Hydrothermal Scheduling Problem Research Articles

Multi-objective Artificial Physical Optimization Algorithm for Daily Economic Environmental Dispatch of Hydrothermal Systems

This article formulates the daily economic/environmental hydrothermal scheduling problem as a multi-objective optimization problem. By introducing non-dominated sorting and crowding distance, the multi-objective artificial physical optimization algorithm is proposed to solve the daily economic/environmental hydrothermal scheduling problem. To enhance the performance of the proposed algorithm, new velocity update equation, which takes advantage of the individual memory and population information, is utilized. To overcome the drawback of premature convergence, a chaotic mutation is adopted in the multi-objective artificial physical optimization algorithm. Especially for handling the equality constraints of daily economic/environmental hydrothermal scheduling, novel heuristic strategies are developed to repair the infeasible solutions. To demonstrate the effectiveness of the multi-objective artificial physical optimization algorithm for solving daily economic/environmental hydrothermal scheduling, the proposed method is implemented on a hydrothermal system and the numerical results are compared with several optimization approaches. It demonstrates that the proposed multi-objective artificial physical optimization algorithm is competent as an alternative for the daily economic/environmental hydrothermal scheduling problem.

Application of non‐dominated sorting gravitational search algorithm with disruption operator for stochastic multiobjective short term hydrothermal scheduling

The hydrothermal scheduling (HTS) is formulated as a stochastic multiobjective short term HTS problem by considering stochastic production cost, NO x emission, SO2 emission and CO2 emission curves for thermal generation plants and uncertainty in load demand. This study presents, a non-dominated sorting gravitational search algorithm integrated with disruption operator (NSGSA-D) to solve this problem. In this approach, a set of Pareto optimal solutions are obtained by adopting the concept of non-dominated sorting. Further, an elite external archive is introduced to keep the Pareto optimal solutions and guide the search process. In addition, a disruption operator is utilised to intensify the search process and also speed up the convergence of the solutions. Furthermore, the most suitable and efficient solution from the non-dominated solution set is obtained with the help of fuzzy decision making policy. The effectiveness of NSGSA-D approach is demonstrated on three sample test systems and simulation results thus obtained are compared with the results reported in literature. The obtained results affirm that the NSGSA-D approach yields good quality solutions and competitive performance for solving stochastic multiobjective short term HTS, while handling the diverse constraints of the problem effectively.

Assessment of risk-averse policies for the long-term hydrothermal scheduling problem

The goal of the long-term hydrothermal scheduling (LTHS) problem is to determine an optimal policy that minimises the expected operational cost over a multi-annual planning horizon. In this problem, inflows are naturally random; thus, the development of policies requires the use of specialised techniques such as stochastic optimization algorithms. Although the optimal policy defined by means of the expected cost is economically efficient, the associated decisions can incur a high risk of energy deficit. To overcome such disadvantages, one alternative is to include a risk-measure approach in the LTHS modeling. In this study, we compared two different risk-measure strategies applied to the LTHS problem: (i) a convex combination between the conditional value at risk (CVaR) and the expected operational cost, (ii) a reservoir risk-curve. To accomplish the comparison, we consider the Brazilian power system with a 5-year planning horizon discretized in monthly stages. The policies supplied by the risk-averse strategies are simulated in a set of synthetic inflow scenarios. Thus, the results are obtained in terms of the expected long-term hydrothermal decisions, such as the total operational cost and the reservoir storage. In summary, the CVaR-based policies provided better operational results than the risk-curve one.

