Non-convex Economic Load Dispatch Problem Research Articles

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

A non-convex economic load dispatch problem using chameleon swarm algorithm with roulette wheel and Levy flight methods

A non-convex economic load dispatch problem using chameleon swarm algorithm with roulette wheel and Levy flight methods

Oppositional Pigeon-Inspired Optimizer for Solving the Non-Convex Economic Load Dispatch Problem in Power Systems

Economic Load Dispatch (ELD) belongs to a non-convex optimization problem that aims to reduce total power generation cost by satisfying demand constraints. However, solving the ELD problem is a challenging task, because of its parity and disparity constraints. The Pigeon-Inspired Optimizer (PIO) is a recently proposed optimization algorithm, which belongs to the family of swarm intelligence algorithms. The PIO algorithm has the benefit of conceptual simplicity, and provides better outcomes for various real-world problems. However, this algorithm has the drawback of premature convergence and local stagnation. Therefore, we propose an Oppositional Pigeon-Inspired Optimizer (OPIO) algorithm—to overcome these deficiencies. The proposed algorithm employs Oppositional-Based Learning (OBL) to enhance the quality of the individual, by exploring the global search space. The proposed algorithm would be used to determine the load demand of a power system, by sustaining the various equality and inequality constraints, to diminish the overall generation cost. In this work, the OPIO algorithm was applied to solve the ELD problem of small- (13-unit, 40-unit), medium- (140-unit, 160-unit) and large-scale (320-unit, 640-unit) test systems. The experimental results of the proposed OPIO algorithm demonstrate its efficiency over the conventional PIO algorithm, and other state-of-the-art approaches in the literature. The comparative results demonstrate that the proposed algorithm provides better results—in terms of improved accuracy, higher convergence rate, less computation time, and reduced fuel cost—than the other approaches.

Opposition-mutual learning differential evolution with hybrid mutation strategy for large-scale economic load dispatch problems with valve-point effects and multi-fuel options

The economic load dispatch (ELD) problem plays a crucial role in power system operation. In practice, the ELD problem becomes a non-convex, multi-constraint, non-linear optimization problem when considering the valve point effects, the prohibited operation zones, the ramp rate limit, and the multi-fuel options. To effectively solve this problem, this paper puts forward an improved differential evolution (DE) named OMLIDE based on opposition-mutual learning, hybrid mutation strategy, and parameters adaptive mechanism. OMLIDE differs from the traditional DE in that: (1) an opposition-mutual learning strategy is employed for population initialization to increase the probability of finding an optimal solution; (2) two novel mutation operators named DE/elite-to-ordinary/1 and DE/elite-to-ordinary/2 are hybridized and a selection probability is introduced to regulate them adaptively at different evolutionary stages; and (3) a parameters adaptive mechanism is presented to adjust the scaling factor and crossover rate. The proposed OMLIDE is first validated by the numerical benchmark functions of CEC 2014. Then it is applied to five non-convex ELD problems with valve-point effects and multi-fuel options. Simulation results demonstrate that OMLIDE provides better or highly competitive results in different terms compared with other peer algorithms.

A Cost-Effective Solution for Non-Convex Economic Load Dispatch Problems in Power Systems Using Slime Mould Algorithm

Slime Mould Algorithm (SMA) is a newly designed meat-heuristic search that mimics the nature of slime mould during the oscillation phase. This is demonstrated in a unique mathematical formulation that utilizes adjustable weights to influence the sequence of both negative and positive propagation waves to develop a method to link food supply with intensive exploration capacity and exploitation affinity. The study shows the usage of the SM algorithm to solve a non-convex and cost-effective Load Dispatch Problem (ELD) in an electric power system. The effectiveness of SMA is investigated for single area economic load dispatch on large-, medium-, and small-scale power systems, with 3-, 5-, 6-, 10-, 13-, 15-, 20-, 38-, and 40-unit test systems, and the results are substantiated by finding the difference between other well-known meta-heuristic algorithms. The SMA is more efficient than other standard, heuristic, and meta-heuristic search strategies in granting extremely ambitious outputs according to the comparison records.

An innovative hybrid algorithm to solve nonconvex economic load dispatch problem with or without valve point effects

An innovative hybrid algorithm to solve nonconvex economic load dispatch problem with or without valve point effects

Solving practical economic load dispatch problem using crow search algorithm

The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirm the high-quality solutions and the effectiveness of the proposed method for solving the non-convex practical economic load dispatch problem.

