International Journal of Emerging Technology and Advanced Engineering
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PSO Based an Optimal Power Flow with Economical
Generation and Dispatch by Inserting FACTS Devices
K.Venkateswarlu1,Dr.Ch.Saibabu2,K.Srikanth3,Dr.G.Srinivasan4
1
Associateprofessor,Dept.of EEE,M.L.Engg.College,S.Konda,Prakasam(Dt.),A.P.,India. 2
Professor and Director of Evaluation,JNTUKUnivesity,Kakinada,A.P.,India. 3
Asistant Engineer,APCPDCL,Gooty,Anatapuram(Dt.),A.P.,India. 4
Professor,Dept.of EEE, Intel Engg.college,Anatapuram,A.P.,India.
Abstract-- This paper presents an efficient approach for solving optimal power flow (OPF) problem using an particle swarm optimization technique. Economical generation and dispatch is one of the main problems of optimal power flow. In a recent technological development a Flexible alternating transmission system(FACTS) devices can be able to control power flow, increase transmission stability line limits, minimize the transmission power loss and enhance the loadability of the system .This paper presents optimal location and ratings of FACTS devices such as Static Var Compensator(SVC), Thyristor Controlled Series Compensator(TCSC) and Unified Power Flow Controller(UPFC).The main objective is to achieve the minimization of losses, Economical generation allocation and dispatch in deregulated electricity market within the security limits . In the proposed work, a non-traditional optimization technique, Particle Swarm Optimization technique (PSO) is used to optimize the size and location of various types of FACTS devices .The Simulation was performed on five bus system and IEEE 30bus systems with various FACTS controllers, modeled for steady state studies. It is to obtain feasible solutions with in minimal CPU time, and the Numerical results are presented and comparison is made between various FACTS devices.
Index Terms-- Optimal Power Flow (OPF), Static Var Compensator (SVC), Thyristor Controlled Series Compensator (TCSC), Unified Power Flow Controller(UPFC), Particle Swarm Optimization(PSO).
I. INTRODUCTION
Optimal power Flow (OPF) is one of the most useful tools operation and planning in modern energy Management system. It plays an important role in maintaining the economical power generation, operation and control.The OPF optimizes the power system operating objective function while satisfying a set of equality and in-equality constraints.The in-equality constraints are optimal power flow equations and inequality constraints are the limits of power variables.
The control variables include generator active powers, the generator bus voltage magnitudes,the transformer tap settings and reactive power of switchable shunt devices,while the functional operating constraints include the load bus voltage magnitudes, the generator reactive powers, the line flows and slack bus power.
OPF is a nonlinear, non-convex, large-scale, static optimization problem with both continuous and discrete variables. Even in the absence of discrete control variables, the OPF problems non convex due to the existence of the nonlinear(AC) power flow equality constraints. The presence of discrete controlvariables,such as switchable shunt devices, transformer tap positions, phase shifters and Flexible AC Transmission Systems (FACTS) devices further complicates the problem solution.
OPF solution based on mathematical programming approaches is not guaranteed to converge to the global optimum of the general non-convex OPF problem. although there exists some empirical evidence on the uniqueness of the OPF solution with in domain of interest.
In recent years, with the deregulation of the electricity market, the traditional concepts and practices of power systems are changed. This led to introduction of Flexible
transmission System(FACTS) such asStatic VAR
Compensator(SVC), Thyristor Controlled Series
Compensator(TCSC) and Unified Power Flow
Controller)UPFC).These devices controls the power flow in the network, reduces the flow in heavily loaded lines there by resulting in an increase loadability, low system losses, improved stability of network and reduced cost of production[2,10,11,13].It is important to ascertain the location of these devices because of their significant costs.S.Jerbex et al[4] provides an idea regarding the optimal locations of facts devices, without considering the investment cost of FACTS devices and their impact on the generation cost.
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A new optimization technique called particle swarm Optimization(PSO)isused to solve OPF with economical constrained[4].PSO has a flexible and well-balanced mechanism to enhance and adapt the global and local exploration abilities.
This thesis is organized as follows: following the introduction, OPF with FACTS devices, which includes Mathematical modeling of TCSC,UPFC and SVC are described section II.Then in section III, Objective functions and Practical Swarm Optimization technique are described. In section IV, Numerical Results and discussion and section V Conclusion.
II. MATHEMATICAL MODELING OF FACTSDEVICES
In this paper, the mathematical models of the FACTS devices are developed mainly to perform the steady-state analysis. Therefore the TCSC is modeled to modify the reactance of the transmission line directly. SVC and UPFC are modeled using the power/current injection method[4]. Furthermore, for the TCSC and UPFC, their mathematical model is integrated into the model of the transmission line, where as the SVC model is only incorporated into the sending-end as a shunt element of the transmission line.
