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\title{Voltage Profile Augmentation and Minimization of Real Power Loss in Transmission Lines by using Improved Hybrid Particle Swarm Optimization-Based on Harmony Search Algorithm}
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             \author[1]{K.  Lenin}

             \affil[1]{  Jawaharlal Nehru Technological University Kukatpally}

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\date{\small \em Received: 9 December 2013 Accepted: 1 January 2014 Published: 15 January 2014}

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\begin{abstract}
        


In this paper, a new particle swarm search algorithm is proposed to solve the optimal reactive power dispatch (ORPD) Problem. The ORPD problem is formulated as a nonlinear constrained single-objective optimization problem where the real power loss and the bus voltage deviations are to be minimized separately. As an optimization technique, particle swarm optimization (PSO) has obtained much attention during the past decade. It is gaining popularity, especially because of the speed of convergence and the fact that it is easy to realize. To enhance the performance of PSO, an improved hybrid particle swarm optimization (IHPSO) is proposed to solve complex optimization problems more efficiently, accurately and reliably. It provides a new way of producing new individuals through organically merges the harmony search (HS) method into particle swarm optimization (PSO). During the course of evolvement, harmony search is used to generate new solutions and this makes IHPSO algorithm have more powerful exploitation capabilities. In order to evaluate the performance of the proposed algorithm, it has been tested on IEEE 30 bus system.

\end{abstract}


\keywords{modal analysis, optimal reactive power, transmission loss, particle swarm, harmony search metaheuristic.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
n recent years the optimal reactive power dispatch (ORPD) problem has received great attention as a result of the improvement on economy and security of power system operation. Solutions of ORPD problem aim to minimize object functions such as fuel cost, power system loses, etc. while satisfying a number of constraints like limits of bus voltages, tap settings of transformers, reactive and active power of power resources and transmission lines and a number of controllable Variables \hyperref[b0]{[ 1,}\hyperref[b1]{2]}. In the literature, many methods for solving the ORPD problem have been done up to now. At the beginning, several classical methods such as gradient based \hyperref[b2]{[3]}, interior point \hyperref[b3]{[4]}, linear programming \hyperref[b4]{[5]} and quadratic programming \hyperref[b5]{[6]} have been successfully used in order to solve the ORPD problem. However, these methods have some disadvantages in the Process of solving the complex ORPD problem. Drawbacks of these algorithms can be declared insecure convergence properties, long execution time, and algorithmic complexity. Besides, the solution can be trapped in local minima \hyperref[b0]{[1,}\hyperref[b6]{7]}. In order to overcome these disadvantages, researches have successfully applied evolutionary and heuristic algorithms such as Genetic Algorithm (GA) \hyperref[b1]{[2]}, Differential Evolution (DE) \hyperref[b7]{[8]}, Particle Swarm Optimization (PSO) \hyperref[b8]{[9]} and harmony search algorithms \hyperref[b9]{[10]}\hyperref[b10]{[11]}.This paper formulates the reactive power dispatch as a multi-objective optimization problem with loss minimization and maximization of static voltage stability margin (SVSM) as the objectives. Voltage stability evaluation using modal analysis \hyperref[b11]{[12]} is used as the indicator of voltage stability. Function optimization has received extensive research attention, and several optimization algorithm such as neural networks \hyperref[b12]{[13]}, evolutionary algorithms \hyperref[b13]{[14]}, genetic algorithms \hyperref[b14]{[15]} and