Solving Economic Dispatch Problems Research Articles

Investigation of Equilibrium Optimizer to Solve Economic Dispatch with Practical Constraints

Now a day’s power demand keep on increasing due to rapid changes occurs in power industry. For that purpose establishing new generating is costlier rather than effectively utilize the available generating stations. In order to properly planning of power system generation sharing Economic Dispatch (ED) plays vital role. In this paper, Equilibrium Optimizer (EO) is used to solve the ED problem with effect of valve-point, prohibited operating zones (POZs), ramp rate up/down limits and pollution like practical constraints. In order to analyze the capability of the EO algorithm, the algorithm is applied to four test systems with 6 unit systems and the results are compared with other optimization algorithms. The comparative results proven that EO is better optimization technique to solve ED problem with practical constraints.

Non-smooth/non-convex economic dispatch through modified particle swarm optimization

Economic Dispatch (ED) is the foremost typical task in the power system engineering. Its aim to minimize the total generation cost while satisfying system constraints. Considering some practical features like prohibited operating zones, transmission losses and ramp rate limits ED becomes a non-convex, non-smooth, non-linear, and multi-constraint optimization problem. To solve complex optimization problems, particle swarm optimization (PSO) have proved noticeable success. However, it may suffer to trap at local minima, slow convergence and poor solutions. Thus, to address these issues and solve ED problem, a modified particle swarm optimization (mPSO) is introduced. In mPSO, new factors for inertia, cognitive and social components (i.e. acceleration coefficients and inertia weight) are familiarized. As per the concerts these factors are dynamically changed and properly maintained the diversity of the PSO. The projected mPSO is implemented to solve three altered unit test structures (3, 6 and 15) of ED problem. The experimental and compared results shows that proposed mPSO produce more appropriate economic cost.

Reinforcement learning-based modified cuckoo search algorithm for economic dispatch problems

One of the crucial tasks of social development is carbon neutrality, which is mainly due to the emission of greenhouse gases. However, thermal power, which produces plenty of harmful gases, is still the main component of electric energy. Therefore, Economic Dispatch (ED) is proposed to utilize energy resources more efficiently and reduce the cost of power generation. ED is a nonlinear and nonconvex-constrained optimization problem that is difficult to optimize. In this paper, we propose a Reinforcement Learning-based Modified Cuckoo Search algorithm (RLMCS) to solve ED problems. The proposed algorithm employs the concept of Reinforcement Learning (RL) and develops an RL-based method to process population obtained from the explorative phase. The RL-based method can dynamically enhance the population based on cumulative rewards and the current environmental state. Thus, the comprehensive search ability of RLMCS has been well improved. Moreover, some proven technologies, i.e., Gaussian random walk, quasi-opposition learning, and adaptive switch parameter, are introduced to further enhance the efficiency of RLMCS. The performance of the RLMCS is tested on standard ED problems (6 and 11 units) and ED problems with valve-point effects (10, 14, and 40 units). RLMCS is also compared with some well-established CS variants. The experimental results have demonstrated that RLMCS is more competitive and robust.

Hybrid Optimization Technique for Solving Economic Dispatch Problem: A Case Study of Nigerian Thermal Power System

Economic Dispatch Problem (EDP) is a power system optimization problem that is required to be solved accurately using an efficient optimization technique. Hybrid optimization solutions have provided better optimum results than either deterministic or non-deterministic optimization methods. The hybridization of both Particle Swarm Optimization (PSO) and Bat Algorithm (BA) to for Hybrid Particle Swarm Bat Algorithm (H-PS-BA) optimization technique for solving EDP of Nigerian 21 thermal generating station power system was carried out in this work. The result of the work revealed that H-PS-BA performed better and gave the best optimal generation costs when compared to other methods such as PSO, Interior Point Method and BA.

