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Short-term combined economic and emission hydrothermal optimization by surrogate differential evolution

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Abstract

This paper present short-term combined economic and emission hydrothermal optimization, addressing total fuel costs and emissions minimization. This paper uses the fuel cost function with valve-point effect, which increases the degree of optimization problem difficulty. The optimal balance between the addressed objectives, that conflict with each other, can be obtained with appropriate hydro and thermal generation schedules. A surrogate differential evolution is applied in order to satisfy 24-h system demand and final states of hydro power plant reservoirs by minimized total fuel costs and emissions. This paper proposes a novel master–slave model optimization algorithm, where the optimal thermal schedules are obtained within the slave model. The data obtained from the slave model are saved into a matrix, which serves as a surrogate model for a master model, where the hydrothermal optimization with all objectives and constraints is conducted by using a parallel self-adaptive differential evolution algorithm. In order to show the effectiveness of the proposed method, different case studies are used: economic load scheduling, economic emission scheduling, and combined economic emission scheduling. The proposed method is verified on a model consisting of four hydro power plants and three thermal power plants.

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... In more detail, short-term load dispatch joint with emission consideration has been formulated in Refs. [5,14], while Luiz Diniz et al. [5] have discussed a more precise scheme for hydrothermal dispatch in which the impact of river routing, consisting of wave propagation along the channel has been considered. Authors in Refs. ...
... In more detail, short-term load dispatch joint with emission consideration has been formulated in Refs. [5,14], while Luiz Diniz et al. [5] have discussed a more precise scheme for hydrothermal dispatch in which the impact of river routing, consisting of wave propagation along the channel has been considered. Authors in Refs. ...
... Thermal Units participated in UC 4,5,10,11,20,21,24,25,27,28,29,36,39,40,43,44,45 4,5,7,10,11,16,19,20,21,23,24,25,27,28,29,34,35,36,37,40, ...
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The paper presents the info-gap theory for the sake of developing a robust framework for short-term hydrothermal scheduling to tackle severe load uncertainty. Deploying this method, the system operator is provided with a robust decision-making strategy to guarantee the minimum cost under load variation condition while practical and technical limitations such as dynamic ramp rate are taken into consideration. For this purpose, the proposed Unit Commitment (UC) problem considering all above advantages would be modeled in a linear framework, which is in turn taken into account as another outstanding feature of this study as it is compatible to apply to real-world systems. In order to investigate the model efficiency, the modified version of the IEEE 118-bus test system having 54 thermal beside 8 hydro plants is chosen as the case study. Eventually, the results demonstrate how demand fluctuations and errors in the predicted load can be tolerated by allocating additional robust cost. The personalized Share Link: https://authors.elsevier.com/c/1XsUx1H~c~3mkX
... Nguyen and Vo [33] have tested effectiveness of modified CSA (MCSA) over CSA by producing optimal cost of different test systems of HTS problem. Glotić and Zamuda [34] have solved different cases of HTS problem using parallel self-adaptive DE (PSADE) technique. Dubey et al. [35] have considered wind power with HTS problem and applied ant lion optimization algorithm on the considered problem to determine optimal fuel. ...
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... It was first proposed by Storn and Price [20] to solve global numerical optimization problems over continuous search spaces. It is a simple yet powerful evolutionary algorithm and exhibits excellent capability in solving a variety of numerical and real-world optimization problems, such as space trajectory design [21][22][23][24][25], hydrothermal optimization [26], underwater glider path planning [27], vehicle routing problem [28,29], short-term optimal hydrothermal scheduling [30], satellite scheduling [31,32], and satellite image enhancement [33]. 2 Computational Intelligence and Neuroscience ...
... (2) e investigations in [21][22][23][24][25][26][27][28][29][30][31][32][33] indicate that DE has been successfully used in a variety of domains. However, the use of DE for the weight parameters determination of ILAIS has not been reported. ...
