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The Arab Academy for Science & Technology
and Maritime Transport
M. Sc. Thesis
Minimizing Power Loss in a Distribution
System by Optimal Sizing and Sitting of
Distributed Generators with Network
Reconfiguration using Grey Wolf,
Particle Swarm, and Hybrid Grey Wolf-
Particle Swarm Optimizers
Presented By:
Eng. Mirna Fouad Abd-Elsalam Abu-Haggar
Supervised By:
Prof. Dr. Mahmoud Magdy Bahgat Eteiba
Dr. Eman Hassan Beshr
ii
DECLARATION
I certify that all the material in this thesis that is not my own work has been identified
and that no material is included for which a degree has previously been conferred on
me.
The contents of this thesis reflect my own personal views and are not necessarily
endorsed by the University.
Signed: _____________________________
Date:
iii
APPROVAL OF EXAMINING COMMITTEE
We hereby certify that we have read the present work and that in our opinion it is fully
adequate in scope and quality as thesis towards the partial fulfillment of the Master
Degree requirements in
Electrical Power and Control Department
From
College of Engineering (AASTMT)
Date …………….…………
Supervisor (s): Prof. Mahmoud Magdy Bahgat Eteiba Professor of Electrical Power and Machines Dept. Faculty of Engineering, Fayoum University.
Name: Position: Signature:
Dr. Eman Hassan Beshr Professor of Electrical Power and Computer Dept. Faculty of Engineering, AASTMT.
Name: Position: Signature:
Examiners:
Name: Position: Signature:
Name: Position: Signature:
iv
ACKNOWLEDGMENT
Most importantly I thank God for discernment in what I was undertaking and also for
keeping me healthy during the thesis period.
My sincere gratitude goes to Prof. M. Magdy Eteiba and Dr. Eman Beshr, the
supervisors of this thesis for supporting, continuously guiding, helpful suggestions,
sharing with me their experience, continued monitoring of my progress during the thesis
work and giving me their time. Thank you for believing in me.
Much appreciation goes to my lecturers in Electrical and Control Department for
imparting on me this worthy knowledge. I am also very grateful to Eng. Ibtihal Zahran
for her time help, and support.
I am very grateful to my dearest fiancé Eng. Ahmed Ellakany for his motivation,
encouragement, and support. His continuous care had always inspired me.
I would like to express my love and sincere gratitude to my beloved family; my parents,
grandma, and brother. They are always there for me for every up and down of my life.
They have been blessing me with unconditional love and support through my life.
Finally, I would like to thank all my sweetest friends especially Nourhan Tarek and
Sandra Amir for their unconditional love, encouragement, and help. They are always
there for me.
God bless you all.
v
ABSTRACT
The necessity for implementing new solutions in distribution systems using advanced
technologies is growing rapidly due to the increased use of distributed and variable
power generation sources and system reconfiguration. As distributed generators
penetration levels increase, instability of the distribution network rises. Thus, there is a
need to raise the reliability and stability of the network by using advanced techniques. It
is a requirement to find the optimal solution for distributed generators sizing and
location while taking into consideration the reduction of electrical power losses and
voltage profile improvement. Many types of research have been done to find the optimal
DG size and location and system reconfiguration aiming to improve the voltage profile
and reduce the energy losses. Although most of this work in the literature use different
techniques like analytical approaches, computation, and artificial intelligence, they still
have several disadvantages. This leads to searching for new techniques and algorithms
in order to improve the already existing work and try to overcome their disadvantages
and come up with better results.
This thesis presents three metaheuristic based algorithms Grey Wolf Optimizer
(GWO), Particle Swarm Optimizer (PSO), and the hybridization of the two
metaheuristics based GWO and PSO to solve network reconfiguration problem in the
presence of installing multiple DGs with different types (conventional, renewable).
Results of new Hybrid GWO-PSO were compared with both GWO and PSO techniques
to show the improvement of the results obtained by this hybridization. The proposed
algorithm is applied to IEEE 33-, IEEE 69-bus radial distribution system, and 78-bus
practical real distribution system in 6th October city, Egypt to minimize the real power
loss. The results clearly indicate that there is a considerable improvement in the voltage
profile, active losses, and reactive losses. MATPOWER and MATLAB® software are
used for simulations. The simulated results illustrate well the performance and
effectiveness of the proposed techniques.
vi
TABLE OF CONTENTS
TABLE OF CONTENTS ............................................................................................................................VI
LIST OF FIGURES ................................................................................................................................ VIII
LIST OF TABLES ....................................................................................................................................... X
LIST OF ACRONYMS/ABBREVIATIONS ............................................................................................XI
1 INTRODUCTION .................................................................................................................................. 1
1.1 ELECTRICAL DISTRIBUTION NETWORK .......................................................... 1 1.2 DISTRIBUTION NETWORK CONGESTION ......................................................... 2 1.3 NETWORK RECONFIGURATION .......................................................................... 2 1.4 DISTRIBUTED GENERATORS ................................................................................ 3 1.5 SYSTEM LOSSES MINIMIZATION ........................................................................ 6 1.6 VOLTAGE PROFILE IMPROVEMENT .................................................................. 7 1.7 THESIS OUTLINE ...................................................................................................... 7
2 LITERATURE SURVEY ...................................................................................................................... 9
2.1 INTRODUCTION ........................................................................................................ 9 2.2 PREVIOUS RESEARCH WORKS ON SYSTEM RECONFIGURATION .......... 10 2.3 PREVIOUS RESEARCH WORKS ON DISTRIBUTED GENERATORS
LOCATING AND SIZING .................................................................................................... 10 2.4 PREVIOUS RESEARCH WORKS ON SYSTEM RECONFIGURATION with
DISTRIBUTED GENERATORS LOCATING AND SIZING ............................................ 13
3 PROBLEM FORMULATION ............................................................................................................ 15
3.1 INTRODUCTION ...................................................................................................... 15 3.2 OBJECTIVE FUNCTION ......................................................................................... 15 3.3 CONSTRAINTS ......................................................................................................... 16 3.4 POWER LOSS USING SYSTEM RECONFIGURATION ..................................... 17 3.5 POWER LOSS USING DG INSTALLATION ........................................................ 18
4 OPTIMIZATION TECHNIQUES ..................................................................................................... 19
4.1 PROPOSED ALGORITHMS.................................................................................... 19 4.1.1 Grey Wolf Optimizer ............................................................................................................. 19 4.1.2 Mathematical Model of PSO ................................................................................................. 20 4.1.3 Implementation Steps of GWO ............................................................................................. 22 4.1.4 Particle Swarm Optimizer ..................................................................................................... 25 4.1.5 Mathematical Model of PSO ................................................................................................. 26 4.1.6 Implementation Steps of PSO ............................................................................................... 27 4.1.7 Hybrid GWO-PSO Optimizer ............................................................................................... 30 4.1.8 Implementation Steps of Hybrid GWO-PSO ........................................................................ 30
vii
4.2 IMPLEMENTATION FOR SYSTEM RECONFIGURATION AND DG
ALLOCATION ....................................................................................................................... 33
5 SIMULATIONS & RESULTS ............................................................................................................ 35
5.1 INTRODUCTION ...................................................................................................... 35 5.2 IEEE 33-BUS TEST SYSTEM .................................................................................. 36
5.2.1 Active Power Loss Reduction ............................................................................................... 36 5.2.2 Reactive Power Loss Reduction ............................................................................................ 41 5.2.3 Voltage Profile Improvement ................................................................................................ 42 5.2.4 Methods Performance ............................................................................................................ 44
5.3 IEEE 69-BUS TEST SYSTEM .................................................................................. 46 5.3.1 Active Power Loss Reduction ............................................................................................... 46 5.3.2 Reactive Power Loss Reduction ............................................................................................ 51 5.3.3 Voltage Profile Improvement ................................................................................................ 52 5.3.4 Methods Performance ............................................................................................................ 54
5.4 78-BUS REAL TEST SYSTEM ................................................................................ 56 5.4.1 Active Power Loss Reduction ............................................................................................... 57 5.4.2 Reactive Power Loss Reduction ............................................................................................ 62 5.4.3 Voltage Profile Improvement ................................................................................................ 63 5.4.4 Methods Performance ............................................................................................................ 66
6 CONCLUSIONS & FUTURE WORK ............................................................................................... 67
6.1 CONCLUSIONS ........................................................................................................ 67 6.2 FUTURE WORK ....................................................................................................... 69
REFERENCES ............................................................................................................................................ 70
APPENDICES ............................................................................................................................................. 79
viii
LIST OF FIGURES
Figure 1-1: Illustrative Radial Distribution System .......................................................................3
Figure 1-2: Illustrative penetration of distributed generators ........................................................4
Figure 1-3: Installed buildings sector renewable DG capacity in AEO2017 Reference case
(gigawatts)......................................................................................................................................5
Figure 1-4: Installed buildings sector non-renewable DG capacity in AEO2017 Reference case
(gigawatts)......................................................................................................................................6
Figure 4-1: Hierarchy of the grey wolf. .......................................................................................20
Figure 4-2: Hunting behavior of grey wolves ..............................................................................21
Figure 4 -3: Flow chart of GWO. .................................................................................................24
Figure 4-4: Group of fish movement in the search space. ...........................................................25
Figure 4-5: Group of bird movement in the search space ............................................................25
Figure 4-6: Search point modification by PSO. ...........................................................................26
Figure 4-7: Flowchart of PSO. .....................................................................................................29
Figure 4-8: Flowchart of hybrid GWO-PSO. ...............................................................................32
Figure 5-1: Single line diagram of the 33-bus system. ................................................................36
Figure 5-2: Single line diagram of a 33-bus system for scenario 8..............................................40
Figure 5-3: Power loss of 33-bus system using three different techniques. .................................40
Figure 5-4: Reactive loss of 33-bus system using three different techniques. .............................41
Figure 5-5: Voltage profile of a 33-bus system using GWO technique. ......................................42
Figure 5-6: Voltage profile of a 33-bus system using PSO technique. ........................................43
Figure 5-7: Voltage profile of a 33-bus system using the hybrid technique. ...............................43
Figure 5-8: Conversion curve of the 33-bus system using three different techniques for scenario
8. ..................................................................................................................................................44
Figure 5-9: Single line diagram of the 69-bus system. ................................................................46
Figure 5-10: Single line diagram of a 69-bus system for scenario 8. ..........................................50
Figure 5-11: Power loss of 69-bus system using three different techniques. ...............................51
Figure 5-12: Reactive loss of 69-bus system using three different techniques. ...........................52
Figure 5-13: Voltage profile of a 69-bus system using GWO technique. ....................................53
Figure 5-14: Voltage profile of a 69-bus system using PSO technique. ......................................53
Figure 5-15: Voltage profile of a 69-bus system using the hybrid technique. .............................54
Figure 5-16: Conversion curve of the 69-bus system using three different techniques for
scenario 8. ....................................................................................................................................56
Figure 5-18: Single line diagram of a 78-bus system for scenario 8. ..........................................61
ix
Figure 5-19: Power loss of 78-bus system using three different techniques. ...............................62
Figure 5-20: Reactive loss of 78-bus system using three different techniques. ...........................63
Figure 5-21: Voltage profile of a 78-bus system using GWO technique. ....................................64
Figure 5-22: Voltage profile of a 78-bus system using PSO technique. ......................................65
Figure 5-23: Voltage profile of a 78-bus system using the hybrid technique. .............................65
Figure 5-24: Conversion curve of the 78-bus system using three different techniques for
scenario 8. ....................................................................................................................................66
x
LIST OF TABLES
Table 5-1: Different penetration of DG units for the 33-bus system. ......................................... 37
Table 5-2: Comparison of simulation results for P-type DG units of the 33-bus system. ........... 38
Table 5-3: Comparison of simulation results for PQ+-type DG units of the 33-bus system. ...... 39
Table 5-4: Comparison of methods performance for the 33-bus system. ................................. 45
Table 5-5: Different penetration of DG units for the 69-bus system. ......................................... 47
Table 5-6: Comparison of simulation results for P-type DG units of the 69-bus system. ........... 48
Table 5-7: Comparison of simulation results for PQ+-type DG units of the 69-bus system. ...... 49
Table 5-8: Comparison of methods performance for the 69-bus system. ................................... 55
Table 5-9: Different penetration of DG units for the 78-bus system. ......................................... 58
Table 5-10: Comparison of simulation results for P-type DG units of the 78-bus system. ........ 59
Table 5-11: Comparison of simulation results for PQ+-type DG units of the 78-bus system. .... 60
xi
LIST OF ACRONYMS/ABBREVIATIONS
ACRONYM Definition of Acronym
ABC Artificial Bee Colony algorithm
A⃗⃗ Coefficient Vector
AC-LF AC-Load Flow
BA Bat Algorithm
BB-BC Big Bang Big Crunch method
BFOA Bacterial Foraging Optimization Algorithm
BSOA Back Tracking Search Optimization Algorithm
BPSO Binary Particle Swarm Optimization
BFOA Bacterial Foraging Optimization Algorithm
CSA Cuckoo Search Algorithm
CSOS Chaotic Symbiotic Organisms Search algorithm
C⃗ Coefficient Vector
DE Differential Evolutionary
DNR Distribution Network Reconfiguration
DGs Distributed Generators
DABC Discrete Artificial Bee Colony
DCGA Decimal Codification Genetic Algorithm
xii
𝐷 Distance from source to the DG bus location in km
EP Evolutionary Programming
EA Efficient Analytical
EA Evolutionary Algorithm
EVs Electric Vehicles
FA Firefly Algorithm
FMGA Fuzzy Mutated Genetic Algorithm
FWA Fire Work Algorithm
FW/BW Forward-Backward Sweep algorithm
FCM Fuzzy C-means Clustering algorithm
GA Genetic Algorithms
GWO Grey Wolf Optimizer
GSA Gravitational Search Algorithm
G⃗⃗ (k) Global Best Particle
HGWO Hybrid Grey Wolf Optimizer
HSA Harmony Search Algorithm
INSGA-II Improved Non dominated Sorting Genetic Algorithm–II
𝐼𝑖,𝑖+1 Current in the line section between buses i and i+1
𝐼𝑖,𝑖+1,𝑚𝑎𝑥 Current’s maximum limit of the line between buses i and i+1
k Iteration Number
LSF Loss Sensitivity Factor
xiii
LP linear programming
𝐿 The total length of the feeder from source to bus
𝐿 Location of DG
LMP Location Marginal Pricing
MFO Moth Flame Optimization
MHA Meta-Heuristic Algorithms
MPGSA Modified Plant Growth Simulation Algorithm
MOF Multi-Objective Function
NSGA-II Non-Dominated Sorting Genetic Algorithm II
OPF Optimal Power Flow
ODGP optimal DG placement
OCOA Oppositional Cuckoo Optimization Algorithm
𝑂𝑆 Opened Switch
PSO Particle Swarm Optimizer
PSO-CFA Particle Swarm Optimization with Constriction Factor Approach
technique
𝑃𝐿𝑜𝑠𝑠(𝑖,𝑖+1) Real power loss from buses 𝑖 to 𝑖 + 1
𝑃𝑖 Real power flowing out of bus 𝑖
𝑃𝐷𝑖 Real power supplied by DG at bus 𝑖
𝑃𝐷𝑖,𝑚𝑎𝑥 Maximum power supplied by DG
𝑃𝐷𝑖,𝑚𝑖𝑛 Minimum power supplied by DG
xiv
𝑃𝐿𝑖+1 Real load power at bus 𝑖 + 1
𝑃′𝑇,𝐿𝑜𝑠𝑠 Summation of all real power losses after reconfiguration
𝑃𝐷𝐺,𝐿𝑜𝑠𝑠 Real power loss with DG installation
𝑃𝐷 Real power supplied by DG
P𝑖⃗⃗ (k) Personal Best Particle 𝑖
PV Photovoltaic
𝑄𝐿𝑜𝑠𝑠(𝑖,𝑖+1) Reactive power loss from buses 𝑖 to 𝑖 + 1
𝑄𝑖 Reactive power flowing out of bus 𝑖
𝑄𝐿𝑖+1 Reactive load power at bus 𝑖 + 1
𝑄𝑖 Reactive power flowing out of bus 𝑖
𝑄𝐷 Reactive power supplied by DG
RDS Radial Distribution System
𝑅𝑖 Resistance of the line section between buses 𝑖 and 𝑖 + 1
𝑟1 Random numbers between 0 and 1
𝑟2 Random numbers between 0 and 1
SFLA Shuffled Frog Leaping Algorithm
RGA Refined Genetic Algorithm
SOCP Second-Order Cone Programming
SPSO Selective Particle Swarm Optimization
𝑠1 Weighting Factor
𝑠2 Weighting Factor
xv
𝑆 Size of DG unit
SA Simulated Annealing algorithm
TLBO Teaching Learning Based Optimization technique
t Iteration Number
VSI Voltage Stability Index
VLI Voltage Limitation Index
𝑉𝑖 The voltage at bus 𝑖
𝑉𝑚𝑎𝑥 Maximum bus voltage
𝑉𝑚𝑖𝑛 Minimum bus voltage
V𝑖⃗⃗⃗ (k) The velocity of particle 𝑖 at iteration k
V𝑖⃗⃗⃗ (k + 1) Updated Velocity of particle 𝑖
𝑊 Weighting Function
𝑋𝑖 The reactance of the line section between buses 𝑖 and 𝑖 + 1
X⃗⃗ p Position vector of the prey
X⃗⃗ Position vector of the grey wolf
𝑌𝑖 Shunt Admittance at bus 𝑖
Y𝑖⃗⃗⃗ (k) Particle 𝑖 Position at iteration k
Y𝑖⃗⃗⃗ (k + 1) Updated Position of Particle 𝑖
α Alphas Wolves
β Betas Wolves
xvi
δ Delta Wolves
ω Omega Wolves
1
C h a p t e r O n e
1 INTRODUCTION
1.1 ELECTRICAL DISTRIBUTION NETWORK
A power system is a network consisting of generation, transmission, and distribution
systems. It aims to fulfill all the networks loads with the most reliability and efficiency.
