Hydrothermal Scheduling Problem Research Articles

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.

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.

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.

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.

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.

Application of chaos assisted sine cosine algorithm on wind–solar integrated hydrothermal scheduling problem

AbstractIn recent times, renewable energy sources are essential for generating low‐cost, pollution‐free power. Since the last two decades, hydrothermal coordination system has been used to fulfill the demand power. The traditional generating model's two biggest flaws are high generation cost and excessive fossil fuel emission. In the proposed work, generation process of traditional hydrothermal scheduling (HTS) has been improved by integrating wind–solar energy. To overcome current issues of HTS, that is, excessive emission and generation cost, hydrothermal–solar–wind scheduling (HTSWS) problem has been introduced where two wind and two solar power generating units have been considered with four hydro and three thermal power generating units. Here, effective performance of low cost‐emission based proposed HTSWS has been examined by using chaos‐based sine cosine algorithm (SCA) (CSCA). Chaos has been used in sine cosine function of SCA to improve searching process for finding global optimal results. The proposed CSCA has been used to investigate three separate situations of standard HTS and recommended HTSWS problems including generation cost, emission, and combined cost‐emission. The cost of generation and emissions from conventional HTS can be reduced by 11% and 68%, respectively, by the suggested renewable energy source‐based generation model. The results of several case studies of proposed HTSWS and standard HTS reveal that wind–solar energy is effective in the HTS issue, and chaos assists in the SCA to improve its optimization process. In this study, effectiveness and robustness of the CSCA have been demonstrated by comparing the CSCA‐based results to existing methods for the challenges under consideration.

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.

Multistage adaptive robust optimization for the hydrothermal scheduling problem

The current water scarcity faced by many countries increases the need to consider an appropriate representation of future hydro inflows in power system operation and planning models. Hydrothermal scheduling is the problem that seeks to use the water stored in reservoirs throughout time in order to find an optimal dispatch policy between hydro and thermal power plants. Due to both the inherent randomness of water inflows and the intertemporal decision process, this problem has been typically approached through multistage stochastic optimization, minimizing the total expected operational cost over the entire planning horizon. However, this approach has some practical disadvantages. Among the main ones we highlight (i) the complexity of balancing the statistical representativeness of the stochastic processes and the computational efficiency of the optimization model; (ii) the need to employ computationally intensive decomposition methods for its solvability; and (iii) the need to carry out network simplifications to tackle tractability issues arising in large networks. As an alternative, we propose a multistage adaptive robust optimization model for the hydrothermal scheduling problem. Robust optimization is useful to prevent the previous disadvantages because it does not make any distributional assumption and it works with the so-called uncertainty sets instead of carrying out sampling processes. In particular, we propose an efficient formulation based on linear decision rules and vector autoregressive models to represent the uncertainty in hydro inflows. Our experiments, based on the Chilean electric power system with hundreds of hydro nodes and connections, show the proposed model’s efficiency for large-scale systems and provide insights into the adequate balance between cost-effectiveness and reliability that robust optimization models guarantee.

Solution for short-term generation scheduling of cascaded hydrothermal system with turbulent water flow optimization

For economic operation of hybrid power systems, short-term hydrothermal planning is a significant operation which is focused to reduce the fuel costs of thermal power plants while fulfilling the different constraints of electrical and hydraulic networks. This paper addresses a newly developed algorithm, turbulent water flow optimization (TWFO) to solve the hydrothermal scheduling problem. TWFO is based on the whirlpool phenomenon which is formed through turbulent flow of water in seas or oceans. To enrich the solution quality of TWFO and to avoid trapping into local optimum, a chaotic logistic map is employed in the algorithm. The proposed TWFO is used to offer an optimal hourly generation schedule of hydrothermal power system considering the spillage effects of hydro plants, and the valve point loading effects, transmission losses and multi-fuel sources of thermal power plants. Besides, a repair mechanism is applied to fulfil all the equality and inequality constraints and to govern the solutions in the direction of feasible search space. The superiority of the proposed TWFO is examined on three hybrid power systems and the results of TWFO are compared with the performance of recent heuristic approaches including monarch butterfly optimization, Harris hawks optimization, red fox optimizer, remora optimization algorithm, student psychology-based optimization, and other erstwhile approaches reported in the literature. Numerical results demonstrate that the TWFO shows a superior performance in comparison with other approaches.

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.

Performance analysis of distance metrics on the exploitation properties and convergence behaviour of the conventional firefly algorithm

The nature of the distance metric used to compare the span between two fireflies in conventional firefly algorithm can significantly enhance the exploitation properties of the algorithm and improve its convergence towards the optimum solution. Therefore, this research proposes several variants of the firefly algorithm based on different distance relations like Minkowski distance, Canberra distance, and Angular Cosine distance. To compare the performance of these variants, benchmark non-linear and non-convex objective functions are solved under the varying nature of the medium absorption coefficient and attractiveness constant. It is observed from detail analysis of results that Canberra distance provides optimal results for almost all of the benchmark functions. Furthermore, the importance of the distance metric for real-world optimization problems with very large or small magnitude of decision variables is also presented by solving a practical hydro thermal scheduling problem. It is also presented that the optimal set of parameters for a particular distance criterion may not always be optimal and better convergence results can be achieved by varying the distance metric to measure the length between the fireflies.

