step-down
distribution transformers, secondary circuits, consumer services, and meters to measure
the consumer energy consumption. They are single-phase when they serve residential
customers and three-phase when they serve industrial or commercial customers.
The most commonly used secondary power systems are the radial systems. The
general requirements from a secondary power distribution system are that it gives
customers as stable a voltage as possible, operate safely and effectively at the minimum
possible cost and is well balanced. One line diagram of a typical primary distribution
feeder is shown in Figure 1.1 below, as depicted from standard Handbook for electrical
Engineers [3].
2
Figure 1.1 One-line diagram of typical primary distribution feeders.
Source: (From Fink, D.G., and H. W. Beaty, Standard Handbook for Electrical Engineers,
11th edition, McGraw-Hill, New York, 1978. With permission.)
3
Unfortunately, the reliability of service continuity of the radial primary feeders is
low. A fault occurrence at any location on the radial primary feeder causes a power
outage for every consumer on the feeder unless the fault can be isolated from the source
by a disconnecting device such as a fuse, sectionalizer, disconnect switch, or recloser.
Additionally, the operation and planning of electric power systems involve even a long
list of challenging activities, many of which are directly or indirectly related with the
optimization of certain objective functions [13].
The complex algorithms can be obtained from the cited references, which have
been developed in order to examine whether a radial secondary power distribution system
fulfills several criterions. Conductor tapering, network conductors having sufficient
thermal short-circuit strength, power flow in each network segment less than the thermal
of the conductor used there, acceptable percent voltage drop from the distribution
transformer (source node) up to any one of the ends of the network, and adequate fault
current to operate the network protection are essential part of this criteria [4].
While we acknowledge those methodologies and we ideally wish to create those
features in a comprehensive software program, we are somewhat limited to essential
math functions in our Matlab program, and therefore, we recognize that we have no way
of implementing all of them in our Matlab program. Use of power flow programs can
perhaps facilitate their implementation caption.
4
Switching mechanisms and over current protections are usually associated with
the type of configurations and they do not necessarily follow exactly into an optimization
program. Additionally, the cost of the over-current protection does not always vary
linearly with the size of the system. For simplicity, they have been put aside here as an
economical or fault current constraint in our program [6].
Safigianni has shown the methodology behind an elaborate optimization program
[4] and [5]. In her program, each stage is analyzed for the constraints by examination. If
the result of the above examination is that any of the previously mentioned technical
constraints is not satisfied, the program which implements the algorithm suggests a
number of alternative solutions concerning transformer changes or conductor
replacement combinations or both of them, in order to optimize technically the system
operation. This number depends on the load distribution and the conductor types and
sizes, which are available for the network construction. Finally, the program estimates
economically the alternative technically acceptable solutions and selects the most
economical one. The algorithm of Safigianni is an improvement and extension of the
algorithm used in her first reference and it is using more constraints, a load flow analysis
method to calculate the currents, voltages, economic data, and functions to estimate the
resulting technical solutions, which make final results more accurate and reliable.
Ultimately, a capable optimization method could expand to power flow modeling of a
portion of network.
5
Chapter 2
DISTRIBUTION SYSTEM DESCRIPTION
2.1 Distribution System Design Requirement
Secondary power distribution systems are used to deliver power to consumers in
residential or commercial businesses. We cannot imagine living without efficient
constant source of power. The best distribution system is one that will supply adequate
power to present and future loads safely and cost effectively. Distribution design
engineers choose the best distribution system, when they have considered all the design
parts, installation, and the cost. Design needs to be safe, effective, and reliable. Then, at
the same time, it needs to be not necessarily cheap, but cost effective.
In order to design the best distribution system, the system design engineer must
have information concerning the loads and knowledge of the various types of distribution
systems that are applicable. The various categories of buildings have many specific
design challenges, but certain basic principles are common to all. Such principles, if
followed, will provide a soundly executed design.
Understanding of the entire component in the power distribution system and their
functions are essential for implementing a proper design. The components in such a
system are power distribution transformers, primary and secondary conductors, and
power poles. For choosing the right component in this system, the most important
6
information is how consumer uses this power. Most important piece of information is the
amount of load that consumer will use considering present load and future load given the
load value will constantly change both within a day and over time. The future load
increase also needs to be considered because the system will not be cost effective if the
system need to be replace in 1, 2, or even 10 years.
In this paper, we report on the creation of a Matlab program for a simplified
residential block, which is illustrative of city development, and it explores a secondary
distribution system design that supply an area block with 24 loads. A reasonable load
demand could be input for each consumer. The demand assumption relies on average
monthly electrical usage for the area with some extra spare capacity (20 percent) for
safety before reaching the threshold and of course some extra room for future usage. The
program calculates the total annualized cost for the design and then this cost is optimized
with transformers, primary system enhancements, service laterals, and service drop
secondary conductors. The service is size optimized (or sub-optimized) based on
optimized cost and number of pertaining constraints. After the entire initial components’
selection, the program calculates the voltage drop to ascertain, if it is in an acceptable
range and if it is not, the design needs to be changed. Conductors can be overhead or
underground. In case of overhead conductor, the cost of poles and other component will
add to the overall layout cost, and for underground distribution, the cost of trenching,
conduits, and pull boxes will have to be added which usually are substantially more.
7
2.2 Distribution System Planning Methodology
The costs and reliability of power distribution systems are beginning to receive as
much attention as those of power generation and transmission systems. Modern planning
of these large-scale and complicated systems relies heavily on computers and
mathematical optimization tools [12].
Especially, in the developing countries where the growing power demand
provides needs for substantial expansion of power distribution systems, the long-term
benefit brought by using computerized optimization tools are tremendous, as compared
to widely practiced ad hoc methods involving only local computation.
The goal of modern power distribution system planning is to satisfy the growing
and changing system load demand during the planning period and within operational
constraints, economically, reliably and safely, by making optimized decisions on the
following: voltage levels of the distribution network; locations, sizes, servicing areas,
loads and building or expanding schedules of the substations; routes, conductor types,
loads and building schedules of the sub-transmission lines and feeders; other important
issues such as the types and locations of switching devices, load voltage levels, network
configuration, and load reliability levels, etc. The optimization problem is usually very
complicated, considering the scale of the system and the existence of many interrelated
factors.
8
The new approach for the systemized optimization of power distribution systems
is presented in Yifan Tang’s paper [12]. In Yifan’s paper the distribution system
reliability is modeled in the optimization objective function via outage costs and costs of
switching devices, along with the nonlinear costs of investment, maintenance and energy
losses of both the substations and the feeders. The optimization model establishes a
multi-stage, mixed-integer and nonlinear function, which is solved by a network-flow
programming algorithm. A multi-stage interlacing strategy and a nonlinearity iteration
method are also designed by him.
It is noteworthy to mention that the investment and maintenance costs of the
substations and the feeders are fixed costs (zero-order), while their operational costs are
variable costs squarely depending on their loads (second-order) [16], making the
objective function inherently nonlinear.
The need to seriously consider reliability in terms of capital costs in distribution system
planning is being recognized, as emphasized recently by an IEEE task force on
distribution reliability modeling and applications [17]. Unfortunately, few papers had
extensively tackled this problem [18] and [19]. Most of methodology by Yifan Tang is
based on the original Dr. Gonen’s work on Optimal Multi-Stage Planning of Power
System [21], and Pseudo-Dynamic Planning of Dr. Ramirez-Rosado and Gonen [22].
9
In this paper, of course for simplicity reasons we do not model reliability in our
simple secondary distribution optimization solution, however, when a designer is
considering the primary distribution design or a large portion of a city, one needs to
account for it. Usually selection of the switching configurations and degrees of
redundancy provide a certain level of reliability. Reliability inherently reflects into the
overall objective function via outage costs and costs of switching devices, along with the
present value of the costs of investment, maintenance and energy losses for both the
substations and the feeders.
10
Chapter 3
LITERATURE REVIEW
3.1 Design Criteria
Problem formulation and definition is important to arrive at a correct optimized
value in a multi- variable equation. There are various yet interrelated factors affecting the
selection of a primary-feeder rating [1]. Examples are:
1. Nature of the load connected
2. The load density of the area served
3. The growth rate of the load
4. The need for providing spare capacity for emergency operations
5. The type and cost of circuit construction employed
6. The design and capacity of the substation involved
7. The type of regulating equipment used
8. The quality of service required
9. The continuity of service required
There are many methods to design the distribution system and we will not concern
ourselves to discuss the other methods in detail here. However, we chose a radial type
primary feeder with uniform loading for the simplicity and ease of developing established
methodology into a Matlab optimization program. The simplest and the lowest cost, and
11
hence, the most common form of the primary feeder is the radial-type primary feeder as
shown in Figure 3.1, as shown below.
Figure 3.1 Radial-type Primary Feeders
Source: Electric Power Distribution System Engineering by Gonen [1]
12
The main primary feeder branches into various primary laterals, which in turn
separate into several sub-laterals to serve all the distribution transformers. Generally, the
main feeder and sub feeders are three-phase three-or four-wire circuits and laterals are
three or single-phase. The current magnitude is the greatest in the circuit conductors that
leave the substation. The current magnitude continually lessens out toward the end of the
feeder as laterals and sub-laterals are branched off the feeder, tapering down. Usually, as
the expected current value reduces in the service lateral, the size of feeder conductors
reduces in the design. However, the permissible voltage regulation may restrict any
feeder size reduction, since the thermal capacity of the feeder is also a consideration.
The reasons for making a secondary power distribution system radial are the low
investment cost, the simplicity of the protection circuits, and the easy control of the
power method convenient for radial networks. In this project, we analyzed and
concentrated on the three important components of the secondary distribution system.
These components are distribution transformers, primary electrical conductors, and
secondary electrical conductors. Focus of this paper will be cost effectiveness of the
design and optimizing this cost. Cost, reliability, and life of the component will be
discussed and these components will be analyzed and chosen mainly based on load
demands and voltage drops. Electrical companies are facing very challenging situation,
not only the energy price for the consumer need to be reasonably affordable and
comparative in value, but the electric supply system also need to be reliable and
13
available constantly. In addition, the electric utility needs to be adapting to the change in
load demand continuously.
In the older neighborhood, the secondary distribution system is aging and need to
be replaced. The cost of components, installation and labor, and maintenance compared
to fifty years ago is significantly more, and with all the new technology that consumers
use, the demand tends to be significantly higher, also. The design should be efficient and
cost effective otherwise it will cost the utility company a lot of money and that extra cost
will pass on to the consumer, and consequently, the price of electricity will go up.
The operational objectives of a power grid are to provide continuous quality service at an
acceptable voltage and frequency with adequate security, reliability, and an acceptable
impact upon the environment—without damage to power grid equipment—all at a
minimum cost. In Figure 3.2, the direction of arrows indicates the priority in which the
objectives are implemented.
14
Figure 3.2 One-line diagram of a typical distribution system
Source: Electric Power Distribution System Engineering by Dr. Gonen
15
Quality service that is environmentally acceptable, secure, and reliable, and
entails minimum cost is the main objective in power grid operations. However, during the
emergency conditions, the system may be operated without regard for the economy and
environmental restriction such as the use of high polluting energy source, instead
concentrating on the security and reliability of the service for energy users, while
maintaining power grid stability. [7]
The term continuous service means “secure and reliable service.” The term
secure, as it is used here, means that upon occurrence of a contingency, the power grid
could recover to its original state and supply the same quality electric power energy as
before. Later definitions have been added to signify the innovative technologies in the
smart grid arena, such as resiliency, and self- healing characteristics.
3.2 Components of Secondary Distribution System
In the design of secondary distribution system, three essential components are
distribution transformers, primary conductors, and secondary conductors. Load demand,
voltage drop, and voltage fluctuation should be considered and examined for sizing the
components because of their effect on both transformers and conductors. Overhead or
underground cables will be discussed in brief in this paper since most likely the
underground installation requires the trenching and conduit, and therefore, it will be
substantially more expensive than the overhead’s cost of the poles and reinforcements.
16
3.3 Voltage and Load Criteria
The present and future electrical needs of the consumers must be anticipated by
utility companies and system should be planned accordingly. An electric load defines the
rate at which the supply system is required to do work [24]. The unit of power
measurement is Watt and electric power is the rate at which electric circuit performs
work. The electric load power consumption is measured by kilowatt-hour, which the
amount of work (1000watt) is done over the period of an hour. The amount of energy per
unit time, which should be supplied by the utility, is load. (This is the total energy
consumers are using or need in worst-case scenario to run all their electrical equipment
such as lights, appliances, motors, etc. This load can be changed depending on time of the
day or year. Planning an efficient design requires that a good forecast of load
characteristics to be developed. It is very important that the utility can meet this
maximum load demand. This maximum load demand is usually determined after review
of a residential neighborhood over a year. The total power consumption (household load)
for each residential unit is determined, or at least estimated. Then, the total power for that
area is calculated. The utility can develop their plan for the size of components when they
arrive at the load calculations.
