The **optimal** RPD is a constrained, nonlinear, discrete optimization problem. The traditional approach is to formulate this problem as a single- objective optimization problem with constraints. In this approach, the objective may consist of a single term [3-7] or it may consist of multiple terms [8, 9]. One may use dynamic programming or genetic **algorithm** to solve. However, this approach only results in a single **optimal** solution where tradeoffs between different components of the objective function must be fixed in advance of solution. In order to provide a means to assess tradeoffs between two conflicting objectives, one may formulate the RPD problem as a multi-objective problem. In this case, solution requires a multi-objective **algorithm** such as NSGA-II. Srinivas and Deb developed NSGA in which a ranking selection method emphasizes current non-dominated solutions and a niching method maintains diversity in the population [10]. Multi-objective evolutionary algorithms including NSGA that use non-dominated sorting and sharing have been criticized mainly for i) computational complexity, ii) non-elitism approach and iii) the need for specifying a sharing parameter. Deb et al. alleviated these difficulties in NSGA-II [11, 12].

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The proper selection of HS parameter values is considered as one of the challenging task not only for HS **algorithm** but also for other metaheuristic algorithms. This difficulty is a result of different reasons, and the most important one is the absence of general rules governing this aspect. Actually, setting these values is problem dependant and therefore the experimental trials are the only guide to the best values. However, this matter guides the **research** into new variants of HS. These variants are based on adding some extra components or concepts to make part of these parameters dynamically adapted. The proposed **algorithm** includes dynamic adaptation for both pitch adjustment rate (PAR) and bandwidth (bw) values. The PAR value is linearly increased in each iteration of HS by using the following equation:

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while the one with highest score will win and output as the final solution. In the experiments, social emotional optimization **algorithm** (SEOA) has a remarkable superior performance in terms of accuracy and convergence speed [22-26]. In this **research** paper social emotional optimization **algorithm** has been utilized to solve the ORPD Problems. This **algorithm** (SEOA) is applied to obtain the **optimal** control variables so as to improve the voltage stability level of the system. The performance of the proposed method has been tested on IEEE 30 bus system and the results are compared with the standard GA and PSO method.

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Much **research** has been devoted to cope with the ORPD problem. These techniques include the nonlinear programming method [1], mixed-integer programming method [2], interior point method [3], © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE). Open access under CC BY-NC-ND license.

This **research** presents a Hybrid Particle Swarm Optimization with Bat **Algorithm** (HPSOBA) based approach to solve **Optimal** **Reactive** **Power** **Dispatch** (ORPD) problem. The primary objective of this project is minimization of the active **power** transmission losses by optimally setting the control variables within their limits and at the same time making sure that the equality and inequality constraints are not violated. Particle Swarm Optimization (PSO) and Bat **Algorithm** (BA) algorithms which are nature-inspired algorithms have become potential options to solving very difficult optimization problems like ORPD. Although PSO requires high computational time, it converges quickly; while BA requires less computational time and has the ability of switching automatically from exploration to exploitation when the optimality is imminent. This **research** integrated the respective advantages of PSO and BA algorithms to form a hybrid tool denoted as HPSOBA **algorithm**. HPSOBA combines the fast convergence ability of PSO with the less computation time ability of BA **algorithm** to get a better **optimal** solution by incorporating the BA’s frequency into the PSO velocity equation in order to control the pace. The HPSOBA, PSO and BA algorithms were implemented using MATLAB programming language and tested on three (3) benchmark test functions (Griewank, Rastrigin and Schwefel) and on IEEE 30- and 118-bus test systems to solve for ORPD without DG unit. A modified IEEE 30-bus test system was further used to validate the proposed hybrid **algorithm** to solve for **optimal** placement of DG unit for active **power** transmission line loss minimization. By comparison, HPSOBA **algorithm** results proved to be superior to those of the PSO and BA methods.

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Abstract— Development of Metaheuristic **Algorithm** in engineering problems grows really fast. This **algorithm** is commonly used in optimization problems. One of the metaheuristic algorithms is called **Firefly** **Algorithm** (FA). **Firefly** **Algorithm** is a nature-inspired **algorithm** that is derived from the characteristic of fireflies. **Firefly** **Algorithm** can be used to solve **optimal** **power** flow (OPF) problem in **power** system. To get the best performance, **firefly** **algorithm** can be combined with fuzzy logic. This **research** presents the **application** of hybrid fuzzy logic and **firefly** **algorithm** to solve **optimal** **power** flow. The simulation is done using the MATLAB environment. The simulations show that by using the fuzzy-**firefly** **algorithm**, the **power** losses, as well as the total cost, can be reduced significantly.

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genetic algorithms have been proposed to solve the **reactive** **power** optimization problem [5]. Genetic **algorithm** is a random search technique based on the mechanics of natural selection. But in the recent **research** some insufficiencies are distinguished in the GA performance. This abasement in efficiency is apparent in applications with highly hypostasis objective functions i.e. where the parameters being optimized are extremely correlated. In addition, the untimely convergence of GA degrades its performance and reduces its search capability. In addition to this, these algorithms are found to take more time to reach the **optimal** result.