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... To deal with multiple targets in power system scheduling, multi-objective optimization models are used. Many works cooptimize cost and emission in deterministic or stochastic unit commitment problems [8][9][10][11][12]. Glotic and Zamuda [8] compare minimizing fuel cost and minimizing emissions in a hydro thermal power system, and formulate a decomposition model to cooptimize these two objectives together. ...
... Many works cooptimize cost and emission in deterministic or stochastic unit commitment problems [8][9][10][11][12]. Glotic and Zamuda [8] compare minimizing fuel cost and minimizing emissions in a hydro thermal power system, and formulate a decomposition model to cooptimize these two objectives together. In [9,10], similar power generation scheduling models with thermal and hydro units are formulated, and the cost vs. ...
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... As motivated within the technical report [23], "research on single objective optimization algorithms often forms the foundation for more complex scenarios, such as niching algorithms and both multiobjective and constrained optimization algorithms. " The usefulness of such research is demonstrated clearly for approaches in complex mission planning, like underwater glider path planning in deep ocean scenarios [38,39], or energy scheduling [10] and spatial computer vision [34]. ...
... Several recent surveys and insights exist with the DE algorithm's base name [6-8, 16, 21, 35] and its metaphors [4,24], stemming from the progress on computational mechanisms, mainly from the branches of the DE, as well as applications [7,10,20,34,38]. Binary versions of DE have been published before in the works like [13,14,19]. ...
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... Lately, nature inspired (NI) methods have gained popularity against gradient based algorithms, due to their numerous advantages [10,27] such as (i) Non dependence on nature of optimization problem (ii) Non dependence on initial solution (iii) Global search capability due to population based direct search (iv) Simple implementation and (v) Effective constraint handling. Among popular NI techniques, EP [9], PSO [10,15], DE [8,11,12], ABC [13,18,32], GS [14,17] PPO [15], and cultural algorithm with PSO [16], are successfully implemented. In Ref. [19] normal boundary intersection method, a MO fuzzy optimization model [20] and Lexicographic optimization technique [21] are proposed for hydro-thermal scheduling. ...
... 12) 2.5. Inequality constraints due to operating limits on generating units ...
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A solution to the combined hydro-thermal-wind scheduling problem of multi reservoir cascaded hydro plants is presented employing a novel ant lion optimization (ALO) algorithm. Five objectives, cost, various emissions and power loss, are simultaneously optimized. The optimal schedules of thermal, hydro and wind power (WP) units are determined for continuously varying load subject to a large number of practical operational constraints. The effect of reserve and penalty coefficients and WP uncertainty is also investigated for the multi-objective (MO) problem. The newly proposed ALO algorithm has unique features like random walk, roulette wheel, and boundary shrinking. These operations provide a judicious balance between exploration and exploitation, and create a powerful optimization technique for complex real-world problems. Finding the best compromise solution (BCS) is a tedious task when multiple objectives are involved. A composite ranking index (CRI) is proposed as a performance metrics for MO problems. The CRI helps the decision maker in ranking the large number of Pareto-optimal solutions. The developed model is tested on three standard systems, having a mix of hydro, thermal and wind generators. The performance is found to be superior to published results and comparable with established algorithms like artificial bee colony (ABC) and differential evolution (DE).
... In the literature, many methods have been developed and applied to solve STHCP. Some of these methods use the particle swarm optimization technique [1], the differential evolution based methods [2], the artificial bee colony algorithm [3], the benders decompositions based methods [4], the genetic algorithm [5] and the pseudo spot price algorithm [6]. In addition to these, a survey on the optimization methods applied to solve the STHCP can be found in [7]. ...
... In order to express the total cost rate function in terms of independent variables of our optimization model, line flows should be written in terms of bus voltage magnitudes and phase angles, off-nominal tap settings, susceptance values of svar systems (see equations (1), (2) and (3)).The necessary equations, giving the active and reactive power flows (p ik,j and q ik,j ) over the line that is connected between buses i and k in the j th subinterval in terms of the independent variables, can be found in reference [9]. Using those equations and equation (2), the active and reactive power generations of the i th unit connected to bus i in the j th subinterval can be calculated as below: ...
