A PSO Procedure for a Coordinated Tuning of Power System Stabilizers for Multiple Operating Conditions | Journal of Applied Research and Technology. JART

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Belhocine, M. Bouchetara" "autores" => array:2 [ 0 => array:2 [ "nombre" => "A." "apellidos" => "Belhocine" ] 1 => array:2 [ "nombre" => "M." 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Sait, Ahmad T. Sheikh, Aiman H. El-Maleh" "autores" => array:3 [ 0 => array:2 [ "nombre" => "Sadiq M." "apellidos" => "Sait" ] 1 => array:2 [ "nombre" => "Ahmad T." "apellidos" => "Sheikh" ] 2 => array:2 [ "nombre" => "Aiman H." "apellidos" => "El-Maleh" ] ] ] ] ] "idiomaDefecto" => "en" "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S1665642313715736?idApp=UINPBA00004N" "url" => "/16656423/0000001100000005/v2_201505081700/S1665642313715736/v2_201505081700/en/main.assets" ] "en" => array:16 [ "idiomaDefecto" => true "titulo" => "A PSO Procedure for a Coordinated Tuning of Power System Stabilizers for Multiple Operating Conditions" "tieneTextoCompleto" => true "paginas" => array:1 [ 0 => array:2 [ "paginaInicial" => "665" "paginaFinal" => "673" ] ] "autores" => array:1 [ 0 => array:3 [ "autoresLista" => "Amin Safari" "autores" => array:1 [ 0 => array:3 [ "nombre" => "Amin" "apellidos" => "Safari" "email" => array:1 [ 0 => "a-safari@iau-ahar.ac.ir" ] ] ] "afiliaciones" => array:1 [ 0 => array:2 [ "entidad" => "Department of Electrical Engineering, Ahar Branch, Islamic Azad University, Ahar, Iran" "identificador" => "aff0005" ] ] ] ] "resumenGrafico" => array:2 [ "original" => 0 "multimedia" => array:7 [ "identificador" => "fig0035" "etiqueta" => "Figure 7" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr7.jpeg" "Alto" => 1843 "Ancho" => 1858 "Tamanyo" => 449406 ] ] "descripcion" => array:1 [ "en" => "System response at scenario 1 with different operating conditions: Solid (PSOPSS) and dotted (GAPSS)." ] ] ] "textoCompleto" => "1IntroductionIn the past three decades, the utilization of supplementary excitation control signals for improving the dynamic stability of power systems has received much attention. Nowadays, the CPSS is widely used by power system utilities. Power system stabilizers (PSSs) are auxiliary control devices on synchronous generators, used in conjunction with their excitation system by providing supplementary feedback stabilizing signals to provide control signals toward enhancing the system damping and extending power transfer limits [<a class="elsevierStyleCrossRefs" href="#bib0005">1–3</a>]. Recently, several approaches such as optimization based techniques like genetic algorithms (GA), evolutionary programming, tabu search, simulated annealing and rule based bacteria foraging [<a class="elsevierStyleCrossRefs" href="#bib0020">4–11</a>] have been applied to PSSs parameter optimization problem. These population based algorithms search procedures that incorporate random variation and selection operators. Appearing suitable for optimizing the PSS parameters, these approaches have long simulation time and degraded efficiency to obtain the global optimum solution when there is a large number of optimization parameters or when the system has a highly complex objective function (i.e., where parameters being optimized are highly correlated in large power system). In this paper, the PSO based PSS is proposed which is used for optimal tuning of the PSS parameters to improve optimization synthesis and the speed of the convergence. The PSO algorithm [<a class="elsevierStyleCrossRef" href="#bib0060">12</a>] is a derivative free promising algorithm for handling the combinatorial optimization problems. It has been proved theoretically that PSO algorithm converges to the optimal solution [<a class="elsevierStyleCrossRef" href="#bib0065">13</a>]. In addition, the PSO algorithm is robust i.e., the final solution quality does not strongly depend on the choice of the initial solution. Another strong feature of the PSO algorithm is that a complicated mathematical model is not required and the problem constraints can be easily incorporated [<a class="elsevierStyleCrossRef" href="#bib0070">14</a>].In this study, the PSO is used to solve the problem of the PSSs design (PSOPSS) which is formulated as a multi-objective optimization problem. The multi-objective problem is concocted to optimize a composite set of two eigenvalue-based functions and the integral of the time multiplied absolute value of the error (ITAE)-based objective function. The effectiveness of the proposed PSOPSS is tested on a large scale multi-machine power system under different operating conditions in comparison with the<a name="p666"></a> GAPSS [<a class="elsevierStyleCrossRef" href="#bib0055">11</a>]. Results evaluation show that the designed PSSs with proposed method achieves good robust performance for damping lowfrequency oscillations under different operating conditions and is superior to the other methods.2Particle swarm optimizationParticle swarm optimization algorithm, which is tailored for optimizing difficult numerical functions and based on a metaphor of human social interaction, is capable of mimicking the ability of human societies to process knowledge. It has roots in two main component methodologies: artificial life (such as bird flocking, fish schooling and swarming); and, evolutionary computation [<a class="elsevierStyleCrossRef" href="#bib0070">14</a>]. The higher dimensional space calculations of the PSO concept are performed over a series of time steps. The population is responding to the quality factors of the previous best individual values and the previous best group values. This optimization technique can be used to solve many of the same kinds of problems as GA, and does not suffer from some of the GAs difficulties. It has been found also to be robust in solving problem featuring non-linearing, non-differentiability and high-dimensionality [<a class="elsevierStyleCrossRef" href="#bib0070">14</a>].In the PSO technique a number of simple entities, the particles, are placed in the search space of some problem or function, and each evaluates the objective function at its current location. Each particle then determines its movement through the search space by combining some aspect of the history of its own current and best locations by those with one or more members of the swarm with some random perturbations. The next iteration takes place after all particles have been moved. Eventually the swarm as a whole, like a flock of birds collectively foraging for food, is likely to move close to an optimum of the fitness function [<a class="elsevierStyleCrossRef" href="#bib0065">13</a>]. In the PSO technique, the trajectory of each individual in the search space is adjusted by dynamically altering the velocity of each particle, according to its own flying experience and the flying experience of the other particles in the search space. The position vector and the velocity vector of the ith particle in the D-dimensional search space can be represented as: Xi = (xi1,xi2,…,xiD) and Vi = (vi1,vi2…viD) respectively. According to the user defined fitness function, let us say the best position of each particle, which corresponds to the best fitness value (pbest) obtained by that particle at time, be Pi = (pi1,pi2,…,piD), and the global version of the PSO keeps track of the overall best value (gbest), and its location obtained, thus far from any particle in the population. Then, the new velocities and the positions of the particles for the next fitness evaluation are calculated using the following two equations [<a class="elsevierStyleCrossRef" href="#bib0065">13</a>, <a class="elsevierStyleCrossRef" href="#bib0070">14</a>]:<elsevierMultimedia ident="eq0005"></elsevierMultimedia><elsevierMultimedia ident="eq0010"></elsevierMultimedia>Where, Pid and Pgd are pbest and gbest. Here w is the inertia weight parameter which controls the global and local exploration capabilities of the particle. Constants c1, c2 are cognitive and social coefficients, respectively, and r1r2 are random numbers between 0 and 1. A larger inertia weight factor is used during initial exploration its value is gradually reduced as the search proceeds. <a class="elsevierStyleCrossRef" href="#fig0005">Figure 1</a>, shows the flowchart of the PSO algorithm.