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.     

Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization

This paper describes teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal power flow (MOOPF) problems while satisfying various operational constraints. To improve the convergence speed and quality of solution, quasi-oppositional based learning (QOBL) is incorporated in original TLBO algorithm. The proposed quasi-oppositional teaching learning based optimization (QOTLBO) approach is implemented on IEEE 30-bus system, Indian utility 62-bus system and IEEE 118-bus system to solve four different single objectives, namely fuel cost minimization, system power loss minimization and voltage stability index minimization and emission minimization; three bi-objectives optimization namely minimization of fuel cost and transmission loss; minimization of fuel cost and L-index and minimization of fuel cost and emission and one tri-objective optimization namely fuel cost, minimization of transmission losses and improvement of voltage stability simultaneously. In this article, the results obtained using the QOTLBO algorithm, is comparable with those of TLBO and other algorithms reported in the literature. The numerical results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal non-dominated solutions of the multi-objective OPF problem. The simulation results also show that the proposed approach produces better quality of the individual as well as compromising solutions than other algorithms.     

Chaotic krill herd algorithm for optimal reactive power dispatch considering FACTS devices

Conventionally, optimal reactive power dispatch (ORPD) is described as the minimization of active power transmission losses and/or total voltage deviation by controlling a number of control variables while satisfying certain equality and inequality constraints. This article presents a newly developed meta-heuristic approach, chaotic krill herd algorithm (CKHA), for the solution of the ORPD problem of power system incorporating flexible AC transmission systems (FACTS) devices. The proposed CKHA is implemented and its performance is tested, successfully, on standard IEEE 30-bus test power system. The considered power system models are equipped with two types of FACTS controllers (namely, thyristor controlled series capacitor and thyristor controlled phase shifter). Simulation results indicate that the proposed approach yields superior solution over other popular methods surfaced in the recent state-of-the-art literature including chaos embedded few newly developed optimization techniques. The obtained results indicate the effectiveness for the solution of ORPD problem of power system considering FACTS devices. Finally, simulation is extended to some large-scale power system models like IEEE 57-bus and IEEE 118-bus test power systems for the same objectives to emphasis on the scalability of the proposed CKHA technique. The scalability, the robustness and the superiority of the proposed CKHA are established in this paper.     

Krill herd algorithm for optimal location of distributed generator in radial distribution system

Distributed generator (DG) is recognized as a viable solution for controlling line losses, bus voltage, voltage stability, etc. and represents a new era for distribution systems. This paper focuses on developing an approach for placement of DG in order to minimize the active power loss and energy loss of distribution lines while maintaining bus voltage and voltage stability index within specified limits of a given power system. The optimization is carried out on the basis of optimal location and optimal size of DG. This paper developed a new, efficient and novel krill herd algorithm (KHA) method for solving the optimal DG allocation problem of distribution networks. To test the feasibility and effectiveness, the proposed KH algorithm is tested on standard 33-bus, 69-bus and 118-bus radial distribution networks. The simulation results indicate that installing DG in the optimal location can significantly reduce the power loss of distributed power system. Moreover, the numerical results, compared with other stochastic search algorithms like genetic algorithm (GA), particle swarm optimization (PSO), combined GA and PSO (GA/PSO) and loss sensitivity factor simulated annealing (LSFSA), show that KHA could find better quality solutions.     

Adaptive differential evolution algorithm for efficient reactive power management

This paper introduces a proposed procedure to solve the optimal reactive power management (ORPM) problem based on a multi-objective function using a modified differential evolution algorithm (MDEA). The proposed MDEA is investigated in order to enhance the voltage profile as well as to reduce the active power losses by solving the ORPM problem. The ORPM objective function aims to minimize transmission power losses and voltage deviation considering the system constraints. The MDEA aims to enhance the convergence characteristic of the differential evolution algorithm through updating the self-adaptive scaling factor, which can exchange information dynamically every generation. The scaling factor dynamically adopts the global and local searches to efficiently eliminate trapping in local optima. In addition, a strategy is developed to update the penalty factor for alleviating the effects of various system constraints. Numerical applications of different case studies are carried out on three standard IEEE systems, i.e., 14-bus, 30-bus and 57-bus test systems. Also, the proposed procedure is applied on Western Delta Network, which is a real part of the Egyptian main grid system. The flexibility of synchronous machines to provide controllable reactive power is proven with less dependency on the discrete reactive power controllers, such as installing the switchable devices and variations of tap changers. The obtained results show the effectiveness of the proposed enhanced optimization algorithm as an advanced optimization technique that was successively implemented with good performance characteristics.     

