Genetic evolving ant direction particle swarm optimization algorithm for optimal power flow with non-smooth cost functions and statistical analysis

This paper presents an evolving ant direction particle swarm optimization algorithm for solving the optimal power flow problem with non-smooth and non-convex generator cost characteristics. In this method, ant colony search is used to find a suitable velocity updating operator for particle swarm optimization and the ant colony parameters are evolved using genetic algorithm approach. To update the velocities for particle swarm optimization, five velocity updating operators are used in this method. The power flow problem is solved by the Newton–Raphson method. The feasibility of the proposed method was tested on IEEE 30-bus, IEEE 39-bus and IEEE-57 bus systems with three different objective functions. Several cases were investigated to test and validate the effectiveness of the proposed method in finding the optimal solution. Simulation results prove that the proposed method provides better results compared to classical particle swarm optimization and other methods recently reported in the literature. An innovative statistical analysis based on central tendency measures and dispersion measures was carried out on the bus voltage profiles and voltage stability indices.     

Differential evolution approach for optimal reactive power dispatch

Differential evolution based optimal reactive power dispatch for real power loss minimization in power system is presented in this paper. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts to be switched, for real power loss minimization in the transmission system. The problem is formulated as a mixed integer nonlinear optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling. The formulation also checks for the feasibility of the optimal control variable setting from a voltage security point of view by using a voltage collapse proximity indicator. The algorithm is tested on standard IEEE 14, IEEE 30, and IEEE 118-Bus test systems. To show the effectiveness of proposed method the results are compared with Particle Swarm Optimization and a conventional optimization technique – Sequential Quadratic Programming.     

Optimal reactive power dispatch for real power loss minimization and voltage stability enhancement using Artificial Bee Colony Algorithm

Reactive Power Dispatch (RPD) plays important role in power system reliability and security. This paper proposes the Optimal Reactive Power Dispatch (ORPD) for real power loss minimization, voltage deviation minimization and voltage stability enhancement using Artificial Bee Colony (ABC) Algorithm. ORPD is a mixed integer nonlinear optimization problem which includes both continuous and discrete control variables. The ABC algorithm is used to find the setting of control variables such as generator voltage magnitude, tap position of tap changing transformer and reactive power output of the compensation devices. The proposed algorithm is tested on IEEE 30 and 57 bus systems, Simulation results show that the proposed approach converges to better solutions and much faster than the earlier reported approaches in the literature. The optimization strategy is general and can be used to solve other power system optimization problems.     

Exchange market algorithm based optimum reactive power dispatch

In this paper, an exchange market algorithm (EMA) approach is applied to solve highly non-linear power system optimal reactive power dispatch (ORPD) problems. ORPD is most vital optimization problems in power system study and are usually devised as optimal power flow (OPF) problem. The problem is formulated as nonlinear, non-convex constrained optimization problem with the presence of both continuous and discrete control variables. The EMA searches for optimal solution via two main phases; namely, balanced market and oscillation market. Each of the phases comprises of both exploration and exploitation, which makes the algorithm unique. This uniqueness of EMA is exploited in this paper to solve various vital objectives associated with ORPD problems. Programs are developed in MATLAB and tested on standard IEEE 30 and IEEE 118 bus systems. The results obtained using EMA are compared with other contemporary methods in the literature. Simulation results demonstrate the superiority of EMA in terms of its computational efficiency and robustness. Consumed function evaluation for each case study is mentioned in the convergence plot itself for better clarity. Parametric study is also performed on different case studies to obtain the suitable values of tuneable parameters.     

Multiagent based differential evolution approach to optimal power flow

This paper proposes a new differential evolution approach named as multiagent based differential evolution (MADE) based on multiagent systems, for solving optimal power flow problem with non-smooth and non-convex generator fuel cost curves. This method integrates multiagent systems (MAS) and differential evolution (DE) algorithm. An agent in MADE represents an individual to DE and a candidate solution to the optimization problem. All agents live in a lattice like environment, with each agent fixed on a lattice point. In order to obtain optimal solution quickly, each agent competes and cooperates with its neighbors and it can also use knowledge. Making use of these agent-agent interaction and DE mechanism, MADE realizes the purpose of minimizing the value of objective function. MADE applied to optimal power flow is evaluated on 6 bus system and IEEE 30 bus system with different generator characteristics. Simulation results show that the proposed method converges to better solutions much faster than earlier reported approaches.     