... DE is relatively simple to implement and was demonstrated to be very effective on a large number of cases. In the past few decades, DE has been successfully used in many real-world applications, such as space trajectory design [8][9][10], hydrothermal optimization [11], underwater glider path planning [12], and vehicle routing problem [13]. ...
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... Padhye, et al. [22] have suggested elitist selection. Many DE variants have been constructed, such as DE with adaptive mutation [20][21], DE with elitist selection [22], DE with ancestor tree [23], DE with adaptive mutation and elitist selection [24], DE with penalty method [25], and surrogate differential evolution (SDE) [26]. ...
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This paper proposes the Novel Differential Evolution (NDE) method for solving the environmental economic hydrothermal system dispatch (EEHTSD) problem with the aim to reduce electricity generation fuel costs and emissions of thermal units. The EEHTSD problem is constrained by limitations on generations, active power balance, and amount of available water. NDE applies two modified techniques. The first one is modified mutation, which is used to balance global and local search. The second one is modified selection, which is used to keep the best solutions. When performing this modified selection, the proposed method completely reduces the impact of crossover by setting it to one. Moreover, the task of tuning this factor can be canceled. Original Differential Evolution (ODE), ODE with the first modification (MMDE), and ODE with the second modification (MSDE), and NDE were tested on two different hydrothermal systems for comparison and evaluation purposes. The performance of NDE was also compared to existing methods. It was indicated that the proposed NDE is a very promising method for solving the EEHTSD problem.
... In fact, CDE selection is a comparison between the previous solution Xd and the solution Zd, which was chosen via crossover. Derived from the indication of the limitations of CDE, many DE variants have been constructed by modifying mutation and selection operation such as DE with the adaptive mutation [40,41], DE with elitist selection [42], DE with ancestor tree [43], DE with adaptive mutation and elitist selection [44], DE with a penalty method [45], and surrogate differential evolution (SDE) [46]. DE variants with adaptive mutation and/or elitist selection can find better solutions than CDE; however, these methods have to cope with fundamental limitations such as spending a great deal of time tuning the crossover factor and several factors in the adaptive mutation operation, missing promising solutions of good quality, and keeping identical solutions in the current population. ...
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This paper proposes an efficient and new modified differential evolution algorithm (ENMDE) for solving two short-term hydrothermal scheduling (STHTS) problems. The first is to take the available water constraint into account, and the second is to consider the reservoir volume constraints. The proposed method in this paper is a new, improved version of the conventional differential evolution (CDE) method to enhance solution quality and shorten the maximum number of iterations based on two new modifications. The first focuses on a self-tuned mutation operation to open the local search zone based on the evaluation of the quality of the solution, while the second focuses on a leading group selection technique to keep a set of dominant solutions. The contribution of each modification to the superiority of the proposed method over CDE is also investigated by implementing CDE with the self-tuned mutation (STMDE), CDE with the leading group selection technique (LGSDE), and CDE with the two modifications. In addition, particle swarm optimization (PSO), the bat algorithm (BA), and the flower pollination algorithm (FPA) methods are also implemented through four study cases for the first problem, and two study cases for the second problem. Through extensive numerical study cases, the effectiveness of the proposed approach is confirmed.
... In general, DE is a floating-point encoding optimization algorithm that can be applied for global optimization over continuous or discrete function spaces [13], [14], [25], [15], [16], [17]. DE has many application domains, from multi-objective optimization [16], [18] to real world problems tacked [19], [20], [21], [22]. Advances, success, and comprehensive survey on DE are found in papers like [23], [24], [2], [3], which demonstrate the vast applicability of DE in recent decades. ...
... Among these evolution algorithms, DE is an efficient method for optimizing real-valued optimization problems (Storn 1996), with overall excellent performance for a wide range of criterion problems. Furthermore, because of its simple but powerful searching algorithm, DE has a number of real-world applications (Price et al. 2005) and has been successfully applied to problems across diverse fields such as physics (Pang et al. 2013), computer science (Zhong and Cai 2015), water resources (Zheng et al. 2015;Zahmatkesh et al. 2015;Guo et al. 2014), environment (Kişi 2010;Niu et al. 2015), biology (Zhao et al. 2013), and economics (Glotić and Zamuda 2015). Zhong and Cai (2015) used DE with sensitivity analysis and Powell's method to calibrate a crowd model for industry, academia, and government. ...
