Hydrothermal Scheduling Research Articles

A Fresh Manner Cuckoo Search Algorithm to Hydrothermal Scheduling in Short Term

The main goal of the short-term hydrothermal scheduling (HS) challenge is to drastically reduce the large fuel cost of producing power by scheduling the hydrothermal energy producers while taking power balance restrictions, the reservoir's storage restrictions, the water's gross discharge, and the thermal power generators' and hydropower plants' operating restrictions into account. Many algorithms have been employed to solve this similar problem, and relevant research have been published in the literature; nevertheless, their scope is limited in terms of the number of 16 iterations required to achieve the solution state and the solution state itself. In order to solve the HS problem, this article suggests applying an improved cuckoo search (CS) algorithm known as the fresh manner cuckoo search (FMCS) algorithm, a modified variant of the conventional CS. The suggested FMCS

Approximating hydropower systems by feasibility spaces in stochastic dual dynamic programming

This work investigates and improves methodology for approximating hydropower systems by feasibility spaces, which can be embedded in the stochastic dual dynamic programming algorithm and applied in the context long-term hydrothermal scheduling. The feasibility spaces are derived from optimization of the detailed hydropower system and are expressed in few dimensions to facilitate efficient computations. Test results from a case study for the Norwegian power system demonstrate how feasibility spaces serve to realistically constrain the hydropower system.

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.

Hydrothermal–pumped-storage scheduling considering renewable energy uncertainty by improved cheetah optimization

The growth of renewable wind and solar energy in modern power systems affects the short-term scheduling of hydrothermal power generation. This article presents the optimum day-ahead scheduling of wind–solar–hydrothermal systems with pumped-storage plants (PSPs). To assess the contribution of PSPs in decreasing the generation costs of a renewable integrated power system, a scheduling model is formulated that considers different security constraints. An improved cheetah optimizer (ICO) is implemented on a renewable integrated test power system to solve the short-term optimum wind–solar–pumped-storage plant–hydrothermal scheduling (OWSPHTS) problem, taking into account all thermal, hydraulic and network constraints. Optimum solutions are obtained with different objectives considering renewable uncertainties. The proposed ICO solution method is compared with the similar algorithms in terms of optimal fuel costs, emissions, convergence success rate and computation time. The comparative solutions show that the introduced optimization technique is efficient for solving the real-world OWSPHTS problem.

Chaotic‐quasi‐opposition based whale optimization technique applied to multi‐objective complementary scheduling of grid connected hydro‐thermal–wind–solar‐electric vehicle system

AbstractThe sources of fossil fuel are impoverishing in upcoming future. In the current research scenario, sincere effort has been taken worldwide to explore the use of renewable energy sources in electrical power system for the economic benefits and environmental consciousness. The main contribution of the proposed work is first, to find optimal hydro‐thermal scheduling (HTS) with wind, solar, and electric vehicles (EVs) for variable load. The target is to find out maximum utilization of renewable energy sources for economic power generation with less emission. Thus, a new approach of EV to grid has been adopted with wind–solar based HTS system for improving grid reliability and resilience. Second, there is a requirement to overcome the local optima problems with less convergence speed. This is obtained by employing a relatively new methodology, known as chaotic‐quasi‐opposition‐based whale optimization algorithm (WOA) (CQOWOA). The proposed algorithm is tested on HTS and wind–solar‐electric vehicle‐based HTS (HTWSVS) for three different cases. Different nonlinearities like valve point effect of thermal units, transmission losses, spillage rate of hydro reservoir units and uncertainties of wind, solar as well as EV are considered to judge the effectiveness of the proposed CQOWOA technique on realistic problems. The presence of wind, solar, and EV energy sources with HTS is evident from the test results of CQOWOA, for multi‐objective problem where cost and emission both are reduced significantly. The robustness of the proposed solution has been verified by implementing the statistical analysis on two systems with least variation of mean and optimal values of cost with the tolerance of less than 0.025%. The comparative analysis of CQOWOA with the other optimization techniques validates its superiority on both the test systems by minimizing the generation cost and emission.