1. Transmission line
A simple transmission line represented by its lumped 𝜋
equivalent parameters connected between busr and s as in fig(1).The real and reactive power flow from r bus to s bus can be written as
𝑃𝑟𝑠=𝑉𝑟2𝐺𝑟𝑠− 𝑉𝑟 𝑉𝑠 𝐺𝑟𝑠cos 𝛿𝑟𝑠
+ 𝐵𝑟𝑠sin 𝛿𝑟𝑠 (1)
𝑄𝑟𝑠=𝑉𝑟2 ( 𝐵𝑟𝑠 + 𝐵𝑠) + 𝑉𝑟𝑉𝑠 𝐺𝑟𝑠sin 𝛿𝑟𝑠 −
𝐵𝑟
cos𝛿𝑟𝑠 (2)
Where 𝛿𝑟𝑠 = 𝛿𝑟− 𝛿𝑠. Similarly, the real and reactive
power flow from s bus to r bus as
Psr=Vs2Grs+VrVs Grscos δrs
− Brssin δrs (3)
𝑄𝑟𝑠 = −𝑉𝑠2 𝐵𝑟𝑠+ 𝐵𝑠 + 𝑉𝑟𝑉𝑠[𝐺𝑟𝑠sin δ𝑟𝑠
+ 𝐵𝑟𝑠cos δ𝑟𝑠 (4)
Bus-r𝑌𝑟𝑠 = 𝐺𝑟𝑠+ 𝑗𝐵𝑟𝑠 Bus-s
𝑉
𝑟∠
δ
𝑉
𝑠∠
δ
j𝐵𝑠 j𝐵𝑠
Fig(1).Transmission line model
2. TCSC Model
Fig(2).Shows the model of transmission line with TCSC
connected between buses r and s. -jXc is considered as a
static reactance of TCSC, the real and reactive power flow from bus r to s , and from bus s to r of a line having series impedance and a series reactance are[9]:
𝑃
𝑟𝑠𝑇𝐶𝑆𝐶= 𝑉
𝑟2𝐺
𝑟𝑠′− 𝑉
𝑟𝑉
𝑠𝐺
𝑟𝑠′cos δ
𝑟𝑠+ 𝐵
𝑟𝑠′sin δ
𝑟𝑠
(5)
𝑄
𝑟𝑠𝑇𝐶𝑆𝐶= −𝑉
𝑟2𝐵
𝑟𝑠′+ 𝐵
𝑠− 𝑉
𝑟𝑉
𝑠[𝐺
𝑟𝑠′sin δ
𝑟𝑠− 𝐵
𝑟𝑠′cos 𝛿
𝑟𝑠
] (6)
𝑃
𝑠𝑟𝑇𝐶𝑆𝐶= 𝑉
𝑠2
𝐺
𝑟𝑠′− 𝑉
𝑟𝑉
𝑠[𝐺
𝑟𝑠′cos δ
rs−
B
rs′sin δ
rs
]
(7)
𝑄
𝑠𝑟𝑇𝐶𝑆𝐶= 𝑉
𝑠2
𝐵
𝑟𝑠′+ 𝐵
𝑠− 𝑉
𝑟𝑉
𝑠𝐺
𝑟𝑠′sin δ
𝑟𝑠− 𝐵
𝑟𝑠′cos δ
𝑟𝑠(8)
Where
𝐺
𝑟𝑠′=
𝑟𝑟𝑠𝑟𝑟𝑠2+(𝑥𝑟𝑠−𝑥𝑐)2
&
𝐵
𝑟𝑠′=
−(𝑥𝑟𝑠−𝑥𝑐)𝑟𝑟𝑠2+(𝑥𝑟𝑠−𝑥𝑐)2
Bus-r
𝑍
𝑟𝑠= 𝑟
𝑟𝑠+ 𝑗𝑥
𝑟𝑠− 𝑗𝑥
𝑐Bus-s
𝑉
𝑟∠
δ
𝑉
𝑠∠
δ
jBsh jBsh
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Bus-r 𝑟𝑟𝑠 + 𝑗𝑥𝑟𝑠 Bus-s
𝑆𝑟𝑠𝑇𝐶𝑆𝐶
𝑆
𝑠𝑠𝑇𝐶𝑆𝐶Fig3.Injection model of TCSC
The change in the line flow‟ due to series capacitance can be represented as a line without series capacitance with power injected the receiving and sending ends of the line as shown in fig(3). The real and reactive power injects at r and s can be written as
𝑃
𝑟𝑇𝐶𝑆𝐶= 𝑉
𝑟2∆𝐺
