Short-term Hydrothermal Scheduling Problem Research Articles

Hybridization of Chaotic Grey Wolf Optimizer and Dragonfly Algorithm for Short-Term Hydrothermal Scheduling

The short-term hydrothermal scheduling (STHS) is a complicated optimization problem, considering valve-point effect (VPE) and transmission losses, it exhibits the characteristics of nonlinearities and non-smoothness which increase the difficulty of solving the problem. Responding to these challenges, a hybrid algorithm that comprises chaotic local search technique, grey wolf optimizer, and dragonfly algorithm (CGWO-DA) is proposed to settle the STHS problem. The grey wolf optimizer (GWO) has strong local search ability with the slow convergence rate. The dragonfly algorithm (DA) owns superior global search capability and fast convergence rate, however, it exerts premature convergence and is easy to fall into local optimum. Using the chaotic local search as a supplement, the hybrid algorithm combined by two excellent algorithms can improve the shortcoming of each algorithm and enhance the exploration and exploitation of the algorithm simultaneously. In addition, two novel constraints handling strategies are presented to resolve the complicated equality constrains and guarantee the feasibility of solutions. Three systems have been tested by the proposed methodology. The solutions are compared with the ones from other available literatures, the feasibility and effectiveness of the proposed approach are well demonstrated, and the findings of case studies show that the proposed method has great competitive advantages to obtain better scheduling schemes.

Combined PSO and IBF Algorithm for Short Term Hydro Thermal Scheduling

Hydro and thermal power plants are planned to reduce the overall operation cost of the thermal power plants by optimally allocating the hydro units and thermal units in the power generation system. In this research work a combined particle swarm optimization (PSO) and improved bacterial foraging algorithm (IBFA) is proposed for short term hydro thermal scheduling (STHTS) with prohibited operating zones (POZs). The PSO algorithm yields the fastest convergence rate and possesses maximum capability of finding the global optimal solutions to the HTS (Hydro Thermal Scheduling) problems. Also BFA has succeeded in solving several issues in optimization, but it demonstrates poor convergence characteristics for large-scale issues such as the STHTS problem. Critical improvements to the basic BFA are implemented to tackle this complex issue in view of its high-dimension search space. The chemotactic step is changed in IBF, so that the convergence becomes dynamic rather than static. The combined PSO-IBF algorithm is assessed on a typical power generation plants consists of a hydroelectric power plant and an equivalent thermal power plant with a time slot of six 12-hour intervals and simulated using the MATLAB software. The simulation result shows that the combined PSO-IBF algorithm yields minimum cost value and optimal convergence rate than the existing algorithms.

Statistical Performances Evaluation of APSO and Improved APSO for Short Term Hydrothermal Scheduling Problem

The Accelerated Particle Swarm Optimization (APSO) algorithm is an efficient and the easiest to implement variant of the famous Particle Swarm Optimization (PSO) algorithm. PSO and its variant APSO have been implemented on the famous Short-Term Hydrothermal Scheduling (STHTS) problem in recent research, and they have shown promising results. The APSO algorithm can be further modified to enhance its optimizing capability by deploying dynamic search space squeezing. This paper presents the implementation of the improved APSO algorithm that is based on dynamic search space squeezing, on the short-term hydrothermal scheduling problem. To give a quantitative comparison, a true statistical comparison based on comparing means is also presented to draw conclusions.

Hybrid ABC-BAT for Solving Short-Term Hydrothermal Scheduling Problems

The main objective of short-term hydrothermal scheduling is the optimal allocation of the hydro and thermal generating units, so that the total cost of thermal plants can be minimized. The time of operation of the functioning units are considered to be 24 h. To achieve this objective, the hybrid algorithm combination of Artificial Bee Colony (ABC) and the BAT algorithm were applied. The swarming behavior of the algorithm searches the food source for which the objective function of the cost is to be considered; here, we have used two search algorithms, one to optimize the cost function, and another to improve the performance of the system. In the present work, the optimum scheduling of hydro and thermal units is proposed, where these units are acting as a relay unit. The short term hydrothermal scheduling problem was tested in a Chilean system, and confirmed by comparison with other hybrid techniques such as Artificial Bee Colony–Quantum Evolutionary and Artificial Bee Colony–Particle Swarm Optimization. The efficiency of the proposed hybrid algorithm is established by comparing it to these two hybrid algorithms.