Assessment of the Modeling of Demand Response as a Dispatchable Resource in Day-Ahead Hydrothermal Unit Commitment Problems: The Brazilian Case

Modern power systems have experienced large increases in intermittent and non-dispatchable sources and a progressive reduction in the size of hydro reservoirs for inflow regularization. One method to mitigate the high uncertainty and intermittency of the net load is by Demand Response (DR) mechanisms, to allow a secure and reliable system dispatch. This work applied a mixed integer linear programming formulation to model DR as a dispatchable resource in the day-ahead hydrothermal scheduling problem, taking into account minimum load curtailment constraints, minimum up/down load deduction times, as well as piecewise linear bid curves for load shedding in eligible loads. The methodology was implemented in the official model used in Brazil and tested in large-scale problems to obtain the optimal daily dispatch and hourly pricing. The results show the positive impact of dispatchable DR loads in cost reduction and in mitigating peak values of energy prices, even for predominantly hydro systems, helping to preserve the reservoir levels and increasing the security of the supply in the future.

Artificial Gorilla Troop Optimization for Optimization Operation of a Complicated Hydrothermal System

This study implements a novel meta-heuristic method called artificial gorilla troop optimization (AGTO) to handle the short-term fixed-head hydrothermal scheduling problem (ST-HTS). In the study, the constraints of reservoir and the fuel function of total generating electricity cost for thermal power plants are taken into account. AGTO is a newly published method and the main inspiration is based on the living practice of gorilla in nature. While tested by the hydrothermal power system, AGTO have demonstrated its striking performance to other state-of-the-art meta-heuristic algorithms and other popular algorithms. In this study, AGTO is implemented alongside with improved particle swarm optimization (IPSO) and tunicate swarm algorithm (TSA) for assessing the raw performance. The results obtained by these methods see that AGTO is a highly effective computing method for an engineering problem such ST-HTS besides IPSO and TSA in all compared criteria.

Solution of short term integrated hydrothermal-solar-wind scheduling using sine cosine algorithm

The combined scheduling of hydro, thermal and hybrid energy (i.e., wind and solar) is attracting more and more attention nowadays. This paper explores the contribution of renewable energy sources in the traditional hydrothermal scheduling problem in order to overcome the prevailing issues like high generation cost and more emissive particles of fuel. This paper presents a new wind-solar based generation scheduling model that reduces the aforementioned issues. The proposed hydrothermal-solar-wind scheduling (HTSWS) model is very effective. It can reduce the price rate of generation and different emissive particles of fuel of the traditional scheduling model. A solution approach i.e., robust sine cosine algorithm (SCA) is employed to determine the minimum generation cost and fuel emission based best generating schedule for traditional scheduling problem. The same approach has been carried out in the context of the suggested HTSWS problems. The different control parameters of the SCA have been properly utilized to balance the exploration and the exploitation phases. These parameters lead to determination of the near-optimal global solution. The results show that the combined application of renewable sources and hydrothermal units benefit both economic and emission goals of the utility houses with operating costs and pollutant emissions falling by 10% and 64%, respectively. Here, another two powerful algorithms (i.e., backtracking search algorithm and whale algorithm) have also been applied to determine the minimum values of generation cost, emission, and combined generation cost-emission. Effectiveness and robustness of the proposed algorithm have been presented by comparing the SCA based results with other established latest algorithms for the considered problems.

Dealing with Negative Inflows in the Long-Term Hydrothermal Scheduling Problem

The long-term hydrothermal scheduling (LTHS) problem seeks to obtain an operational policy that optimizes water resource management. The most employed strategy to obtain such a policy is stochastic dual dynamic programming (SDDP). The primary source of uncertainty in predominant hydropower systems is the reservoirs inflow, usually a linear time series model (TSM) based on the order-p periodic autoregressive [PAR(p)] model. Although the linear PAR(p) can represent the seasonality and autocorrelation of the inflow datasets, negative inflows may appear during SDDP iterations, leading to water balance infeasibilities in the LTHS problem. Different from other works, the focus of this paper is not avoiding negative inflows but instead dealing with the negative values that cause infeasibilities. Hence, three strategies are discussed: (i) inclusion of a slack variable penalized in the objective function, (ii) negative inflow truncation to zero, and (iii) optimal inflow truncation, among which the latter is a novel approach. The strategies are compared individually and combined. Methodological conditions and evidence of the algorithm convergence are presented. Out-of-sample simulations show that the choice of negative inflow strategy significantly impacts the performance of the resultant operational policy. The combination of strategy (i) and (iii) reduces the expected operation cost by 15%.