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Nowadays, economic load dispatch between generation units with least cost involved is one of the most important issues in utilizing power systems. In this paper, a new method i.e. Water Cycle Algorithm (WCA) which is similar to other intelligent algorithm and is based on swarm, is employed in order to solve the economic load dispatch problem betwee...
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... order to reach to optimal production for each power plant, curve of fuel cost has to be modeled as a mathematical relation. In classic case, this function is modeled as quadratic function (Figure 1) but in practical and developed cases; this model is modeled as non-linear and discontinues form due to several constraints. ...
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... For this purpose, heuristic optimization techniques like GA [4][5][6][7][8], Tabu search, Particle swarm optimization (PSO), Simulated Annealing are best suited for this purpose. Water Cycle Algorithm (WCA), another algorithm which was used [9] to solve the ELD problem. It is similar to other intelligent algorithms and is based on swarm. ...
Optimization techniques have been emerged as a powerful tool in solving real life engineering problems of the modern world. Economic Load Dispatch (ELD) is a well-known electrical engineering problem of running the power system economically. In a unified power generation system, the objective is to select the optimum values of power units within the specific ranges provided to achieve the desired solution of the minimization of the total cost by satisfying the system constraints. In this paper, optimization technique of Genetic algorithm (GA) is suggested to solve the ELD problem of 3-units power system. A study of three generating units having a maximum demand of load to be 850 MW along with valve-point loading effects is considered. GA technique efficiently computed the optimum value of the power units and the minimum cost function of the three generating units along with satisfying all the constraints. The value of minimum cost acquired is compared with the minimum values acquired through the previous techniques. The results show the superiority of the proposed technique.
... The research community has introduced a variety of optimization techniques to ELD problems based on classical, as well as, modern meta-heuristic solvers. Few potential applications of conventional algorithms in the field of ELD are based on linear programming (LP), interior point methods, reduced gradient methods and Newton methods [5,6] while the artificial intelligence techniques to solve the ELD problems are based on genetic algorithm [7,8], evolutionary programming [9,10], hybrid imperialist competitive-sequential quadratic programming (HIC-SQP) algorithm [11], biogeography-based optimization (BBO) algorithm [12], modified krill herd algorithm [13], modified harmony search method [14], artificial bee colony (ABC) algorithm [15], firefly algorithm [16], interactive differential evolution (DE) [17], Cuckoo search algorithm [18], species-based quantum PSO [19], teaching-learning-based optimization method [20], backtracking search algorithm [21], bacterial foraging optimization method [22], modulated PSO [23] and modified aggregation based PSO [24]. Few potential contributions of hybrid approaches in the domain of ELD problems include memetic computing approach [25], PSO hybrid with a gravitational search algorithm (GSA) [26], DE hybrid with clonal section method [27], harmony search algorithm aided with interiorpoint method [28], PSO-GSA based fuzzy logic [29], fuzzy adaptive hybrid PSO algorithm [30] and hybrid approach GA-PS-SQP [31]. ...
... Normally, cost model based on valve-point loading is given as the sum of quadratic and sinusoidal functions related to the power output of generation units. Mathematical formulation of fitness function of ELD problem with the valve-point effect is given as follows: [8] ...
... The min and max generator output powers P min i and P max i , for 3-Gus, are provided in Table 4. Accordingly, for 6 and 13 GUs, the fitness functions and constraint equations can be constructed from Eqs. (6)(7)(8), while P min i and P max i for these GUs are also listed in Table 4. ...
In the present study, bio-inspired computational heuristics are exploited for finding the solution of economic load dispatch (ELD) problem with valve point loading effect using variants of genetic algorithm (GA) hybrid with sequential quadratic programming (SQP) and interior-point algorithms (IPAs). Variants of GAs are constructed using different sets of routines for its fundamental operators in order to explore the entire search space for global optimum solutions while SQP and IPA are integrated with GAs for rapid local convergence. Nine variants of each design scheme based on GAs, GA-SQP and GA-IPAs are applied on three different ELD problems of thermal power plant systems. Comparative studies of the proposed schemes are performed through the results of statistical performance indices in order to establish the worth and effectiveness in terms of accuracy, convergence and complexity measures.