swarm intelligence-based algorithms \hyperref[b15]{[16]}\hyperref[b16]{[17]} have been developed and applied successfully to solve a wide range of complex optimization problems. Most stochastic optimization algorithms including particle swarm optimizer (PSO) \hyperref[b17]{[18,}\hyperref[b18]{19]} and genetic algorithm (GA) \hyperref[b14]{[15]} have shown inadequate to complex optimization problems, as they rapidly push an artificial population toward convergence. That is, all individuals in the population soon become nearly identical. To improve PSO performance, several methods have been proposed. Many of these methods concerned predefining numerical coefficients, consisting of the maximum velocity, inertia weight, social factor and individual factor, which can affect various characteristics of the algorithm, such as convergence rate or the ability of global optimization. Recently, some hybrid I Global Journal of Researches in Engineering ( ) methods. NM-PSO (Nelder-Mead-PSO) \hyperref[b19]{[20]} comprises NM method at the top of level, and PSO at the lower level. CPSO (Chaotic PSO) \hyperref[b20]{[21]} applies PSO to perform global exploration and chaotic local search to perform local search on the solutions produced in the global exploration process. These methods can equip PSO with extra facilities. In this paper, an improved PSO (IPSO) based of harmony search (HS) \hyperref[b21]{[22,}\hyperref[b22]{23]} is proposed to solve complex optimizations. The PSO algorithm includes some tuning parameters that greatly influence the algorithm performance, often stated as the exploration-exploitation trade off: Exploration is the ability to test various regions in the problem space in order to locate a good optimum, hopefully the global one. Exploitation is the ability to concentrate the search around a promising candidate solution in order to locate the optimum precisely.\par
Facing complicated optimizations, it's difficult to explore every possible region of the search space. Recently, harmony search (HS) algorithm imitates the improvisation process of music players and had been very successful in a wide variety of optimization problems \hyperref[b23]{[24]}\hyperref[b24]{[25]}, presenting several advantages with respect to traditional optimization techniques such as the following \hyperref[b23]{[24]}:(a) HS algorithm imposes fewer mathematical requirements and does not require initial value settings of the decision variables. ( b) As the HS algorithm uses stochastic random searches, derivative information is also unnecessary. (c) The HS algorithm generates a new vector, after considering all of the existing vectors, whereas the genetic algorithm (GA) only considers the two parent vectors. These features increase the flexibility of the HS algorithm and produce better solutions. In this study, one of the ways of integrating the concepts of these two optimization algorithms for solving complex optimization problems is explored. The performance of IHPSO has been evaluated in standard IEEE 30 bus test system and the results analysis shows that our proposed approach outperforms all approaches investigated in this paper. 
\section[{II.}]{II.} 
\section[{Voltage Stability Evaluatio a) Modal analysis for voltage stability evaluation}]{Voltage Stability Evaluatio a) Modal analysis for voltage stability evaluation}\par
The linearized steady state system power flow equations are given by. Î?"V = Incremental change in bus voltage Magnitude J p? , J PV , J Q? , J QV jacobian matrix are the sub-matrixes of the System voltage stability is affected by both P and However at each operating point we keep P constant and evaluate voltage stability by considering incremental relationship between and V.? ??? ??? ? = ? ?? ???? ?? ???? ?? ???? ?? ???? ?\textbf{(1)}\par
To reduce \hyperref[b0]{(1)}, let Î?"P = 0 , then.?Q = ?J QV ? J Q? J P? ?1 J PV ??V = J R ?V (2) ?V = J ?1 ? ?Q\textbf{(3)}\par
WhereJ R = ?J QV ? J Q? J P? ?1 JPV?\textbf{(4)}\par
J R is called the reduced Jacobian matrix of the system. 
