Solution to economic dispatch problem with valve-point loading effect by using catfish PSO algorithm

This paper proposes application of a catfish particle swarm optimization (PSO) algorithm to economic dispatch (ED) problems. The ED problems considered in this paper include valve-point loading effect, power balance constraints, and generator limits. The conventional PSO and catfish PSO algorithms are applied to three different test systems and the solutions obtained are compared with each other and with those reported in literature. The comparison of solutions shows that catfish PSO outperforms the conventional PSO and other methods in terms of solution quality though there is a slight increase in computational time.     

A new honey bee mating optimization algorithm for non-smooth economic dispatch

The non-storage characteristics of electricity and the increasing fuel costs worldwide call for the need to operate the systems more economically. Economic dispatch (ED) is one of the most important optimization problems in power systems. ED has the objective of dividing the power demand among the online generators economically while satisfying various constraints. The importance of economic dispatch is to get maximum usable power using minimum resources. To solve the static ED problem, honey bee mating algorithm (HBMO) can be used. The basic disadvantage of the original HBMO algorithm is the fact that it may miss the optimum and provide a near optimum solution in a limited runtime period. In order to avoid this shortcoming, we propose a new method that improves the mating process of HBMO and also, combines the improved HBMO with a Chaotic Local Search (CLS) called Chaotic Improved Honey Bee Mating Optimization (CIHBMO). The proposed algorithm is used to solve ED problems taking into account the nonlinear generator characteristics such as prohibited operation zones, multi-fuel and valve-point loading effects. The CIHBMO algorithm is tested on three test systems and compared with other methods in the literature. Results have shown that the proposed method is efficient and fast for ED problems with non-smooth and non-continuous fuel cost functions. Moreover, the optimal power dispatch obtained by the algorithm is superior to previous reported results.     

Solving the economic dispatch problem with a modified quantum-behaved particle swarm optimization method

In this paper, a modified quantum-behaved particle swarm optimization (QPSO) method is proposed to solve the economic dispatch (ED) problem in power systems, whose objective is to simultaneously minimize the generation cost rate while satisfying various equality and inequality constraints. The proposed method, denoted as QPSO-DM, combines the QPSO algorithm with differential mutation operation to enhance the global search ability of the algorithm. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zones, and nonsmooth cost functions are considered when the proposed method is used in practical generator operation. The feasibility of the QPSO–DM method is demonstrated by three different power systems. It is compared with the QPSO, the differential evolution (DE), the particle swarm optimization (PSO), and the genetic algorithm (GA) in terms of the solution quality, robustness and convergence property. The simulation results show that the proposed QPSO–DM method is able to obtain higher quality solutions stably and efficiently in the ED problem than any other tested optimization algorithm.     

Artificial bee colony optimization for economic dispatch with valve point effect

In recent years, various heuristic optimization methods have been proposed to solve economic dispatch (ED) problem in power systems. This paper presents the well-known power system ED problem solution considering valve-point effect by a new optimization algorithm called artificial bee colony (ABC). The proposed approach has been applied to various test systems with incremental fuel cost function, taking into account the valve-point effects. The results show that the proposed approach is efficient and robust when compared with other optimization algorithms reported in literature.     

A new technique for solving the multi-objective optimization problem using hybrid approach

Energy efficiency, which consists of using less energy or improving the level of service to energy consumers, refers to an effective way to provide overall energy. But its increasing pressure on the energy sector to control greenhouse gases and to reduce CO₂ emissions forced the power system operators to consider the emission problem as a consequential matter besides the economic problems. The economic power dispatch problem has, therefore, become a multi-objective optimization problem. Fuel cost, pollutant emissions, and system loss should be minimized simultaneously while satisfying certain system constraints. To achieve a good design with different solutions in a multi-objective optimization problem, fuel cost and pollutant emissions are converted into single optimization problem by introducing penalty factor. Now the power dispatch is formulated into a bi-objective optimization problem, two objectives with two algorithms, firefly algorithm for optimization the fuel cost, pollutant emissions and the real genetic algorithm for minimization of the transmission losses. In this paper the new approach (firefly algorithm-real genetic algorithm, FFA-RGA) has been applied to the standard IEEE 30-bus 6-generator. The effectiveness of the proposed approach is demonstrated by comparing its performance with other evolutionary multi-objective optimization algorithms. Simulation results show the validity and feasibility of the proposed method.     