<a name="p667"></a><elsevierMultimedia ident="fig0005"></elsevierMultimedia>3Problem formulation3.1Power system modelThe aim of this study is to determine the parameters of power system stabilizers for damping oscillations. For this reason, appropriate modeling of the power system has a main role on better designing of stabilizers. To model the n-machine interconnected system, a set of differential algebraic equations is used and the model provided by assembling the models for each equipment such as generators, loads, controls etc. and connecting them appropriately via the network algebraic equations [<a class="elsevierStyleCrossRef" href="#bib0075">15</a>]. In this paper, the two-axis model [<a class="elsevierStyleCrossRef" href="#bib0010">2</a>], given in the Appendix, is used for time domain simulations and by linearizing the multi-machine power system around the operating points the simulation is done. The main objective of the PSS is increasing the rotor damping of a synchronous generator. By introducing appropriate supplementary control signals to the generator excitation system, this objective is achieved. <a class="elsevierStyleCrossRef" href="#fig0010">Figure 2</a>, shows a schema of a synchronous generator control components. The typical PSS block diagram used in this study is showed in <a class="elsevierStyleCrossRef" href="#fig0015">Figure 3</a>. The PSS operating function [<a class="elsevierStyleCrossRef" href="#bib0015">3</a>] is to produce a torque on the rotor of the machine involved in such a way that compensates the phase lag between the exciter input and the machine electrical torque. The dynamic compensator is made up to two lead-lag stages, an additional gain and a washout filter where Δωi, is the deviation in speed from the synchronous speed, T1i-T4i are the lead-lag time constants, Kpss is the gain of the PSS and Tw is the washout time constant. The adjustable PSS parameters are the gain of the PSS, Ki, and the time constants, T1i-T4i which these time constants are usually not critical and they can range from 0.5 to 20 s. Hence, for each PSS, there are five parameters comprise of 4 time constants and a gain constant that should be determined to achieve optimal output. The output signal is fed as a supplementary input signal, Vpss to the regulator of the excitation system.<elsevierMultimedia ident="fig0010"></elsevierMultimedia><elsevierMultimedia ident="fig0015"></elsevierMultimedia>3.2PSO based PSSs designIn this paper, for our optimization problem, the PSO is employed to minimize a multi-objective fitness function comprise of the ITAE-based and eigenvalue-based functions for the PSSs design problem. These objectives are defined as follows:<elsevierMultimedia ident="eq0015"></elsevierMultimedia><elsevierMultimedia ident="eq0020"></elsevierMultimedia><elsevierMultimedia ident="eq0025"></elsevierMultimedia>Where, σi, is the real part of the ith eigenvalue. Also, speed deviation (Δω), of the machines are considered for the evaluation of the j2. The α1 and α2 are weighting factors and tsim is the time range of simulation. The NG is the number of machines and NP is the total number of operating points for which the optimization is carried out. The value of σ0 determines the relative stability in terms of damping factor margin provided for constraining the placement of eigenvalues during the process of optimization. By optimizing J1, closed loop system poles are consistently pushed further left from the imaginary axis with simultaneous reduction in real parts. By optimizing J2, the sum of deviation of speed in each generator speed response is getting minimized. The design problem can be formulated as the following constrained optimization problem, where the constraints are the PSS parameter bounds:<elsevierMultimedia ident="eq0030"></elsevierMultimedia><a name="p668"></a>By employing the PSO, the proposed approach solves this optimization problem and search for optimal or near optimal set of the PSS parameters (Ki, T1i−T4ifor i=1,2,…,m where, m is the number of machines) [<a class="elsevierStyleCrossRef" href="#bib0050">10</a>].4Case studyIn this study, the sixteen-machine five-area power system shown in <a class="elsevierStyleCrossRef" href="#fig0020">Figure 4</a> is considered. The system comprises the five coherent groups representing a reduced model of the New England and New York interconnected system. Details of the system data are given in [<a class="elsevierStyleCrossRef" href="#bib0080">16</a>]. To assess the effectiveness and robustness of the proposed method over a wide range of loading conditions, five operating conditions (<a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a>) without PSSs are considered.<elsevierMultimedia ident="fig0020"></elsevierMultimedia><elsevierMultimedia ident="tbl0005"></elsevierMultimedia>4.1PSO-based PSSs designIn the proposed method, we must tune the PSSs parameters optimally to improve the overall system dynamic stability in a robust way under different operating conditions and disturbances. For each PSS, the optimal setting of five parameters is determined by the PSO algorithm, i.e., 60 parameters to be optimized, namely Ki, T1iT2i,T3i and T4ifor i= 1, 2, …,12.The optimization of the PSS parameters is carried out by evaluating the multi-objective function as given in <a class="elsevierStyleCrossRef" href="#eq0025">Equation 5</a>. In this work, in order to acquire better performance, number of particle, particle size, number of iteration, C1, C2, and C is chosen as 80, 60, 60, 2, 2 and 1, respectively. It should be noted that PSO algorithm is run several<a name="p669"></a> times and then optimal set of the PSSs parameters is selected. Results of the PSSs parameter achieved from the PSO algorithm are given in <a class="elsevierStyleCrossRef" href="#tbl0010">Table 2</a>. The convergence rate of algorithm is illustrated in <a class="elsevierStyleCrossRef" href="#fig0025">Figure 5</a>.<elsevierMultimedia ident="tbl0010"></elsevierMultimedia><elsevierMultimedia ident="fig0025"></elsevierMultimedia>4.2Eigenvalue analysisThe PSSs were placed in all generators, except for the ones numbered as 13, 14, 15 and 16 in <a class="elsevierStyleCrossRef" href="#fig0020">Figure 4</a>. To assess the effectiveness and robustness of the proposed controller, a multiple of operating conditions according to <a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a> are considered and simulation studies are carried out for various fault disturbances and fault clearing sequences for two scenarios. The eigenvalues analysis from the two cases with proposed PSSs and from the base case without PSSs is depicted in <a class="elsevierStyleCrossRef" href="#fig0030">Figure 6</a>. Moreover, it is also clear that the system damping with the proposed PSO based tuned PSSs with multi-objective function has improved significantly.<elsevierMultimedia ident="fig0030"></elsevierMultimedia>4.3Nonlinear simulation resultsScenario 1In this scenario, by applying a three-cycle, three phase fault at bus 1, on line 1–2 the performance of the proposed controller under transient conditions is verified. The fault is cleared after 0.06 seconds and the original system is restored upon the clearance of the fault. The performance of the tuned multi-objective based PSSs is compared to that of the PSSs tuned using the GA for different operating conditions as given in <a class="elsevierStyleCrossRef" href="#tbl0010">Table 2</a>. The speed deviations of generators G3, G8, G10, G12, G13 and G14 and the power flow on lines 1–30, 9–36, 9–30, 78 and 17–18 under the above conditions are shown in <a class="elsevierStyleCrossRef" href="#fig0035">Figure 7</a>. It can be seen that the PSOPSSs with multi-objective function achieves good robust performance and provides superior damping in comparison with the other methods.<elsevierMultimedia ident="fig0035"></elsevierMultimedia>Scenario 2In this scenario, another severe disturbance is considered for different loading conditions; that is, a five-cycle, three-phase fault is applied at bus 10, on line 10–11. The fault is cleared after 0.1 seconds and the original system is restored upon the clearance of the fault. The system response is shown in <a class="elsevierStyleCrossRef" href="#fig0040">Figure 8</a>. It can be seen that the proposed PSOPSSs have good performance in damping of the low frequency oscillations and stabilizes the system quickly.<elsevierMultimedia ident="fig0040"></elsevierMultimedia>To demonstrate the performance robustness of the proposed method, two indices for system performance characteristics are defined as follows [<a class="elsevierStyleCrossRef" href="#bib0015">3</a>]:<elsevierMultimedia ident="eq0035"></elsevierMultimedia><elsevierMultimedia ident="eq0040"></elsevierMultimedia><a name="p670"></a><a name="p671"></a><a name="p672"></a>Where ω is the speed rotor; overshoot (OS); undershoot (US) and settling time (Ts) of all generators, speed deviations are considered for the evaluation of the ITAE and FD indices. The tsim is the simulation time which is 10 seconds here. The lower the value of these indices is, the better the performance of system in disturbances. The results of evaluating these two indices for different operating conditions under various disturbances for PSOPSS in comparison with GAPSS are brought in <a class="elsevierStyleCrossRef" href="#tbl0015">Table 3</a>. It can be seen that the value of these indices for the proposed method are much smaller than other methods. This demonstrates that the overshoot, undershoot, settling time and speed deviations of the machine are greatly reduced by applying the proposed stabilizers.