Nonconvex Economic Environmental Load Dispatch Using Fuzzy Based Squirrel Search Algorithm

Dangerous emanation of gases and nano particles from fossil fuels during power generation taints the air leading to long lasting destruction to the environment. To handle this issue, wider research works in various points of view are conducted to reduce the fuel cost in addition to the harmful gases emission. The aforementioned power generation problem is named as economic environmental load dispatch problem. In this study, a novel fuzzy based squirrel search algorithm is presented to solve the non-convex economic environmental load dispatch problem. The valve point loading effects formulate the problem as a non-convex optimization issue. Since, the two objective functions (cost and emissions) are contradictory practices; a fuzzy based concessive technique is utilized to designate the best concessive solution from the non-dominated solution set. In order to substantiate the competence of the suggested framework, the simulations are executed on different case studies and compared with recently published techniques. Simulation results divulge that the fuzzy based squirrel search algorithm performs better than the other compared techniques to efficiently solve the economic environmental load dispatch problem.

A non-convex economic load dispatch problem with valve loading effect using a hybrid grey wolf optimizer

Economic load dispatch (ELD) is a crucial problem in the power system which is tackled by distributing the required generation power through a set of units to minimize the fuel cost required. This distribution is subject to two main constraints: (1) equality and inequality related to power balance and power output, respectively. In the optimization context, ELD is formulated as a non-convex, nonlinear, constrained optimization problem which cannot be easily solved using calculus-based techniques. Several optimization algorithms have been adapted. Due to the complexity nature of ELD search space, the theoretical concepts of these optimization algorithms have been modified or hybridized. In this paper, the grey wolf optimizer (GWO) which is a swarm intelligence is hybridized with $$\beta$$ -hill climbing optimizer ( $$\beta$$ HC) which is a local search algorithm, to improve convergence properties. GWO is very powerful in a wide search, while $$\beta$$ HC is very powerful in deep search. By combining the wide and deep search ability in a single optimization framework, the balance between the exploration and exploitation is correctly managed. The proposed hybrid algorithm is named $$\beta$$ -GWO which is evaluated using five different test cases of ELD problems: 3 generating units with 850 MW; 13 generating units with 1800 MW; 13 generating units with 2520 MW; 40 generating units with 10,500 MW; and 80 generating units with 21,000 MW. $$\beta$$ -GWO is comparatively measured using 49 comparative methods. The results obtained by $$\beta$$ -GWO outperform others in most test cases. In conclusion, the proposed $$\beta$$ -GWO is proved to be a powerful method for ELD problem or for any other similar problems in the power system domain.

Nonconvex/nonsmooth economic load dispatch using modified time‐varying particle swarm optimization

AbstractIn this paper, a modified time‐varying particle swarm optimization (MTVPSO) is proposed for solving nonconvex economic load dispatch problems. It is a variant of the traditional particle swarm optimization (PSO) algorithm. In an MTVPSO, novel acceleration coefficients for cognitive and social components are presented as linear time‐varying parameters in the velocity update equation of the PSO algorithm. In the early stages of the optimization process, it improves the global search capability of particles and directs the global optima at the end stage. Additionally, a linearly decreased inertia weight is introduced in an MTVPSO, instead of a fixed constant value, which helps improve the diversity of the population. Through this modification mechanism in PSO, the proposed algorithm has a higher probability of avoiding local optima, and it is likely to find global optima more quickly. Six complex benchmark functions have been used to validate the effectiveness of the proposed algorithm. Furthermore, to demonstrate its efficiency, feasibility, and fastness, six different cases (3‐, 6‐, 13‐, 15‐, and 40‐unit systems and one large‐scale Korean power 140‐unit system) of the economic load dispatch problem are solved by an MTVPSO. The results of the proposed algorithm have been compared with state‐of‐the‐art algorithms. It was found that the proposed MTVPSO can deliver better results in terms of solution quality, convergence characteristics, and robustness.

A new solution to the non-convex economic load dispatch problems using phasor particle swarm optimization

The economic load dispatch (ELD) problems considering nonlinear characteristics such as valve point effects (VPE), multiple fuels (MF), transmission network losses, ramp rate limits and prohibited operating zones (POZ) are convex or non-convex/non-smooth optimization problems having equality and inequality constraints. This paper proposes using an improved particle swarm optimization algorithm called phasor particle swarm optimization (PPSO), which substitutes the control parameters of PSO with a phasor angle (θ) to solve different types of convex and non-convex/non-smooth ELD problems in different benchmark power systems including 10-unit system considering multiple fuels with/without VPE, 15-unit system considering POZ and transmission losses with/without ramp rate limits, 40-unit system with VPE, 80-unit system with VPE, and also 140-unit large-scale real test system for convex ELD problem. The comparative simulation results show that PPSO has efficient performance and is a reliable tool in obtaining higher quality solutions in solving different types of ELD problems.