Weighted elitism based Ant Lion Optimizer to solve optimum VAr planning problem

In this paper, a newly proposed Ant-Lion Optimizer (ALO) is applied to solve Optimal Reactive Power Dispatch (ORPD) problem of power system. The ORPD is a VAr planning problem and is a highly non linear, non convex, challenging optimization problem; usually devised as constrained Optimal Power Flow (OPF). This paper also proposes the improvement in the search capability of ALO. A novel weighted elitism concept is introduced in the elitism phase of the original ALO to improve the exploration property of the algorithm. The proposed Modified ALO (MALO) intelligently balances both exploration and exploitation, which enhances the hunting capability of ALO. Both ALO and MALO is used to determine the optimal settings of generator voltages, tap positions of tap changer transformers and VAr output of shunt capacitors to optimize objectives: like, the active power loss, total voltage deviation and voltage stability index. The proposed algorithm is programmed and simulated on MATLB and tested on IEEE-30 and 57 bus systems. The results are compared with ALO and other methods. The effectiveness of MALO is further verified by solving few benchmark mathematical functions. The numerical results reveal that, MALO gives better optimum solutions for the benchmark functions compare to original ALO and outperforms several other methods used in the literature to solve ORPD problems. The t-Test and parametric analysis confirms the robustness and consistency of the MALO over ALO and other similar methods.     

A mixed integer programme for optimal static capacitor allocation in power systems

A method is presented for the determination of optimal size and location of static capacitor installations in a power system network for maintenance of the bus voltage magnitudes within prescribed limits under highly loaded or outage conditions. The problem is formulated as an optimization problem with the objective function representing the cost of capacitor installations and the constraints represent the reactive power flow equation of the system and the limits on the variations of the tap settings of the tap changing transformers and the generator bus voltages. The generator bus voltage magnitudes are continuously variable and the capacitor units to be installed and the tap settings are treated as discrete or integer variables. By partioning the variables into control and controlled quantities, a number of variables are eliminated from the problem. The problem is then decomposed into two smaller subproblems with integer or continuous variables. These result in the reduction of the computer memory and time requirements.     

Optimal reactive power dispatch with uncertainties in load demand and renewable energy sources adopting scenario-based approach

Optimizing reactive power flow in electrical network is an important aspect of system study as the reactive power supports network voltage which needs to be maintained within desirable limits for system reliability. A network consisting of only conventional thermal generators has been extensively studied for optimal active and reactive power dispatch. However, increasing penetration of renewable sources into the grid necessitates power flow studies incorporating these sources. This paper presents a formulation and solution procedure for stochastic optimal reactive power dispatch (ORPD) problem with uncertainties in load demand, wind and solar power. Appropriate probability density functions (PDFs) are considered to model the stochastic load demand and the power generated from the renewable energy sources. Numerous scenarios are created running Monte-Carlo simulation and scenario reduction technique is implemented to deal with reduced number of scenarios. Real power loss and steady state voltage deviation of load buses in the network are set as the objectives of optimization. Success history based adaptive differential evolution (SHADE) is adopted as the basic search algorithm. SHADE has been successfully integrated with a constraint handling technique, called epsilon constraint (EC) handling, to handle constraints in ORPD problem. The effectiveness of a proper constraint handling technique is substantiated with case studies for deterministic ORPD on base configurations of IEEE 30-bus and 57-bus systems using SHADE-EC algorithm. The single-objective and multi-objective stochastic ORPD cases are also solved using the SHADE-EC algorithm. The results are discussed, compared and critically analyzed in this study.     

Multi-objective GA with fuzzy decision making for security enhancement in power system

Power system security enhancement is a major concern in the operation of power system. In this paper, the task of security enhancement is formulated as a multi-objective optimization problem with minimization of fuel cost and minimization of FACTS device investment cost as objectives. Generator active power, generator bus voltage magnitude and the reactance of Thyristor Controlled Series Capacitors (TCSC) are taken as the decision variables. The probable locations of TCSC are pre-selected based on the values of Line Overload Sensitivity Index (LOSI) calculated for each branch in the system. Multi-objective genetic algorithm (MOGA) is applied to solve this security optimization problem. In the proposed GA, the decision variables are represented as floating point numbers in the GA population. The MOGA emphasize non-dominated solutions and simultaneously maintains diversity in the non-dominated solutions. A fuzzy set theory-based approach is employed to obtain the best compromise solution over the trade-off curve. The proposed approach has been evaluated on the IEEE 30-bus and IEEE 118-bus test systems. Simulation results show the effectiveness of the proposed approach for solving the multi-objective security enhancement problem.     

Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem

Solution of optimal power flow (OPF) problem aims to optimize a selected objective function such as fuel cost, active power loss, total voltage deviation (TVD) etc. via optimal adjustment of the power system control variables while at the same time satisfying various equality and inequality constraints. In the present work, a particle swarm optimization with an aging leader and challengers (ALC-PSO) is applied for the solution of the OPF problem of power systems. The proposed approach is examined and tested on modified IEEE 30-bus and IEEE 118-bus test power system with different objectives that reflect minimization of fuel cost or active power loss or TVD. The simulation results demonstrate the effectiveness of the proposed approach compared with other evolutionary optimization techniques surfaced in recent state-of-the-art literature. Statistical analysis, presented in this paper, indicates the robustness of the proposed ALC-PSO algorithm.     

