Skill optimization algorithm for solving optimal power flow problem

This chapter proposes a newly improved particle swarm optimization (IPSO) method for solving optimal power flow (OPF) problem. The proposed IPSO is the particle swarm optimization with constriction factor and the particle’s velocity guided by a pseudo-gradient. The pseudo-gradient is to determine the direction for the particles so that they can quickly move to optimal solution. The proposed method has been tested on benchmark functions, the IEEE 14-bus, IEEE 30-bus, IEEE 57-bus, and IEEE-118 bus systems, in which the IEEE 30-bus system is tested with different objective functions including quadratic function, valve point effects, and multiple fuels. The test results have shown that the proposed method can efficiently obtain better total costs than the conventional PSO method. Therefore, the proposed IPSO could be a useful method for implementation in the OPF problem.

The optimal power flow (OPF) problem was introduced by Carpentier in 1962 as a network constrained economic dispatch problem. Since then, it has been intensively studied and widely used in power system operation and planning. In the past few decades, many stochastic optimization methods such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm Optimization (PSO) have been applied to solve the OPF problem. In particular, PSO is a newly proposed population based stochastic optimization algorithm. The main idea behind it is based on the food-searching behavior of birds and fish. Compared with other stochastic optimization methods, PSO has comparable or even superior search performance for some hard optimization problems in real power systems. Nowadays, some modifications such as breeding and selection operators are considered to make the PSO superior and robust. In this paper, we propose the Modified PSO (MPSO), in which the mutation operator of GA is incorporated into the conventional PSO to improve the search performance. To verify the optimal solution searching ability, the proposed approach has been evaluated on an IEEE 30-bus test system. The results showed that performance of the proposed approach is better than that of the standard PSO.

This paper presents performance comparative study of various particle swarm optimization (PSO) techniques for the placement of generator units in the distributed generation (DG) system. For the installation of generator units in the distributed generation system, it is very important to know the generator sizing and its placement in the network system for reducing the line losses and hence the cost. Various PSO techniques such as Canonical PSO, Hierarchical PSO (HPSO), Time varying acceleration coefficient (TVAC) PSO, Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients (HPSO-TVAC), Stochastic inertia weight (Sto-IW) PSO and Time varying inertia weight (TVIW) PSO have been used for comparative study. Here the main objective function (OF) is to minimize the system cost. These techniques have been tested on the standard IEEE-14 bus, IEEE-30 bus and IEEE-57 bus network system by the use of MATLAB software.

In this paper, a multi-objective hybrid firefly and particle swarm optimization (MOHFPSO) was proposed for different multi-objective optimal power flow (MOOPF) problems. Optimal power flow (OPF) was formulated as a non-linear problem with various objectives and constraints. Pareto optimal front was obtained by using non-dominated sorting and crowding distance methods. Finally, an optimal compromised solution was selected from the Pareto optimal set by applying an ideal distance minimization method. The efficiency of the proposed MOHFPSO technique was tested on standard IEEE 30-bus and IEEE 57-bus test systems with various conflicting objectives. Simulation results were also compared with non-dominated sorting based multi-objective particle swarm optimization (MOPSO) and different optimization algorithms reported in the current literature. The achieved results revealed the potential of the proposed algorithm for MOOPF problems.

An efficient and most famous tool to enhance damping of the power system low frequency oscillations is the conventional widely used lead-lag Power System Stabilizer (PSS). To achieve the desired level of robust performance under transient situation, selecting a suitable design method for optimal tuning of PSS parameters is very important in multi-machine power system. Because, it is a multimodal and difficult combinatorial optimization problem, this paper presents a novel parameter automation strategy for Particle Swarm Optimization (PSO) called PSO with Time-Varying Acceleration Coefficients (PSO-TVAC). This optimization method has a strong ability to successfully control both global and local search in each iteration process for considerably increasing the probability of finding the global optimum solution. The PSO-TVAC algorithm is applied to optimal tuning PSS parameters problem in order to reduce the PSS design effort and find the best possible solution within a reasonable computation time. For this reason, the robustly selection of PSSs parameters is converted as an optimization problem based on the time domain-based objective function under different operating conditions. The robustness of the proposed method is demonstrated on a multi-machine power system in comparison with the classical PSO and conventional method based designed PSSs. It is shown through the nonlinear time domain simulation and some performance indices for a wide range of loading condition. The analysis of the results shows that the improved PSO-TVAC is not only very effective but also provides an excellent ability for damping low frequency oscillations and greatly enhance the dynamic stability of the power system. Moreover, the proposed PSO-TVAC algorithm is superior than that of the classical PSO one in terms of accuracy, convergence and computational effort. Key words: Power system stabilizer (PSS) design, particle swarm optimization, power system dynamics, time-varying acceleration coefficients.