Not only the load demand fluctuates hourly, daily, monthly and yearly, but it also
can increase and grow over time due to technology changes. Also of importance is
estimating how the load may grow over time and at what rate [25]. Usually the new
technology brings newer energy efficient devices that should decrease the load demand.
17
However, since we are using more devices the load demand is still higher. In particular,
we can refer to the air conditioning loading, the most variable and disproportionally
dominant component of bus load, which has brought to older neighborhoods that were
not designed or built with it in the designer’s mind [26]. Another example, is super screen
televisions that consume increasingly more watts than their older smaller predecessors. It
is necessary for utility companies to re-evaluate the existing distribution system
frequently to make sure the size of existing component are adequate for the increased
loads. Furthermore, one can step in future and explore the frustration felt by homeowners
when they may encounter difficulty in charging their electric vehicles all simultaneously,
and finding that the neighborhood distribution circuit to be inadequate [10].
3.4 Main Factors
Utility companies consider two factors for load demands when designing a
secondary distribution system. These two factors are Diversity factor and Coincident
factor. The diversity factor is ratio of sum of the individual demands of the individual
loads to maximum demand of the entire system [25]. Maximum individual demand for
each customer does not occur at the same time and if all maximum individual demands
are added, the result will be much higher than the maximum load of the system. If there
was no diversity of the maximum load timing for each customer, then there would be a
need for very large system capacity. Hence, the diversity factor is an important economic
consideration for electric utilities when designing distribution system [24]. Diversity
factor is usually equal to or greater than unity.
18
The coincident factor, the reciprocal of diversity factor, is often preferred because
it is a way to describe load characteristics using a value that is usually less than unity
[25]. This factor is used to calculate secondary voltage drops.
One of the most critical components of the distribution system is transformers.
When a transformer breaks and fails, it is noticeable to customers and whole
neighborhood. It is hard to replace overhead transformer in timely manner and it is hard
to service them. “Hot Spot Area”, or the highest temperature in the winding Area, is the
most important factor relating to the loading capacity and aging of an oil-paper-installed
distribution transformer. Hot spot temperature and data for life span of transformers are
unknown and because of this lack of information transformers are often overrated.
However, due to possible over-loading situation in the face of unavailable monitoring
techniques, it is still possible that hot-spot temperatures can rise to undesirable levels
[27].
In order to maintain transformer ageing within desirable limits, the goal is to keep
the maximum hot –spot and top oil temperatures and the current load under allowed
limits [28]. The following limits are given in [29]. Hot-spot temperature can range
between 120C and 160C and top oil temperature can be between 105C and 115C.
Transformers current rating can exceed its typical rating for a short duration by 30 to 100
percent. Distribution Transformers are usually designed for peak efficiency at or near
19
average power level. However, their actual efficiency is dependent upon their loading
schedule [30].
3.5 Changing Paradigm of the Power Distribution Systems
Over the last twenty years, renewable energy sources have been attracting great
attention due to the cost increase, limited reserves, and adverse environmental impact of
fossil fuels. In the meantime, technological advancements, cost reduction, and
governmental incentives have made some renewable energy sources more competitive in
the market. Among them, wind energy is one of the fastest growing renewable energy
sources. [11]
Solar technology is also developing fast and has much to offer despite the
currently high costs. However, to make a significant contribution to bulk electricity
generation, a major technology and cost reduction is required. Thin film PV has the
potential to deliver cheaper electricity. Currently, commercial interest centers around
thin film nano-crystalline hybrid cells and the hetero junction cells based on copper
indium di-selenide and cadmium telluride. Both of the latter provide reasonably stable
efficiencies and are expected to benefit from improved manufacturing techniques. There
is currently a flurry of investment activity in these technologies that includes
manufacturing on to glass, and metal and polymer foils. Industry experts confidently
expect that the new mass production technologies will deliver cells capable of generating
20
electricity competitively with conventional forms and nuclear perhaps within the next 10
years. [2]
Future grid developments undoubtedly will have to accommodate for the
integration of renewable energies in the transmission and distribution grid. Due to rapid
development of renewable energies and their integration into the grid, the grid codes in
many countries have been updated to address the issues related to renewable energy
power generation. Differences in various grid codes also stem from regional and
geographical conditions, usually based on the experience of operating the power system,
acquired by the utility. However, their ultimate goal is to ensure safe, reliable, and
economic operation of power system. The main elements in the grid codes include fault
ride through requirements, active / reactive power control, frequency / voltage regulation,
power quality, and system protection. [9]
Power systems have developed over the years to supply a varying demand from a
centralized generation sourced from fossil and nuclear fuels, There seems to be a
universal agreement that by the end of this century the majority of our electrical energy
will be supplied from Renewable Energy (RE) sources. Unfortunately, due to the small
sizes of these generators, they cannot connect to the transmission system because of the
high cost of high voltage transformers and switchgears. In addition, the transmission
system is often a long way away as the geographical location of the generator is
constrained by the geographical availability of the resource. Small generators must
21
therefore connect to the distribution network. Such generation is known as distributed or
dispersed generation. [2]
In traditional power systems power invariably flows from the large centralized
power stations, which connect to the EHV network down through the HV and LV
systems to distribute power to consumers. In power system with the distributed
generation, power may travel from point to point within the distribution system. This
unusual flow pattern has some serious implications in the effective operation and
protection of the distributed network [35].
It may be concluded that present power systems will gradually have to evolve and
adapt so that, in the far future, a managed demand will be supplied from distributed,
mostly variable, RE generation. This transformation will be aided by the liberal use of
power electronic interfaces capable of maximizing the effectiveness of RE sources,
controlling power flows, and ensuring reliability of supply.
Additionally, other changing technology changes are affecting the utility planning
process. Today, e.g., we have more than 3,300 plug-in vehicles on San Diego roads, and
the numbers could grow quickly. However, the challenge for operating utility is not
necessarily the number, as much as it is when the vehicles charge. The utility’s goal is to
make sure the vehicles are grid integrated, which means that the majority of charging will
happen at times of day when the grid has an abundance of energy, and not at times when
22
energy is scarce. With this kind of integration, charging costs and emissions will be lower
due to more efficient use of the grid and our generation resources, which will help the
utility customers to realize the many benefits of these environmentally friendly vehicles.
This concept of effective integration is vital because of the charging capability of each
vehicle. Right now most of these vehicles can charge at a rate of about 3 to 7 kilowatts,
and some models just entering the market are capable of charging at up to 20 kilowatts or
more [14].
Another technique the utility company has in their tool box of solutions is the
Conservation Voltage Reduction (CVR) [15]. CVR is a proven technology for reducing
energy and peak demand. By more fully utilizing existing distribution automation
equipment, smart grid technologies, and communicating with meters and switchable
devices, capital purchases can be avoided or delayed. In addition, CVR has the potential
to be Energy Efficiency (EE) resource by helping utilities maximize returns while
meeting EE goals. Today, technologies exist to change the CVR operating paradigm.
Pilot projects based on smart grid technologies and real-time operating systems show
energy savings and demand reductions of 3% are possible. In fact, the Pacific Northwest
National Laboratory (PNNL) estimated total CVR energy savings in the US alone to be
6,500 MWs or 56,940,000 MWh—or the equivalent of Grand Coulee Dam operating at
nameplate capacity for a year [15]. Pilot projects, funded in part with stimulus dollars, are
uncovering promising results: Voltage regulation has been a critical part of power system
operation since Thomas Edison first lit electric lights over Menlo Park on New Year's
23
Eve in 1880. For many years, electric utility companies initiated load reductions during
critical peak load periods by reducing voltages delivered to air conditioners, home
appliances and industrial machinery.
CVR can be accomplished through a variety of conventional technologies (tapchanging transformers, line drop compensators, generator excitation controls, voltage
regulators, line switchable capacitor banks, static VAR compensators, circuit
reconfiguration, and load control) enhanced with microprocessor controls and
communication packages.
The challenge quickly becomes defining specific control schemes, monitoring points,
sensor technologies, protocols, triggering mechanisms, etc. Energy is saved by
maintaining voltages close to lower thresholds without going below them. If the priority
is to regulate end-user voltages, energy consumption is reduced, saving dollars for the
end-user. If losses are to be minimized, feeder volts and VARs are regulated, reducing
energy, releasing line capacity and saving dollars for the utility company.
24
Chapter 4
OPTIMIZATION METHODOLOGY
The dynamic programming technique should be used to optimize the objective
function of power distribution system planning. In its simplest sense, dynamic
programming can be thought of as an attempt to break large, complex problems into a
series of smaller problems that are easier to solve separately.
There are number of decision stages in the dynamic programming at each stage
and there are several alternate courses of action with each stage. The decision generated
by stage one, acts as conditions of the problem for stage two and so on. In other words, at
each of the several stages there is a choice of decisions and the decisions, initially taken
affect the choice of subsequent decisions. The various rules of decision making can be
established after considering the effects of each decision (separately) and the optimum
policy for further decisions. The basis of dynamic programming is to select the best
amongst the final possible alternative decisions. This process is then repeated, ignoring
all those alternatives which do not lead to selected best (optimum). The best sequence of
decisions can thus be defined, by repeating the above process. Safigianni’s paper [4] has
shown remarkably that the full optimization process depends on optimization of a full
multi-objective function. Please refer to the flow chart of the optimization process as
shown below.
25
Figure 4.1 Flow Chart of Safigianni’s Optimization Process
Role of optimization undoubtedly can be broad and comprehensive, or narrow and
specific. For example based on the pioneering earlier works cited by Dr. Gonen, a
Nigerian team took it one step further by the use of integer programming technique.
26
(Alternatively, and more comprehensively, one may look at the distribution system sizing
to include the reliability of the distribution system as well [13]. Depending on the choice,
these many other considerations may do enter into the algorithm formulation. Ultimately,
distribution engineers need to present a dynamic approach towards the sustainability of
power distribution system using a comprehensive application. The cost of energy losses,
substation cost, feeder cost, and outage cost can be developed using dynamic
programming technique and a three stage iterative solution with the aim to optimize the
outage costs. For example, the three stages of optimization could be carried out to
determine, the number of substation sites and exact location, the feeder routes and the
load flow in the network, and the outage cost to cover system node reliability evaluation.
In our paper, we implemented a method for minimizing Total Annual Cost (TAC)
of installing and operating the secondary portion of a three-wire single-phase distribution
system in a residential area, as has been elaborated in Dr. Gonen’s Distribution Book.
This can be applied to underground or overhead distribution. Similarly, one can apply
the optimization techniques to sectors of the power system, ignoring the reliability
aspects for the moment (since integer programming is beyond our current solution to the
problem). We have formulated and written a MATLAB program for the calculation and
we obtained the near optimized results, by using computer math power for speed and
accuracy in selecting the most economically justified alternative in a simple residential
radial distribution section.
27
The numerical tabulated example run results in chapter 6 are the testimony to this
endeavor. A few of these MATLAB computer calculations have been compared with
hand formulated calculation, for verification purpose. Results match very well for all
practical purposes.
The constraint in the program is the degree of voltage drop that system
encounters.
The distribution system design engineer must of course take the optimum design size
calculated and assure the utility with confidence that load is not going to affect the
system voltage severely. Sometimes, the design requires upsizing the secondary
conductors and occasionally in the existing systems, re-conductoring with bigger size
wires will be needed. The aim of the re-conductoring process is the satisfaction of the
voltage drop criterion or the protective devices condition, or both of them.
Every
combination of conductor replacements, which satisfies the above conditions, is a
solution to the problem. Theoretically, there are many solutions for a given network but
only a few of them are technically acceptable.
Our implementation of the Matlab
program depended on making some assumptions. The technically acceptable solutions
satisfy the given constraints below:
1. A conductor of a bigger size but of the same type must always replace one span
conductor. (There are three conductor types: overhead bare lines, underground
cables and overhead twisted cables).
28
2. New type conductors must replace old type conductors, which are no longer in
use (e.g. XLPE cables replace paper insulated cables).
3. Because of the big replacement cost, the underground cables are the last solution
in the reconductoring process and they are replaced if nothing else can be done.
Obviously, our approach has to contain simplicity to be programmed with the help of
computer program. (Dr. Gonen has added the costs of a uniform residential distribution
system in his Distribution book.) It entails dividing the costs into installation costs and
operating costs of the distribution system, annualized over the asset life. (It is important
to use asset life annualized since different modifications may have different life and it
provides a uniform basis for our comparison).
We then take a partial differential
derivative with respect to each variable, size of the transformer, cross section area of
service lateral, and cross area of the Service Drop. Equating each of these equations to
zero will yield us the computationally optimal value. However, this value does not
necessarily yield to a standard size of transformer or wire, per se. Therefore, we have
created a logic ladder where the program ascertains the sizes against the input given
values and automatically progresses to the next size. When the transformer is chosen,
then the next wire SL will be selected, and then finally SD size will be determined by the
program. We have provided the voltage drop as a major constraint where the value
obtained will be tested with a logic statement for being over five (5) percent of the value
29
allowed in distribution voltage drop. A sample of the Optimization Program is provided
in Appendix A.
