Short-term Hydrothermal Scheduling Research Articles

A short-term wind-hydrothermal operational framework in the presence of pumped-hydro storage

Short-term operation is one of the most significant aspects of power systems operation and planning and it mainly includes resource scheduling including renewable and non-renewable energy sources. The mentioned problem is modeled as an optimization problem with one or more objectives depending upon the priorities of the decision maker (system operator) and several equality and inequality constraints. In this respect, this paper proposes a short-term operational model for the hydrothermal power systems in the presence of wind power generation and pumped-hydro storage (PHS) units. The problem is formulated as a single-objective optimization problem that aims to minimize the total operating cost including the fuel cost of thermal units. The problem has been comprehensively investigated through five case studies where the first case study is used for the sake of validation. Then, the other case studies assessed the impacts of wind power generation, PHS unit, and uncertainty on the problem. The five case studies are as follows: Case 1: Short-term hydrothermal (STH) scheduling which aims to minimize the total cost. Case 2: Deterministic short-term hydrothermal-wind (STHTW) scheduling which aims to minimize the total cost. Case 3: Stochastic wind-hydro-thermal scheduling that seeks to minimize the total cost taking into consideration the uncertainty of the wind power generation. Case 4: Deterministic wind-hydro-thermal scheduling in the presence of the PHS unit with the total cost minimization as the objective function. Case 5: Stochastic wind-hydro-thermal scheduling in the presence of the PHS unit that is used to evaluate the impact of uncertainty of wind power generation with the total cost minimization as the objective function. It is noteworthy that the first three case studies have been formulated using a non-linear programming (NLP) model and solved using the CONOPT solver in GAMS. Case studies 4 and 5 have been presented using a mixed-integer non-linear programming (MINLP) model and solved using the DICOPT solver in GAMS. A sensitivity analysis has also been carried out to assess the system's performance with different loading conditions. In this respect, the total cost and PHS operation with different amounts of load demand were evaluated and the results have been presented and discussed.

A modified adaptive beluga whale optimization based on spiral search and elitist strategy for short-term hydrothermal scheduling

Short-term hydrothermal scheduling is a complex dynamic nonlinear optimization problem which considers various hydropower constraints. In this study, an adaptive beluga whale optimization method based on a spiral search and elitist strategy is proposed to solve this complex problem. The proposed method has three main advantages: First, an adaptive parameter strategy based on a cosine function achieves a better balance between exploration and exploitation. Second, the spiral search and elite strategy guides search agents to search for focused areas and effectively narrows the scope of the invalid search space. Third, instead of the penalty function method, a feasibility-based selection comparison technique and heuristic strategy are adopted to address complex constraints in STHS. In comparison to the results of benchmark functions from CEC 2015, ASEBWO generally demonstrates superior convergence accuracy when compared to the other seven algorithms. Additionally, the feasibility and effectiveness of ASEBWO are verified using two hydrothermal scheduling systems and compared with those of more than 10 algorithms. The comparison results demonstrate that ASEBWO achieves the best solution quality.

Generation cost optimisation of hydrothermal system using arithmetic optimisation algorithm considering transmission loss and valve point loading effect

Hydrothermal scheduling is a crucial issue in the field of power system economics. The goal of short-term hydrothermal scheduling is to reduce the total cost of generation by optimising the hourly output of power generation for specific time intervals. This paper presents a new population-based approach called the arithmetic optimisation algorithm for solving the short-term hydrothermal scheduling problem. To verify the performance of the arithmetic optimisation approach, six different test systems with different cost functions were investigated. It has been observed that the proposed AOA reduced the generation cost by 3.41%. Furthermore, upon considering non-linearity in the fitness function by involving the valve-point effect, AOA diminished the generation cost by 8.54%. An appreciable 25.08% reduction in the algorithm execution time was also observed when the proposed AOA was used as the optimisation tool. Numerical results and non-parametric statistical analysis claim the superiority of the proposed approach.