\section[{a) Modes of Voltage instability}]{a) Modes of Voltage instability}\par
Voltage Stability characteristics of the system can be identified by computing the eigen values and eigen vectorsLet J R = ???\textbf{(5)}\par
Where,? = right eigenvector matrix of J R ? = left eigenvector matrix of J R ? = diagonal eigenvalue matrix of J R and J R ?1 = ?? ?1 ?\textbf{(6)}\par
From ( \hyperref[formula_1]{3}) and ( \hyperref[formula_4]{6}), we have?V = ?? ?1 ??Q\textbf{(7)}\par
or?V = ? ? i ? i ? i I ?Q\textbf{(8)}\par
Where ? i is the ith column right eigenvector and ? the ith row left eigenvector of J R . ? i is the ith eigen value of J R . The ith modal reactive power variation is,?Q mi = K i ? i\textbf{(9)}\par
where,K i = ? ? ij 2 j ? 1\textbf{(10)}\par
Where? ji is the jth element of ? i\par
The corresponding ith modal voltage variation is?V mi = [1 ? i ? ]?Q mi\textbf{(11)}\par
In \hyperref[b7]{(8)}, let Î?" = e k where e k has all its elements zero except the kth one being 1. Then,Global Journal of Researches in Engineering ( ) Q Q. Q Q ?V = ? ? 1k ? 1 ? 1 i (12) ? 1k k th element of ? 1 V -Q sensitivity at bus k ?V K ?Q K = ? ? 1k ? 1 ? 1 i = ? P ki ? 1 i (13) III. 
\section[{PROBLEM FORMULATION}]{PROBLEM FORMULATION}\par
The objectives of the reactive power dispatch problem considered here is to minimize the system real power loss and maximize the static voltage stability margins (SVSM). 
\section[{a) Minimization of Real Power Loss}]{a) Minimization of Real Power Loss}\par
Minimization of the real power loss (Ploss) in transmission lines of a power system is mathematically stated as follows.P loss = ? g k(V i 2 +V j 2 ?2V i V j cos ? ij ) n k=1 k=(i,j) (\textbf{14})\par
Where n is the number of transmission lines, g k is the conductance of branch k, V i and V j are voltage magnitude at bus i and bus j, and ?ij is the voltage angle difference between bus i and bus j. 
\section[{b) Minimization of Voltage Deviation}]{b) Minimization of Voltage Deviation}\par
Minimization of the Deviations in voltage magnitudes (VD) at load buses is mathematically stated as follows.Minimize VD = ? |V k ? 1.0| nl k=1 (15)\par
Where nl is the number of load busses and V k is the voltage magnitude at bus k. 
\section[{c) System Constraints}]{c) System Constraints}\par
In the minimization process of objective functions, some problem constraints which one is equality and others are inequality had to be met. Objective functions are subjected to these constraints shown below. 
\section[{Load flow equality constraints:}]{Load flow equality constraints:}?? ???? -?? ???? ? ?? ?? ? ?? ?? ???? ?? =1 ? ?? ???? cos ?? ???? +?? ???? sin ?? ???? ? = 0, ?? = 1,2 ? . , ???? (16) ?? ???? ? ?? ???? ?? ?? ? ?? ?? ???? ?? =1 ? ?? ???? cos ?? ???? +?? ???? sin ?? ???? ? = 0, ?? = 1,2 ? . , ???? (17)\par
where, nb is the number of buses, P G and Q G are the real and reactive power of the generator, P D and Q D are the real and reactive load of the generator, and G ij and B ij are the mutual conductance and susceptance between bus i and bus j.\par
Generator bus voltage (V Gi ) inequality constraint?? ???? ?????? ? ?? ???? ? ?? ???? ?????? , ?? ? ????\textbf{(18)}\par
Load bus voltage (V Li ) inequality constraint?? ???? ?????? ? ?? ???? ? ?? ???? ?????? , ?? ? ????\textbf{(19)}\par
Switchable reactive power compensations (Q Ci ) inequality constraint:?? ???? ?????? ? ?? ???? ? ?? ???? ?????? , ?? ? ????\textbf{(20)}\par
Reactive power generation (Q Gi ) inequality constraint:?? ???? ?????? ? ?? ???? ? ?? ???? ?????? , ?? ? ????\textbf{(21)}\par
Transformers tap setting (T i ) inequality constraint:?? ?? ?????? ? ?? ?? ? ?? ?? ?????? , ?? ? ????\textbf{(22)}\par
Transmission line flow (S Li ) inequality constraint:?? ???? ?????? ? ?? ???? ?????? , ?? ? ????\textbf{(23)}\par
Where, nc, ng and nt are numbers of the switchable reactive power sources, generators and transformers.\par
IV. 
