Non-convex Economic Dispatch Problem Research Articles

Heat Transfer Search Algorithm for Non-convex Economic Dispatch Problems

This paper presents Heat Transfer Search (HTS) algorithm for the non-linear economic dispatch problem. HTS algorithm is based on the law of thermodynamics and heat transfer. The proficiency of the suggested technique has been disclosed on three dissimilar complicated economic dispatch problems with valve point effect; prohibited operating zone; and multiple fuels with valve point effect. Test results acquired from the suggested technique for the economic dispatch problem have been fitted to that acquired from other stated evolutionary techniques. It has been observed that the suggested HTS carry out superior solutions.

Improved Artificial Bee Colony Algorithm for Non-Convex Economic Power Dispatch Problem

Improved Artificial Bee Colony Algorithm for Non-Convex Economic Power Dispatch Problem

A Non-convex Economic Dispatch Problem with Valve Loading Effect Using a New Modified $$\beta $$ β -Hill Climbing Local Search Algorithm

In this paper, the problem of economic load dispatch (ELD) is tackled using a recently introduced local search-based method called $$\beta $$ -hill climbing optimizer. In a power system, the ELD problem is tackled by arranging a set of generation units’ outputs in a specific order to minimize the cost of the operating fuel and to match the power system load demand. This goal is achieved by satisfying all the power balance equality constraints and power output inequality constraints. $$\beta $$ -hill climbing algorithm is a new local search algorithm which uses an intelligent stochastic operator called $$\beta $$ -operator to escape the trap of local optima. The proposed method is evaluated using five real-world ELD benchmarks which vary in terms of complexity and size. The sensitivity analysis to study the effect of the proposed method parameters is conducted based on eight different convergence cases. The evaluation results of the proposed method are compared with 45 state-of-the-art methods using the same tested ELD benchmarks. Interestingly, the proposed method is able to produce a very closed-to-optimum result for almost all the tested ELD systems and the best result for one of them.

Orthogonal learning competitive swarm optimizer for economic dispatch problems

Power system economic dispatch (ED), mathematically, is a typical complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering the valve-point effects. In this paper, a novel variant of competitive swarm optimizer (CSO) referred to as OLCSO is proposed to solve both convex and non-convex ED problems. In the canonical CSO, the loser particle in each pair updates its position by learning from the winner particle. Such a learning strategy is easy to implement, but is not efficient enough because even a bad particle can contain useful information while a good particle may have misleading features. To solve this issue, an orthogonal learning (OL) strategy based on orthogonal experimental design is developed for CSO to quickly discover more useful information that contained in the winner and the loser particles. The OL strategy can easily construct a more promising solution to provide a more systematic search strategy for OLCSO. A set of 24 numerical benchmark functions and three ED cases with diverse complexities and characteristics are used to comprehensively verify the performance of OLCSO. The experimental results and comparison results consistently indicate that OLCSO can be used as a competitive alternative for ED problems.

A Distributed Randomized Gradient-Free Algorithm for the Non-Convex Economic Dispatch Problem

In this paper, a distributed randomized gradient-free algorithm (DRGF) is employed to solve the complex non-convex economic dispatch problem whose non-convex constraints include valve-point loading effects, prohibited operating zones, and multiple fuel options. The DRGF uses the Gauss approximation, smoothing parameters, and a random sequence to construct distributed randomized gradient-free oracles. By employing a consensus procedure, generation units can gather local information through local communication links and then process the economic dispatch data in a distributed iteration format. Based on the principle of projection optimization, a projection operator is adopted in the DRGF to deal with the discontinuous solution space. The effectiveness of the proposed approach in addressing the non-convex economic dispatch problem is demonstrated by simulations implemented on three standard test systems.