Optimal scheduling of short-term hydrothermal with integration of renewable energy resources using Lévy spiral flight artificial hummingbird algorithm

Short-term hydrothermal scheduling (STHS) is taking an important consideration in the power system for economics operation. The solution to the STHS problem gives time-varying scheduling of power generation with available hydro and thermal units aims to attain the cost saving of thermal units for a given time period. It is a non-convex optimization problem with a set of inequality and equality constrains such as load balancing, transmission losses as well as valve-point effect to the thermal power units. The permeation of renewable energy is frequently used into the power networks aims to reduce the cost of generation and emissions. The two foremost resources such as wind and photo-voltaic are frequently used in the power networks. In the research, the use of both powers integrated into the STHS problem to reduce the fuel cost ($) by using the modified artificial hummingbird algorithm (MAHA). To modelled the uncertainty in solar irradiance and windspeed, the lognormal and Weibull distribution are used. The novel MAHA is based on two enhancing methods; (1). updating the positions of the hummingbirds in stochastic motion via Lévy flight walk and (2). updating the location of the hummingbirds via pitch adjustment motion. The MAHA is further tested on the four STHS cases such as; four hydro one thermal (non-vple and vple), four hydro three thermal (vple without and with losses), four hydro three thermal with integration of RERs including direct cost only (VPLE without and with losses) and four hydro three thermal with uncertainty of RERs including direct, reverse and penalty costs (vple without losses), respectively. Moreover, for validation the performance of MAHA is further compared to the outcomes of AHA and other state-of-the-arts techniques.

Application of henry gas solubility optimization algorithm for short-term hydrothermal scheduling considering variable water transportation delay and penstock head loss

This paper deals with the solution of short-term hydrothermal scheduling considering some practical scenario of hydro system like variable water time delay and penstock head loss along with other constraints related to hydro and thermal plant. The problem has been solved using Henry gas solubility optimization algorithm. This algorithm is basically works based on the principle of Henry's law. A test system consists of seven hydro units and eight thermal units have been adopted for study purpose. This test system is mainly inspired from Damodar valley corporation, India. The problem has been solved in MATLAB platform. The simulation results have been compared with symbiotic organism search algorithm, ion motion optimization algorithm, crow search algorithm and sine cosine algorithm. The results suggest that the proposed algorithm outperforms other algorithms in terms of quality solution and computation efficiency.

Non-Dominated Sorting-Based Hybrid Optimization Technique for Multi-Objective Hydrothermal Scheduling

Short-term hydrothermal scheduling problem plays an important role in maintaining a high degree of economy and reliability in power system operational planning. Since electric power generation from fossil fired plants forms a major part of hydrothermal generation mix, therefore their emission contributions cannot be neglected. Hence, multi-objective short term hydrothermal scheduling is formulated as a bi-objective optimization problem by considering (a) minimizing economical power generation cost, (b) minimizing environmental emission pollution, and (c) simultaneously minimizing both the conflicting objective functions. This paper presents a non-dominated sorting disruption-based oppositional gravitational search algorithm (NSDOGSA) to solve multi-objective short-term hydrothermal scheduling (MSHTS) problems and reveals that (i) the short-term hydrothermal scheduling problem is extended to a multi-objective short-term hydrothermal scheduling problem by considering economical production cost (EPC) and environmental pollution (EEP) simultaneously while satisfying various diverse constraints; (ii) by introducing the concept of non-dominated sorting (NS) in gravitational search algorithm (GSA), it can optimize two considered objectives such as EPC and EEP simultaneously and can also obtain a group of conflicting solutions in one trial simulation; (iii) in NSDOGSA, the objective function in terms fitness for mass calculation has been represented by its rank instead of its EPC & EEP values by using the NS approach; (iv) an elite external archive set is defined to keep the NS solutions with the idea of spread indicator; (v) the optimal schedule value is extracted by using fuzzy decision approach; (vi) a consistent handling strategy has been adopted to handle effectively the system constraints; (vii) finally, the NSDOGSA approach is verified on two test systems with valve point loading effects and transmission loss, and (viii) computational discussion show that the NSDOGSA gives improved optimal results in comparison to other existing methods, which qualifies that the NSDOGSA is an effective and competitive optimization approach for solving complex MSHTS problems.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