带峰值能耗约束流水线调度的协同群智能优化

当今社会环境问题日益严重,能源成本日益提高,峰值能耗在生产制造中备受关注.针对带峰值能耗约束的流水线调度问题,即生产过程中各时间节点机器总功耗不得超过给定阈值,以最小化最大完工时间为目标,提出一种协同群智能算法.首先,协同多种解码方法产生多样化的可行调度,融合启发式方法与随机方法以初始化种群;其次,设计两类基于问题特性的搜索操作,分别调整工件序列和加工速度;接着,根据目标空间中个体的分布,设计多种搜索操作的协同机制,对不同区域的个体执行不同的搜索操作,并对精英个体进行局部增强搜索以进一步改善性能;最后,采用大量算例开展数值实验,验证了所设计协同机制的有效性,并通过与数学求解器和现有算法的对比结果表明所提出算法能够更有效求解带峰值能耗约束的流水线调度问题.     

基于改进遗传算法的电力系统无功优化的研究

电力系统无功优化问题是一个多变量、多约束的混合非线性规划问题,其操作变量既有连续变量又有离散变量,其优化过程比较复杂。遗传算法是模拟生物在自然环境中的遗传和进化过程而形成的一种自适应的全局优化搜索算法,可用于解决含有离散变量的复杂优化问题。本文选用遗传算法求解电力系统无功优化问题,并对基本遗传算法的编码、初始种群、适应度函数和交叉、变异策略等进行改进,使用本文提出的改进算法对IEEE1 4节点进行无功优化计算,结果证明本文模型和算法的实用性、可靠性和优越性。     

Security optimal power flow considering loading margin stability using hybrid FFA–PS assisted with brainstorming rules

This paper presents a new power system planning strategy which combines firefly algorithm (FFA) with pattern search algorithm (PS). The purpose is minimizing total fuel cost, total power loss and reducing total voltage deviation, with the objective of enhancing the loading margin stability and consequently the power system security. A new interactive and simple mechanism, inspired in brainstorming process, is proposed that allows FFA and PS algorithms to explore new regions of the search space. In this study the Static VAR compensator (SVC) is modeled and integrated in an efficient location which is chosen considering the voltage stability index. The proposed algorithm is interactive and tries to optimize a set of control variables at the same time, namely, active power generations, voltage of generators, tap transformers, and the reactive power of shunt compensators to optimize three objective functions such as: fuel cost, total power loss and total voltage deviation. These variables are optimized using a flexible interactive and competitive search mechanism. The proposed planning strategy has been examined and applied to two practical test systems IEEE 14-Bus and IEEE 30-Bus. Simulation results confirm the effectiveness of this hybrid strategy for solving the security optimal power flow.     

An improved artificial bee colony optimization algorithm based on orthogonal learning for optimal power flow problem

The increasing fuel price has led to high operational cost and therefore, advanced optimal dispatch schemes need to be developed to reduce the operational cost while maintaining the stability of grid. This study applies an improved heuristic approach, the improved Artificial Bee Colony (IABC) to optimal power flow (OPF) problem in electric power grids. Although original ABC has provided robust solutions for a range of problems, such as the university timetabling, training neural networks and optimal distributed generation allocation, its poor exploitation often causes solutions to be trapped in local minima. Therefore, in order to adjust the exploitation and exploration of ABC, the IABC based on the orthogonal learning is proposed. Orthogonal learning is a strategy to predict the best combination of two solution vectors based on limited trials instead of exhaustive trials, and to conduct deep search in the solution space. To assess the proposed method, two fuel cost objective functions with high non-linearity and non-convexity are selected for the OPF problem. The proposed IABC is verified by IEEE-30 and 118 bus test systems. In all case studies, the IABC has shown to consistently achieve a lower cost with smaller deviation over multiple runs than other modern heuristic optimization techniques. For example, the quadratic fuel cost with valve effect found by IABC for 30 bus system is 919.567 $/hour, saving 4.2% of original cost, with 0.666 standard deviation. Therefore, IABC can efficiently generate high quality solutions to nonlinear, nonconvex and mixed integer problems.     