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This **research** presents a Teaching Learning Based Optimization (TLBO) **algorithm** to solve **Optimal** **Reactive** **Power** **Dispatch** (ORPD) problem. The aim of the **power** system is to ensure safe and reliable **power** is delivered to consumers. **Reactive** **power** **dispatch** although contributes little or no cost in **power** systems, it is important in sustaining the voltages of the **power** system and ensuring efficiency of the transmission system and all electromagnetic equipment. Excess **reactive** **power** in the **power** system can contribute to losses in the transmission grid. Therefore, **reactive** **power** sources and sinks need to be provided to ensure balance. The primary objective of this paper is to minimize the active **power** transmission losses by the **optimal** settings of the control variables (generator set point voltages, tap changers on transformers and **reactive** **power** shunt compensators) within their limits and avoiding violations on the constraints. TLBO is a population- based **algorithm** and requires few **algorithm** specifications to compute making it a recommended option to solve various degrees of optimization problems. The TLBO **algorithm** was implemented using MATLAB programming and by

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In the **firefly** **algorithm** there are two important issues of the variation of light intensity and the formulation of the attractiveness. For simplicity, it is assumed that the attractiveness of a **firefly** is determined by its brightness which in turn is associated with the encoded objective function of the optimization problems. On the attractiveness of the FFA the main form of attractiveness function or β(r) can be any monotonically decreasing functions such as the following generalized form of

The results obtained with the proposed approach are presented and compared favorably with results of other approaches, like the Linear Programming (LP) method. All data used this analysis is taken from the Iraqi Operation and Control Office, which belongs to the ministry of electricity [3]. An echolocation based **algorithm** known as the BAT search **algorithm** inspired by the behaviour of bats to **optimal** **reactive** **power** **dispatch** (ORPD) problem. The minimization of active **power** transmission losses through controlling a number of control variables is defined as the ORPD problem. The **optimal** **reactive** **power** **dispatch** is then developed as a non-linear optimization problem in regard to **power** transmission loss, voltage stability and voltage profile [4]. A Genetic **Algorithm** (GA) - based approach for solving **optimal** **Reactive** **Power** **Dispatch** (RPD) including voltage stability limit in **power** systems. The monitoring methodology for voltage stability is based on the L-index of load buses. Bus voltage magnitudes, transformer tap settings and **reactive** **power** generation of capacitor banks are the control variables. A binary-coded GA with tournament selection, two point crossover and bit-wise mutation is used to solve this complex optimization problem.

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, 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 is used as the indicator of voltage stability. In recent years, several new optimization techniques have emerged. The evolutionary algorithms (EAs) for **reactive** **power** optimization problem have been extensively studied. Several global optimization algorithms such as differential evolution (DE) (Dib.N et al .2010; Lin. C et al.2010), genetic **algorithm** (GA) (Zhang et al.2009 ; Vaitheeswaran.S et al.2008) , simulated annealing (SA) (Ferreira, J. A et al.1997 ), Ant colony optimization (ACO) (Hosseini.S. A et al 2008 ), particle swarm optimization (PSO) (Perez Lopez et al.2009; Liu, D et al.2009; Li, W.-T et al.2010 ; Goudos, S et al.2010 ; Shavit, R et al.2005) are used for **reactive** **power** optimization problem. However, these methods present certain drawbacks with the possibility of premature convergence to a local optimum. In this paper, a novel **chaotic** PSO **algorithm** (CPSO) is proposed. Based on the ergodicity, regularity and pseudo-randomness of the **Chaotic** variable, **chaotic** search is used to explore better solutions. The performance of (CPSO) 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.

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We consider a two-tier HSDPA cellular network with one macrocell base station (MBS) and a group of picocell base stations (PBSs) in an enterprise environment which share the same frequency channels. We assume the closed-access mode is used, where a UE will connect to a PBS only if it receives higher pilot **power** strength from its host PBS than from MBS; otherwise, the UE camps on MBSs.

In [1], OPF problem formulation has been presented along with considering effects of FACTS devices and **power** flow constraints. To solve OPF problem a two stage problem formulation has been proposed. This reference [2], Presents the performance comparison of PSO and GA optimization techniques for FACTS based controller design. In [3], the main aim is the **optimal** allocation of TCSC device in the **power** system so the **power** loss becomes minimized and also increase **power** transfer capacity of the transmission line that ultimately yields minimum operating cost with different load conditions. In this, first the locations of the TCSC device is identified by calculating line flows. TCSC is placed in line where **reactive** **power** flows are very high. To solve OPF problem Hybrid GA incorporating TCSC is proposed. To select best control variables to minimize the generation cost and maintain the **power** flow within the control range Hybrid GA is integrated with conventional OPF [4].