The generation system can be classified into traditional energy resources such as
thermal, nuclear and fossil fuels, and renewable energy resources such as wind,
hydroelectric, photovoltaic cells, and biomass. The operation of a power system relies
on a centralized control unit. For the time being, the use of a central power plant is less
needed considering the draining of conventional generation, the high costs of
transmission and distribution systems, the technological developments, and the massive
environmental concerns. The generation is connected to the transmission system
through step-up transformers to increase the voltage of the generated electrical power
hereby reduce its current. At the end of the transmission, the voltage is decreased using
a step-down transformer to be distributed. The distribution system is considered the
final stage of the power system as it delivers the amount of electric power required by
the consumers.
A distribution system is classified, according to the nature of the operation, as radial
and ring (mesh) systems. In a radial system, the main feeders supply the electric power
from the distribution substation to the consumers by the means of sub-feeders and
lateral distributors. It is the most used system since it is simple and has a low initial
cost. Radial feeders are characterized by having unidirectional electricity transportation
from the substation to each load. Therefore, without adding DG units, a radial
distribution system is considered to be passive. It can be considered as active by
inserting DG units to the network, as the power flow becomes bidirectional.
In comparison with the passive network, an active network has fewer power losses
while transmitting electricity as it is generated closer to the loads. Active networks also
have many benefits such as improvement of voltage profile, minimized pollutants
emission, improved power quality, high overall efficiency, and relieved transmission
and distribution congestion. The voltage stability improvement and the reduction of line
2
losses are the most crucial advantages because they determine the location and size of
the DG unit to be inserted in the distribution system. Studies show that poor choice of
size and locations of the DG unit would result in more energy losses than before
inserting the DG.
1.2 DISTRIBUTION NETWORK CONGESTION
Congestion of the distribution system is an issue that can take different forms such as
a sudden increase in the load demand and an outage of transmission lines and
generators.
In order to solve this issue, several methods are used such as Distribution Network
Reconfiguration (DNR) and Optimal Placement and sizing of Distributed Generators
(DGs). Network Reconfiguration is a method that deals with the uncertainty of loads by
opening a few sectionalizing switches and closing a few tie switches. Optimal
Penetration of DGs has many advantages including improvement in the voltage profile,
security, reliability, and minimization of transmission losses by installing DGs in
proximity to the user.
Several algorithms have been proposed for distributed generation placement and
sizing in distribution networks to minimize real power loss and improve the voltage
stability of the power system. However, very few of these algorithms have used network
reconfiguration in parallel with the DG location and size for the maximum system loss
reduction.
1.3 NETWORK RECONFIGURATION
Distribution networks consist of normally closed switches (sectionalized switches)
and normally open switches (tie switches) as shown in Figure 1-1. Tie switches
normally operate as ‘’radial networks ’’and connect between loops type laterals or two
substations. Sectionalize switches connect the line sections between busses. These
switches are used to permit configuration management and alternative protection
functions.
Network reconfiguration is a very important operational issue in the networks;
improve active and reactive power in the network, improve the voltage profile and
3
minimize the losses. It’s obvious that network reconfiguration can considerably enhance
the reliability of the system, security, balance system load and reduce the system losses
of the distribution network within short-time. Within the long-term, reconfiguration will
shave the peak load demand and produce concerning vital economic advantages.
Distribution network switches are reconfigured periodically, therefore, reduce current
losses in line sections, transfer system loads from overloaded feeders to lightly loaded
feeders or to assist service to be renovated when the fault happens.
Figure 1-1: Illustrative Radial Distribution System
1.4 DISTRIBUTED GENERATORS
Distributed generation (DG) penetration has become attractive because of its
technical, economic and environmental benefits, although placement and sizing of DGs
in the distribution network is an issue, as any inappropriate location and size of DGs
may increase the overall system loss. DG is a small-scale power generation that is
Su
bst
ati
on
=Tie Switches =sectionalized switches
4
connected to the distribution system. The Electric Power Research Institute (EPRI)
introduces Distributed generation as a generation from a few kilowatts up to 50MW [1].
As shown in Figure 1-2, Penetration of distributed generators (DGs) and particularly
small roof-top photovoltaic installations are widely accepted due to their different
advantages:
DGs are installed close to the customer on the distribution side, leading to
lower transmission losses.
Optimal placement and size of DGs improve voltage profile, the reliability,
and security of the system.
Most of DGs can be easily moved to other locations as they have short
installation periods.
DGs are classified into two types: Renewable Energy Resources (RES) DGs and
non-RES DGs. On the one hand, some of the RES DGs are only capable of injecting
active power such as photovoltaic cells and fuel cells (P-type) or injecting active and
Figure 1-2: Illustrative penetration of distributed generators
Su
bsta
tio
n
DG
DG
DG
5
reactive power by adding smart inverters to them. Others are capable of injecting active
power and consuming reactive power like induction generators of wind turbines (PQ--
type).
The main advantage of RES DGs is the minimization of the total cost, given that they
are cheaper than conventional DGs, minimizing global warming and reducing system
losses.
On the other hand, some of the Non-RES DGs are capable of injecting both active
and reactive power such as combined combustion technology (PQ+-type), the internal
combustion engine and combined cycle-based DGs. Non-RES DGs are characterized by
minimizing active and reactive losses whereas their main disadvantage is that they have
a small effect on the total generation cost reduction and lead to an increase in global
warming. Reference [2] shows in Figure 1-3 and Figure 1-4 the upcoming penetration of
renewable and non-renewable DG units.
Figure 1-3: Installed buildings sector renewable DG capacity in AEO2017 Reference case
(gigawatts)
6
Figure 1-4: Installed buildings sector non-renewable DG capacity in AEO2017 Reference case
(gigawatts)
1.5 SYSTEM LOSSES MINIMIZATION
As previously declared, among the numerous advantages of distributed generation,
reduction of line losses in the system is one of them. Normally, the minimization of real
power loss draws more attraction for the utilities, because real power loss reduces the
efficiency of transmitting energy to the users. However, reactive power loss is certainly
not less important than real power loss. This is because of the fact that the system
reactive power flow has to be preserved at a specific amount for adequate voltage level.
Moreover, Due to the presence of reactive power, real power is transferred to
customers through distribution and transmission lines. Reduction of System loss by
system reconfiguration and placing distributed generators along the network can be very
valuable if the objective function is to reduce system losses and to improve the
performance of the network.
7
1.6 VOLTAGE PROFILE IMPROVEMENT
In the power system, the voltage level of each bus has to be maintained by the
system operator within specific limits. In order to guarantee that the voltage profiles are
satisfying in distribution systems, many standards have been determined to provide
recommendations or stipulations.
For instance, the American National Standards Institute (ANSI) standard C84.1 has
pledged that voltage variations of the distribution system have to be limited among the
range of -13% to 7% [3]. In fact, most of the electricity companies control the voltage
variations in the range of ±6%. System reconfiguration and placement of distributed
generators are upcoming widely accepted methods for improving distribution systems
voltage profiles. Distributed generators location and size have a considerable impact on
voltage profile improvement.
1.7 THESIS OUTLINE
In order to accomplish the above-mentioned objectives, this thesis is organized into
six chapters:
Chapter 1:
This chapter introduces a brief introduction about the electrical distribution
network, distribution network congestion, network reconfiguration, distributed
generators, system losses minimization, and voltage profile improvement and
thesis outline.
Chapter 2:
A summarized literature review is presented on three main aspects of previous
research works; system reconfiguration, distributed generators placement and sizing,
and system reconfiguration in parallel with distributed generators placement and
sizing.
Chapter 3:
This chapter presents the problem formulation of the objective function and its
constraints. Furthermore, the objective function formulation will be illustrated
after system reconfiguration and distributed generators penetration.
8
Chapter 4:
This chapter illustrates three optimization techniques; Grey Wolf Optimizer
(GWO), Particle Swarm Optimizer (PSO), hybrid GWO-PSO, and mathematical
model and implementation steps of each optimization.
Chapter 5:
This chapter presents all the simulation results for IEEE 33-, IEEE 69-bus radial
distribution system, and 78-bus practical real distribution system. Minimization
of system losses and voltage profile improvement will be highlighted.
Comparison between the performances of the above mentioned three optimizers.
Moreover, Comparison between the results of the above mentioned three
optimizers with those of Fire Work Algorithm, Harmony Search Algorithm,
Genetic Algorithm and Refined Genetic Algorithm in terms of power loss
minimization.
Chapter 6:
Finally, the conclusion of this thesis and future work fields will be presented.
9
C h a p t e r T w o
2 LITERATURE SURVEY
2.1 INTRODUCTION
This chapter presents previous work that had been mentioned in the three areas;
System Reconfiguration, Distributed Generators (DGs) Locating and Sizing, System
Reconfiguration with Distributed Generators Locating and Sizing. Latter research
studies develop optimization techniques, which are classified into meta-heuristic
methods, heuristic methods, hybrid methods and analytical methods to solve single or
multiple objective functions. Meta-heuristic methods such as Particle Swarm Optimizer
(PSO), Genetic Algorithms (GA), Bat Algorithm (BA), Grey Wolf Optimizer (GWO),
and Artificial Bee Colony algorithm (ABC), and deterministic methods such as the
analytical method.
This work proposes a new hybrid GWO-PSO technique to solve system
reconfiguration, DGs sizing and DGs sitting. This hybridization eliminates the
disadvantages and emphasizes the advantages of both techniques simultaneously. Many
researchers use metaheuristic or heuristic methods to determine the optimal allocation
and sizing of DGs using the single optimization technique to solve both location and size
of DG however it may not reach the optimal solution every time especially in large
systems.
Other researchers use sensitivity analysis to find constant placement for DG units to
minimize the number of iterations but do not reach the optimal solution as well. In the
present investigation, minimizing the number of iterations is not considered as the most
important issue compared with the vital concern that the system would be able to
withstand the increase of load demand requirements. The presented work uses this
hybridization to find not only the optimal sizing and sitting of DGs but also the optimal
reconfiguration of the system.
Moreover, this work injects active and reactive power into the system unlike most of
the studies that inject active power only. Some of the results will be compared to a
reference that uses analytical analysis to identify DG sitting.
10
2.2 PREVIOUS RESEARCH WORKS ON SYSTEM
RECONFIGURATION
Several studies use system reconfiguration to both minimize real power loss and
improve the voltage stability of the power system. The metaheuristic and heuristic
methods are used for system reconfiguration only and they include Discrete Artificial
Bee Colony (DABC) algorithm, which is used to maximize system load ability [4],
Cuckoo Search Algorithm (CSA) that is used to minimize active power loss and
maximize voltage magnitude [5], Bacterial Foraging Optimization Algorithm (BFOA)
that is used to minimize real power loss [6], and Fuzzy multi-objective optimization [7].
Authors in [8] have used two algorithms namely Fuzzy Mutated Genetic Algorithm
(FMGA) and Evolutionary Programming (EP) to reconfigure the Radial Distribution
System (RDS) by minimizing the real and reactive power losses and improving the
power quality at the same time. PSO and GA using graph theory are applied to find the
radial configuration for two different distribution networks in order to minimize losses
and improve voltage profile [9]. Improved Binary Particle Swarm Optimization is used
to reconfigure system with capacitor placement for power loss reduction of distribution
system [10]. Heuristic algorithm and optimal power flow (OPF) have been considerably
enhanced to find out optimal system reconfiguration for minimizing total reconfiguration
cost [11].
A computational implementation of an Evolutionary Algorithm (EA) is proposed in
order to solve the reconfiguring problem of radial distribution systems [12]. A mixed-
integer conic programming formulation is presented for the minimum loss distribution
network reconfiguration problem [13]. A simple and fast heuristic approach for solving
the distribution feeder reconfiguration problem with an objective of system losses
reduction and improvement of voltage profile [14].
