computational intelligence based tehnique for load shedding scheme
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COMPUTATIONAL INTELLIGENCE BASED TEHNIQUE FOR LOAD SHEDDING SCHEME
LUKMAN HAKIM BIN HAMRON
i
FACULTY OF ELECTRICAL ENGINEERING
UNIVERSITI TEKNOLOGI MARA
MALAYSIA
COMPUTATIONAL INTELLIGENCE BASED TECHNIQUE FOR LOAD SHEDDING SCHEME
Project report is presented in partial fulfillment for the award of the
Bachelor of Electrical Engineering (Hons)
Universiti Teknologi MARA (UiTM)
ii
LUKMAN HAKIM BIN HAMRON
Faculty of Electrical Engineering
UNIVERSITI TEKNOLOGI MARA
40450 SHAH ALAM, SELANGOR
A report submitted to Faculty of Electrical Engineering, Universiti Teknologi MARA in partial fulfillment of the requirement for Bachelor of Electrical Engineering (Hons).
This thesis is approved by:
……………………………….
Associate Professor Dr. Ismail Musirin
Project supervisor
Faculty of Electrical Engineering
Universiti Teknologi MARA (UiTM)
40450 Shah Alam
Selangor.
Date:………………..
iii
DECLARATION
It is hereby declared that all materials in this thesis are the result of my own work and
all the materials that are not the result of my own work have been clearly
acknowledged. Although, certain result on this thesis is effort from other dispute.
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ACKNOWLEGMENT
First and foremost, all praise to Allah S.W.T. The Most Gracious and Most Merciful
who had given me the strength, ability and patient upon completing this final year
project.
I wish to conveymy deepest gratitude and appreciation to my supervisor, Assoc. Prof.
Dr. Ismail Musirin for his guidance, concern, valuable time, effort, constant
encouragement and patience in supervising this project from the start until the
completion if this thesis.
I also wish to take this opportunity to express my gratitude to my family especially to
my mother and my father for supporting me along way my journey in this field. They
have encourage me throughout my education , and I will always be grateful for their
sacrifice, generosity and love. May Allah S.W.T. bless them all.
Not forget to my friends and anyone who directly or indirectly giving their support
and contribution to finished this project. May Almighty Allah bless and reward them
for their generosity. Thank you very much.
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ABSTRACT
Losses in generation and overloading effect are two phenomena that may
occur due to progressing demand at the load side. This may lead to system instability
in forms of voltage and frequency. In order to avoid this problem, the under voltage
load shedding scheme can be performed to shed some amount of load before the
disturbance occur. This paper presents computational intelligence technique for load
shedding. The study involves the development of fuzzy rules in order to make
decision on load shedding. This method functions will determine the amount of load
that needs to be shed depending on the measured minimum voltage of the system.
The result of this paper will show the performance of under voltage load shedding
scheme in determining power system stability by shedding some amount of the load
demand. The technique has been validated on the IEEE 30-bus system.
Index Terms—voltage collapse, system stability, fuzzy logic, under voltage load shedding
vi
TABLE OF CONTENTS
CHAPTER DESCRIPTION PAGE
DECLARATION i
ACKNOWLEDGEMENT ii
ABSTRACT iii
TABLE OF CONTENTS iv
LIST OF FIGURES vi
LIST OF TABLES vii
LIST OF ABBREVIATIONS viii
1.0 INTRODUCTION 1
1.1 INTRODUCTION 1
1.2 PROBLEM STATEMENT 3
1.3 OBJECTIVE 3
1.4 SCOPE OF THE PROJECT
1.5 RESEARCH FRAMEWORK
1.6 OVERVIEW OF THE REPORT
4
5
6
2.0 LITERATURE REVIEW 5
2.1 ECONOMIC DISPATCH (ED) 5
2.2 DYNAMIC ECONOMIC DISPATCH(DED) 6
2.2.1 Ramp Rate Constraint 8
2.3 PARTICLE SWARM OPTIMIZATION (PSO)
2.4 METHOD TO SOLVE DED
9
10
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3.0 METHODOLOGY 15
3.1 INTRODUCTION 15
3.2 DYNAMIC ECONOMIC DISPATCH (DED)
FORMULATION 15
3.2.1 Objective Function 15
3.2.2 Equality Constraint 16
3.2.3 Inequality Constraint 17
3.2.4 Dynamic Constraint 17
3.2.5 Fitness Function 18
3.3 PARTICLE SWARM OPTIMIZATION (PSO) 19
3.3.1 Basic PSO Algorithm 19
3.3.2 Particle’s Velocity Update 20
3.3.3 Constriction Factor Approach (CFA) 20
3.3.4 Particle’s Position Update 21
3.3.5 Representation of Particle’s Position 21
3.4 DED BASED ON PSO TECHNIQUE 23
4.0 RESULTS AND DISCUSSION 26
4.1 DATA FOR IEEE 26-BUS TEST SYSTEM 26
4.2 PSO PARAMETERS SETTING 28
4.3 SIMULATION RESULTS FOR SOLUTION
OF DED BASED ON PSO 29
4.4 ANALYSIS OF PSO METHOD ON DED
SOLUTION 32
5.0 CONCLUSION 36
6.0 RECOMMENDATIONS FOR FUTURE WORKS 37
REFERENCES 38
APPENDICES 43
viii
LIST OF FIGURES
FIGURE TITLE PAGE
2.1 Single line diagram of transmission line 6
3.1 Matrix representation of particle’s position 22
3.2 Modification of gBest according to generator constraints 22
3.3 Flow chart for DED based on PSO process 25
4.1Variation of Cost with Power Demand Curve for 6 units
system30
4.2Variation of Power loss with the Load Demand for 6
units system30
4.3Graph of Fuel Cost against Load Demand for
comparison between PSO and Newton Raphson method33
4.4Convergence Characteristics of PSO Method for 6 units
system34
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LIST OF TABLES
TABLE TITLE PAGE
4.1 Generating Unit Capacity and Coefficients for IEEE 26-
bus system
26
4.2Initial output power and Ramp Rate limits for IEEE 26-
bus system27
4.3 Load Demand for IEEE 26-bus system of 24 hours 27
4.4 Transmission loss Coefficients for IEEE 26-bus system 28
4.5 PSO parameters 28
4.6Optimal MW Generation for each unit, Transmission loss
and Fuel Cost of 24 hours29
4.7 Comparison of PSO and Newton Raphson Result 32
4.8 Result for the Variation Number of Particles 35
x
LIST OF ABBREVIATIONS
ED - Economic Dispatch
DED - Dynamic Economic Dispatch
PSO - Particle Swarm Optimization
SED - Static Economic Dispatch
AI - Artificial Intelligent
FACTS - Flexible Alternative Current Transmission Systems
DP - Dynamic programming
GA - Genetic Algorithm
SA - Simulated Annealing
EP - Evolutionary Programming
LP - Linear Programming
NLP - Non-Linear Programming
QP - Quadratic Programming
DE - Differential Evolution
ANN - Artificial Neural Network
HNN - Hopfield Neural Network
CFA - Constriction Factor Approach
IEEE - Institute of Electrical and Electronics Engineers
xi
CHAPTER 1.0
INTRODUCTION
1.1 BACKGROUND OF THE STUDY
In power system operation, the balance between load demand and the available
generation is important to make sure the stability of the system is in good condition
[1]. Nowadays, there are many situation occur where the demand load have reached
the limit of an available generation in certain place. When this condition occurs, there
will be same situation as in 2005 where there was power outage in Malaysia where
many states of Malaysia’s northern peninsular, including Perlis, Perak, Penang and
Kedah due to the occurred fault. This situation happened due to the load demand used
by the user has exceed the limit that the available generation can support. From this
situation a load shedding scheme is initiated to avoid the system from collapsed [2].
There are many factories have take improvement step to prevent this phenomena
happening again by developing a new alternative extensively to ensure the power
system network operates in the normal steady state condition conveniently [3].
A system enters a state of voltage instability when a disturbance, increase in
load demand, or change in system condition causes a progressive and uncontrollable
drop in voltage [4]. The main factor for instability is the inability of the power system
to meet the demand of increased reactive power. Literally, it will cause the system
collapse.
There are several studies that indicate about voltage stability of the power
system. One of these studies is about estimating the voltage stability of power system
[5]. This study is based on the fast calculation of indicators of risk of voltage
1
instability has been developed. These indicators can detect on-line voltage instability
and signal the tendency towards a critical situation.
Several methods have been developed to prevent the voltage from collapse. In this
paper load shedding is applied to the selected bus so the voltage minimum will
increase and the system become stable. This technique is proposed to make sure the
system in a balanced condition. In [6], there are several methods to perform the load
shedding technique such as under-voltage load shedding and under-frequency load
shedding. The best way to perform load shedding scheme in a system is by
minimizing the amount of load to be shed [7] for voltage collapse prevention. In [7],
the paper study about the practical approach to perform the load shedding scheme.
In order to perform the developed technique, a fuzzy logic algorithm was
proposed. This algorithm provides solution as decision making to determine which
load bus that need to be shed and how much load will be shed to make sure the system
recover to the normal operation. Fuzzy logic was a useful algorithm where it can be
used in wide area of study. In [8], fuzzy logic was used to solve the unit commitment
problem. While in [9], fuzzy load shedding based algorithm is performed by using
voltage stability indicator for averting voltage collapse. In this paper, fuzzy logic is
performed by monitoring the minimum voltage by running the load flow. Then under
voltage load shedding will be perform to get the system back to normal operation. The
variable is selected from the load flow results.
This paper presents computational intelligence based technique for load
shedding scheme. The study involves the development of fuzzy rules in order to make
decision on load shedding. Results from the experiment indicated that the proposed
technique is successful to solve the load shedding problems. The load levels increase
are divided into several different loading factors. The fuzzy technique is applied to
each case to select load bus to be shed and to calculate the amount load to be shed to
prevent voltage instability.
2
1.2 PROBLEM STATEMENT
Everyday people are using equipment continuously and the load demand for
each distribution network is increasing with the increasing of electric usage among the
user. Each generation that was established in Malaysia is enough to support the load
demand in certain area depending on the load usage. There are some cases where the
load demand is higher than the generation level. This will cause voltage collapse in
the area. For example in 1995, blackout situations happen in Malaysia due to high
load usage. The reason why this situation happened is because of the hot weather at
that time. The same situation occurred in 2005 where the biggest blackout happened in
Malaysia where there is no electricity due to the fault of the main cable transmission
line grid.