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... The Genetic Algorithm is applied to generate optimal generation scheduling of a short-term hydrothermal system in [6,7]. An evolutionary algorithm is employed for addressing STHTS in [8,9]. Following evolutionary algorithms, swarm intelligence-based optimisation algorithms received wide acceptance due to the lower number of computational steps and control variables involved. ...
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Hydro-thermal-wind generation scheduling (HTWGS) with economic and environmental factors is a multi-objective complex nonlinear power system optimization problem with many equality and inequality constraints. The objective of the problem is to generate an hour-by-hour optimum schedule of hydro-thermal-wind power plants to attain the least emission of pollutants from thermal plants and a reduced generation cost of thermal and wind plants for a 24-h period, satisfying the system constraints. The paper presents a detailed framework of the HTWGS problem and proposes a modified particle swarm optimization (MPSO) algorithm for evolving a solution. The competency of selected heuristic algorithms, representing different heuristic groups, viz. the binary coded genetic algorithm (BCGA), particle swarm optimization (PSO), improved harmony search (IHS), and JAYA algorithm, for searching for an optimal solution to HTWGS considering economic and environmental factors was investigated in a trial system consisting of a multi-stream cascaded system with four reservoirs, three thermal plants, and two wind plants. Appropriate mathematical models were used for representing the water discharge, generation cost, and pollutant emission of respective power plants incorporated in the system. Statistical analysis was performed to check the consistency and reliability of the proposed algorithm. The simulation results indicated that the proposed MPSO algorithm provided a better solution to the problem of HTWGS, with a reduced generation cost and the least emission, when compared with the other heuristic algorithms considered.
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... DE is also used for constraint optimization and there are several variants which entered competitions held at the IEEE Congress on Evolutionary Computation (CEC) [9], [10]. A surrogate matrix DE was recently applied in scheduling hydro and thermal power systems production [11]. DE was also used for the reconstruction of procedural tree models [12] within the EcoMod ecosystem rendering framework [13], which is an biogeography-like algorithm for virtual ecosystem afforestation; in numerical optimization, a biogeography-like algorithm was also applied to a grid map discretized robot path planning [14]. ...
... The LD problem considered has, however, few constraints and no hydro plants or photovoltaic units. Another approach using DE to target a LD problem considering storage hydro plants is presented in [12]. In this recent work, an adaptive DE is proposed to solve the problem. ...
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Unit commitment and load dispatch problems are important and complex problems in power system operations that have being traditionally solved separately. In this paper, both problems are solved together without approximations or simplifications. In fact, the problem solved has a massive amount of grid-connected photovoltaic units, four pump-storage hydro plants as energy storage units and ten thermal power plants, each with its own set of operation requirements that need to be satisfied. To face such a complex constrained optimization problem an adaptive repair method is proposed. By including a given repair method itself as a parameter to be optimized, the proposed adaptive repair method avoid any bias in repair choices. Moreover, this results in a repair method that adapt to the problem and will improve together with the solution during optimization. Experiments are conducted revealing that the proposed method is capable of surpassing exact method solutions on a simplified version of the problem with approximations as well as solve the otherwise intractable complete problem without simplifications. Moreover, since the proposed approach can be applied to other problems in general and it may not be obvious how to choose the constraint handling for a certain constraint, a guideline is provided explaining the reasoning behind. Thus, this paper open further possibilities to deal with the ever changing types of generation units and other similarly complex operation/schedule optimization problems with many difficult constraints.