Optimal placement of UPFC in power systems using immune algorithm

This paper presents the application of immune algorithm (IA) to find optimal location of unified power flow controller (UPFC) to achieve optimal power flow (OPF) and congestion management. Objective function in the OPF, that is to be minimized, is the overall cost functions, which includes the total active and reactive production cost function of the generators and installation cost of UPFCs. The OPF constraints are generators, transmission lines and UPFCs limits. In power system, it may not always be possible to dispatch all of the contracted power transactions due to congestion of the transmission corridors. We propose IA method to minimize the objective function under all equality and inequality constraints. Simulations are performed on 4-bus, IEEE 14-bus and IEEE 30-bus test systems for optimal location of UPFC and the results obtained are encouraging and will be useful in electrical restructuring.     

A novel fuzzy adaptive configuration of particle swarm optimization to solve large-scale optimal reactive power dispatch

Management and scheduling of reactive power resources is one of the important and prominent problems in power system operation and control. It deals with stable and secure operation of power systems from voltage stability and voltage profile improvement point of views. To this end, a novel Fuzzy Adaptive Heterogeneous Comprehensive-Learning Particle Swarm Optimization (FAHCLPSO) algorithm with enhanced exploration and exploitation processes is proposed to solve the Optimal Reactive Power Dispatch (ORPD) problem. Two different objective functions including active power transmission losses and voltage deviation, which play important roles in power system operation and control, are considered in this paper. In order to authenticate the accuracy and performance of the proposed FAHCLPSO, it applied on three different standard test systems including IEEE 30-bus, IEEE 118-bus and IEEE 354-bus test systems with six, fifty-four and one-hundred-sixty-two generation units, respectively. Finally, outcomes of the proposed algorithm are compared with the results of the original PSO and those in other literatures. The comparison proves the supremacy of the proposed algorithm in solving the complex optimization problem.     

A multiobjective approach for optimal placement and sizing of distributed generators and capacitors in distribution network

Both active and reactive power play important roles in power system transmission and distribution networks. While active power does the useful work, reactive power supports the voltage that necessitates control from system reliability aspect as deviation of voltage from nominal range may lead to inadvertent operation and premature failure of system components. Reactive power flow must also be controlled in the system to maximize the amount of real power that can be transferred across the power transmitting media. This paper proposes an approach to simultaneously minimize the real power loss and the net reactive power flow in the system when reinforced with distributed generators (DGs) and shunt capacitors (SCs). With the suggested method, the system performance, reliability and loading capacity can be increased by reduction of losses. A multiobjective evolutionary algorithm based on decomposition (MOEA/D) is adopted to select optimal sizes and locations of DGs and SCs in large scale distribution networks with objectives being minimizing system real and reactive power losses. MOEA/D is the process of decomposition of a multiobjective optimization problem into a number of scalar optimization subproblems and optimizing those concurrently. Case studies with standard IEEE 33-bus, 69-bus, 119-bus distribution networks and a practical 83-bus distribution network are performed. Output results of MOEA/D method are compared with similar past studies and notable improvement is observed.     

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.     

基于序列二次规划法的分布式电源优化配置研究

针对分布式电源配置对配电网的影响,提出一种带二阶项配网潮流约束的方法解决分布式电源优化配置问题,以实现分布式电源价值的最大化。从降损角度出发建立优化配置的数学模型,并用序列二次规划求解优化问题。在充分发挥序列二次规划法收敛性好的基础上,提高计算精度,并适用于各种复杂的配电网络。以IEEE33节点系统为例,验证所提方法在分布式电源优化配置问题求解中具有很强的全局搜索能力,可以有效、准确地实现分布式电源的最优配置,计算过程简单可靠,具有实用价值。     

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.     

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.     

Bacterial foraging optimization and adaptive version for economically optimum sitting,sizing and harmonic tuning orders setting of LC harmonic passive power filters in radial distribution systems with linear and nonlinear loads

This paper presents bacterial foraging optimization (BFO) algorithm and its adaptive version to optimize the planning of passive harmonic filters (PHFs).The important problem of using PHFs is determining location, size and harmonic tuning orders of them, which is reach standard levels of harmonic distortion with applying minimum cost of passive filters.In this study to optimize the PHFs location, size and setting the harmonic tuning orders in the distribution system, considered objective function includes the reduction of power loss and investment cost of PHFs. At the same time, constraints include voltage limits, number/size of installed PHFs, limit candidate buses for PHFs installation and the voltage total harmonic distortion (THDv) in all buses. The harmonic levels of system are obtained by current injections method and the load flow is solved by the iterative method of power sum, which is suitable for the accuracy requirements of this type of study. It is shown that through an economical placement and sizing of PHFs the total voltage harmonic distortion and active power loss could be minimized simultaneously.The considered objective function is of highly non-convex manner, and also has several constraints. On the other hand due to significant computational time reduction and faster convergence of BFO in comparison with other intelligent optimization approach such as genetic algorithm (GA), particle swarm optimization (PSO) and artificial bee colony (ABC) the simple version of BFO has been implemented. Of course other versions of BFO such as Adaptive BFO and combination of BFO with other method due to complexity of harmonic optimization problem have not considered in this research.The simulation results for small scale test system with 10 buses, showed the significant computational time reduction and faster convergence of BFO in comparison with GA, PSO and ABC. Therefore in large scale radial system with 34 buses, the proposed method is solved using BFO.The simulation results for a 10-bus system as a small scale and 34-bus radial system as a large scale show that the proposed method is efficient for solving the presented problem.     