Particle swarm optimisation (PSO) was developed by Kennedy and Eberhart in 1995 (Kennedy & Eberhart, 1995) inspired by the collective behaviour of natural birds or fish. PSO is a stochastic optimisation technique that uses a behaviour of population composed by many search points called particle. In spite of easy implementation in computer algorithms, it is well known as a powerful numerical optimizer. In the typical PSO algorithms, a set of particles searches the optimal solution in the problem space efficiently, by sharing the common attractor called global best. There are many modified versions of PSO by improving convergence property to a certain problem. While, a standard PSO is defined by Bratton and Kennedy (Bratton & Kennedy, 2007) to give a real standard for PSO studies. PSO seems as one of the evolutionary computations (ECs), and it has been shown that PSO is comparable to a genetic algorithm (Angeline, 1998). Thus, a lot of studies have demonstrated the effectiveness of PSO family in optimizing various continuous and discrete optimization problems. And a plenty of applications of PSO, such as the neural network training, PID controller tuning, electric system optimisation have been studied and achieved well results (Kennedy, 1997). However, PSO is often failed in searching the global optimal solution in the case of the objective function has a large number of dimensions. The reason of this phenomenon is not only existence of the local optimal solutions, the velocities of the particles sometimes lapsed into the degeneracy, so that the successive range is restricted in the sub-plain of the whole search hyper-plain. The sub-plane that is defined by finite number of particle velocities is a partial space in the whole search space. The issue of local optima in PSO has been studied and proposed several modifications on the basic particle driven equation (Parsopoulos et al., 2001; Hendtlass, 2005; Liang et al., 2006). There used a kind of adaptation technique or randomized method (e.g. mutation in evolutionary computations) to keep particles velocities or to accelerate them. Although such improvements work well and have ability to avoid fall in the local optima, the problem of early convergence by the degeneracy of some dimensions is still remaining, even if there are no local optima. Hence the PSO algorithm does not always work well for the high-dimensional function.

This study introduces an innovative Honey Badger Optimization (HBO) designed to address the Optimal Power Flow (OPF) challenge in electrical power systems. HBO is a unique population-based searching method inspired by the resourceful foraging behavior of honey badgers when hunting for food. In this algorithm, the dynamic search process of honey badgers, characterized by digging and honey-seeking tactics, is divided into two distinct stages, exploration and exploitation. The OPF problem is formulated with objectives including fuel cost minimization and voltage deviation reduction, alongside operational constraints such as generator limits, transformer settings, and line power flows. HBO is applied to the IEEE 30-bus test system, outperforming existing methods such as Particle Swarm Optimization (PSO) and Gray Wolf Optimization (GWO) in both fuel cost reduction and voltage profile enhancement. Results indicate significant improvements in system performance, achieving 38.5% and 22.78% better voltage deviations compared to GWO and PSO, respectively. This demonstrates HBO’s efficacy as a robust optimization tool for modern power systems. In addition to the single-objective studies, a multi-objective OPF formulation was investigated to produce the complete Pareto front between fuel cost and voltage deviation objectives. The proposed HBO successfully generated a well-distributed set of trade-off solutions, revealing a clear conflict between economic efficiency and voltage quality. The Pareto analysis demonstrated HBO’s strong capability to balance these competing objectives, identify knee-point operating conditions, and provide flexible decision-making options for system operators.

Flexible AC transmission systems (FACTS) and optimal power-flow (OPF) solutions play an important role in solving power operation problems. The volatile nature of the power generation profiles from renewable energy sources, solar and wind systems, and determining the optimal locations and sizes of FACTS devices increase the complexity of the OPF problems in modern power network models, such as transmission power loss, power generation operation cost and voltage deviation, as a highly nonlinear-nonconvex optimization problem. Therefore, this article introduces and employs four new independent, reliable and efficient optimization algorithms inspired by nature and biological nature, namely: Slime Mould Algorithm (SMA), Artificial Ecosystem-based Optimization (AEO), Marine Predators Algorithm (MPA) and Jellyfish Search (JS), for solving both multi- and single-OPF objective problems for a power network incorporating FACTS and stochastic renewable energy sources. The proposed new metaheuristic optimization techniques are compared to the common and available alternatives in the literature, Particle Swarm Optimization (PSO), Moth Flame Optimization (MFO) and Grey Wolf Optimizer (GWO), using IEEE 30-bus test system. To consider and address the challenges of the OPF in modern power network models, the proposed optimization techniques tested under different operation cases such as an increasing in the load, with and without FCTAS and renewable energy sources, different renewable energy sources locations on the network. The result showed that the MPA, SMA, JS and AEO algorithms are more effective solvers for the OPF problems cases compared to the PSO, GWO and MFO algorithms. For example, the AEO obtained 0.0844 p.u. in case of minimizing the voltage deviation compared to 0.1155 p.u. for PSO, which means that the AEO algorithm improved the voltage deviation term by 27% compared to the PSO algorithm.

This paper proposes an artificial bee colony (ABC) algorithm for solving optimal power flow (OPF) problem. The objective of the OPF problem is to minimize total cost of thermal units while satisfying the unit and system constraints such as generator capacity limits, power balance, line flow limits, bus voltages limits, and transformer tap settings limits. The ABC algorithm is an optimization method inspired from the foraging behavior of honey bees. The proposed algorithm has been tested on the IEEE 30-bus, 57-bus, and 118-bus systems. The numerical results have indicated that the proposed algorithm can find high quality solution for the problem in a fast manner via the result comparisons with other methods in the literature. Therefore, the proposed ABC algorithm can be a favorable method for solving the OPF problem.

In this article, an efficient optimization procedure based on herding behavior of krill individuals, krill herd algorithm (KHA), for the solution of multi-objective optimal power flow (OPF) with the objective of fuel cost minimization, voltage deviation minimization and voltage stability improvement is proposed. This algorithm is based on the effect of the influence of a teacher on the output of learners in a class. The proposed KHA approach is carried out on the standard IEEE 30-bus, IEEE 57-bus and IEEE 118-bus systems to solve different single and multi-objective OPF problems. Simulation results of the proposed approach are compared to differential evolution (DE), modified DE (MDE), multi-objective DE (MODE), evolving ant direction DE (EADDE), particle swarm optimization (PSO), improved genetic algorithm (IGA), gradient method, biogeography-based optimization (BBO), PSO with inertia weight approach (PSOIWA), PSO with constriction factor approach (PSOCFA), real-coded GA (RGA), artificial bee colony (ABC), general passive congregation PSO (GPAC), local passive congregation PSO (LPAC), coordinated aggregation (CA), interior point method (IPM) and quantum-inspired evolutionary algorithm (QEA). The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve multi-objective OPF problems. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, three new particle swarm optimization (PSO) algorithms are compared with the state of the art PSO algorithms for the optimal steady-state performance of power systems, namely, the reactive power and voltage control. Two of the three introduced, the enhanced GPAC PSO and LPAC PSO, are based on the global and local-neighborhood variant PSOs, respectively. They are hybridized with the constriction factor approach together with a new operator, reflecting the physical force of passive congregation observed in swarms. The third one is based on a new concept of coordinated aggregation (CA) and simulates how the achievements of particles can be distributed in the swarm affecting its manipulation. Specifically, each particle in the swarm is attracted only by particles with better achievements than its own, with the exception of the particle with the best achievement, which moves randomly as a crazy agent. The obtained results by the enhanced general passive congregation (GPAC), local passive congregation (LPAC), and CA on the IEEE 30-bus and IEEE 118-bus systems are compared with an interior point (IP)-based OPF algorithm, a conventional PSO algorithm, and an evolutionary algorithm (EA), demonstrating the excellent performance of the proposed PSO algorithms