Improved real coded genetic algorithm-based short-term hydrothermal generation planning

Real coded genetic algorithm (RCGA) and improved real coded genetic algorithm (IRCGA) have been applied for the solution of short-term hydrothermal scheduling problem. The improved technique has been developed and tested on a multi reservoir cascaded hydroelectric system having generation-load power balance, upper and lower limits on reservoir capacity, water discharge rate, water spillage rate, hydraulic continuity restriction and operating capacity limits of different hydro and thermal units. The water transport delay between connected reservoirs has also been taken into consideration. The performance of the proposed approach is validated with four test systems. The results of the proposed algorithm are compared with those of modified differential evolution (MDE), teaching learning-based optimisation (TLBO), clonal selection algorithm (CSA), improved fast evolutionary programming (IFEP), improved particle swarm optimisation (IPSO), and genetic algorithm (GA). From numerical results, it has been found that the IRCGA-based approach is able to provide better solutions in lesser computational time.

Improved real coded genetic algorithm-based short-term hydrothermal generation planning

Real coded genetic algorithm (RCGA) and improved real coded genetic algorithm (IRCGA) have been applied for the solution of short-term hydrothermal scheduling problem. The improved technique has been developed and tested on a multi reservoir cascaded hydroelectric system having generation-load power balance, upper and lower limits on reservoir capacity, water discharge rate, water spillage rate, hydraulic continuity restriction and operating capacity limits of different hydro and thermal units. The water transport delay between connected reservoirs has also been taken into consideration. The performance of the proposed approach is validated with four test systems. The results of the proposed algorithm are compared with those of modified differential evolution (MDE), teaching learning-based optimisation (TLBO), clonal selection algorithm (CSA), improved fast evolutionary programming (IFEP), improved particle swarm optimisation (IPSO), and genetic algorithm (GA). From numerical results, it has been found that the IRCGA-based approach is able to provide better solutions in lesser computational time.

Couple-based particle swarm optimization for short-term hydrothermal scheduling

A novel couple-based particle swarm optimization (CPSO) is presented in this paper, and applied to solve the short-term hydrothermal scheduling (STHS) problem. In CPSO, three improvements are proposed compared to the canonical particle swarm optimization, aimed at overcoming the premature convergence problem. Dynamic particle couples, a unique sub-group structure in maintaining population diversity, is adopted as the population topology, in which every two particles compose a particle couple randomly in each iteration. Based on this topology, an intersectional learning strategy using the partner learning information of last iteration is employed in every particle couple, which can automatically reveal useful history information and reduce the overly rapid evolution speed. Meanwhile, the coefficients of each particle in a particle couple are set as distinct so that the particle movement patterns can be described and controlled more precisely. In order to demonstrate the effectiveness of our proposed CPSO, the algorithm is firstly tested with four multimodal benchmark functions, and then applied to solve an engineering multimodal problem known as STHS, in which two typical test systems with four different cases are tested, and the results are compared with those of other evolutionary methods published in the literature.

Nondominated sorting-based disruption in oppositional gravitational search algorithm for stochastic multiobjective short-term hydrothermal scheduling

This article presents a novel framework of nondominated sorting-based disruption in oppositional gravitational search algorithm (NSDOGSA) for solving an inventive stochastic multiobjective short-term hydrothermal scheduling (SMSHTS) problems. An innovative SMSHTS mathematical formulation is derived in terms of stochastic objective functions subject to stochastic hydro- and thermal constraints. Also, a versatile constraint handling procedure is proposed to satisfy all the constraints. Besides, an opposition-based learning perception is assimilated in a gravitational search algorithm (GSA) to explore the excellence of the present population and disruption operator is integrated to hasten the convergence of solutions. Moreover, a nondominated sorting procedure is hybridized to attain a set of nondominated solutions for SMSHTS problems. In addition, an elite external archive is created to keep the nondominated solutions with the help of spread indicator and also to guide the search process toward global optima. Further, a fuzzy decision making is employed for selecting the best trade-off solution among the nondominated solution set. Finally, the proposed NSDOGSA approach is validated on four test systems that consist of two fixed-head and two variable-head stochastic multiobjective hydrothermal scheduling problems. Thus, the obtained simulation results are found to be better in terms of objective function values as well to satisfy constraints compared to other methods within a reasonable execution time.