Hydro-thermal scheduling under RE uncertainties using an improved cheetah optimization

Hydro-thermal scheduling under RE uncertainties using an improved cheetah optimization

Improving operating policies in stochastic optimization: An application to the medium-term hydrothermal scheduling problem

In decision-making under uncertainty, a robust representation of uncertainty is vital for optimal operational and strategic solutions. We extend existing methods by utilizing Fourier decomposition to create multivariate synthetic time series, capturing stochastic seasonal patterns while preserving correlations. These synthetic time series are transformed into a recombining scenario tree via K-means clustering. To enhance the resulting policy in the Stochastic Dual Dynamic Programming (SDDP) framework, we propose an additional sampling within scenario-tree nodes to consider a better representation of the cost-to-go function. A convergence proof for this sampling technique is provided. Moreover, two new stopping criteria are introduced for better solution accuracy and robustness. The first criterion extends traditional stopping rules to all scenario-tree nodes. The second criterion enforces a minimum count of Benders cuts per node, promoting accurate and robust solutions. Our approach is evaluated on the Spanish hydrothermal system, incorporating synthetic time series with seasonal-trend uncertainty in optimization and simulation. Policies from traditional SDDP and our technique were tested over a thousand realizations, demonstrating that our proposals yield reservoir operation policies closer to the thresholds set by the operator compared to traditional SDDP. Computational efficiency is maintained. The proposed sampling mitigates the impact of discretizing stochastic variables into scenario trees by evaluating more scenarios per node. Our framework offers robust policies under uncertainty through stochastic seasonal patterns by Fourier analysis, novel SDDP sampling, and additional stopping criteria.

Medium-term stochastic hydrothermal scheduling with short-term operational effects for large-scale power and water networks

The high integration of variable renewable sources in electric power systems entails a series of challenges inherent to their intrinsic variability. A critical challenge is to correctly value the water available in reservoirs in hydrothermal systems, considering the flexibility that it provides. In this context, this paper proposes a medium-term multistage stochastic optimization model for the hydrothermal scheduling problem solved with the stochastic dual dynamic programming algorithm. The proposed model includes operational constraints and simplified mathematical expressions of relevant operational effects that allow more informed assessment of the water value by considering, among others, the flexibility necessary for the operation of the system. In addition, the hydrological uncertainty in the model is represented by a vector autoregressive process, which allows capturing spatio-temporal correlations between the different hydro inflows. A calibration method for the simplified mathematical expressions of operational effects is also proposed, which allows a detailed short-term operational model to be correctly linked to the proposed medium-term linear model. Through extensive experiments for the Chilean power system, the results show that the difference between the expected operating costs of the proposed medium-term model, and the costs obtained through a detailed short-term operational model was only 0.1%, in contrast to the 9.3% difference obtained when a simpler base model is employed. This shows the effectiveness of the proposed approach. Further, this difference is also reflected in the estimation of the water value, which is critical in water shortage situations.

A Novel Hybrid Approach for Hydrothermal Scheduling Using Mathematical and Metaheuristic Search Methods

A Novel Hybrid Approach for Hydrothermal Scheduling Using Mathematical and Metaheuristic Search Methods

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.

PSO with Mixed Strategy for Global Optimization

Particle swarm optimization (PSO) is an evolutionary algorithm for solving global optimization problems. PSO has a fast convergence speed and does not require the optimization function to be differentiable and continuous. In recent two decades, a lot of researches have been working on improving the performance of PSO, and numerous PSO variants have been presented. According to a recent theory, no optimization algorithm can perform better than any other algorithm on all types of optimization problems. Thus, PSO with mixed strategies might be more efficient than pure strategy algorithms. A mixed strategy PSO algorithm (MSPSO) which integrates five different PSO variants was proposed. In MSPSO, an adaptive selection strategy is used to adjust the probability of selecting different variants according to the rate of the fitness value change between offspring generated by each variant and the personal best position of particles to guide the selection probabilities of variants. The rate of the fitness value change is a more effective indicator of good strategies than the number of previous successes and failures of each variant. In order to improve the exploitation ability of MSPSO, a Nelder–Mead variant method is proposed. The combination of these two methods further improves the performance of MSPSO. The proposed algorithm is tested on CEC 2014 benchmark suites with 10 and 30 variables and CEC 2010 with 1000 variables and is also conducted to solve the hydrothermal scheduling problem. Experimental results demonstrate that the solution accuracy of the proposed algorithm is overall better than that of comparative algorithms.