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

According to no free lunch (NFL) theorem, a metaheuristic optimization method is superior to other metaheuristic optimization methods when it has focused on specific class of optimization problems. Thus, this paper focuses on developing artificial cooperative search (ACS) optimization algorithm to solve economic dispatch (ED) problems more precisely with less complexity than other metaheuristic optimization methods. ACS is a recently developed two population search algorithm based on coevolution process with high probability of finding optimal solution in complex and non-convex optimization problems. This merit is provided by balancing exploration of the problem's search space and exploitation of better results through use of two advanced evolutionary operators and only one control parameter. The constraint handling strategy of the proposed method for solving economic power load dispatch problems is to generate and work with feasible solutions along all the optimization iterations without any mismatch between the total amount of electric power generation and electricity demand plus network transmission loss. Unlike the penalty method, this strategy is unaffected by parameter setting of applied optimization method that complicates its applicability for solving economic power load dispatch problems. The feasibility of ACS for solving ED problem is tested on different lossy non-convex test systems of various sizes and complexities. The practical aspects such as satisfaction of power demand constraint, generation limits of generators and value-point loading effect are undertaken to solve ED problem in medium to relatively large-scale electric power systems. Obtained results confirm the ACS's capability in converging to a better solution highly robust within the reasonable computational time in all independent trials; all these as compared with other optimization algorithms reported in the literature for solving lossy non-convex ED problems. The results are analyzed statistically in terms of solution quality and computational efficiency. The statistical analyses reveal that ACS is a potential method to solve economic power load dispatch problems as it provides higher quality solution in comparison with other optimization algorithms.

A modified crow search algorithm (MCSA) for solving economic load dispatch problem

This paper presents a novel evolutionary optimization algorithm namely the modified crow search algorithm (MCSA) for solving the non-convex economic load dispatch (ELD) problem which improves the crow search algorithm (CSA) by an innovative selection of the crows and adaptive adjustment of the flight length. MCSA is a population-based technique based on the intelligent behavior of the crows in finding food sources. In MCSA, each crow saves its food in hiding-places for the time it needs. Also, each crow searches environment to find the better foods by stealthily following other crows to discover their hiding-places. The proposed MCSA develops the search capability of crows in the original CSA and introduces a new way by which a destination is selected by a crow to follow. To indicate the applicability of MCSA in the ELD problem, it is applied on five different well-known test systems. The results are compared in terms of the solution quality, robustness, and computing time with other methods implying that the proposed method has a superior performance than the other techniques.

Improved Fireworks Algorithm with Chaotic Sequence Operator for Large-Scale Non-convex Economic Load Dispatch Problem

Fireworks algorithm (FWA) is one of the recently developed meta-heuristic techniques, which has shown potential to solve non-shifted optimization functions. However, several engineering optimization problems have shifted optima where the performance of the algorithm heavily degrades owing to the intrinsic limitations of FWA. This paper proposes an Improved FWA with Chaotic Sequence Operator (IFWA-CSO) to efficiently solve diverse engineering optimization problems having shifted optima. The proposed algorithm is validated on benchmark mathematical functions. The IFWA-CSO algorithm is then proposed to solve complex economic dispatch problem of power systems considering several practical constraints such as valve-point loading effect, ramp rate limits, prohibited operating zones, etc. The application results of the proposed method on 140 generator system are presented and compared with existing methods available in literature.

Economic load dispatch problem: quasi-oppositional self-learning TLBO algorithm

This paper proposes a meta-heuristic algorithm named as quasi-oppositional self-learning teacher-learner-based-optimization (QOSLTLBO) for solving non-convex economic load dispatch (ELD) problem. The ELD problem is an essential concern of power system and its main objective is to allocate optimal power generation to each generating unit so as to minimize the total cost of generation while satisfying all constraints available in the system. The problem considered in this paper is a non-convex quadratic generation cost of the units (with or without valve-point loading effects) with power balance and generation limits as the system constraints. This model of generation cost is a continuous model of the ELD problem. The proposed algorithm includes a quasi-oppositional approach for better initialization of population. A self-learning phase is added after teacher phase and learner phase of basic teacher-learner-based-optimization (TLBO) algorithm to improve the convergence rate. To prove the efficacy and robustness of proposed algorithm, it is applied to solve ELD problem on different standard IEEE generator systems and the results, thus obtained are compared with other state-of-art algorithms. The minimum total cost of generation in all the cases are obtained from the proposed algorithm which proves its effectiveness over others. The additional advantage of the proposed QOSLTLBO algorithm is that it is kept free from algorithm-specific parameters like basic TLBO.