𝑟𝑠− 𝑉
𝑟𝑉
𝑟[∆𝐺
𝑟𝑠𝑐𝑜𝑠δ
𝑟𝑠+ ∆𝐵
𝑟𝑠𝑠𝑖𝑛δ
𝑟𝑠] (9)
𝑃
𝑠𝑇𝐶𝑆𝐶= 𝑉
𝑠2
∆𝐺
𝑟𝑠− 𝑉
𝑟𝑉
𝑠[∆𝐺
𝑟𝑠𝑐𝑜𝑠δ
𝑟𝑠−
∆𝐵
𝑟𝑠𝑠𝑖𝑛δ
𝑟𝑠] (10)
𝑄
𝑟𝑇𝐶𝑆𝐶= −𝑉
𝑟2∆𝐵
𝑟𝑠− 𝑉
𝑟𝑉
𝑠∆𝐺
𝑟𝑠𝑠𝑖𝑛δ
𝑟𝑠− ∆𝐵
𝑟𝑠𝑐𝑜𝑠δ
𝑟𝑠(11)
𝑄
𝑠𝑇𝐶𝑆𝐶= −𝑉
𝑠2∆𝐵
𝑟𝑠
− 𝑉
𝑠𝑉
𝑟∆𝐺
𝑟𝑠𝑠𝑖𝑛δ
𝑟𝑠+ ∆𝐵
𝑟𝑠𝑐𝑜𝑠δ
𝑟𝑠(12)
Where
∆𝐺𝑟𝑠
=
𝑟 𝑥𝑐𝑟𝑟𝑠(𝑥𝑐−2𝑥𝑟𝑠) 𝑟𝑠2+𝑥 𝑟𝑠 2 (𝑟
𝑟𝑠 2+𝑥
𝑟𝑠−𝑥𝑐 2)and
∆𝐵
𝑟𝑠=
−𝑥
𝑐(𝑟
𝑟𝑠2− 𝑥
𝑟𝑠2
+ 𝑥
𝑐𝑥
𝑟𝑠)𝑟
𝑟𝑠2+ 𝑥
𝑟𝑠2
(𝑟
𝑟𝑠2+ 𝑥
𝑟𝑠− 𝑥
𝑐 2)
3.UPFC Model
The model of UPFC placed in line k connected between bus r and bus s is shown in fig(4).It has three controlled parameters namely, the magnitude and the angle of inserted
voltage(𝑉𝑇, ∅𝑇) and the magnitude of the current(Iq).Based
on principle of UPFC and the vector diagram, the basic mathematical relations given as
𝑉
𝑟′= 𝑉
𝑟
+ 𝑉
𝑇, 𝐴𝑟𝑔 𝐼
𝑞= 𝐴𝑟𝑔 𝑉
𝑟±
𝜋
2
,
𝐴𝑟𝑔 𝐼
𝑇= 𝐴𝑟𝑔 𝑉
𝑟𝑎𝑛𝑑 𝐼
𝑇= 𝑅𝑒
[𝑉𝑇𝐼𝑟∗]𝑉𝑟
(13)
The power flow equations from r- bus to s- bus and from s-bus to r-bus can be written as
𝑆
𝑟𝑠= 𝑃
𝑟𝑠+ 𝑗𝑄
𝑟𝑠= 𝑉
𝑟𝐼
𝑟𝑠∗= 𝑉
𝑟(𝑗𝑉
𝑟 𝐵2
+ 𝐼
𝑇+
𝐼
𝑞+ 𝐼
𝑟′)
∗(14
)
𝑆
𝑠𝑟= 𝑃
𝑠𝑟+ 𝑗𝑄
𝑠𝑟= 𝑉
𝑠𝐼
𝑠𝑟∗=
𝑉
𝑠𝑗𝑉
𝑠𝐵
2
− 𝐼
𝑟′ ∗
(15)
The active and reactive power flow in the line with UPFC can be written as
𝑃
𝑟𝑠𝑈𝑃𝐹𝐶= 𝑉
𝑟2
+ 𝑉
𝑇2𝑔
𝑟𝑠+ 2𝑉
𝑟𝑉
𝑇𝑔
𝑟𝑠cos ∅
𝑇− 𝛿
𝑟− 𝑉
𝑠𝑉
𝑇𝑔
𝑟𝑠cos ∅
𝑇− δ
𝑠− 𝑏
𝑟𝑠sin ∅
𝑇− δ
𝑠− 𝑉
𝑟𝑉
𝑠𝑔
𝑟𝑠cosδ
rs+ b
rssinδ
rs16
𝑃
𝑠𝑟𝑈𝑃𝐹𝐶= 𝑉
𝑠2𝑔
𝑟𝑠− 𝑉
𝑠𝑉
𝑇𝑔
𝑟𝑠cos ∅
𝑇− δ
𝑠− 𝑏
𝑟𝑠sin ∅
𝑇− δ
𝑠− 𝑉
𝑟𝑉
𝑠𝑔
𝑟𝑠𝑐𝑜𝑠δ
𝑟𝑠− 𝑏
𝑟𝑠𝑠𝑖𝑛δ
𝑟𝑠(17)
𝑄
𝑟𝑠𝑈𝑃𝐹𝐶= −𝑉
𝑟
𝐼
𝑞− 𝑉
𝑟2𝑏
𝑟𝑠+
𝐵
2
− 𝑉
𝑟𝑉
𝑇[𝑔
𝑟𝑠𝑠𝑖𝑛 ∅
𝑇− δ
𝑠+ 𝑏
𝑟𝑠+
𝐵
2
cos ∅
𝑇− δ
𝑟]
− 𝑉
𝑟𝑉
𝑠𝑔
𝑟𝑠𝑠𝑖𝑛δ
𝑟𝑠− 𝑏
𝑟𝑠𝑐𝑜𝑠δ
𝑟𝑠(18)
𝑄
𝑠𝑟𝑈𝑃𝐹𝐶= −𝑉
𝑠2
𝑏
𝑟𝑠+
𝐵2
+ 𝑉
𝑠𝑉
𝑇𝑔
𝑟𝑠sin ∅
𝑇−
δ𝑠+𝑏𝑟𝑠cos∅∅𝑇−δ𝑟+𝑉𝑟𝑉𝑠
(
𝑔𝑟𝑠𝑠𝑖𝑛δ𝑟𝑠+𝑏𝑟𝑠𝑐𝑜𝑠
δ
𝑟𝑠) (19)
Where
𝑔
𝑟𝑠=
𝑟𝑟𝑠(𝑟𝑟𝑠2+𝑥𝑟𝑠2)and
𝑏
𝑟𝑠=
𝑥
𝑟𝑠(𝑟
𝑟𝑠2+ 𝑥
𝑟𝑠2
)
UPFC
𝐵𝑢𝑠 𝑟 𝑟
𝑉
𝑟𝑠+ 𝑥
𝑟𝑠Bus-s
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𝑰
𝒓𝑰
𝒓′𝑉