Solution of Economic Dispatch Problem Using Hybrid Multi-Verse Optimizer

Economic Dispatch (ED) is one of the important problems among numerous vital operational problems of power economics. ED is a non-convex, non-drivable, and non-linear optimization issue along with diverse constraints. In this research work, a neoteric natural influential optimization tool Multi-verse Optimizer (MVO) hybridized with sequential quadratic programming (SQP) termed as Hybrid MVO (MVO-SQP) is proposed for the solution of multi-constrained ED problem. This contemporary effort contemplates on ED problem in the milieu of convergence features, numerical proficiency, and stoutness.The non-convex ED problem is encrypted at Hybrid Multi-verse Optimizer (HMVO) framework and employed in MATLAB for 30 trials, 300 iterations, and 30 exploration universes. The presented mechanism is verified on typical standard test systems comprising of 6, 13, 15, and 40 unit test systems, and experimental outcomes are juxtaposed with the reported approaches in the literature. The statistical analysis shows that the proposed approach saves 2.927 $/h for 6 units test system, 9.0618 $/h for 13 units test system, 1.831 $/h for 15 units test system, and 113.515 $/hr for 40 units test system with losses. It is envisioned that this work will equip the researchers with an improved tool to solve ED problem.

A novel space contraction based on evolutionary strategy for economic dispatch

With economic development, environmental issues have become a top priority in urban governance. Furthermore, various energy conservation issues have emerged. To allocate energy resources rationally, Economic Dispatch (ED) has been proposed. ED is a common problem in power systems. It aims to minimize the cost while meeting the overall load demand. In this study, a Dynamically adjusted Space Contraction based on the Adaptive Tradeoff Model and Adaptive Evolutionary Strategy (DSC-ATM-AES) has been proposed to solve ED problems. This algorithm proposes a definition for the Differential Variance (DV) and self-adaptive slack F to enhance the searching capacity of Evolutionary Strategy (ES). It also introduces a Space Contraction (SC) technique and further improves it. The algorithm is tested on various ED problems (including 6,11,13, and 40 generators), namely standard ED problems and ED problems with valve-point effects. Moreover, DSC-ATM-AES and some popular heuristic algorithms are compared. The experimental results indicate that the DSC-ATM-AES algorithm obtains competitive results and powerful performances.

Penyelesaian Masalah Economic Dispatch Menggunakan Equilibrium Optimizer

This paper presents a metaheuristic method, namely Equilibrium Optimizer (EO) to solve the economic dispatch (ED) problem. The main objective function to be achieved is to minimize the total fuel costs of all generating units to meet the total load demand and to satisfy various operating constraints. Three case studies are used to test the effectiveness of the EO method in solving ED problems, they are three generators case, six generators case, and fifteen generators case. The simulation of solving ED problems using the EO method is implemented using MATLAB software and is carried out 30 times for each case study. The results of EO method are compared with Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA) methods. The simulation results show that the EO method can solve the ED problem more optimal than all other comparison methods for all the case studies by producing the minimum total fuel costs.

A Developed Approach to Solve Economic and Emission Dispatch Problems Based on Moth-Flame Algorithm

The solution of Combined Economic and Emission dispatch (CEED) problems aims to minimize the operating fuel cost and emission levels simultaneously, while satisfying load demand and operational constraints. The CEED problem can be formulated as a nonlinear optimization problem with equality and inequality operating constraints. Moth-flame optimization algorithm (MFO) is one of the newest bio inspired optimization techniques. However, this paper proposes a modified moth-flame optimization algorithm (MMFO) to find the optimal solution of CEED problems. MMFO is mainly based on the concept of MFO with modification the path of moths in new spirals around the flame. The developed MMFO algorithm can be used to improve the convergence characteristics of CEED optimal solutions compared to other optimization algorithms. The performance of MMFO is compared with different optimization techniques. Valve point effect, environmental emissions, and transmission line losses are included in the CEED analysis to provide more practical results. MMFO is validated using different standard test systems. The simulated results show the effectiveness and the superiority of the developed MMFO against other well-known optimization techniques.