Furthermore, we have completed this constraint as a separate Matlab program by
itself where students can input different distribution problem input data and verify the
voltage drop within a sector of a secondary radial configuration. A sample of this
program is shown in Appendix C.
Of course the extent of introducing a multi objective function with the introduction
of reliability parameters, maintenance, protection systems, etc. into our study is beyond
the concept of this master’s project, given the wealth of information topics that were
collected for these authors,. What we had to reduce, however, was the essential parts of a
secondary system that we could grapple with and could introduce it with our simple
Matlab programming. The following page flow chart Figure 4.1 shows the concept of
our work from the adapted flow chart as shown by Safigianni’s paper [4].
30
Read the Input Data
Calculate Load
Obtain the second order
polynomials and obtain
the derivative equations
Calculate Optimum
Transformer Size
and Distribution Wires
Provide a Safe
Reserve Margin
For Future Growth
Formulate Criteria
Choose Next Standard
Available Transformer
Size
Block dimensions are asked
via queries Input to the
Program
Standard Lateral Distribution
configuration is assumed
Calculate Optimum and then
Choose Standard Available
Service Lateral Size
Is the Chosen Standard
Size Cost Optimal?
Yes
No
Calculate Optimum and then
Choose standard Service
Drop available Size
Calculate the Voltage Drop
Constraint to see Feasibility
Is the Voltage
Regulation too high?
Yes
No
Print the Optimal
Combinations that met the
Criteria
MATLAB PROGRAM FLOW CHART
Figure 4.2 Matlab Program Flow Chart
Source Provided by Authors
Comments ?
Requested
31
We recognize, of course, that the primary and secondary systems can be simple
or complex as well. Figure 4.3 below shows an extensive primary system. Typically, in
the residential developments, one block of residential area consists of two pole mounted
distribution transformers, which feed twelve houses. This design determines the optimal
size for transformers, primary conductors, and secondary conductors. The optimization
process requires meeting a certain condition and perhaps holding some assumptions as
well to do it properly.
In this project, we constructed and analyzed the Total Annual Cost (TAC) of
initial procurement, installation, and operating cost of secondary distribution system and
provided a Matlab computer program to solve for optimum commercially available size
of transformer and wires. We also elaborated on the calculation method to minimize TAC
and approximately optimize the system the way that will be most efficient. Furthermore,
we illustrated thru the program that this minimized design satisfies the voltage drop
constraint, and therefore, the voltage dip will not exceed the tolerance criteria.
32
Figure 4.3 One Line Diagram of Multiple Primary System for John Hancock Center
Source: (From Fink, D.G., and H. W. Beaty, Standard Handbook for Electrical Engineers,
11th edition, McGraw-Hill, New York, 1978. With permission.)
The Following Figure 4.4 shows one section of secondary distribution system
which has two transformers, and each is feeding 12 customers (loads). This system is in a
straight line design and is expected to have width ‘d’ which makes each section of
secondary line (SL) length ‘2d’. If a secondary line is not used every four customer will
have one transformer.
33
Figure 4.4 Typical Residential Area Lot Layout and Service Arrangement
Source: Electric Power Distribution System Engineering, by Dr. Gonen
In this system over head cable or underground cable can be used. If over head
cable is used, then the transformers are pole mounted and if the underground cable is
used, the transformers are grade-mounted on a concrete slab. The SL and the SD can be
either open-wire or triplex cable construction.
Pole or underground pad-mounted
submersible transformer
Pedestal or hand hole
(on pole or underground)
ST
SD
SD
SD
SD
SD
SD
SD
SD
SD
SD
SD
SD
Alley or Near Lot Line
Illustration of a Typical Pattern
Figure 4.5 Illustration of a Typical Residential Secondary Pattern
Source By Authors
34
The following parameters are used in our calculations:
ST=transformer capacity, continuously rated kVA
Iexc=per unit exciting current (based on ST)
PT, Fe=Transformer core loss at rated voltage and rated frequency, kW
PT, Cu=transformer copper loss at rated kVA load, kW
ASL and ASD=conductor area, kcmil
P=conductor resistivity, (Ω- cmil)/ft
The following assumptions are made to make the calculation easier and possible:
1. All services are single-phase, three-wire, 120/240V
2. All three wire circuits have perfectly balanced loading
3. The system is energized at all the time 8760 hours per year
4. The annual loss factor is calculated by Fls=0.3*Fld+j0.7*Fld^2
5. All loads have the same power factor (constant)
The total cost depends on number of transformer, type and size of conductors,
distance and other parameters, which for simplicity and calculation purposes we will
make some assumption in our calculation. For calculation of the TAC we need to
know the followings:
1. Annual installed cost of transformer and associated protective equipment(ICT)
2. Annual installed cost of triplex aluminum SL cable (ICSL)
3. Annual installed cost of triplex aluminum SD cable (ICSD)
4. Annual installed cost of pole and hardware on it (ICPH)
35
5. Annual operation cost of transformer exciting current (OCexc)
6. Annual operating cost of transformer due to iron losses (OCT, Fe)
7. Annual operating of transformer due to copper losses (OCT, Cu)
8. Annual operating cost of copper loss in a unit length of SL (secondary
line)(OCSL)
9. Annual operating cost of copper loss in a unit length of SD (Service
Drop)(OCSD)
TAC formula has three main variables: Transformer Capacity, Conductor Area of
SL (ASL), and Conductor Area of SD (ASD). For minimizing the ATC, we will take
three partial derivatives and set each derivative to zero.
However, this optimized number is not necessarily a practical one by any means.
Since the sizes of materials are usually given in discrete values, we must choose the
next size Up or Down, depending on the choice. Here is where our logic selection
ladder automatically chooses the next commercial available size, subject to the
voltage constraint.
MATLAB programs are written for the calculation and getting the result faster
and more accurately. Towards the end of this assignment, we will have some
examples to test our MATLAB program and compare the result in MATLAB with
hand calculation.
36
1. ICT which is the annual installed cost of distribution transformer and associated
protective devices is calculated by following formula
ICT = (2000 + 58.08 x ST) x i
$/transformer
ST is transformer rated kVA and is between 15kVA and 100kVA
2. ICSL is annual installed cost of triplex aluminum SL cable is calculated by
following formula:
ICSL = (480+ 36 x ASL) x i $/1000ft
ASL is conductor Area in kcmil. This cost is for 1000 ft of cable, which is 3000
ft conductor.
3. ICSD is annual installed cost of triplex aluminum SD cable is calculated by
following formula
ICSL= (480+36 x ASD) x i $/1000ft
ASD is conductor Area in kcmil.
The ICSD and ICSL are alike since in this example the same kind of conductor
will be used for both SL and SD
4. ICPH is the annual installed cost of pole and hardware on it.
ICPH =1280 x i
$/pole
37
5. OCexe is the annual operating cost of transformer exciting current
OCexe = Iexc x ST x ICcap x i
$/transformer
ICcap is total installed cost of primary-voltage shunt capacitor = $5.00 /kvar
Iexc is the average value of the transformer exciting current base on ST = 0.015
pu
6. OCTFe is annual operating cost of transformer due to core (iron) losses.
OCTFe = (ICsys x i + 8760 x ECoff) x PTFe $/transformer
ICsys is the average investment cost of power system upstream toward the
generator from distribution transformer = $2,800/kVA
ECoff is incremental cost of electric energy (off-peak) = $ 0.015/kWh
PTFe is the annual transformer core loss kW = 0.004 x ST
7. OCTCu is the annual operation cost of transformer due to copper losses
OCTCu = (ICsys x i +8760 x Econ x FLS) (Smax/ST)^2 x PTCU $/transformer
ECon is the incremental cost (on-peak) = $0.02 /kWh
Smax is the annual maximum kVA demand on transformer
PTCu is the transformer copper loss, kW at rated kVA
PTCu = 0.073 + 0.00905 x ST
FLS is the annual loss factor
8. OCSLCu is the annual operating cost of copper loss in unit length of SL
OCSLCu = (ICsys x i +8760 x ECon x FLS) x PSLCu
38
PSLCu is the power loss in unit of SL at the time of annual peak load due to
copper losses kW
PSLCu is an R x I^2, and it must be related to conductor area ASL with R =
pL/ASL
9. OCSDCu is the annual operating cost of copper loss in unit length of SD
OCSDCu = (ICsys x i +8760 x Econ x FLS) x PSDCu
PSLCu is the power loss in unit of SD at the time of annual peak load due to
copper losses kW
PSDCu is an R x I^2, and it must be related to conductor area ASL with R =
pL/ASD
To find the equation for TAC, the above nine formulas need to be added together.
When these formulas are added together (and with some assumption), TAC equation will
be reduced to a function of three design variables,
TAC = f (ST, ASD, ASL)
It has to be noted that many parameter, such as the fixed charge rate i, transformer core
and copper losses, installed cost of poles and lines are contained in constant coefficients
A to H in TAC function.
TAC = A+ B/ST^2 + C/ST + D x ST + E x ASD + F/ASD + G x ASL + H/ASL
39
After substituting the fixed parameter (approximate assumption) we will have;
TAC = (6.048*ASD) + (4.32*ASL) + (14.9522*ST) + 374.536*L1*(L1/ASD) +
2141.28*L4*(L4/ASL) + (6589.33*(L12/ST)*(L12/ST)) + (816.9*L12*(L12/ST)) +
1306.24;
L1= Max load for 1 costumer
L4= Max load for 4 customers
La12= Max load for 12 customers
From Table (4.1), Class 2, we have:
L1=10, L4=6, and La12= 4.4
TABLE 4.1
Load Data for Book Example 6.1,
Source: Electric Power Distribution System Engineering Book, by Dr. Gonen
40
Basically, if above loads and the dimensions of SL and SD cable and the size of
transformer are known, TAC for secondary distribution system can be calculated.
For example if 39 kVA transformer with ASL of 205 kcmil and ASD of 85.4 kcmil are
used with above loads the TAC = $4595 /block
And if 50 kVA transformer with ASL of211.6 kcmil and ASD of 105.5 kcmil are used
with above loads the TAC = $4693 /block
And if 50 kVA transformer with ASL of250 kcmil and ASD of 133.1 kcmil are used
with above loads, the TAC = $4896 /block
Minimizing TAC
For minimizing TAC, since TAC is a function of three variable, using TAC
equation and taking three partial derivatives will set each derivative equal to zero and it
follows;
d(TAC) / d(ST) = 0
d(TAC) / d(ASL) = 0
d(TAC) / d(ASD) = 0
The result of above equations that are used henceforth merely serve as indicators
of the region that contains the minimum TAC achievable with standard commercial
equipment size. The problem is further continued by computing TAC for the standard
commercial sizes of equipment nearest to the results of above equations.
41
There are additional criteria which must be met in the total design of the
distribution system, whether or not minimum TAC is realized. The further
criteria involve quality of utility service. Minimum TAC designs may be
encountered which will violate one or more of the commonly used criteria:
1. A minimum allowable steady-state voltage at the most remote service
entrance may have been set by law, public utility commission order, or
company policy.
2. A maximum allowable motor-starting voltage dip at the most remote service
entrance similarly may have been established.
3. Ordinarily the ampacity of no section of SLs or SDs should be exceeded by the
designer.
4. The maximum allowable distribution transformer loading, in per unit of
the transformer continuous rating should not be exceeded, by the designer.
Matlab Programs
There are two Matlab program written for TAC. An extra third Matlab program is
also provided to calculate voltage drop in a secondary system.
The first one is called Optimize-TAC.Rev24 (Appendix A) and it minimizes TAC
by asking for loads as inputs. It then calculates the optimized sizes for ST, ASL and
ASD, and it finally determines the optimized TAC. In this program not only the
42
optimized sizes of equipment and TAC are calculated, but also, the standard size and
TAC for standard size equipment will be picked by the program.
The second one (Appendix B) calculates the TAC by asking the three loads and
sizes of ST (in kVA), ASL (in kcmil) and ASD (in kcmil), as inputs. It is called TACtotal and it is basically serving as a calculator for arriving at TAC value.
The third program (Appendix C) is provided as a courtesy in addition to the other
matlab programs so the future students can calculate or analyze a typical secondary
system voltage drop. This program is called OnlyVoltageDrop and it queries for the size
of transformer, SL, and SD and it then calculates the voltage drop total and by element.
Voltage drop is an independent constraint set to alter program calculation in the
Optimize-TAC program. However, we felt it will be useful to provide it also
independently as a calculator.
Copies of each program and program instructions are also attached for your
review (in Appendices). Furthermore, the computer program flow diagram was also
provided in Chapter 3.