Medium-Term Hydrothermal Scheduling of the Infiernillo Reservoir Using Stochastic Dual Dynamic Programming (SDDP): A Case Study in Mexico

This article aims to obtain and evaluate medium-term operating policies for the hydrothermal scheduling problem by using the stochastic dual dynamic programming (SDDP) approach. To this end, to feed the mathematical model and build the probability distribution functions that best fit each month of the actual inflow volume, monthly inflow data recorded from 1938 to 2018 for the Infiernillo reservoir located in Mexico were employed. Moreover, we simulated inflow volume scenarios using the Monte Carlo method for each month of a one-year planning period. The SDDP approach to solving the optimization problem consisted of the simulation of one forward scenario per iteration and the stabilization of the total operating cost as a convergence criterion, which results in an operating policy. We then assessed its quality by estimating the one-sided optimality gap. It is worth mentioning that the best operation policy required scenario trees of up to 17,000 inflow realizations per stage. Additionally, to study the evolution of the expected value along the planning horizon of the main variables involved in the medium-term hydrothermal scheduling problem, we simulated the best operation policy over 10,000 inflow scenarios. Finally, to show the practical value of the proposed approach, we report its computational complexity.

An antigravity-based fuzzy Gravitational Search Algorithm for economic dispatch problems

This paper presents an antigravity-based fuzzy Gravitational Search Algorithm (AFGSA) to solve the economic dispatch problem (EDP) with various constraints. Based on an antigravity mechanism combined with an adaptive fuzzy parameter controller AFGSA is designed. By doing so, it ensures a proper balance between exploration and exploitation of GSA. Furthermore, the simulated annealing (SA) process is introduced to control the application of anti-gravitation forces and guarantee the convergence rate. A fuzzy optimizing system is applied to adaptively control the parameters in GSA. The success of the suggested algorithm is firstly shown in eight various test EDPs including static and dynamic economic load problems as well as hydrothermal scheduling problems by varying the complex constraints. Then, the efficiency of the proposed optimizer is validated through ten CEC2020 test functions. The performance of AFGSA is verified by comparison with numerous state-of-the-art techniques. The experimental results show that AFGSA provides a more competing and robust solution to the EDPs than the compared algorithms.

Fixed head hydrothermal scheduling considering uncertainty of load demand and renewable energy sources

AbstractThis manuscript suggests quasi‐oppositional fast convergence evolutionary programming (QOFCEP) technique to determine short‐term generation scheduling of fixed head hydrothermal system comprising pumped storage hydro plants (PSHPs), solar PV plants (SPVPs) and wind turbine generators (WTGs) with demand response program (DRP). PSHPs are used with fixed head hydro power plants (FHPPs), thermal generating units (TGUs), SPVPs and WTGs to operate system conveniently. Uncertainties related to renewable generations and load demands have been considered. Self‐adaptive tent mapped scenarios of uncertain parameters are generated within higher level of confidence space to deal with the system uncertainties. DRP is applied to level the load demand curve and to enhance system flexibility and reduce operational cost. Numerical results of typical test system are matched with those attained by fast convergence evolutionary programming (FCEP) and evolutionary programming (EP).

Coordinated Economic Operation of Hydrothermal Units with HVDC Link Based on Lagrange Multipliers

Coordinated operation of hydrothermal scheduling with HVDC links considering network constraints becomes a vital issue due to their remote location and recent induction in the existing power system. The nonlinear and complex nature of the problem introduces many variables and constraints which results in a heavy computational burden. A widespread approach for handling these complexities is to reformulate the problem by several linearization methods. In this paper, a Lagrange multipliers-based method is proposed for the solution of hydrothermal economic scheduling including HVDC link. This method solves equality constraint optimization problems. The linear programming approach is embedded with the Lagrange method to consider both equality and inequality constraints. The proposed technique has been used on piecewise linear variables and constraints of the system considering generation, water volume, and line power flow limits. The formulated method efficiently minimizes the operational cost of thermal units and maximizes the utilization of hydro units while meeting all generation, water volume, and the HVDC link constraints. The method was successfully implemented in two scenarios of a case study. In the first scenario, hydrothermal scheduling was performed on the typical network without an HVDC line limit and equal nodal prices were found with minimal thermal generation cost of $278,822.3. In the second scenario, the proposed method optimally dispatches units to meet the HVDC line limit and minimizes thermal generation cost to $279,025.4 while satisfying hydro, thermal, and other operating constraints. Both scenarios are implemented for a 24 h period. The results have been presented to illustrate the performance of the proposed method.

Non-anticipative risk-averse analysis with effective scenarios applied to long-term hydrothermal scheduling

Non-anticipative risk-averse analysis with effective scenarios applied to long-term hydrothermal scheduling

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.