An effortless hybrid method to solve economic load dispatch problem in power systems

This paper proposes a new approach and coding scheme for solving economic dispatch problems (ED) in power systems through an effortless hybrid method (EHM). This novel coding scheme can effectively prevent futile searching and also prevents obtaining infeasible solutions through the application of stochastic search methods, consequently dramatically improves search efficiency and solution quality. The dominant constraint of an economic dispatch problem is power balance. The operational constraints, such as generation limitations, ramp rate limits, prohibited operating zones (POZ), network loss are considered for practical operation. Firstly, in the EHM procedure, the output of generator is obtained with a lambda iteration method and without considering POZ and later in a genetic based algorithm this constraint is satisfied. To demonstrate its efficiency, feasibility and fastness, the EHM algorithm was applied to solve constrained ED problems of power systems with 6 and 15 units. The simulation results obtained from the EHM were compared to those achieved from previous literature in terms of solution quality and computational efficiency. Results reveal that the superiority of this method in both aspects of financial and CPU time.     

Reactive power dispatch in wind farms using particle swarm optimization technique and feasible solutions search

In this paper, an optimization method for the reactive power dispatch in wind farms (WF) is presented. Particle swarm optimization (PSO), combined with a feasible solution search (FSSPSO) is applied in order to optimize the reactive power dispatch, taking into consideration the reactive power requirement at point of common coupling (PCC), while active power losses are minimized in a WF. The reactive power requirement at PCC is included as a restriction problem and is dealt with feasible solution search. Finally an individual set point, particular for each wind turbine (WT), is found. The algorithm is tested in a WF with 12 WTs, taking into consideration different control options and different active power output levels.     

Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using the hybrid bacterial foraging-Nelder-Mead algorithm

In this paper, a new approach is proposed to solve the economic load dispatch (ELD) problem. Power generation, spinning reserve and emission costs are simultaneously considered in the objective function of the proposed ELD problem. In this condition, if the valve-point effects of thermal units are considered in the proposed emission, reserve and economic load dispatch (ERELD) problem, a non-smooth and non-convex cost function will be obtained. Frequency deviation, minimum frequency limits and other practical constraints are also considered in this problem. For this purpose, ramp rate limit, transmission line losses, maximum emission limit for specific power plants or total power system, prohibited operating zones and frequency constraints are considered in the optimization problem. A hybrid method that combines the bacterial foraging (BF) algorithm with the Nelder-Mead (NM) method (called BF-NM algorithm) is used to solve the problem. In this study, the performance of the proposed BF-NM algorithm is compared with the performance of other classic (non-linear programming) and intelligent algorithms such as particle swarm optimization (PSO) as well as genetic algorithm (GA), differential evolution (DE) and BF algorithms. The simulation results show the advantages of the proposed method for reducing the total cost of the system.     

A novel evolutionary algorithm for dynamic economic dispatch with energy saving and emission reduction in power system integrated wind power

An optimization algorithm is proposed in this paper to solve the economic dispatch problem that includes wind farm using the Chaotic Quantum Genetic Algorithm (CQGA). In addition to the detailed models of economic dispatch introduction and their associated constraints, the wind power effect is also included in this paper. The chaotic quantum genetic algorithm used to solve the economic dispatch process and discussed with real scenarios used for the simulation tests. After comparing the proposed algorithm with several other algorithms commonly used to solve optimization problems, the results show that the proposed algorithm is able to find the optimal solution quickly and accurately (i.e. to obtain the minimum cost for power generation in the shortest time). At the end, the impact to the total cost savings for power generation after adding (or not adding) wind power generation is also discussed. The actual implementation results prove that the proposed algorithm is economical, fast and practical. They are quite valuable for further research.     