An effectively adaptive selective cuckoo search algorithm for solving three complicated short-term hydrothermal scheduling problems

This paper proposes an effectively adaptive selective cuckoo search algorithm (ASCSA) for solving short-term hydrothermal scheduling problems with available water constraint, reservoir volume constraints, and transmission network constraints. The proposed ASCSA is a newly improved version of the conventional cuckoo search algorithm to enhance the solution quality and reduce the maximum number of iterations based on two new techniques including the new ratio of the difference between the fitness function values and the integration of solutions into one group. The effectiveness of ASCSA has been validated via eight hydrothermal systems, in which the last two systems consisting of the IEEE 30-bus and IEEE 118-bus systems are considered with a set of constraints in the transmission network. To investigate the performance of ASCSA, several algorithms are also implemented in the paper such as conventional cuckoo search algorithm, modified cuckoo search algorithm, particle swarm optimization, global vision of particle swarm optimization with inertia weight, differential evolution, and improved differential evolution. From result comparisons of the test systems, the proposed ASCSA method has obtained lower total costs than other methods implemented for solving the problems. Therefore, the proposed ASCSA is a very efficient and favorable method for solving the considered hydrothermal scheduling problems.

A novel two-swarm based PSO search strategy for optimal short-term hydro-thermal generation scheduling

The optimal power generation of hydro-thermal systems to minimize total operating costs is one of the most important targets in short-term hydro-thermal scheduling (STHS) and its evaluation is complicated by several complex and interconnected equality and inequality constraints.To solve this type of problem, it is necessary to develop on one side a model of the system characterized by a fair and proper treatment of all the equality and inequality constraints and on the other a performing optimization algorithm simultaneously considering not only the minimization of the operating costs but also the feasibility of the proposed solution.The paper presents a novel two-swarm based PSO (Particle Swarm Optimization) search strategy developed for solving these kinds of STHS problems. To exclude constraint violations as far as possible during the optimization process, first a complete inequality and equality constraints treatment of the hydrothermal systems was developed, combined with a fair spillage modelling. Then, a recent evolution of the particle swarm optimization algorithm ASD-PSO (Adaptive Search Diversification-Particle Swarm Optimization) was modified, introducing a secondary swarm able to exploit the potential contribution of the infeasible solutions. Within the context of this new strategy, two different swarms were designed, each characterized by a different treatment of the infeasible solutions, and each interacting properly with the other at every iteration.The primary swarm dealt with feasible solutions, resulting from the manipulation of constraint repairing strategies, and with a limited number of infeasible solutions whose potential contribution in the search process was not wasted out but it was properly weighted on the basis of the violation degree. The secondary swarm involved less manipulated solutions that were subjected only to one repair strategy in order to foster the exploration capability of the swarm. At each iteration, the two swarms independently update their position and velocity but partially interact with each other to obtain mutual advantages from their different peculiarities.This novel two-swarm based strategy for solving short-term hydro-thermal scheduling (STHS) problems was validated by comparing the achieved performance in terms of accuracy with those of several algorithms proposed in literature. Six different test cases, widely analysed in the literature and characterized by increasing complexity, were considered. In all the considered Test Cases, the algorithm performed very well with minimum total fuel costs that were still lower than all the feasible solutions proposed in the literature, and that satisfied all the equality and inequality constraints of the system.

Improved harmony search algorithm for the solution of non-linear non-convex short-term hydrothermal scheduling

The short-term hydrothermal scheduling (SHTS) problem is defined as one of the most important and challenging scheduling problems, which aims to obtain the minimum cost of electrical energy production. Considering an insignificant generation cost of hydropower systems, the objective of STHS is to minimize the operation cost of thermal generation plants. The optimal generation scheduling of hydro and thermal units is a complex non-convex optimization problem taking into account a set of equality and inequality constraints. The challenging constraints of the STHS problem are valve-point loading effect of thermal units, power transmission loss of the system, generation capacity of thermal and hydro units, and load balance. In this paper, an improved harmony search (IHS) optimization algorithm is employed on the non-linear non-convex STHS problem. The proposed method is employed on two test systems in order to evaluate the performance of the applied optimization method on the STHS problem. The simulation results are provided and compared with those reported in recent publications, which proves the effectiveness of the proposed IHS method in the solution of the STHS problem.

Modified Differential Evolution Algorithm: A Novel Approach to Optimize the Operation of Hydrothermal Power Systems while Considering the Different Constraints and Valve Point Loading Effects

This paper proposes an efficient and new modified differential evolution algorithm (ENMDE) for solving two short-term hydrothermal scheduling (STHTS) problems. The first is to take the available water constraint into account, and the second is to consider the reservoir volume constraints. The proposed method in this paper is a new, improved version of the conventional differential evolution (CDE) method to enhance solution quality and shorten the maximum number of iterations based on two new modifications. The first focuses on a self-tuned mutation operation to open the local search zone based on the evaluation of the quality of the solution, while the second focuses on a leading group selection technique to keep a set of dominant solutions. The contribution of each modification to the superiority of the proposed method over CDE is also investigated by implementing CDE with the self-tuned mutation (STMDE), CDE with the leading group selection technique (LGSDE), and CDE with the two modifications. In addition, particle swarm optimization (PSO), the bat algorithm (BA), and the flower pollination algorithm (FPA) methods are also implemented through four study cases for the first problem, and two study cases for the second problem. Through extensive numerical study cases, the effectiveness of the proposed approach is confirmed.