A New Sine Cosine Optimization Algorithm for Solving Combined Non-Convex Economic and Emission Power Dispatch Problems

The current study presents a modified sine cosine optimization (MSCO) algorithm for solving the non-smooth environmental/economic power dispatch problem. In the proposed MSCO algorithm, random search agents’ population is initialized in the search domain for simultaneous optimization of both the combined economic and environmental objectives. Added to that, the proposed MSCO proposes an opposition strategy to preserve the diversity of solutions purposefully. Hence, the Pareto optimal solutions are customized according to the Pareto front concepts. These solutions are evolved using a modified version of the sine cosine algorithm (SCA), where the best agent is selected randomly from the stored Pareto solutions. Furthermore the parameter-based tuning mechanism is designed to improve the balance between the exploration and exploitation abilities. The correctness and effectiveness of the proposed MSCO are validated through experiments results and comparisons on EELD problem. Simulations were conducted on two test systems with non-smooth fuel cost and emission issues. The first system constitutes 6-unit benchmarking system, while the second one constitutes 10- units, and their results are compared with the results of other optimization techniques that were reported in the literature. The numerical comparisons reveal the robustness and effectiveness of the proposed MSCO algorithm.

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.

Hybrid Mean-Variance Mapping Optimization for Non-Convex Economic Dispatch Problems

The economic dispatch (ED) is one of the important optimization problems in power system generation for fuel cost saving. This paper proposes a hybrid variant of mean-variance mapping optimization (MVMO-SH) for solving such problem considering the non-convex objective functions. The new proposed method is a hybrid variant of the original mean-variance mapping optimization algorithm (MVMO) with the embedded local search and multi-parent crossover to enhance its global search ability and improve solution quality for optimization problems. The proposed MVMO-SH is tested on different non-convex ED problem including valve point effects, multiple fuels and prohibited operating zones characteristics. The result comparisons from the proposed method with other methods in the literature have indicated that the proposed method is more robust and provides better solution quality than the others. Therefore, the proposed MVMO-SH is a promising method for solving the complex ED problems in power systems.

Distributed auction optimization algorithm for the nonconvex economic dispatch problem based on the gossip communication mechanism

This paper presents an efficient distributed auction optimization algorithm (DAOA) based on the gossip communication mechanism for the nonconvex economic dispatch problem. The problem contains several constraints such as generation output limits, valve-point loading effects, multiple fuels, and the supply-demand balance. The gossip communication mechanism runs as two layers. The first layer triggers the leaders to conduct the local auction optimization, and the second layer is the auction protocol that selects the optimal neighbors to cooperate with the leaders to implement the auction decision. Auction optimization is a local optimization method, in which the units evaluate the bids of a certain amount of output power and the paired bid winners update their output power to reduce the generation cost. Better solutions can be obtained through gossip communication and local optimizations. Numerous simulations are conducted to demonstrate the effectiveness of the proposed strategy.

Solving convex and non-convex static and dynamic economic dispatch problems using hybrid particle multi-swarm optimization

Solving convex and non-convex static and dynamic economic dispatch problems using hybrid particle multi-swarm optimization

A new coding for solving large-scale non-convex economic dispatch problems without a penalty factor

In some optimization problems, it is necessary that a sum of variables converges to an expected value during the optimization process. In solving this type of problem, a penalty factor is usually employed in the objective function. Thus, some disadvantages such as increased search space is unavoidable. This research proposes a new coding based on particle swarm optimization in order to solve economic dispatch problems without a penalty factor, which, in turn, controls the sum of all variables. The suggested coding could effectively escape from infeasible solutions; thereby, search efficiency and solution quality would be dramatically improved. In order to verify the effectiveness of the proposed coding, it is implemented on various economic dispatch problems, i.e. test systems with 6, 15 and 40 generating units as well as a typical Korean system with 140 generating units, all with non-convex and non-smooth cost functions. In addition, the numerical results are compared with those of other well-established and valid techniques.