2.3 PREVIOUS RESEARCH WORKS ON DISTRIBUTED
GENERATORS LOCATING AND SIZING
Another metaheuristic, heuristic and hybrid methods are used to determine the
optimal allocation and sizing of DGs to improve the network performance. Some of
these methods are used to tackle Multi-Objective Function (MOF) such as Moth Flame
11
Optimization (MFO) [15], GWO algorithm in [16] and [17], combination of Genetic
Algorithm (GA), PSO in [18], [19], [20], [21] ,[22],and [23], Improved Non dominated
Sorting Genetic Algorithm–II (INSGA-II) [24] , GA and PSO [25], a novel Chaotic
Symbiotic Organisms Search (CSOS) algorithm [26], Dynamic Adaptation of Particle
Swarm Optimization (DAPSO) [27], and Non-Dominated Sorting Genetic Algorithm II
(NSGA-II) [28].
Others such as Artificial Bee Colony algorithm (ABC) [29] and [30],Selective
Particle Swarm Optimization (SPSO) [31],Hybrid Grey Wolf Optimizer (HGWO)
algorithm [32], PSO algorithm in [33], [34], and [35] is used to minimize power loss. In
[36] the authors came up with the DG location and size using Bat Algorithm (BA).
Optimal DG Placement (ODGP) and sizing are presented using selected four heuristic
algorithms; Cuckoo Search Algorithm (CSA); Gravitational Search Algorithm (GSA);
Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) so as to minimize real
power loss [37]. Simulated Annealing (SA) algorithm and Forward-Backward Sweep
(FW/BW) algorithm are used for determining the optimal placement of multiple
distributed generations in the radial distribution system in order to solve multi-objective
function [38].
GA is presented for a distribution generation (DG) allocation strategy for radial
distribution networks under uncertainties of load and generation so as to minimize
network power loss and node voltage deviation [39]. PSO and Differential Evolutionary
(DE) algorithms are used for optimum placement of DGs in radial distribution systems
with the objective of minimizing real power losses of distribution system by the least
injected power from DGs [40]. New Modified Differential Evolution (MDE) technique is
proposed to find the optimal placement and size of multiple distributed generator units
for minimizing overall system losses[41]. Cuckoo Optimization Algorithm (COA) and
Oppositional Cuckoo Optimization Algorithm (OCOA) are proposed for the optimal of
sizing and sitting of DG in 33-bus and 69-bus radial distribution systems where, the
results are compared with those by Genetic Algorithm (GA), Particle Swarm
Optimization (PSO), GA-PSO algorithm, Bacteria Foraging Optimization Algorithm
(BFOA) [42].
Authors in [43] use Firefly Algorithm (FA) to find out optimal DG sitting in order to
minimize power loss and results are compared with those obtained by Genetic Algorithm
(GA) for IEEE 69-bus radial distribution system and Shuffled Frog Leaping Algorithm
12
(SFLA) for IEEE 33-bus radial distribution system. Authors in [44] present Optimal
location and sizing of the voltage controlled DG units using Big Bang Big Crunch (BB-
BC) method.
The analytical methods are also used for DGs installment so as to reduce losses. They
include two different sensitivity analyses is employed for single DG placement [45].
Efficient Analytical (EA) method for multiple DGs placement [46]. In [47] the
formulated sensitivity factor is used for the determination of the optimal size and sitting
of DG to minimize total power losses by an analytical method without use of admittance
matrix, the inverse of admittance matrix or Jacobian matrix. In [48] Loss Sensitivity
Analysis and Voltage Sensitivity Analysis are used to find single DG allocation and DG
sizes are taken in step size of 0.5 MVA starting from 0.5 MVA till 4 MVA at different
power factors. For maximizing Voltage stability, An analytical approach is used for
multiple DG allocation [49]. Trust-Region Sequential Quadratic Programming (TRSQP)
method is proposed to investigation optimal power flow (OPF) problem for distribution
networks with the integration of DGs with a nonconvex multi-objective problem which
is transformed to the single-objective problem [50]. Monte-Carlo Simulation is presented
to find out optimal DG allocation [51]. A hybrid Decimal Codification Genetic
Algorithm (DCGA) and linear programming (LP) technique are proposed in [52] for the
extension planning of the sub-transmission system in the presence of distributed
generators units.
In order to combine the advantages and avoid the disadvantages of the latter methods,
a hybridization between the metaheuristic method and the analytical approach has been
implemented in [53] which uses Loss Sensitivity Factor (LSF) and Back Tracking Search
Optimization Algorithm (BSOA). In [1] the authors used PSO to determine the optimal
size of distributed generators and Loss sensitivity to determine optimal locations. In [54]
authors present the optimal placement of Electric Vehicles (EVs) on IEEE-33 radial
distribution standard test system using The Particle Swarm Optimization with
Constriction Factor Approach (PSO-CFA) technique with the main objective is to
minimize the total power losses and improve the system voltage profile.
Other researches carried on the effect of optimal DG placement in the deregulated
electricity market to maximize Social welfare [55], minimize location marginal pricing
(LMP) in [56] and [57], congestion management [58], and minimization of total
generation cost [59].
13
2.4 PREVIOUS RESEARCH WORKS ON SYSTEM
RECONFIGURATION WITH DISTRIBUTED GENERATORS
LOCATING AND SIZING
Few studies use different methods to tackle the network reconfiguration problem in
parallel with the DG locating and sizing. Reference [60] proposes Binary Particle Swarm
Optimization (BPSO) for system reconfiguration, Loss Sensitivity Factor (LSF) for
finding DG optimal location, and Harmony Search Algorithm (HSA) for DG sizing.
Reference [61] presents Mixed-Integer Second-Order Cone Programming (SOCP) to
determine network reconfiguration, DG locating, and DG sizing problems. Reference
[62] maximizes system load ability by solving the above mentioned three problems
based on Discrete Artificial Bee Colony (DABC) algorithm. Reference [63] solved the
three problems based on Genetic Algorithm (GA).
Reference [64] solves network reconfiguration and DG sizing the based on Harmony
Search Algorithm (HSA) and relies on sensitivity analysis to determine DG units
allocation. Reference [65] suggests the solution of reconfiguration and DG sizing based
on Fire Work Algorithm (FWA) and DGs allocation based on Voltage Stability Index
(VSI). The authors in [66] proposed a system reconfiguration problem of an unbalanced
distribution network using Fuzzy Firefly algorithm, where the loss sensitivity factor is
used to get the appropriate location of distribution generator and Bacterial Foraging
optimization Algorithm (BFOA) is used to find the rating of DGs.
In [67] the authors developed a modified Teaching Learning Based Optimization
technique (TLBO) to reconfigure the distribution network and find the optimal sizing
and location of DGs so as to minimize the total system loss. In [68] the authors proposed
a technique to solve the DG location and size problem, which they named Meta-
Heuristic Algorithms (MHA) and proposed a Binary Particle Swarm Optimization
algorithm (BPSO) for solving network reconfiguration which cannot be used for solving
the DG sizing problem.
The authors in [69] used Selective Particle Swarm Optimization (SPSO) to solve the
network reconfiguration problem and sensitivity analysis method to determine optimal
size and location. In [70] the authors developed an analytical method which is Voltage
Limitation Index (VLI) to solve network reconfiguration, DG sizing, and sitting. In [71]
the authors proposed the Modified Plant Growth Simulation Algorithm (MPGSA) to
14
solve reconfiguration and DG sizing and used Loss Sensitivity Factor (LSF) to find the
optimal location of DG. In [72] and [73] the authors used Particle Swarm Optimizer
(PSO) to solve reconfiguration and DG sizing and locations of DGs are fixed at buses
with the lowest voltage profile.
Further, utilizing power demand and DG profile data are found using fuzzy C-means
(FCM) clustering algorithm and optimum system configurations are found using a
genetic algorithm (GA) to minimize annual energy losses [74].
15
C h a p t e r T h r e e
3 PROBLEM FORMULATION
3.1 INTRODUCTION
This chapter presents the problem formulation of the presented work. The problem
involves minimizing power loss based on system reconfiguration, DGs sizing and
sitting. Eight case studies will be illustrated to reach the maximum reduction of losses.
Using real power loss as an objective function will not only reduce real power losses but
also will reduce reactive power losses and improve the voltage profile of the system.
This problem will be solved using the proposed Grey Wolf Optimizer (GWO), Particle
Swarm Optimizer (PSO) and hybrid GWO-PSO technique.
3.2 OBJECTIVE FUNCTION
The total losses in the line section connecting buses 𝑖 and 𝑖 + 1 are derived in [75] as
follows:
𝐿𝑜𝑠𝑠𝑒𝑠 =
|𝑉𝑖 − 𝑉𝑖+1|2
𝑅𝑖 − 𝑗 𝑋𝑖
(3-1)
𝑃𝐿𝑜𝑠𝑠(𝑖,𝑖+1) = 𝑅𝑒𝑎𝑙|𝐿𝑜𝑠𝑠𝑒𝑠| (3-2)
𝑄𝐿𝑜𝑠𝑠(𝑖,𝑖+1) = 𝐼𝑚𝑎𝑔|𝐿𝑜𝑠𝑠𝑒𝑠| (3-3)
Where,
𝑉𝑖 is voltage at bus 𝑖.
𝑅𝑖 is the resistance of the line section between buses 𝑖 and 𝑖 + 1.
𝑋𝑖 is the reactance of the line section between buses 𝑖 and 𝑖 + 1.
𝑃𝐿𝑜𝑠𝑠(𝑖,𝑖+1) is real power loss from buses 𝑖 to 𝑖 + 1 .
𝑄𝐿𝑜𝑠𝑠(𝑖,𝑖+1) is reactive power loss from buses 𝑖 to 𝑖 + 1 .
16
3.3 CONSTRAINTS
The problem inequality constraints are given as follows:
1) The voltage at each bus should be within specific limits:
𝑉𝑚𝑖𝑛 ≤ |𝑉𝑖| ≤ 𝑉𝑚𝑎𝑥 (3-4)
Where,
𝑉𝑚𝑎𝑥 is the maximum bus voltage.
𝑉𝑚𝑖𝑛 is the minimum bus voltage.
2) Current at each line should be within specific limits:
|𝐼𝑖,𝑖+1| ≤ |𝐼𝑖,𝑖+1,𝑚𝑎𝑥| (3-5)
Where,
𝐼𝑖,𝑖+1 is the current in the line section between buses i and i+1.
𝐼𝑖,𝑖+1,𝑚𝑎𝑥 is the current’s maximum limit of the line between buses i and i+1.
3) Total generated power at each bus should be less than the summation of total load
and total losses:
Where,
𝑃𝑖 is real power flowing out of bus 𝑖.
𝑃𝐷𝑖 is real power supplied by DG at bus 𝑖.
4) Size of DG units should be within specific limits:
𝑃𝐷𝑖,𝑚𝑖𝑛 ≤ 𝑃𝐷𝑖 ≤ 𝑃𝐷𝑖,𝑚𝑎𝑥 (3-7)
∑𝑃𝐷𝑖
𝑛
𝑖=1
≤∑(𝑃𝑖 +
𝑛
𝑖=1
𝑃𝐿𝑜𝑠𝑠(𝑖,𝑖+1)) (3-6)
17
Where,
𝑃𝐷𝑖,𝑚𝑎𝑥 is maximum power supplied by DG
𝑃𝐷𝑖,𝑚𝑖𝑛 is minimum power supplied by DG.
5) The following balance equations [76] must be applied at each bus :
𝑃𝑖+1 = 𝑃𝑖 − 𝑃𝐿𝑜𝑠𝑠,𝑖 − 𝑃𝐿𝑖+1
= 𝑃𝑖 −𝑅𝑖|𝑉𝑖|2
{𝑃𝑖2 + (𝑄𝑖 + 𝑌𝑖|𝑉𝑖|
2)2} − 𝑃𝐿𝑖+1 (3-8)
𝑄𝑖+1 = 𝑄𝑖 − 𝑄𝐿𝑜𝑠𝑠,𝑖 − 𝑄𝐿𝑖+1
=𝑄𝑖 −𝑋𝑖
|𝑉𝑖|2{𝑃𝑖2 + (𝑄𝑖 + 𝑌𝑖1|𝑉𝑖|
2)2}
−𝑌𝑖1|𝑉𝑖|2 − 𝑌𝑖2|𝑉𝑖+1|
2 − 𝑄𝐿𝑖+1
(3-9)
|𝑉𝑖+1|2 = |𝑉𝑖|
2 +𝑅𝑖2 + 𝑋𝑖
2
|𝑉𝑖|2(𝑃𝑖
2 + 𝑄𝑖′ 2) − 2(𝑅𝑖𝑃𝑖 + 𝑋𝑖𝑄𝑖)
= |𝑉𝑖|2 +
𝑅𝑖2 + 𝑋𝑖
2
|𝑉𝑖|2(𝑃𝑖
2 + (𝑄𝑖 + 𝑌𝑖|𝑉𝑖|2)2)
−2(𝑅𝑖𝑃𝑖 + 𝑋𝑖(𝑄𝑖 + 𝑌𝑖|𝑉𝑖|2)) (3-10)
Where,
𝑄𝑖 is the reactive power flowing out of bus 𝑖 .
𝑌𝑖 is shunt admittance at bus 𝑖.
𝑃𝐿𝑖+1 is real load power at bus 𝑖 + 1.
𝑄𝐿𝑖+1 is reactive load power at bus 𝑖 + 1.
3.4 POWER LOSS USING SYSTEM RECONFIGURATION
The network reconfiguration is used to reduce system losses and to handle the system
during any emergencies such as supplying loads during faults. The solution to the
reconfiguration problem is to divide the system into five loops formed by each tie switch.
𝑃′𝑇,𝐿𝑜𝑠𝑠 is the summation of all real power losses after reconfiguration.
18
𝑃′𝑇,𝐿𝑜𝑠𝑠 =∑𝑃′𝐿𝑜𝑠𝑠(𝑖,𝑖+1)
𝑛
𝑖=1
(3-11)
3.5 POWER LOSS USING DG INSTALLATION
Distributed Generators optimal allocation and sizing will postpone the system
upgrade, and shave peak demand. The real power loss when a DG is installed at any
location in the system is given by:
𝑃𝐷𝐺,𝐿𝑜𝑠𝑠 =𝑅𝑖
𝑉𝑖2(𝑃𝑖
2 + 𝑄𝑖2) +
𝑅𝑖
𝑉𝑖2 (𝑃𝐷
2 + 𝑄𝐷2
− 2𝑃𝑖𝑃𝐷 − 2𝑄𝑖𝑄𝐷)(𝐷
𝐿) (3-12)
Where,
𝑄𝑖 is the reactive power flowing out of bus 𝑖.
𝑃𝐷 is real power supplied by DG.
𝑄𝐷 is reactive power supplied by DG.
𝐷 is the distance from the source (DG) to the DG bus location in km.
𝐿 is the total length of the feeder from source to bus.
19
C h a p t e r F o u r
4 OPTIMIZATION TECHNIQUES
4.1 PROPOSED ALGORITHMS
This chapter proposes three optimization techniques; Grey Wolf Optimizer (GWO),
Particle Swarm Optimizer (PSO), and a new hybrid GWO-PSO technique to solve
system reconfiguration, DGs sizing and DGs sitting problems in parallel. This work
eliminates the disadvantages of using sensitivity analysis to find DG units location and
emphasizes the advantages of solving the three problems simultaneously.