A new hybrid approach for nonconvex economic dispatch problem with valve-point effect

In literature, economic dispatch problems are generally categorized as convex and nonconvex optimization problems. In this study, a solution is proposed for economic dispatch problem with valve point effect, which is one of the nonconvex optimization problems. For this reason the hybrid approach used for solution of this problem is formed as a combination of modified subgradient (MSG) and harmony search (HS) algorithms. This approach (MSG-HS) is applied in three different lossy test systems (Three machines 6-bus, IEEE 5-machines 14-bus, IEEE 6-machines 30-bus systems) solved with different methods in the literature. System losses are calculated by using B loss matrix. The resulting optimal solution values are compared with the solution values in the literature and the results are discussed.     

Application of the invasive weed optimization algorithm to economic dispatch problems

In this paper the invasive weed optimization algorithm has been applied to a variety of economic dispatch (ED) problems. The ED problem is concerned with minimizing the fuel cost by optimally loading the electrical generators which are committed to supply a given demand. Some involve prohibited operating zones, transmission losses and valve point loading. In general, they are non-linear non-convex optimization problems which cannot be directly solved by conventional methods. In this work the invasive weed algorithm, a meta-heuristic method inspired by the proliferation of weeds, has been applied to four numerical examples and has resulted in promising solutions compared to published results.     

A particle swarm optimization based power dispatch algorithm with roulette wheel re-distribution mechanism for equality constraint

In this paper, a particle swarm optimization (PSO)-based power dispatch algorithm is proposed to deal with the energy management problem of the hybrid generation system (HGS). For conventional PSO method, the search space is only defined by inequality constraints. However, as for power dispatch problems, it is vital to maintain power balance, which can be represented as an equality constraint. To address this issue, a roulette wheel re-distribution mechanism is proposed. With this re-distribution mechanism, unbalanced power can be reallocated to more superior element and the searching diversity can be preserved. In addition, the effect of depth of discharge on the life cycle of the battery bank is also taken into account by developing a penalty mechanism. The proposed method is then applied to a HGS consisting of photovoltaic array, wind turbine, microturbine, battery banks, utility grid and residential load. To validate the effectiveness and correctness of the proposed method, simulation results for a whole day will also be provided. Comparing with three other power dispatching methods, the proposed method can achieve the lowest accumulated cost.     

An analytical solution to the economic dispatch problem

This letter treats the basic problem of economic operation of power systems and presents a mathematical derivation that proves that the classic economic dispatch (ED) problem, with quadratic-convex cost functions, can be solved analytically, i.e., without any approximations or need for numerical iterative optimization algorithms. Duality theory is employed to determine both the exact primal and exact dual solutions. All this requires, at most, are 2n function evaluations. It is stated, therefore, that the use of an ED model as an optimization-based electricity auction does not cause any conflict of interest     

A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem

The increasing costs of fuel and operation of thermal power generating units warrant development of optimization methodologies for economic dispatch (ED) problems. Optimization methodologies that are based on meta-heuristic procedures could assist power generation policy analysts to achieve the goal of minimizing the generation costs. In this context, the objective of this study is to present a novel approach based on harmony search (HS) algorithm for solving ED problems, aiming to provide a practical alternative for conventional methods. To demonstrate the efficiency and applicability of the proposed method and for the purposes of comparison, various types of ED problems are examined. The results of this study show that the new proposed approach is able to find more economical loads than those determined by other methods.     