\section[{STANDARD PSO}]{STANDARD PSO}\par
PSO is a population-based, co-operative search meta-heuristic introduced by Kennedy and Eberhart. The fundament for the development of PSO is hypothesis that a potential solution to an optimization problem is treated as a bird without quality and volume, which is called a particle, coexisting and evolving simultaneously based on knowledge sharing with neighbouring particles. While flying through the problem search space, each particle modifies its velocity to find a better solution (position) by applying its own flying experience (i.e. memory having best position found in the earlier flights) and experience of neighbouring particles (i.e. best-found solution of the population). Particles update their positions and velocities as shown below:?? ??+1 ?? = ð??"ð??" ?? . ?? ?? ?? + ?? 1 . ?? 1 . ??? ?? ?? ? ?? ?? ?? ? + ?? 2 . ?? 2 . ??? ?? ?? ? ?? ?? ?? ? (24) ?? ??+1 ?? = ?? ?? ?? + ?? ??+1 ??\textbf{(25)}\par
Where ?? ?? ?? represents the current position of particle i in solution space and subscript t indicates an iteration count; ?? ?? ?? is the best-found position of particle i up to iteration count t and represents the cognitive contribution to the search velocity ?? ?? ?? . Each component of ?? ?? ?? can be clamped to the range to control excessive roaming of particles outside the search space; ?? ?? ?? is the global best-found position among all particles in the swarm up to iteration count t and forms the social contribution to the velocity vector; ?? 1 and ?? 2 are random numbers uniformly distributed in the interval (0,1), where?? 1 and?? 2 are the cognitive and social scaling parameters, respectively;ð??"ð??" ?? is the particle inertia, which is reduced dynamically to decrease the search area in a gradual fashion \hyperref[b24]{[25]}. The variable ð??"ð??" ?? is updated as 
\section[{Global Journal of Researches in Engineering (}]{Global Journal of Researches in Engineering (}\par
)ð??"ð??" ?? = (ð??"ð??" ?????? ? ð??"ð??" ?????? ). (?? ?????? ???) ?? ?????? + ð??"ð??" ??????\textbf{(26)}\par
Whereð??"ð??" ?????? and ð??"ð??" ?????? denote the maximum and minimum of ð??"ð??" ?? respectively; ?? ?????? is a given number of maximum iterations. Particle i fly toward a new position according to Eq. (  {\ref 24}) and \hyperref[b24]{(25)}. In this way, all particles of the swarm find their new positions and apply these new positions to update their individual best ?? ?? ?? points and global best ?? ?? ?? of the swarm. This process is repeated until termination conditions are met.\par
V. 
\section[{HARMONY SEARCH}]{HARMONY SEARCH}\par
Harmony search (HS) algorithm is based on natural musical performance processes that occur when a musician searches for a better state of harmony, such as during jazz improvisation. The engineers seek for a global solution as determined by an objective function, just like the musicians seek to find musically pleasing The steps in the procedure of harmony search are as follows:\par
Step 1: Initialize the problem and algorithm parameters.\par
Step 2: Initialize the harmony memory (HM).\par
Step 3: Improvise a new harmony from the HM.\par
Step 4: Update the HM.\par
Step 5: Repeat Steps 3 and 4 until the termination criterion is satisfied. 
\section[{VI. THE REALIZATION OF IHPSO BASED OF HS}]{VI. THE REALIZATION OF IHPSO BASED OF HS}\par
This section describes the implementation of proposed improvement in PSO using HS approach. The proposed method, called, IHPSO (improved hybrid particle swarm optimization) is based on the common characteristics of both PSO and HS algorithms. HS algorithm provides a new way to produce new particles. Different from PSO and GA, HS algorithm generates a new vector after considering all of the existing vectors. HS algorithm can produce new solution and the parameters of HMCR and PAR are introduced to allow the solution to escape from local optima and to improve the global optimum prediction of the algorithm. Enlightened by this, the HS realization concept has been used in the PSO in this paper to exploration the potential solution space. In summary?the realization of improved PSO algorithm for solving reactive power dispatch is described as follows:\par
Step 1: Initializing the parameters of PSO and HS;\par
Step 2: Initailizing the particles;\par
Step 3: Evaluating particles according to their fitness then descending sort them;\par
Step 4: Performing HS and generating a new solution;\par
Step 5: If the new solution is better than the worst particle then replacing it with the new one;\par
Step 6: Update the particles by using equation's (  {\ref 24}) \& \hyperref[b24]{(25)} Step 7: The program is finished if the terminations conditions are met otherwise go to step3.\par
Improvising a new harmony from the HM can be realized as follows:\par
A New Harmony vector ?? ? = \{?? 1 ? , ?? 2 ? , ?, ?? ?? ? \} is generated from the HM based on memory considerations, pitch adjustments, and randomization. For instance, the value of for the new vector can be chosen from any value in the specified HM rang (?? 1 1 ? ?? harmony as determined by an aesthetic \hyperref[b25]{[26]}- \hyperref[b26]{[27]}. In music improvisation, each player sounds any pitch within the possible range, together making one harmony vector. If all the pitches make a good solution, that experience is stored in each variable's memory, and the possibility to make a good solution is also increased next time. HS algorithm includes a number of optimization operators, such as the harmony memory (HM), the harmony memory size (HMS, number of solution vectors in harmony memory), the harmony memory considering rate (HMCR), and the pitch adjusting rate (PAR). In the HS algorithm, the harmony memory (HM) stores the feasible vectors, which are all in the feasible space. The harmony memory size determines how many vectors it stores. A new vector is generated by selecting the components of different vectors randomly in the harmony memory. For example, Consider a jazz trio composed of saxophone, double bass and guitar. There exist certain amount of preferable pitches in each musician's memory: saxophonist, \{Do, Mi, Sol\}; double bassist, \{Si, Sol, Re\}; and guitarist, \{La, Fa, Do\}. If saxophonist randomly plays \{Sol\} out of \{Do, Mi, Sol\}, double bassist \{Si\} out of \{Si, Sol, Re\}, and guitarist \{Do\} out of \{La, Fa, Do\}, that harmony (Sol, Si, Do) makes another harmony (musically C-7 chord). And if the New Harmony is better than existing worst harmony in the HM, the New Harmony is included in the HM and the worst harmony is excluded from the HM. This procedure is repeated until fantastic harmony is found. When a musician improvises one pitch, usually he (or she) follows any one of three rules: (a) playing any one pitch from his (or her) memory, (b) playing an adjacent pitch of one pitch from his (or her) memory, and (c) playing totally random pitch from the possible sound range. Similarly, when each decision variable chooses one value in the HS algorithm, it follows any one of three rules: (i) choosing any one value from HS memory (defined as memory considerations), (ii) choosing an adjacent value of one value from the HS memory (defined as pitch adjustments), and (iii) choosing totally random value from the possible value range (defined as randomization). The three rules in HS algorithm are effectively directed using two parameters, i.e., harmony memory considering rate (HMCR) and pitch adjusting rate (PAR).\par