A New Fast Deterministic Economic Dispatch Method and Statistical Performance Evaluation for the Cascaded Short-Term Hydrothermal Scheduling Problem

The Cascaded Short-Term Hydrothermal Scheduling (CSTHTS) problem is a highly non-linear, multi-modal, non-convex, and NP-hard optimization problem that has been solved by conventional and metaheuristic algorithms in the past. As the CSTHTS problem falls under the category of applied operational research, therefore, the work is still on-going to find new algorithms and variants of the existing algorithms that would better approximate the optimal global solution in a shorter computational time. This article proposes a novel deterministic thermal economic dispatch method embedded with the improved Accelerated Particle Swarm Optimization (APSO) algorithm to infinitesimally reduce the Big O time complexity for the standard benchmark test case of the CSTHTS optimization problem. Then, it discusses and presents the importance of performing standard statistical tests to establish the supremacy of one metaheuristic algorithm over the other one in solving the CSTHTS problem. The results obtained are better than the results of the many state-of-the-art algorithms applied to solve the considered test case of the CSTHTS problem in the literature, and the superiority of the improved APSO algorithm has been established statistically using the parametric independent samples t-test and the non-parametric Mann–Whitney U-test over the other metaheuristic algorithms such as particle swarm optimization in solving the chosen test case of the CSTHTS problem.

Salp swarm algorithm to solve Short-Term hydrothermal scheduling problem

Abstract Hydrothermal scheduling possibility is regarding the possible performance of the power system was suggested in this article. Hydrothermal power production largely relies on constraints, which are unpredictable in reality. To catch the difficulty associated with hydrothermal power to get optimize power production and then to manage the optimization section, a recently improved optimization technique named Salp Swarm Algorithm has been employed. It essentially operates on the style of Salps. A procedure has been tested for supporting the capacity for solving challenges and for checking the outcome of the hydrothermal power system. To approach the problem very practical the valve-point charging outcome has been regarded also.

Introducing Adaptive Machine Learning Technique for Solving Short-Term Hydrothermal Scheduling with Prohibited Discharge Zones

The short-term hydrothermal scheduling (STHTS) problem has paramount importance in an interconnected power system. Owing to an operational research problem, it has been a basic concern of power companies to minimize fuel costs. To solve STHTS, a cascaded topology of four hydel generators with one equivalent thermal generator is considered. The problem is complex and non-linear and has equality and inequality constraints, including water discharge rate constraint, power generation constraint of hydel and thermal power generators, power balance constraint, reservoir storage constraint, initial and end volume constraint of water reservoirs, and hydraulic continuity constraint. The time delays in the transport of water from one reservoir to the other are also considered. A supervised machine learning (ML) model is developed that takes the solution of the STHTS problem without PDZ, by any metaheuristic technique, as input and outputs an optimized solution to STHTS with PDZ and valve point loading (VPL) effect. The results are quite promising and better compared to the literature. The versatility and effectiveness of the proposed approach are tested by applying it to the previous works and comparing the cost of power generation given by this model with those in the literature. A comparison of results and the monetary savings that could be achieved by using this approach instead of using only metaheuristic algorithms for PDZ and VPL are also given. The slipups in the VPL case in the literature are also addressed.

Quasi-oppositional turbulent water flow-based optimization for cascaded short term hydrothermal scheduling with valve-point effects and multiple fuels