𝑟∠δ
𝑟𝐼
𝑞𝐼
𝑇𝑗
𝐵2
j
𝐵2
𝑉
𝑠∠ δ
𝑠V
sδ
Fig4.Model of UPFC.
𝐵𝑢𝑠 − 𝑟 𝑌
𝑟𝑠= 𝑔
𝑟𝑠+ 𝑗𝑏
𝑟𝑠Bus-s
𝑆
𝑟𝑈𝑃𝐹𝐶𝑆
𝑠𝑈𝑃𝐹𝐶Fig5.Injection model of UPFC.
The injected active and reactive powers at r and bus-s with UPFC can be written abus-s
𝑃
𝑟𝑈𝑃𝐹𝐶= −𝑉
𝑇2𝑔
𝑟𝑠
− 2𝑉
𝑟𝑉
𝑇𝑔
𝑟𝑠cos ∅
𝑇− δ
𝑟+ 𝑉
𝑠𝑉
𝑇𝑔
𝑟𝑠cos ∅
T− δ
𝑠+ 𝑏
𝑟𝑠sin ∅
𝑇− δ
𝑠(20)
𝑃
𝑠𝑈𝑃𝐹𝐶= 𝑉
𝑠
𝑉
𝑇𝑔
𝑟𝑠cos ∅
𝑇− δ
𝑠− 𝑏
𝑟𝑠sin ∅
𝑇− δ
𝑠(21)
𝑄
𝑟𝑈𝑃𝐹𝐶= 𝑉
𝑟𝐼
𝑞+ 𝑉
𝑟𝑉
𝑇[𝑔
𝑟𝑠sin ∅
𝑇− δ
𝑟+ 𝑏
𝑟𝑠+
𝐵
2
cos ∅
𝑇− δ
𝑟( 22)
𝑄
𝑠𝑈𝑃𝐹𝐶= −𝑉
𝑠
𝑉
𝑇[𝑔
𝑟𝑠sin ∅
𝑇− δ
𝑠+ 𝑏
𝑟𝑠cos ∅
𝑇− 𝛿
𝑠(23)
4. SVC Model
The model of Static Var compensator(SVC) is shunt
connected Static Var generator or absorber with the Qvas
shown in fig(6).
Bus-r
𝑉
𝑟𝐼
𝑆𝑉𝐶𝐵
𝑆𝑉𝐶Fig(6). Susceptance model of SVC
The reactive power drawn by the SVC,which is also the reactive power injected at bus-r is
𝑄
𝑆𝑉𝐶= − 𝑉
𝑟2𝐵
𝑆𝑉𝐶(24)
III. PROBLEM FORMULATION
1.0 Placements of FACTS Devices
The location of FACTS Devices are obtained on the basis of Static and/or dynamic performances. There are several methods for finding the placements FACTS devices, in this paper Voltage Stability Index(L-index) method is used for finding the location ofFACTS Devices.
1.1 Voltage Stability Index(VSI):
Consider the power system network having „n‟ total number of buses with 1,2,….g generator buses and g+1,……n remaining n-g buses. For given operating condition, using load flow results the voltage stability index „L‟can be calculated as
𝐿
𝑗= 1 − 𝐹
𝑗𝑖𝑉
𝑖𝑉
𝑗𝑔
𝑖=1
(25)
Where j=g+1,…. .n and all the terms inside the sigma on the right hand side of above eq.(25) are complex
quantities.The complex values ofFij are obtained from the
Y-bus matrix of power system for given operating condition.