Density-Enhanced Multiobjective Evolutionary Approach for Power Economic Dispatch Problems

Economic dispatching of generating units in a power system can significantly reduce the energy cost of the system. However, the economic dispatch (ED) problem is highly constrained, and often has disconnected feasible regions because of various physical features. Enhancing population diversity is critical for the evolutionary approach to fully explore and exploit the feasible regions. In this article, we propose a density-enhanced multiobjective evolutionary approach to solve ED problem. An ED problem is first transformed into a tri-objective optimization problem, and then multiobjective optimization techniques are employed to fully optimize the constraints and cost function simultaneously. The first two objectives are derived from the original ED problem, while the third one is a novel density objective constructed by niching methods to enhance population diversity. These three objectives are optimized simultaneously by a dynamic dominance relation, which can make a good balance among feasibility, diversity, and convergence. To evaluate the performance of this proposed approach, 22 benchmark problems and seven real-world ED problems with different features are tested in this article. The experimental results show that our approach performs better than or at least competitive to the state-of-the-art algorithms, especially on large-scale ED problems.

Multiple Hybrid of Lambda Iteration and Bee Colony Optimization Method for Solving Economic Dispatch Problem

Multiple Hybrid of Lambda Iteration and Bee Colony Optimization Method for Solving Economic Dispatch Problem

A novel constraints handling mechanism based on virtual generator unit for economic dispatch problems with valve point effects

The economic dispatch (ED) with valve point effects is a multi-constraint, non-linear, non-convex hybrid optimization problem, where dealing with the constraints of equality and inequality will seriously affect the quality of the solution. In this paper, based on the characteristics of the valve point effects of the generator unit, a novel constraints handling mechanism (NCHM) is proposed for solving ED problems with valve point effects. The NCHM consists of the virtual generator unit (VGU) method and the power allocation scheme (PAS) to address the constraints of equality and inequality. In VGU method, as a penalty function, the virtual generator unit is added to the ED objective function. Unlike the traditional penalty function, the characteristics of the virtual generator unit are close to that of the actual generator unit, which breaks the difficulty of parameter selection and makes the convergence better. For PAS method, the power of the generator unit is locked at the valve point with a certain probability to accelerate convergence. To demonstrate the effectiveness of the NCHM, it is tested on 13-, 40- and 80-unit systems combined with differential evolution algorithm. The simulation results show that the proposed NCHM is significantly superior in accuracy, stability and computing time compared with other previous constraints handling mechanism for solving the ED problems with valve point effects.

Economic dispatching Optimization of power grid based on IGWO Algorithm

An improved grey Wolf optimization algorithm (IGWO) is proposed to solve economic dispatch (ED) of power systems is proposed in this paper. The column vector composed of the active power of each generator in the power grid system is taken as the decision variable, and the total power generation cost of the power grid is taken as the objective function. The improved grey Wolf optimization algorithm is used to search for the optimal value by introducing the inertial characteristic constant and Gaussian mutation operator, and is compared with particle swarm optimization (PSO). The simulation results show that the proposed method has the characteristics of fast convergence speed, high solution accuracy and easy to jump out of the local optimal solution, and can be used as an effective means to solve ED problems.

Solving Power Economic Dispatch Problem with a Novel Quantum-Behaved Particle Swarm Optimization Algorithm

This paper proposes the shrink Gaussian distribution quantum-behaved optimization (SG-QPSO) algorithm to solve economic dispatch (ED) problems from the power systems area. By shrinking the Gaussian probability distribution near the learning inclination point of each particle iteratively, SG-QPSO maintains a strong global search capability at the beginning and strengthen its local search capability gradually. In this way, SG-QPSO improves the weak local search ability of QPSO and meets the needs of solving the ED optimization problem at different stages. The performance of the SG-QPSO algorithm was obtained by evaluating three different power systems containing many nonlinear features such as the ramp rate limits, prohibited operating zones, and nonsmooth cost functions and compared with other existing optimization algorithms in terms of solution quality, convergence, and robustness. Experimental results show that the SG-QPSO algorithm outperforms any other evaluated optimization algorithms in solving ED problems.