Solving Short-Term Cascaded Hydrothermal Scheduling Problem Using Modified Cuckoo Search Algorithm

This paper presents a modified cuckoo search algorithm (MCSA) for solving shortterm cascaded hydrothermal scheduling (ST-CHTS) problem. The short-term cascaded hydrothermal scheduling is to determine the optimal operation for thermal plants and a cascaded reservoir system while satisfying all constraints including electrical constraints of both hydro and thermal plants and hydraulic constraints of reservoirs. The MCSA has been developed by modifying the search strategy via Levy flights to improve the performance of the conventional cuckoo search algorithm. The proposed method has been widely and successfully applied to many optimization problems in engineering fields; however, this is first time employed to search for the optimal solution of the ST-CHTS problem. The proposed method has been tested on two systems where thermal plants with nonconvex fuel cost function and a cascaded reservoir system are taken into account. The result comparison from the MCSA compared to other methods reported in the literature has revealed that the proposed MCSA is very efficient for solving the ST-CHTS problem.

Meta-Heuristic Algorithms for Solving Hydrothermal System Scheduling Problem Considering Constraints in Transmission Lines

This paper presents the applications of Cuckoo search algorithm (CSA) for solving the problem of optimal power flow for hydrothermal system (OPF-HTS) where IEEE 30-bus test system with both thermal plants and hydropower plants is considered. The problem is first developed in the paper by the combination of optimal power flow (OPF) problem and short-term hydrothermal scheduling (STHTS) problem and it becomes much more complicated than the two sub-problems because it includes all constraints of transmission grid from the comer and all hydraulic constraints from the later in addition to the multi optimal subintervals. In order to validate the performance of the CSA when applied to the problem, another existing meta-heuristic algorithm, Particle swarm optimization has been employed to solve the same problem and compare the obtained results. The analysis on the obtained results has indicated that the CSA is more effective and robust than PSO. Consequently, it can be sated that CSA is a very efficient method for solving the problem.

Stochastic network constrained hydro-thermal scheduling using a linearized progressive hedging algorithm

A method for solving the stochastic network constrained hydro-thermal scheduling problem based on the progressive hedging algorithm (PHA) is presented. The quadratic penalty terms in the PHA are dynamically linearized to retain a linear problem structure. Furthermore, a technique for efficient treatment of linear power flow constraints in scenario-based decomposition methods is proposed and tested. The method is applied to a case study, emphasizing on computational performance. It is demonstrated how the PHA convergence properties can be compared with those of the multi-stage Benders decomposition method by using bounds.

Finite-time recurrent neural networks for solving nonlinear optimization problems and their application

This paper focuses on finite-time recurrent neural networks with continuous but non-smooth activation function solving nonlinearly constrained optimization problems. Firstly, definition of finite-time stability and finite-time convergence criteria are reviewed. Secondly, a finite-time recurrent neural network is proposed to solve the nonlinear optimization problem. It is shown that the proposed recurrent neural network is globally finite-time stable under the condition that the Hessian matrix of the associated Lagrangian function is positive definite. Its output converges to a minimum solution globally and finite-time, which means that the actual minimum solution can be derived in finite-time period. In addition, our recurrent neural network is applied to a hydrothermal scheduling problem. Compared with other methods, a lower consumption scheme can be derived in finite-time interval. At last, numerical simulations demonstrate the superiority and effectiveness of our proposed neural networks by solving nonlinear optimization problems with inequality constraints.

Krill herd algorithm applied to short-term hydrothermal scheduling problem

Abstract In this paper, krill herd algorithm (KHA) technique is employed to solve the short-term hydrothermal scheduling (HTS) problem. In this article, the potentialities of DE are used in KHA technique to improve the convergence speed and robustness. The practical short-term HTS problem is solved here using KHA technique in which the crossover and mutation operation of differential evolution algorithm (DEA) is employed to efficiently control the local and global search, so that premature convergence may be avoided and global solutions can be achieved. The quality and usefulness of the proposed algorithm is demonstrated through its application to two standard test systems. The simulation results reveal that the current proposal is better in comparison with the other existing techniques in terms of computational time and the quality of the solutions obtained.