𝐼
𝐺𝐼
𝐿=
𝑌
𝐺𝐺𝑌
𝐺𝐿𝑌
𝐿𝐺𝑌
𝐿𝐿𝑉
𝐺𝑉
𝐿(26)
Where,𝐼𝐺, 𝐼𝐿 and 𝑉𝐺, 𝑉𝐿 represents complex currents and
International Journal of Emerging Technology and Advanced Engineering
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136 𝑌𝐺𝐺 , 𝑌𝐿𝐺 , 𝑌𝐿𝐿 and 𝑌𝐿𝐺 are corresponding portioned
portion of network. Y-bus matrix rearranging the above equation(26) we get
𝑉
𝐿𝐼
𝐺=
𝑍
𝐿𝐿𝐹
𝐿𝐺𝐾
𝐺𝐿𝑌
𝐺𝐺𝐼
𝐿𝐼
𝐺(27)
Where 𝐹𝐿𝐺 = − 𝑌𝐿𝐿 −1 𝑌𝐿𝐺 . 𝐹𝑗𝑖 are the complex
elements of [FLG] matrix, this analysis carried out only for
the load buses. For stability the index „L‟ must not be more than one for any of the nodes j. The index for away from1 and closes to 0 indicates improves the voltage stability, ‟L‟ for a given load conditions are calculated for all load buses and the maximum of the „L‟ indices gives the proximity of the system to voltage collapse.
2.0 Objective Function
The main aim of this work is to minimize theover all cost function consisting of generating cost and FACTS devices investment cost as well as the system real power loss, and at the same time, some constraints including entire power flow equations,generation limits,voltage ranges and the variable parameters of FACTS devicesetc.. has to be satisfied. The generation cost typically is considered as quadratic function, the OPF problem can be formulated as
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑎
𝑖𝑃
𝑔𝑖2+ 𝑏
𝑖𝑃
𝑔𝑖+ 𝑐
𝑖$/𝑟 28
Subject to:
Equivalent constraints:
𝑃𝑔𝑖 − 𝑃𝑑𝑖 − 𝑉𝑖𝑉𝑗𝑌𝑖𝑗cos ∅𝑖𝑗 + δ𝑖− δ𝑗 = 0 𝑁
𝑗 =1
𝑄𝑔𝑖− 𝑄𝑑𝑖 − 𝑉𝑖𝑉𝑗𝑌𝑖𝑗 sin ∅𝑖𝑗 + δ𝑖 − δ𝑗 = 0 𝑁
𝑗 =1
𝑃
𝑟𝑠𝑠𝑝𝑒𝑐− 𝑃
𝑟𝑠= 0
Inequality constraints
𝑃
𝑔𝑖𝑚𝑖𝑛≤ 𝑃
𝑔𝑖≤ 𝑃
𝑔𝑖𝑚𝑎𝑥∀𝑖 Ԑ 𝑁𝐺
𝑄
𝑔𝑖𝑚𝑖𝑛≤ 𝑄
𝑔𝑖
≤ 𝑄
𝑔𝑖𝑚𝑎𝑥∀𝑖 Ԑ 𝑁𝐺
𝑉
𝑖𝑚𝑖𝑛≤ 𝑉
𝑖≤ 𝑉
𝑖𝑚𝑎𝑥∀𝑖 Ԑ 𝑁
δ
𝑖𝑗𝑚𝑖𝑛≤ δ
𝑖𝑗≤ δ
𝑖𝑗𝑚𝑎𝑥∀𝑖Ԑ 𝑁
Where 𝐼𝐶 (𝑓) is the installation investment cost of
FACTS devices in𝑈𝑆$ 𝑟
𝐼𝐶 𝑓 =
𝐶(𝑓)
8760(5)
𝑈𝑆$/𝑟 (30)
C(f) investment cost of FACTS controllers are in
US$.They must be unified in to $ 𝑟.Normally the
FACTS controllers will be service in many years. How ever only the part of life time is employed to regulate the power flow.In this paper 5 years is employed to evaluate cost function.