As the usage of equipment is increasing, the load demand will also increase.
This condition will burden the generation to support the load demand. A generation
has their limit to support the load demand in each area. When the consumer load
demand has gone beyond the limit of available generation, it may lead to blackout.
When this situation happens, it will cause problem to all consumer. This reason
becomes the why a new method is needed to overcome this problem.
1.3 OBJECTIVE
i. To develop load shedding scheme in power systemii. To identify the Selected bus for load shedding and amount of load demand
that should be shed for stable power system operation
iii. To improve the power balance in power system operation by using
computational intelligence
3
1.4 SCOPE OF THE PROJECT
The scope of this project is to analyze the balance between the load demand
and the available generation. The data will be taken from legal resource as the first
step of this project. Later, it will be analyzed to match with the load shedding
technique. This technique is used to develop an algorithm as the solution for solving
the load shedding problem. A selected load bus will be chosen for shedding based on
the output of the develop algorithm.
The under voltage load shedding scheme is employed in order to determine
which load and amount of load that need to be shed. The voltage magnitude, active
power and reactive power at load bus will be assigned as the input variable to fuzzy
logic system. This fuzzy system will be implemented using MATLAB software. The
proposed method gives satisfactory results in term of blackouts prevention and
minimum voltage improvement.
Moreover, this project will show the performance of fuzzy logic algorithm to
be effective and useful in problem concerning the load shedding. The results of this
method will be used to decide which of the load is the most suitable to be removed for
maintaining the stability of the system.
Flow chart in Figure 1 below summarizes the involved process:
4
Preparing the system data
Initialize the load shedding scheme
Develop the fuzzy logic algorithm in matlab
Determine the shedding load to balance the system
Figure 1: Scope of project
1.5 RESEARCH FRAMEWORK
5
START
KNOWLEDGE ACQUISITION
MATLAB PROGRAMMING
FUZZY LOGIC ALGORITHM
LOADSHEDDING
DEVELOPMENT OF SIMPLELOAD SHEDDING TECHNIQUE
AND UVLS
DEVELOPMENT OF CONCEPTUAL MODEL OF
LOAD SHEDDING
DEVELOP THE PROGRAMMING CODES IN MATLAB
IMPLEMENTATION OF FUZZY LOGIC ALGORITHM FOR LOAD
SHEDDING
Figure 2: Research framework
1.6 OVERVIEW OF THE REPORT
This thesis consist of five chapters explain about solving under voltage load shedding
(UVLS) schemes implemented by using fuzzy logic system. Chapter 1 describes an
introduction of the project which includes the objective of this research and also scope
of work to complete this project.
In Chapter 2, the theory and basic of voltage stability, under voltage load shedding
and fuzzy logic systems are reviewed and explained properly. The summary are
include the full details of problem in power system, theory of UVLS scheme, theory
of fuzzy logic and its application and some literature review on method to solve the
load shedding problems.
This project thesis was followed by the design methodology that explained clearly in
Chapter 3. This chapter explains the DED formulation algorithm including all the
constraints and the PSO techniques algorithm and lastly implementation of PSO
techniques to DED problems. This chapter also indicates the flow chart of DED based
on PSO techniques.
Next is Chapter 4 that illustrated all the results obtained together with the discussion
of the results. All the tables and graph plotted are discussed clearly in this chapter
including the analysis of PSO techniques on DED solution.
On the Chapter 5, a conclusion that has been made upon the result obtains and the last
chapter is Chapter 6 which discusses the recommendations for future works in order to
improve the solution for DED problems. The last parts of this thesis are the references
and appendix.
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CHAPTER 2.0
LITERATURE REVIEW
2.1 POWER SYSTEM VOLTAGE STABILITY
In a power system, the operation condition should be in a stable condition
where the voltage and the frequency is in equilibrium state. It means that the criteria
of the system operation should be meet the various operational, and it should also be
secure in the event of any credible contingency. That is why it is important to
maintaining the system in stable condition and secures the power system operation.
Nowadays, the problem and the challenges keep coming causing the power system
that being operated closer to their stability limits and the voltage in the system
dropping where it become unstable. Voltage instability and voltage collapse have been
considered as a major threat to present power system networks due to their stressed
operation. The disturbance that occur cause the voltage decreasing continuously and
lead to voltage collapse where the value of the voltage below its normal value. To
prevent the system collapse, lots of mechanism has been develop such as VAR
compensators, undervoltage load shedding and underfrequency load shedding [10].
Voltage collapse is the process by which the voltage falls to a low, unacceptable value
as a result of an avalanche of events accompanying voltage instability [11]. Once
associated with weak systems and long lines, voltage problems are now also a source
of concern in highly developed networks as a result of heavier loading.
In this chapter, the concept of voltage stability and the conventional method of
voltage stability analysis which is undervoltage load shedding is presented. Simulation
results on test power systems are presented to illustarate the problem of voltage
stability and the under voltage load shedding scheme to analyze the problem. The
undervoltage load shedding scheme the being implemented by using one of the
artificial intelligence technique which is called fuzzy logic.
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2.2 VOLTAGE STABILITY
According to the IEEE Power System Engineering Committee, voltage
stability is being defined as “Voltage stability is the ability of a system to maintain
voltage so that when load admittance is increased, load power will increase, and so
that both power and voltage are controllable.” [12]. If there is disturbance occur and
the voltage in the system dropping, it will become voltage instability and lastly it will
cause voltage collapse. And nowadays, this voltage collapse is one of the major
problems which electric power networks might face [13]. The voltage stability
practically can be classified into two subcategories which are Long term and Short
term.
2.2.1 LONG TERM VOLTAGE STABILITY
In power system, the long-term voltage stability involves rather slow acting
equipment such as tap changing transformers, thermostatically controlled loads, and
generator current limiters. To analyze system dynamic performance, the long term
simulation is required. In these studies, stability is usually determined by the resulting
outage of equipment, rather than the severity of the initial disturbance.
2.2.2 SHORT TERM VOLTAGE STABILITY
The short-term voltage stability in power system involves dynamics of fast
acting load components such as induction motors, electronically controlled loads, and
HVDC converters. The study period of interest is in the order of at most several
seconds, and analysis requires solution of appropriate system differential equations
which is similar to analysis of rotor angle stability. Dynamic modeling of loads is
often essential. In contrast to angle stability, short circuits near loads are important.
This kind of voltage instability could easily happen in the result of a serious fault
occurrence in the power system network. So, it would have close relations with
electric power system protection methods [4].
8
2.3 VOLTAGE INSTABILITY
Figure 2.0-1: Power System with Remote Generation
Fig. 2.1 illustrates a simplified power system with a remote generator
supplying a substantial portion of the load at the load center through six transmission
lines. Es is the voltage at the remote generator buses 4 and Eg is the voltage at the
load center buses. As lines between the remote generators and the load center trip, the
MW power flows over fewer lines resulting in increased Var losses.
Figure 2.0-2: Real Power (MW) vs. Voltage (P-V) Curve
9
Figure 2.2 illustrates how voltage decays as lines trip. In power system, the
utilities system planners use this type of P-V curves analysis as an analysis tool to
determine the real power transfer capability across a transmission interface to supply
local load. Generally, all the planning engineers call this type of curves as nose
curves. The reason why this type of P-V curves is called as nose curves is because
when there is condition starting from a base-case system (all lines in-service),
computer-generated load flow cases are run with increasing power transfers while
monitoring voltages at critical buses. When power transfers reach a high enough level,
a stable voltage cannot be sustained and the system voltage collapses. As illustrates in
Figure 2.2, the shape of the nose of the curve depends on the nature of the load at the
load center. High levels of motor load combined with capacitor bank support of load
center voltage tend to make the voltage drop very rapidly for a small increase of
power at the nose of the curve.
The set of P-V curves illustrates that for baseline conditions shown in curve A,
the voltage remains relatively steady (changing along the vertical axis) aslocal load
increases. System conditions are secure and stable to the left of point A1. After a
contingency occurs, such as a transmission circuit tripping, the new condition is
represented by curve B, with lower voltages (relative to curve A). This is because the
power being transmitted from the remote generators now follows through five, rather
than six, transmission lines. The system must be operated to stay well inside the load
level for the nose of curve B. If the B contingency occurs, then the next worst
contingency must be considered. The system operators must increase local generation
(Eg) to reduce the power being transmitted for the remote generators to reduce losses,
as well as increase voltage at the load center to within the safe zone, to avoid going
over the nose of curve C.
2.4 DISTURBANCE IN POWER SYSTEM
Usually all the electrical energy that has been provided by the electrical utility is
safe and reliable. The problem comes when there are disturbance, disruptions,
irregularities and nature of electricity occurred. For an example there are lightning,
equipment failures, and high winds can cause power line disturbance and also will
affect the voltage in the system. If electrical equipment is being used and the is power
disturbance occur, it will cause data or memory losses, altered data and other
10
functional errors, as well as equipment damage. And if there is no preventive method
towards this problem, then it may cause scheduling problems, downtime and
expensive troubleshooting. Before proceeding to the preventive method, first thing to
do is by understanding the causes of the problems.
2.5 CAUSES OF DISTURBANCE
There are several types of irregularities that affect electrical power which are
surges, sags. transients, noises and power outage.
2.4.1 SAGS
Sags is the condition when the voltage in a system is lower than the stable
range which caused by power failures, down lines, utility recloser operations and
storms. In power system, sags are the most common problem compared to others and
it can be assume that voltage below 0.95p.u. is considered sags.. This problem can be
corrected by using backup power sources such as UPSs, generators or voltage
restoration technologies.
2.4.2 SURGES
The different between surges and sags is the surges is the condition when the
voltage in a system is above from the stable range. The voltage that considered as
stable range is between 0.95p.u. to 1.05p.u.. The affect of surges in a system is it will
damage the equipment used. They may be seen more frequently in facilities with
rapidly varying electrical loads, often caused by the switching on / off of electric
motors (inductive load switching). Air conditioners, electrical power tools, furnace
igniters or ignition systems, arc welders, electrostatic copy machines and elevators are
most likely to create surges.