Cost/environmentally compromised dispatch for cascaded hydrothermal system using artificial bee colony algorithm

This paper evaluates the robustness of the artificial bee colony (ABC) algorithm while allocating optimal power generation in a hydrothermal power system at the level of minimum fuel cost and minimum pollutant emission impacts on the environment subjected to physical and technical constraints. The hydrothermal scheduling (HTS) is devised in a bi‐objective framework so as to optimize both objectives of fuel cost and emission release, individually and simultaneously subjected to a verity of intricate equality and inequality constraints. Initially, all feasible solutions are obtained through random search, and then the ABC algorithm is used for the exploration and exploitation processes together in the search space, thereby discovering the optimal hourly schedule of power generation in the hydrothermal system. Meanwhile, a dependent hydro‐discharge computation handles the equality constraints; especially, the reservoir end volume and slack thermal generating unit for each sub‐interval handle the power balance equality constraint. The performance of the proposed approach is illustrated on a multi‐chain interconnected hydrothermal power system with due consideration of the water transport delay between connected reservoirs and transmission loss of system load. The results obtained from the proposed technique are compared with those of other techniques. The results demonstrate that the ABC algorithm is feasible and efficient for solving the HTS problem. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Hybridized Gravitational Search Algorithm for Short-Term Hydrothermal Scheduling

ABSTRACTThis paper presents a new approach for solving the short-term hydrothermal scheduling (STHTS) problem using a disruption operator in an oppositional gravitational search algorithm. The nonlinear and non-convex nature of the STHTS problem coupled with the cascading nature of reservoirs, water transport delays and scheduling time linkages makes the solution of this optimization problem quite difficult using the conventional optimization methods. Here, an opposition-based learning concept is introduced in a gravitational search algorithm to improve the quality of the current population towards global optimal solutions and a disruption operator is integrated to accelerate the convergence of solutions. This method is evaluated on two test systems consisting of four hydro and an equivalent thermal plant and four hydro and three thermal plants. The detailed statistical results prove that the proposed approach performs better in terms of production cost and smooth convergence characteristics when compared with other recently reported methods in the literature.

Enhanced Particle Swarm Optimization for Short-Term Non-Convex Economic Scheduling of Hydrothermal Energy Systems

This paper presents an Enhanced Particle Swarm Optimization (EPSO) to solve short-term hydrothermal scheduling (STHS) problem with non-convex fuel cost function and a variety of operational constraints related to hydro and thermal units. The operators of the conventional PSO are dynamically controlled using exponential functions for better exploration and exploitation of the search space. The overall methodology efficiently regulates the velocity of particles during their flight and results in substantial improvement in the conventional PSO. The effectiveness of the proposed method has been tested for STHS of two standard test generating systems while considering several operational constraints like system power balance constraints, power generation limit constraints, reservoir storage volume limit constraints, water discharge rate limit constraints, water dynamic balance constraints, initial and end reservoir storage volume limit constraints, valve-point loading effect, etc. The application results show that the proposed EPSO method is capable to solve the hard combinatorial constraint optimization problems very efficiently.

Solving Short Term Multi Chain Hydrothermal Scheduling Problem by Artificial Bee Colony Algorithm

This paper presents an artificial bee colony algorithm for solving optimal short term hydrothermal scheduling problem. To demonstrate the effectiveness of the proposed algorithm, hydrothermal test system consists of three thermal units and four cascaded hydro power plants has been tested. The valve point loading effect is taken into consideration. In order to show the feasibility and robustness of the proposed algorithm, a wide range of thermal and hydraulic constraints are taken into consideration. The numerical results obtained by ABC algorithm are compared with those obtained from other methods such as genetic algorithm (GA), simulated annealing (SA), evolutionary programming (EP) and constriction factor based particle swarm optimization (CFPSO) technique to reveal the validity and verify the feasibility of the proposed method. The experimental results indicate that the proposed algorithm can obtain better schedule results with minimum execution time when compared to other methods.