43
Chapter 5
ECONOMIC ESTIMATION AND ANALYSIS
We began our master’s project, of course, with the understanding that we will be
solving the Secondary Distribution System Optimization problem with the help of
computer provided Matlab programming and using a simplified radial distribution as an
example. In doing so, we had to gather a more current set of data, which we also verified
by a utility company recent purchases for a close approximation and validity of material
and labor costs. Similarly, we obtained in place unit cost of these material and equipment
with National Construction Estimator (NCE) tabulated book index to arrive at the Total
Annualized Cost function.
Consequently, several other factors, such as the cost of electricity, capacitors, and
transformers had to be revised upward from the figures initially shown in Dr. Gonen’s
Distribution System book about three decades earlier. We wanted to compare the
efficiency of the transformers to earlier values, as it was not clear to us if significant
technological advances have been made in this area. We then provided several linear
regressions of Matlab algorithms to be able to categorize choices and result in the final
determined values in our Optimization Program.
Cost analyzes have been discussed in this paper. The Two Matlab programs that
have been provided work out the TAC cost if the input data file is provide in the Matlab
44
folder. The OptimizeTAC program will figure out the best combination of elements when
optimized for their size and subject to the voltage constraints and its TAC cost, as shown
in Appendix A. This optimization program provides the near optimized cost for the
components. It will further reflect the annualized cost for the given design parameters of
our distribution system.
We have surveyed the L.E Means and National Construction Estimator books to
obtain more recent cost data. The cost figures reported are for the mineral insulated
aluminum conductors with the steel cores. We had to provide the linear regression
function for the obtained data to make sure it would be in that window of 4 to 8 times
cost escalation that we had arrived at before. The data is shown in the input Excel sheet
that the program reads from.
Additionally, we contacted SMUD for transformers and capacitors data, and we
obtained their more recent purchases. We have performed linear regression functions on
these data as well, to arrive at the best-fit cost for the given size. Across the board, we
observed the typical economical values have increased between 4 to 8 times of
preliminary Westinghouse number reported by Dr. Gonen in his Distribution book
example, page 299. (Refer to Transformer cost in Figure 5.1 and 5.2, shown below
retrospectively.)
45
Current Cost vs. Transformer kVA
14000
12000
Cost ($)
10000
8000
6000
4000
2000
0
10
15
25
37.5
50
75
100
167
100
167
Transformer in kVA
Figure 5.1 Current Transformers Cost
Source Provided by NCE
Historic Cost vs. Transformer KVA
1600
1400
Cost ($)
1200
1000
800
600
400
200
0
10
15
25
37.5
50
75
Transformer in kVA
Figure 5.2 Historic Cost of Transformers
Source Provided by NCE
46
Surprisingly, capacitor mass production technology has managed to provide
relatively lower cost despite the inflation. SMUD purchases reflect cost to be about three
to four times the original indicated values. Similarly, the utilities markup for on-peak and
off-peak energy generation has been relatively contained due to the competition in a
heavily regulated electric market. We suspect that markup to be between three to four
times what originally assumed in the reference.
Given the approximation that cost of material and labor have at least risen four to
six percent a year, Every 12 to 14 years it will be twice the cost. Carrying that
methodology forward 36 years, one can reasonably expect the material and prices to have
increased by a factor of 6 to 8 times more than original reported in the Distribution Book
Since these data were originally taken from the late seventies references, it translate into
4 to 8 times the original estimates. In fact, current cost of transformers and wires support
this assertion, and furthermore, the two graphs we have provided above and below
(Figures 5.3 and 5.4) sustain this assertion.
47
Current Cable Cost vs. kcmil
12000
10000
Cost ($)
8000
6000
4000
2000
0
41.74
52.74
66.36
83.69
105.6
133.1
kcmil
Figure 5.3 Current Cable Cost
Source Provided by NCE
167.8
211.6
250
48
Historic Cable Cost vs. kcmil
1600
1400
1200
Cost ($)
1000
800
600
400
200
0
41.74
52.74
66.36
83.69
105.6
133.1
kcmil
Figure 5.4 Historic Cable Cost
Source Provided by NCE
167.8
211.6
250
49
Chapter 6
NUMERICAL RESULTS
Many low voltage distribution networks in the United States are typically a 12 kV
primary 120/ 240 secondary system, and in the residential areas they are usually served
by single-phase distribution circuit, as shown in Figure 4.5.
We performed linear regression data fit into a third order polynomial function based on
the transformer cost data we had obtained from the utility company (SMUD in this case)
and also the typical construction cost reporting (Means). The data from transformers cost
was fit perfectly into a third order polynomial, per earlier book citation [1]. The total
variations never exceeded more than about 2 to 4 percent from the data, and that is
practically the error margin in the survey in the first place. The conductor data were also
consecutively fit into the second order polynomial, as well. Matlab command Polyfit was
extremely powerful to help fit data into other polynomial orders. The results are shown in
Figures 6.1 and 6.2.
The data provided below along with the Figures are the testimony for this data
match:
50
Single-Phase Residential Distribution Transformers
No
Total
Rated
Load
Load
Cu
Z
Mat.
Labor
OH
Total
Volt
Z
Actual
I@
208
V
Loss
Losses
Loss
(%)
$
$
$
$
Base
Ohms
X
10
48.1
28.5
176
148
1.900
1100
455
325
1880
240
9.480
0.109
15
72.1
31.9
265
233
1.900
1500
605
445
2550
240
6.325
0.073
25
120.2
53.6
344
290
2.200
2050
730
545
3325
240
4.393
0.051
37.5
180.3
71
462
391
1.800
2650
910
715
4275
240
2.396
0.028
50
240.4
90.1
566
476
1.800
3150
1050
800
5000
240
1.797
0.021
75
360.6
130.5
694
564
2.300
4175
1125
950
6250
240
1.531
0.018
100
480.8
185
864
679
2.000
5747
995
1011
7753
240
0.998
0.012
167
802.9
500
2100
1600
2.100
9000
1125
1513
11638
240
0.628
0.007
Size
51
Transformer Data Vs. Third order model
Series1
Series2
Unit Cost ($)
11567
7391
6297
11638
5031
4249
3322
2453
1970
1880
1
2550
2
3
5000
4275
3325
4
5
7431
6250
6
7
8
Transformer Sizes
Figure 6.1 Transformer Cost Fit Into Third Order Model
Source Provided by NCE
Distribution Aluminum Wires in Triplex arrangement for Residential Sectors
Wire
(Values given are for 1000 ft length)
Wire
No.
Size
Rating
Resis
I (A)
R
Z
DC
AC
#6
X
IZ
I2R
Mat.
Labor
Indirect
Total
Area
$
$
& OH $
$
kcmils
26.24
#4
1
140
0.4
0.52
0.3323
2130
1660
1000
4790
41.74
#3
2
155
0.32
0.41
0.2563
2310
1740
1080
5130
52.74
#2
3
185
0.25
0.32
0.1997
2520
1820
1150
5490
66.36
#1
4
210
0.2
0.27
0.1814
2890
1820
1150
5860
83.69
#1/0
5
240
0.16
0.21
0.136
3200
1920
1230
6350
105.6
#2/0
6
275
0.12
0.17
0.1204
4000
2020
1380
7400
133.1
#3/0
7
315
0.1
0.14
0.098
4600
2150
1520
8270
167.8
#4/0
8
360
0.08
0.12
0.0894
5200
2280
1670
9150
211.6
#250
9
450
0.06
0.08
0.0529
6450
2430
1870
10750
250
52
Cable Data Vs. Second Order Model
Axis Title
300
200
Series1
100
Series2
0
1
2
3
4
5
6
Series1
7
8
Cable Sizes
Figure 6.2 Cable Cost Fit Into Second Order Model
Source Provided by Authors
Cable Size vs. Cost
12000
10000
Cost $
8000
6000
4000
2000
0
#4
#3
#2
#1
#1/0
#2/0
#3/0
Cable Size
Figure 6.3 Cable Cost For Different Sizes
Source Provided by Authors
#4/0
#250
53
Table 6.1 --Summary of the Runs
(Source Provided by Authors)
i=10%
Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,
2.5 kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,
2.5 kVA
SL=480ft
SD=120ft
ST-kVA
80.94
80.94
38.71
38.71
13.217
13.217
ASL-kcmil
267.19
267.19
133.59
133.59
33.4
33.4
ASD-kcmil
141.7
141.7
78.72
78.72
19.68
19.68
TAC-$
8127
10447
4750
6005
2254
2626
ST-kVA
100
100
50
50
15
15
ASL-kcmil
300
300
167.8
167.8
41.74
41.74
ASD-kcmil
167.8
167.8
83.69
83.69
41.74
41.74
TAC-$
8230
10573
4827
6099
2348..5
2766
Total -percentage (%)
6
7.27
6.18
7.45
5.55
6.364
VDT-Transformer
2
2.4
1.9
1.9
1.824
1.824
3
3.845
3.539
4.44
3.365
3.997
0.684
1.026
0.742
1.113
0.3615
0.542
Low Electric Markup ,
ECoff= 0.015, ECon = 0.02,
Power Factor = 0.9
Optimized
Standard
Voltage Drop
VDSL-Service Lateral
VDSD-Service Drop
54
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=15%
Run7
Run 8
Run 9
Run 10
Run 11
Run 12
Low Electric Markup ,
ECoff= 0.015, ECon = 0.02,
Power Factor = 0.9
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,
2.5 kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,
2.5 kVA
SL=480ft
SD=120ft
ST-kVA
80.48
80.48
38.5
38.5
13.15
13.15
ASL-kcmil
262.4
262.4
131.2
131.2
32.8
32.8
ASD-kcmil
139.16
139.16
77.31
77.31
19.32
19.32
TAC-$
11968
15387
7016
8866
3350
3901
ST-kVA
100
100
50
50
15
15
ASL-kcmil
300
300
133.1
133.1
41.74
41.74
Optimized
Standard
ASD-kcmil
167.8
167.8
83.69
83.69
41.74
41.74
TAC-$
12142
15603
7086
8939
3498
4120
Total -percentage (%)
5.648
7.2719
6.923
7.45
5.55
6.364
VDT-Transformer
2.4
2.4
1.9
1.9
1.824
1.824
VDSL-Service Lateral
2.563
3.845
4.28
4.44
3.365
3.997
VDSD-Service Drop
0.684
1.0264
0.742
1.113
0.3615
0.0542
Voltage Drop
55
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=10%
Run13
Run14
Run15
Run16
Run17
Run18
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,2.5
kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,2.5
kVA
SL=480ft
SD=120ft
82.2
82.2
39.28
39.28
13.39
13.278
ASL-kcmil
281.07
281.07
140.54
140.54
35.134
33.99
ASD-kcmil
149.06
149.06
82.81
82.81
20.7
20.03
8563
10999
4966
6282
2313
3977
ST-kVA
100
100
50
50
15
15
ASL-kcmil
300
300
167.8
167.8
41.74
41.74
ASD-kcmil
167.8
167.8
83.69
83.69
41.74
41.74
TAC-$
8638
11084
5027
6354
2397
4179
Total -percentage (%)
5.648
7.272
6.182
7.453
5.55
6.364
VDT-Transformer
2.4
2.4
1.9
1.9
1.824
1.824
VDSL-Service Lateral
2.563
3.845
3.539
4.44
3.365
3.997
VDSD-Service Drop
0.684
1.026
0.742
1.113
0.3615
0.5423
High Electric Markup ,
ECoff= 0.03, ECon =
0.04, Power Factor = 0.9
Optimized
ST-kVA
TAC-$
Standard
Voltage Drop
56
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=15%
Run19
Run20
Run21
Run22
Run23
Run24
High Electric Markup ,
ECoff= 0.03, ECon= 0.04,
Power Factor = 0.9
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,
2.5 kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,
2.5 kVA
SL=480ft
SD=120ft
ST-kVA
81.39
81.39
38.91
38.91
13.278
13.278
ASL-kcmil
271.9
271.9
135.95
135.95
33.987
33.987
ASD-kcmil
144.2
144.2
80.11
80.11
20.03
20.03
TAC-$
12411
15949
7234
9148
3411
3977
ST-kVA
100
100
50
50
15
15
ASL-kcmil
300
300
167.8
167.8
41.74
41.74
Optimized
Standard
ASD-kcmil
167.8
167.8
83.69
83.69
41.74
41.74
TAC-$
12549
16114
7341
9276
3547
4179
Total -percentage (%)
5.648
7.27
6.182
7.453
5.55
6.36
VDT-Transformer
2.4
2.4
1.9
1.9
1.824
1.824
VDSL-Service Lateral
2.564
3.845
3.539
4.44
3.365
3.997
VDSD-Service Drop
0.684
1.026
0.742
1.113
0.3615
0.5423
Voltage Drop
57
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=10%
Run 25
Run 26
Run 27
Run 28
Run 29
Run 30
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,
2.5 kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5, 2.5
kVA
SL=480ft
SD=120ft
ST-kVA
80.94
80.94
38.71
38.71
13.217
13.217
ASL-kcmil
267.19
267.19
133.59
133.59
33.4
33.4
ASD-kcmil
141.7
141.29
78.72
78.72
19.68
19.68
TAC-$
8127
10447
4750
6005
2254
2626
ST-kVA
100
100
50
50
15
15
ASL-kcmil
300
300
167.8
167.8
41.74
41.74
ASD-kcmil
167.8
167.8
83.69
83.69
41.74
41.74
TAC-$
8230
10573
4827
6099
2349
2766
Total -percentage (%)
5.6
7.2
6.405
7.854
5.643
6.45
VDT-Transformer
2.4
2.4
1.9
1.9
1.824
1.824
VDSL-Service Lateral
2.479
3.718
3.732
4.795
3.448
4.07
VDSD-Service Drop
0.721
1.0826
0.7721
1.158
0.3705
0.555
Low Electric Markup ,
ECoff= 0.015, ECon=0.02,
Low Power Factor = 0.7
Optimized
Standard
Voltage Drop
58
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=15%
Run 31
Run 32
Run 33
Run 34
