Quadratic Fuel Cost Function Research Articles

Impact of parameter control on the performance of APSO and PSO algorithms for the CSTHTS problem: An improvement in algorithmic structure and results.

Cascaded Short Term Hydro-Thermal Scheduling problem (CSTHTS) is a single objective, non-linear multi-modal or convex (depending upon the cost function of thermal generation) type of Short Term Hydro-Thermal Scheduling (STHTS), having complex hydel constraints. It has been solved by many metaheuristic optimization algorithms, as found in the literature. Recently, the authors have published the best-achieved results of the CSTHTS problem having quadratic fuel cost function of thermal generation using an improved variant of the Accelerated PSO (APSO) algorithm, as compared to the other previously implemented algorithms. This article discusses and presents further improvement in the results obtained by both improved variants of APSO and PSO algorithms, implemented on the CSTHTS problem.

Improved Firefly Algorithm: A Novel Method for Optimal Operation of Thermal Generating Units

This paper presents a novel improved firefly algorithm (IFA) to deal the problem of the optimal operation of thermal generating units (OOTGU) with the purpose of reducing the total electricity generation fuel cost. The proposed IFA is developed based on combining three improvements. The first is to be based on the radius between two solutions, the second is updated step size for each considered solution based on different new equations, and the third is to slightly modify a formula producing new solutions by using normally distributed random numbers and canceling uniform random numbers of conventional firefly algorithm (FA). The effect of each proposed improvement on IFA is investigated by executing five benchmark functions and two different systems. The performance of IFA is investigated on six other study cases consisting of different types of objective function and complex level of constraints. The objective function considers single fuel with quadratic form and nonconvex form, and multifuels with the sum of several quadratic and nonconvex functions while a set of constraints taken into account are power loss, prohibited zone, ramp rate limit, spinning reserve, and all constraints in transmission power networks. The obtained results indicate the proposed improvements in terms of high optimal solution quality, stabilization of search ability, and fast convergence compared with FA. In addition, the comparisons with other methods also lead to a conclusion that the proposed method is a very promising optimization tool for systems with quadratic fuel cost function and with complicated constraints.

Modified Differential Evolution for Multi-objective Load Dispatch Problem Considering Quadratic Fuel Cost Function

This paper proposes a Modified Differential Evolution (MDE) for solving multiobjective load dispatch (MOLD) problem where transmission power losses are considered. MDE is an improved version of conventional Differential Evolution (CDE) in which the mutation operation of the CDE is improved by using five differential solutions instead of three ones similar to CDE. In the MOLD problem, three cases of dispatch including economic dispatch, emission dispatch and multi-objective dispatch are carried out by considering fuel cost function, emission function and both fuel cost and emission functions. In the third case of dispatch, there is a price penalty factor employed to determine the best compromise solution instead of using Fuzzy-based mechanism similar to other studies. The performance of MDE is verified by testing on two systems with three units and one system with six units. In the two systems, the fuel cost and emission from MDE are compared to those from CDE and other existing meta-heuristic algorithms, and the analysis on the result comparison indicates that the MDE is a promising algorithm for solving the MOLD problem.

Cuckoo search algorithm for combined heat and power economic dispatch

This paper proposes a cuckoo search algorithm (CSA) for solving for the combined heat and power economic dispatch (CHPED) problem considering valve point loading effects on fuel cost function of pure power generation units and electrical power losses in transmission systems. The main objective of the CHPED problem is to minimize the total fuel cost for producing electricity and heat supplying to a load demand. The proposed CSA method inspired from the reproduction behavior of cuckoo birds has attracted many researchers implementing to engineering optimization problems since it has showed several advantages of few control parameters, high solution quality and fast computational time. The effectiveness and robustness of the proposed CSA have been validated on five different systems including three systems with quadratic fuel cost function of pure power units neglecting transmission losses and two systems with nonconvex fuel cost function of pure power units. The result comparisons between the CSA method and other methods for the test systems have revealed that the CSA method can obtain higher quality solution with faster computational time than many other methods. Therefore, the proposed CSA method can be a very efficient method for solving the CHPED problem.

비볼록 발전비용함수 경제급전문제의 개선된 밸브지점 최적화 알고리즘

There is no polynomial-time algorithm that can be obtain the optimal solution for economic load dispatch problem with non-convex fuel cost functions. Therefore, electrical field uses quadratic fuel cost function unavoidably. This paper proposes a valve-point optimization (VPO) algorithm for economic load dispatch problem with non-convex fuel cost functions. This algorithm sets the initial values to maximum powers for each generator. It then reduces the generation power of generator i with an average power cost of to a valve point power . The proposed algorithm has been found to perform better than the extant heuristic methods when applied to 13 and 40-generator benchmark data. This paper consequently proves that the optimal solution to economic load dispatch problem with non-convex fuel cost functions converges to the valve-point power of each generator.

The application of one rank cuckoo search algorithm for solving economic load dispatch problems

In this paper, a one rank cuckoo search algorithm (ORCSA) is proposed for solving economic load dispatch (ELD) problems. The main objective of the ELD problem is to minimize total cost of thermal generators while satisfying power balance constraint, prohibited operating zones, ramp rate constraints and operating limits of generators. Moreover, the generating units considered in this paper have different characteristics such as quadratic fuel cost function, nonconvex fuel cost function and multiple fuel options. The proposed ORCSA method has been developed by performing two modifications on the original cuckoo search algorithm (CSA) to improve optimal solution quality and computational time. The first modification is to merge new solution generated from both Lévy flights and replacement a fraction of egg together and to evaluate and rank the solutions at once only. A bound by best solution mechanism has been used in the second modification for properly handling the inequality constraints. The proposed ORCSA method has been tested on different systems with different characteristics of thermal units and constraints. The results obtained by ORCSA have been compared to those from other methods available in the literature and the result comparison has indicated that the ORCSA method can obtain better solution quality than many other methods. Therefore, the proposed ORCSA can be a very effective and efficient method for solving ELD problems.