𝐶 𝑓 = 𝐶
𝐹𝐴𝐶𝑇𝑆∗ 𝑆 ∗ 1000 𝑈𝑆$ (31)
𝐶𝐹𝐴𝐶𝑇𝑆 is the cost functions of TCSC SVC and UPFCare developed as follows[3]:
𝐶
𝑆𝑉𝐶= 0.0003𝑆
2− 0.3051𝑆
+ 127.38
𝑈𝑆$
𝐾𝑉𝑎𝑟
(32)
𝐶
𝑇𝐶𝑆𝐶= 0.0015𝑆
2− 0.7130𝑆
+ 153.75
𝑈𝑆$
𝐾𝑉𝑎𝑟
(33)
𝐶
𝑈𝑃𝐹𝐶= 0.0003𝑆
2− 0.2691𝑆
+ 188.22
𝑈𝑆$
𝐾𝑉𝑎𝑟
(34)
3.0 ParticleSwarm Optimization(PSO)
PSO is a population based stochastic optimization technique developed by Dr.Eberhart and Dr.Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling. It applicable to solving a number of problems where local methods fail or their usage is in-effective, as in this case. One of the most important features of PSO is the ability of optimizing large complex multi-criteria combinatorial problems where the problem with the design of criteria function occurs, forexample, it is hard to derive or is not continuous.
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maximum and minimum values, toward the current optimal position. The particle has its direction and speed of movement but it can also randomly decide to move the best position.Each particle keepsof its coordinates in the problem space which are associated with the best solution it has achieved so far. This value is called Pbest. Another „best „value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the neighbors of the particle. When the particle takes all the population as its topological neighbors, the best value is a global best and is called gbest.
The PSO changes the velocity of each particle towards its pbest and gbest at each time step. The movement is weighted by a separated random number which is generated for acceleration toward the pbest and gbest.
3.1 Implementation of PSO
The search procedure of the proposed method for solving optimal power flow problem is described as follows:
Let Xi=(xi1,xi2,……,xid) and Vi=(vi1,vi2,….,vid) are the
position vector and the velocity vector respectively in d dimensions search space,then according to a fitness
function,where Pi=(pi1,pi2,….,pid) is the pbest vector and
Pg=(pg1,pg2,….,pgd) is the gbest vector,i.e the fittest particle
of pi.
Step1:Read the system input data which consisting of fuel cost curve coefficients, active power generation limits, load demands, voltage limits and lower and upper limits FACTS devices.
Step2: Initialize the particles of the population in a random manner according to the limits of each unit including individual dimensions, search points and velocities. These initial particles must be feasible solution that satisfies the particle operating constraints.
Step3: Calculate the cost value Ct for each individual Pg
in the population.
Step4:Compare the cost of each particle with that of its p
best. If the new cost value for Pg is less than that obtained
with pbest,then replace the co-ordinates of pbest with the
present co-ordinates of Pg .
Step5:Compare the cost values of PBestof all particles to
determine the best particle,store the co-ordinates of the best
particle as GBest.
Step6:Modify the member velocity of each particle according to following equation:
𝑉
𝑖𝑑𝑘+1= 𝜔𝑉
𝑖𝑑𝑘+ 𝐶
1∗ 𝑟𝑎𝑛𝑑1 ∗ 𝑃
𝑖𝑑− 𝑋
𝑖𝑑𝑘+ 𝐶
2∗ 𝑟𝑎𝑛𝑑2 ∗ 𝑃
𝑔𝑑− 𝑋
𝑖𝑑𝑘30
Where
𝜔 = 𝜔
𝑚𝑎𝑥−
(𝜔𝑚𝑎𝑥−𝜔𝑚𝑖𝑛)𝑖𝑡𝑒𝑟𝑚𝑎𝑥
𝑖𝑡𝑒𝑟
Step7:Modify the member current position (searching point) of each particle according to the equation(31)
𝑋
𝑖𝑑𝑘 +1= 𝑋
𝑖𝑑𝑘+ 𝑉
𝑖𝑑𝑘 +1(31)
Step8:If the number of iterations reaches the maximum, then go to step9 otherwise, go to step3.
Step9:The particle that generates the latest Gbest is the optimal solution of the given problem.
In this paper, the parameters used PSO are as follows:
Table1.
PSO parameters and their setting values.
PSO Parameter Setting
values
Papulation size 20
Number of generations 100
Initial weight function (𝜔𝑚𝑎𝑥) 0.9
Final weight function (𝜔𝑚𝑖𝑛) 0.4
Acceleration constants (𝐶1 𝑎𝑛𝑑 𝐶2 2
IV. NUMERICAL RESULTS
In this section, a standard 5bus system and IEEE 30 bus system[4]has been considered to demonstrate the effectiveness and robustness of PSO(proposed algorithm) with and without FACTS devices(i.e TCSC,SVC and UPFC).In 30bus system, bus 1 considered as slack bus, while buses 2,35,8,11 and 13 buses are generator buses and the remaining buses are load buses .A MATLAB program is implemented for the test system on personal computer with Intel Pentium dual core 2.4Ghz processor and 512MB RAM,7 runs have been performed for the test system. The optimal solution results over seven runs have been tabulated. The input parameters of PSO for the system are given table(1).
The optimal power flow solution i.e active power generation, power loss, voltage magnitude and generation cost for 5 bus and IEEE 30 bus system of proposed method with out and with SVC,TCSC and UPFC are calculated.
Table2.