<elsevierMultimedia ident="tbl0015"></elsevierMultimedia>5ConclusionsIn order to improve the transient stability and damp the low frequency oscillations, robust PSSs design based on a multi-objective fitness function consist of a composite set of two eigenvalue based and the ITAE-based objective functions was proposed in large power systems. The design problem was formulated as a nonlinear optimization problem for multiple operating conditions. Then, the PSO algorithm was successfully applied to find the optimal solution of the design problem. The nonlinear simulation results under different operating conditions show the effectiveness of the proposed controllers and their ability to provide good damping of low frequency oscillations in comparison to the GAPSS method and the results demonstrated the superiority of the proposed method in solution quality. The ITAE and FD indices revealed that by using the proposed objective based function controllers, the overshoot, undershoot, settling time and power system oscillations are greatly reduced at various loading conditions." "textoCompletoSecciones" => array:1 [ "secciones" => array:8 [ 0 => array:3 [ "identificador" => "xres498887" "titulo" => "Abstract" "secciones" => array:1 [ 0 => array:1 [ "identificador" => "abst0005" ] ] ] 1 => array:2 [ "identificador" => "xpalclavsec520377" "titulo" => "Keywords" ] 2 => array:2 [ "identificador" => "sec0005" "titulo" => "Introduction" ] 3 => array:2 [ "identificador" => "sec0010" "titulo" => "Particle swarm optimization" ] 4 => array:3 [ "identificador" => "sec0015" "titulo" => "Problem formulation" "secciones" => array:2 [ 0 => array:2 [ "identificador" => "sec0020" "titulo" => "Power system model" ] 1 => array:2 [ "identificador" => "sec0025" "titulo" => "PSO based PSSs design" ] ] ] 5 => array:3 [ "identificador" => "sec0030" "titulo" => "Case study" "secciones" => array:3 [ 0 => array:2 [ "identificador" => "sec0035" "titulo" => "PSO-based PSSs design" ] 1 => array:2 [ "identificador" => "sec0040" "titulo" => "Eigenvalue analysis" ] 2 => array:3 [ "identificador" => "sec0045" "titulo" => "Nonlinear simulation results" "secciones" => array:2 [ 0 => array:2 [ "identificador" => "sec0050" "titulo" => "Scenario 1" ] 1 => array:2 [ "identificador" => "sec0055" "titulo" => "Scenario 2" ] ] ] ] ] 6 => array:2 [ "identificador" => "sec0060" "titulo" => "Conclusions" ] 7 => array:1 [ "titulo" => "References" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "PalabrasClave" => array:1 [ "en" => array:1 [ 0 => array:4 [ "clase" => "keyword" "titulo" => "Keywords" "identificador" => "xpalclavsec520377" "palabras" => array:4 [ 0 => "Power system stabilizer" 1 => "multi-machine power system" 2 => "PSO" 3 => "dynamic stability" ] ] ] ] "tieneResumen" => true "resumen" => array:1 [ "en" => array:2 [ "titulo" => "Abstract" "resumen" => "The problem of coordinated tuning stabilizers in multi-machine power systems is formulated here as a sequence of optimization problems. The design problem of stabilizers is converted to a nonlinear optimization problem with a multi-objective fitness function. The proposed method employs particle swarm optimization (PSO), an algorithm to search for optimal parameter settings of a widely used conventional fixed-structure lead-lag power system stabilizers (CPSSs). One of the main advantages of the proposed approach is its robustness to the initial parameter settings. In addition, the quality of the optimal solution does not rely on the initial guess. The robustness and performance of the newly designed controllers is evaluated in a large sixteen-machine power system subjected to different loading conditions in comparison with the genetic algorithm (GA) based PSSs design. The superiority of the controller designed is demonstrated through the nonlinear time-domain simulation and some performance indices studies. The results analysis reveals that the tuned PSSs with proposed objective function has an excellent capability in damping power system low-frequency oscillations." ] ] "apendice" => array:1 [ 0 => array:1 [ "seccion" => array:1 [ 0 => array:3 [ "apendice" => "Machine models [<a class="elsevierStyleCrossRef" href="#bib0080">16</a>]<elsevierMultimedia ident="eq0045"></elsevierMultimedia><elsevierMultimedia ident="eq0050"></elsevierMultimedia><elsevierMultimedia ident="eq0055"></elsevierMultimedia><elsevierMultimedia ident="eq0060"></elsevierMultimedia><elsevierMultimedia ident="eq0065"></elsevierMultimedia>" "titulo" => "Appendix" "identificador" => "sec0065" ] ] ] ] "multimedia" => array:24 [ 0 => array:7 [ "identificador" => "fig0005" "etiqueta" => "Figure 1" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr1.jpeg" "Alto" => 922 "Ancho" => 523 "Tamanyo" => 98639 ] ] "descripcion" => array:1 [ "en" => "Flowchart of the PSO technique." ] ] 1 => array:7 [ "identificador" => "fig0010" "etiqueta" => "Figure 2" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr2.jpeg" "Alto" => 499 "Ancho" => 897 "Tamanyo" => 54279 ] ] "descripcion" => array:1 [ "en" => "Control diagram of synchronous machine." ] ] 2 => array:7 [ "identificador" => "fig0015" "etiqueta" => "Figure 3" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr3.jpeg" "Alto" => 213 "Ancho" => 937 "Tamanyo" => 28304 ] ] "descripcion" => array:1 [ "en" => "The structure of the PSS." ] ] 3 => array:7 [ "identificador" => "fig0020" "etiqueta" => "Figure 4" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr4.jpeg" "Alto" => 534 "Ancho" => 823 "Tamanyo" => 72348 ] ] "descripcion" => array:1 [ "en" => "A New England–New York interconnected power system model." ] ] 4 => array:7 [ "identificador" => "fig0025" "etiqueta" => "Figure 5" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr5.jpeg" "Alto" => 409 "Ancho" => 750 "Tamanyo" => 41002 ] ] "descripcion" => array:1 [ "en" => "Variations of objective function." ] ] 5 => array:7 [ "identificador" => "fig0030" "etiqueta" => "Figure 6" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr6.jpeg" "Alto" => 1774 "Ancho" => 780 "Tamanyo" => 149408 ] ] "descripcion" => array:1 [ "en" => "Eigenvalues of case study in three different operating conditions a) Without PSS-base case b) With PSS base case c) With PSS case 1." ] ] 6 => array:7 [ "identificador" => "fig0035" "etiqueta" => "Figure 7" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr7.jpeg" "Alto" => 1843 "Ancho" => 1858 "Tamanyo" => 449406 ] ] "descripcion" => array:1 [ "en" => "System response at scenario 1 with different operating conditions: Solid (PSOPSS) and dotted (GAPSS)." ] ] 7 => array:7 [ "identificador" => "fig0040" "etiqueta" => "Figure 8" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr8.jpeg" "Alto" => 1960 "Ancho" => 1982 "Tamanyo" => 563367 ] ] "descripcion" => array:1 [ "en" => "System response at scenario 2 with different operating conditions: Solid (PSOPSS) and dotted (GAPSS)." ] ] 8 => array:7 [ "identificador" => "tbl0005" "etiqueta" => "Table 1" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Operating condition \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Description \t\t\t\t\t\t\n \t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Base case \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">All lines in service \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">Lines 33–34 are out of service \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 2 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">Power generation at G6 increased 50% \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">Lines 17–27 and 30–31 are out of service \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 4 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">Lines 17–27 and 30–31 are out of service and Power generation at G8 and G10 increased 30% \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab796427.png" ] ] ] ] "descripcion" => array:1 [ "en" => "Operating condition considered in the coordinated designing of the PSSs parameters." ] ] 9 => array:7 [ "identificador" => "tbl0010" "etiqueta" => "Table 2" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">PSS number \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">K \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">T1 \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">T2 \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">T3 \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">T4 \t\t\t\t\t\t\n \t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">62.13 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.9037 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.0534 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6332 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.4148 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G2 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">197.7 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.7673 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1747 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.4140 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.2492 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">194.8 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8147 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1826 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6761 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.7490 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G4 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">126.62 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6721 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8259 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8120 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8544 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G5 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">136.19 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6690 