... Dhanalakshmi et al. [34] solved the aggregated problem using a genetic algorithm. A differential evolution algorithm was used by Roche [35] and by Glotić and Zamuda [36]. Other metaheuristic methods also have been applied to solve the EED problem, such as a gravitational search algorithm [37], a bacterial foraging/ Nelder-Mead algorithm [38], dynamic fuzzy optimization [39], a multi-objective line-up competition algorithm [40], an artificial bee colony algorithm [41], a flower pollination algorithm [42], a firefly algorithm [43], a cultural algorithm [44], a floating search space [45], a harmony search algorithm [46], relaxed deep learning [47], and the shuffled frog-leaping algorithm [48], and so on. ...
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Recently, concerns about greenhouse gas reduction in the power generation sector have increased significantly. The introduction of environmental economic dispatch is being discussed in depth, particularly in countries where there is insufficient investment in fundamental greenhouse gas mitigation measures, such as renewable energy, or carbon capture and storage. The most significant problem with the existing environmental economic dispatch studies for greenhouse gas reduction is that they do not consider the time horizon difference between the greenhouse gas emission target (allocated on an annual basis) and environmental economic dispatch formulation (optimized on an hourly basis). Most of the existing environmental economic dispatch studies assume that hourly greenhouse gas emission targets are given, or if they are formulated as an annual optimization problem, they only deal with relatively small systems. In this manuscript, we propose a novel environmental shutdown method that can find the near optimal solution to the environmental economic dispatch problem for greenhouse gas reduction, simultaneously considering the hourly allocation problem and environmental economic dispatch optimization. In order to verify the effectiveness of the proposed method, it is applied to a large-scale power system with actual system and technical parameters. As a result, the proposed method is considered to be one of the effective methods of environmental economic dispatch that can be used to achieve short-term greenhouse gas reduction targets in countries where investment in renewable energy is not sufficient.
... The L-SHADE has been applied in several application domains [1] and also extended to improved versions [9]. The paper [13] also compared several other continuous optimization algorithms, mainly Differential Evolution, which was already studied using high-performance computing earlier in works like [11], and also applied to other important challenges, like energy scheduling [3]. ...
Conference Paper
The real-world implementation of Underwater Glider Path Planning (UGPP) over the dynamic and changing environment in deep ocean waters requires complex mission planning under very high uncertainties. Such a mission is also influenced to a large extent by remote sensing for forecasting weather models outcomes used to predict spatial currents in deep sea, further limiting the available time for accurate run-time decisions by the pilot, who needs to re-test several possible mission scenarios in a short time, usually a few minutes. Hence, this paper presents the recently proposed UGPP mission scenarios' optimization with a recently well performing algorithm for continuous numerical optimization, Success-History Based Adaptive Differential Evolution Algorithm (SHADE) including Linear population size reduction (L-SHADE). An algorithm for path optimization considering the ocean currents' model predictions, vessel dynamics, and limited communication, yields potential way-points for the vessel based on the most probable scenario; this is especially useful for short-term opportunistic missions where no reactive control is possible. The newly obtained results with L-SHADE outperformed existing literature results for the UGPP benchmark scenarios. Thereby, this new application of Evolutionary Algorithms to UGPP contributes significantly to the capacity of the decision-makers when they use the improved UGPP expert system yielding better trajectories.
... The short-term optimization approach follows the hours-ahead to day-ahead time horizon. In power system operations, unit commitment is one of the central approaches [6][7][8][9][10][11]. For achieving accuracy in testing, all daily operations and market clearing is done in advance. ...
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The hydro generation scheduling problem has a unit commitment sub-problem which deals with start-up/shut-down costs related hydropower units. Hydro power is the only renewable energy source for many countries, so there is a need to find better methods which give optimal hydro scheduling. In this paper, the different optimization techniques like lagrange relaxation, augmented lagrange relaxation, mixed integer programming methods, heuristic methods like genetic algorithm, fuzzy logics, nonlinear approach, stochastic programming and dynamic programming techniques are discussed. The lagrange relaxation approach deals with constraints of pumped storage hydro plants and gives efficient results. Dynamic programming handles simple constraints and it is easily adaptable but its major drawback is curse of dimensionality. However, the mixed integer nonlinear programming, mixed integer linear programming, sequential lagrange and non-linear approach deals with network constraints and head sensitive cascaded hydropower plants. The stochastic programming, fuzzy logics and simulated annealing is helpful in satisfying the ramping rate, spinning reserve and power balance constraints. Genetic algorithm has the ability to obtain the results in a short interval. Fuzzy logic never needs a mathematical formulation but it is very complex. Future work is also suggested.