4.1.1 Grey Wolf Optimizer
The Grey Wolf Optimizer (GWO) is a meta-heuristic based optimization algorithm
presented by Mirjalili, Mirjalili, and Lewis in 2014 [77]. Grey Wolf (Canis lupus)
belongs to the Canidae family. The grey wolves prefer to live in a pack, following a
social strict dominant hierarchy. The pack size is 5-12 members. The hierarchy level
decreases from α to ω as shown in Figure 4-1. Alphas (α) are at the highest level of the
hierarchy and are the leaders (male or a female). They take all decisions pertaining to
walking time, hunting, sleeping location, and so on. Betas (β) are at the second highest
level and they help group leaders in making decisions. Delta (δ) wolves have to follow
and submit to alphas and betas. The lowest level gray wolf is omega (ω). Omega wolves
have to submit to all other controlling wolves. The mathematical formulation steps are
simulated by:
I. The social hierarchy of GWO.
II. Encircling prey.
III. Hunting prey.
20
Figure 4-1: Hierarchy of the grey wolf.
4.1.2 Mathematical Model of PSO
I. Social Hierarchy of GWO
α is considered to be the best solution. β and δ are considered to be the second and
third best solution respectively. The rest of the solutions are considered to be ω wolves.
II. Encircling Prey
First, the grey wolf encircles the prey. In [77] the encircling procedure is determined
as follows:
D⃗⃗ = |C⃗ . X⃗⃗ p(t) − X⃗⃗ (t)| (4-1)
X⃗⃗ (t + 1) = X⃗⃗ p(t) − A⃗⃗ . D⃗⃗ (4-2)
Where,
t is the iteration number.
A⃗⃗ and C⃗ are coefficient vectors.
X⃗⃗ p indicates the position vector of the prey.
X⃗⃗ is the position vector of the grey wolf.
FIGURE 2. Hierarchy of grey wolf
21
A⃗⃗ and C⃗ vectors are calculated as follows:
A⃗⃗ = 2a⃗ . r 1 − a⃗ (2-3)
C⃗ = 2. r 2 (4-4)
III. Hunting
After encircling the prey as shown in Figure 4-2, the hunting process of grey wolf is
simulated mathematically by supposing that α, β, and δ have better information about the
position of prey. The prey is considered to be the objective function. α, β, and δ are the
first three best solutions so far to reach the objective function. The rest of the solutions
are considered to be the ω wolves and they will update their location according to the
location of α, β, and δ.
Figure 4-2: Hunting behavior of grey wolves
22
The hunting procedure is given in [77] as follows:
D⃗⃗ α = |C⃗ 1. X⃗⃗ α − X⃗⃗ | (4-5)
D⃗⃗ β = |C⃗ 2. X⃗⃗ β − X⃗⃗ | (4-6)
D⃗⃗ δ = |C⃗ 3. X⃗⃗ δ − X⃗⃗ | (4-7)
X⃗⃗ 1 = X⃗⃗ α − A⃗⃗ 1. (D⃗⃗ α) (4-8)
X⃗⃗ 2 = X⃗⃗ β − A⃗⃗ 2. (D⃗⃗ β) (4-9)
X⃗⃗ 3 = X⃗⃗ δ − A⃗⃗ 3. (D⃗⃗ δ) (4-10)
X⃗⃗ (t + 1) =X⃗⃗ 1 + X⃗⃗ 2 + X⃗⃗ 3
3 (4-11)
4.1.3 Implementation Steps of GWO
In GWO algorithm, there is a number of population wolves that represent a candidate
of solutions. Every wolf has dimension real value vector. Where the dimension is the
number of parameters that have to be optimized. Further, each optimized parameter has
upper and lower limits of the solution space. Figure 4 -3 shows the flowchart of GWO.
The GWO technique can be illustrated in the following steps:
Step 1: Set number of iterations t.
Step 2: Set initial random generation of hunting wolves.
Step 3: Run AC-load flow using MATPOWER software package of Matlab®.
Step 4: Determine the objective function and fitness value of each wolf.
Step 5: Identify the best alpha wolf, the second best beta wolf and the third best Delta
wolf using equation (4-5) to equation (4-10).
Step 6: Update the location of the wolves using equation (4-11).
23
Step 7: Run AC-load flow using MATPOWER software package of Matlab®.
Step 8: calculate the fitness value of each wolf.
Step 9: update alpha, beta, and delta wolves.
Step 10: update the iteration t counter.
Step 11: If the stopping criteria are satisfied go to step 12, else go to step 6.
Step 12: Stop. The alpha wolf is the optimal solution of GWO optimizer.
24
Start
Set iteration(it) = 0
it<Maximum iteration
For i=1:number of search agents
Run AC-load flow with constraints
Success Objective function =
infinity
Calculate objective function
Update alpha, beta and delta
For i=1:number of search agents
Update alpha, beta , delta and omega positions
Yes
No
Convergence_curve(it)=alpha_score
End
Initialize GWO: Dimension of search agents, number of search agents, maximum iteration, and search
boundaries (alpha, beta and delta) positions
Yes
No
it=it+1
Figure 4 -3: Flowchart of GWO.
25
4.1.4 Particle Swarm Optimizer
The Particle Swarm Optimizer (PSO) is a meta-heuristic-based optimization
technique presented by James Kennedy and Russell Eberhart in 1995 [33]. It is inspired
by the social behavior of birds and fishes as shown in Figure 4-4 and Figure 4-5. The
fundamental idea of PSO is that a group of particles is moving in the search space
looking for the food or best solution mathematically. Each particle has a position and
velocity vector.
Figure 4-4: Group of fish movement in the search space.
Figure 4-5: Group of bird movement in the search space
26
Figure 4-6 shows how the particles update their movements depending on their
experiences, and personal and global best particles.
Figure 4-6: Search point modification by PSO.
4.1.5 Mathematical Model of PSO
The updating procedure of the particle position is given in [33] as follows:
V𝑖⃗⃗⃗ (k + 1) = 𝑊. V𝑖⃗⃗⃗ (k) + 𝑠1𝑟1. (P𝑖⃗⃗ (k) − Y𝑖⃗⃗⃗ (k))
+ 𝑠2𝑟2. (G⃗⃗ (k) − Y𝑖⃗⃗⃗ (k)) (4-12)
Y𝑖⃗⃗⃗ (k + 1) = Y𝑖⃗⃗⃗ (k) + V𝑖⃗⃗⃗ (k + 1) (4-13)
Where,
k is the iteration number.
𝑠1 and 𝑠2are the weighting factors.
𝑟1 and 𝑟2are random numbers between 0 and 1.
𝑊 indicates the weighting function.
V𝑖⃗⃗⃗ (k) is particle 𝑖 velocity at iteration k
a V𝑖⃗⃗⃗ (k + 1) indicates the updated veloca ity of particle 𝑖,
27
Y𝑖⃗⃗⃗ (k) is particle 𝑖 position at iteration k.
Y𝑖⃗⃗⃗ (k + 1) indicates the updated position of particle 𝑖.
P𝑖⃗⃗ (k) is the personal best particle 𝑖.
G⃗⃗ (k) is the global best particle.
4.1.6 Implementation Steps of PSO
In the PSO algorithm, the number of population particles represents a candidate for
solutions. Every particle has a dimensional vector. Where this dimension is the number
of parameters that have to be optimized. Consequently, each optimized parameter has
upper and lower boundaries of the solution space. Further, Figure 4-7 shows the
flowchart of the PSO optimizer.
The PSO technique can be illustrated in the following steps:
Step 1: Set number of iterations k.
Step 2: the Set an initial random population of particles
Step 3: Set random initial velocity of each particle for evaluating of the fitness function.
Step 4: Run AC-load flow using MATPOWER software package of Matlab®.
Step 5: Determine the fitness function and fitness value of each particle. During the first
iteration, the fitness value of each particle becomes its personal best. The best fitness
value among all the personal best particles is denoted as a global best particle.
Step 6: Evaluate the velocity of each particle using equation (4-12).
Step 7: Calculate the new particles positions based on equation (4-13).
Step 8: Run AC-load flow using MATPOWER software package of Matlab®.
Step 9: Updating of personal best particle: Compare the fitness value of each new
particle with its personal best particle. If the fitness value of the new particle is better
than the previous personal best particle, then the personal best particle is updated with
the current value of the new particles.
28
Step 10: Updating of global best particle: If the best personal best particle is better than
the global best particle, then the global best particle is substituted with the best personal
best particle.
Step 11: Update the iteration k counter.
Step 12: If the stopping criteria are satisfied go to step 13, else go to step 6.
Step 13: Stop. The global best particle is the optimal solution of PSO optimizer.
29
Start
Initialize PSO: Number of decision variables(Swarm dimension), swarm size(population size), maximum
iteration, and swarm positions
For i=1: swarm size
Run AC-load flow with constraints
Success Objective function =
infinity
Calculate objective function (fitness)
Update personal best and set best of personal best as global
best
Yes
No
For it=1: maximum iteration
For i=1: swarm size
Update velocities and positions
Run optimal load flow with constraints
Success Objective function =
infinity
Calculate objective function
Update personal best and set best of personal best as global
best
Yes
No
Best fitness(Iteration)=GlobalBest.fitness
End
Figure 4-7: Flowchart of PSO.
30
4.1.7 Hybrid GWO-PSO Optimizer
The system reconfiguration problem consists of discrete line numbers while the DG
allocation problem consists of discrete bus numbers while the DG unit capacities
problem is limited by system constraints.
Instead of relying on sensitivity analysis to find the optimal allocation of DG units, a
code will be formulated to search for an optimal reconfiguration, DG allocation, and
capacity at the same time.
Due to the nature of the nonlinear behavior of our problem, running GWO or PSO
optimizers particularly in large systems, will not lead to the same results at each run and
may not reach the optimal solution. Using the proposed hybridization technique
eventually will solve this problem and the same optimal solution will be obtained at each
simulation.
4.1.8 Implementation Steps of Hybrid GWO-PSO
In Hybrid GWO-PSO algorithm, the number and dimension of searching agents that
represent solutions candidate are the same for both optimization techniques GWO and
PSO. Consequently, each optimized parameter has the same upper and lower boundaries
of the solution space for both optimization techniques.
Further, Figure 4-8 shows a flowchart with the main steps of the hybrid GWO-PSO
optimizer.
The Hybrid GWO-PSO technique can be illustrated in the following steps:
Step 1: Set number of iterations.
Step 2: the Set an initial random population of search agents.
Step 3: Run GWO optimizer.
Step 4: pass the minimized searching space points to PSO optimizer as starting points.
Step 5: Run PSO optimizer.
Step 6: Pass these updated new searching space points back to GWO optimizer.
Step 7: Update the iteration counter.
31
Step 8: If the stopping criteria are satisfied go to step 9, else go to step 3.
Step 9: Stop. The global best particle is the optimal solution of the Hybrid GWO-PSO
optimizer.
32
Start
Set iteration(it) = 0
it<Maximum iteration
For i=1:number of search agents
Run AC-load flow with constraints
Success Objective function =
infinity
Calculate objective function
Update alpha, beta and delta
For i=1:number of search agents
Update alpha, beta , delta and omega positions
Yes
No
End
Initialize GWO: Dimension of search agents, number of search agents, maximum iteration, and search boundaries
(alpha, beta and delta) positions
Yes
No
Call PSO
Initialize PSO: Swarm dimension=Dimension of search agents of GWO, swarm size=number of search agents, and
swarm positions=Updated GWO positions
For i=1: swarm size
Run AC-load flow with constraints
Success Objective function =
infinity
Calculate objective function (fitness)
Update personal best and set best of personal best as global
best
Yes
No
For i=1: swarm size
Update velocities and positions
Run AC-load flow with constraints
Success Objective function =
infinity
Calculate objective function
Update personal best and set best of personal best as global
best
Yes
No
it=it+1
Convergence_curve(it)=alpha_score
Convergence_curve_hybrid(it)=GlobalBest.fitness
GWO positions=Updated PSO positions
Figure 4-8: Flowchart of hybrid GWO-PSO.
33
4.2 IMPLEMENTATION FOR SYSTEM RECONFIGURATION
AND DG ALLOCATION
System reconfiguration and DG units’ allocation in appropriate places reduce system
losses, improve the system voltage profile, and reduce distribution lines overloading.
The problem control variables are the system reconfiguration, DGs allocation, and
DGs capacities, which control the fitness function. The complexity of solving those three
variables in parallel lies in the fact that they have been solved them separately using
several optimization techniques or using sensitivity analysis with optimization
techniques.
In the present study, these three problems are dealt with simultaneously by using
GWO, PSO, and the hybrid GWO-PSO technique.
The solution vector V for the three optimization techniques to solve scenario 2 to 8 is
given below:
V={𝑂𝑆1 𝑂𝑆2 𝑂𝑆3 𝑂𝑆4 𝑂𝑆5⏟ 𝑟𝑒𝑐𝑜𝑛𝑓𝑖𝑔𝑢𝑟𝑎𝑡𝑖𝑜𝑛
} (4-14)
V={ 𝐿1 𝐿2 𝐿3⏟ 𝐷𝐺𝑠 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠
𝑆1 𝑆2 𝑆3⏟ 𝐷𝐺𝑠 𝑠𝑖𝑧𝑖𝑒𝑠 𝑜𝑓 𝑝+
} (4-15)
V={𝑂𝑆1 𝑂𝑆2 𝑂𝑆3 𝑂𝑆4 𝑂𝑆5⏟ 𝑟𝑒𝑐𝑜𝑛𝑓𝑖𝑔𝑢𝑟𝑎𝑡𝑖𝑜𝑛
𝐿1 𝐿2 𝐿3⏟ 𝐷𝐺𝑠 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠
𝑆1 𝑆2 𝑆3⏟ 𝐷𝐺𝑠 𝑠𝑖𝑧𝑖𝑒𝑠 𝑜𝑓 𝑝+
} (4-16)
V={ 𝐿1 𝐿2 𝐿3⏟ 𝐷𝐺𝑠 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠
𝑆1 𝑆2 𝑆3⏟ 𝐷𝐺𝑠 𝑠𝑖𝑧𝑖𝑒𝑠 𝑜𝑓 𝑝+
𝑆4 𝑆5 𝑆6⏟ 𝐷𝐺𝑠 𝑠𝑖𝑧𝑖𝑒𝑠 𝑜𝑓 𝑄+
} (4-17)
34
V={𝑂𝑆1 𝑂𝑆2 𝑂𝑆3 𝑂𝑆4 𝑂𝑆5⏟ 𝑟𝑒𝑐𝑜𝑛𝑓𝑖𝑔𝑢𝑟𝑎𝑡𝑖𝑜𝑛
𝐿1 𝐿2 𝐿3⏟ 𝐷𝐺𝑠 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠
𝑆1 𝑆2 𝑆3⏟ 𝐷𝐺𝑠 𝑠𝑖𝑧𝑖𝑒𝑠 𝑜𝑓 𝑝+
𝑆4 𝑆5 𝑆6⏟ 𝐷𝐺𝑠 𝑠𝑖𝑧𝑖𝑒𝑠 𝑜𝑓 𝑄+
} (4-18)
Where,
𝑂𝑆1, 𝑂𝑆2, 𝑂𝑆3, 𝑂𝑆4, and 𝑂𝑆5are five opened switches corresponding to 69, 70, 71,
72, and 73 tie switches.