chosen in the same manner. Here, it's possible to choose the new value using the HMCR parameter, which varies between 0 and 1 as follows:?? ?? ? ? ? ?? ?? ? ? ??? ?? 1 , ?? ?? 2 , ?, ?? ?? ?????? ? ??????? ?????????????????????? ???????? ?? ?? ? ? ?? ?? ??????? ?????????????????????? 1 ? ???????? (\textbf{27})\par
The HMCR is the probability of choosing one value from the historic values stored in the HM, and (1-HMCR) is the probability of randomly choosing one feasible value not limited to those stored in the HM. For example, an HMCR of 0.95 indicates that the HS algorithm will choose the design variable value from historically stored values in the HM with a 95\% probability and from the entire feasible range with a 5\% probability. An HMCR value of 1.0 is not recommended because of the possibility that the solution may be improved by values not stored in the HM. This is similar to the reason why the genetic algorithm uses a mutation rate in the selection process. Every component of the New Harmony vector ?? ? = \{?? 1 ? , ?? 2 ? , ?, ?? ?? ? \} is examined to determine whether it should be pitch-adjusted. This procedure uses the parameter that set the rate of adjustment for the pitch chosen from the HM as follows: Pitch adjusting decision for?? ?? ? ? ? ?????? ??????? ?????????????????????? ?????? ???? ??????? ?????????????????????? 1 ? ??????\textbf{(28)}\par
The Pitch adjusting process is performed only after a value is chosen from the HM. The value (1-PAR) sets the rate of doing nothing. A PAR of 0.3 indicates that the algorithm will choose a neighbouring value with probability. If the pitch adjustment decision for ?? ? is Yes, and ?? ? is assumed to be ?? ?? (??) i.e., the kth element in ?? ?? , the pitch-adjusted value of?? ?? (??) is:?? ? = ?? ? + ??\textbf{(29)}\par
Where ?? ? the value of is ???? ? (1, ?1), ???? is an arbitrary distance bandwidth for the continuous design variable, and u (?1, 1) is a uniform distribution between -1 and 1. The HMCR and PAR parameters introduced in the harmony search help the algorithm escape from local optima and to improve the global optimum prediction of the HS algorithm. After improvising a new harmony, evaluating the new one and if it is better than the worst one in the HM in terms of the objective function value, the new one is included in the HM and the existing worst harmony is excluded from the HM. The HM is then sorted by the objective function value. 
\section[{VII.}]{VII.} 
\section[{SIMULATION RESULTS}]{SIMULATION RESULTS}\par
The accuracy of the proposed IHPSO Algorithm method is demonstrated by testing it on standard IEEE-30 bus system. The IEEE-30 bus system has 6 generator buses, 24 load buses and 41 transmission lines of which four branches are (6-9), (6-10) , (4-12) and (28-27) -are with the tap setting transformers. The lower voltage magnitude limits at all buses are 0.95 p.u. and the upper limits are 1.1 for all the PV buses and 1.05 p.u. for all the PQ buses and the reference bus. The simulation results have been presented in Tables 1, 2, 3 \&4. And in the Table  {\ref 5} shows the proposed algorithm powerfully reduces the real power losses when compared to other given algorithms. The optimal values of the control variables along with the minimum loss obtained are given in Table \hyperref[tab_1]{1}. Corresponding to this control variable setting, it was found that there are no limit violations in any of the state variables. ORPD together with voltage stability constraint problem was handled in this case as a multi-objective optimization problem where both power loss and maximum voltage stability margin of the system were optimized simultaneously. Table \hyperref[tab_2]{2} indicates the optimal values of these control variables. Also it is found that there are no limit violations of the state variables. It indicates the voltage stability index has increased from 0.2482 to 0.2498, an advance in the system voltage stability. To determine the voltage security of the system, contingency analysis was conducted using the control variable setting obtained in case 1 and case 2. The Eigen values equivalents to the four critical contingencies are given in Table \hyperref[tab_3]{3}. From this result it is observed that the Eigen value has been improved considerably for all contingencies in the second case.  \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}WhereÎ?"P=}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.47841530054644804\textwidth}P{0.3715846994535519\textwidth}}
