Particle swarm optimization with time varying acceleration coefficents for economic dispatch considering valve point loading effects

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.

This paper presents a particle swarm optimization (PSO) to solve hard combinatorial constrained optimization problems such as nonconvex and discontinuous economic dispatch (ED) problem of large thermal power plants. Several measures have been suggested in the control equation of the classical PSO by modifying its operators for better exploration and exploitation. The inertia operator of the PSO is modulated by introducing a new truncated sinusoidal function. The cognitive and social behaviors are dynamically controlled by suggesting new exponential constriction functions. The overall methodology effectively regulates the velocity of particles during their flight and results in substantial improvement in the classical PSO. The effectiveness of the proposed method has been tested for economic load dispatch of three standard test systems considering various operational constraints like valve-point loading effect, prohibited operating zones (POZs), network power loss, and so forth. The application results show that the proposed PSO method is very promising.

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.

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.

High-precision wireless localization has attractive application prospects. Cooperative localization is an effective tool to improve localization accuracy. However, compared with non-cooperative localization, in cooperative localization networks, large-scale neighboring links and nonlinear measurement functions cause the associated objective function to be non-convex. It is difficult to obtain global optimum using classical particle swarm optimization (PSO) algorithm or analytical methods. In order to solve this problem, a classified particle swarm optimization (CPSO) algorithm is proposed in this paper. For classical PSO, all search particles have the same inertial weight and learning factor. Unlike classical PSO, the proposed CPSO algorithm classified different search particles based on particle cost value and set different inertial weights and learning factors for search particles. Meanwhile, considering the unavoidable reference node location error, localization result could be achieved by calculating the weighted average of close-range particle locations. Simulation results prove that the CPSO algorithm improves positioning accuracy by 25.3% compared with classical PSO algorithm.

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.

Economic dispatch (ED) is one of the optimization problems in power system operation and planning. The practical ED problems have non-smooth cost functions with equality and inequality constraints. It becomes more complicated problem when valve point effects of generator are considered and results multiple local minima. This makes the ED problems are difficult to find global optimum solution when using any mathematical approach due to non-convex cost function. The Classical particle swarm optimization (PSO) has ability to reach near global optimum solution by tuning some parameters but always stuck at local minima. In this paper, an iteration particle swarm optimization (IPSO) is proposed to solve ED problems with valve point effects. The proposed algorithm is introduced a new parameter in the original velocity equation of PSO in order to enrich searching behaviour, solution quality and avoid being trapped at local minima. The proposed IPSO algorithm has been implemented on two test power systems (consisting 3 and 13 generating units) to validate its effectiveness. The simulation results confirmed that IPSO algorithm has better convergence characteristic and more robust compared to PSO and some published results.

A novel hybrid particle swarm optimization for economic dispatch with valve-point loading effects

In this paper a novel differential particle swarm optimization (DPSO) algorithm is proposed. The proposed algorithm includes an additional term in the velocity equation of the classical particle swarm optimization (PSO) algorithm. The additional term in DPSO is the experience of a particle selected randomly from the swarm for a target particle. The difference of the selected and the target particle is scaled and added to the velocity equation which try the particle to escape from trapping into local minima. The proposed algorithm has been used to solve economic load dispatch (ELD) problem of the IEEE 10 unit system. The results obtained by DPSO have been validated by comparing the results obtained by PSO.

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

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.

Experimental study of a new hybrid PSO with mutation for economic dispatch with non-smooth cost function

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

This paper applies a novel hybrid rough set theory-particle swarm optimizer technique, namely rough particle swarm optimization (RPSO) algorithm, for solving nonconvex economic load dispatch (NELD) problem. The RPSO algorithm is based on the notion of rough patterns that uses rough values defined with upper and lower intervals in which represent a set of values. This RPSO method is suggested to deal with the practical constraints such as valve point loading effect, generation limitation, ramp rate limits and prohibited operating zones in the NELD problems. Simulations were performed on four different power systems with 3, 6, 15 and 40 generating units and the results are compared with classical PSO and crazy PSO algorithms. The results of this study reveal that the proposed approach is able to find appreciable NELD solutions than those of previous algorithms.

This paper proposes a particle swarm optimization approach with time varying acceleration coefficients(TVAC_PSO) for an extensive study of the economic dispatch problem with valve point loading(EDVPL). An optimal short-term thermal generation schedule for 24 time intervals has been presented for the same purpose. In this paper, transmission losses and valve-point loading(VPL) have been considered. The VPL effect results in higher order nonlinearities in the input-output characteristics of a generator. For demonstrating the effectiveness of the proposed method two test systems, first one comprisingof three generators and the second one comprising of thirteen generators,have been considered. The performance of the proposed method has been compared with variousPSOstrategies. The results show that the proposed TVAC_PSO strategy provides comparatively better solutions in terms of total fuel cost as compared to other PSO strategies.Also, the global search capability is enhanced and premature convergence is avoided.