An approach to mitigate the risk of voltage collapse accounting uncertainties using improved particle swarm optimization

This paper describes a new viewpoint for static voltage stability enhancement based on an improved particle swarm optimization technique. The objective function is selected for maximization of reactive power reserve subjected to usual operating constraints at an operating point. Probabilistic risk of voltage collapse has been used for maintaining desired level of voltage stability margin. This risk of voltage collapse is calculated accounting uncertainties in system parameters and control variables. Probabilistic risk of voltage collapse has been obtained by a trained Radial Basis Function network. Developed algorithm has been implemented on 6-bus, 14-bus and 25-bus IEEE test systems. Results have been compared with those obtained using Davidon–Fletcher–Powell's (DFP) method.     

A multi-objective approach to optimal placement and sizing of multiple active power filters using a music-inspired algorithm

This paper proposes a new multi-objective framework for optimal placement and sizing of the active power filters (APFs) with satisfactory and acceptable standard levels. total harmonic distortion (THD) of voltage, harmonic transmission line loss (HTLL), motor load loss function (MLLF), and total APFs currents are the four objectives considered in the optimization, while harmonic distortions within standard level, and maximum allowable APF size, are modeled as constraints. The proposed model is one of non-convex optimization problem having a non-linear, mixed-integer nature. Since, a new modified harmony search algorithm (MHSA) is used and followed by a min–max technique in order to obtain the final optimal solution. The harmony search algorithm is a recently developed optimization algorithm, which imitates the music improvisation process. In this process, the Harmonists improvise their instrument pitches searching for the perfect state of harmony. The newly developed method has been applied on the IEEE 18-bus test system and IEEE 30-bus test system by different scenarios and cases to demonstrate the feasibility and effectiveness of the proposed method. The detailed results of the case studies are presented and thoroughly analyzed. The obtained results illustrate the sufficiency and profitableness of the newly developed method in the placement and sizing of the multiple active power filters, when compared with other methods.     

A modified MOEA/D approach to the solution of multi-objective optimal power flow problem

This study presents a modified multi-objective evolutionary algorithm based decomposition (MOEA/D) approach to solve the optimal power flow (OPF) problem with multiple and competing objectives. The multi-objective OPF considers the total fuel cost, the emissions, the power losses and the voltage magnitude deviations as the objective functions. In the proposed MOEA/D, a modified Tchebycheff decomposition method is introduced as the decomposition approach in order to obtain uniformly distributed Pareto-Optimal solutions on each objective space. In addition, an efficiency mixed constraint handling mechanism is introduced to enhance the feasibility of the final Pareto solutions obtained. The mechanism employs both repair strategy and penalty function to handle the various complex constraints of the MOOPF problem. Furthermore, a fuzzy membership approach to select the best compromise solution from the obtained Pareto-Optimal solutions is also integrated. The standard IEEE 30-bus test system with seven different cases is considered to verify the performance of the proposed approach. The obtained results are compared with those in the literatures and the comparisons confirm the effectiveness and the performance of the proposed algorithm.     

Adaptive PSODV algorithm for OPF with non-smooth cost functions and statistical analysis

This paper presents a particle swarm optimization with differentially perturbed velocity hybrid algorithm with adaptive acceleration coefficient (APSO-DV) for solving the optimal power flow problem with non-smooth and non-convex generator fuel cost characteristics. The APSO-DV employs differentially perturbed velocity with adaptive acceleration coefficient for updating the positions of particles for the particle swarm optimization. The feasibility of the proposed approach was tested on IEEE 30-bus and IEEE 118-bus systems with three different objective functions. Several cases were investigated to test and validate the robustness of the proposed method in finding the optimal solution. The effectiveness of the proposed approach was tested including contingency also. Simulation results demonstrate that the APSO-DV provides superior results compared to classical DE, PSO, PSO-DV 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.     

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.     

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 power flow of HVDC system using teaching–learning-based optimization algorithm

In this paper, a solution to the optimal power flow (OPF) problem in electrical power networks is presented considering high voltage direct current (HVDC) link. Furthermore, the effect of HVDC link converters on the active and reactive power is evaluated. An objective function is developed for minimizing power loss and improving voltage profile. Gradient-based optimization techniques are not viable due to high number of OPF equations, their complexity and equality and inequality constraints. Hence, an efficient global optimization method is used based on teaching–learning-based optimization (TLBO) algorithm. The performance of the suggested method is evaluated on a 5-bus PJM network and compared with other algorithms such as particle swarm optimization, shuffled frog-leaping algorithm and nonlinear programming. The results are promising and show the effectiveness and robustness of TLBO method.