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.2189 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.7219 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.9637 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G6 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">198.37 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6380 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.4256 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.9287 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6872 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G7 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">119.21 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.4391 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.2381 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8901 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.5729 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G8 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">128.07 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.7237 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1584 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8570 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8297 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G9 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">105.08 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.7803 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.9372 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8173 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.2460 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">174.77 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6620 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1454 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.9333 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.6595 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G11 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">167.32 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.7904 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1278 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8422 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8867 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">G12 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">116.73 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8844 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.4280 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.8454 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.3693 \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab796425.png" ] ] ] ] "descripcion" => array:1 [ "en" => "Optimal PSSs parameters obtained by proposed method." ] ] 10 => array:7 [ "identificador" => "tbl0015" "etiqueta" => "Table 3" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="table-head " rowspan="3" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Operating condition</th><th class="td" title="table-head " colspan="4" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Scenario 1</th><th class="td" title="table-head " colspan="4" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Scenario 2</th></tr><tr title="table-row"><th class="td" title="table-head " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">PSOPSS</th><th class="td" title="table-head " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">GAPSS</th><th class="td" title="table-head " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">PSOPSS</th><th class="td" title="table-head " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">GAPSS</th></tr><tr title="table-row"><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD \t\t\t\t\t\t\n \t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Base case \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">82.45 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">83.20 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">402.22 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1231.59 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">231.25 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">322.60 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">2021.78 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">2862 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">88.02 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">101.12 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">501.04 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1349.96 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">293.30 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">490.68 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">2496.60 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">4506 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 2 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">137.13 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">129.83 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">503.10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1381.11 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">310.67 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">612.43 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">2360.85 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">3085 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">82.90 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">86.04 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">457.70 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1262.32 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">287.63 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">504.13 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1405.71 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1890 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Case 4 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">104.98 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">118.53 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">642.57 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1356.65 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">297.14 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">543.98 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1420.46 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1910 \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab796426.png" ] ] ] ] "descripcion" => array:1 [ "en" => "Values of ITAE and FD indices in different operating conditions at different scenarios." ] ] 11 => array:6 [ "identificador" => "eq0005" "etiqueta" => "(1)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "vid=w×vid+c1×rand()×Pid−xid      +c2×rand()×Pgd−xid" "Fichero" => "si1.jpeg" "Tamanyo" => 3979 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A PSO Procedure for a Coordinated Tuning of Power System Stabilizers for Multiple Operating Conditions

Amin Safari

Department of Electrical Engineering, Ahar Branch, Islamic Azad University, Ahar, Iran

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    "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">1</span><span class="elsevierStyleSectionTitle" id="sect0015">Introduction</span><p id="par0005" class="elsevierStylePara elsevierViewall">In the past three decades&#44; the utilization of supplementary excitation control signals for improving the dynamic stability of power systems has received much attention&#46; Nowadays&#44; the CPSS is widely used by power system utilities&#46; Power system stabilizers &#40;PSSs&#41; are auxiliary control devices on synchronous generators&#44; used in conjunction with their excitation system by providing supplementary feedback stabilizing signals to provide control signals toward enhancing the system damping and extending power transfer limits &#91;<a class="elsevierStyleCrossRefs" href="#bib0005">1&#8211;3</a>&#93;&#46; Recently&#44; several approaches such as optimization based techniques like genetic algorithms &#40;GA&#41;&#44; evolutionary programming&#44; tabu search&#44; simulated annealing and rule based bacteria foraging &#91;<a class="elsevierStyleCrossRefs" href="#bib0020">4&#8211;11</a>&#93; have been applied to PSSs parameter optimization problem&#46; These population based algorithms search procedures that incorporate random variation and selection operators&#46; Appearing suitable for optimizing the PSS parameters&#44; these approaches have long simulation time and degraded efficiency to obtain the global optimum solution when there is a large number of optimization parameters or when the system has a highly complex objective function &#40;i&#46;e&#46;&#44; where parameters being optimized are highly correlated in large power system&#41;&#46; In this paper&#44; the PSO based PSS is proposed which is used for optimal tuning of the PSS parameters to improve optimization synthesis and the speed of the convergence&#46; The PSO algorithm &#91;<a class="elsevierStyleCrossRef" href="#bib0060">12</a>&#93; is a derivative free promising algorithm for handling the combinatorial optimization problems&#46; It has been proved theoretically that PSO algorithm converges to the optimal solution &#91;<a class="elsevierStyleCrossRef" href="#bib0065">13</a>&#93;&#46; In addition&#44; the