Hybrid Differential Evolution and Harmony Search for Optimal Power Flow

In this paper, we presents a novel approach for solving optimal power flow (OPF) problems using a hybrid differential evolution and harmony search (DEHS). The DEHS method is an improved differential evolution method based on the harmony search scheme. Harmony Search has strong and easy to combine with other methods in optimization and the Differential Evolution algorithm has a very great ability to search solutions with a fast speed to converge, contrary to the most meta-heuristic algorithms. The DEHS method has the flexible adjustment of the parameters to get a better optimal solution. Moreover, an effective constraint handling framework in the method is employed for properly handling equality and inequality constraints of the problem. The proposed DEHS has been tested on three systems including IEEE-30 bus system with quadratic fuel cost function, IEEE-30 bus system with valve point effects fuel cost function and IEEE-57 bus system with quadratic fuel cost function. The obtained results from DEHS algorithm have been compared to those from other methods in the literature. The result comparison has indicated that the proposed DEHS method is more effective than many other methods for obtaining the optimal solution for the test systems. Therefore, the proposed DEHS is a very favorable method for solving the optimal power flow problems.

Optimal power flow using artificial bee colony algorithm with global and local neighborhoods

Optimal power flow (OPF) is one of the most requisite tools for power system operation analysis. This problem has a complex mathematical formulation which is relatively hard to solve. This paper presents a swarm intelligence-based approach to solve the OPF problem. The proposed approach describes the use of a modified artificial bee colony (ABC) algorithm called ABC with global and local neighborhoods (ABCGLN) to determine the optimal settings of OPF control variables. ABCGLN is a recent modified version of basic ABC algorithm that can handle non-differentiable, non-linear, and multi modal objective functions. The ABCGLN approach is tested here on the standard IEEE 30-bus test system with three different objective functions for minimizing quadratic fuel cost function, piecewise quadratic cost function and quadratic cost function with valve point effects. The simulation results demonstrate the potential of ABCGLN algorithm of finding effective and robust quality solutions to solve OPF problem with various objective functions for the considered system as compared to those available in the literature.

Environmental Economic Load Dispatch with Quadratic Fuel Cost Function Using Cuckoo Search Algorithm

In this paper, a Cuckoo Search Algorithm (CSA) is proposed for solving environmental economic load dispatch (EELD) problem with quadratic fuel function. Cuckoo Search is a new meta-heuristic algorithm inspired from the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds of other species for solving optimization problems with promising results. However, Cuckoo Search has not been applied to EELD problem so far. Therefore, the paper presents application of CSA to the problem. The effectiveness of the proposed method is tested on several cases of dispatch and loads. The obtained result including fuel cost, emission and computation time from CSA are compared to those from other method reported in the paper. The comparison result has indicated that the proposed CSA is a very efficient method for solving EELD problem.

Solving practical power system problems using hierarchical interactive PSO strategy considering SVC controllers

This paper presents a hierarchical interactive particle swarm optimization (HIPSO) for solving the static multi objective optimal power flow (OPF) considering multi SVC controllers and dynamic economic dispatch (DED). This study introduces a variant of PSO using new mechanism search based dynamic adjustment of PSO parameters coordinated with a hierarchical strategy for reactive power planning stage to improve the performances of the original PSO in terms of solution quality and convergence characteristics. The HIPSO algorithm optimizes a combined control variables such as: active power generations, voltage control of generators, tap transformer and the reactive power of multi SVC Controllers installed at a specified buses to minimize fuel cost, total power loss and voltage deviation while satisfying the generators constraints and power system security. The proposed approach examined and applied to many practical test systems: IEEE 57-Bus, IEEE 118-Bus, 40 generating units and 10 generating units to solving; the static multi objective OPF with quadratic fuel cost function, the economic dispatch considering valve point effects and the dynamic economic dispatch considering both valve point effects and ramp rate limits. Simulation results compared to Matpower, to the standard PSO and others recent metaheuristic methods confirm the effectiveness of the proposed combined approach.

A new MILP-based approach for unit commitment in power production planning

This paper presents a complete, quadratic programming formulation of the standard thermal unit commitment problem in power generation planning, together with a novel iterative optimisation algorithm for its solution. The algorithm, based on a mixed-integer formulation of the problem, considers piecewise linear approximations of the quadratic fuel cost function that are dynamically updated in an iterative way, converging to the optimum; this avoids the requirement of resorting to quadratic programming, making the solution process much quicker.From extensive computational tests on a broad set of benchmark instances of this problem, the algorithm was found to be flexible and capable of easily incorporating different problem constraints. Indeed, it is able to tackle ramp constraints, which although very important in practice were rarely considered in previous publications.Most importantly, optimal solutions were obtained for several well-known benchmark instances, including instances of practical relevance, that are not yet known to have been solved to optimality. Computational experiments and their results showed that the method proposed is both simple and extremely effective.