... Algumas estratégias já foram propostas para resolver tal problema, dentre elas uma formulação utilizando Programação não Linear (Mariano et al., 2010). Alguns autores utilizam algoritmos evolutivos para resolver o problema, como o Particle Swarm Optimization (Jiekang, 2008), e o algoritmo de evolução diferencial (Glotić, 2015). Uma abordagem diferente considerando também incertezas do processo foi realizada utilizando uma modelagem multiobjetivo (Da Silva, 2017). ...
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Este trabalho apresenta uma estratégia para tratamento de restrições no algoritmo Nelder-Mead baseada na projeção no espaço nulo de restrições de igualdade e na criação de um operador de dominância lexicográfica para tratamento de restrições de desigualdade. Uma vez que o operador é definido e a projeção é realizada, o tratamento de restrições é naturalmente absorvido pelo algoritmo original. O algoritmo modificado é então aplicado no problema de otimização da programação diária da operação de usinas hidreléricas, que é um problema de grande porte e muitas vezes formulado em termos de funções não-diferenciáveis, tornando natural o uso de algoritmos de otimização que não dependam de avalições do gradiente, como é o caso do algoritmo Nelder-Mead. Testes são conduzidos na programação da operação de uma usina real e os resultados são comparados com uma solução de referência otimizada. Os resultados mostram a viabilidade da estratégia implementada e seu potencial de aplicação.
... One of these algorithms is the Differential Evolution algorithm (DE) (Storn and Price, 1997;Price et al., 2005;Neri and Tirronen, 2010;Das et al., 2016), which is a simple and effective algorithm for global optimization. It has been proved to be efficient at solving different optimization problems involving real valued numbers which interact non-linearly with each other Zhou et al., 2011;Bošković et al., 2011;Glotić and Zamuda, 2015;Mlakar, 2014;Bošković and Brest, 2016). The DE algorithm is an evolutionary based algorithm where each individual from the population is described as a vector of models' weights. ...
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... This simplification resulted due to the lack of reliable data needed to model head variation with storage level for some reservoirs. Future work could employ approaches proposed for short-term hydrothermal dispatch [34,46] if proper data and the required computational resources are available. ...
... These emissions can be taken as an objective function in economic dispatch problem. Beside these solutions, various other techniques such as Simulated Annealing, 2 Bacterial Foraging Algorithm, 3 Gravitational Search Algorithm, 4,5 Bi-objective Approach using Evolutionary Algorithm, 6 Improved Genetic Algorithm, 7,8 Particle Swarm Optimization (PSO), 9,10 and Differential Evolution (DE) 11,12 have already been successfully evaluated to reduce the emissions. ...
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... Also, in the case of EU project RIVR (Upgrading National Research Structures in Slovenia) supported by European Regional Development Fund (ERDF), an important sideeffect of cHiPSet COST action was leveraging it's experts' inclusiveness to gain capacity recognition at a national ministry for co-financing HPC equipment 1 . In the view of future possibilities for modelling and simulation in CI context, gain from HPC is clearly seen in improving upon techniques with DE like in energy applications [148], constrained trajectory planning [149], artificial life of full ecosystems [150] including HPC-enabled evolutionary computer vision in 2D [151,152] and 3D [151], many other well recognized real-world optimization challenges [153], or even insight to deep inner dynamics of DE over full benchmarks, requiring large HPC capacities [154]. ...
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Modelling and Simulation (M&S) offer adequate abstractions to manage the complexity of analysing big data in scientific and engineering domains. Unfortunately, big data problems are often not easily amenable to efficient and effective use of High Performance Computing (HPC) facilities and technologies. Furthermore, M&S communities typically lack the detailed expertise required to exploit the full potential of HPC solutions while HPC specialists may not be fully aware of specific modelling and simulation requirements and applications.