基于混合蛙跳算法的电力系统经济负荷分配

针对带阀点效应的经济负荷分配(ELD)问题高维、非凸、非线性的特点,应用混合蛙跳算法(SF-LA)解决电力系统ELD问题。该算法结合了模因演算算法(MA)和粒子群优化(PSO)算法二者的优点,在确保全局收敛和满足约束条件下,能够快速有效地搜索到最优解。通过对多个ELD问题实例进行仿真计算,并与参考文献做比较,结果表明:SFLA对于解决电力系统ELD问题是有效、可行的。     

基于循环寻优RRT算法的无人机航迹规划

针对快速扩展随机树（RRT）算法在无人机在线自主航迹规划中的寻优性问题,提出基于循环寻优RRT算法。将航迹长度代价约束作为启发条件引入RRT算法,可以有效地剪除搜索空间的无用节点,获得较优航迹。通过引入已规划可行航迹的航迹长度代价约束作为下一次算法运行的启发条件,采用循环迭代策略有效地剪除搜索空间的无用节点,使得算法每次运行后的航迹长度代价减小,多次运行后最终得到的航迹接近最优航迹,充分利用航迹长度代价的启发性,克服了RRT算法的缺点,同时获得了一系列不同航迹代价的可行备选航迹,在协同任务中可以根据协同到达时间进行快速选择。仿真结果表明该算法能够快速生成安全并且满足无人机动力学约束的较优航迹。     

Optimum placement of active power conditioner in distribution systems using improved discrete firefly algorithm for power quality enhancement

This paper presents an improved solution for optimal placement and sizing of active power conditioner (APC) to enhance power quality in distribution systems using the improved discrete firefly algorithm (IDFA). A multi-objective optimization problem is formulated to improve voltage profile, minimize voltage total harmonic distortion and minimize total investment cost. The performance of the proposed algorithm is validated on the IEEE 16- and 69-bus test systems using the Matlab software. The obtained results are compared with the conventional discrete firefly algorithm, genetic algorithm and discrete particle swarm optimization. The comparison of results showed that the proposed IDFA is the most effective method among others in determining optimum location and size of APC in distribution systems.     

Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints

Optimal reactive power dispatch (ORPD) is well known as a complex mixed integer nonlinear optimization problem where many constraints are required to handle. In the last decades, many artificial intelligence-based optimization methods have been used to solve ORPD problem. But, these optimization methods lack an effective means to handle constraints on state variables. Thus, in this paper, the novel and feasible conditional selection strategies (CSS) are devised to handle constraints efficiently in the proposed improved gravitational search algorithm (GSA-CSS). In addition, considering the weakness of GSA itself, the improved GSA-CSS (IGSA-CSS) is presented which employs the memory property of particle swarm optimization (PSO) to enhance global searching ability and utilizes the concept of opposition-based learning (OBL) for optimizing initial population. The presented GSA-CSS and IGSA-CSS methods are applied to ORPD problem on IEEE14-bus, IEEE30-bus and IEEE57-bus test systems for minimization of power transmission losses (P_loss) and voltage deviation (V_d), respectively. The comparisons of simulation results reveal that IGSA-CSS provides better results and the improvements of algorithm in this work are feasible and effective.     

Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique

In this paper, a newly surfaced nature-inspired optimization technique called moth-flame optimization (MFO) algorithm is utilized to address the optimal reactive power dispatch (ORPD) problem. MFO algorithm is inspired by the natural navigation technique of moths when they travel at night, where they use visible light sources as guidance. In this paper, MFO is realized in ORPD problem to investigate the best combination of control variables including generators voltage, transformers tap setting as well as reactive compensators sizing to achieve minimum total power loss and minimum voltage deviation. Furthermore, the effectiveness of MFO algorithm is compared with other identified optimization techniques on three case studies, namely IEEE 30-bus system, IEEE 57-bus system and IEEE 118-bus system. The statistical analysis of this research illustrated that MFO is able to produce competitive results by yielding lower power loss and lower voltage deviation than the selected techniques from literature.     

Comprehensive learning particle swarm optimization for reactive power dispatch

Reactive power dispatch (RPD) is an optimization problem that reduces grid congestion by minimizing the active power losses for a fixed economic power dispatch. RPD reduces power system losses by adjusting the reactive power control variables such as generator voltages, transformer tap-settings and other sources of reactive power such as capacitor banks and provides better system voltage control, resulting in an improved voltage profile, system security, power transfer capability and over all system operation. In this paper, RPD problem is solved using particle swarm optimization (PSO). To overcome the drawback of premature convergence in PSO, a learning strategy is introduced in PSO, and this approach called, comprehensive learning particle swarm optimization (CLPSO) is also applied to this problem and a comparison of results is made between these two. Three different test cases have been studied such as minimization of real power losses, improvement of voltage profile and enhancement of voltage stability through a standard IEEE 30-bus and 118-bus test systems and their results have been reported. The study results show that the approaches developed are feasible and efficient.