In an interconnected power system, short-term hydrothermal scheduling (SHTS) portrays a paramount important task in the economic operation of electric power system. SHTS is discerned as a formidable non-convex constrained optimization problem considering the cascade nature of hydro plants, and valve-point loading (VPL) and multi-fuel sources of thermal plants. In the present study, a novel metaheuristic approach, a quasi-oppositional turbulent water flow-based optimization (QOTWFO) is proposed to solve the SHTS problem. Turbulent water flow-based optimization (TWFO) is evolved by the whirlpool prodigy formed in a turbulent flow of water. QOTWFO is an amended version of TWFO, where the quasi-opposition-based learning is pioneered for population initialization and iteration vaulting. It generates a quasi-oppositional solution which has the highest probability to elicit the global optimum solution than a randomly generated solution. Thus, the global searching ability and computational efficiency of the algorithm is enhanced. A new heuristic constraints handling mechanism is proposed to fulfil the equality constraints notably active power balance and dynamic water flow balance. The cogency of proposed QOTWFO is examined on standard benchmark functions, and multi-reservoir cascaded hydrothermal test systems with the cogitation of VPL effects and multi-fuel sources of thermal plants. Besides, Newton Raphson load flow approach is employed to determine power losses and line flows in a 16-bus, and 35 transmission lines hydrothermal power system. To model a realistic power system model, the maximum power transfer capability of each transmission line is taken into account. Simulation outcomes substantiate that, compared with state-of-the-art heuristic techniques, QOTWFO offers better feasible solutions as well as guarantees the robustness of the algorithm.

Scenario-Based Fuel Constrained Short-Term Hydrothermal Scheduling

For electric power companies, the economic utilization of existing fossil fuel is currently primary issue because of the diminishing supply of fossil fuel. Thermal power plants have fuel limitations and contractual restrictions that must be adhered to. Therefore this work presented the scenario-based fuel constrained short-term hydrothermal scheduling problem with the incorporation of renewable energy sources. The elephant clan optimization (ECO) approach is offered for short-term hydro-thermal scheduling (STHTS) with thermal generators, cascaded hydro, solar PV plants, wind-turbine-generators (WTG), and pumped-storage-hydro (PSH) with and without demand side management (DSM) for various scenarios. On a typical test system, the suggested approach is shown to be successful. Analysis of the typical test system’s numerical results is compared to those produced via the HPSO-TVAC and grey wolf algorithms (GWO). The comparison shows that the suggested ECO is capable of providing a better solution.

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.

Backtracking search optimization applied to solve short-term electrical real power generation of hydrothermal plant

This article aims to determine the feasible optimal solution for the short-term hydrothermal scheduling (STHS) problem using the efficient backtracking search optimization technique. The problem formulation for hydrothermal systems is highly complex owing to its nonlinear nature. Hydrothermal scheduling is considered with two decision variables simultaneously: thermal states and water discharge. These two variables are instrumental in determining the optimal hourly schedule of power generation in hydrothermal power plants. The optimum solution is obtained using the backtracking search algorithm (BSA) with two primary operations, namely, mutation and crossover. The BSA is an optimization technique free from high-sensitivity control parameters, because it has only one control parameter for finding the optimal solution. It also has powerful exploration and exploitation capabilities. The simulation results corroborate that BSA is highly efficient compared to existing optimization techniques (e.g. oppositional real coded chemical reaction-based optimization, differential evolution) in terms of overall efficiency and the quality of the solutions.

Short-Term Hydrothermal Scheduling using Imperialist Competitive Algorithm

In this study, the Imperialist Competitive Algorithm (ICA) is proposed to solve a multi-chain Short-Term Hydrothermal Scheduling problem (STHTS). It aims to minimize the generation cost of the thermal plants while satisfying the thermal and hydro plants constraints. In order to evaluate the effectiveness of the ICA, it has been tested on a system having a hydro plant with four-cascaded reservoir and a thermal plant. The results are compared with that obtained by other techniques. The ICA has the good convergence and the better results.

Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling

Short-term hydrothermal scheduling (STHS) can improve water use efficiency, reduce carbon emissions, and increase economic benefits by optimizing the commitment and dispatch of hydro and thermal generating units together. However, limited by the large system scale and complex hydraulic and electrical constraints, STHS poses great challenges in modeling for operators. This paper presents an improved proximal bundle method (IPBM) within the framework of Lagrangian relaxation for STHS, which incorporates the expert system (ES) technique into the proximal bundle method (PBM). In IPBM, initial values of Lagrange multipliers are firstly determined using the linear combination of optimal solutions in the ES. Then, each time PBM declares a null step in the iterations, the solution space is inferred from the ES, and an orthogonal design is performed in the solution space to derive new updates of the Lagrange multipliers. A case study in a large-scale hydrothermal system in China is implemented to demonstrate the effectiveness of the proposed method. Results in different cases indicate that IPBM is superior to standard PBM in global search ability and computational efficiency, providing an alternative for STHS.