Voltage profile of ieee 5 bus test systemwith and with out FACTS devices:
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No. case in p.u
out device in p.u
in p.u
TCSC SVC UPFC
1 1.0600 1.0600 1.0600 1.0600 1.0600
2 1.0000 1.0000 1.0000 1.0000 1.0000
3 0.9872 0.9874 0.9888 0.9981 1.0000
4 0.9841 0.9843 0.9827 0.9928 0.9878
5 0.9717 0.9717 0.9711 0.9746 0.9728
6 - - 0.9855 - 0,9919
Table3.
Summery of test Results of IEEE 5 bus test system:
Parameter Base case
OPF with PSO
OPF with FACTS Devices PSO
TCSC SVC UPFC
PG1 in MW 131.122
2 82.9232 82.8521 82.9122 82.8029
PG2 in MW 40.0 87.4548 87.5182 87.4037 87.4900
Total Generation in MW
171.122 2
170.378 0
170.370
3 170.3159 170.2930
Total losses
in MW 6.12 5.38 5.37 5.32 5.29
Total generation cost in $/hr
785.543
8 765.902
765.873
1 765.6451 760.5541
Fig7:Convergence characteristics of fitness function for ieee 5bus opf with out FACTS Devices.
Fig8:Convergence characteristics of fitness function for ieee 5bus opf with TCSC
0 10 20 30 40 50 60 70 80 90 100
771.28 771.285 771.29 771.295 771.3 771.305 771.31 771.315 771.32 771.325 771.33
No. of Generations
F
it
n
e
s
s
v
a
lu
e
0 10 20 30 40 50 60 70 80 90 100
771.2 771.25 771.3 771.35 771.4 771.45 771.5 771.55 771.6 771.65 771.7
No.ofGenerations
F
it
n
e
s
s
v
a
lu
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Fig9:Convergence characteristics of fitness function for ieee 5bus opf with SVC
From table (2) & (4), It is clear that the voltage profile has been improved with FACTS devices in most of the buses. It is observed that the highest improvement of voltage profile with UPFC compare to all other devices.
Fig10:Convergence characteristics of fitness function for ieee 5bus opf with UPFC
Table4.
Voltage profile of ieee 30 bus test systemwith and with out FACTS devices:
Bus No.
Base case in
p.u
OPF with out device
in p.u
OPF with FACTS Devices in p.u
TCSC SVC UPFC
1 1.0600 1.0600 1.0600 1.0600 1.0600
2 1.0430 1.0430 1.0430 1.0430 1.0430
3 1.0238 1.0250 1.0248 1.0255 1.0257
4 1.0156 1.0168 1.0166 1.0174 1.0176
5 1.0100 1.0100 1.0100 1.0100 1.0100
6 1.0098 1.0106 1.0103 1.0112 1.0114
7 1.0016 1.0221 1.0019 1.002 1.0026
8 1.0100 1.0100 1.0100 1.0100 1.0100
9 1.0117 1.0127 1.0123 1.0146 1.0153
10 0.9890 0.9902 0.9897 0.9927 0.9936
11 1.0587 1.0594 1.0593 1.0615 1.0621
0 10 20 30 40 50 60 70 80 90 100
771.2 771.25 771.3 771.35 771.4 771.45 771.5 771.55 771.6 771.65 771.7
No. of Generations
F
it
n
e
s
s
v
a
lu
e
0 10 20 30 40 50 60 70 80 90 100
770.5 771 771.5 772 772.5 773 773.5
No.ofGenerations
F
it
n
e
s
s
v
a
lu
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12 1.0099 1.0105 1.0104 1.0129 1.0137
13 1.0420 1.0426 1.0425 1.0449 1.0457
14 0.9929 0.9936 0.9935 0.9963 0.9972
15 0.9868 0.9876 0.9874 0.9905 0.9916
16 0.9929 0.9940 0.9940 0.9964 0.9972
17 0.9848 0.9861 0.9856 0.9886 0.9895
18 0.9747 0.9757 0.9754 0.9785 0.9795
19 0.9709 0.9720 0.9716 0.9747 0.9757
20 0.9746 0.9757 0.9753 0.9784 0.9794
21 0.9755 0.9767 0.9762 0.9799 0.9810
22 0.9759 0.9772 0.9767 0.9805 0.9816
23 0.9724 0.9734 0.9731 0.9775 0.9790
24 0.9622 0.9633 0.9630 0.9690 0.9710
25 0.9653 0.9662 0.9661 0.9781 0.9819
26 0.9466 0.9476 0.9474 0.9597 0.9636
27 0.9764 0.9772 0.9771 0.9928 0.9978
28 0.1004
6 1.0052 1.0052 1.0071 1.0078
29 0.9555 0.9563 0.9564 0.9806 1.0000
30 0.9434 0.9442 0.9438 0.9779 0.9718
31 - - 0.9557 - 0.9882
Table5.