2.4.3 TRANSIENTS
Transient can be define as a change happen in voltage causes by the short
duration and sharp impulse. In power system and if there is disturbance occur, a
transient voltage may exceed the normal voltage level by five or ten times. Present,
the transients normally caused by a lightning strike and the normal operation of
11
electrical equipment such as switching on/ off electrical motors. Normally, the
presence of transient voltage can only be detected with special monitoring equipment.
2.4.4 NOISES
Noises can be classified as interferences that can be generated by any electrical
equipment. Usually the noise comes from equipment that not being installed correctly
and properly. This equipment may include: radio transmitters, fluorescent lights,
computers, business machines and even simple devices such as light sockets, wall
receptacles, plugs and loose electrical connections. These types of disturbances can
result in computer errors.
2.4.5 POWER OUTAGE
In power system, power outage can be defined as total losses of power. This
condition can be momentarily or last for extended periods of time. Generally, the
power in generation system must be equal to the load demand by customer plus the
losses. So if the load demand increase higher than the generation can support, it may
lead to the power outage. Besides that, the power outage also can be caused by
electrical load switching in utility power stations. Even a momentary outage, of only a
fraction of a second, will affect a computer and can result in data loss and the need for
data re-entry or reprogramming.
2.6 UNDERVOLTAGE LOAD SHEDDING SCHEME
Theoretically, the philosophy of UVLS is that when there is a system
disturbance and the voltage drops to a pre-selected level for a pre-determined time,
then selected loads are shed. It means that when there is voltage instability occurs due
to a disturbance and the load shedding is performed, the voltage will recover to
acceptable level thereby avoiding a more widespread system voltage collapse.
Practically, combination between protection engineers and system planners, who
together can determine the amount of load and time in the shedding program is
required to develop the undervoltage load shedding program. The system planning
engineers will analyze numerous studies using P-V curves as well as other analytical
methods to determine the amount of loads that to be shed to retain voltage stability
under credible contingencies. Voltage collapse is most probable under heavy load
12
conditions where large amounts of power are to be transported from remote generation
sites and the bulk of the system load consists of motors.
In under voltage load shedding scheme, there are two types that being applied
in the system which are centralized and decentralized (distributed). A centralized
scheme is a method where it has undervoltage relay installed at key system buses
within the area and trip information is transmitted to shed load at various locations. As
the security is added to the system, sometimes the additional logic is applied. While a
decentralized scheme is where it has relays installed at the loads to be shed. The relays
will start to shed the load at the selected location when the voltage condition at the
locations begins to collapse. Moreover, this type of scheme is similar to the under
frequency load shedding schemes. Many of these schemes are categorized as “special
protection“or “wide area” protection schemes. These schemes require high-speed and
reliable communication to properly operate.
In [11, 14], it is been shown that load shedding is an effective counter measure
against voltage collapse. As been mention before, generally undervoltage load
shedding scheme is designed to shed a specific amount of load from one or more
locations within a power system after finite amount of time upon detecting the onset
of voltage collapse. There are three main areas for consideration in under voltage load
shedding which are the amount of load to shed, and the location where load is to be
shed.
2.6.1 THE AMOUNT OF LOAD TO BE SHED
Theoretically, there are many research indicate that as certain the amount of
load that is appropriate to shed under given conditions. If there is less load that been
trip than necessary, it is obvious that it would be not effective in arresting voltage
collapse. But if tripping too much load may result in transitioning the system from an
under-voltage to an over-frequency condition as the resulting system will have more
generation than load.
Load characteristic in power system play an important role in determining the
ability of the system to regain a stable equilibrium after a disturbance. The incorrect
presumption of load characteristics in load-flow and dynamic studies may render a
UVLS scheme ineffective and perhaps even inadvertently impose an over-frequency
13
condition upon the power system. In [14], the paper discuss about procedure to
calculate the amount of load to be shed where the amount of load to be shed is
calculated based upon the difference between the pre-contingency (steady-state)
power drawn by load and the instantaneous power drawn at the instant of system
disturbance. In this case, dynamic load model parameters are estimated on-line using a
non-linear least squares method in order to calculate the load shed amount.
In an actual power system, the granularity with which load can be shed is
limited due to pragmatic considerations. In general, the smallest block of load that can
be shed is equal to the load served through one substation-class distribution breaker
since it is this breaker that is employed to interrupt the load. Furthermore, the
distribution feeders served out of a particular substation in most cases have different
aggregate load characteristics and demand profiles making the predetermination of the
amount of load available for shedding challenging. This means that the design of a
UVLS should incorporate the impact of errors as a result of the differences between
the load that is presumed to be shed and the load that is actually shed.
The design should also take into account the impact of intentional load
shedding on distribution feeders serving, for example, police and fire stations,
hospitals, schools, power plant or bulk transmission system control centers, prisons
and army bases.
2.6.2 THE LOCATION WHERE LOAD IS TO BE SHED
An important factor to consider within a UVLS design is the location where
load is shed. Small disturbance analysis coupled with dynamic simulation and in some
cases optimal power flow methodology is some tools employed in the determination
of the location of load shed [15]. In this case, the load buses are ranked in the order of
the weakest to the strongest. The weakest bus tends to have the highest component
and tends to be most susceptible to voltage collapse given the relatively large reactive
power consumption for a small reduction in bus voltage. Therefore, often it is this bus
that is the most appropriate candidate for load shedding initially.
14
In [14], the proposed UVLS scheme detects voltage collapse at every bus in
the ten bus system considered. Rather than shedding load at the weakest one through
ranking buses, each bus is monitored for voltage collapse and upon detection of this,
the UVLS is triggered at that bus. A major drawback to this approach, as noted by the
authors of the paper, is that the optimum amount of load will not be shed given that
the power-voltage characteristics of the lines would change upon load shed at one bus.
Furthermore, this approach does not distinguish between the bus at which the reactive
power demand is increased and the adjacent buses whose voltages follow suit. This
means that the load at adjacent buses may be shed in the case where load rejection at
the weakest bus alone would have arrested voltage collapse.
In [15], the system overcomes this approach by pre-determining the weakest
buses in the system under various contingencies (N-1, N-2 and N-3). In this instance,
training scenarios consisting of eight different system configurations were subjected to
these contingencies. The resulting unstable scenarios were identified and the weakest
buses were noted for each unstable scenario. This was followed by a common ranking
of the load buses as it was postulated that the optimal load shedding locations will be
nearly the same for all unstable scenarios of the set. The preceding approach identifies
the common weakest buses for all conceivable contingencies and optimizes the
location of the load to be shed.
2.7 CONCEPT OF UNDER VOLTAGE LOAD SHEDDING
15
When a transmission system becomes stressful due to the overload, the
voltage instability or voltage collapse could be experience by the system [16]. The
philosophy of UVLS is that whenever the system is perturbed and voltage drops to
a certain pre-selected level for a certain pre-determined time period, then selected
loads may be cut off [17]. In some research, by shedding some of the loads in a
system the voltage magnitude will recover to its normal level. In practical, load
shedding schemes requires coordination between protection engineers and system
planners to set up the amount to be shed without affecting its security.
Data below shows the acceptable range value to be the reference during
generation of data. Some function has been created to devide the results to
determine their range of stable voltage.
Min(Vm)<0.95 = unstable
0.95<min(Vm)<1.05 = stable
2.8 FUZZY LOGIC
Seminal paper on fuzzy logic was introduced by Prof. Lofti A. Zadeh
in 1965 [19].Since then, many developments have taken place in different
parts of the world. Since the 1970s Japanese researchers have been the primary
force in the implementation of fuzzy theory and now have thousands of patents
in the area.
The world response to fuzzy logic has been varied. On the one hand,
western cultures are mired with the yes or no, guilty or not guilty, of the binary
Aristotelian logic world and their interpretation of the fuzziness causes a
conflict because they are given a negative connotation. On the other hand,
Eastern cultures easily accommodate the concept of fuzziness because it does
not imply disorganization and imprecision in their languages as it does in
English.
Practically, fuzzy logic is a powerful problem-solving methodology with a
myriad of applications in embedded control and information processing. Fuzzy
provides a simple way to draw definite conclusions from vogue, ambiguous or
imprecise information [20]. Moreover in computational intelligence, fuzzy logic
16
resembles human decision making with its ability to work from approximate data and
find precise solutions
Classical set theory is based on the fundamental concept of a set, in
which individuals are either a member or not a member. A sharp, crisp, and
ambiguous distinction exists between a member and a non-member for any
well-defined set of entities in this theory, and there is a very precise and clear
boundary to indicate if an entity belongs to a set. Thus, in classical set theory
an element is not allowed to be in a set (1) or not in a set (0) at the same time.
This means that many real-world problems cannot be handled by classical set
theory. On the contrary, the fuzzy set theory accepts partial membership values
μ ƒ ϵ [0, +1], and therefore, in a sense generalizes the classical set theory to
some extent.
As Prof. Lotfi A. Zadeh suggests by his principle of incompatibility:
“The closer one looks at a real-world problem, the fuzzier becomes the
solution,” and thus, imprecision and complexity are correlated [21].
Complexity is inversely related to the understanding we can have of a problem
or system. When little complexity is presented, closed-loop forms are enough
to describe the systems. More complex systems need methods such as neural
networks that can reduce some uncertainty. When systems are complex
enough that only few numerical data exist and the majority of this information
is vague, fuzzy reasoning can be used for manipulating this information.
2.8.1 Concept of Fuzzy Logic
A simple way to define fuzzy logic is logical system which is the
extension of mutivalued logic. In a specific way, fuzzy logic is almost
synonymous with the theory of fuzzy sets, a theory which relates to classes of
object with unsharp boundaries in which membership is a matter of degree
[25]. Fuzzy inference is the process of formulating the mapping from a given
input to an output using fuzzy logic. The mapping then provides a basis from
which decisions can be made.
In MATLAB, fuzzy logic can be implementing by using fuzzy logic
toolbox as the decision making. The fuzzy logic system consists of three parts
which are fuzzification, fuzzy inference and defuzzification [22, 23]. In
17
fuzzification, it will involve the process of transforming input variable into a
membership for linguistic terms of fuzzy sets. While fuzzy inference system is
used as a drawing conclusion from the set of fuzzy rules. The fuzzy rule is a
set of if-then linguistic term [15]. For the defuzzification, it converts
the fuzzy output values back into output actions. In this paper,
fuzzy logic algorithm is allowed to determine the suitability of
each bus and the one with the highest suitability chosen for
load shedding. The FLS Editor displays general information
about the fuzzy inference system.
2.8.2 Membership Function
The purposed of membership function is to determine or find the input and
output of the system. It is a curve that defines how each point in the input space is
mapped to a membership value between 0 and 1.It is the first step of the fuzzy logic
control process where a fuzzy algorithm categorises the information entering a system
and assigns values that represent the degree of membership in those categories.
In fuzzy logic, the membership function is a graphical representation of the
magnitude of participation of each input. It associates a weighting with each of the
inputs that are processed, defined functional overlap between inputs, and determines
and output response. The rules use the input membership values as weighting factors
to determine their influence on the fuzzy outputs sets of the final output conclusion.
Once the the functions are inferred, scaled, and combined, they are defuzzified into
crisp output which drives the system.
Input membership functions themselves can take any form the designer of the
system requires triangles, trapezoids, bell curves or any other shape as long as those
shapes accurately represent the distribution of information within the system, and as
long as a region of transition exists between adjacent membership functions.
18
Figure 1: Membership function
Due to their simple formulas and computational efficiency, both
triangular membership functions and trapezoidal membership functions have
been used extensively, especially in real-time implementation. However since
the membership functions are composed of straight-line segments, they are not
smooth at the switching points specified by the parameters.
2.8.3 Fuzzy Inference System
Fuzzy inference is the process of formulating the mapping from a given
input to an output using fuzzy logic. The mapping then provides a basis from
which decision can be made, or pattern discerned. The process of fuzzy
inference involves all of the pieces that are described which are the
membership function or fuzzification, fuzzy logic operators, and the fuzzy
rules. In fuzzy logic toolbox, there are two type of fuzzy logic system which is
Mamdani and Sugeno.
Mamdani’s fuzzy inference method is the most commonly used in
fuzzy methodology. Mamdani’s method is among the first control systems
built using fuzzy set theory. It was proposed in 197 5 by Ebrahim Mamdani as
an attempt to control a steam engine and boiler combination by synthesizing a
set of linguistic control rules obtained from experienced human operators.
Mamdani’s effort was based on Lofti Zadeh’s 1973 paper on fuzzy algorithm
for complex systems and decision processes. Although the inference process
19
describe differs from the methods described I the original paper, the basic idea
is much the same.
Mamdani type expects the output membership functions to be fuzzy
sets. After the aggregation process, there is fuzzy set for each fuzzy output
variable that needs fdefuzzification. It is possible and in many cases much
more efficient to use a single spike as the output membership functions rather
than a distributed fuzzy set. This is sometimes known as a singleton output
membership function and it can be thought of as a pre-defuzzified fuzzy set. It
enhance the efficiency of the defuzzification process because it greatly
simplifies the computation required by the more general Mamdani method,
which finds the centroid of a two dimensional function. Rather than integrating
across the two-dimensional function to find the centroid, that used the weight
average of a few data points. Sugeno type systems support this type of model.
Generally, Sugeno type systems can be used to model any inference system in
which the output membership functions areeither linear or constant.
2.8.4 Defuzzification
A defuzzifiation process is use to obtain the crisp output. This result is
obtained from fuzzy inference system where it maps an input vector to a crisp output.
The input to the defuzzification process is a fuzzy set (the aggregated output fuzzy
set), and the output of the defuzzification process is a single number. Many
defuzzification techniques have been proposed in the literature. The most commonly
used method is the centroid. Other methods include the maximum, the means of
maxima, height, and modified height method.
20
CHAPTER 3.0
METHODOLOGY
3.1 INTRODUCTION
The objective of a UVLS scheme is to restore reactive power balance in
the power system, to prevent voltage collapse and to keep a voltage problem
within a local area rather than allowing it to spread out by shedding some loads
[18]. In power system, the power generated by the generation system must be
equal to the load demand and the total losses. If the load demand is higher than
the generation can support, the it may lead to voltage collapse. To solve the
problems, fuzzy logic has been implemented to the UVLS schemes by testing
it o IEEE 30 bus system that has six generators, four under load tap changing
transformers, two shunt capacitor and thirty seven lines. The program for the
implementation of fuzzy logic to the UVLS schemes was done using
MATLAB programming.
3.2 UNDERVOLTAGE LOAD SHEDDING SCHEME
3.2.1 Preparing System Data
The test system used in this study is the IEEE-30 RTS. The system has
six generators, four under load tap changing transformers, two shunt capacitor
and thirty seven lines. In the base case the total system load is 2.834 pu, the
swing bus (bus number 1) generates real power of 2.5687 pu, while the other
21
generators generate 0.4 pu real power. Figure 1 illustrates the single line
diagram of IEEE 30-bus system.
Figure 0-3: IEEE 30-BUS TEST SYSTEM
(Source: ljs.academicdirect.org)
Fuzzy logic load shedding need data to perform the rules. As IEEE 30
bus system, it has five generator buses, one slack bus, 6
intermediate buses and eighteen load buses. The load
shedding technique is performed by creating several
conditions. Load factor is increased in order to indicate load
variation in the system. By increasing the load bus, the system
stability will change and may cause voltage instability due to
the load increase in the system. Load shedding then perform
by selecting the weakest bus.
22
3.2.2 Power Flow Analysis
Power flow analysis, coomonly referred as load flow is an important
tool of power system analysis and design. It is use for planning, operation and
economic scheduling. In this project, the transmission system is modelled by a
set of buses or nodes interconnected y transmissionlink. Generators and loads,
connector to various nodes of the system inject and remove power from the
transmission system. However in power system, power are known rather than
current. So the resulting equation is in terms of power, known as the power
flow equation become non-linear and must be solve by iterative solution. The
most common technique used for the iterative solution of non-linear algebraic
equation are Newton-Raphson, Gauss-Seidel and Quasi-Newton methods.
Newton-Raphson load flow is implement in this project to get the desired
output.
3.2.2.1 Newton-Raphson load flow
In power system, this method is widely used to solve the simultaneous algebraic
equations. Newton-Rahpson method is a successive approximation procedure based
on an initial estimate of the unknown and the use of Taylor’s series expension.
Because of its quadratic convergence, Newton-Raphson method is mathematically
superior to the Gauss-Seidel method and is less prone to divergence with ill-
conditioned problems. For large power systems, the Newton-Raphson method is found
to be more efficient and practical. The number of iterations required to obtain a
solution is independent of the system size, but more functional evaluations are
required at each iteration. Since the power flow problem, real power and voltage
magnitude are specified for the voltage-controlled buses, the power flow equation is
formulated in polar form.
3.2.3 Load Shedding Algorithm
Load shedding algorithm involves several steps before it complete.
First thing to do is by creating the cases. Generally, it is a fact that in base
case, the system is already stable. UVLS scheme is perform when the system
23
in unstable. To makes system unstable, the values of the load at the load bus
need to be increased. The load bus consists of active power (Pd) and reactive
power (Qd).
After increasing the value of voltage in the load bus, the Newton-Raphson load
flow will execute. Upon execution, the programme will read the bus data of IEEE 30
RTS and run the power flow solution. The programme also will call necessary
routines to display the desired results. Upon completion of the load flow, the
programme will display minimum voltage in the system, the new value of the load,
and the minimum voltage at each bus. From the results, it can be determine whether
the system become unstable or not. If the system becomes unstable, then the UVLS
scheme can be perform. If the system still stable, then the programme will increase
again the load until the system become unstable. For this project, several cases is
developed to perform analysis of the system.
As been discussed, UVLS scheme is perform by selecting the appropriate
location for load shedding before it can shed the load. In IEEE 30 bus RTS, the
programme will determine the weakest bus in the system to perform the load
shedding. When the load at the weakest bus has been shed, then the Newton-Raphson
will run again the power flow solution to determine whether the system become stable
or not. If yes, it means that the programme is success but if no the programme need to
shed again the load in the system so that the system comeback to the stable state. The
step to perform the UVLS scheme can be found in Figure 4.
The used of fuzzy logic system in this project is it will implement the method
of undervoltage load shedding by determining the suitable location of load shedding
and how much the value of the load that need to be shed. The fuzzy logic will use
IF… THEN rules to control the input and output variable.
24
3.3 FUZZY LOGIC SYSTEM
When there is disturbance or an unexpected event occurs in a large network of
power system, in some cases the probability and uncertainties of the incidence
represented. However, it is made clear that some of the uncertain functions are
intrinsically fuzzy in nature and difficult to handle to handle effectively by
probability. By using fuzzy logic, it provide a good solution that is not easily solve by
other methods and are readily applicable to power system problems [24]. The function
of fuzzy logic in this project as been mention before is to determines the suitability of
each bus for load shedding where the bus with the lowest value of the voltage is
chosen as the most appropriate bus for load shedding. The same system is develop in
fuzzy logic to determine the amount of the load that need to be shed where the fuzzy
will decide how much of the amount in the particular bus that need to be shed to
restore back the system into stable condition. The input variable and the output has
been develop and the rules has been created.
3.3.1 Bus Selection for load shedding
The fuzzy FIS Editor for selected bus load shedding is illustrated in Figure 3, 4
and 5. The input variable of the FIS Editor are voltage magnitude (Vm) which divides
into four categories as shown in Figure 4 and loading factor in Figure 3. The output is
the percentage of selected bus to be shed also divides into 4 categories as shown in
Figure 5.
Inputs: Lf (Loading factor) Trapezoidal membership function as shown in Figure 3
VM (Voltage Magnitude) Triangle membership function as shown in Figure 4.
Output: PSBLS (Percentage Selected Bus Load Shedding) Triangle membership
function as shown in Figure 5.
26
Figure 0-5: loading factor
Figure 0-6: Voltage Magnitude (Vm)
Figure 0-7: Percentage selected bus
In fuzzy logic system, an IF-THEN basic rule-based system is used. IF
statement is refer as antecendent while THEN statement is as consequent. In this
section, fuzzy rule system is determined to form decision on the fuzzy input derived
from the voltage magnitude and loading factor. For this fuzzy to find the selected bus
for load shedding, 4 rules were developed which are:
Rule 1: IF loading factor is 1.1 AND Voltage magnitude is low THEN percent
selected bus is high
Rule 2: IF loading factor is 1.1 AND Voltage magnitude is medium THEN percent
selected bus is high-medium
Rule 3: IF loading factor is 1.1 AND Voltage magnitude is high-medium THEN
percent selected bus is medium
Rules 4: IF loading factor is 1.1 AND Voltage magnitude is high THEN percent
selected bus is low
27
As illustrated in Figure 10, the rows of plots represent the rules while the
columns represent the variables. The first two columns of plots (yellow) show the
membership functions of the input variables, while the fourth column of plots (blue)
shows the membership functions of the output.
3.3.2 Algorithm for Amount of Load to be Shed
The fuzzy FIS Editor for selected bus load shedding is illustrated in
Figure 6, 7, 8 and 9. The input variable of the FIS Editor are voltage
magnitude (Vm), active power (Pd) and reactive power (Qd) while the output
is the percentage amount of load to be shed.
Inputs: Pd (Active Power) Triangle membership function as shown in Figure 6
Qd (Reactive Power) Triangle membership function as shown in Figure 7
VM (Voltage Magnitude) Trapezoidal membership functions as shown in
Figure 8.
Output: PAL (Percentage amount of load to be shed) Triangle membership function
as shown in Figure 9.
28
Figure 0-8: Active Power (Pd)
Figure 0-9: Reactive Power (Qd)
Figure 0-10: Voltage Magnitude (Vm)
Figure 0-11: Percentage Amount Load to be shed
The fuzzy analysis of this method was developed using the same technique
as described in the previous method. The fuzzy rules to find the amount load to
be shed are as in Table 1. It is necessary to establish a meaningful system for
representing the linguistic variables in the matrix. For this case the following
will be used:
29
Table 1: Fuzzy decision matrix
AND
Voltage Magnitude
L LM M HM H
Pd,
Qd
L M M LM LM L
LM HM M M LM LM
M HM HM M M LM
HM H HM HM M M
H H H HM HM M
“L”: “low”
“LM”: “low-medium”
“M”: “medium”
“HM”: “high-medium”
“H”: “high”
25 fuzzy rules are derived and here are some examples of the fuzzy rules
listed in Table 1:
Rule 1: IF Pd is low AND Qd is low AND Voltage magnitude is low THEN
percent load to be shed is medium
Rule 2: IF Pd is low-medium AND Qd is low-medium AND Voltage
magnitude is low THEN percent load to be shed is high-medium
When fuzzy rule has multiple antecedents or input variable, the fuzzy operator
AND for minimization operator is used to obtain a single number that represents the
result of the antecedent evaluation. Fuzzy rules involve the operations between input
fuzzy sets, as illustrated graphically in Figure 10. It is based on fuzzy inference
described previously.
30
Figure 0-12: Fuzzy rules analysis
As illustrated in Figure 10, the rows of plots represent the rules while the
columns represent the variables. The first three columns of plots (yellow) show the
membership functions of the input variables, while the fourth column of plots (blue)
shows the membership functions of the output.
31
CHAPTER 4.0
RESULTS AND DISCUSSIONS
4.1 INTRODUCTION
Based on the developed methodology, all the results and discussion of
the Under-voltage Load Shedding scheme are presented in this chapter. The
results include output of fuzzy logic system to determine the bus Selection for
load shedding and the amount that need to be shed to stabilize the
system.Several cases has been selected to represent the output of the program.
The cases includes of loading factor from base case until loading factor = 2.
This study is conduct to show how reliable of computational intelligence
system to perform the load shedding in a system.
1.1.1. loading factor = 1.4
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 11. This fuzzy system performed by referring the data from
the load flow results as shown in Table 2. Loading factor = 1.4 is selected as the test
case conditions.
Table 2: Fuzzy output for selected bus of load shedding at loading factor 1.4
B
us
N
o.
Minim
um
Voltag
e (Vm)
Percent
age
selected
bus (%)
B
us
N
o.
Minim
um
Voltag
e (Vm)
Percent
age
selected
bus (%)
1 1.0600 27.2 16 1.0098 33.1
2 1.0230 32.4 17 1.0010 33.3
3 0.9983 34.2 18 0.9848 39.7
4 0.9859 39.3 19 0.9806 41.2
32
5 0.9800 41.4 20 0.9864 39.1
6 0.9850 39.6 21 0.9899 37.8
7 0.9710 44.2 22 0.9907 37.5
8 0.9900 37.8 23 0.9829 40.4
9 1.0256 32.2 24 0.9730 43.6
10 1.0082 33.2 25 0.9706 44.3
11 1.0820 20.7 26 0.9444 51.5
12 1.0291 31.9 27 0.9818 40.8
13 1.0610 27 28 0.9820 40.7
14 1.0068 33.2 29 0.9520 49.5
15 0.9996 33.5 30 0.9348 54.1
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which at 0.9348 p.u..
Fuzzy logic system operates by using the data from newton-raphson load flow results
to determine the suitable bus for load shedding.
Figure 11: FIS for Selected Bus for Load Shedding at Bus (30) with 1.4 loading factor
As illustrated in Table 2, it shows that bus 30 is the weakest in the system.
Therefore bus 30 is selected as the appropriate bus to perform the load shedding.
Figure 12 shows the fuzzy based load shedding system to determine the amount load
to be shed at bus 30.
33
At bus 30 with 1.4 loading factor, the value of active power and reactive power
are 14.84MW and 2.66MVAR respectively.
Figure 13: FIS for percentage amount to be shed at Bus (30) with loading factor = 1.4
Based on the Figure 12, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 65.1%. As the results, the amount of load to
be shed is 9.6608MW and 1.7317MVAR. The minimum voltage at the system
increases from 0.9348 p.u. to 0.9631 p.u. at bus 26. It is shown that the system is
improved to a stable condition.
As the result, the total amount load to be shed in loading factor = 1.4 is 9.6608MW
and 1.7317MVAR. At loading factor = 1.4, the program need to perform 1 stage of
load shedding to get back the system to a stable condition.
1.1.2.loading factor = 1.5
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 12. This fuzzy system is performed by referring to the data
from the load flow results as shown in Table 3. Loading factor = 1.5 is selected as the
test case conditions.
Table 3: Fuzzy output for selected bus of load shedding at loading factor 1.5
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
34
1 1.060 27.2 16 0.9969 34.8
2 1.0230 32.4 17 0.9880 38.5
3 0.9916 37.1 18 0.9697 44.6
4 0.9782 42 19 0.9655 45.8
5 0.9800 41.4 20 0.9719 43.9
6 0.9765 42.5 21 0.9761 42.6
7 0.9649 45.9 22 0.9768 42.4
8 0.9800 41.4 23 0.9674 45.2
9 1.0173 32.8 24 0.9569 48.1
10 0.9961 35.2 25 0.9546 48.8
11 1.0820 20.7 26 0.9260 56.7
12 1.0171 32.8 27 0.9671 45.3
13 1.0510 28.9 28 0.9721 43.9
14 0.9930 36.5 29 0.9344 54.2
15 0.9853 39.5 30 0.9155 60.1
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which is 0.9155 p.u.
Fuzzy logic system operated by using the data from newton-raphson load flow results
to determine the selected bus for load shedding.
Figure 14: FIS for Selected Bus for Load Shedding at Bus (30) with loading factor =
1.5
35
From the result above, it shows that bus 30 is the weakest in the system.
Therefore bus 30 is selected as the appropriate bus to perform the load shedding.
Figure 14 shows the fuzzy based load shedding system to determine the amount load
to be shed at bus 30.
At bus 30 loading factor = 1.5, the value of active power and reactive power
are 15.9MW and 2.85MVAR respectively.
Figure 15: FIS for percentage amount to be shed at Bus (30) with loading factor = 1.5
Based on the Figure 14, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 71.4%. As the results, the amount of load to
be shed is 11.3526MW and 2.0349MVAR. The minimum voltage in the system
increase from 0.9155 p.u. to 0.9469 p.u. which occur at bus 26. It shows that the
system is still in unstable condition.
Therefore the program decides to shed load at bus 26 as the next stages to
make the system in stable condition. At bus 26 with loading factor= 1.5, the value of
active power and reactive power are 5.25MW and 3.45MVAR respectively.
36
Figure 16: FIS for percentage amount to be shed at Bus (26) with loading factor = 1.5
Based on the Figure 14, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 59.2%. As the results, the amount of load to
be shed is 3.108MW and 2.0424MVAR. The minimum voltage in the system increase
from 0.9469 p.u.to 0.9700p.u. which occur at bus 19. It is shown that the system is
improved to a stable condition.
As the result, the total amount load to be shed in loading factor = 1.5 is
14.4606MW and 4.0773MVAR. At loading factor = 1.5, the program need to perform
2 stages of load shedding to get back the system to a stable condition.
1.1.3.loading factor = 1.6
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 15. This fuzzy system is performed by referring to the data
from the load flow results as shown in Table 3. Loading factor = 1.6 is selected as the
test case conditions.
Table 4: Fuzzy output for selected bus of load shedding at loading factor 1.6
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
1 1.06 27.2 16 0.9845 39.8
2 1.013 33 17 0.9758 42.7
3 0.9848 39.7 18 0.9552 48.6
4 0.9704 44.4 19 0.951 49.7
37
5 0.97 44.5 20 0.9581 47.8
6 0.9704 44.4 21 0.9633 46.4
7 0.9561 48.4 22 0.964 46.2
8 0.98 41.4 23 0.9527 49.3
9 1.01 33.1 24 0.9421 52.1
10 0.985 39.7 25 0.9408 52.5
11 1.082 20.7 26 0.9097 62.4
12 1.0052 33.3 27 0.9552 48.6
13 1.041 30.5 28 0.9662 45.6
14 0.9794 41.6 29 0.9196 58.8
15 0.9715 44 30 0.899 66.7
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which is 0.899 p.u.
Fuzzy logic system operated by using the data from newton-raphson load flow results
to determine the selected bus for load shedding.
Figure 175: FIS for Selected Bus for Load Shedding at Bus (30) with loading factor =
1.6
From the result above, it shows that bus 30 is the weakest in the system.
Therefore bus 30 is selected as the appropriate bus to perform the load shedding.
Figure 16 shows the fuzzy based load shedding system to determine the amount load
to be shed at bus 30.
38
At bus 30 loading factor = 1.6, the value of active power and reactive power
are 16.96MW and 3.04MVAR respectively.
Figure 18: FIS for percentage amount to be shed at Bus (30) with loading factor = 1.6
Based on the Figure 16, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75%. As the results, the amount of load to be
shed is 12.72MW and 2.28MVAR. The minimum voltage increased in the system
increase from 0.899 p.u. to 0.9183 p.u. which occur at bus 26. It shows that the
system is still in unstable condition.
Therefore the program decides to shed load at bus 26 as the next stages to
make the system in stable condition. At bus 26 with loading factor= 1.6, the value of
active power and reactive power are 5.6MW and 3.68MVAR respectively.
39
Figure 19: FIS for percentage amount to be shed at Bus (26) with loading factor = 1.5
Based on the Figure 17, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 63.5%. As the results, the amount of load to
be shed is 3.556MW and 2.3368MVAR. The minimum voltage in the system increase
from 0.9381 to 0.9644p.u.. which occur at bus 24. It is shown that the system is
improved to a stable condition.
As the result, the total amount load to be shed in loading factor = 1.6 is
16.276MW and 4.6168MVAR. At loading factor = 1.6, the program need to perform 2
stages of load shedding to get back the system to a stable condition.
1.1.4.loading factor = 1.7
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 18. This fuzzy system is performed by referring to the data
from the load flow results as shown in Table 5. Loading factor = 1.7 is selected as the
test case conditions.
Table 5: Fuzzy output for selected bus of load shedding at loading factor 1.7
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
1 1.06 27.2 16 0.9708 44.3
2 1.013 33 17 0.962 46.8
3 0.9778 42.1 18 0.9391 52.9
4 0.9623 46.7 19 0.9348 54.1
5 0.97 44.5 20 0.9426 52
6 0.9617 46.8 21 0.9484 50.4
7 0.9498 50.1 22 0.9492 50.2
8 0.97 44.5 23 0.9361 53.8
9 1.0011 33.3 24 0.9248 57.1
10 0.9721 43.9 25 0.9235 57.5
11 1.082 20.7 26 0.8897 66.9
12 0.9926 36.7 27 0.9392 52.9
13 1.031 31.7 28 0.956 48.4
14 0.9648 46 29 0.9003 66.5
15 0.9563 48.3 30 0.8778 67.6
40
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which is 0.8778 p.u.
Fuzzy logic system operated by using the data from newton-raphson load flow results
to determine the selected bus for load shedding.
Figure 208: FIS for Selected Bus for Load Shedding at Bus (30) with loading factor = 1.7
From the result above, it shows that bus 30 is the weakest in the system.
Therefore bus 30 is selected as the appropriate bus to perform the load shedding.
Figure 16 shows the fuzzy based load shedding system to determine the amount load
to be shed at bus 30.
At bus 30 loading factor = 1.7, the value of active power and reactive power
are 18.02MW and 3.23MVAR respectively.
41
Figure 21: FIS for percentage amount to be shed at Bus (30) with loading factor = 1.7
Based on the Figure 19, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75.1%. As the results, the amount of load to
be shed is 13.533MW and 2.4257MVAR. The minimum voltage increased in the
system increase from 0.8778 p.u. to 0.9183 p.u. which occur at bus 26. It shows that
the system is still in unstable condition.
Therefore the program decides to shed load at bus 26 as the next stages to
make the system in stable condition. At bus 26 with loading factor= 1.7, the value of
active power and reactive power are 5.95MW and 3.91MVAR respectively.
Figure 22: FIS for percentage amount to be shed at Bus (26) with loading factor = 1.7
42
Based on the Figure 20, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75%. As the results, the amount of load to be
shed is 4.4625MW and 2.9325MVAR. The minimum voltage in the system increase
from 0.9183 to 0.9497p.u.. which occur at bus 19. It is shown that the system is still
not improved to the stable condition.
Therefore the program decides to shed load at bus 19 as the next stages to
make the system in stable condition. At bus 19 with loading factor= 1.7, the value of
active power and reactive power are 16.15MW and 5.78MVAR respectively.
Figure 23: FIS for percentage amount to be shed at Bus (19) with loading factor = 1.7
Based on the Figure 21, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 57.6%. As the results, the amount of load to
be shed is 9.3024MW and 3.3293MVAR. The minimum voltage in the system
increase from 0.9497 to 0.9597p.u.. which occur at bus 24. It is shown that the system
is improved to a stable condition.
As the result, the total amount load to be shed in loading factor = 1.7 is
27.2979MW and 8.6875MVAR. At loading factor = 1.7, the program need to perform
3 stages of load shedding to get back the system to a stable condition.
1.1.5.loading factor = 1.8
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 22. This fuzzy system is performed by referring to the data
43
from the load flow results as shown in Table 6. Loading factor = 1.8 is selected as the
test case conditions.
Table 6: Fuzzy output for selected bus of load shedding at loading factor 1.8
Bus
No.
Minimum
Voltage
(Vm)
Percentage
selected bus
(%)
Bus
No.
Minimum
Voltage
(Vm)
Percentage
selected bus
(%)
1 1.06 27.2 16 0.9589 47.6
2 1.013 33 17 0.9503 49.9
3 0.9731 43.6 18 0.925 57
4 0.9571 48.1 19 0.9207 58.4
5 0.96 47.3 20 0.9293 55.7
6 0.9573 48 21 0.9361 53.8
7 0.942 52.1 22 0.9369 53.5
8 0.97 44.5 23 0.9217 58.1
9 0.9946 35.9 24 0.9103 62.1
10 0.9616 46.9 25 0.91 62.2
11 1.082 20.7 26 0.8735 67.9
12 0.9815 40.9 27 0.9277 56.2
13 1.021 32.5 28 0.9513 49.7
14 0.9518 49.5 29 0.8855 67.1
15 0.943 51.9 30 0.8612 69.2
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which is 0.8612 p.u.
Fuzzy logic system operated by using the data from newton-raphson load flow results
to determine the selected bus for load shedding.
44
Figure 22: FIS for Selected Bus for Load Shedding at Bus (30) with loading factor = 1.8
From the Table 3, it shows that bus 30 is the weakest in the system. Therefore
bus 30 is selected as the appropriate bus to perform the load shedding. Figure 23
shows the fuzzy based load shedding system to determine the amount load to be shed
at bus 30.
At bus 30 loading factor = 1.8, the value of active power and reactive power
are 19.08MW and 3.42MVAR respectively.
Figure 23: FIS for percentage amount to be shed at Bus (30) with loading factor = 1.8
Based on the Figure 23, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 77.4%. As the results, the amount of load to
be shed is 14.7679MW and 2.6471MVAR. The minimum voltage increased in the
45
system increase from 0.8612 p.u. to 0.9055 p.u. which occur at bus 26. It shows that
the system is still in unstable condition.
Therefore the program decides to shed load at bus 26 as the next stages to
make the system in stable condition. At bus 26 with loading factor= 1.8, the value of
active power and reactive power are 6.3MW and 4.14MVAR respectively.
Figure 24: FIS for percentage amount to be shed at Bus (26) with loading factor = 1.8
Based on the Figure 24, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75%. As the results, the amount of load to be
shed is 4.725MW and 3.105MVAR. The minimum voltage in the system increase
from 0.9055 to 0.9353p.u.. which occur at bus 19. It is shown that the system is still
not improved to the stable condition.
Therefore the program decides to shed load at bus 19 as the next stages to
make the system in stable condition. At bus 19 with loading factor= 1.8, the value of
active power and reactive power are 17.1MW and 6.12MVAR respectively.
46
Figure 25: FIS for percentage amount to be shed at Bus (19) with loading factor = 1.8
Based on the Figure 25, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 64%. As the results, the amount of load to be
shed is 10.944MW and 3.9168MVAR. The minimum voltage in the system increase
from 0.9353 to 0.9485p.u.. which occur at bus 24. It is shown that the system is still
not improved to a stable condition.
Therefore the program decides to shed load at bus 24 as the next stages to
make the system in stable condition. At bus 24 with loading factor= 1.8, the value of
active power and reactive power are 15.66MW and 12.06MVAR respectively.
Figure 26: FIS for percentage amount to be shed at Bus (24) with loading factor = 1.8
47
Based on the Figure 26, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 61.7%. As the results, the amount of load to
be shed is 9.6622MW and 7.441MVAR. The minimum voltage in the system increase
from 0.9485 to 0.9659p.u.. which occur at bus 7. It is shown that the system is still not
improved to a stable condition.
As the result, the total amount load to be shed in loading factor = 1.8 is
40.0991MW and 17.1099MVAR. At loading factor = 1.8, the program need to
perform 4 stages of load shedding to get back the system to a stable condition.
1.1.6. loading factor = 1.9
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 27. This fuzzy system is performed by referring to the data
from the load flow results as shown in Table 7. Loading factor = 1.8 is selected as the
test case conditions.
Table 7: Fuzzy output for selected bus of load shedding at loading factor 1.9
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
Bus
No.
Minimum
Voltage (Vm)
Percentage
selected bus (%)
1 1.06 27.2 16 0.9474 50.7
2 1.003 33.3 17 0.9371 53.5
3 0.9638 46.3 18 0.9105 62
4 0.9464 51 19 0.9055 64.1
5 0.96 47.3 20 0.9145 60.5
6 0.9466 50.9 21 0.9212 58.2
7 0.9346 54.2 22 0.922 58
8 0.96 47.3 23 0.9067 63.6
9 0.9851 39.6 24 0.893 66.8
10 0.9487 50.3 25 0.8915 66.8
11 1.082 20.7 26 0.852 70.6
12 0.9726 43.7 27 0.9099 62.3
48
13 1.021 32.5 28 0.9396 52.8
14 0.9404 52.6 29 0.8639 68.9
15 0.9305 55.4 30 0.8374 73.4
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which is 0.8374 p.u.
Fuzzy logic system operated by using the data from newton-raphson load flow results
to determine the selected bus for load shedding.
Figure 27: FIS for Selected Bus for Load Shedding at Bus (30) with loading factor = 1.8
From the Table 7, it shows that bus 30 is the weakest in the system. Therefore
bus 30 is selected as the appropriate bus to perform the load shedding. Figure 28
shows the fuzzy based load shedding system to determine the amount load to be shed
at bus 30.
At bus 30 loading factor = 1.9, the value of active power and reactive power
are 20.14MW and 3.61MVAR respectively.
49
Figure 28: FIS for percentage amount to be shed at Bus (30) with loading factor = 1.9
Based on the Figure 28, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 80.4%. As the results, the amount of load to
be shed is 16.1926MW and 2.9024MVAR. The minimum voltage increased in the
system increase from 0.8374 p.u. to 0.8877 p.u. which occur at bus 26. It shows that
the system is still in unstable condition.