A Rigid Cuckoo Search Algorithm for Solving Short-Term Hydrothermal Scheduling Problem

The key criteria of the short-term hydrothermal scheduling (StHS) problem is to minimize the gross fuel cost for electricity production by scheduling the hydrothermal power generators considering the constraints related to power balance; the gross release of water, and storage limitations of the reservoir, and the operating limitations of the thermal generators and hydropower plants. For addressing the same problem, numerous algorithms were being used, and related studies exist in the literature; however, they possess limitations concerning the solution state and the number of iterations it takes to reach the solution state. Hence, this article proposes using an enhanced cuckoo search algorithm (CSA) called the rigid cuckoo search algorithm (RCSA), a modified version of the traditional CSA for solving the StHS problem. The proposed RCSA improves the solution state and decreases the iteration numbers related to the CSA with a modified Lévy flight. Here, the movement distances are divided into multiple possible steps, which has infinite diversity. The effectiveness of RCSA has been validated by considering the hydrothermal power system. The observed results reveal the superior performance of RCSA among all other compared algorithms that recently have been used for the StHS problem. It is also observed that the RCSA approach has achieved minimum gross costs than other techniques. Thus, the proposed RCSA proves to be a highly effective and convenient approach for addressing the StHS problems

A grasshopper optimization algorithm for optimal short-term hydrothermal scheduling

The optimal generation for short-term hydrothermal scheduling (OGStHS) with the deliberation of various purposes is a complex non-linear constrained optimization problem. There exist numerous constraints, which make the OGStHS optimization problem more complicated. The considered constraints for this problem are mostly related to energy performance, operational conditions, water, and power infrastructure. All these constraints would generally influence the cost of fuel. In this study, a multi-objective optimization form of OGStHS is suggested to estimate the minimum cost of fuel, which mainly influences industrial operation. The water transfer delays among multi-related reservoirs and the thermal plants’ valve-point influences are considered for the accurate formulation of the OGStHS problem. Meantime, a grasshopper optimization algorithm (GOA) is performed to handle the OGStHS problem by getting optimized for both objectives concurrently. A modern approach is shown in this study to get a solution to the OGStHS problem. Furthermore, to deal with the complex restraints efficiently, modern heuristic restriction treatment processes with no drawback impact frames have been offered in this study. Two hydrothermal power systems have illustrated the suggested GOA technique’s utility and performance. Compared with other available approaches, the analytical results are admitted that GOA can provide a better understanding by decreasing fuel cost and emission concurrently.

Conventional and Metaheuristic Optimization Algorithms for Solving Short Term Hydrothermal Scheduling Problem: A Review

Short term hydrothermal scheduling (STHTS) is a non-linear, multi-modal and very complex constrained optimization problem which has been solved using several conventional and modern metaheuristic optimization algorithms. A number of research articles have been published addressing STHTS using different techniques. This article presents a comprehensive review of research published for solving the STHTS problem in the last four decades.

Short-Term Hydrothermal Scheduling With Solar and Wind Farms Using Second-Order Cone Optimization With Chance-Box Constraints

Short-Term Hydrothermal Scheduling (STHS) is a classic problem in power system operation where the aim is to decide the dispatch of both thermal and hydroelectric units. This problem is complex due to its non-linear non-convex nature, and the requirements for fast solving for daily operation. Technologies such as wind and solar generation introduce stochastic behaviors, which have to be considered within the mathematical model. Although the problem is frequently solved by traditional and heuristic techniques, this paper proposes a new formulation based on convex approximations, and in particular, Second-Order Cone optimization, which addresses the nonlinear relation among water discharge, reservoir volume, and hydropower generation in a rigorous mathematical approach. Moreover, the impact of wind and solar generation on the power system is analyzed, modeling their stochastic behavior in a robust way by using chance-box constraints. Numerical results demonstrate that the Second-Order Cone approximation is precise and faster than techniques proposed recently and that the chance-box constraint approach guarantees a robust solution.