Comment on ‘Reliability constrained unit commitment with combined hydro and thermal generation embedded using self-learning group search optimizer’ by J.H. Zheng, J.J. Chen, Q.H. Wu, and Z.X. Jing [Energy 81 (2015) 245–254

This paper deals with the inaccuracy in results of the “Reliability constrained unit commitment with combined hydro and thermal generation embedded using self-learning group search optimizer proposed presented Energy 81 (2015) 245–254”. The hydrothermal scheduling problem is defined as a non-convex optimization problem, which is necessary to meet several equality and inequality constraints such as power balance and technical limitations of cascaded and thermal hydro units. The driven solutions in the original paper do not satisfy the constraint on the final storage volume of the hydro units' reservoir one at the last hour. Therefor, this paper demonstrates this inaccuracy situated in the original paper.

An oppositional learning based gravitational search algorithm for short term hydrothermal scheduling

This paper presents an oppositional based gravitational search algorithm (OGSA) for solving the short term hydrothermal scheduling (STHTS) problem. The STHTS problem involves the optimization of nonlinear constrained objective function by taking into consideration of multireservoir cascaded nature hydro plants, water transportation delay between cascaded reservoirs and scheduled time linkages, variable system active load balance, water discharge and reservoir storage limits, initial and final reservoir storage limits, reservoir flow balance and operating limits of hydro and thermal plants. A stochastic search algorithm known as gravitational search algorithm (GSA) inspired from the law of gravity and mass interactions is used to solve this complex constrained STHTS problem. In order to improve the convergence rate of GSA, the opposite numbers are utilized in the evolution process of GSA. Finally, the proposed oppositional gravitational search algorithm (OGSA) approach is evaluated on two test systems, one consisting of four hydro plants and an equivalent thermal plant and the other one with nine cascaded hydro and three thermal plants. The results obtained with the proposed approach give better solution in terms of less production cost, execution time and better convergence characteristics while comparing with the results of other methods reported in the literature.

Investigation on the effectiveness of ABC algorithm for hydrothermal energy management considering emission aspects

Purpose– The purpose of the paper is to solve hydrothermal scheduling (HTS) problem for energy-efficient management by allocating the optimal real power outputs for thermal and hydroelectric generators.Design/methodology/approach– HTS can be formulated as a complex and non-linear optimization problem which minimizes the total fuel cost and emissions of thermal generators subject to various physical and operational constraints. As the artificial bee colony algorithm has proven its ability to solve various engineering optimization problems, it has been used as a main optimization tool to solve the fixed-head HTS problem.Findings– A meta-heuristic search technique-based algorithm has been implemented for hydrothermal energy management, and the simulation results show that this approach can provide trade-off between conflict objectives and keep a rapid convergence speed.Originality/value– The proposed methodology is implemented on the standard test system, and the numerical results comparison indicates a considerable saving in total fuel cost and reduction in emission.

Disruption based gravitational search algorithm for short term hydrothermal scheduling

This paper proposes a disruption based gravitational search algorithm (DGSA) to find the optimum solution for short term hydrothermal scheduling (STHTS) problem, which considers the cascading nature of hydro plants, water transportation time delays between reservoirs, variable hourly water discharge limits, reservoir storage volume limits, hydraulic continuity constraint, initial and final reservoir storage volume limits, power system load balance, generation limits of hydro and thermal units and valve point loading effects of thermal plants. In the proposed approach, a disruption operator based on astrophysics has been integrated into gravitational search algorithm (GSA) to enhance its performance. It is found that the disruption operator increases both of the exploration and exploitation abilities in comparison with the conventional GSA. Moreover, an effective strategy is utilized to handle the end storage volume constraints and system load balance constraints. Finally, the proposed approach is evaluated on two hydrothermal test systems, one consisting of four hydro plants and an equivalent thermal plant and another with four hydro and three thermal plants. The comparative result analysis shows that the DGSA approach has better solution results and convergence accuracy than the GSA and other approaches reported in literature for solving STHTS problem.