Therefore the program decides to shed load at bus 26 as the next stages to
make the system in stable condition. At bus 26 with loading factor = 1.9, the value of
active power and reactive power are 6.65MW and 4.37MVAR respectively.
Figure 27: FIS for percentage amount to be shed at Bus (26) with loading factor = 1.9
50
Based on the Figure 29, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75%. As the results, the amount of load to be
shed is 4.9875MW and 3.2775MVAR. The minimum voltage in the system increase
from 0.8877 to 0.9286p.u.. which occur at bus 19. It is shown that the system is still
not improved to the stable condition.
Therefore the program decides to shed load at bus 19 as the next stages to
make the system in stable condition. At bus 19 with loading factor= 1.9, the value of
active power and reactive power are 18.05MW and 6.46MVAR respectively.
Figure 30: FIS for percentage amount to be shed at Bus (19) with loading factor = 1.9
Based on the Figure 30, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75%. As the results, the amount of load to be
shed is 13.5375MW and 4.845MVAR. The minimum voltage in the system increase
from 0.9186 to 0.9365p.u.. which occur at bus 24. It is shown that the system is still
not improved to a stable condition.
Therefore the program decides to shed load at bus 24 as the next stages to
make the system in stable condition. At bus 24 with loading factor= 1.9, the value of
active power and reactive power are 16.53MW and 12.73MVAR respectively.
51
Figure 31: FIS for percentage amount to be shed at Bus (24) with loading factor = 1.9
Based on the Figure 31, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 65.6%. As the results, the amount of load to
be shed is 10.8437MW and 8.3509MVAR. The minimum voltage in the system
increase from 0.9365 to 0.9641p.u.. It is shown that the system is improved to a stable
condition.
As the result, the total amount load to be shed in loading factor = 1.9 is
45.5613MW and 19.3758MVAR. At loading factor = 1.9, the program need to
perform 4 stages of load shedding to get back the system to a stable condition.
1.1.7. loading factor = 2
Determination of selected bus for load shedding using the proposed fuzzy
system is shown in Figure 32. This fuzzy system is performed by referring to the data
from the load flow results as shown in Table 8. Loading factor = 2.0 is selected as the
test case conditions.
Table 8: Fuzzy output for selected bus of load shedding at loading factor 1.9
Bus
No.
Minimum
Voltage
Percentage
selected bus
Bus
No.
Minimum
Voltage
Percentage
selected bus
52
(Vm) (%) (Vm) (%)
1 1.06 27.2 16 0.9397 52.8
2 1.003 33.3 17 0.9283 56
3 0.96 47.3 18 0.9002 66.6
4 0.9424 52 19 0.8947 66.7
5 0.96 47.3 20 0.9043 64.6
6 0.9436 51.7 21 0.9112 61.8
7 0.9317 55 22 0.912 61.5
8 0.96 47.3 23 0.8961 66.7
9 0.9799 41.4 24 0.881 67.3
10 0.9405 52.6 25 0.8796 67.4
11 1.082 20.7 26 0.8372 73.5
12 0.967 45.4 27 0.8994 66.7
13 1.021 32.5 28 0.9359 53.8
14 0.9325 54.8 29 0.8498 70.9
15 0.9218 58 30 0.8213 78.1
Based on the newton-raphson load flow results, it is shown that the minimum
voltage of the system has dropped below the stable condition which is 0.8213 p.u.
Fuzzy logic system operated by using the data from newton-raphson load flow results
to determine the selected bus for load shedding.
53
Figure 32: FIS for Selected Bus for Load Shedding at Bus (30) with loading factor = 2.0
From the Table 7, it shows that bus 30 is the weakest in the system. Therefore
bus 30 is selected as the appropriate bus to perform the load shedding. Figure 33
shows the fuzzy based load shedding system to determine the amount load to be shed
at bus 30.
At bus 30 loading factor = 2.0, the value of active power and reactive power
are 21.2MW and 3.8MVAR respectively.
Figure 33: FIS for percentage amount to be shed at Bus (30) with loading factor = 2.0
Based on the Figure 33, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 83.7%. As the results, the amount of load to
be shed is 17.7444MW and 3.1806MVAR. The minimum voltage increased in the
system increase from 0.8213 p.u. to 0.8699 p.u. which occur at bus 26. It shows that
the system is still in unstable condition.
Therefore the program decides to shed load at bus 26 as the next stages to
make the system in stable condition. At bus 26 with loading factor = 2.0, the value of
active power and reactive power are 7MW and 4.6MVAR respectively.
54
Figure 34: FIS for percentage amount to be shed at Bus (26) with loading factor = 2.0
Based on the Figure 29, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 76.1%. As the results, the amount of load to
be shed is 5.327MW and 3.5006MVAR. The minimum voltage in the system increase
from 0.8699 to 0.9092p.u.. which occur at bus 19. It is shown that the system is still
not improved to the stable condition.
Therefore the program decides to shed load at bus 19 as the next stages to
make the system in stable condition. At bus 19 with loading factor= 2.0, the value of
active power and reactive power are 19MW and 6.8MVAR respectively.
Figure 35: FIS for percentage amount to be shed at Bus (19) with loading factor = 2.0
55
Based on the Figure 35, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 75%. As the results, the amount of load to be
shed is 13.5375MW and 4.845MVAR. The minimum voltage in the system increase
from 0.9092 to 0.93247p.u.. which occur at bus 24. It is shown that the system is still
not improved to a stable condition.
Therefore the program decides to shed load at bus 24 as the next stages to
make the system in stable condition. At bus 24 with loading factor = 2.0, the value of
active power and reactive power are 17.4MW and 13.4MVAR respectively.
Figure 36: FIS for percentage amount to be shed at Bus (24) with loading factor = 2.0
Based on the Figure 36, it is shown that fuzzy based load shedding system
decided to shed the amount of load up to 71.1%. As the results, the amount of load to
be shed is 12.3714MW and 9.5274MVAR. The minimum voltage in the system
increase from 0.9247 to 0.9524 p.u.. It is shown that the system is improved to a stable
condition.
As the result, the total amount load to be shed in loading factor = 1.9 is
49.6928MW and 21.3086MVAR. At loading factor = 2.0, the program need to
perform 4 stages of load shedding to get back the system to a stable condition.
2.1.
56
CHAPTER 5.0
CONCLUSIONS
In this paper, particle swarm optimization (PSO) technique was use to solve the unit
commitment problem with several constraint as stated before. The result shows that
the proposed method was capable of obtaining optimum operating cost for UC
problem for 24 hour period interval of load demand.. In addition, the wind turbine
generator was attached to improve an operating cost. The wind generator was
successfully shown the effectiveness in minimizing the operating cost. Thus, the
purpose of unit commitment to meet a demand with minimum cost has been achieved.
For recommendation, PSO can be combined with another algorithm such as
Evolutional Programming (EP), Ann Colony and Bee Colony to improve a
performance of the technique to solve unit commitment problem. Moreover, the others
green energy such as solar and nuclear can be implement to study their effect toward
the UC problem.
57
CHAPTER 6.0
RECOMMENDATIONS FOR FUTURE WORKS
There are several addition and development that can be done on DED problems in
order to have high quality and accurate solutions. The improvement that can be done
is such as taking into account other generator constraints such as spinning reserve
requirement and emission constraint. All the constraints will give more accurate result
to the solution of DED problems. In addition, accurate modeling of DED problem will
be improved when the valve point loadings effects in the generating units are taken
into account. Valve point effect are are usually modelled in two form which is i)
consider the prohibited zones as the inequality constraint and ii) implement the effect
as the non-smooth cost function for the fuel cost function[10]
58
REFERENCE
[1] Atputharajah, Arulampalam, and Tapan K. Saha. "Power system blackouts-Literature review." Industrial and Information Systems (ICIIS), 2009 International Conference on. IEEE, 2009.
[2] Taylor, Carson W. "Concepts of undervoltage load shedding for voltage stability." Power Delivery, IEEE Transactions on 7.2 (1992): 480-488.
[3] Calderaro, V., Galdi, V., Lattarulo, V., & Siano, P. (2010). A new algorithm for steady state load-shedding strategy. Optimization of Electrical and Electronic Equipment (OPTIM), 2010 12th International Conference on, 48-53.
[4] P. Kundur, Power System Stability and Control, vol. IV. New York: McGraw Hill, 1994, pp. 959- 1024
[5] Kessel, P., and H. Glavitsch. "Estimating the voltage stability of a power system." Power Delivery, IEEE Transactions on 1.3 (1986): 346-354.
[6] Saffarian, Alireza, and Majid Sanaye-Pasand. "Enhancement of power system stability using adaptive combinational load shedding methods." Power Systems, IEEE Transactions on 26.3 (2011): 1010-1020.
[7] Wang, Y., Pordanjani, I. R., Li, W., Xu, W., & Vaahedi, E. (2011). Strategy to minimise the load shedding amount for voltage collapse prevention. Generation, Transmission & Distribution, IET, 5(3), 307-313.
[8] Kadam, D. P., et al. "Fuzzy Logic Algorithm for Unit Commitment Problem."Control, Automation, Communication and Energy Conservation, 2009. INCACEC 2009. 2009 International Conference on. IEEE, 2009.
[9] Abdelaziz, A. Y., et al. "Fuzzy based load shedding approach against voltage instability." International Journal of Engineering, Science and Technology 4.3 (2013): 15-44.
[10]Terzija, Vladimir V. "Adaptive underfrequency load shedding based on the magnitude of the disturbance estimation." Power Systems, IEEE Transactions on 21.3 (2006): 1260-1266.
[11]C. W. Taylor, Power System Voltage Stability, McGraw-Hill, 1994.[12]A. Wiszniewski, “New criteria of voltage stability margin for the purpose of load
shedding,” IEEE trans.Power del., vol. 22, no. 3, July 2007, pp. 1367-1371.[13] A. Guzmán, D. Tziouvaras, E. O. Schweitzer and Ken E. Martin, “Local and wide-
area network protectionsystems improve power system reliability,” Schweitzer Engineering Laboratories technical papers, 2004.
[14] R. Balanathan, N. Pahalawaththa, and U. Annakkage, “A strategy for undervoltage load shedding in power systems,” International Conference on Power System Technology, vol. 2, pp. 1494–1498, Aug. 1998.