Optimal scheduling of hydrothermal system considering different Environmental Emissions using NSTLBO approach

In this paper, a simple and reliable approach of non-dominated sorting teaching learning based optimization (NSTLBO) algorithm has been prescribed to determine the optimal solution for multi-objective short-term hydrothermal scheduling (STHTS) problem. The problem has been modelled in the form of multi-objective functions which includes fuel cost, transmission loss and environmental emissions such as NOx, SOx and COx With various constraints of hydrothermal systems. Added to that, the effect of valve-point loading process has also been considered. The interaction of the present NSTLBO algorithm is to decrease the cost of the fuel, transmission losses and different kinds of emissions. By applying this algorithm a set of non-dominated solutions are created. A fuzzy decision making approach has been involved on these solution in order to identify the best comprise solution among the group of solutions. The practicability of the proposed approach has been demonstrated on a sample test system which consists of four hydro and six thermal units. The experimental finding of this method has been compared with that of well established techniques in order to validate the performance of the test results. The results confirm that the NSTLBO approach delivers a reliable solution and competitive performance for solving Multi-objective short-term hydrothermal scheduling (MOSTHTS) problem combined with emission constraints.

Solution of Short-Term Hydrothermal Scheduling Problem Using Quasi-Reflected Symbiotic Organisms Search Algorithm Considering Multi-fuel Cost Characteristics of Thermal Generator

Hydrothermal scheduling is an important issue in the field of power system economics. The aim of the short-term hydrothermal scheduling is to optimize the hourly output of power generation for different hydrothermal units for certain intervals of time to minimize the total cost of generations. In this paper, quasi-reflected symbiotic organisms search is implemented for optimal scheduling of hydrothermal problems. In symbiotic organisms search, the word “symbiosis” defines the relationship between two different species. The relationships are mutualism, commensalism and parasitism, depending on which the algorithm works. Further, the quasi-reflected scheme is incorporated into symbiotic organisms search in order to improve the performance of the algorithm. To investigate the performance of quasi-reflected symbiotic organisms search algorithm, the algorithm is tested on three test systems. Along with this, some statistical tests have also been performed. The results obtained by the quasi-reflected symbiotic organisms search algorithm are compared with other recently proposed methods to establish its robustness.

Multi-objective programming of pumped-hydro-thermal scheduling problem using normal boundary intersection and VIKOR

The issue of environmental emissions has forced the power systems to use cleaner energy sources such as renewable and hydroelectric technologies. However, during recent decades due to the limitations on the available water in many regions, the optimal water reservoir usage has been highlighted. In this regard, this paper proposes a multi-objective model for short-term hydrothermal scheduling problem in the presence of the pumped-storage technology. It is noted that the framework well models the cascaded configuration of hydro reservoirs. Besides, in order to more accurately model the mentioned problem, a Mixed-Integer Non-Linear Programming (MINLP) optimization framework is presented. In this respect, the valve-loading effects occurred in thermal power generation technologies have been taken into account which turns the existing convex optimization problem into a non-convex one. In order to solve the mentioned problem, the Normal Boundary Intersection (NBI) method has been used while the VIKOR decision maker is employed to choose the most compromise solution amongst the Pareto optimal solutions obtained by NBI method. Finally, the efficiency of the proposed model has been verified through implementing four case studies and comparing the obtained results with those obtained by different methods.

Application of Dynamic Non-Linear Programming Technique to Non-Convex Short-Term Hydrothermal Scheduling Problem

Short-term hydro-thermal scheduling aims to obtain optimal generation scheduling of hydro and thermal units for a one-day or a one-week scheduling time horizon. The main goal of the problem is to minimize total operational cost considering a series of equality and inequality constraints. The problem is considered as a non-linear and complex problem involving the valve-point loading effect of conventional thermal units, the water transport delay between connected reservoirs, and transmission loss with a set of equality and inequality constraints such as power balance, water dynamic balance, water discharge, initial and end reservoir storage volume, reservoir volume limits and the operation limits of hydro and thermal plants. A solution methodology to the short-term hydro-thermal scheduling problem with continuous and non-smooth/non-convex cost function is introduced in this research applying dynamic non-linear programming. In this study, the proposed approach is applied to two test systems with different characteristics. The simulation results obtained in this paper are compared with those reported in recent research studies, which show the effectiveness of the presented technique in terms of total operational cost. In addition, the obtained results ensure the capability of the proposed optimization procedure for solving short-term hydro-thermal scheduling problem with transmission losses and valve-point effects.