\multicolumn{2}{l}{Variables}\\
Control variables\tabcellsep Variable setting\\
V1\tabcellsep 1.040\\
V2\tabcellsep 1.041\\
V5\tabcellsep 1.040\\
V8\tabcellsep 1.030\\
V11\tabcellsep 1.003\\
V13\tabcellsep 1.041\\
T11\tabcellsep 1.01\\
T12\tabcellsep 1.00\\
T15\tabcellsep 1.0\\
T36\tabcellsep 1.0\\
Qc10\tabcellsep 3\\
Qc12\tabcellsep 4\\
Qc15\tabcellsep 4\\
Qc17\tabcellsep 0\\
Qc20\tabcellsep 3\\
Qc23\tabcellsep 4\\
Qc24\tabcellsep 3\\
Qc29\tabcellsep 3\\
Real power loss\tabcellsep 4.2985\\
SVSM\tabcellsep 0.2482\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.4438888888888889\textwidth}P{0.40611111111111114\textwidth}}
Control Variables\tabcellsep Variable Setting\\
V1\tabcellsep 1.043\\
V2\tabcellsep 1.044\\
V5\tabcellsep 1.042\\
V8\tabcellsep 1.031\\
V11\tabcellsep 1.005\\
V13\tabcellsep 1.035\\
T11\tabcellsep 0.090\\
T12\tabcellsep 0.090\\
T15\tabcellsep 0.090\\
T36\tabcellsep 0.090\\
Qc10\tabcellsep 4\\
Qc12\tabcellsep 4\\
Qc15\tabcellsep 3\\
Qc17\tabcellsep 4\\
Qc20\tabcellsep 0\\
Qc23\tabcellsep 3\\
Qc24\tabcellsep 3\\
Qc29\tabcellsep 4\\
Real power loss\tabcellsep 4.9690\\
SVSM\tabcellsep 0.2498\end{longtable} \par
 
\caption{\label{tab_2}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.05882352941176471\textwidth}P{0.044117647058823525\textwidth}P{0.10294117647058823\textwidth}P{0.5264705882352941\textwidth}P{0.11764705882352942\textwidth}}
\tabcellsep \tabcellsep \tabcellsep Method\tabcellsep Minimum loss\\
\tabcellsep \tabcellsep \tabcellsep Evolutionary\tabcellsep 5.0159\\
\tabcellsep \tabcellsep \tabcellsep programming[28]\\
\tabcellsep \tabcellsep \tabcellsep Genetic algorithm[29]\tabcellsep 4.665\\
\tabcellsep \tabcellsep \tabcellsep Real coded GA with\tabcellsep 4.568\\
\tabcellsep \tabcellsep \tabcellsep Lindex as SVSM[30]\\
\tabcellsep \tabcellsep \tabcellsep Real coded genetic\\
\tabcellsep \tabcellsep \tabcellsep algorithm[31]\tabcellsep 4.5015\\
\tabcellsep \tabcellsep \tabcellsep Proposed IHPSO method\tabcellsep 4.2985\\
\multicolumn{2}{l}{Sl.No Contigency}\tabcellsep ORPD\tabcellsep VSCRPD\\
\tabcellsep \tabcellsep Setting\tabcellsep Setting\\
1\tabcellsep 28-27\tabcellsep 0.1410\tabcellsep 0.1425\\
2\tabcellsep 4-12\tabcellsep 0.1658\tabcellsep 0.1665\\
3\tabcellsep 1-3\tabcellsep 0.1774\tabcellsep 0.1783\\
4\tabcellsep 2-4\tabcellsep 0.2032\tabcellsep 0.2045\end{longtable} \par
  {\small\itshape [Note: www.GlobalJournals.org]} 
\caption{\label{tab_3}Table 3 :}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US) implementations of PSO algorithm with other search} 			\footnote{© 2014 Global Journals Inc. (US)} 			\footnote{© 2014 Global Journals Inc. (US) Voltage Profile Augmentation and Minimization of Real Power Loss in Transmission Lines by using} 		 		\backmatter  			 
\subsection[{CONCLUSION}]{CONCLUSION}\par
In this paper, one of the recently developed stochastic algorithms IHPSO has been demonstrated and applied to solve optimal reactive power dispatch problem. The problem has been formulated as a constrained optimization problem. Different objective functions have been considered to minimize real power loss, to enhance the voltage profile. The proposed approach is applied to optimal reactive power dispatch problem on the IEEE 30-bus power system. The simulation results indicate the effectiveness and robustness of the proposed algorithm to solve optimal reactive power dispatch problem in test system.			 			  				\begin{bibitemlist}{1}
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\end{document}