PSO algorithm is robust i&#46;e&#46;&#44; the final solution quality does not strongly depend on the choice of the initial solution&#46; Another strong feature of the PSO algorithm is that a complicated mathematical model is not required and the problem constraints can be easily incorporated &#91;<a class="elsevierStyleCrossRef" href="#bib0070">14</a>&#93;&#46;</p><p id="par0010" class="elsevierStylePara elsevierViewall">In this study&#44; the PSO is used to solve the problem of the PSSs design &#40;PSOPSS&#41; which is formulated as a multi-objective optimization problem&#46; The multi-objective problem is concocted to optimize a composite set of two eigenvalue-based functions and the integral of the time multiplied absolute value of the error &#40;ITAE&#41;-based objective function&#46; The effectiveness of the proposed PSOPSS is tested on a large scale multi-machine power system under different operating conditions in comparison with the<a name="p666"></a> GAPSS &#91;<a class="elsevierStyleCrossRef" href="#bib0055">11</a>&#93;&#46; Results evaluation show that the designed PSSs with proposed method achieves good robust performance for damping lowfrequency oscillations under different operating conditions and is superior to the other methods&#46;</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">2</span><span class="elsevierStyleSectionTitle" id="sect0020">Particle swarm optimization</span><p id="par0015" class="elsevierStylePara elsevierViewall">Particle swarm optimization algorithm&#44; which is tailored for optimizing difficult numerical functions and based on a metaphor of human social interaction&#44; is capable of mimicking the ability of human societies to process knowledge&#46; It has roots in two main component methodologies&#58; artificial life &#40;such as bird flocking&#44; fish schooling and swarming&#41;&#59; and&#44; evolutionary computation &#91;<a class="elsevierStyleCrossRef" href="#bib0070">14</a>&#93;&#46; The higher dimensional space calculations of the PSO concept are performed over a series of time steps&#46; The population is responding to the quality factors of the previous best individual values and the previous best group values&#46; This optimization technique can be used to solve many of the same kinds of problems as GA&#44; and does not suffer from some of the GAs difficulties&#46; It has been found also to be robust in solving problem featuring non-linearing&#44; non-differentiability and high-dimensionality &#91;<a class="elsevierStyleCrossRef" href="#bib0070">14</a>&#93;&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">In the PSO technique a number of simple entities&#44; the particles&#44; are placed in the search space of some problem or function&#44; and each evaluates the objective function at its current location&#46; Each particle then determines its movement through the search space by combining some aspect of the history of its own current and best locations by those with one or more members of the swarm with some random perturbations&#46; The next iteration takes place after all particles have been moved&#46; Eventually the swarm as a whole&#44; like a flock of birds collectively foraging for food&#44; is likely to move close to an optimum of the fitness function &#91;<a class="elsevierStyleCrossRef" href="#bib0065">13</a>&#93;&#46; In the PSO technique&#44; the trajectory of each individual in the search space is adjusted by dynamically altering the velocity of each particle&#44; according to its own flying experience and the flying experience of the other particles in the search space&#46; The position vector and the velocity vector of the <span class="elsevierStyleItalic">i</span>th particle in the <span class="elsevierStyleItalic">D</span>-dimensional search space can be represented as&#58; <span class="elsevierStyleItalic">X</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span> &#61; <span class="elsevierStyleItalic">&#40;x</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i1</span></span>&#44;<span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i2</span></span>&#44;&#8230;&#44;<span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">iD</span></span><span class="elsevierStyleItalic">&#41;</span> and <span class="elsevierStyleItalic">V</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span> &#61; <span class="elsevierStyleItalic">&#40;v</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i1</span></span>&#44;<span class="elsevierStyleItalic">v</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i2</span></span>&#8230;<span class="elsevierStyleItalic">v</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">iD</span></span><span class="elsevierStyleItalic">&#41;</span> respectively&#46; According to the user defined fitness function&#44; let us say the best position of each particle&#44; which corresponds to the best fitness value &#40;<span class="elsevierStyleItalic">pbest</span>&#41; obtained by that particle at time&#44; be <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span> &#61; <span class="elsevierStyleItalic">&#40;p</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i1</span></span>&#44;<span class="elsevierStyleItalic">p</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i2</span></span>&#44;&#8230;&#44;<span class="elsevierStyleItalic">p</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">iD</span></span><span class="elsevierStyleItalic">&#41;</span>&#44; and the global version of the PSO keeps track of the overall best value &#40;<span class="elsevierStyleItalic">gbest</span>&#41;&#44; and its location obtained&#44; thus far from any particle in the population&#46; Then&#44; the new velocities and the positions of the particles for the next fitness evaluation are calculated using the following two equations &#91;<a class="elsevierStyleCrossRef" href="#bib0065">13</a>&#44; <a class="elsevierStyleCrossRef" href="#bib0070">14</a>&#93;&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia><elsevierMultimedia ident="eq0010"></elsevierMultimedia></p><p id="par0025" class="elsevierStylePara elsevierViewall">Where&#44; <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">id</span></span> and <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">gd</span></span> are <span class="elsevierStyleItalic">pbest</span> and <span class="elsevierStyleItalic">gbest</span>&#46; Here <span class="elsevierStyleItalic">w</span> is the inertia weight parameter which controls the global and local exploration capabilities of the particle&#46; Constants <span class="elsevierStyleItalic">c</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span>&#44; <span class="elsevierStyleItalic">c</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span> are cognitive and social coefficients&#44; respectively&#44; and <span class="elsevierStyleItalic">r</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">r</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span> are random numbers between 0 and 1&#46; A larger inertia weight factor is used during initial exploration its value is gradually reduced as the search proceeds&#46; <a class="elsevierStyleCrossRef" href="#fig0005">Figure 1</a>&#44; shows the flowchart of the PSO algorithm&#46;<a name="p667"></a></p><elsevierMultimedia ident="fig0005"></elsevierMultimedia></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">3</span><span class="elsevierStyleSectionTitle" id="sect0025">Problem formulation</span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">3&#46;1</span><span class="elsevierStyleSectionTitle" id="sect0030">Power system model</span><p id="par0030" class="elsevierStylePara elsevierViewall">The aim of this study is to determine the parameters of power system stabilizers for damping oscillations&#46; For this reason&#44; appropriate modeling of the power system has a main role on better designing of stabilizers&#46; To model the n-machine interconnected system&#44; a set of differential algebraic equations is used and the model provided by assembling the models for each equipment such as generators&#44; loads&#44; controls etc&#46; and connecting them appropriately via the network algebraic equations &#91;<a class="elsevierStyleCrossRef" href="#bib0075">15</a>&#93;&#46; In this paper&#44; the two-axis model &#91;<a class="elsevierStyleCrossRef" href="#bib0010">2</a>&#93;&#44; given in the Appendix&#44; is used for time domain simulations and by linearizing the multi-machine power system around the operating points the simulation is done&#46; The main objective of the PSS is increasing the rotor damping of a synchronous generator&#46; By introducing appropriate supplementary control signals to the generator excitation system&#44; this objective is achieved&#46; <a class="elsevierStyleCrossRef" href="#fig0010">Figure 2</a>&#44; shows a schema of a synchronous generator control components&#46; The typical PSS block diagram used in this study is showed in <a class="elsevierStyleCrossRef" href="#fig0015">Figure 3</a>&#46; The PSS operating function &#91;<a class="elsevierStyleCrossRef" href="#bib0015">3</a>&#93; is to produce a torque on the rotor of the machine involved in such a way that compensates the phase lag between the exciter input and the machine electrical torque&#46; The dynamic