Solution of short-term hydrothermal scheduling using sine cosine algorithm

Hydrothermal scheduling is an important issue in the field of power system economics. The aim of the short-term hydrothermal scheduling is to optimize the hourly output of power generation for different hydrothermal units for certain intervals of time to minimize the total cost of generations. The purpose of this article is to propose a new population-based algorithm named sine cosine algorithm to solve short-term hydrothermal scheduling problem. Hydrothermal scheduling problem is considered as an optimization problem by formulating objective function taking different equality and inequality constraints. Along with valve point loading effect, transmission loss is also considered. Here six different test systems are considered with different cost functions to verify the performance of sine cosine algorithm. The results obtained by sine cosine algorithm are compared with the results obtained by other recently developed techniques, and it was observed that it provides superior results than others in terms of generation cost as well as simulation time. Sine cosine algorithm is still new and has not yet been applied by the researchers in the field of power system. Therefore, the researchers may apply this algorithm in a different power system-related problems.

Improved Cuckoo Search Algorithm for Nonconvex Hydrothermal Scheduling with Volume Constraint

This paper presents an improved cuckoo search algorithm (ICSA) for solving the short-term hydrothermal scheduling (ST-HTS) problem. In the proposed ICSA, the initial eggs are first classified into two groups including top group and abandoned group and each egg in the two groups is then newly generated via Levy flights. The two new egg groups will be integrated into only one group before ranking and evaluating to choose the best egg, which will be used to generate new eggs via the action of discovery of alien eggs in the host bird’s nest. Moreover, the fraction of the alien eggs to be abandoned will be adaptive at each iteration instead of a fixed value during the search process like the conventional Cuckoo Search Algorithm (CSA). The performance of the proposed ICSA has been tested on two different systems and the obtained results have been compared to those from many methods including CSA, modified CSA and other methods in the literature in terms of solution quality. The result comparison has revealed that the proposed ICSA is very efficient for solving the ST-HTS with reservoir storage constraints.DOI: http://dx.doi.org/10.5755/j01.eie.23.3.12657

A New Nested Benders Decomposition Strategy for Parallel Processing Applied to the Hydrothermal Scheduling Problem

Several optimization strategies are suitable for parallel processing, such as mathematical-programming based decomposition strategies, like Lagrangian relaxation and two-stage Benders decomposition, and evolutionary programming-like algorithms. In such cases, most subproblems can be solved independently by different processors. However, parallel processing is not suitable for some problems solved by nested Benders decomposition, due to the hierarchy between subproblems related to different time steps. In particular, for the deterministic case, parallel programming has been restricted to thread processing in lower-level machine computation and optimization solver codes. This paper proposes a new nested Benders decomposition strategy that is suitable for parallel processing, where time-coupled stages are solved simultaneously and an alternative procedure is employed to share initial conditions for the next stages as well as Benders cuts for the previous stages. The methodology is applied to the deterministic short term hydrothermal scheduling problem for the real large-scale Brazilian system, where the advantages of the proposed approach become more evident. In order to show the applicability of the method in low-budget and small parallel environments, the case study was processed with up to 24 process on multi-core computers.

Optimal short-term generation scheduling of hydrothermal systems by implementation of real-coded genetic algorithm based on improved Mühlenbein mutation

The short-term hydrothermal scheduling (STHS) problem is providing a daily planning of hydro and thermal generations, aiming to minimize the total fuel cost of thermal plants. The minimization of total operation cost of hydrothermal power system is considered as a complex nonlinear hard optimization problem with a series of several equality and inequality constraints. This paper proposes real-coded genetic algorithm with an improved Mühlenbein mutation (RCGA-IMM) for the solution of STHS optimization problem, considering the minimization of operation cost which satisfies hydraulic and electrical constraints. The proposed optimization procedure is employed on two test systems in which different constraints have been taken into account including valve point loading effect of thermal units and transmission losses. The provided optimal solutions have been compared with recent studies in this area, which manifest superiority of the proposed method. It is found that the proposed RCGA-IMM has the capability of obtaining better solutions with respect to other optimization methods which are implemented on STHS problem.