[15] C. Moors, D. Lefebvre, and T. V. Custem, “Design of load shedding schemes against
voltage instability,” ser. 23-27, vol. 2, Power Engineering Society Winter Meeting, 2000. IEEE, Jan 2000, pp. 1495–1500.
[16] Verayiah, R., Ramasamy, A., Abidin, H. Z., & Musirin, I. (2009, December). Under Voltage Load Shedding (UVLS) study for 746 test bus system. In Energy and Environment, 2009. ICEE 2009. 3rd International Conference on (pp. 98-103). IEEE.
59
[17] M. Begovic, D. Fulton, M. R. Gonzalez, J. Goossens, E. A. Guro, R. W. Haas, C. F. Henville, G. Manchur, G. L. Michel, R. C. Pastore, J. Postforoosh, G. L. Schmitt, J. B. Williams, K. Zimmerman, and A. A. Burzese, "Summary of "System Protection and Voltage Stability"," IEEE Transactions on Power Delivery, vol. 10, pp. 631-638, 1995.
[18] Mozina, Charles. "Undervoltage load shedding." Power Systems Conference: Advanced Metering, Protection, Control, Communication, and Distributed Resources, 2007. PSC 2007. IEEE, 2007.
[19] Zadeh LA (1965) Fuzzy sets. Info Control 8(3):338–353[20] E. Cox. “ Fuzzy fundamentals” (IEEE Spectrum, October 1992, pp. 58-61).[21] Zadeh LA (1973) Outline of a new approach to the analysis of complex systems and
decision processes, IEEE Trans Syst Man Cyber SMC 3:28–44[22] Grewal, G.S.; Konowalec, J.W.; Hakim, M. “Optimization of a load shedding scheme” ,
Industry Applications Magazine, IEEE, vol 4, pp 25-30, July/August 1998
[23] Afiqah, R. N., Musirin, I., Johari, D., Othman, M. M., Rahman, T. K. A., & Othman, Z. (2009). Fuzzy logic application in DGA methods to classify fault type in power transformer. SELECTED TOPICS in POWER SYSTEMS and REMOTE SENSING, 83-88
[24] Momoh J. and Tomsovic K., 1995. Overview and literature survey of fuzzy set theory in power systems, IEEE Transactions on Power Systems, Vol. 10, No. 3, pp. 1676-1690.
[25] Naaz, Sameena, et al. "Effect of different defuzzification methods in a fuzzy based load balancing application." IJCSI International Journal of Computer Science Issues 8.5: 261-267.
APPENDICES
MATLAB PROGRAMMING
Main Program
60
Momoh J. and Tomsovic K., 1995. Overview and literature survey of fuzzy set theory in power systems, IEEE Transactions on Power Systems, Vol. 10, No. 3, pp. 1676-1690.clear, close allclc
pso.psoMethod = 'constriction'; pso.saveResults = 'true'; pso.maxIter = 10 pso.noParticles =30;M. Begovic, D. Fulton, M. R. Gonzalez, J. Goossens, E. A. Guro, R. W. Haas, C. F. Henville, G. Manchur, G. L. Michel, R. C. Pastore, J. Postforoosh, G. L. Schmitt, J. B. Williams, K. Zimmerman, and A. A. Burzese, "Summary of "System Protection and Voltage Stability"," IEEE Transactions on Power Delivery, vol. 10, pp. 631-638, 1995.
Mozina, Charles. "Undervoltage load shedding." Power Systems Conference: Advanced Metering, Protection, Control, Communication, and Distributed Resources, 2007. PSC 2007. IEEE, 2007.
Grewal, G.S.; Konowalec, J.W.; Hakim, M. “Optimization of a load shedding scheme” , Industry Applications Magazine, IEEE, vol 4, pp 25-30, July/August 1998
Afiqah, R. N., Musirin, I., Johari, D., Othman, M. M., Rahman, T. K. A., & Othman, Z. (2009). Fuzzy logic application in DGA methods to classify fault type in power transformer. SELECTED TOPICS in POWER SYSTEMS and REMOTE SENSING, 83-88.
pso.noVars = 6; pso.c1 = 2.05; pso.c2 = 2.05; pso.xMin = 0; pso.xMax = 1; pso.vMax = 1;pso.vMin = -1; pso.pMin = [100,50,80,50,50,50];pso.pMax = [500,200,300,150,200,120]; pso.consFactor = getConstrictionFactor(pso.c1,pso.c2);
saveStringInit = 'F:\Final Year Project\FYP azuwam\Matlab Programming\PSO editted azuwam.mat';
saveString = 'F:\Final Year Project\FYP azuwam\Matlab Programming\PSO editted azuwam.mat'; gBest = PSO(pso, seed, saveStringInit, saveString);
61
FinalResult;
PSO Main Program
function gBest =PSO(pso, seed, saveString1, saveString2)
gBest.fitness = 0;gBest.xVal = zeros(1, pso.noVars);
if strcmp(pso.saveResults,'true') gBest.hist = zeros(pso.maxIter, 2 + pso.noVars);end for i = 1 : 1 : pso.noParticles for j = 1 : 1 : pso.noVars particles(i).velocity(j) = rand; particles(i).xVal(j) = rand; particles(i).bestXVal(j) = particles(i).xVal(j); end % particles(i).fitness = fitnessFcn(outputPower(particles(i).xVal, pso));
particles(i).pBest = particles(i).fitness; end gBest.xVal = particles(1).xVal; gBest.fitness = particles(1).fitness; diff = 1000; for i = 2 : 1 : pso.noParticles if (abs(gBest.fitness - particles(i).fitness) < diff) gBest.fitness = particles(i).fitness; gBest.xVal = particles(i).xVal; diff = abs(gBest.fitness - particles(i).fitness); end if strcmp(pso.saveResults,'true') gBest.hist(1,:) = [0, gBest.fitness, gBest.xVal]; end
62
end gBest.iter = 0;
if strcmp(pso.saveResults,'true') save(saveString1); end
iter = 1; t = cputime; while ((iter ~= pso.maxIter) && (gBest.fitness < pso.objective)) for i = 1 : 1 : pso.noParticles for j = 1 : 1 : pso.noVars vid = particles(i).velocity(j); pid = particles(i).bestXVal(j); xid = particles(i).xVal(j); pgd = gBest.xVal(j); if strcmp(pso.psoMethod,'constriction') vid = pso.consFactor * (vid + pso.c1 * rand * (pid - xid) + pso.c2 * rand * (pgd - xid)); end if (vid > pso.vMax) vid = pso.vMax; elseif vid < pso.vMin vid = pso.vMin; end xid = xid + vid; if xid > pso.xMax xid = pso.xMax; vid = 0; elseif xid < pso.xMin xid = pso.xMin; vid = 0; end particles(i).velocity(j) = vid; particles(i).xVal(j) = xid;
63
end end for i = 1:1:pso.noParticles particles(i).fitness = fitnessFcn(outputPower(particles(i).xVal, pso)); if (particles(i).fitness > particles(i).pBest) particles(i).pBest = particles(i).fitness; particles(i).bestXVal = particles(i).xVal; end if (particles(i).fitness > gBest.fitness) gBest.fitness = particles(i).fitness; gBest.xVal = particles(i).xVal; gBest.iter = iter if strcmp(pso.saveResults,'true') gBest.hist(iter + 1,:) = [iter, gBest.fitness, gBest.xVal]; end end end iter = iter + 1; end gBest.optTime = cputime - t; if strcmp(pso.saveResults,'true') save(saveString2); end
Fitness Ramp Rate Program
function [PD,PL,Fcost] = fitnessRamprate(Pi) pMin = [100,50,80,50,50,50];pMax = [500,200,300,150,200,120]; UR = [80,50,65,50,50,50]; DR = [120,90,100,90,90,90]; Po = [440,170,200,150,190,110];
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Prmin = [320,80,100,60,100,20]; Prmax = [520,220,265,200,240,160]; for i = 1:1:6 if Pi(i) < pMin(i) fitness = 0; return; elseif Pi(i) > pMax(i) fitness = 0; return; endend for i = 1:1:6 if Pi(i) < Prmin(i) Pi(i)= Prmin; Po(i)= Pi(i); Prmin(i)= Po(i)-DR(i); elseif Pi(i) > Prmax(i) Pi(i)= Prmax; Po(i)= Pi(i); Prmax(i)= Po(i)+UR(i); endend B = [0.0017, 0.0012, 0.0007, -0.0001, -0.0005, -0.0002;... 0.0012, 0.0014, 0.0009, 0.0001, -0.0006, -0.0001;... 0.0007, 0.0009, 0.0031, 0.0000, -0.0010, -0.0006;... -0.0001, 0.0001, 0.0000, 0.0024, -0.0006, -0.0008;... -0.0005, -0.0006, -0.0010, -0.0006, 0.0129, -0.0002;... -0.0002, -0.0001, -0.0006, -0.0008, -0.0002, 0.0150]; Bo = (1.0e-03)*[-0.3908, -0.1297, 0.7047, 0.0591, 0.2161, -0.6635]; Boo = 0.0056; basemva = 100; PL = Pi*(B/basemva)*Pi'+Bo*Pi'+Boo*basemva; P = sum(Pi) - PL;PD = round(sum(P)); loaddemand = 955; if PD < loaddemand fitness = 0;
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return;end cost = [240,7,0.007;... 200,10,0.0095;... 220,8.5,0.009;... 200,11,0.009;... 220,10.5,0.008;... 190,12,0.0075]; alpha = cost(:,1);beta = cost(:,2);gamma = cost(:,3); for i = 1:1:6 F(i) = alpha(i) + beta(i)*Pi(i) + gamma(i) * (Pi(i)^2);endFcost = sum(F);Ppbc = sum(Pi) - loaddemand - PL; fitness = 1 / (Fcost + Ppbc);
Constriction Factor Program
function consFactor = getConstrictionFactor(c1,c2) theta = c1 + c2; if theta <= 4 error('Theta must be more than 4.')end consFactor = 2/abs(2-theta-sqrt(theta^2-4*theta));
Output Power Program
function powerOut = outputPower(xVal, pso) for i = 1:1:pso.noVars powerOut(i) = (pso.pMax(i) - pso.pMin(i)) * xVal(i) + pso.pMin(i);end powerOut
Final Result Program
clear, close all
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