Run 35
Run 36
Low Electric Markup ,
ECoff= 0.015, ECon = 0.02,
Power Factor = 0.7
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,
2.5 kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,
2.5 kVA
SL=480ft
SD=120ft
ST-kVA
80.48
80.48
38.5
38.5
13.15
13.15
ASL-kcmil
262.4
262.4
131.2
131.2
32.8
32.8
ASD-kcmil
139.14
139.14
77.31
77.31
19.33
19.33
TAC-$
11968
15387
7016
8866
3350
3901
ST-kVA
100
100
50
50
15
15
ASL-kcmil
300
300
133.1
133.1
41.74
41.74
ASD-kcmil
167.8
167.8
83.69
83.69
41.74
41.74
TAC-$
12142
15603
7086
8939
3498
4120
Total -percentage (%)
5.6
7.2
7.206
7.854
5.643
6.45
VDT-Transformer
2.4
2.4
1.9
1.9
1.824
1.824
VDSL-Service Lateral
2.478
3.718
4.53
4.795
3.448
4.07
VDSD-Service Drop
0.721
1.0826
0.772
1.158
0.3705
0.555
Optimized
Standard
Voltage Drop
59
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=10%
Run 37
Run 38
Run 39
Run 40
Run 41
Run 42
Low Electric Markup ,
ECoff= 0.015, ECon =
0.02, Power Factor = 0.9
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,2.5
kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,2.5
kVA
SL=480ft
SD=120ft
13.217
13.217
Optimized
*
*
ST-kVA
80.94
80.94
38.71
38.71
ASL-kcmil
267.19
267.19
133.59
133.59
33.4
33.4
ASD-kcmil
141.7
141.29
78.72
78.72
19.68
19.68
TAC-$
8127
10447
4750
6005
2254
2626
100
100
50
50
15
15
ASL-kcmil
350
300
205
300
66.36
105.6
ASD-kcmil
167.8
Out
83.69
83.69
41.74
41.74
TAC-$
8230
Of
4827
6099
2349
2626
Standard
ST-kVA
Voltage Drop
Bound
Total -percentage (%)
5.37
4.69
7.85
4.27
4.40
VDT-Transformer
2.40
1.90
1.90
1.82
1.82
VDSL-Service Lateral
2.28
2.06
4.80
2.08
2.03
VDSD-Service Drop
0.68
0.74
1.16
0.36
0.54
60
Table 6.1 --Summary of the Runs Continued
(Source Provided by Authors)
i=15%
Run 43
Run 44
Run 45
Run 46
Run 47
Run 48
Low Electric Markup ,
ECoff= 0.015, ECon =
0.02, Power Factor = 0.9
Class 1
10,12,18
kVA
SL=320ft
SD=80ft
Class 1
10,12,18
kVA
SL=480ft
SD=120ft
Class 2
4.4,6,10
kVA
SL=320ft
SD=80ft
Class 2
4.4,6,10
kVA
SL=480ft
SD=120ft
Class 3
1.2,1.5,2.5
kVA
SL=320ft
SD=80ft
Class 3
1.2,1.5,2.5
kVA
SL=480ft
SD=120ft
Optimized
*
*
ST-kVA
80.48
80.48
38.5
38.5
13.15
13.15
ASL-kcmil
262.4
262.4
131.2
131.2
32.8
32.8
ASD-kcmil
139.14
139.14
77.31
77.31
19.33
19.33
TAC-$
11968
15387
7016
8866
3350
3901
ST-kVA
100
100
50
50
15
15
ASL-kcmil
350
300
205
300
66.36
66.36
ASD-kcmil
167.8
Out
83.69
83.69
41.74
41.74
TAC-$
12142
Of
7086
8939
3498
4120
Standard
Voltage Drop
Bound
Total -percentage (%)
5.37
4.70
4.94
4.27
4.40
VDT-Transformer
2.40
1.90
1.90
1.82
1.82
VDSL-Service Lateral
2.28
2.06
1.92
2.08
2.03
VDSD-Service Drop
0.68
0.74
1.11
0.36
0.54
We made sure we run the program for at least several cases. We also subjected the
runs to the constraints of at least five (5) percent voltage drop for service lateral, and 10
percent overall.
61
We first ran the Matlab program (OptimizeTAC) for class 3 residence customer,
as specified in the Table 4.1 (reflecting Table 6.4 of the Dr. Gonen’s Distribution book
[1], and as provided earlier here in this paper. The program (OptimizeTAC) reached a
solution and gave a 15-kVA transformer with a No. 4 conductor, as the answer. Service
Lateral (SL) and Service Drop (SD) were both optimized at a No. 4 conductor (ASL = 41
kcmil).
We then ran the program similarly for the Class 2 residences (Table 4.1) and
obtained the answer as a 50-kVA transformer, with a No. 2/O conductor (ASL = 133.1
kcmil) for SL and a No. 1 conductor (ASL = 83.69 kcmil) for the SD. In both program
runs for Class 1, 2 and 3, the voltage drops were within the specified tolerance limits of 5
percent per component (10 percent total).
When we entered the Class 1 data in the program, TAC equation derivative
answer is a complex value for the transformer (ST). The imaginary part is probably due
to the large maximum load. Long blocks, which will have longer wire lengths, can cause
the voltage drop constraint in the program to be violated earlier. That effect is more
profound when we lower the tolerance level of the voltage constraint to much below 10
percent. Class 1 data in the program run yielded the answer of a 100-kVA transformer, a
No. 300 MCM service lateral (ASL = 300 kcmil), and a No. 3/O conductor (ASL = 167.8
kcmil) for SD.
62
In fact, we ran each of the normal Runs with a 50 percent longer length to see
this effect. We did not notice any constraint violations until we increased the lengths to
about twice long and Class 1 with high loading showed constraint violations earlier.
Alternately, one can reduce the tolerance of the voltage drop in the program to see similar
change taking place.
We also wanted to test the sensitivity of the program to the higher electricity
mark-up cost. We have provided 12 runs under high electric mark-up case (twice the
normal value in Runs 13 thru 24).
We have also provided an alternate similar run of each case with lower
capitalization value to see the results. We replaced the capitalization rate (utility rate of
return) to lower (10%) and higher (15%) values to discover program sensitivity to the
solution based on the assumed capitalization rate (ὶ ), as tabulated in the above tables, to
obtain the utility valuation based upon a conservative long-term policy towards higher
capital investment.
Finally, we first executed the program with the original runs at power factor of 90
percent and then we lowered the power factor to 70 percent to compare the results. The
results do not show that lower power factor exacerbates the voltage drop constraint,
which is counter-intuitive to our initial expectations. The reality, however, is that
constant energy loads under lower power factor condition will demand higher current,
63
which ultimately result in higher kVA and cause program to choose higher conductor
sizes, consequently. However, we have no way of reflecting that in our simple program
as we input the Table 4.1 column values. We have to increase the loads proportionately to
capture that lowered power factor effect. Higher conductor sizes will undoubtedly affect
cost and cause higher TAC for the utility company.
We also wanted to show the effect of lowering the Voltage Drop constraint. By
setting the constraint to 2.5 percent in SL and SD, and 5 percent overall voltage drop, we
force the Matlab program to choose larger size conductors, as it is shown in the Runs 37
to 48. The TAC equation yields complex solution and it results in out-of-bound answers
for the longer lengths in Class 1 column data. High loading is the main cause of not
reaching solution and ultimately, the designed distribution calls for a revision.
64
Chapter 7
CONCLUSIONS
Optimization of the secondary distribution is a tedious process. It first requires an
understanding and familiarity of the primary and secondary system to identify the
uniqueness (if any) of the system. Based on this layout, demographical expectations and
growth anticipated, the system designer can then derive the cost figure for this Primary
system.
In more sophisticated optimization models, the integer programming and
dynamic programming techniques are employed, as they are more appropriate solutions.
However, our assignment was confined with use of simple Matlab programming to
devise a method to optimize the system secondary, and still account for a constraint,
which in this case was the overall voltage drop for the secondary system. We were
destined to prove the point using only Matlab programming technique and capability.
In our program, the dimension of the blocks, and therefore the lots, are parameters
that can be safely changed for sensitivity analysis. The program constraint limit of
voltage drop can also be altered for ease of analysis. We have justified our cost structure
in chapter 6 (Economic Estimation and Analysis), but those cost data may also be
adjusted for fine tuning or sensitivity analysis, as well. Finally, the number of the
transformers and radial feeding configuration can be altered without many great
obstacles. Of course, the optimization program will have to be accordingly revised to
account for the required formulation.
65
With the procedures described above the voltage profile, the conductor thermal
capacity, tapering and short-circuit strength and the protective grounding of a radial
secondary power distribution system can be examined. If the results of this examination
are not satisfactory to the system designer, alternative optimizing technical solutions must
be proposed, which concern transformer changes or conductor replacements or both.
These solutions are economically estimated and the most economical one is finally
adopted.
Adjusting for load growth is also challenging for the distribution designers, as it
will pose the predicament for the system designers to be more conservative with their
initial designs and allow higher equipment rating or better specification to fit into the
primary side. Higher protection standards and non-linear nature of many loads cause
equipment to fail prematurely, or heat up and result in shorter life due to harmonics.
Adding to this challenge will be the integration of renewable Distributed Energy
Resources (DER) that will dominate the future distribution grid. Many of these DERs
have solid state inverters that will exacerbate the harmonics effect.
Furthermore, the planned procedures must provide for some degree of the
flexibility from the norm. Electric Cars charging needs, e.g., requires direct upgrade of
the transformers and conductors in some neighborhoods distribution systems, and
therefore, the concept of effective integration is vital because of the charging capability
66
of each vehicle. Future distribution system engineers and designers undoubtedly are faced
with great many challenges and game changes, as well.
The loading on the distribution transformers will be significantly increased once the
ownership of Plug-In-Hybrid Electrical Vehicle (PHEV) becomes prevalent in our
modern society and when the average neighborhood displays a significant presence of
these cars. The average electric car will need about 20 to 30 kW-hour of charge for a
round trip of about 60 miles. While that is not a huge load by itself, relative to size of
transformers and wires, it puts undue burden on the grid [14]. One can imagine that while
the early adoption may be low, even only two out of twelve houses owning and charging
these electrical vehicles can seriously burden the neighborhood distribution grid. Finally,
the new utility tariff and rate structure must be provided by the regulators to provide for
the shifting paradigm in the utility industry and its ultimate migration to the Smart grid
domain.
The purpose of this masters project was to demonstrate that (1) the optimization
process is essential between main components of the distribution system, being primary
or secondary and (2) the optimization process can be implemented between the main
components on the basis of fixed initial cost and operating cost of the system, and even a
basic Matlab Program is capable of obtaining solutions to the design problem. Future
Smart grid vision is to develop and deploy a more reliable, secure, economic, efficient,
safe, and environmentally friendly electric system. It will hinge on optimization of
67
several sub system to attain that goal. Advanced grid technologies will help attaining that
goal with the increase in grid efficiency and reliability
68
APPENDIX A
Matlab Optimization Program for Secondary Distribution System
Instructions for Running the Matlab Optimization Program in Distribution System
The following are instruction steps to utilize the Matlab Optimization program:
1. The program is designed to provide the design parameters to the distribution
designer who will layout the typical urban area City block. It can easily be
modified to use it for bigger acreages available in the agricultural areas as well.
This program is constructed with the idea that configuration of distribution
system greatly affects the outcome as the layout will determine the efficient
means of distribution, and hence, we have assumed a city residential block
typically found in the urban areas of most major U.S cities (typically 960 feet
long by 330 feet wide).