Summery of test Results of ieee30 bus test system:
Parameter Base OPF OPF with FACTS
case with PSO
Devices PSO TCSC SVC UPFC
PG1 in MW 229.6
504
176.5 439
174.39 19
174.2 739
175.27 11
PG2 in MW 20.00 49.96
22
49.375 5
49.34 24
50.033 9
PG3 in MW
15.00 15.00 22.172
4
22.16 02
22.322 3
PG4 in MW 10.00
26.11
98 25.00
25.09 16
22.868 5
PG5 in MW
10.00 13.68 10.00 10.00 10.00
PG6 in MW 12.00 12.00 12.00 12.00 12.327
3
Total Generation
in MW
296.6 504
293.3 059
292.93 98
292.8 681
292.83 21
Total losses
in MW 13.25 9.91 9.54 9.47 9.42
Total generation cost in $/hr
833.5 697
806.0 451
803.36 24
803.1 479
803.14 08
From table(3)&(5), It can be seen that the total active power generation, power loss has been reduced with FACTS devices. It is observed that total power generation, power loss and total cost is a significant reduction with UPFC device compare to TCSC and SVC devices.
V. CONCLUSION
This paper made an attempt to find out the optimal location and parameter settings of TCSC,SVC and UPFC devices to minimize the total power loss,total generation fuel cost and the investment cost of FACTS Devices and maximize the voltage stability of power system using PSO. From the result of IEEE 5 bus and 30 bus systems, it is observed that the minimization of real power losses, total generation cost and maximize the voltage stability of power system UPFC is significantly better than other devices.
REFERENCES
[1] I.OElgrd “Electric Energy System Theory-An Introduction”,McGrawHill Inc., New York,1971.
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[3] K.Habur and.Oleary, “Flexiable AC Transmission system for cost effective and reliable Transmission of Electrical Energy” on line available:http://www.siemenstd.com
[4] Chung T.S.,Li.Y.Z., “ A hybrid GA approach for OPF with consideration of FACTS devices”,IEEE Power Engineering Review,vol.21,No.2, pp-47-57,Feb.2001.
[5] Bansilal,D.Thukaram and K.Parathasarathy, “Optimal reactive power dispatch algorithm for voltage stability improvement”, Electrical power energysyst. Vol.18,No.7,pp 461-468,1996. [6] C.R.Fuerte-Esuivel,E.Acha, “Unified power flow controller: a
critical comparision of Newton-Raphson UPFC algorithms in power flow studies”, IEEE proc-Gener,Transm.Distrib.Vol.144,No.5.Sept.1997
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[8] Cerma.K.s,Singh.S.N,Gupta.H.O ;2001 FACTS Devices location for enhancement of total transfer capability,Power system Engineering society Winter meeting,IEEE Vol.2.pp-522-527.
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Fig11:Voltage profile of ieee 5bus system with and With out FACTS Devices
1 2 3 4 5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
bus numbers
bu
sv
ol
ta
ge
s
5 bus voltage profile
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Fig12:Voltage profile of ieee 30 bus system with and With out FACTS Devices
Acknowledgement
The authors greatly acknowledge the Directors, Principal and Staff of Electrical and Electronics Engineering Department, M.L. Engineering College,Singaraya Konda, Prakasam(Dt.),Andhra Pradesh, India for their continuous support encouragement and the extensive facilities provided to carry out this work.
BIOGRAPHIES
1. K. Venkateswarlu received his B.Tech degree in
Electrical and Electronics Engineering from S.V. University, Tirupati in 1994 and M. Tech Degree in Electrical power systems from J.N.T. University, Hyderabad, A.P. in 1999 and his currently pursing Ph.D degree at JNT University Kakinada, A. P..He has been working as faculty of Electrical & Electronics Engineering. His research interest is in the areas FACTS applications and their control and Power system stability.
0 5 10 15 20 25 30
0 0.2 0.4 0.6 0.8 1 1.2 1.4
bus numbers
bu
sv
ol
ta
ge
s
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2. Dr. CH. SaiBabu received his graduation from Andhra university and Masters from REC, Warangal and Ph.D from JNTU,Hyd. He is the Professor in the Department of Electrical and Electronics Engineering and working as Director(Evaluations) at JNT University, Kakinada. He has about 10 publications in international journals and 44 national and international conferences. He authored a text book, “Elements of Power Electronics” published by S.Chand and Co. He is the member of AICTE team and Member of governing council for various affiliated engineering colleges of JNTU, Kakinada
3.K. Srikanth, received B.Tech Degree from Jawaharlal Nehru Technological University,Hyderabad in 2006 and M.Tech in 2009 from Jawaharlal Nehru Technological University, Anantapur,Anantapuram, Andhra Pradesh, India in the field of Electrical Power Systems and currently working as a Assistant Engineer at APCPDCL, Gooty, Anantapuramu, Andhra Pradesh, India. His fields of Interest are Power Systems, Reliability Engineering, Analysis of Linear Systems, Electric Circuit Analysis and Control Systems.