compensator is made up to two lead-lag stages&#44; an additional gain and a washout filter where &#916;<span class="elsevierStyleItalic">&#969;</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span>&#44; is the deviation in speed from the synchronous speed&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1i</span></span>-<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">4i</span></span> are the lead-lag time constants&#44; <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">pss</span></span> is the gain of the PSS and <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">w</span></span> is the washout time constant&#46; The adjustable PSS parameters are the gain of the PSS&#44; <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span>&#44; and the time constants&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1i</span></span>-<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">4i</span></span> which these time constants are usually not critical and they can range from 0&#46;5 to 20 s&#46; Hence&#44; for each PSS&#44; there are five parameters comprise of 4 time constants and a gain constant that should be determined to achieve optimal output&#46; The output signal is fed as a supplementary input signal&#44; <span class="elsevierStyleItalic">V</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">pss</span></span> to the regulator of the excitation system&#46;</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia><elsevierMultimedia ident="fig0015"></elsevierMultimedia></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">3&#46;2</span><span class="elsevierStyleSectionTitle" id="sect0035">PSO based PSSs design</span><p id="par0035" class="elsevierStylePara elsevierViewall">In this paper&#44; for our optimization problem&#44; the PSO is employed to minimize a multi-objective fitness function comprise of the ITAE-based and eigenvalue-based functions for the PSSs design problem&#46; These objectives are defined as follows&#58;<elsevierMultimedia ident="eq0015"></elsevierMultimedia><elsevierMultimedia ident="eq0020"></elsevierMultimedia><elsevierMultimedia ident="eq0025"></elsevierMultimedia></p><p id="par0040" class="elsevierStylePara elsevierViewall">Where&#44; <span class="elsevierStyleItalic">&#963;</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span>&#44; is the real part of the <span class="elsevierStyleItalic">i</span>th eigenvalue&#46; Also&#44; speed deviation &#40;&#916;&#969;&#41;&#44; of the machines are considered for the evaluation of the <span class="elsevierStyleItalic">j</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span>&#46; The <span class="elsevierStyleItalic">&#945;</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span> and <span class="elsevierStyleItalic">&#945;</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span> are weighting factors and t<span class="elsevierStyleInf">sim</span> is the time range of simulation&#46; The <span class="elsevierStyleItalic">N</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">G</span></span> is the number of machines and <span class="elsevierStyleItalic">N</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">P</span></span> is the total number of operating points for which the optimization is carried out&#46; The value of <span class="elsevierStyleItalic">&#963;</span><span class="elsevierStyleInf">0</span> determines the relative stability in terms of damping factor margin provided for constraining the placement of eigenvalues during the process of optimization&#46; By optimizing <span class="elsevierStyleItalic">J</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span>&#44; closed loop system poles are consistently pushed further left from the imaginary axis with simultaneous reduction in real parts&#46; By optimizing <span class="elsevierStyleItalic">J</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span>&#44; the sum of deviation of speed in each generator speed response is getting minimized&#46; The design problem can be formulated as the following constrained optimization problem&#44; where the constraints are the PSS parameter bounds&#58;<elsevierMultimedia ident="eq0030"></elsevierMultimedia></p><p id="par0045" class="elsevierStylePara elsevierViewall"><a name="p668"></a>By employing the PSO&#44; the proposed approach solves this optimization problem and search for optimal or near optimal set of the PSS parameters &#40;<span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span>&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1i</span></span>&#8722;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">4i</span></span><span class="elsevierStyleItalic">for i</span>&#61;<span class="elsevierStyleItalic">1&#44;2</span>&#44;&#8230;&#44;<span class="elsevierStyleItalic">m</span> where&#44; <span class="elsevierStyleItalic">m</span> is the number of machines&#41; &#91;<a class="elsevierStyleCrossRef" href="#bib0050">10</a>&#93;&#46;</p></span></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">4</span><span class="elsevierStyleSectionTitle" id="sect0040">Case study</span><p id="par0050" class="elsevierStylePara elsevierViewall">In this study&#44; the sixteen-machine five-area power system shown in <a class="elsevierStyleCrossRef" href="#fig0020">Figure 4</a> is considered&#46; The system comprises the five coherent groups representing a reduced model of the New England and New York interconnected system&#46; Details of the system data are given in &#91;<a class="elsevierStyleCrossRef" href="#bib0080">16</a>&#93;&#46; To assess the effectiveness and robustness of the proposed method over a wide range of loading conditions&#44; five operating conditions &#40;<a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a>&#41; without PSSs are considered&#46;</p><elsevierMultimedia ident="fig0020"></elsevierMultimedia><elsevierMultimedia ident="tbl0005"></elsevierMultimedia><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">4&#46;1</span><span class="elsevierStyleSectionTitle" id="sect0045">PSO-based PSSs design</span><p id="par0055" class="elsevierStylePara elsevierViewall">In the proposed method&#44; we must tune the PSSs parameters optimally to improve the overall system dynamic stability in a robust way under different operating conditions and disturbances&#46; For each PSS&#44; the optimal setting of five parameters is determined by the PSO algorithm&#44; i&#46;e&#46;&#44; 60 parameters to be optimized&#44; namely <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span>&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1i</span></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2i</span></span>&#44;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">3i</span></span> and <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">4i</span></span>for <span class="elsevierStyleItalic">i</span>&#61; <span class="elsevierStyleItalic">1&#44; 2</span>&#44; &#8230;&#44;<span class="elsevierStyleItalic">12</span>&#46;</p><p id="par0060" class="elsevierStylePara elsevierViewall">The optimization of the PSS parameters is carried out by evaluating the multi-objective function as given in <a class="elsevierStyleCrossRef" href="#eq0025">Equation 5</a>&#46; In this work&#44; in order to acquire better performance&#44; number of particle&#44; particle size&#44; number of iteration&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span>&#44; and <span class="elsevierStyleItalic">C</span> is chosen as 80&#44; 60&#44; 60&#44; 2&#44; 2 and 1&#44; respectively&#46; It should be noted that PSO algorithm is run several<a name="p669"></a> times and then optimal set of the PSSs parameters is selected&#46; Results of the PSSs parameter achieved from the PSO algorithm are given in <a class="elsevierStyleCrossRef" href="#tbl0010">Table 2</a>&#46; The convergence rate of algorithm is illustrated in <a class="elsevierStyleCrossRef" href="#fig0025">Figure 5</a>&#46;</p><elsevierMultimedia ident="tbl0010"></elsevierMultimedia><elsevierMultimedia ident="fig0025"></elsevierMultimedia></span><span id="sec0040" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">4&#46;2</span><span class="elsevierStyleSectionTitle" id="sect0050">Eigenvalue analysis</span><p id="par0065" class="elsevierStylePara elsevierViewall">The PSSs were placed in all generators&#44; except for the ones numbered as 13&#44; 14&#44; 15 and 16 in <a class="elsevierStyleCrossRef" href="#fig0020">Figure 4</a>&#46; To assess the effectiveness and robustness of the proposed controller&#44; a multiple of operating conditions according to <a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a> are considered and simulation studies are carried out for various fault disturbances and fault clearing sequences for two scenarios&#46; The eigenvalues analysis from the two cases with proposed PSSs and from the base case without PSSs is depicted in <a class="elsevierStyleCrossRef" href="#fig0030">Figure 6</a>&#46; Moreover&#44; it is also clear that the system damping with the proposed PSO based tuned PSSs with multi-objective function has improved significantly&#46;</p><elsevierMultimedia ident="fig0030"></elsevierMultimedia></span><span id="sec0045" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">4&#46;3</span><span class="elsevierStyleSectionTitle" id="sect0055">Nonlinear