... Эволюционные алгоритмы применяются для решения множества практических задач, таких как составление расписаний в промышленности [15,16], оптимизация разводки печатных плат [17][18][19][20], построение систем управления [21][22][23][24][25][26][27], сегментирование изображений [28], а также приближенного решения других задач комбинаторной [29][30][31][32] и вещественной оптимизации [33][34][35]. ...
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... In fact, the subtle combination of the parameterization simulation optimization (PSO) method and a surrogate of the original simulation model can provide a judicious strategy. This strategy has proved powerful to address high-dimensional multi-reservoir hydropower generation [19,20] and flood control operations [21] as long as the surrogate retains the main features of the original model [22,23]. ...
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... They are all elitist algorithms, and have already received different degrees of success in solving CROO problems. The modern heuristic random search algorithms include the Genetic Algorithm (GA) [22], Particle Swarm Optimization (PSO) [23], Ant Colony Optimization (ACO) [24], Fuzzy Neural Network (FNN) [25], and the Differential Evolution algorithm (DE) [26][27][28]. These have been extensively used to solve the CROO problem, and have also received a good application effect. ...
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Transmission and Distribution modelling.- Recent Developments in Optimal Power Flow Modeling Techniques.- Algorithms for Finding Optimal Flows in Dynamic Networks.- Signal Processing for Improving Power Quality.- Transmission Valuation Analysis based on Real Options with Price Spikes.- Forecasting in Energy.- Short-term Forecasting in Power Systems: A Guided Tour.- State-of-the-Art of Electricity Price Forecasting in a Grid Environment.- Modelling the Structure of Long-Term Electricity Forward Prices at Nord Pool.- Hybrid Bottom-Up/Top-Down Modeling of Prices in Deregulated Wholesale Power Markets.- Energy Auctions and Markets.- Agent-based Modeling and Simulation of Competitive Wholesale Electricity Markets.- Futures Market Trading for Electricity Producers and Retailers.- A Decision Support System for Generation Planning and Operation in Electricity Markets.- A Partitioning Method that Generates Interpretable Prices for Integer Programming Problems.- An Optimization-Based Conjectured Response Approach to Medium-term Electricity Markets Simulation.- Risk Management.- A Multi-stage Stochastic Programming Model for Managing Risk-optimal Electricity Portfolios.- Stochastic Optimization of Electricity Portfolios: Scenario Tree Modeling and Risk Management.- Taking Risk into Account in Electricity Portfolio Management.- Aspects of Risk Assessment in Distribution System Asset Management: Case Studies.
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A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch (EED) problem. Furthermore, the polynomial functions of both objective functions are aggregated into a single objective function using the weighted sum approach. This thus reduces the problem to a standard polynomial optimization problem which was formulated as a hierarchy of semi-definite relaxation problems. The resulting SDP problem was then solved at different degrees of approximation. The performance of the proposed approach was evaluated by conducting experiments on the standard 6-unit and the 13-unit IEEE test systems. The results obtained were compared with those reported in the literature and indicated that SDP has inherently good convergence property and provides better exploration of the Pareto front.
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In order to optimize hydro power plants generator scheduling according to 24-h system demand, a parallel self-adaptive differential evolution algorithm has been applied. The proposed algorithm presents a novel approach to considering the multi-population and utilization of the preselection step for the improvements of the algorithm's global search capabilities. A preselection step with the best, middle, and worst populations' individuals establishes the new trial vectors. This algorithm has been verified on two different models. The first one consists of eight power plants with real parameters, and the second one consists of four power plants, mostly used as a test model in scientific papers. The main goal of the optimization process is to satisfy system demand for 24 h with a decreased usage of water quantity per electrical energy unit. The initial and final states of the reservoirs must also be satisfied.