2. Typically, the utility would like to reduce the voltage drop at the end of the line
and hence would bring the distribution high voltage side to the middle of the
circuit so that two almost equal strings can service the two sides of the pattern.
The utility therefore serves the two strings by the two transformers from the
utility Right of Way which service these blocks, by single-phase distribution
circuit of the serving electric utility. We provided the input queries for the
69
dimensions of this block as to the length and width, which will have a bearing
upon the length of service laterals and service drop conductors serving the
neighborhood area. The example in the book has assumed two single-phase
transformers serving this block, and each transformer serving power to twelve
customers (we have assumed 12 kV primary distributions for these transformers,
and 240- volt secondary to customers). [1]
3. The utilities have to justify their cost expenditures to their financial managers
and public agencies involved, as the total expenditures will undoubtedly affect
the tiered electric rates that ratepayers must pay. Therefore, extra prudence is
applied so that the utility is not heavily weighted in the purchase of non-utilized
assets. Of course, different assets have different life spans and that is why the
utility industry has developed the annualized asset cost to have comparison basis
of measuring alternative proposals on an equal footing. When the assets are
compared on the basis of their amortized life, it will simplify the job of planning
managers to develop the consensus for funding the suitable alternatives.
4. The optimized equations in the program are derived from the absolute
maximized or minimized equations to provide the optimal value for the
variables. However, the standard sizes available in the commercial market do
not render themselves to exact sizes. It is pertinent for a distribution system
designer to obtain a standard size that can still provide near optimal value to the
70
utility, minimizing the Total Annualized Cost (TAC) that service utility must
burden with.
5. The average load a house may use may greatly depend on the neighborhood
demography and its location. Over the past century electricity consumption has
increased substantially per capita, mainly due to exponential use of automation in
human life in the developed world, while it provides the advances in quality of
life. Interestingly, while the utilities seek to dampen the peak power usage to
curtail high cost of their spot generation, they have to design their distribution
conservatively to accommodate the perceived peak load, even though this
equipment may not be fully utilized a great portion of the time. Hence, sizing
their equipment for average load is allowed, which is somewhat diversified by
the local authorities having jurisdictions. The average household load is also
provided thru an input to the program, as different type of residential areas may
vary in their demography and their electrical usage. The program calculates the
load, sizes the next commercially available transformer, and provides the
appropriate sizes for the Service Lateral (SL) and Service Drop (SD) conductors.
It then calculates the TAC.
6. Two files are attached with this instruction sheet. One is the Matlab program
called OptimizeTAC.m and the other is the Excel input data called
TransfDataTryVD24.xls. You would need to save the TransfDataTryVD24.xls in
71
the folder that Matlab works with to be able to import the table values
automatically into Matlab.
72
Matlab Optimization Program in Distribution System
%This program evaluates the distribution circuit requirements for a
block %development and then determines the transformers' size, Service
Laterals, %and Service Drops. Block length and widths are inputs given
to the program %as specifications as well as the residential load,
voltage and power factor.
clear all
clc
foadfile1='TransfDataTryVD24.xls';
%reads data from the first
worksheet in
sheet=1;
%the Excel spreadsheet file named 'foadfile1' and returns
the
x1range='B10:N17';
% numeric data in array num.
subsetA=xlsread(foadfile1,sheet,x1range);
A=subsetA;
foadfile2='TransfDataTryVD24.xls';
%reads data from the second
worksheet in
sheet=2;
%the Excel spreadsheet file named 'foadfile2' and returns
the
x2range='B10:N22';
% numeric data in array num.
subsetB=xlsread(foadfile2,sheet,x2range);
B=subsetB;
Lab=input('Enter the spacing for block length Lab in ft: ');
Wac=input('Enter the spacing for block width Wab in ft: ');
volt=input('Enter the secondary distribution voltage: ');
prompt1 = 'What is Max Average Load for each of 12 customers in KVA? ';
La12=input (prompt1);
prompt2= 'What is the Load for 4 customers in KVA ? ';
L4=input (prompt2);
prompt3 = 'What is Max Load for 1 customer in KVA? ';
L1=input (prompt3);
pf=input('Enter the distribution system power factor (pf)cos(Phi): ');
%Lab=1*960;Wac=1*330;volt=240;La12=4.4;L4=6;L1=10;pf=0.9;
i=0.15; % The utility cost annualized Rate (Capitalization Rate)
ICCAP=15;ICsys=8*350;Iexc=0.015;FLD=0.35;ECoff=.015;ECon=.02;
% Defining the parameters;
XX=2;
% No of Transformers
YY=12;
% No of Customers
poles=6;
% No. of Poles
LotW=Lab/12;
% Lot Width
LotL=Wac/2;
% Lot Length
LSL=4*LotW;
% Length of SL
LSD=0.5*LotL;
% Length of SD
phi=acos(pf);
% Phi Angle (phi)
Smin=YY*1.1;
% In kVA
Aload=YY*La12;
if Aload<Smin
ST=Smin;ASL=41.74;ASD=26.24;
73
else
ST=iscolumn(A(1));ASL=iscolumn(B(12));ASD=iscolumn(B(12));RSL=iscolumn(
B(3));
XSL=iscolumn(B(5));RSD=iscolumn(B(3));XSD=iscolumn(B(5));AMP=iscolumn(B
(2));
SD1=iscolumn(B(2));
end
syms ST positive
syms ASL positive
syms ASD positive
C1=XX*8*(250+7.26*ST)*i; % $/Block-2 trx per block & 12 services per
ea. trx
C2=XX*8*(60+4.5*ASL)*i*2*(LSL/1000); %Triplex aluminum cable cost for
Service Lateral per transformer
C3=XX*8*(60+4.5*ASD)*i*YY*LSD/1000; % Service Drop initial cost
($/block)
C4=8*160*poles*i;
% Cost of Poles $/ block
C5=2*Iexc*ST*ICCAP*i; % Capacitors’cost for System energizing and I
excitation
C6=2*(ICsys*i+8760*ECoff)*0.004*ST; % Cost of iron losses/ upleg of
Secondary ($/ block)
FLS=0.3*FLD+0.7*FLD^2;
Smax=YY*La12; % This is found from Table 6.4 for 12 class 2 customers,
per book example
PTcu=(0.073+0.00905*ST);% Transformer copper losses Where 15
kVA<=ST<=100 kVA % This is found from (Eq. 6.10)
C7=XX*(ICsys*i+8760*ECon*FLS)*(PTcu)*(Smax/ST)^2;
%From Eq.6.9, The annual OC of tx copper losses per
block
RSL=(20.5*(LSL)*2)/(1000*ASL); % RSL=p*L/1000*ASL (Ohm.kcmil/trx.)
PSLcu=(((4*L4*1000)/(volt))^2)*(RSL/1000);
%PSLcu=((4*L4/volt)^2)*(12.3/ASL)/1000;
C8=XX*(ICsys*i+8760*ECon*FLS)*PSLcu;
% From Eq. 6.11, annual OC of copper losses in the
4 SLs
RSD=(20.5*LSD*24*2)/(1000*ASD); %Rc=p*(LSD/1000)*ASD=68.88/ASD
(Ohm.kcmil/block),
PSDcu=(((L1*1000/volt))^2)*(RSD/1000); %
PSDcu=((Lmax/volt)^2)*(68.88/ASD)*1/1000;
C9=(ICsys*i+8760*ECon*FLS)*PSDcu; % From Eq. 6.11, annual OC of copper
losses in 24 SDs)
TAC=C1+C2+C3+C4+C5+C6+C7+C8+C9;
disp(TAC);
diff(TAC,ST);ST1=ans;
E=ans;
ST=vpa(solve(E),5);ST1=ST;
diff(TAC,ASL);
F=ans;
ASL=vpa(solve(F),5);ASL1=ASL;
74
diff(TAC,ASD);
G=ans;
ASD=vpa(solve(G),5);ASD1=ASD;
ST0=ST1;
ASL0=ASL1;
ASD0=ASD1;
disp(ST1);
disp(ASL1);
disp(ASD1);
C01=XX*8*(250+7.26*ST0)*i;% $/Block-2 trx per block & 12 services per
ea. trx
C02=XX*8*(60+4.5*ASL0)*i*2*(LSL/1000); %Triplex aluminum cable cost for
Service Lateral per transformer
C03=XX*8*(60+4.5*ASD0)*i*YY*LSD/1000; % Service Drop initial cost
($/block)
C04=8*160*poles*i;
% Cost of Poles $/ block
C05=2*Iexc*ST0*ICCAP*i; % Capacitors’cost for System energizing & I
excitation
C06=2*(ICsys*i+8760*ECoff)*0.004*ST0; % Cost of iron losses/ upleg of
Secondary ($/ block)
FLS=0.3*FLD+0.7*FLD^2;
Smax=YY*La12; % This is found from Table 6.4 for 12 class 2 customers,
per book example
PTcu=(0.073+0.00905*ST0);% Transformer copper losses Where 15
kVA<=ST<=100 kVA
% This is found from (Eq. 6.10)
C07=XX*(ICsys*i+8760*ECon*FLS)*(PTcu)*(Smax/ST0)^2;
%From Eq.6.9, The annual OC of tx copper losses per
block
RSL=(20.5*(LSL)*2)/(1000*ASL0); % RSL=p*L/1000*ASL (Ohm.kcmil/trx.)