simulation results</span><span id="sec0050" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0060">Scenario 1</span><p id="par0070" class="elsevierStylePara elsevierViewall">In this scenario&#44; by applying a three-cycle&#44; three phase fault at bus 1&#44; on line 1&#8211;2 the performance of the proposed controller under transient conditions is verified&#46; The fault is cleared after 0&#46;06 seconds and the original system is restored upon the clearance of the fault&#46; The performance of the tuned multi-objective based PSSs is compared to that of the PSSs tuned using the GA for different operating conditions as given in <a class="elsevierStyleCrossRef" href="#tbl0010">Table 2</a>&#46; The speed deviations of generators <span class="elsevierStyleItalic">G</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">3</span></span>&#44; <span class="elsevierStyleItalic">G</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">8</span></span>&#44; <span class="elsevierStyleItalic">G</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">10</span></span>&#44; <span class="elsevierStyleItalic">G</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">12</span></span>&#44; <span class="elsevierStyleItalic">G</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">13</span></span> and <span class="elsevierStyleItalic">G</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">14</span></span> and the power flow on lines 1&#8211;30&#44; 9&#8211;36&#44; 9&#8211;30&#44; 78 and 17&#8211;18 under the above conditions are shown in <a class="elsevierStyleCrossRef" href="#fig0035">Figure 7</a>&#46; It can be seen that the PSOPSSs with multi-objective function achieves good robust performance and provides superior damping in comparison with the other methods&#46;</p><elsevierMultimedia ident="fig0035"></elsevierMultimedia></span><span id="sec0055" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0065">Scenario 2</span><p id="par0075" class="elsevierStylePara elsevierViewall">In this scenario&#44; another severe disturbance is considered for different loading conditions&#59; that is&#44; a five-cycle&#44; three-phase fault is applied at bus 10&#44; on line 10&#8211;11&#46; The fault is cleared after 0&#46;1 seconds and the original system is restored upon the clearance of the fault&#46; The system response is shown in <a class="elsevierStyleCrossRef" href="#fig0040">Figure 8</a>&#46; It can be seen that the proposed PSOPSSs have good performance in damping of the low frequency oscillations and stabilizes the system quickly&#46;</p><elsevierMultimedia ident="fig0040"></elsevierMultimedia><p id="par0080" class="elsevierStylePara elsevierViewall">To demonstrate the performance robustness of the proposed method&#44; two indices for system performance characteristics are defined as follows &#91;<a class="elsevierStyleCrossRef" href="#bib0015">3</a>&#93;&#58;<elsevierMultimedia ident="eq0035"></elsevierMultimedia><elsevierMultimedia ident="eq0040"></elsevierMultimedia><a name="p670"></a><a name="p671"></a><a name="p672"></a></p><p id="par0085" class="elsevierStylePara elsevierViewall">Where &#969; is the speed rotor&#59; overshoot &#40;OS&#41;&#59; undershoot &#40;US&#41; and settling time &#40;T<span class="elsevierStyleInf">s</span>&#41; of all generators&#44; speed deviations are considered for the evaluation of the ITAE and FD indices&#46; The t<span class="elsevierStyleInf">sim</span> is the simulation time which is 10 seconds here&#46; The lower the value of these indices is&#44; the better the performance of system in disturbances&#46; The results of evaluating these two indices for different operating conditions under various disturbances for PSOPSS in comparison with GAPSS are brought in <a class="elsevierStyleCrossRef" href="#tbl0015">Table 3</a>&#46; It can be seen that the value of these indices for the proposed method are much smaller than other methods&#46; This demonstrates that the overshoot&#44; undershoot&#44; settling time and speed deviations of the machine are greatly reduced by applying the proposed stabilizers&#46;</p><elsevierMultimedia ident="tbl0015"></elsevierMultimedia></span></span></span><span id="sec0060" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">5</span><span class="elsevierStyleSectionTitle" id="sect0070">Conclusions</span><p id="par0090" class="elsevierStylePara elsevierViewall">In order to improve the transient stability and damp the low frequency oscillations&#44; robust PSSs design based on a multi-objective fitness function consist of a composite set of two eigenvalue based and the ITAE-based objective functions was proposed in large power systems&#46; The design problem was formulated as a nonlinear optimization problem for multiple operating conditions&#46; Then&#44; the PSO algorithm was successfully applied to find the optimal solution of the design problem&#46; The nonlinear simulation results under different operating conditions show the effectiveness of the proposed controllers and their ability to provide good damping of low frequency oscillations in comparison to the GAPSS method and the results demonstrated the superiority of the proposed method in solution quality&#46; The ITAE and FD indices revealed that by using the proposed objective based function controllers&#44; the overshoot&#44; undershoot&#44; settling time and power system oscillations are greatly reduced at various loading conditions&#46;</p></span></span>"
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        "titulo" => "Abstract"
        "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><p id="spar0060" class="elsevierStyleSimplePara elsevierViewall">The problem of coordinated tuning stabilizers in multi-machine power systems is formulated here as a sequence of optimization problems&#46; The design problem of stabilizers is converted to a nonlinear optimization problem with a multi-objective fitness function&#46; The proposed method employs particle swarm optimization &#40;PSO&#41;&#44; an algorithm to search for optimal parameter settings of a widely used conventional fixed-structure lead-lag power system stabilizers &#40;CPSSs&#41;&#46; One of the main advantages of the proposed approach is its robustness to the initial parameter settings&#46; In addition&#44; the quality of the optimal solution does not rely on the initial guess&#46; The robustness and performance of the newly designed controllers is evaluated in a large sixteen-machine power system subjected to different loading conditions in comparison with the genetic algorithm &#40;GA&#41; based PSSs design&#46; The superiority of the controller designed is demonstrated through the nonlinear time-domain simulation and some performance indices studies&#46; The results analysis reveals that the tuned PSSs with proposed objective function has an excellent capability in damping power system low-frequency oscillations&#46;</p></span>"
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                  \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Operating condition&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Description&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">All lines in service&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">Power generation at G6 increased 50&#37;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">Case 3&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">Lines 17&#8211;27 and 30&#8211;31 are out of service and Power generation at G8 and G10 increased 30&#37;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G1&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">62&#46;13&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;9037&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;0534&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6332&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;4148&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G2&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">197&#46;7&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;7673&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;1747&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;4140&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;2492&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G3&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">194&#46;8&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8147&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;1826&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6761&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;7490&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G4&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">126&#46;62&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6721&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8259&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8120&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8544&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G5&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">136&#46;19&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6690&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;2189&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;7219&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