• Journal of Electrical Engineering and Technology
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• 제4권3호
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• pp.301-309
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• 2009

A simple and efficient Lambda logic (${\lambda}-logic$) based algorithm is proposed for the solution of the generator constrained economic dispatch problem when the generating units having prohibited zones. The proposed method solves the economic dispatch (ED) problem that takes into account ramprate limits, transmission losses and prohibited operating zones in the power system operation. The proposed method uses a simple heuristic rule based on average power of prohibited operating zones which produces the feasibility of solution for the restricted operating units. The effectiveness of the algorithm is tested on five different test systems and the performance compared with other relevant methods reported in the literature. In all the cases, the proposed algorithm performs better than the previous existing algorithms with a less computational burden.

• Journal of Electrical Engineering and Technology
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• 제10권4호
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• pp.1441-1452
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• 2015

This paper proposes a new Hybrid Particle Swarm Optimization (HPSO) method that integrates the Evolutionary Programming (EP) and Particle Swarm Optimization (PSO) techniques. The proposed method is applied to solve Economic Dispatch(ED) problems considering prohibited operating zones, ramp rate limits, capacity limits and power balance constraints. In the proposed HPSO method, the best features of both EP and PSO are exploited, and it is capable of finding the most optimal solution for the non-linear optimization problems. For validating the proposed method, it has been tested on the standard three, six, fifteen and twenty unit test systems. The numerical results show that the proposed HPSO method is well suitable for solving non-linear economic dispatch problems, and it outperforms the EP, PSO and other modern metaheuristic optimization methods reported in the recent literatures.

• 대한전기학회논문지:전력기술부문A
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• 제50권11호
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• pp.520-527
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• 2001

This paper suggests a new methodology of evolutionary computations - an Adaptive Evolutionary Algorithm (AEA) for solving the Economic Load Dispatch (ELD) problem which has piecewise quadratic cost functions and prohibited operating zones with many local minima. AEA uses a genetic algorithm (GA) and an evolution strategy (ES) in an adaptive manner in order to take merits of two different evolutionary computations: global search capability of GA and local search capability of ES. In the reproduction procedure, proportions of the population by GA and the population by ES are adaptively modulated according to the fitness. Case studies illustrate the superiority of the proposed methods to existing conventional methods in power generation cost and computation time. The results demonstrate that the AEA can be applied successfully in the solution of ELD with piecewise quadratic cost functions and prohibited operating zones

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 제38회 하계학술대회
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• pp.850-851
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• 2007

This paper presents an efficient approach for solving the economic dispatch (ED) problems with prohibited operating zones using an improved particle swarm optimization (PSO). Although the PSO-based approaches have several advantages suitable to the heavily constrained nonconvex optimization problems, they still have the drawbacks such as local optimal trapping due to the premature convergence (i.e., exploration problem) and insufficient capability to find nearly-by extreme points (i.e., exploitation problem). This paper proposes an improved PSO framework adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. The proposed method is applied to ED problem with prohibited operating zones. Also, the results are compared with those of the state-of-the-art methods.

• 한국인터넷방송통신학회논문지
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• 제15권5호
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• pp.155-162
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• 2015

본 논문은 운전금지영역을 가진 이차 볼록 발전비용 함수를 적용하는 경제급전의 최적화 문제에 대한 결정론적 최적화 알고리즘을 제안하였다. 제안된 알고리즘은 운전금지구역을 가진 발전기는 운전금지구역을 벗어나도록 분할하고, 초기치 $P_i{\leftarrow}P_i^{max}$에 대해 발전단가가 큰 순서대로 발전량을 감소시키고, $_{max}\{F(P_i)-F(P_i-{\beta})\}$ > $_{min}\{F(P_j+{\beta})-F(P_j)\}$, $i{\neq}j$, ${\beta}=1.0,0.1,0.01,0.001$에 대해 $P_i{\leftarrow}P_i-{\beta}$, $P_j{\leftarrow}P_j+{\beta}$의 교환 최적화 과정을 수행하였다. 제안된 방법을 15-발전기의 3가지 사례에 적용한 결과 간단하면서도 항상 동일한 결과로 휴리스틱 알고리즘들에 비해 최적의 결과를 나타내었다.

• Journal of Electrical Engineering and Technology
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• 제3권3호
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• pp.320-330
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• 2008

This paper presents an improved dynamic programming (IDP) approach to solve the economic power dispatch problem including transmission losses in power systems. A detailed mathematical derivation of recursive dynamic programming approach for the economic power dispatch problem with transmission losses is presented. The transmission losses are augmented with the objective function using price factor. The generalized expression for optimal scheduling of thermal generating units derived in this article can be implemented for the solution of the economic power dispatch problem of a large-scale system. Six-unit, fifteen-unit, and forty-unit sample systems with non-linear characteristics of the generator, such as ramp-rate limits and prohibited operating zones are considered to illustrate the effectiveness of the proposed method. The proposed method results have been compared with the results of genetic algorithm and particle swarm optimization methods reported in the literature. Test results show that the proposed IDP approach can obtain a higher quality solution with better performance.

• Journal of Electrical Engineering and Technology
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• 제3권4호
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• pp.476-483
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• 2008

This paper is aimed at presenting techniques of hybrid differential evolution for solving various kinds of Economic Dispatch(ED) problems such as those including prohibited zones, emission dispatch, multiple fuels, and multiple areas. The results obtained for typical problems are compared with those obtained by other techniques such as Particle Swarm Optimization(PSO) and Classical Evolutionary Programming(CEP) techniques. The comparison of the results proves that hybrid differential evolution is quite favorable for solving ED problems with no restrictions on the shapes of the input-output functions of the generator.

• International Journal of Control, Automation, and Systems
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• 제6권4호
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• pp.468-476
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• 2008

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the $\lambda$-P table method is used to calculate ED for the fitness function of GA. The $\lambda$-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• Environmental Engineering Research
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• 제15권4호
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• pp.231-237
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• 2010

With increased chemical and economic development activities in upstream areas, the amounts of pollutants released have increased, and as such, so has the need for positive management of water supply source areas. Although more than 90% of the water supply sources in Korea depend on direct intake from surface water, the interest in indirect intake, such as riverbank filtration water, has recently risen, with some local governments currently undertaking indirect intake. Even in cases of indirect intake, water supply source protection zones need to be assigned for the comprehensive control of pollutants. To establish water quality protection zones for indirect intake, the scope of the protection zones needed to reflect the hydrological features of the water-bearing deposits of each site. Water source protection areas were estimated and presented as the 1st (within a 100 m radius from an intake well) and 2nd (within a 2 km radius from an intake well) zones. The 1st zone was more sensitive; hence, the installation of various facilities should be prohibited, and the area should be regarded as off-limits. For the 2nd zone, appropriate management should prohibit and restrict activities already present in the water source protection zone.

• 전기학회논문지
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• 제58권8호
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• pp.1485-1495
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• 2009

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the ${\lambda}-P$ function method is used to calculate ED for the fitness function of GA. The ${\lambda}-P$ function method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with two kinds of ED problems, namely ED with multiple fuel units (EDMF) and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all the ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.