Hybrid of Lambda Iteration and Meta-Heuristic Methods for Solving Economic Dispatch Problem

Hybrid of Lambda Iteration and Meta-Heuristic Methods for Solving Economic Dispatch Problem

Improvement of the PSO Algorithm to Solve the Nonlinear Economic Dispatch Problem with a New Local Search Algorithm

This paper suggests a new PSOHHC algorithm for solving the economic dispatch (ED). This algorithm was created by integrating two algorithms: PSO (particle swarm optimization) algorithm, an evolutionary algorithm based on collective intelligence, and a new search algorithm for HHC (Hybrid Hill Climbing) which is based on searching. The aim of presenting this algorithm is to improve the performance of the PSO algorithm in terms of convergence to achieve the best possible solution with the required accuracy. This new algorithm is able to improve the responses obtained from the PSO algorithm with a controllable local search. The most important goal of economic dispatch is the optimal allocation of each generator's contribution to provide the load and reduce the costs of active units in the power system. This is generally due to the nonlinear factors and limitations, such as: the effect of steam inlet valve (valve point effect (VPE)), the balance between the production and consumption of the system, the prohibited operating zones (POZS), production limits, slope rate, and lines' losses. This algorithm is implemented on 3 test systems of 13 units, 31 units and 40 units with different operating conditions, independently and also in combination with the PSO evolutionary algorithm, and simulation results illustrate the efficiency of this algorithm in solving ED problems.

A Proposed Improved Hybrid Hill Climbing Algorithm with the Capability of Local Search for Solving the Nonlinear Economic Load Dispatch Problem

This paper introduces a new hybrid hill-climbing algorithm (HHC) for solving the Economic Dispatch (ED) problem. This algorithm solves the ED problems with a systematic search structure with a global search. It improves the results obtained from an evolutionary algorithm with local search and converges to the best possible solution that grabs the accuracy of the problem. The most important goal of economic load dispatch is the optimal allocation of each generator's contribution to provide the load and reduce the costs of active units in the power system. This is generally due to presence of the nonlinear factors and limitations, such as the effect of the steam inlet valve (valve point effect (VPE)), the balance between the power generation and power demand of the system, the prohibited operating zones (POZS), power generation limits, ramp rate limits, and transmission losses. This algorithm is implemented on three 13-unit, 15-unit and 40-unit test systems with different operating conditions, and also for the same three test systems in combination with the evolutionary PSO algorithm. The simulation results show the efficiency of the proposed algorithm in solving ED problems.

Multi-Objective Evolutionary Programming for Solving Economic Dispatch Problem

Multi-Objective Evolutionary Programming for Solving Economic Dispatch Problem

An improved adaptive differential evolution optimizer for non-convex Economic Dispatch Problems

The present paper proposes an improved adaptive differential evolution algorithm, the IL-SHADE algorithm, to solve Economic Dispatch Problems (EDPs) taking into account practical constraints, such as transmission network losses, ramp rate limit, prohibited operation zone and valve point effect. The IL-SHADE algorithm is introduced as an improved version of the L-SHADE algorithm (Success-History based Adaptive Differential Evolution algorithm with Linear population size reduction). The proposed algorithm is first tested on eight CEC’05 standard benchmark test functions. Then, the efficiency of the proposed optimizer is demonstrated by solving different practical EDPs related to three IEEE power test systems, the IEEE 6-unit, 40-unit and 140-unit test systems. The comparison with various recent state-of-the-art approaches proves that IL-SHADE outperforms the L-SHADE and other cited approaches. Finally, the Wilcoxon sign rank test is used to validate the results.

Hydrothermal Economic Dispatch Using Hybrid Big Bang-Big Crunch (HBB-BC) Algorithm

In power generation, it is expected to generate required amount of power based on the load system with minimum cost which is generally called as economic dispatch (ED). Therefore, providing an approach which can be used to solve ED problem in electric systems for effective operation is important. In this paper, hybrid big bang-big crunch (HBB-BC) algorithm was proposed to solve hydrothermal ED problem. Basically, HBB-BC is an algorithm which combined between BB-BC and PSO that use the PSO to improve ability of BB-BC algorithm. To examine the performance of HBB-BC algorithm for hydrothermal ED, IEEE 26 bus was utilized as test system with 6 generators (3 thermal and 3 hydro generator units). Next, simulation output was compared with improved PSO, and modified improved PSO algorithm. From results, HBB-BC algorithm shown the best result under tested case. It confirmed by obtained total operating cost for HBB-BC algorithm was the lowest (11,344.593 $/h) compared to IPSO (11,451.001 $/h) and MIPSO algorithms (11,387.000 $/h).

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.