Optimal coordination of wind-hydro-thermal based on water complementing wind

The increasing integration of wind power into the existing power system demands for effective strategies to deal with wind intermittency and uncertainty. Relying solely on thermal power to cover wind uncertainty will sacrifice the operating efficiency and economy of thermal generators. In view of this, the adjustable hydropower is preferred for complementing wind fluctuation and uncertainty and the coordinated dispatch problem of wind-hydro-thermal power is established. Based on a newly designed water supplementing wind strategy, the original complex problem is decomposed into wind-hydro subproblem and thermal subproblem. A novel stochastic constraint related to wind power uncertainty is proposed and handled according to stochastic programming theory. By introducing the concept of expected breed rate and elitist preservation strategy, the particle swarm optimization (PSO) algorithm is improved and combined with the exterior penalty function method for solving the complete optimization problem. Optimal generation scheduling schemes that can make full use of wind energy and ensure efficient and economic operating of thermal generators are obtained by the proposed approach. Meanwhile the coordinating operation of wind, hydro and thermal power under different water resources and wind penetrations respectively are revealed and discussed.     

A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems

This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem.     

Energy production cost minimization in a combined heat and power generation systems using cuckoo optimization algorithm

In this paper, cuckoo optimization algorithm is implemented to solve energy production cost minimization in a combined heat and power (CHP) generation system. This problem is also known as combined heat and power economic dispatch problem, which looks for optimal values of power and heat generation of each CHP unit to minimize the total production cost. Cuckoo optimization algorithm is a new metaheuristic algorithm. It is inspired by the life of a bird family, called cuckoo, that special lifestyle of these birds and their characteristics in egg laying and breeding has been the basic motivation for development of this algorithm. Unlike of the some previous approaches, the effect of valve point is considered in the cost function and clearly formulated in the conventional polynomial cost function as absolute sinusoidal term. The proposed method is applied to three small (with three different test cases), medium, and large test systems in order to evaluate its efficiency and feasibility. The obtained results demonstrated a higher quality solution and superior performance of the proposed cuckoo optimization algorithm method in comparison with many existing methodologies.     

A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem

Economic dispatch (ED) plays an important role in power system operation. ED problem is a non-smooth and non-convex problem when valve-point effects of generation units are taken into account. This paper presents an efficient hybrid evolutionary approach for solving the ED problem considering the valve-point effect. The proposed algorithm combines a fuzzy adaptive particle swarm optimization (FAPSO) algorithm with Nelder–Mead (NM) simplex search called FAPSO-NM. In the resulting hybrid algorithm, the NM algorithm is used as a local search algorithm around the global solution found by FAPSO at each iteration. Therefore, the proposed approach improves the performance of the FAPSO algorithm significantly. The algorithm is tested on two typical systems consisting of 13 and 40 thermal units whose incremental fuel cost functions take into account the valve-point loading effects.     

A new fuzzy adaptive particle swarm optimization for non-smooth economic dispatch

This paper proposes a novel method for solving the Non-convex Economic Dispatch (NED) problems, by the Fuzzy Adaptive Modified Particle Swarm Optimization (FAMPSO). Practical ED problems have non-smooth cost functions with equality and inequality constraints when generator valve-point loading effects are taken into account. Modern heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution for ED problems. PSO is one of modern heuristic algorithms, in which particles change place to get close to the best position and find the global minimum point. However, the classic PSO may converge to a local optimum solution and the performance of the PSO highly depends on the internal parameters. To overcome these drawbacks, in this paper, a new mutation is proposed to improve the global searching capability and prevent the convergence to local minima. Also, a fuzzy system is used to tune its parameters such as inertia weight and learning factors.     

Accurate estimation of cost function parameters for thermal power plants using a novel optimization approach

Accurate parameter estimation of the input-output characteristics in thermal power plants is an important issue in power system because these characteristics directly affect the economic dispatch calculations. Parameter estimation is an optimization problem in which the optimal values of the unknown parameters should be estimated by an optimization technique. By considering the valve-point effect, the parameter estimation will be more difficult since the fitness function of this optimization problem turns into a non-smooth and non-convex function in which finding the global optimal is a challenging task. In this paper, a recently proposed metaheuristic approach, crow search algorithm (CSA), is proposed for accurate estimation of the input-output characteristics of thermal power plants with and without valve-point effect. Simulation results show that CSA finds more promising results than least squares method (LSM), particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC).