An Efficient Particle Swarm Optimization with Time Varying Acceleration Coefficients to Solve Economic Dispatch Problem with Valve Point Loading

This paper presents an efficient approach for solving economic dispatch(ED) problem with non-convex cost functions using particle swarm optimization with time varying acceleration coefficients. PSO_TVAC is applied to 3, 13, & 14 unit test system with and without valve point loading effects. The results of PSO_TVAC are compared with PSO From simulation results, it is clear that PSO_TVAC performance is better than many well settled nature inspired algorithms.Economic dispatch is one of the key functions of the modern energy management system. Classical particle swarm optimization (PSO) algorithm is capable of achieving near global solutions for such problems but it tends to converge prematurely. The practical Non Convex Economic Dispatch problem is solved here using PSO with a novel parameter automation strategy in which time varying acceleration coefficients (TVAC) are employed to efficiently control the local and global search, such that premature convergence is avoided and global solutions are achieved.

In this paper, an effective and reliable variant of particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC) technique is proposed for the economic load dispatch problem considering valve-point loading effect. Main objective of the economic load dispatch (ELD) problem is to minimize the fuel cost by allocating the generation of the committed units subjected to the equality and inequality constraints. Equation of the economic dispatch objective function gets modified with the addition of a new parameter which represents the effect of valve-point loading. While exploring the use of PSO and its other variants to the economic dispatch problem, a number of research works have not considered the transmission losses properly. This paper represents the usefulness of the proposed PSO-TVAC algorithm to significantly reduce the fuel cost while taking into account the effect of transmission losses along with the non-convex characteristic due to valve loading. The results have been demonstrated for three-generator and ten-generator test systems.

In past two decades solution to the Dynamic Economic Load Dispatch (DELD) problem considering emission and transmission losses along with Valve Point Loading (VPL) effect has been investigated by researchers using several meta-heuristic techniques. Numerical techniques such as lambda iteration method, dynamic programming etc. have been unable to solve the ELD problem with VPL effect. This paper presents a systematic performance evaluation of meta-heuristic techniques named as Particle Swarm Optimization and the Genetic Algorithm for combined economic emission dispatch problem considering Valve Point Loading (VPL) to meet 24 hr. load profile on IEEE 9 bus test case with 3 generator units.

Evolutionary optimization algorithms, including particle swarm optimization (PSO), have been successfully applied in oil industry for production planning and control. Such optimization studies are quite challenging due to large number of decision variables, production scenarios, and subsurface uncertainties. In this work, multi-stage, multi-swarm PSO (MS2PSO) algorithm is proposed to fix certain issues with canonical PSO algorithm such as premature convergence, excessive influence of global best solution, and oscillation. Multiple experiments are conducted using Olympus benchmark to compare the efficacy of algorithms. Results from canonical PSO are first compared with two PSO variations in which hyperparameters are tuned to prioritize exploration in early phase and exploitation in late phase. Firstly, linearly decreasing inertia weight (LDIW-PSO) is used to have greater weight of current particle position during initial iterations, and vice versa. Then, time-varying acceleration coefficients (TVAC-PSO) are used to have greater weight of personal best and lesser weight of global best during the initial iterations, and vice versa. Next, a two-stage multi-swarm PSO (2SPSO) is used where multiple-swarms of the first stage collapse into a single swarm in the second stage. Finally, MS2PSO with multiple stages and multiple swarms is used in which swarms recursively collapse after each stage. Multiple swarm strategy ensures that diversity is retained within the population and multiple modes are explored. Staging ensures that local optima found during initial stage does not lead to premature convergence. Optimization test case comprises of 90 control variables of which 72 are well control related and 18 are well placement related. Swarm intelligence refers to global patterns emerging from simple interactions among population. Algorithmic rules at micro level lead to social interaction at meso level, which then further leads to collective behavior at macro level. It is observed that different algorithm designs have their own benefits and drawbacks. Decreasing inertia weight in LDIW-PSO enables exploration in early stages and convergence around global best in the later stages. TVAC-PSO on the other hand restricts social learning and aids exploration in the early iterations. Social learning component is increased as run progresses, and population moves towards global best. 2SPSO aids in exploring multi-modal objective space, thus preventing premature convergence to a local optima. Swarms collapse into one group in the second stage, and run finally converges towards global best. Multiple swarms and stages in MS2PSO ensure that diversity in population is maintained throughout the run which enables continuous learning, and thus mitigates premature convergence. Both 2SPSO and MS2PSO are found to be helpful for problems with high dimensions and multiple modes where greater degree of exploration is desired. Commercial cloud computing and parallel programming were used to handle high computational workload and reduce run-time from weeks to days. Coefficients of canonical PSO are tuned in LDIW-PSO and TVAC-PSO, which helps in mitigating issues like premature convergence and oscillation. Two-stage PSO (2SPSO) where multiple swarms of first stage collapse into one in second stage, and multi-stage multi-swarm PSO (MS2PSO) where swarms recursively collapse into one are proposed. These algorithms modify the social behavior at meso scale based on number of swarms, number of stages and iterations in each stage.

This paper presents a new resolution approach of Economic Dispatch (ED) problem considering wind power penetration planning with specified wind farm locations. Firstly, the total fuel cost of conventional generating units is optimized with a wind power contribution. When the optimal wind power penetration for each wind farm location is specified, a planning process is performed to get the total number and the total cost of wind generators. Three levels of the total wind power penetration are examined, which are 25%, 30% and 35%. The Wind Power Planning (WPP) is effected based on the practical weather report for each wind farm location. The ED problem is solved taking in the account the valve point effects of thermal generating units and using Time Varying Acceleration Coefficients (TVAC) based Particle Swarm Optimization method (PSO) due to its effectiveness overcoming the conventional PSO. The model is applied on the well known IEEE 30 bus test system.

Non-convex emission constrained economic dispatch using a new self-adaptive particle swarm optimization technique

The krill herd (KH) approach is proposed in this article for tackling the dynamic economic dispatch (DED) problem with the integration of wind power generation, including constraints such as valve-point loadings and prohibited operating zones (PoZs). The purpose of resolving the DED problem is to determine the optimum feasible combination of power outputs for all allocated generating units within a given period while simultaneously meeting dynamic operational constraints and power demand. Due to the addition of valve points and PoZs to the cost characteristics of the generating unit, the DED issue becomes a highly non-linear and non-convex optimization issue. When transmission losses are taken into account, the DED problem becomes significantly more complex to solve. KH is a swarm-inspired algorithm based on krill individual herding behavior. KH employs two global and two local tactics, and these work in parallel, making KH a powerful algorithm. The effectiveness of the KH method is investigated and validated through extensive testing on various test systems, including 5-, 6-, 10-, 16-, and 30-unit test systems. Extensive studies are conducted to evaluate the efficacy of the proposed KH algorithm; the present research work compares the convergence properties of the suggested approach with those of the other recently published methods. In addition to reduced generation costs compared to other results published in recent literature, the numerical findings of the KH approach reveal that it has strong convergence qualities.

This paper presents a new improved self adaptive particle swarm optimization technique to avoid premature convergence for economic load dispatch problem. Many evolutionary techniques such as particle swarm optimization (PSO), differential evolution (DE) have been applied to solve this problem and found to perform in a better way in comparison with conventional optimization methods. But often these methods converge to a sub-optimal solution prematurely. In this method, the inertia weight is made self adaptive depending on the population size and the fitness rank of the particle along with time variant acceleration coefficients. A thirteen-unit test system is considered to demonstrate the effectiveness of the proposed method. The results obtained by the proposed algorithm are compared with other classical as well as modern heuristic techniques. It is found that the proposed method can produced improved results.KeywordsParticle Swarm OptimizationDifferential EvolutionFuel CostInertia WeightPremature ConvergenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper proposes a self‐organizing hierarchical particle swarm optimization (SPSO) with time‐varying acceleration coefficients (TVAC) for solving economic dispatch (ED) problem with non‐smooth functions including multiple fuel options (MFO) and valve‐point loading effects (VPLE). The proposed SPSO with TVAC is the new approach optimizer and good performance for solving ED problems. It can handle the premature convergence of the problem by re‐initialization of velocity whenever particles are stagnated in the search space. To properly control both local and global explorations of the swarm during the optimization process, the performance of TVAC is included. The proposed method is tested in different ED problems with non‐smooth cost functions and the obtained results are compared to those from many other methods in the literature. The results have revealed that the proposed SPSO with TVAC is effective in finding higher quality solutions for non‐smooth ED problems than many other methods.

Quasi-oppositional group search optimization for multi-area dynamic economic dispatch

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.

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.

Aiming at the power economic dispatch problem (PEDP) of generating units having valve-point loadings, this research investigates a hybrid artificial immune system and multiplier update technique (AIS-MUT). Artificial immune system (AIS) containing a migrating function can actively hunt for extremum values and effectively evaluate answers. Multiplier update technique (MUT) is employed to prevent the Lagrange function which deforms searching difficult. The proposed approach synthesizes AIS and MUT, and its merits are that it can automatically regulate the stochastically assignment penalty to a suitable numeric and need only a minisize population for the PEDP of considering generating plants having valve-point loadings. System simulated results show that this study is very proper than the former studies for considering an actual economic dispatching problem of power systems.

The major issue in power system is economic dispatch (ED) problem. The Economic dispatch problem is aim to distribute electrical power generators in some active electrical system to minimize the total of cost of generators. Here, the purpose of this paper is to achieve the combination of power output, maximum total of demand with the transmission losses, minimum the total cost of generating unit and design web based application to simplify the calculation of economic dispatch problem for user at PT. Indonesia Power. This paper introduces a solution to ED problem using Dr. Xin She Yang developed firefly algorithm. The result obtained by the proposed algorithm have been compared with the result from the data source and that results is more optimal using firefly algorithm than the results of the data source. Based on the result, it can be concluded that this web based application is very useful to user in calculating the economic dispatch problem with transmission losses at PT. Indonesia Power.

This paper involves a novel application of the improved particle swarm optimization (IPSO) in an economic dispatch problem (EDP) that consists influence of valve-point loading, power balance, and generators constraints. This method is able to improve the best value of the cost function with a slight increase in the average time trials. This procedure is suitable for solving large-scale and complex economic dispatch problems. In this report, IPSO algorithm is tested on three systems and experimental results are compared with other efficient methods. Simulation results demonstrate the efficiency of proposed algorithms for solving economic dispatching problems.