𝐿1, 𝐿2, and 𝐿3are locations of DGs units.
𝑆1, 𝑆2, and 𝑆3are sizes of DGs units in MW.
𝑆4, 𝑆5, and 𝑆6are sizes of DGs units in MVar.
35
C h a p t e r F i v e
5 SIMULATIONS & RESULTS
5.1 INTRODUCTION
This chapter shows the validity of the proposed three methods for solving DG units’
installation and network reconfiguration using GWO, PSO, and hybrid GWO-PSO. It is
tested on two IEEE standard radial distribution systems (33-bus, 69-bus) and 78-bus
real distribution system in 6th October city, Egypt. The results are compared to
reference [65]. It is proved that there is a small improvement in loss reduction
percentage when DG locations are more than three units. The number of DGs in each
bus is limited to one. Most of the previous studies focused on the injection of active
power only. In this work, the effect of active and reactive power injection of DG units is
studied. The whole simulations had been implemented on Matlab® software package.
Eight scenarios are considered to demonstrate the performance of the proposed
techniques with two different DG types:
1) Scenario 1: Base Case which is only AC-LF (AC-load flow).
2) Scenario 2: System Reconfiguration.
3) Scenario 3: P type (photovoltaic (PV)) DGs installations before Reconfiguration.
4) Scenario 4: P-type (PV) DGs installations after Reconfiguration.
5) Scenario 5: P-type (PV) DGs installations while Reconfiguration.
6) Scenario 6: PQ+ type (Conventional Combustion Turbine) DGs installations
before Reconfiguration.
7) Scenario 7: PQ+ type (Conventional Combustion Turbine) DGs installations
after Reconfiguration.
8) Scenario 8: PQ+ type (Conventional Combustion Turbine) DGs installations
while Reconfiguration.
For all test systems, the minimum and maximum voltage constraints are set at 0.9
p.u. and 1.1 p.u. respectively and the substation voltage is 1 p.u. Voltage decreases from
the source to the end nodes. The voltage profile is improved by adding DG units to the
bus to cover part of the load, sequentially, reducing flowing current and line losses.
36
5.2 IEEE 33-BUS TEST SYSTEM
IEEE 33-bus test system data are given in [Appendix A]. This system base
configuration has 1-32 sectionalized switches normally closed and 33-37 tie switches
are normally opened as shown in Figure 5-1.
Five loops are formed by each tie switch. Tie switches are closed during an
emergency case such as faults to cover unsupplied loads or to reduce system losses.
The total real and reactive power loads are 3.715 MW and 2.3 MVAR respectively.
The system base voltage is 12.66 KV. The limits of real and reactive power injected by
DGs are 0 to 2 MW and 0 to 2 MVAR respectively.
1
2
32
3 4
54
5 6
76
7 8
98
9 10
1110
11 12
12
13
13
14
14
15
1
Su
bsta
tio
n1
32
/1
2.6
6 k
V
1615
16 17
17
18
23
23
24
26
26 27
27
28
28
29
29
30
3130
31 32
32
33
25
1819
19
20
20
21
21
22
=Tie Switches =sectionalized switches
LP1LP3
LP2
LP4LP522
24
25
36
34
37
33
35
Figure 5-1: Single line diagram of the 33-bus system.
5.2.1 Active Power Loss Reduction
Table 5-1 shows that there is a small improvement in loss reduction percentage when
DG locations are more than three units. Table 5-2 and Table 5-3 show switches opened
for all the scenarios.
37
The comparison between the results using the hybrid GWO-PSO and the individual
use of GWO and PSO all scenarios are simulated with GWO and PSO results are
provided in Table 5-2 and Table 5-3. The population size is 50 in all techniques and
scenarios. The below tables show that the proposed hybrid technique yields the lowest
iteration numbers in most of the scenarios. The optimal candidate location using two
DG types for scenario 3 to 8 are highlighted in Table 5-2 and Table 5-3.
It can also be observed from Table 5-2 and Table 5-3 that the base case power loss is
202.67 kW which is reduced to 139.55, 71.4571, 58.8769, 50.8905, 11.6570, 25.1486,
and 8.9540 by GWO using scenario 2 to 8 respectively. Also, Power loss is reduced to
139.55, 71.4571, 58.8768, 51.3088, 11.6299, 18.3104, and 10.8466 by PSO using
scenario 2 to 8 respectively. Consequently, Power loss is reduced to 139.55, 71.4571,
58.8768, 50.7175, 11.6299, 16.3000, and 8.9162 by Hybrid GWO-PSO using scenario 2
to 8 respectively.
From Table 5-2 and Table 5-3, Power loss percentage reduction is 31.14%, 64.74%,
70.95%, 74.89%, 94.24%, 87.59%, and 94.42% by GWO using scenario 2 to 8
respectively. Also, Power loss percentage reduction is 31.14%, 64.74%, 70.95%,
Table 5-1: Different penetration of DG units for the 33-bus system.
Scenarios Proposed Hybrid GWO-PSO
Base case P loss(kW) 202.67
One DG DG size in MW (bus) 2.5753(6)
P loss(KW ) 103.9659
reduction% 48.703%
Two DGs DG size in MW (bus) 0.8465(13),1.1585(30)
P loss( kW ) 85.9101
reduction% 57.61%
Three DGs
DG size in Mw (bus) 1.0717(30),1.1003(24),0.7540(14)
P loss( kW ) 71.4571
reduction% 64.74%
Four DGs DG size in MW (bus) 0.96600(6),0.6856(31),0.9688(24), 0.6035(14)
P loss( kW ) 65.9861
reduction% 67.4428 %
38
74.68%, 94.26%, 90.96%, and 94.64% by PSO using scenario 2 to 8 respectively.
Further, Power loss percentage reduction is 31.14%, 64.74%, 70.95%, 74.97%, 94.26%,
91.95%, and 95.60% by Hybrid GWO-PSO using scenario 2 to 8 respectively.
Table 5-2: Comparison of simulation results for P-type DG units of the 33-bus
system.
Scenarios GWO PSO Proposed Hybrid GWO-PSO
Scenario 1
Switches opened 33,34,35,36,37
33,34,35,36,37
33,34,35,36,37
P loss(kW) 202.67
202.67 202.67
Scenario 2
Switches opened 7,9,14,32,37
7,9,14,32,37 7,9,14,32,37
P loss( kW ) 139.55
139.55 139.55
reduction% 31.14%
31.14% 31.14%
Iterations 50
50 10
Scenario 3
Switches opened 33,34,35,36,37
33,34,35,36,37 33,34,35,36,37
DG size in MW (bus)
1.0709(30), 1.0997(24), 0.7541(14)
1.0714(30), 1.0994(24), 0.7539(14)
1.0717(30), 1.1003(24), 0.7540(14)
P loss( kW ) 71.4571
71.4571 71.4571
reduction% 64.74%
64.74% 64.74%
Iterations 200
100 60
Scenario 4
Switches opened 7,9,14,32,37
7,9,14,32,37 7,9,14,32,37
DG size in Mw (bus)
0.9317(8), 1.0670(24), 0.9520(30)
0.9316(8), 1.0681(24), 0.9503(30)
0.9316(8), 1.0678(24), 0.9507(30)
P loss( kW ) 58.8769
58.8768 58.8768
reduction% 70.95%
70.95% 70.95%
Iterations 100
100 100
Scenario 5
Switches opened 11,28,30,33,34
11,28,31,33,34 11,28,30,33,34
DG size in MW (bus)
0.9581(7), 1.1257(25), 0.8546(33)
0.8141(8), 0.7540(17), 1.3085(25)
0.9569(7), 0.7529(17), 1.2795(25)
P loss( kW ) 50.8905
51.3088 50.7175
reduction% 74.89%
74.68% 74.97%
Iterations 6000 6000 2000
39
Table 5-3: Comparison of simulation results for PQ+-type DG units of the 33-
bus system.
Scenarios GWO PSO Proposed Hybrid GWO-PSO
Scenario 6
Switches opened
33,34,35,36,37 33,34,35,36,37 33,34,35,36,37
DG size in MW (bus)
0.7401+j 0.3533(14), 1.0703+j 0.4869(24), 1.0389+j 1.0118(30)
0.74748+j 0.3501(14), 1.0782+j 0.5212(24), 1.0485+j 1.0209(30)
0.7474+j 0.3501(14), 1.0782+j 0.5212(24), 1.0485+j 1.0209(30)
P loss(KW) 11.6570
11.6299 11.6299
reduction% 94.24%
94.26% 94.26%
Iterations 200
100 100
Scenario 7
Switches opened
7,9,14,32,37 7,9,14,32,37 7,9,14,32,37
DG size in Mw (bus)
0.5314+j 0.3147(12), 0.5030+j 0.1485(16), 1.0403+j 0.9996(30)
1.2444+j 0.6028(21), 1.0413+j 0.5036(24), 0.9281+j 0.9510(30)
0.9316+j 0.4345(8), 0.9321+j 0.9530(30), 1.0547+j 0.5108(24)
P loss(KW) 25.1486
18.3104 16.3000
reduction% 87.59%
90.96% 91.95%
Iterations 600
600 200
Scenario 8
Switches opened
5,11,13,15,26 7,16,21,25,34 5,11,13,15,23
DG size in MW (bus)
1.0818 +j 0.5138(8), 1.1327 +j 0.8311(25), 0.7528 +j 0.5720(32)
0.7826 +j 0.3752(12), 0.9533+j 0.4627 24), 1.1959 +j 1.0738(30)
1.09745+j 0.5593(8), 1.1523+j 0.8047(25), 0.7491+j 0.5620(32)
P loss(KW) 8.9540
10.8466 8.9162
reduction% 94.42%
94.64% 95.60%
Iterations 8000 8000 3000
40
Figure 5-2 shows the single line diagram of scenario 8 for hybrid GWO-PSO
technique.
1
2
32
3 4
54
5 6
76
7 8
98
9 10
1110
11 12
12
13
13
14
14
15
1
Sub
stat
ion
13
2/1
2.6
6 k
V
1615
16 17
17
18
23
23
24
26
26 27
27
28
28
29
29
30
3130
31 32
32
33
25
1819
19
20
20
21
21
22
=Tie Switches =Reconfigured Lines
LP1 LP3
LP2
LP4LP522
24
25
36
34
37
33
35
DG
2
DG
3
DG
1
Figure 5-2: Single line diagram of a 33-bus system for scenario 8.
In Figure 5-3, Scenario 7 shows that power loss for the PQ+ type DG installation
after reconfiguration is not less than DG installation before reconfiguration. Power loss
reduction for scenario 8 is higher than any other scenario using the three proposed
techniques.
Figure 5-3: Power loss of 33-bus system using three different techniques.
0
50
100
150
200
250
P Lo
ss (k
W)
GWO PSO Hybrid
41
5.2.2 Reactive Power Loss Reduction
From Figure 5-4, Base case reactive power loss is 135.141 kVar, which is reduced to
102.305, 49.3907, 44.2879, 40.1381, 9.6676, 17.8765, and 7.5318 for scenarios 2, 3, 4,
5, 6, 7, and 8 respectively using GWO. Also, reactive power loss is reduced to 102.305,
49.3908, 44.2867, 38.6601, 9.6918, 17.0472, and 8.7988 for scenarios 2, 3, 4, 5, 6, 7,
and 8 respectively using PSO. Consequently, reactive power loss is reduced to 102.305,
49.3921, 44.2868, 38.7201, 9.6926, 14.8282, and 7.4668 for scenarios 2, 3, 4, 5, 6, 7,
and 8 respectively using the proposed hybrid technique. It is observed that some
reconfigured lines increase losses in Q injection.
Reactive power loss percentage reduction is 24.2976%, 63.4525%, 67.2283%,
70.299%, 92.8462%, 86.7719%, and 94.4267% by GWO using scenario 2 to 8
respectively. Also, Reactive power loss percentage reduction is 24.2976%, 63.4525%,
67.2292%, 71.3928%, 92.8284%, 87.3855%, and 93.4891% by PSO using scenario 2 to
8 respectively. Further, Reactive power loss percentage reduction is 24.2976%,
63.4525%, 67.2291%, 71.3483%, 92.8291%, 89.0283%, and 94.4749% by Hybrid
GWO-PSO using scenario 2 to 8 respectively.
Figure 5-4: Reactive loss of 33-bus system using three different techniques.
0
20
40
60
80
100
120
140
160
Q L
oss
(k
Va
r)
GWO PSO Hybrid
42
5.2.3 Voltage Profile Improvement
Voltage profile curves for all scenarios are shown in Figure 5-5, Figure 5-6, and
Figure 5-7 using GWO, PSO, and hybrid GWO-PSO techniques respectively. It is
clearly indicated that the system voltage profile for scenario 8 is the best.
The minimum voltage magnitude of the network is 0.91309 (p.u.), which is improved
to 0.93782, 0.96864, 0.97406, 0.96997, 0.99167, 0.98035, and 0.99154 using scenarios
2, 3, 4, 5, 6, 7, and 8 respectively for GWO technique. Also, the minimum voltage
magnitude of the network is improved to 0.93782, 0.96866, 0.97406, 0.97343, 0.99207,
0.97473, and 0.99208 using scenarios 2, 3, 4, 5, 6, 7, and 8 respectively for PSO
technique. Further, the minimum voltage magnitude of the network is improved to
0.93782, 0.96867, 0.97406, 0.97344, 0.99206, 0.98051, and 0.99165 using scenarios 2,
3, 4, 5, 6, 7, and 8 respectively for hybrid GWO-PSO technique.
Figure 5-5: Voltage profile of a 33-bus system using GWO technique.
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3
Vo
lta
ge
P
ofi
le (
pu
)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
43
Figure 5-6: Voltage profile of a 33-bus system using PSO technique.
Figure 5-7: Voltage profile of a 33-bus system using the hybrid technique.
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3
Vo
lta
ge
P
ofi
le (
pu
)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3
Vo
lta
ge
P
ofi
le (
pu
)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
44
5.2.4 Methods Performance
In order to show the performance of the proposed hybrid GWO-PSO, some of the
results are compared to different techniques in Table 5-4. It is observed that the
performance of the proposed technique is better than FWA, HSA, GA and Refined
Genetic Algorithm (RGA) in terms of power loss minimization.
Figure 5-8 shows the conversion characteristics of GWO, PSO, and hybrid GWO-
PSO for scenario 8. PSO reaches a reasonable solution but not the optimal. GWO and
hybrid technique reach the optimal solution. It can be observed that the proposed hybrid
technique provides the best improvement for both the optimal solution and convergence
speed.