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Treating the bus voltage limits as constraints in ORPD often re- sults in all the voltages toward their maximum limits after optimi- zation, which means the **power** system lacks the required reserves to provide **reactive** **power** during contingencies. One of the effec- tive ways to avoid this situation is to choose the minimization of the absolute deviations of all the actual bus voltages from their de- sired voltages as an objective function. Minimization of TVD of load buses can allow the improvement of voltage proﬁle [1] . In this case, the **power** system operates more securely and there will be an in- crease in service quality. This objective function may be formu- lated as follows

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In this paper, a different approach, Enriched particle Swarm optimization (EPSO) **Algorithm** for solving **optimal** **reactive** **power** **dispatch** problem has been presented. Particle swarm optimization is affected by early convergence, no assurance in finding **optimal** solution. This paper proposes EPSO using multiple sub swarm PSO in blend with multi exploration space **algorithm**. The particles are alienated into equal parts and arrayed into the number of sub swarms available. Multi-exploration space **algorithm** is used to obtain an optimum solution for each sub swarm and these solutions are then arrayed yet into a new swarm to obtain the best of all the solution. The proposed EPSO **algorithm** has been tested on standard IEEE 30 bus test system and simulation results show the commendable performance of the proposed **algorithm** in reducing the real **power** loss.

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The aim of this paper is to solve the **optimal** **reactive** **power** **dispatch** (ORPD) prob lem. Metaheuristic algorithms have b een extensively used to solve optimization problems in a reasonab le time without requiring in-depth knowledge of the treated prob lem. The perform ance of a metaheuristic requires a compromise b etween exploitation and exploration of the search space. However, it is rarely to have the two characteristics in the same search method, where the current emergence of hyb rid methods. This paper presents a hyb rid formulation b etween two different metaheuristics: differential evolution (b ased on a population of solution) and simulated annealing (b ased on a unique solution) to solve ORPD. The first one is characterized with the high capacity of exploration, whil e the second has a good exploitation of the search space. For the control variab les, a mixed representation (continuous/discrete), is proposed. The rob ustness of the method is tested on the IEEE 30 b us test system.

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There are two general methods to optimize a function, namely, mathematical programming and Meta heuristic methods. Various mathematical programming methods such as linear programming, homogenous linear programming, integer programming, dynamic programming, and nonlinear programming have been applied for solving optimization problems. These methods use gradient information to search the solution space near an initial starting point. In general, gradient-based methods converge faster and can obtain solutions with higher accuracy compared to stochastic approaches in fulfilling the local search task. However, for effective implementation of these methods, the variables and cost function of the generators need to be continuous. Furthermore, a good starting point is vital for these methods to be executed successfully. In many optimization problems, prohibited zones, side limits, and non-smooth or non-convex cost functions need to be considered. As a result, these non-convex optimization problems cannot be solved by the traditional mathematical programming methods. Although dynamic programming or mixed integer nonlinear programming and their modifications offer some facility in solving non-convex problems, these methods, in general, require considerable computational effort. As an alternative to the conventional mathematical approaches, the meta-heuristic optimization techniques have been used to obtain global or near-global optimum solutions. Due to their capability of exploring and finding promising regions in the search space in an affordable time, these methods are quite suitable for global searches and furthermore alleviate the need for continuous cost functions and variables used for mathematical optimization methods. Though these are approximate methods, i.e., their solution are good, but not necessarily **optimal**, they do not require the derivatives of the objective function and constraints and employ probabilistic transition rules instead of deterministic ones [14]. Nature has always been a major source of inspiration to engineers and natural philosophers and many meta-heuristic approaches are inspired by solutions that nature herself seems to have chosen for hard problems. The Evolutionary **Algorithm** (EA) proposed by Fogel et al. [15], De Jong [16] and Koza [17], and the Genetic **Algorithm** (GA) proposed by Holland [18] and Goldberg [19] are inspired from the biological evolutionary process. Studies on animal behavior led to the method of Tabu Search (TS) presented by Glover [20], Ant Colony Optimization (ACO) proposed by Dorigo et al. [21] and Particle Swarm Optimizer (PSO) formulated by Eberhart and Kennedy [22]. Also, Simulated Annealing proposed by Kirkpatrick et al. [23], the Big Bang–Big Crunch **algorithm** (BB–BC)

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Over the years numerous methods with various degrees of near-optimality, efficiency, ability to handle difficult constraints and heuristics, are suggested in the literature for solving the **dispatch** problems. These problems are traditionally solved using mathematical programming techniques such as lambda iteration method, gradient method, linear programming, dynamic programming method and so on. Many of these methods suffer from natural complexity and converge slowly. However, the classical lambda-iteration method has been in use for a long time. The additional constraints such as line flow limits cannot be included in the lambda iteration approach and the convergence of the iterations is dependent on the initial choice of lambda. In large **power** systems, this method has oscillatory problems that increase the computation time [1,2].

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