Detection of maximum loadability limits and weak buses using Chaotic PSO considering security constraints

In the current research chaotic search is used with the optimization technique for solving non-linear complicated power system problems because Chaos can overcome the local optima problem of optimization technique. Power system problem, more specifically voltage stability, is one of the practical examples of non-linear, complex, convex problems. Smart grid, restructured energy system and socio-economic development fetch various uncertain events in power systems and the level of uncertainty increases to a great extent day by day. In this context, analysis of voltage stability is essential. The efficient method to assess the voltage stability is maximum loadability limit (MLL). MLL problem is formulated as a maximization problem considering practical security constraints (SCs). Detection of weak buses is also important for the analysis of power system stability. Both MLL and weak buses are identified by PSO methods and FACTS devices can be applied to the detected weak buses for the improvement of stability. Three particle swarm optimization (PSO) techniques namely General PSO (GPSO), Adaptive PSO (APSO) and Chaotic PSO (CPSO) are presented for the comparative study with obtaining MLL and weak buses under different SCs. In APSO method, PSO-parameters are made adaptive with the problem and chaos is incorporated in CPSO method to obtain reliable convergence and better performances. All three methods are applied on standard IEEE 14 bus, 30 bus, 57 bus and 118 bus test systems to show their comparative computing effectiveness and optimization efficiencies.     

Chaotic catfish particle swarm optimization for solving global numerical optimization problems

Chaotic catfish particle swarm optimization (C-CatfishPSO) is a novel optimization algorithm proposed in this paper. C-CatfishPSO introduces chaotic maps into catfish particle swarm optimization (CatfishPSO), which increase the search capability of CatfishPSO via the chaos approach. Simple CatfishPSO relies on the incorporation of catfish particles into particle swarm optimization (PSO). The introduced catfish particles improve the performance of PSO considerably. Unlike other ordinary particles, the catfish particles initialize a new search from extreme points of the search space when the gbest fitness value (global optimum at each iteration) has not changed for a certain number of consecutive iterations. This results in further opportunities of finding better solutions for the swarm by guiding the entire swarm to promising new regions of the search space and accelerating the search. The introduced chaotic maps strengthen the solution quality of PSO and CatfishPSO significantly. The resulting improved PSO and CatfishPSO are called chaotic PSO (C-PSO) and chaotic CatfishPSO (C-CatfishPSO), respectively. PSO, C-PSO, CatfishPSO, C-CatfishPSO, as well as other advanced PSO procedures from the literature were extensively compared on several benchmark test functions. Statistical analysis of the experimental results indicate that the performance of C-CatfishPSO is better than the performance of PSO, C-PSO, CatfishPSO and that C-CatfishPSO is also superior to advanced PSO methods from the literature.     

Short-term cascaded hydroelectric system scheduling based on chaotic particle swarm optimization using improved logistic map

In order to solve the model of short-term cascaded hydroelectric system scheduling, a novel chaotic particle swarm optimization (CPSO) algorithm using improved logistic map is introduced, which uses the water discharge as the decision variables combined with the death penalty function. According to the principle of maximum power generation, the proposed approach makes use of the ergodicity, symmetry and stochastic property of improved logistic chaotic map for enhancing the performance of particle swarm optimization (PSO) algorithm. The new hybrid method has been examined and tested on two test functions and a practical cascaded hydroelectric system. The experimental results show that the effectiveness and robustness of the proposed CPSO algorithm in comparison with other traditional algorithms.     

Minimum entropy control of chaos via online particle swarm optimization method

One of the recently developed approaches for control of chaos is the minimum entropy (ME) control technique. In this method an entropy function based on the Shannon definition, is defined for a chaotic system. The control action is designed such that the entropy as a cost function is minimized which results in more regular pattern of motion for the system trajectories. In this paper an online optimization technique using particle swarm optimization (PSO) method is developed to calculate the control action based on ME strategy. The method is examined on some standard chaotic maps with error feedback and delayed feedback forms. Considering the fact that the optimization is online, simulation results show very good effectiveness of the presented technique in controlling chaos.     

PID control for chaotic synchronization using particle swarm optimization

In this paper, we attempt to use the proportional-integral-derivative (PID) controller to achieve the chaos synchronization for delayed discrete chaotic systems. Three PID control gains can be optimally determined by means of using a novel optimization algorithm, called the particle swarm optimization (PSO). The algorithm is motivated from the organism behavior of fish schooling and bird flocking, and involves the social psychology principles in socio-cognition human agents and evolutionary computations. It has a good numerical convergence for solving optimization problem. To show the validity of the PSO-based PID control for chaos synchronization, several cases with different initial populations are considered and some simulation results are shown.     

基于混沌粒子群算法的Tikhonov正则化参数选取

Tikhonov正则化方法是求解不适定问题最为有效的方法之一,而正则化参数的最优选取是其关键.本文将混沌粒子群优化算法与Tikhonov正则化方法相结合,基于Morozov偏差原理设计粒子群的适应度函数,利用混沌粒子群优化算法的优点,为正则化参数的选取提供了一条有效的途径.数值实验结果表明,本文方法能有效地处理不适定问题,是一种实用有效的方法.     

Chaos-enhanced accelerated particle swarm optimization

There are more than two dozen variants of particle swarm optimization (PSO) algorithms in the literature. Recently, a new variant, called accelerated PSO (APSO), shows some extra advantages in convergence for global search. In the present study, we will introduce chaos into the APSO in order to further enhance its global search ability. Firstly, detailed studies are carried out on benchmark problems with twelve different chaotic maps to find out the most efficient one. Then the chaotic APSO (CAPSO) will be compared with some other chaotic PSO algorithms presented in the literature. The performance of the CAPSO algorithm is also validated using three engineering problems. The results show that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.     

A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the chaotic systems theory, this paper proposed a novel chaotic PSO combined with an implicit filtering (IF) local search method to solve economic dispatch problems. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed PSO introduces chaos mapping using Hénon map sequences which increases its convergence rate and resulting precision. The chaotic PSO approach is used to produce good potential solutions, and the IF is used to fine-tune of final solution of PSO. The hybrid methodology is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. Simulation results are promising and show the effectiveness of the proposed approach.     

Dynamic guiding particle swarm optimization with embedded chaotic search for solving multidimensional problems

The proposed approach incorporated dynamic guiding approach and chaotic search procedure into particle swarm optimization (PSO), named DCPSO. Chaotic search, enjoyed ergodicity, irregularity and pseudo-randomness in PSO, would refine global best position evidently. And, dynamic guiding approach with fluctuating property would easily conduct unpredictable migrations for PSO to break away from evolutionary stagnation. The experiment reports indicated that the proposed DCPSO approach could improve the evolution performance significantly, and present the superiority in solving complex multidimensional problems.     

Application of particle swarm optimization in chaos synchronization in noisy environment in presence of unknown parameter uncertainty

In this paper, particle swarm optimization (PSO) is applied to synchronize chaotic systems in presence of parameter uncertainties and measurement noise. Particle swarm optimization is an evolutionary algorithm which is introduced by Kennedy and Eberhart. This algorithm is inspired by birds flocking. Optimization algorithms can be applied to control by defining an appropriate cost function that guarantees stability of system. In presence of environment noise and parameter uncertainty, robustness plays a crucial role in succeed of controller. Since PSO needs only rudimentary information about the system, it can be a suitable algorithm for this case. Simulation results confirm that the proposed controller can handle the uncertainty and environment noise without any extra information about them. A comparison with some earlier works is performed during simulations.