Figure 5-8: Conversion curve of the 33-bus system using three different techniques for
scenario 8.
0
10
20
30
40
50
60
70
17
01
39
20
82
77
34
64
15
48
45
53
62
26
91
76
08
29
89
89
67
10
36
11
05
11
74
12
43
13
12
13
81
14
50
15
19
15
88
16
57
17
26
17
95
18
64
19
33
20
02
20
71
21
40
22
09
22
78
23
47
24
16
24
85
25
54
26
23
26
92
27
61
28
30
28
99
29
68
P L
oss (
kW
)
Iteration
Hybrid GWO PSO
45
Table 5-4: Comparison of methods performance for the 33-bus system.
Scenarios Proposed
hybrid
GWO-PSO
FWA [65] HSA [65] GA [65] RGA [65]
Scenario
2
Switches
Opened
7,9,14, 32,37
7,9,14,
32,28
7,9,14,
32,37
33,34,9,
36,28
7,9,14,
32,37
P loss( kW )
139.55
139.98 138.06 141.60 139.46
Reduction%
31.14%
30.93% 31.88% 30.15% 31.20%
Vworst(p.u.)
0.93782
0.9413 0.9342 0.9310 0.9315
Scenario
3 Switches
opened
33,34,35,
36,37
33,34,35,
36,37
33,34,35,
36,37
33,34,35,
36,37
33,34,35,
36,37
P loss( kW ) 71.4571 88.68 96.76 100.1 97.60
Reduction% 64.74% 56.24% 52.26% 50.60% 51.84%
Vworst(p.u.) 0.96867
0.9680 0.9670 0.9605 0.9687
Scenario
4
Switches
opened
7,9,14,
32,37
7,9,14,
32,28
7,9,14,
32,37
33,34,9,
36,28
7,9,14,
32,37
P loss( kW ) 58.8769 83.91 97.13 98.36 98.23
Reduction% 70.95% 58.59% 52.07% 51.46% 51.53%
Vworst(p.u.) 0.97406
0.9612 0.9479 0.9506 0.9479
Scenario
5 Switches
open
11,28,30,
33,34
7,14,11,
32,28
7,14,10,
32,28
7,34,10,
32,28
7,12,9,
32,27
P loss( kW ) 50.8905 67.11 73.05 75.13 74.32
Reduction% 74.89% 66.89% 63.95% 62.92% 63.33%
Vworst(p.u.) 0.97344
0.9713 0.9700 0.9766 0.9691
46
5.3 IEEE 69-BUS TEST SYSTEM
IEEE 69-BUS test system data are given in [Appendix B]. The system base
configuration is having 1-68 sectionalize switches normally closed and 69-73 tie
switches are normally open as shown in Figure 5-9. Five loops formed by each tie
switch.
The total real and reactive power loads are 3.8 MW and 2.69 MVAR respectively.
The system base voltage is 12.66 KV. The limits of real and reactive power injected by
DGs are same as IEEE 33-bus test system.
1
2
32
3 4
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bsta
tio
n1
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/12
.66
kV
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2019
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5352
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5857
58 59
6059
60 61
6261
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45
45
46
72
70
73
36
37
38
39
71
69LP1
LP3
LP2
LP4LP5
=Tie Switches =sectionalized switches
Figure 5-9: Single line diagram of the 69-bus system.
5.3.1 Active Power Loss Reduction
Table 5-5 shows that there is no improvement in loss reduction percentage when DG
locations are more than three units. Table 5-6 and Table 5-7 show switches opened for
all the scenarios.
47
In order to compare the performance of hybrid GWO-PSO, all scenarios are
simulated with GWO and PSO results are provided in Table 5-6 and Table 5-7. The
population size using all the techniques is 50, 50, 50, 100, 60, 60, and 100 in scenarios 2
to 8 respectively. The proposed hybrid technique shows the least iteration numbers for
most of the scenarios, similar to IEEE 33-bus test system. The optimal candidate
location using two DG types for scenario 3 to 8 are highlighted in Table 5-6 and
Table 5-7.
From Table 5-6 and Table 5-7, base case power loss is 224.9295 kW which is
reduced to 98.5687, 71.4131, 39.01865, 35.5060, 9.59208, 8.47849, and 5.47987 by
GWO using scenario 2 to 8 respectively. Also, Power loss is reduced to 98.5687,
69.6525, 36.7430, 36.74120, 7.17099, 7.73888, and 4.40472 by PSO using scenario 2 to
8 respectively. Consequently, Power loss is reduced to 98.5687, 69.3873, 35.5060,
35.13378, 4.486375, 5.88686, and 3.71327 by Hybrid GWO-PSO using scenario 2 to 8
respectively.
From Table 5-6 and Table 5-7, Power loss percentage reduction is 56.1779%,
68.25%, 82.65%, 84.21%, 95.73%, 96.23%, and 97.56% by GWO using scenario 2 to 8
Table 5-5: Different penetration of DG units for the 69-bus system.
Scenarios Proposed Hybrid GWO-PSO
Base case P loss(kW) 224.9295
One DG DG size in MW (bus)
1.87262(61)
P loss(KW )
83.1679
reduction% 63.02 %
Two DGs DG size in MW (bus)
1.7817(61),0.53114(17)
P loss( kW )
71.6356
reduction% 68.15%
Three DGs
DG size in Mw (bus)
0.5271(11),1.7189(61), 0.3799(18)
P loss( kW )
69.3873
reduction% 69.15%
Four DGs DG size in MW (bus)
0.4055(61),0.3121(12),0.1554(21), 0.0806(2)
P loss( kW )
71.8322
reduction% 68.064%
48
respectively. Also, Power loss percentage reduction is 56.17%, 69.03%, 83.66%,
83.66%, 96.81%, 96.55%, and 98.04% by PSO using scenario 2 to 8 respectively.
Additionally, Power loss percentage reduction is 56.17%, 69.15%, 84.21%, 84.38%,
98.00%, 97.38%, and 98.34% by Hybrid GWO-PSO using scenario 2 to 8 respectively.
Table 5-6: Comparison of simulation results for P-type DG units of the 69-bus system.
Scenarios GWO PSO Proposed Hybrid GWO-PSO
Scenario 1
Switches opened
69,70,71,72,73 69,70,71,72,73 69,70,71,72,73
P loss(kW)
224.9295 224.9295 224.9295
Scenario 2
Switches opened
14,57,61, 69,70 14,57,61, 69,70 14,57,61, 69,70
P loss( kW )
98.5687 98.5687 98.5687
reduction%
56.17% 56.17% 56.17%
Iterations
300 200 30
Scenario 3
Switches opened
69,70,71,72,73 69,70,71,72,73 69,70,71,72,73
DG size in MW (bus)
0.5223(18), 1.7779(61), 0.0257( 68)
0.3992(18), 1.7269(61), 0.4596(66)
0.5271(11), 1.7189(61), 0.3799(18)
P loss( kW )
71.4131 69.6525 69.3873
reduction%
68.25% 69.03% 69.15%
Iterations
300 300 100
Scenario 4
Switches opened
14,57,61, 69,70 14,57,61, 69,70 14,57,61, 69,70
DG size in Mw (bus)
1.4344(61), 0.5670(27), 1.0457(2)
1.4339(61),0.5659(27),0.6146(51)
1.4341(61), 0.5661(27), 0.5374(11)
P loss( kW )
39.0186 36.7430 35.5060
reduction%
82.65% 83.66% 84.21%
Iterations
200 200 50
Scenario 5
Switches opened
14,57,61,69,70 13,56,61,69,70 14,55,61, 69,70
DG size in MW (bus)
1.4339(61), 0.5659(27), 0.5375(11)
1.4339(61), 0.5694(27), 0.6072(51)
1.4340(61), 0.4902(64) , 0.5375(11)
P loss( kW )
35.5060 36.7412 35.1337
reduction%
84.21% 83.66% 84.38%
Iterations 8000 8000 2000
49
Table 5-7: Comparison of simulation results for PQ+-type DG units of the 69-bus system.
Scenarios GWO PSO Proposed Hybrid GWO-PSO
Scenario 6
Switches opened
69,70,71,72,73 69,70,71,72,73 69,70,71,72,73
DG size in MW (bus)
0.0006+j 0.0711(69), 1.6913+j 1.2438(61), 0.7718+j 0.2386(68)
0.4402+j 0.3143(36), 1.7345 +j 1.2383(61), 0.5219 +j 0.3530(17)
0.4530+j 0.3219(68), 1.6917+j 1.2081(61), 0.3180+j 0.2111(21)
P loss(KW) 9.5920
7.1709 4.4863
reduction% 95.73%
96.81% 98.00%
Iterations 300
300 100
Scenario 7
Switches opened
14,57,61, 69,70 14,57,61, 69,70 14,57,61, 69,70
DG size in Mw (bus)
0.0871+j 0.2096(68), 1.4155+j 1.0131(61), 0.5643+j 0.3856(27)
0.6137+j 0.4385(51), 1.4171+j 1.01236(61), 0.5629+j 0.3904(27)
0.5366+j 0.3826(11), 1.4167+j 1.0129(61), 0.5629+j 0.3900(27)
P loss(KW) 8.4784
7.7388 5.8868
reduction% 96.23%
96.55% 97.38%
Iterations 300
300 100
Scenario 8
Switches opened
8,13, 20, 24, 55 12,21,40,53,70 14,16,41, 55,64
DG size in MW (bus)
0.08778+j 0.5722(2), 0.8475 +j 0.5899(11), 1.7651+j 1.2605(61)
1.7298+j 1.2346(61), 0.7649+j 0.5493(50), 0.7791+j 0.5339(43)
0.4319+j 0.2913(21), 0.5897+j 0.4161(11), 1.6770+j 1.1979(61)
P loss(KW)
5.4798 4.40472 3.7132
reduction%
97.56% 98.04% 98.34%
Iterations 10000 10000 3000
50
Figure 5-10 shows the single line diagram of scenario 8 for hybrid GWO-PSO
technique.
1
2
32
3 4
54
5 6
76
7 8
98
9 10
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11 12
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V
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2019
20 21
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5352
53 54
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5857
58 59
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60 61
6261
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36
37
38
39
71
69D
G1
DG
2
DG
3
=Tie Switches =Reconfigured Lines
LP1
LP3
LP2
LP4LP5
Figure 5-10: Single line diagram of a 69-bus system for scenario 8.
From Figure 5-11, Scenario 7 shows that power loss for PQ+ type DG installation
after reconfiguration is not less than DG installation before reconfiguration and the best
improvement in power loss reduction is for scenario 8 using the three proposed
techniques same as IEEE 33-bus test system.
51
Figure 5-11: Power loss of 69-bus system using three different techniques.
5.3.2 Reactive Power Loss Reduction
From Figure 5-12, Base case reactive power loss is 102.1456 kVar, which is reduced
to 92.02372, 35.84050, 35.84100, 34.175139, 9.5035477, 8.274102, and 6.54042 for
scenarios 2, 3, 4, 5, 6, 7, and 8 respectively using GWO. Also, reactive power loss is
reduced to 92.02372, 35.05094, 34.61280, 34.672879, 8.020511, 7.55022, and 2.798343
for scenarios 2, 3, 4, 5, 6, 7, and 8 respectively using PSO. Further, the reactive loss is
102.1456 kVar, which is reduced to 92.0237, 34.9527, 34.1729, 34.2659, 7.2140,
6.8968, and 5.6053 using scenarios 2, 3, 4, 5, 6, 7, and 8 respectively using the proposed
hybrid technique. Some reconfigured lines increase losses in Q injection similar to IEEE
33-bus test system.
Reactive power loss percentage reduction is 9.9093%, 64.9124%, 64.9119%,
66.5427%, 90.6961%, 91.8997%, and 93.597% by GWO using scenario 2 to 8
respectively. Also, Reactive power loss percentage reduction is 9.9093%, 65.6853%,
66.1143%, 66.0554%, 92.148%, 92.6084%, and 97.2604% by PSO using scenario 2 to 8
respectively. Additionally, Reactive power loss percentage reduction is 9.9093%,
65.7815%, 84.2146%, 66.4539%, 92.937%, 93.2348%, and 94.5125% by Hybrid GWO-
PSO using scenario 2 to 8 respectively.
0
50
100
150
200
250
P L
oss
(k
W)
GWO PSO Hybrid
52
Figure 5-12: Reactive loss of 69-bus system using three different techniques.
5.3.3 Voltage Profile Improvement
Voltage profile curves for all scenarios are shown in Figure 5-13, Figure 5-14, and
Figure 5-15 using GWO, PSO, and hybrid GWO-PSO techniques respectively. It is
indicated that the system voltage profile for scenario 8 is the best same as IEEE 33-bus
test system.
The minimum voltage magnitude of the network is 0.90919 (p.u.), which is improved
to 0.94947, 0.97891, 0.98134, 0.98133, 0.98669, 0.99288, and 0.99377using scenarios
2, 3, 4, 5, 6, 7, and 8 respectively for GWO technique. Also, the minimum voltage
magnitude of the network is improved to 0.94947, 0.97897, 0.98133, 0.98133, 0.99426,
0.99374, and 0.99524 using scenarios 2, 3, 4, 5, 6, 7, and 8 respectively for PSO
technique. Further, the minimum voltage magnitude of the network is improved to
0.94947, 0.97898, 0.98134, 0.98133, 0.99426, 0.99369, and 0.99486 for scenarios 2, 3,
4, 5, 6, 7, and 8 respectively using the proposed hybrid technique.
53
Figure 5-13: Voltage profile of a 69-bus system using GWO technique.
Figure 5-14: Voltage profile of a 69-bus system using PSO technique.
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7
Vo
lta
ge
Pro
file
(P
U)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7
Vo
lta
ge
Pro
file
(P
U)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
54
Figure 5-15: Voltage profile of a 69-bus system using the hybrid technique.
5.3.4 Methods Performance
Some of the results are compared to several techniques and this is shown in
Table 5-8. The performance of the proposed technique is better than the other
techniques in terms of power loss minimization similar to IEEE 33-bus test system.
Figure 5-16 shows the conversion characteristics of GWO, PSO, and hybrid GWO-
PSO for scenario 8. GWO and PSO reach a reasonable solution but not the optimal.
PSO is faster than GWO with a better solution. It can be observed that the proposed
hybrid technique provides the best improvement for both optimal solution and
convergence speed similar to IEEE 33-bus test system.
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7
Vo
lta
ge
Pro
file
(P
U)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
55
Table 5-8: Comparison of methods performance for the 69-bus system.