A Modern Approach to Solve of Economic Load Dispatch using Group Leader Optimization Technique

Economic load dispatch plays an important role of power system operation & control by using different soft techniques that have been used to solve convex and non-convex economic load dispatch (ELD) problems. This paper presents a new global optimization algorithm to the economic load dispatch problems for minimization of fuel cost of generations with different constraints such as ramp rate limits, valve-point loading and prohibited operating zones of large-scale thermal plants. Power transmission loss has also been considered in few cases. Group leader optimization algorithm (GLOA) is a relatively new optimization technique. Mathematical models of this algorithm demonstrate the efficiency, quality of solution and convergence speed of the method and successful application of the algorithm on ELD problems. Simulation results found that the proposed approach outperforms several other existing optimization techniques in terms quality of solution obtained and computational efficiency. Results also be confirmed the robustness of the proposed methodology.

Non-convex Economic Load Dispatch using Cuckoo Search Algorithm

<p>This paper presents cuckoo search algorithm (CSA) for solving non-convex economic load dispatch (ELD) problems of fossil fuel fired generators considering transmission losses and valve point loading effect. CSA is a new meta-heuristic optimisation technique inspired from the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds of other species. The strength of the proposed meta-heuristic optimization technique CSA has been tested and validated on the standard IEEE 14-bus, 26-bus and 30-bus system with several heuristic load patterns. The results have indicated that the proposed approach is able to obtain significant economic load dispatch solutions than those of Firefly Algorithm (FFA) and other soft computing techniques reported in the literature.</p>

Modified social spider algorithm for solving the economic dispatch problem

The economic load dispatch problem is a non-convex and non-linear optimization problem due to the inclusion of practical features such as valve point effects, prohibited operating zones, ramp rate limits, and transmission losses. For solving the non-convex economic load dispatch problem, a social spider algorithm has been proposed recently. This paper proposes a modified version of the social spider algorithm and studies the application of this version for solving the non-convex economic load dispatch problem. The proposed modification significantly improves the performance of the social spider algorithm. Four benchmark test systems having 6 units, 40 units, 80 units, and 140 units are considered to demonstrate the efficacy of the proposed algorithm. The results obtained from the modified social spider algorithm surpass the results obtained by the original social spider algorithm and significantly compete with the best results presented in previous literature.

Hybrid PSO-ACO technique to solve multi-constraint economic load dispatch problems for 6-generator system

This paper presents a new hybrid soft computing approach in solving typical economic load dispatch (ELD) problem by combining two widely used meta-heuristic techniques, namely particle swarm optimization (PSO) and ant colony optimization (ACO). Though PSO has been popularly used in ELD problems for its flexibility, robustness, and fast convergence, it often produces not so good solution due to premature convergence to local optima. ACO, on the other hand, popular for its good global exploration feature, strikes a fine balance between local and global search for optimum solution when combined with PSO. This aspect has been exploited for the first time by applying a customized combination of PSO and ACO in finding solution for both convex and non-convex ELD problems with smooth and non-smooth cost functions (i.e. with and without valve-point loading) and multiple constraints like generator capacity, transmission loss, ramp rate limits, and prohibited operating zones. This paper showcases the results of different test cases for the proposed approach implemented in a simulated 6-generator thermal power system; the results validate the effectiveness and superiority of PSO–ACO when compared with few other hybrid approaches and pure PSO and ACO approaches under similar test conditions. Considering the quality of solution including convergence characteristics, power loss, and total generation cost, PSO–ACO emerges as a viable alternative for solving ELD problems in a real power generation scenario.

Tournament-based harmony search algorithm for non-convex economic load dispatch problem

This paper proposes a tournament-based harmony search (THS) algorithm for economic load dispatch (ELD) problem. The THS is an efficient modified version of the harmony search (HS) algorithm where the random selection process in the memory consideration operator is replaced by the tournament selection process to activate the natural selection of the survival-of-the-fittest principle and thus improve the convergence properties of HS. The performance THS is evaluated with ELD problem using five different test systems: 3-units generator system; two versions of 13-units generator system; 40-units generator system; and large-scaled 80-units generator system. The effect of tournament size (t) on the performance of THS is studied. A comparative evaluation between THS and other existing methods reported in the literature are carried out. The simulation results show that the THS algorithm is capable of achieving better quality solutions than many of the well-popular optimization methods.