... The objective of ED problem is to determine the optimal combination of power outputs of all the generating units to minimize the total fuel cost while satisfying several equality and inequality constraints. Hence, the ED problem is a constrained optimization problem and it can be expressed as [18], Minimize, ...
In this paper, a novel approach is proposed to solve the non-convex and discontinuous economic dispatch (ED) problem of power system with thermal power plants. All the practical constraints (loss constraint, generators ramp rate constraints and network constraints) are considered for solving the ED problem. Here, the proposed ED problem is solved by considering the generators with valve point loading (VPL) effects and prohibited operating zones (POZs) effects. In this paper, to solve this practical ED problem, an evolutionary based Artificial Fish Swarm Optimization Algorithm (AFSOA) is utilized. The AFSOA is a global search algorithm based on the characteristics of fish swarm and its autonomous model. The detailed algorithm with its flow chart is presented in this paper. To show the effectiveness of the proposed ED approach, 3 test systems (3, 6 and 20 generating unit systems) are considered. The obtained results are compared with other algorithms reported in the literature.
Economic Dispatch is one of the most important issues in power system operation, as a complex optimization problem consisting of some objective functions constrained by various limits. To increase the energy efficiency and reduce environmental concerns, combined heat and power technologies are in the spotlight. To this end, combined heat and power economic emission dispatch is one of the most challenging concepts in power system studies. This paper aims to examine the application of grasshopper optimization algorithm with the binary approach for solving the mentioned problems, including the valve point loading effect, ramp-rate limits, prohibited zones, and transmission losses. In this study, the multi-zone combined heat and power economic emission dispatch problem is investigated and, to evaluate the ability of the mentioned algorithm, a new case study system is introduced and simulated. The results show that the applied method reduces the fuel cost and emission in the range of 0.00234% to 0.69% and 16.978% to 86.3423%, respectively. Also, a new 48-unit test system is introduced considering wind power uncertainty. The effectiveness of the wind farms in reducing fuel costs and emission, is proved by 5.95% to 6.12% and 42.13% to 54.01%, respectively, compared to the case without wind farms.
The unit commitment problem is one of the most significant and basic issues in the monitor, control, and operation of modern power systems, which has always been a subject of great concern to researchers and operators as the most extensive human-made system. Before restructuring, one of the main objectives of unit commitment problem was the minimization of the total operation cost of power plants subject to various constraints, including unit and network ones. As the privatization and restructuring process became more serious, the primary purpose of the unit commitment problem has been changed to maximizing the total profit, which led to the emergence of a new concept known as profit-based unit commitment problem. Accordingly, the maximization of the profit for generation companies, all over the studied period, is a top-priority direction. This paper presents a comprehensive overview of the profit-based unit commitment problem in restructured power systems by investigating the most important studies on this topic and providing a complete classification. It also outlines the challenges facing researchers in this field, offers new insights, and suggests future directions.
Water cycle algorithm (WCA) is a population-based metaheuristic algorithm, inspired by the water cycle process and movement of rivers and streams towards sea. The WCA shows good performance in both exploration and exploitation phases. Further, the relationship between improvised exploitation and each parameter under asymmetric interval is derived and an iterative convergence of WCA is proved theoretically. In this paper, CEC’15 computationally expensive benchmark problems (i.e., 15 problems) have been considered for efficiency measurement of WCA accompanied with other optimisers. Also, a new discretisation strategy for the WCA has been proposed and applied along with other optimisers for solving combinatorial Internet shopping optimisation problem. By applying complexity analysis, it shows that using the WCA intricacy from dimension 10–30 is increased for almost three times. Proposing a unique discretisation approach along with providing iterative convergence proof can be considered as novelty of this research. By observing the attained numerical results, the WCA could find the minimum average error of CEC’15 in 12 and 8 out of 15 cases for dimensions 10 and 30, respectively. Experimental optimisation results for a wide range computationally expensive problems reveal the effectiveness and advantage of WCA for solving both continuous and discrete optimisation problems.