Scenarios Proposed
hybrid
GWO-PSO
FWA [65] HSA [65] GA [65] RGA [65]
Scenario
2
Switches
opened
14,57,61, 69,70
14,56,61, 69,70
69,18,13, 56,61
69,70,14, 53,61
69,17,13, 55,61
P loss( kW ) 98.5687 98.59 99.35 103.29 100.28
Reduction% 56.17% 56.17% 55.85% 54.08% 55.42%
Vworst(p.u.) 0.94947 0.9495 0.9428 0.9411 0.9428
Scenario
3
Switches
opened
69,70,71, 72,73
69,70,71, 72,73
69,70,71, 72,73
69,70,71, 72,73
69,70,71, 72,73
P loss( kW ) 69.3873 77.85 86.77 88.5 87.65
Reduction% 69.15% 65.39% 61.43% 60.66% 61.04%
Vworst(p.u.) 0.97898 0.9740 0.9677 0.9687 0.9678
Scenario
4
Switches
opened
14,57,61, 69,70
14,56,61, 69,70
69,18,13, 56,61
69,70,14,53,61
69,17,13, 55,61
P loss( kW ) 35.5060 43.88 51.30 54.53 52.34
Reduction% 84.21% 80.49% 77.20% 75.76% 76.73%
Vworst(p.u.) 0.98134 0.9720 0.9619 0.9401 0.9611
Scenario
5
Switches
opened
14,55,61, 69,70
69,70,13, 55,63
69,17,13, 58,61
10,15,45, 55,62
10,16,14, 55,62
P loss( kW ) 35.1337 39.25 40.30 46.20 44.23
Reduction% 84.38% 82.55% 82.08% 73.38% 80.32%
Vworst(p.u.) 0.98133 0.9796 0.9736 0.9727 0.9742
56
Figure 5-16: Conversion curve of the 69-bus system using three different techniques for scenario 8.
5.4 78-BUS REAL TEST SYSTEM
This system test data are given in [Appendix C]. The system base configuration
consists of having 1-78 sectionalized switches normally closed whereas five switches
are normally opened as shown in Figure 5-17.
The total real and reactive power loads are 48.25 MW and 20.99 MVAR
respectively. The system base capacity is 1.5 MVA and base voltage is 22 KV. The
limits of real and reactive power injected by DGs are 0 to 20 MW and 0 to 10 MVAR
respectively.
0
10
20
30
40
50
60
70
80
1
92
18
3
27
4
36
5
45
6
54
7
63
8
72
9
82
0
91
1
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02
10
93
11
84
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66
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57
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48
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94
21
85
22
76
23
67
24
58
25
49
26
40
27
31
28
22
29
13
P L
oss (
kW
)
Iterations
Hybrid GWO PSO
57
1
2
3
2
3
4
5
4
5
6
7
6
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7782
78
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1
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31
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74
67
66
63
64
69
68
65
66
71
70
67
68
73
72
69
70
Substation22 kV
=Tie Switches =sectionalized switches
Figure 5-17: Single line diagram of the 78-bus system.
5.4.1 Active Power Loss Reduction
Table 5-5 shows that there is a small improvement in loss reduction percentage when
DG locations are more than three units. Table 5-10 and Table 5-11 show switches
opened for all the scenarios.
58
Table 5-10 and Table 5-11 illustrate the comparison in the same way as test systems
A and B. The population size using all techniques is 50, 60, 60, 100, 60, 60, and 100 in
scenarios 2 to 8 respectively. Tables show that the proposed hybrid technique takes the
least number of iterations for the most of the scenarios, similar to IEEE 33-bus test
system and IEEE 69-bus test system. The optimal candidate location using two DG
types for scenario 3 to 8 are highlighted in Table 5-10 and Table 5-11.
As shown in Table 5-10 and Table 5-11, base case power loss is 421.7192kW, which
is reduced to 209.373, 142.02, 107.68, 88.95, 123.06, 92.96, and 48.93 by GWO using
scenario 2 to 8 respectively. Also, Power loss is reduced to 209.3731, 154.9977, 109.25,
115.61, 101.6025, 90.3978, and 61.5560 by PSO using scenario 2 to 8 respectively.
Further, Power loss is reduced to 209.37, 141.96, 107.6448, 88.95, 89.2335, 88.4952,
and 48.6045 by Hybrid GWO-PSO using scenario 2 to 8 respectively.
From Table 5-10 and Table 5-11, Power loss percentage reduction is 50.3525%,
66.32%, 74.46%, 78.90%, 70.81%, 77.95%, and 88.39% by GWO using scenario 2 to 8
respectively. Also, Power loss percentage reduction is 50.35%, 63.24%, 74.09%,
72.58%, 75.90%, 78.56%, and 85.40% by PSO using scenario 2 to 8 respectively.
Table 5-9: Different penetration of DG units for the 78-bus system.
Scenarios Proposed Hybrid GWO-PSO
Base case
P loss(kW) 421.7192
One DG DG size in MW (bus)
13.0322(29)
P loss(KW )
223.743
reduction% 46.945%
Two DGs DG size in MW (bus)
13.0318(29), 9.08572(7)
P loss( kW )
174.9617
reduction% 58.51%
Three DGs
DG size in Mw (bus)
9.0871(7),13.0333(29),6.6383(67)
P loss( kW )
141.9624
reduction% 66.33%
Four DGs DG size in MW (bus)
6.6436(67 ),9.2305(6),9.2397(25), 6.14282(49)
P loss( kW )
114.4634
reduction% 72.85%
59
Additionally, Power loss percentage reduction is 50.35%, 66.33%, 74.47%, 78.90%,
78.84%, 79.01%, and 88.4747% by Hybrid GWO-PSO using scenario 2 to 8
respectively.
Table 5-10: Comparison of simulation results for P-type DG units of the 78-bus
system.
Scenarios GWO PSO Proposed Hybrid GWO-PSO
Scenario 1
Switches opened
32,34,40,48,63 32,34,40,48,63 32,34,40,48,63
P loss(kW)
421.7192 421.7192 421.7192
Scenario 2
Switches opened
10,28,34,45, 64 10,28,34,45, 64 10,28,34,45, 64
P loss( kW )
209.3731 209.3731 209.3731
reduction%
50.3525% 50.3525% 50.3525%
Iterations
100 100 30
Scenario 3
Switches opened
32,34,40,48,63 32,34,40,48,63 32,34,40,48,63
DG size in MW (bus)
6.6347(67), 9.4411(5), 13.0352(29)
6.6392(67), 8.3307(32), 11.4460(52)
9.0871(7), 13.0333(29), 6.6383(67)
P loss( kW )
142.0250 154.9977 141.9624
reduction%
66.32% 63.24% 66.33%
Iterations
300 300 100
Scenario 4
Switches opened 10,28,34,45, 64 10,28,34,45, 64 10,28,34,45, 64 DG size in Mw (bus)
5.4594(75), 10.5558(3), 6.5508(67)
5.1046(43), 10.3781(16), 6.55061(67)
5.5491(25), 10.3774(16), 6.5501(67)
P loss( kW )
107.6866 109.2588 107.6448
reduction%
74.4648% 74.092% 74.47%
Iterations
300 300 100
Scenario 5
Switches opened
8,23,30,43,64 8,26,34,41,64 8,23,30,43,64
DG size in MW (bus)
15.8913(32), 5.4580(75), 6.5507(67)
9.1835(32), 5.8525(31), 6.9573(25)
6.5505(67), 5.4581(75), 15.8910(32)
P loss( kW )
88.9550 115.6147 88.9550
reduction%
78.90% 72.5849% 78.90%
Iterations 8000 8000 3000
60
Table 5-11: Comparison of simulation results for PQ+-type DG units of the
78-bus system.
Scenarios GWO PSO Proposed Hybrid GWO-PSO
Scenario 6
Switches opened
32,34,40,48,63 32,34,40,48,63 32,34,40,48,63
DG size in MW (bus)
4.2811+j 0.0002 (11), 6.2412+j 4.5606 (3), 12.9952+j 5.6954 (29)
7.0371+j 3.0773(31), 9.0865+j 3.9673 (7), 8.3189+j 3.6267 (25)
13.0438+j 5.7339(29), 6.6376+j 2.8963(67), 9.0840+j 3.9653(7)
P loss(KW)
123.0646 101.6025 89.2335
reduction%
70.81% 75.91% 78.84%
Iterations
300 300 100
Scenario 7
Switches opened
10,28,34,45, 64
10,28,34,45, 64
10,28,34,45, 64
DG size in Mw (bus)
6.5494+j 2.7644(67), 5.4412+j 0.0273(75), 10.5141+j 4.5881(3)
10.3709+j 4.5219(16), 5.1071+j 2.2269(43), 6.5514+j 2.8547(67)
6.5530 +j 2.8517(67), 10.3680 +j 4.5201(16), 5.5462 +j 2.4208(25)
P loss(KW) 92.9695
90.3978 88.4952
reduction% 77.95%
78.56% 79.01%
Iterations 300
300 100
Scenario 8
Switches opened
8,21,42,55,63 8, 20,41,51,63 8,20,42, 55,63
DG size in MW (bus)
5.4565+j 2.3783 (75), 18.2086+j 7.9589(32), 6.6405+j 2.8940(67)
6.6404 +j 2.8937 (67), 16.2463+j 7.0932(24), 5.7228 +j 2.4958(31)
18.4208+j 8.0511(24), 6.6400+j 2.8937(67), 5.4565 +j 2.3779(75)
P loss(KW) 48.93
61.5560 48.6045
reduction% 88.39%
85.40% 88.47%
Iterations 9000 9000 3000
61
System Losses are very small compared to the load capacity due to the fact that the
loads are commercial and are located directly after the substation directly at the primary
side of the transformer. Therefore the line current is small compared to the secondary
side of the transformer that feeds residential loads. Figure 5-18 shows the single line
diagram of scenario 8 for hybrid GWO-PSO technique.
1
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Substation22 kV
=Tie Switches =Reconfigured Lines
DG2
DG1
DG3
Figure 5-18: Single line diagram of a 78-bus system for scenario 8.
62
Figure 5-19 shows that Power loss reduction for scenario 8 is higher than any other
scenario using the three proposed techniques same as IEEE 33-bus test system and
IEEE 69-bus test system.
.
Figure 5-19: Power loss of 78-bus system using three different techniques.
5.4.2 Reactive Power Loss Reduction
As shown in Figure 5-20, the base case reactive power loss is 572.3431 kVar, which
is reduced to 284.15455, 192.75180, 146.14884, 120.7269, 167.01948, 126.17517, and
66.410482 for scenarios 2, 3, 4, 5, 6, 7, and 8 respectively using GWO. Also, reactive
power loss is reduced to 284.15455, 210.357906, 148.282588, 156.90870, 137.89190,
122.685028, and 83.5420028 for scenarios 2, 3, 4, 5, 6, 7, and 8 respectively using PSO.
Further, reactive power loss is reduced to 284.15455, 192.66676, 146.092127,
120.72697, 121.10492, 120.102971, and 65.964515 using scenarios 2, 3, 4, 5, 6, 7, and
8 respectively using the proposed hybrid technique. Some reconfigured lines increase
losses in Q injection similar to IEEE 33-bus test system.
0
50
100
150
200
250
300
350
400
450
P L
oss
(K
W)
GWO PSO Hybrid
63
Reactive power loss percentage reduction is 50.3524%, 66.3223%, 74.4648%,
78.9065%, 70.8183%, 77.9546%, and 88.3967% by GWO using scenario 2 to 8
respectively. Also, Reactive power loss percentage reduction is 50.3524%, 63.2462%,
74.092%, 72.5849%, 75.9075%, 78.5644%, and 85.4035% by PSO using scenario 2 to
8 respectively. Further, Reactive power loss percentage reduction is 50.3524%,
66.3372%, 74.4747%, 78.9065%, 78.8404%, 79.0155%, and 88.4747% by Hybrid
GWO-PSO using scenario 2 to 8 respectively.
Figure 5-20: Reactive loss of 78-bus system using three different techniques.
5.4.3 Voltage Profile Improvement
Voltage profile curves for all scenarios are shown in Figure 5-21, Figure 5-22, and
Figure 5-23 using GWO, PSO, and hybrid GWO-PSO techniques respectively. Similar
to IEEE 33-bus test system and IEEE 69-bus test system, the voltage profile for scenario
8 is the best.
0
100
200
300
400
500
600
700
Q L
oss (
kV
ar)
GWO PSO Hybrid
64
The minimum voltage magnitude of the network is 0.97046 (p.u.), which is improved
to 0.99139, 0.98552, 0.99253, 0.99231, 0.99128, 0.99253, and 0.99598 using scenarios
2, 3, 4, 5, 6, 7, and 8 respectively for GWO technique. Also, the minimum voltage
magnitude of the network is improved to 0.99139, 0.98733, 0.99161, 0.99139, 0.99128,
0.99161, and 0.99161 using scenarios 2, 3, 4, 5, 6, 7, and 8 respectively for PSO
technique. Further, the minimum voltage magnitude of the network is improved to
0.99139, 0.98552, 0.99161, 0.99231, 0.99161, 0.99161, and 0.99598 using scenarios 2,
3, 4, 5, 6, 7, and 8 respectively using the proposed hybrid technique.
Figure 5-21: Voltage profile of a 78-bus system using GWO technique.
0.955
0.96
0.965
0.97
0.975
0.98
0.985
0.99
0.995
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1.005
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7 7 0 7 3 7 6
Vo
lta
ge
P
ofi
le (
pu
)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
65
Figure 5-22: Voltage profile of a 78-bus system using PSO technique.
Figure 5-23: Voltage profile of a 78-bus system using the hybrid technique.
0.955
0.96
0.965
0.97
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0.98
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0.99
0.995
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1.005
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7 7 0 7 3 7 6
Vo
lta
ge P
ofi
le (
pu
)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
0.955
0.96
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0.97
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0.98
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0.99
0.995
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1.005
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7 7 0 7 3 7 6
Vo
lta
ge P
ofi
le (
pu
)
Bus No
scenario 1 scenario 2 scenario 3 scenario 4
scenario5 scenario 6 scenario7 scenario 8
66
5.4.4 Methods Performance
Figure 5-24 shows the conversion characteristics of GWO, PSO, and hybrid GWO-
PSO for scenario 8 where GWO and PSO did not reach the optimal solution. PSO is
faster than GWO. However, GWO is with a better solution than PSO. Furthermore, the
proposed technique is the best, similar to IEEE 33-bus test system and IEEE 69-bus test
system.
Figure 5-24: Conversion curve of the 78-bus system using three different techniques for scenario 8.
0
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oss
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W)
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Hybrid GWO PSO
67
C h a p t e r s i x
6 CONCLUSIONS & FUTURE WORK
6.1 CONCLUSIONS
This thesis presents system reconfiguration and DGs sitting and sizing for (33-bus,
69-bus) IEEE system and 78- real distribution system by comparing the performance of
the proposed new hybrid GWO-PSO technique to Grey Wolf Optimizer (GWO) and
Particle Swarm Optimizer (PSO) individually. This combination of the two
metaheuristic techniques leads to the elimination of the disadvantages of both
techniques, the minimization of the number of iterations and helps reach the optimal
solution at every simulation.
This thesis also compares the proposed technique to several techniques in terms of
power loss minimization; Fire Work Algorithm, Harmony Search Algorithm, Genetic
Algorithm, and Refined Genetic Algorithm.
The results of this proposed technique have proved to be better than the other
published studies that have used sensitivity factors to solve the DG location problem.