Objective: In this paper, an improved hybrid differential evolution (IHDE) algorithm based on differential evolution (DE) algorithm and particle swarm optimization (PSO) has been proposed to solve the optimal power flow (OPF) problem of power system which is a multi-constrained, large-scale and nonlinear optimization problem. Method: In IHDE algorithm, the DE is employed as the main optimizer; and the three factors of PSO, which are inertia, cognition, and society, are used to improve the mutation of DE. Then the learning mechanism and the adaptive control of the parameters are added to the crossover, and the greedy selection considering the value of penalty function is proposed. Furthermore, the replacement mechanism is added to the IHDE for reducing the probability of falling into the local optimum. The performance of this method is tested on the IEEE30-bus and IEEE57-bus systems, and the generator quadratic cost and the transmission real power losses are considered as objective functions. Results: The simulation results demonstrate that IHDE algorithm can solve the OPF problem successfully and obtain the better solution compared with other methods reported in the recent literatures.

Particle swarm optimization (PSO) algorithm has shown promising performances on various benchmark functions and engineering optimization problems. However, it is still difficult to achieve a satisfying trade-off between exploration and exploitation for all the optimization problems and different evolving stages. Furthermore, control parameters of some related mechanisms need pre-experience by the requirement of trial-and-error scheme. This paper presents a novel PSO algorithm, which adaptively adopts various search strategies, called Self-adapting Hybrid Strategy PSO (SaHSPS). Unlike some other peer PSO variants, this method dynamically changes the probabilities of different strategies according to their previous successful searching memories, without any additional control parameters. The probabilities of different strategies would be re-initialized according to a proposed dynamic probabilistic model to diverse the population. Besides, particles are updated by probabilistically selected strategies after niching PSO with Ring topology. Moreover, a dynamic updating mechanism by niching PSO is proposed to guarantee the parallel searching capability during the whole evolution process. Thus, this proposed algorithm might be problem-independent and search-stage-independent, yielding more satisfying solutions on various optimization problems. A comprehensive experimental study is conducted on 28 benchmark functions of CEC 2013 special session on real-parameter optimization, including shifted, rotated, multi-modal, high conditioned, expanded and composition problems, compared with several state-of-the-art variants of PSO and differential evolution (DE) algorithms. Comparison results show that SaHSPS obtains outstanding performances on the majority of the test problems. Moreover, a practical engineering problem, real power loss minimization of IEEE 30-bus power system, is used to further evaluate SaHSPS. The numerical results, compared with other stochastic search algorithms, show that SaHSPS could find high-quality solutions with higher probability.

Thermal power generators have both active power (AP) and reactive power (RP) requirement to meet up the total power demand. Considering the total power demand such generators supply the essential RP along with the AP. Consequently by considering the reactive power demand it is also an important to consider its cost along with the cost based on active power generation. In this paper, the generalised mathematical functions for the cost considering the RP are formulated and incorporated with the cost function based on active power generation. Particle Swarm Optimization (PSO) algorithm has been applied to solve Optimal power flow (OPF) problem (OPFP). The proposed work has been examined and tested on IEEE-9 bus system with different objectives such as total fuel cost based both active and reactive power generation, transmission losses, voltage profile improvement. The results drawn show its validity and effectiveness.

Transfer function (TF) specification is an important research issue in direct volume rendering (DVR). In this paper, the problem has been developed as a parameter optimization model and a modern evolutionary algorithm, the particle swarm optimization (PSO), has been applied to solve it effectively. Initial solutions are formed and encoded into particles of PSO, the particles fly intelligently in the search space to achieve the best sequence. We realize the implementation of the algorithm in automatic and interactive approaches, and modify updating strategy emphasizing the user requirement in the interactive method. Experiments results confirm the performance and efficiency of the automatic implement of origin algorithm with a comparison to genetic algorithm (GA) which has been applying to this field previously. A contrast has been made between the conventional and modified PSO algorithm and GA in interactive implement to verify the feasibility and applicability of modified PSO algorithm.