PSLcu=(((4*L4*1000)/(volt))^2)*(RSL/1000);
%PSLcu=((4*L4/volt)^2)*(12.3/ASL0)/1000;
C08=XX*(ICsys*i+8760*ECon*FLS)*PSLcu;
% From Eq. 6.11, annual OC of copper losses in the
4 SLs
RSD=(20.5*LSD*24*2)/(1000*ASD0); %Rc=p*(LSD/1000)*ASD0=68.88/ASD
(Ohm.kcmil/block),
PSDcu=(((L1*1000/volt))^2)*(RSD/1000); %
PSDcu=((Lmax/volt)^2)*(68.88/ASD)*1/1000;
C09=(ICsys*i+8760*ECon*FLS)*PSDcu; % From Eq. 6.11, annual OC of copper
losses in 24 SDs)
TAC0=C01+C02+C03+C04+C05+C06+C07+C08+C09;
disp(' “Value of TAC0 “');
disp(TAC0);
if ST1<=A(1,1) % Secondary Distribution Transformer (ST) Selection
Logic
ST=A(1,1);XT=A(1,13);
75
disp(ST);
elseif ST1<=A(2,1)
ST=A(2,1);XT=A(2,13);
disp(ST);
elseif ST1<=A(3,1)
ST=A(3,1);XT=A(3,13);
disp(ST);
elseif ST1<=A(4,1)
ST=A(4,1);XT=A(4,13);
disp(ST);
elseif ST1<=A(5,1)
ST=A(5,1);XT=A(5,13);
disp(ST);
elseif ST1<=A(6,1)
ST=A(6,1);XT=A(6,13);
disp(ST);
elseif ST1<=A(7,1)
ST=A(7,1);XT=A(7,13);
disp(ST);
elseif ST1<=A(8,1)
ST=A(8,1);XT=A(8,13);
disp(ST);
elseif ST1<=A(9,1)
ST=A(9,1);XT=A(9,13);
disp(ST);
else disp('Provide a different design');
end
%ASL=B(k,12);AMP=B(k,2);XSL=B(k,5);RSL=B(k,3);
if ASL1<=B(1,12)
% Service Lateral Ampacity (SL) Selection Logic
ASL=B(1,12);AMP=B(1,2);XSL=B(1,5);RSL=B(1,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(2,12)
ASL=B(2,12);AMP=B(2,2);XSL=B(2,5);RSL=B(2,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(3,12)
ASL=B(3,12);AMP=B(3,2);XSL=B(3,5);RSL=B(3,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(4,12)
ASL=B(4,12);AMP=B(4,2);XSL=B(4,5);RSL=B(4,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(5,12)
ASL=B(5,12);AMP=B(5,2);XSL=B(5,5);RSL=B(5,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(6,12)
ASL=B(6,12);AMP=B(6,2);XSL=B(6,5);RSL=B(6,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(7,12)
ASL=B(7,12);AMP=B(7,2);XSL=B(7,5);RSL=B(7,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(8,12)
ASL=B(8,12);AMP=B(8,2);XSL=B(8,5);RSL=B(8,3);
76
disp(ASL);disp(AMP);
elseif ASL1<=B(9,12)
ASL=B(9,12); AMP=B(9,2);XSL=B(9,5);RSL=B(9,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(10,12)
ASL=B(10,12); AMP=B(10,2);XSL=B(10,5);RSL=B(10,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(11,12)
ASL=B(11,12); AMP=B(11,2);XSL=B(11,5);RSL=B(11,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(12,12)
ASL=B(12,12); AMP=B(12,2);XSL=B(12,5);RSL=B(12,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(13,12)
ASL=B(13,12); AMP=B(13,2);XSL=B(13,5);RSL=B(13,3);
disp(ASL);disp(AMP);
else disp('Provide a different design');
end
ASL2=ASL;
VDSL2=4*1000*(L4/(volt)^2)*2*(LSL/1000)*(RSL*cos(phi)+XSL*sin(phi))*100
;
for k=1:1:13
VDSL3=4*1000*(L4/(volt)^2)*2*(LSL/1000)*(RSL*cos(phi)+XSL*sin(phi))*100
;
if VDSL2<5
break
else ASL3=B(k,12);AMP=B(k,2);XSL=B(k,5);RSL=B(k,3);
if VDSL3<5
ASL2=ASL3;
VDSL2=VDSL3;
else
ASL3=B(k+1,12);AMP=B(k+1,2);XSL=B(k+1,5);RSL=B(k+1,3);
end
end
end
VDSL=VDSL2;
if ASD1<=B(1,12)
% Secondary Service Drop (SD) Selection Logic
ASD=B(1,12);SD1=B(1,2);XSD=B(1,5);RSD=B(1,3);
disp(ASD);disp(SD1);
elseif ASD1<=B(2,12)
ASD=B(2,12);SD1=B(2,2);XSD=B(2,5);RSD=B(2,3); %ZSD=B(2,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(3,12)
ASD=B(3,12);SD1=B(3,2);XSD=B(3,5);RSD=B(3,3); %ZSD=B(3,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(4,12)
ASD=B(4,12);SD1=B(4,2);XSD=B(4,5);RSD=B(4,3); %ZSD=B(4,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(5,12)
77
ASD=B(5,12);SD1=B(5,2);XSD=B(5,5);RSD=B(5,3);
disp(ASD);disp(SD1);
elseif ASD1<=B(6,12)
ASD=B(6,12);SD1=B(6,2);XSD=B(6,5);RSD=B(6,3);
disp(ASD);disp(SD1);
elseif ASD1<=B(7,12)
ASD=B(7,12);SD1=B(7,2);XSD=B(7,5);RSD=B(7,3);
disp(ASD);disp(SD1);
elseif ASD1<=B(8,12)
ASD=B(8,12);SD1=B(8,2);XSD=B(8,5);RSD=B(8,3);
disp(ASD);disp(SD1);
elseif ASD1<=B(9,12)
ASD=B(9,12);SD1=B(9,2);XSD=B(9,5);RSD=B(9,3);
disp(ASD);disp(SD1);
else
end
%ZSD=B(5,4);
%ZSD=B(6,4);
%ZSD=B(7,4);
%ZSD=B(8,4);
%ZSD=B(9,4);
ASD2=ASD;
VDSD2=1000*(L1/(volt)^2)*2*(LSD/1000)*(RSD*cos(phi)+XSD*sin(phi))*100;
for j=1:1:9
VDSD3=1000*(L1/(volt)^2)*2*(LSD/1000)*(RSD*cos(phi)+XSD*sin(phi))*100;
if VDSD2<5
break
else ASD3=B(j,12);SD1=B(j,2);XSL=B(j,5);RSL=B(j,3);
if VDSL3<5
ASD2=ASD3;
VDSD2=VDSD3;
else
ASD3=B(j+1,12);SD1=B(j+1,2);XSL=B(j+1,5);RSL=B(j+1,3);
end
end
end
VDSD=VDSD2;
C1=XX*8*(250+7.26*ST)*i;
% $/Block-2 trx per block & 12 services per ea. trx
C2=XX*8*(60+4.5*ASL)*i*2*(LSL/1000); %Triplex aluminum cable cost for
Service Lateral per transformer
C3=XX*8*(60+4.5*ASD)*i*YY*LSD/1000; % Service Drop initial cost
($/block)
C4=8*160*poles*i;
% Cost of Poles $/ block
C5=2*Iexc*ST*ICCAP*i; % Capacitors’cost for System energizing & I
excitation
C6=2*(ICsys*i+8760*ECoff)*0.004*ST; % Cost of iron losses/ upleg of
Secondary ($/ block)
FLS=0.3*FLD+0.7*FLD^2;
Smax=YY*La12; % This is found from Table 6.4 for 12 class 2 customers,
per book example
78
PTcu=(0.073+0.00905*ST);% Transformer copper losses Where 15
kVA<=ST<=100 kVA
% This is found from (Eq. 6.10)
C7=XX*(ICsys*i+8760*ECon*FLS)*(PTcu)*(Smax/ST)^2;
%From Eq.6.9, The annual OC of tx copper losses per block
RSL=(20.5*(LSL)*2)/(1000*ASL); % RSL=p*L/1000*ASL (Ohm.kcmil/trx.)
PSLcu=(((4*L4*1000)/(volt))^2)*(RSL/1000);
%PSLcu=((4*L4/volt)^2)*(12.3/ASL0)/1000;
C8=XX*(ICsys*i+8760*ECon*FLS)*PSLcu;
% From Eq. 6.11, annual OC of copper losses in the 4 SLs
RSD=(20.5*LSD*24*2)/(1000*ASD); %Rc=p*(LSD/1000)*ASD0=68.88/ASD
(Ohm.kcmil/block),
PSDcu=(((L1*1000/volt))^2)*(RSD/1000); %
PSDcu=((Lmax/volt)^2)*(68.88/ASD)*1/1000;
C9=(ICsys*i+8760*ECon*FLS)*PSDcu; % From Eq. 6.11, annual OC of copper
losses in 24 SDs)
TAC2=C1+C2+C3+C4+C5+C6+C7+C8+C9;
disp(' “Value of TAC2 “');
disp(TAC2);
% The Voltage Drop Constraint is tested on the obtained values
%
VoltDrop = VDT+VDSL+VDSD;
%Zpu=0.02; %Zbase=voltage^2/ST;%Zpu is given in input tables
%ZVST=Zpu*Zbase;
VDT=1000*(Aload/(volt)^2)*XT*100; % VDT=12*LoadC*ZVST;
VoltDrop=VDT+VDSL+VDSD;
if VoltDrop>10 % The Voltage Drop Constraint is tested for Optimization
disp('"Voltage Drop Too High! -- Provide a different design."');
disp('"VoltDrop in % = "');
disp(VoltDrop); disp(VDT); disp(VDSL); disp(VDSD)
disp(TAC2);
disp(' “Size of transformer in kVA is = ”');disp(ST);
disp(' “Size of ASL “’');disp(ASL2);disp(AMP);
disp(' “Size of ASD “');disp(ASD2);disp(SD1);
else
disp('"VoltDrop in % = "');
disp(VoltDrop);disp(VDT);disp(VDSL);disp(VDSD)
disp(TAC2);%disp(ST);disp(ASL);disp(AMP),disp(ASD);disp(SD1);
disp(' “Size of transformer in kVA is = ”');disp(ST);
disp(' “Size of ASL “’');disp(ASL2);disp(AMP);
disp(' “Size of ASD “');disp(ASD2);disp(SD1);
end
79
APPENDIX B
Instructions for Matlab TAC Program in Distribution System
The following are instruction steps to utilize the Matlab TAC program:
1. This program is constructed with the idea that configuration of distribution system
greatly affects the outcome as the layout will determine the efficient means of
distribution, and hence, we have assumed a city residential block typically found
in the urban areas of most major U.S cities.
2. Typically, two transformers from the utility Right of Way serve these blocks,
usually by single-phase distribution circuit of the serving electric utility. We
assume the secondary distribution system within a City block, as discussed in
Appendix A. The block dimensions are according to Figure 4.4 Similar to
previous program, it queries for the inputs of Transformer size in KVA, Cable
sizes (ASL and ASD) in kcmil, and loads (L1, L4, and La12) in KVA . Values for
loads L1, L4, and La12 can be obtained from Table 4.1, or can be any
combination of average household load for one (maximum load), four, or 12
customers. Similar to the example in the book, we have assumed 12 kV primary
distributions for these transformers, and 240- volt secondary to customers. As
before, two single-phase transformers are serving this block, and each transformer
serving power to twelve customers [1].
80
3. The following questions will be asked when program is run:
What is ST in kVA?
What is ASL in kcmil?
What is ASD in kcmil?
What is the load for 12 customers in kVA?
What is the load for 4 customer in kVA?
What is Max load (1 customer) in kVA?
Then TAC will be calculated by the program in $/block.
Sample Runs
What is ST in kVA? 100
What is ASL in kcmil? 300
What is ASD in kcmil? 167.8
What is the load for 12 customers in kVA? 10
What is the load for 4 customer in kVA? 12
What is Max load (1 customer)in kVA? 18
TAC = 7746
*****************************************************
What is ST in kVA? 50
What is ASL in kcmil? 167.8
What is ASD in kcmil? 83.69
81
What is the load for 12 customers in kVA? 4.4
What is the load for 4 customer in kVA? 6
What is Max load (1 customer) in kVA? 10
TAC = 4559
*******************************************************
What is ST in kVA? 15
What is ASL in kcmil? 41.74
What is ASD in kcmil? 41.74
What is the load for 12 customers in kVA? 1.2
What is the load for 4 customer in kVA? 1.5
What is Max load (1 customer) in kVA? 2.5
TAC =2255
82
Matlab Program for Total Annualized Cost (TAC) in Distribution System
prompt1 = 'What is transformer rate in kVA? ';
%input, program asking for %transformer rate in kVA
ST = input (prompt1);
prompt2 = 'What is cable size (ASL) in kcmil? ';
%input, program is asking for %cable size in kcmil
ASL = input (prompt2);
prompt3 = 'What is cable size (ASD) in kcmil? ';
%input, program is asking for %cable size in kcmil
ASD = input (prompt3);
prompt4 = 'What is the load for 12 customers in kVA? ';
% input, Program is %asking for average load for 12 customer. Table can be
used
L12 = input (prompt4);
prompt5 = 'What is the load for 4 customer in kVA? ';
%input, Program is %asking for average load for 4 customer. Table can be used
L4 = input (prompt5);
prompt6 = 'What is Max load (1 customer) in kVA? ';
%input, Program is %asking for average load for 1 customer. Table can be used
L1 = input (prompt6);
% this formula was driven for the cost (C1-C9)in the report page
TAC = (6.048*ASD)+ (4.32*ASL) + (14.9522*ST) +374.536*L1*(L1/ASD) +
2141.28*L4*(L4/ASL) + (6589.33*(L12/ST)*(L12/ST))+(816.9*L12*(L12/ST))+
1306.24;
round(TAC); TAC=ans
% TAC is calculated by program
83
APPENDIX C
Secondary Distribution System Voltage Drop Program
Instructions for Running the Matlab Voltage Drop Calculation Program
The following are instruction steps to utilize the Matlab Voltage Drop Program :
1. The program is designed to provide the design parameters to the secondary
distribution system designer who has the layout of the typical urban Area City
block, found in the urban areas of most major U.S cities (typically 960 feet long
by 330 feet wide).
2. It may also be modified to use it for bigger acreages available in the agricultural
areas, or as a calculator on the primary system. This program calculates the
voltage drop within the Transformer, Service Lateral (SL), and Service Drop
(SD).
3. The utility would reduce the voltage drop at the end of the line by bringing the
distribution high voltage side to the middle of the circuit, so that two almost
equal strings can service the two sides of the pattern. The utility therefore serves
the two strings by the two transformers from the utility Right of Way which
service these blocks, by single-phase distribution circuit of the serving electric
utility. We provided the input queries for the dimensions of this block as to the
84
length and width, which will have a bearing upon the length of service laterals
and service drop conductors serving the neighborhood area. The example in the
book has assumed two single-phase transformers serving this block, and each
transformer serving power to twelve customers (we have assumed 12 kV primary
distributions for these transformers, and 240- volt secondary to customers) [1].
4. The utilities have technical designers who are responsible to keep voltage drop
within a tolerance level and at the same time must justify their cost expenditures
to their financial managers and public agencies involved, as the total
expenditures will undoubtedly affect the tiered electric rates that ratepayers must
pay. Therefore, extra prudence is applied so that the utility is not heavily
weighted in the purchase of non-utilized assets
5. The load is queried into this program as energy use of a house may greatly
depend on the neighborhood demography and its location. The program queries
for the single family load, diversified loads, and it then calculates the voltage
drops values at the Transformer (ST), Service Lateral (SL) and Service Drop
(SD) conductors. It then calculates the Total Voltage Drop for all three in the
secondary system.
85
6. Two files are attached with this instruction sheet. One is the Matlab program
called VoltageDrop.m and the other is the Excel input data called
TransfDataTryVD24.xls.
User needs to save the TransfDataTryVD24.xls in the folder that Matlab works
with to be able to import the table values automatically into Matlab.