;9637&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G6&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">198&#46;37&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6380&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;4256&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;9287&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6872&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G7&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">119&#46;21&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;4391&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;2381&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8901&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;5729&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G8&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">128&#46;07&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;7237&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;1584&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8570&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8297&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G9&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">105&#46;08&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;7803&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;9372&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8173&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;2460&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G10&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">174&#46;77&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6620&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;1454&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;9333&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;6595&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G11&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">167&#46;32&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;7904&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;1278&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8422&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8867&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">G12&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">116&#46;73&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8844&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;4280&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;8454&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">0&#46;3693&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr></tbody></table>
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                  \t\t\t\t\tvoid\n
                  \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="table-head  " rowspan="3" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Operating condition</th><th class="td" title="table-head  " colspan="4" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Scenario 1</th><th class="td" title="table-head  " colspan="4" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Scenario 2</th></tr><tr title="table-row"><th class="td" title="table-head  " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">PSOPSS</th><th class="td" title="table-head  " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">GAPSS</th><th class="td" title="table-head  " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">PSOPSS</th><th class="td" title="table-head  " colspan="2" align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">GAPSS</th></tr><tr title="table-row"><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">ITAE&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th><th class="td" title="table-head  " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">FD&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">Base case&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">82&#46;45&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">83&#46;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">402&#46;22&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1231&#46;59&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">231&#46;25&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">322&#46;60&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">2021&#46;78&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">2862&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">Case 1&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">88&#46;02&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">101&#46;12&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">501&#46;04&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1349&#46;96&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">293&#46;30&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">490&#46;68&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">2496&#46;60&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">4506&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">Case 2&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">137&#46;13&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">129&#46;83&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">503&#46;10&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1381&#46;11&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">310&#46;67&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">612&#46;43&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">2360&#46;85&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">3085&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">Case 3&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">82&#46;90&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">86&#46;04&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">457&#46;70&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1262&#46;32&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">287&#46;63&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">504&#46;13&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1405&#46;71&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1890&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry  " align="center" valign="middle">Case 4&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">104&#46;98&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">118&#46;53&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">642&#46;57&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1356&#46;65&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">297&#46;14&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">543&#46;98&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1420&#46;46&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="table-entry  " align="center" valign="middle">1910&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr></tbody></table>
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Article information

ISSN: 16656423
Original language: English

DOI:10.1016/S1665-6423(13)71574-8

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2024 February	113	22	135
2024 January	164	10	174
2023 December	200	27	227
2023 November	172	20	192
2023 October	188	29	217
2023 September	108	16	124
2023 August	104	5	109
2023 July	122	19	141
2023 June	117	13	130
2023 May	199	19	218
2023 April	123	3	126
2023 March	150	8	158
2023 February	91	9	100
2023 January	91	11	102
2022 December	70	6	76
2022 November	54	12	66
2022 October	77	20	97
2022 September	71	8	79
2022 August	69	16	85
2022 July	39	10	49
2022 June	52	10	62
2022 May	44	9	53
2022 April	50	21	71
2022 March	63	9	72
2022 February	66	5	71
2022 January	109	11	120
2021 December	66	19	85
2021 November	62	10	72
2021 October	83	15	98
2021 September	75	14	89
2021 August	64	10	74
2021 July	42	13	55
2021 June	38	16	54
2021 May	57	11	68
2021 April	107	6	113
2021 March	52	17	69
2021 February	36	7	43
2021 January	47	14	61
2020 December	61	11	72
2020 November	50	17	67
2020 October	35	12	47
2020 September	28	16	44
2020 August	31	11	42
2020 July	28	13	41
2020 June	27	8	35
2020 May	44	6	50
2020 April	87	2	89
2020 March	16	9	25
2020 February	32	5	37
2020 January	14	2	16
2019 December	18	8	26
2019 November	44	5	49
2019 October	104	12	116
2019 September	50	3	53
2019 August	32	5	37
2019 July	16	18	34
2019 June	28	22	50
2019 May	79	5	84
2019 April	35	6	41
2019 March	12	4	16
2019 February	11	3	14
2019 January	5	7	12
2018 December	1	0	1
2018 November	20	3	23
2018 October	36	11	47
2018 September	32	2	34
2018 August	8	1	9
2018 July	9	3	12
2018 June	9	1	10
2018 May	12	1	13
2018 April	9	3	12
2018 March	10	2	12
2018 February	13	1	14
2018 January	7	0	7
2017 December	11	3	14
2017 November	8	2	10
2017 October	10	0	10
2017 September	17	10	27
2017 August	9	14	23
2017 July	11	3	14
2017 June	17	12	29
2017 May	19	22	41
2017 April	22	20	42
2017 March	16	27	43
2017 February	16	2	18
2017 January	20	2	22
2016 December	22	7	29
2016 November	10	2	12
2016 October	14	5	19
2016 September	13	6	19
2016 August	17	7	24
2016 July	22	3	25
2016 June	7	4	11
2016 May	8	9	17
2016 April	11	8	19
2016 March	12	8	20
2016 February	21	16	37
2016 January	11	11	22
2015 December	9	4	13
2015 November	15	2	17
2015 October	24	6	30
2015 September	18	6	24
2015 August	31	3	34
2015 July	17	4	21
2015 June	1	1	2
2015 May	4	1	5
2015 April	0	1	1

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