Also, the results show that using the proposed new hybrid technique have proved to be
better than using GWO and PSO individually. It is also concluded that the PSO
technique reaches the optimal solution in a shorter time while the GWO gives a more
accurate solution. Further, it can be observed that using a hybrid GWO-PSO solver will
make use of the advantages of both techniques. The presented hybrid GWO-PSO
technique provides the best improvement for both optimal solution and convergence
speed. Using GWO or PSO optimizers especially in the practical large systems, will not
lead to the same results at each simulation and sometimes may not reach the optimal
solution. However, using the proposed hybridization technique eventually solved this
problem and the same optimal solution obtained at each code simulation.
In the IEEE 33-bus system, active power loss decreases from 202.67 to 8.9540 kW,
reactive power loss decreases from 135.141 to 7.5318 kVar and the minimum voltage
magnitude improved from 0.91309 to 0.99154 (p.u.) using GWO. Also, active power
loss decreases from 202.67 to 10.8466 kW, reactive power loss decreases from 135.141
68
to 8.7988 kVar and the minimum voltage magnitude improved from 0.91309 to 0.99208
(p.u.) using PSO. Further, active power loss decreases from 202.67 to 8.1962 kW,
reactive power loss decreases from 135.141 to 7.4668 kVar and the minimum voltage
magnitude improved from 0.91309 to 0.99165 (p.u.) using hybrid GWO-PSO relative to
the scheme without considering system reconfiguration and DGs placement.
In the IEEE 69-bus system, active power loss decreases from 224.9295 to 5.4798
kW, reactive power loss decreases from 102.1456 to 6.5404 kVar and the minimum
voltage magnitude improved from 0.90919 to 0.99377 (p.u.) using GWO. Also, active
power loss decreases from 224.9295 to 4.4047 kW, reactive power loss decreases from
102.1456 to 2.7983 kVar and the minimum voltage magnitude improved from 0.90919
to 0.99524 (p.u.) using PSO. Further, active power loss decreases from 224.9295 to
3.7132 kW, reactive power loss decreases from 102.1456 to 5.6053 kVar and the
minimum voltage magnitude improved from 0.90919 to 0.99486 (p.u.) using hybrid
GWO-PSO.
In the 78-bus real system, active power loss decreases from 421.7192 to 48.9331
kW, reactive power loss decreases from 572.3431 to 66.41048 kVar and the minimum
voltage magnitude increased from 0.97046 to 0.99598 (p.u.) using GWO. Also, active
power loss decreases from 421.7192 to 61.5560 kW, reactive power loss decreases from
572.3431 to 83.5420 kVar and the minimum voltage magnitude increased from 0.97046
to 0.99161 (p.u.) using PSO. Further, active power loss decreases from 421.7192 to
48.6045 kW, reactive power loss decreases from 572.3431 to 65.9645 kVar and the
minimum voltage magnitude increased from 0.97046 to 0.99598 (p.u.) using hybrid
GWO-PSO.
From the latter results, it is observed that using power loss as an objective function
improves all the other elements of the network. Real power loss as an objective function
will not only reduce real power losses but also will reduce reactive power losses and
improve the voltage profile of the system. Moreover, the combination of network
reconfiguration and optimal placement of DG units has the best improvement compared
to solving each one of them separately.
69
6.2 FUTURE WORK
Up to the presented research in this thesis, more studies could be illustrated in the
future, some of which are:
Compare the results of the proposed objective function with another
objective; minimize reactive power loss, and maximize system load ability.
Study the effect of optimal DG placement in the deregulated electricity
market; Social welfare maximization, minimization of location marginal
pricing (LMP), and minimization of total generation cost.
Investigate the inclusion of congestion management by optimal DG
penetration and system reconfiguration.
Study the impact of capacitor placement only, capacitor placement with
system reconfiguration, capacitor placement in parallel with DG placement,
and capacitor placement with system reconfiguration and DG placement on
the system performance.
Study the effect of optimal capacitor allocation to maximize the cost savings
for different load levels.
70
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APPENDICES
80
Appendix A
Test data for the 33-bus system
Switch
No.
From bus
i
To bus
i+1
Ri, i+1 Xi, i+1 P(KW) Q(kVar)
1 1 2 0.0922 0.0470 100 60
2 2 3 0.4930 0.2511 90 40
3 3 4 0.3660 0.1864 120 80
4 4 5 0.3811 0.1941 60 30
5 5 6 0.8190 0.7070 60 20
6 6 7 0.1872 0.6188 200 100
7 7 8 0.7114 0.2351 200 100
8 8 9 1.0300 0.7400 60 20
9 9 10 1.0440 0.7400 60 20
10 10 11 0.1966 0.0650 45 30
11 11 12 0.3744 0.1238 60 35
12 12 13 1.4680 1.1550 60 35
13 13 14 0.5416 0.7129 120 80
14 14 15 0.5910 0.5260 60 10
15 15 16 0.7463 0.5450 60 20
16 16 17 1.2890 1.7210 60 20
17 17 18 0.7320 0.5740 90 40
18 2 19 0.1640 0.1565 90 40
19 19 20 1.5042 1.3554 90 40
20 20 21 0.4095 0.4784 90 40
21 21 22 0.7089 0.9373 90 40
22 3 23 0.4512 0.3083 90 50
23 23 24 0.8980 0.7091 420 200
24 24 25 0.8960 0.7011 420 200
25 6 26 0.2030 0.1034 60 25
26 26 27 0.2842 0.1447 60 25
27 27 28 1.0590 0.9337 60 20
28 28 29 0.8042 0.7006 120 70
81
Base kV=12.66,
Tie switches=21-8; 9-15; 12-22; 18-33; 25-29
29 29 30 0.5075 0.2585 200 600
30 30 31 0.9744 0.9630 150 70
31 31 32 0.3105 0.3619 210 100
32 32 33 0.3410 0.5302 60 40
33 21 8 2.0000 2.0000 - -
34 9 15 2.0000 2.0000 - -
35 12 22 2.0000 2.0000 - -
36 18 33 0.5000 0.5000 - -
37 25 29 0.5000 0.5000 - -
82
Appendix B
Test data for the 69-bus system
Switch
No.
From bus
i
To bus
i+1
Ri, i+1 Xi, i+1 P(KW) Q(kVar)
1 1 2 0.0005 0.0012 0 0
2 2 3 0.0005 0.0012 0 0
3 3 4 0.0015 0.0036 0 0
4 4 5 0.0251 0.0294 0 0
5 5 6 0.366 0.1864 2.6 2.2
6 6 7 0.381 0.1941 40.4 30
7 7 8 0.0922 0.047 75 54
8 8 9 0.0493 0.0251 30 22
9 9 10 0.819 0.2707 28 19
10 10 11 0.1872 0.0619 145 104
11 11 12 0.7114 0.2351 145 104
12 12 13 1.03 0.34 8 5
13 13 14 1.044 0.345 8 5.5
14 14 15 1.058 0.3496 0 0
15 15 16 0.1966 0.065 45.5 30
16 16 17 0.3744 0.1238 60 35
17 17 18 0.0047 0.0016 60 35
18 18 19 0.3276 0.1083 0 0
19 19 20 0.2106 0.069 1 0.6
20 20 21 0.3416 0.1129 114 81
21 21 22 0.014 0.0046 5 3.5
22 22 23 0.1591 0.0526 0 0
23 23 24 0.3463 0.1145 28 20
24 24 25 0.7488 0.2475 0 0
25 25 26 0.3089 0.1021 14 10
26 26 27 0.1732 0.0572 14 10
27 3 28 0.0044 0.0108 26 18.6
28 28 29 0.064 0.1565 26 18.6
83
29 29 30 0.3978 0.1315 0 0
30 30 31 0.0702 0.0232 0 0
31 31 32 0.351 0.116 0 0
32 32 33 0.839 0.2816 14 10
33 33 34 1.708 0.5646 19.5 14
34 34 35 0.3978 0.1315 6 4
35 3 36 0.0044 0.0108 26 18.55
36 36 37 0.064 0.1565 26 18.55
37 37 38 0.1053 0.123 0 0
38 38 39 0.0304 0.0335 24 17
39 39 40 0.0018 0.0021 24 17
40 40 41 0.7283 0.8509 1.2 1
41 41 42 0.31 0.3623 0 0
42 42 43 0.041 0.0478 6 4.3
43 43 44 0.0092 0.0116 0 0
44 44 45 0.1089 0.1373 39.22 26.3
45 45 46 0.0009 0.0012 39.22 26.3
46 4 47 0.0034 0.0084 0 0
47 47 48 0.0851 0.2083 79 56.4
48 48 49 0.2898 0.7091 384.7 274.5
49 49 50 0.0822 0.2011 384.7 274.5
50 8 51 0.0928 0.0473 40.5 28.3
51 51 52 0.3319 0.1114 3.6 2.7
52 9 53 0.174 0.0886 4.35 3.5
53 53 54 0.203 0.1034 26.4 19
54 54 55 0.2842 0.1447 24 17.2
55 55 56 0.2813 0.1433 0 0
56 56 57 1.59 0.5337 0 0
57 57 58 0.7837 0.263 0 0
58 58 59 0.3042 0.1006 100 72
59 59 60 0.3861 0.1172 0 0
60 60 61 0.5075 0.2585 1244 888
84
Base kV=12.66,
Tie switches=11-43; 13-21; 15-46; 50-59; 27-65
61 61 62 0.0974 0.0496 32 23
62 62 63 0.145 0.0738 0 0
63 63 64 0.7105 0.3619 227 162
64 64 65 1.041 0.5302 59 42
65 11 66 0.2012 0.0611 18 13
66 66 67 0.0047 0.0014 18 13
67 12 68 0.07394 0.2444 28 20
68 68 69 0.0047 0.0016 28 20
69 11 43 0.5 0.5 - -
70 13 21 0.5 0.5 - -
71 15 46 1 0.5 - -
72 50 59 2 1 - -
73 27 65 1 0.5 - -
85
Appendix C
Test data for the 78-bus system
Switch
No.
From bus
i
To bus
i+1
Ri, i+1 Xi, i+1 P(KW) Q(kVar)
1 1 2 0.178125 0.241746 685.8921 298.3631
2 2 3 0.016875 0.022902 685.8921 298.3631
3 3 4 0.0525 0.071251 717.069 311.925
4 4 5 0.0125 0.016965 748.2459 325.487
5 5 6 0.0125 0.016965 174.5907 75.94696
6 6 7 0.00875 0.011875 286.8276 124.77
7 7 8 0.02 0.027143 748.2459 325.487
8 8 9 0.03 0.040715 244.427 106.3257
9 9 10 0.06125 0.083127 255.6507 111.2081
10 10 11 0.04375 0.059376 1153.546 501.7924
11 11 12 0.015625 0.021206 236.9446 103.0709
12 12 13 0.055625 0.075492 265.0038 115.2766
13 13 14 0.0175 0.02375 717.069 311.925
14 14 15 0.02 0.027143 685.8921 298.3631
15 3 16 0.008125 0.011027 717.069 311.925
16 16 17 0.0375 0.050894 685.8921 298.3631
17 17 18 0.025 0.033929 436.4768 189.8674
18 1 19 0.13125 0.178128 286.8276 124.77
19 19 20 0.0125 0.016965 729.5398 317.3498
20 20 21 0.03375 0.045804 717.069 311.925
21 21 22 0.00375 0.005089 271.2392 117.989
22 22 23 0.06625 0.089912 654.7152 284.8011
23 23 24 0.06875 0.093305 685.8921 298.3631
24 24 25 0.0525 0.071251 717.069 311.925
25 25 26 0.0125 0.016965 748.2459 325.487
26 26 27 0.0975 0.132324 729.5398 317.3498
27 27 28 0.05375 0.072948 735.7752 320.0622
86
28 28 29 0.00625 0.008482 654.7152 284.8011
29 29 30 0.10625 0.144199 249.4153 108.4957
30 30 31 0.025 0.033929 467.6537 203.4294
31 31 52 0.01875 0.025447 1153.546 501.7924
32 32 15 0.02 0.027143 149.6492 65.0974
33 32 16 0.055 0.074644 202.6499 88.15273
34 24 32 0.015 0.020358 277.4745 120.7014
35 1 33 0.1375 0.186611 685.8921 298.3631
36 33 34 0.03125 0.042412 779.4229 339.0489
37 34 35 0.04 0.054287 286.8276 124.77
38 35 36 0.06375 0.086519 685.8921 298.3631
39 36 37 0.0025 0.003393 748.2459 325.487
40 37 38 0.0375 0.050894 717.069 311.925
41 38 39 0.00875 0.011875 717.069 311.925
42 39 40 0.0875 0.118752 723.3044 314.6374
43 40 41 0.02125 0.02884 654.7152 284.8011
44 41 42 0.005 0.006786 748.2459 325.487
45 42 43 0.05375 0.072948 717.069 311.925
46 43 25 0.0375 0.050894 748.2459 325.487
47 1 44 0.019625 0.026634 748.2459 325.487
48 44 45 0.0225 0.030536 685.8921 298.3631
49 45 46 0.1225 0.166253 748.2459 325.487
50 46 47 0.015 0.020358 685.8921 298.3631
51 47 48 0.09125 0.123842 174.5907 75.94696
52 48 49 0.01375 0.018661 717.069 311.925
53 49 50 0.0625 0.084823 717.069 311.925
54 50 51 0.0375 0.050894 174.5907 75.94696
55 51 52 0.025 0.033929 717.069 311.925
56 1 53 0.03625 0.049197 221.3561 96.2899
57 53 54 0.04375 0.059376 729.5398 317.3498
58 1 55 0.05 0.067858 717.069 311.925
59 55 56 0.025 0.033929 236.9446 103.0709
87
Base kV = 22,
Tie switches=32-15; 24-32; 37-38; 44-45; 59-60
60 56 57 0.01625 0.022054 26.81215 11.66328
61 57 58 0.08125 0.11027 748.2459 325.487
62 58 59 0.00625 0.008482 685.8921 298.3631
63 59 60 0.01125 0.015268 1122.369 488.2305
64 60 61 0.04875 0.066162 1122.369 488.2305
65 61 62 0.005 0.006786 374.123 162.7435
66 62 63 0.015 0.020358 685.8921 298.3631
67 63 64 0.09375 0.127235 1122.369 488.2305
68 64 65 0.06875 0.093305 685.8921 298.3631
69 65 66 0.025 0.033929 1091.192 474.6685
70 66 67 0.015625 0.021206 748.2459 325.487
71 67 68 0.053125 0.0721 143.4138 62.38501
72 68 69 0.0375 0.050894 1122.369 488.2305
73 69 70 0.039375 0.053438 685.8921 298.3631
74 61 54 0.05375 0.072948 1091.192 474.6685
75 1 71 0.15625 0.212058 717.069 311.925
76 71 72 0.12625 0.171342 685.8921 298.3631
77 72 73 0.015 0.020358 1028.838 447.5446
78 73 74 0.06875 0.093305 - -
79 74 75 0.01875 0.025447 - -
80 75 76 0.0625 0.084823 - -
81 76 77 0.1525 0.206968 - -
82 77 78 0.02 0.027143 - -