An improved chaotic hybrid differential evolution for the short-term hydrothermal scheduling problem considering practical constraints

Short-term hydrothermal scheduling (STHTS) is a non-linear and complex optimization problem with a set of operational hydraulic and thermal constraints. Earlier, this problem has been addressed by several classical techniques; however, due to limitations such as non-linearity and non-convexity in cost curves, artificial intelligence tools based techniques are being used to solve the STHTS problem. In this paper an improved chaotic hybrid differential evolution (ICHDE) algorithm is proposed to find an optimal solution to this problem taking into account practical constraints. A self-adjusted parameter setting is obtained in differential evolution (DE) with the application of chaos theory, and a chaotic hybridized local search mechanism is embedded in DE to effectively prevent it from premature convergence. Furthermore, heuristic constraint handling techniques without any penalty factor setting are adopted to handle the complex hydraulic and thermal constraints. The superiority and effectiveness of the developed methodology are evaluated by its application in two illustrated hydrothermal test systems taken from the literature. The transmission line losses, prohibited discharge zones of hydel plants, and ramp rate limits of thermal plants are also taken into account. The simulation results reveal that the proposed technique is competent to produce an encouraging solution as compared with other recently established evolutionary approaches.

Combining sampling-based and scenario-based nested Benders decomposition methods: application to stochastic dual dynamic programming

Nested Benders decomposition is a widely used and accepted solution methodology for multi-stage stochastic linear programming problems. Motivated by large-scale applications in the context of hydro-thermal scheduling, in 1991, Pereira and Pinto introduced a sampling-based variant of the Benders decomposition method, known as stochastic dual dynamic programming (SDDP). In this paper, we embed the SDDP algorithm into the scenario tree framework, essentially combining the nested Benders decomposition method on trees with the sampling procedure of SDDP. This allows for the incorporation of different types of uncertainties in multi-stage stochastic optimization while still maintaining an efficient solution algorithm. We provide an illustration of the applicability of our method towards a least-cost hydro-thermal scheduling problem by examining an illustrative example combining both fuel cost with inflow uncertainty and by studying the Panama power system incorporating both electricity demand and inflow uncertainties.

Quasi-oppositional gravitational search algorithm applied to short term hydrothermal scheduling problems

This paper describes a successful adaptation of the gravitational search algorithm (GSA) and quasi-oppositional GSA (QOGSA) to solve short term hydrothermal scheduling (HTS) problem in power systems. Quasi-oppositional-based learning approach is integrated with GSA to efficiently control the local and global search, such that premature convergence is avoided and global solutions are achieved. Two test systems having non-convex solution spaces are used to validate the proposed QOGSA algorithm. The results obtained through QOGSA, GSA and those of the previous approaches are compared. The outcome of the comparisons reveals the effectiveness of the proposed QOGSA method in terms of solution quality, and computational speed.

Multiobjective CVaR Optimization Model and Solving Method for Hydrothermal System Considering Uncertain Load Demand

In order to solve the influence of load uncertainty on hydrothermal power system operation and achieve the optimal objectives of system power generation consumption, pollutant emissions, and first-stage hydropower station storage capacity, this paper introduced CVaR method and built a multiobjective optimization model and its solving method. In the optimization model, load demand’s actual values and deviation values are regarded as random variables, scheduling objective is redefined to meet confidence level requirement and system operation constraints and loss function constraints are taken into consideration. To solve the proposed model, this paper linearized nonlinear constraints, applied fuzzy satisfaction, fuzzy entropy, and weighted multiobjective function theories to build a fuzzy entropy multiobjective CVaR model. The model is a mixed integer linear programming problem. Then, six thermal power plants and three cascade hydropower stations are taken as the hydrothermal system for numerical simulation. The results verified that multiobjective CVaR method is applicable to solve hydrothermal scheduling problems. It can better reflect risk level of the scheduling result. The fuzzy entropy satisfaction degree solving algorithm can simplify solving difficulty and get the optimum operation scheduling scheme.