An effective Lightning Flash Algorithm solution to large scale non-convex economic dispatch with valve-point and multiple fuel options on generation units

Generation units with multiple fuel options and valve-point loading effects on the generators are fundamental parts of power system generation. However, economic dispatch (ED) of these units have non-convex, non-continuous generation cost functions. In this paper, a new Lightning Flash Algorithm (LFA) is proposed to solve complex non-convex ED problems in large scale power systems considering multiple fuel options and valve point effects on the generators. Five case study systems including 10-units, 40-units, 80-units, 160-units and 640-units are conducted to validate the applicability and effectiveness of the proposed LFA method for solving ED problems. The results are compared with other published methods in literature and confirm the applicability and effectiveness of LFA against other existing methods. LFA can successfully conduct the best fuel types of the generators and adjust the optimum settings to allocate load demand to the online generation units in power system. The results demonstrate that using proposed LFA method can minimize the total generation costs and optimally satisfy the load demands in the power grid.

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.

Artificial bee colony algorithm for solving economic dispatch problems with non-convex cost functions

The main aim of this paper is to propose an efficient and reliable algorithm to solve the economic dispatch (ED) problem with non-convex cost functions in power systems, using artificial bee colony (ABC) algorithm. For techno-economic reasons along with the high computation time, the ED problem has undergone a significant amount of research over the last years, in an effort to find the more suitable optimisation algorithm which ensures a balance between the optimal economic contribution of each generating unit outputs and the required computation time. The proposed algorithm is applied to different non-convex ED problems, including prohibited operating zone (POZ) with ramp rate limits, valve point effects with consideration of the transmission network losses and the gaseous emission of the generating units. Four different test systems consisting 6, 10, 15, and 20 generating units are used to validate the consistency of the proposed algorithm to detect the optimal solution for a given objective. The simulation results clearly indicate that the ABC algorithm provides better results in term of quality solution and convergence speed compared to those available in the literature.

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.

An efficient crisscross optimization solution to large-scale non-convex economic load dispatch with multiple fuel types and valve-point effects

As one of important optimization problems in power system, economic dispatch (ED) with multiple fuel options is characterized by high non-convexity, non-linearity and discontinuity. The combined action of multiple fuel options and valve-point effects increases the degree of difficulty to solve the ED problem. In this paper, a recently developed heuristic algorithm called crisscross optimization algorithm (CSO) is attempted to address the large-scale and non-convex ED problem with both multiple fuel options and valve-point effects taken into account. The proposed CSO method solves the ED problem through horizontal crossover and vertical crossover. The former searches for the new solutions within a half population of hyper-cubes by adopting a cross-border search approach while the latter provides a unique mechanism to prevent from the premature convergence problems based on the concept of dimensional local minimum. Both operators alternatively generate moderation solutions which are subsequently updated by an elite selection strategy. The proposed method is validated on six test systems consisting of 10–640 generating units and compared with other state-of-the-art methods in the literature. The results show that CSO yields higher quality solutions especially for solving large-scale ED problems with multiple fuel options.

Two-phase mixed integer programming for non-convex economic dispatch problem with spinning reserve constraints

This paper proposes a deterministic two-phase mixed integer programming (TPMIP) approach to solve the non-convex economic dispatch (ED) problem considering ramp rate constraints, valve-point effect (VPE), prohibited operating zones (POZs), transmission loss, and spinning reserve constraints. In the first phase, the non-smooth cost function induced by VPE is piecewise linearized and the POZs constraints are formulated as a set of mathematical formulas via a mixed integer encoding technique. Then, the non-convex ED problem is converted to a mixed integer programming (MIP) problem and can be solved by commercial optimization solvers. In the second phase, based on the solution obtained in the first phase, the range of the power output of each unit is compressed and then solve the MIP problem again to make a further exploitation for an optimal solution in the subspace of the whole solution domain. To demonstrate the effectiveness of TPMIP, it is applied to eight test systems and the simulation results are compared with those obtained by the existing methods cited in this paper. Numerical simulations have verified that the proposed method provides a comprehensive framework in solving the non-convex ED problem.

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.