86
Matlab Program for Voltage Drop in Distribution System
%This program evaluates the distribution circuit voltage drop
requirements for a block %development and then determines if the
constraint threshold is exceeded, based on the transformers' size,
Service Laterals, %and Service Drops. Block length and widths are
inputs given to the program %as specifications as well as the
residential load, voltage and power factor.
clear all
clc
foadfile1='TransfDataTryVD24.xls'; %reads data from first worksheet in
sheet=1; %the Excel spreadsheet file named 'foadfile1' and returns the
x1range='B10:N17';
% numeric data in array num.
subsetA=xlsread(foadfile1,sheet,x1range);
%disp(subsetA)
A=subsetA;
foadfile2='TransfDataTryVD24.xls';
%reads data from the second
worksheet in
sheet=2; %the Excel spreadsheet file named 'foadfile2' and returns the
x2range='B10:N22';
% numeric data in array num.
subsetB=xlsread(foadfile2,sheet,x2range);
%disp(subsetB)
B=subsetB;
Lab=input('Enter the spacing for block length Lab in ft: ');
Wac=input('Enter the spacing for block width Wab in ft: ');
volt=input('Enter the secondary distribution voltage: ');
prompt1 = 'What is Max Average Load for each of 12 customers in KVA? ';
La12=input (prompt1);
prompt2= 'What is the Load for 4 customers in KVA? ';
L4=input (prompt2);
prompt3 = 'What is Max Load for 1 customer in KVA? ';
L1=input (prompt3);
ST1=input('Enter the distribution system Transformer Size: ');
pf=input('Enter the distribution system power factor (pf)cos(Phi): ');
ASL1=input('What is the cross section of SL Line? : ');
%AMP=input('What is the ampacity of SL Line? : ');
ASD1=input('What is the Cross section size of SD Line? : ');
%ASD=input('What is the length of SD Line? : ');
%Lab=1*960;Wac=1*330;volt=240;La12=10;L4=12;L1=18;pf=0.9;
%ST1=75;ASL1=74;ASD1=43;
i=0.1; % The utility cost annualized Rate (Capitalization Rate)
ICCAP=15;ICsys=8*350;Iexc=0.015;FLD=0.35;ECoff=.015;ECon=.02;
% Defining the parameters;
XX=2;
% No of Transformers
YY=12;
% No of Customers
poles=6;
% No. of Poles
LotW=Lab/12;
% Lot Width
LotL=Wac/2;
% Lot Length
87
LSL=4*LotW;
% Length of SL
LSD=0.5*LotL;
% Length of SD
phi=acos(pf);
% Phi Angle (phi)
Smin=YY*1.1;
% In kVA
Aload=YY*La12;
if Aload<Smin
ST=Smin;ASL=41.74;ASD=26.24;
else
ST=iscolumn(A(1));ASL=iscolumn(B(12));ASD=iscolumn(B(12));RSL=iscolumn(
B(3));
XSL=iscolumn(B(5));RSD=iscolumn(B(3));XSD=iscolumn(B(5));AMP=iscolumn(B
(2));
SD1=iscolumn(B(2));
end
%disp(ST1);
%disp(ASL1);
%disp(ASD1);
if ST1<=A(1,1) %Secondary Distribution Transformer (ST) Selection Logic
ST=A(1,1);XT=A(1,13);
disp(ST);
elseif ST1<=A(2,1)
ST=A(2,1);XT=A(2,13);
disp(ST);
elseif ST1<=A(3,1)
ST=A(3,1);XT=A(3,13);
disp(ST);
elseif ST1<=A(4,1)
ST=A(4,1);XT=A(4,13);
disp(ST);
elseif ST1<=A(5,1)
ST=A(5,1);XT=A(5,13);
disp(ST);
elseif ST1<=A(6,1)
ST=A(6,1);XT=A(6,13);
disp(ST);
elseif ST1<=A(7,1)
ST=A(7,1);XT=A(7,13);
disp(ST);
elseif ST1<=A(8,1)
ST=A(8,1);XT=A(8,13);
disp(ST);
elseif ST1<=A(9,1)
ST=A(9,1);XT=A(9,13);
disp(ST);
else disp('Provide a different design');
end
%ASL=B(k,12);AMP=B(k,2);XSL=B(k,5);RSL=B(k,3);
if ASL1<=B(1,12)
% Service Lateral Ampacity (SL) Selection Logic
ASL=B(1,12);AMP=B(1,2);XSL=B(1,5);RSL=B(1,3);
disp(ASL);disp(AMP);
88
elseif ASL1<=B(2,12)
ASL=B(2,12);AMP=B(2,2);XSL=B(2,5);RSL=B(2,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(3,12)
ASL=B(3,12);AMP=B(3,2);XSL=B(3,5);RSL=B(3,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(4,12)
ASL=B(4,12);AMP=B(4,2);XSL=B(4,5);RSL=B(4,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(5,12)
ASL=B(5,12);AMP=B(5,2);XSL=B(5,5);RSL=B(5,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(6,12)
ASL=B(6,12);AMP=B(6,2);XSL=B(6,5);RSL=B(6,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(7,12)
ASL=B(7,12);AMP=B(7,2);XSL=B(7,5);RSL=B(7,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(8,12)
ASL=B(8,12);AMP=B(8,2);XSL=B(8,5);RSL=B(8,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(9,12)
ASL=B(9,12); AMP=B(9,2);XSL=B(9,5);RSL=B(9,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(10,12)
ASL=B(10,12); AMP=B(10,2);XSL=B(10,5);RSL=B(10,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(11,12)
ASL=B(11,12); AMP=B(11,2);XSL=B(11,5);RSL=B(11,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(12,12)
ASL=B(12,12); AMP=B(12,2);XSL=B(12,5);RSL=B(12,3);
disp(ASL);disp(AMP);
elseif ASL1<=B(13,12)
ASL=B(13,12); AMP=B(13,2);XSL=B(13,5);RSL=B(13,3);
disp(ASL);disp(AMP);
else disp('Provide a different design');
end
ASL2=ASL;
VDSL2=4*1000*(L4/(volt)^2)*2*(LSL/1000)*(RSL*cos(phi)+XSL*sin(phi))*100
;
for k=1:1:13
VDSL3=4*1000*(L4/(volt)^2)*2*(LSL/1000)*(RSL*cos(phi)+XSL*sin(phi))*100
;
if VDSL2<15
break
else ASL3=B(k,12);AMP=B(k,2);XSL=B(k,5);RSL=B(k,3);
if VDSL3<15
ASL2=ASL3;
89
VDSL2=VDSL3;
else
ASL3=B(k+1,12);AMP=B(k+1,2);XSL=B(k+1,5);RSL=B(k+1,3);
end
end
end
VDSL=VDSL2;
if ASD1<=B(1,12)
% Secondary Service Drop (SD) Selection Logic
ASD=B(1,12);SD1=B(1,2);XSD=B(1,5);RSD=B(1,3);
disp(ASD);disp(SD1);
elseif ASD1<=B(2,12)
ASD=B(2,12);SD1=B(2,2);XSD=B(2,5);RSD=B(2,3); %ZSD=B(2,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(3,12)
ASD=B(3,12);SD1=B(3,2);XSD=B(3,5);RSD=B(3,3); %ZSD=B(3,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(4,12)
ASD=B(4,12);SD1=B(4,2);XSD=B(4,5);RSD=B(4,3); %ZSD=B(4,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(5,12)
ASD=B(5,12);SD1=B(5,2);XSD=B(5,5);RSD=B(5,3); %ZSD=B(5,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(6,12)
ASD=B(6,12);SD1=B(6,2);XSD=B(6,5);RSD=B(6,3); %ZSD=B(6,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(7,12)
ASD=B(7,12);SD1=B(7,2);XSD=B(7,5);RSD=B(7,3); %ZSD=B(7,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(8,12)
ASD=B(8,12);SD1=B(8,2);XSD=B(8,5);RSD=B(8,3); %ZSD=B(8,4);
disp(ASD);disp(SD1);
elseif ASD1<=B(9,12)
ASD=B(9,12);SD1=B(9,2);XSD=B(9,5);RSD=B(9,3); %ZSD=B(9,4);
disp(ASD);disp(SD1);
else
end
ASD2=ASD;
VDSD2=1000*(L1/(volt)^2)*2*(LSD/1000)*(RSD*cos(phi)+XSD*sin(phi))*100;
for j=1:1:9
VDSD3=1000*(L1/(volt)^2)*2*(LSD/1000)*(RSD*cos(phi)+XSD*sin(phi))*100;
if VDSD2<5
break
else ASD3=B(j,12);SD1=B(j,2);XSL=B(j,5);RSL=B(j,3);
if VDSL3<5
ASD2=ASD3;
90
VDSD2=VDSD3;
else
ASD3=B(j+1,12);SD1=B(j+1,2);XSL=B(j+1,5);RSL=B(j+1,3);
end
end
end
VDSD=VDSD2;
% The Voltage Drop Constraint is tested on the obtained values
%
VoltDrop = VDT+VDSL+VDSD;
%Zpu=0.02; %Zbase=voltage^2/ST;%Zpu is given in input tables
%ZVST=Zpu*Zbase;
VDT=1000*(Aload/(volt)^2)*XT*100; % VDT=12*LoadC*ZVST;
%VDSD=1000*(L1/(volt)^2)*2*(LSD/1000*((RSD*cos(phi))+XSD*sin(phi)))*100
;
VoltDrop=VDT+VDSL+VDSD;
if VoltDrop>20 % The Voltage Drop Constraint is tested for Optimization
disp('"Voltage Drop Too High! -- Provide a different design."');
disp('" VoltDrop in % = "');
disp(VoltDrop);disp(VDT);disp(VDSL);disp(VDSD);
disp(' “Size of transformer in kVA is = ”');disp(ST);
disp(' “Size of ASL “');disp(ASL2);disp(AMP);
disp(' “Size of ASD “');disp(ASD2);disp(SD1);
else
disp('"VoltDrop in % = "');
disp(VoltDrop);disp(VDT);disp(VDSL);disp(VDSD);
disp(' “Size of transformer in kVA is = ”');disp(ST);
disp(' “Size of ASL “');disp(ASL2);disp(AMP);
disp(' “Size of ASD “');disp(ASD2);disp(SD1);
end
91
APPENDIX D
Distribution System Component Information Background
Conductors
For utility companies one of the most expensive components is the conductors.
Due to this fact, it is imperative that distribution system engineer and planner choose the
most appropriate conductor type and size so that optimum operating efficiency can be
realized[38][39]. The designer must come up with best price for a conductor with best
conductivity-to-weight ratio and/or strength -to-weight ratio. For necessary ratio designer
needs to look at all the factors such as voltage stability of the line, loading of the line,
losses of the line, tension load, and environmental factors [40].
For selecting a conductor, technical and financial criteria need to be considered.
Not only maximum power transfer, minimum loss and thermal capacity , per the system
design specification, but also the price should be take in to account. While choosing a
new conductor that has to match or work the existing conductor in the network, it has to
be suitable for environmental conditions, as well.
Most common conductor materials are Aluminum and copper. Copper is the best
conductor and is the base-line reference for conductivity characteristics. On the other
hand, the closest alternative for conductivity is Aluminum with less weight. Aluminum
conductivity is 61 percent, its weight is 30 percent, and its breaking strength is 43 percent
of copper [16].
92
Because of the breaking strength of aluminum, aluminum conductor is made with
strands of high-strength steel in their central core, and the combination is called
Aluminum Cable Steel Reinforced or ACSR. ACSR is lighter than copper and has
strength and conductivity of copper. At the same time, ACSR has longer life span and it
last much longer than conductor usual 40 years. Following figure shows various
configuration and size of ACSR conductors.
93
94
Distribution Transformers
In the beginning, working power systems used direct current (DC) which carries
low voltage and high current. Because of this combination there were a very large voltage
drops and power losses especially in long distance distribution. The development of
Alternating Current (AC) eliminated above problems and issues and made efficient and
cost effective long-distance transmission and distribution a possibility.
The first modern transmission was built in 1885 by William Stanley [37]. A
simple transformer consist of two set of coil wrapped around a ferromagnetic core. When
there is current in primary coil there will be flux created in the core and these flux going
troughs the secondary coil create current in secondary circuit. The powers in primary and
secondary circuits are identical (for ideal transformer). Because of that if the current goes
up in secondary voltage goes down in secondary and if current goes down in secondary
voltage goes up in secondary. Voltage ratio of primary over secondary is equal to the
ratio of coil turn in primary over the coil turn in secondary
(Vp/Vs)=(Np/Ns)
,
Pp=Ps
Vp
Primary voltage
Vs
Secondary voltage
Np
Number of turn in primary coil
Ns
Number of turn in secondary coil
Pp
Power in primary
Ps
Power in secondary
, (Ip/Is)=(Ns/Np)
95
Ip
Current in primary
Is
Current in secondary
Distribution Transformers are typically rated up to 500kVA, whereas power
transformers maintain rating of over 500 kVA at voltage levels of 69kV or greater [36].
Following page shows some typically rated transformers and associated data.
96
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