Article
The optimal dispatching of cascade Hydro Power Plants is known as a complex optimization problem. In order to solve this problem the authors have applied an adapted differential evolution algorithm by using a fixed and dynamic population size. According to the dynamic population size, the proposed algorithm uses novel random and minimum to maximum sort strategy in order to create new populations with decreased or increased sizes. This implementation enables global search with fast convergence. It also uses a multi-core processor, where all the necessary optimization data are sent to the individual core of a central processing unit. The main aim of the optimization process is to satisfy 24 h demand by minimizing the water quantity used per electrical energy produced. This optimization process also satisfies the desired reservoir levels at the end of the day. The models used in this paper were the real parameters' models of eight cascade Hydro Power Plants located in Slovenia (Europe). Also the standard model from the literature is used in order to compare the performance of the adapted optimization algorithm.
Article
This paper presents a vectorized matrix parameters encoding aspect for an evolutionary computer vision approach to procedural tree modeling. A serialized fixed-size floating-point encoded tree parameter set consists of a set of auxiliary local and other global parameters. The main goal of paper is to lower problem dimensionality needed for encoding local parameters. For evolution simulation, differential evolution algorithm is used. The optimizer evolves a parameterized procedural model by fitting a set of its rendered images to a set of automatically preprocessed reference photo images. The reconstructed tree morphology is then used for reconstructed tree animation, to generate similar geometrical tree models based on similar morphology. Examples of reconstructed model animation are shown, such as simulation of its growth, sway in the wind, or adding leaves.
Article
The design trade-offs between thermodynamics and economics for thermal systems can be studied with the aid of multi-objective optimization techniques. The investment costs usually increase with increasing thermodynamic performance of a system. In this paper, an enhanced differential evolution with diversity-preserving and density-adjusting mechanisms, and a newly-proposed algorithm for searching the decision space frontier in a single run were used, to conduct the multi-objective optimization of large-scale, supercritical coal-fired plants. The uncertainties associated with cost functions were discussed by analyzing the sensitivity of the decision space frontier to some significant parameters involved in cost functions. Comparisons made with the aid of an exergoeconomic analysis between the cost minimum designs and a real industrial design demonstrated how the plant improvement was achieved. It is concluded that the cost of electricity could be reduced by a 2–4%, whereas the efficiency could be increased by up to two percentage points. The largest uncertainty is introduced by the temperature-related and reheat-related cost coefficients of the steam generator. More reliable data on the price prediction of future advanced materials should be used to obtain more accurate fronts of the objective space.
Article
Multimodal optimization is one of the most challenging tasks for optimization. It requires an algorithm to effectively locate multiple global and local optima, not just single optimum as in a single objective global optimization problem. To address this objective, this paper first investigates a cluster-based differential evolution (DE) for multimodal optimization problems. The clustering partition is used to divide the whole population into subpopulations so that different subpopulations can locate different optima. Furthermore, the self-adaptive parameter control is employed to enhance the search ability of DE. In this paper, the proposed multipopulation strategy and the self-adaptive parameter control technique are applied to two versions of DE, crowding DE (CDE) and species-based DE (SDE), which yield self-CCDE and self-CSDE, respectively. The new algorithms are tested on two different sets of benchmark functions and are compared with several state-of-the-art designs. The experiment results demonstrate the effectiveness and efficiency of the proposed multipopulation strategy and the self-adaptive parameter control technique. The proposed algorithms consistently rank top among all the competing state-of-the-art algorithms.
Article
Economic dispatch (ED) is an important task in power system operation. It is able to decrease the operating cost, save energy resources, and reduce environmental load. In this paper, a multi-strategy ensemble biogeography-based optimization (MsEBBO) based method for ED problems is proposed. BBO is a population-based meta-heuristic algorithm inspired by the science of biogeography and mainly consists of three components: migration model, migration operator, and mutation operator. It has good local exploitation ability but lacks satisfactory global exploration ability. To keep a proper balance between exploration and exploitation, MsEBBO has three extensions to BBO’s three components according to the no free lunch theorem. First, a nonlinear migration model based on sinusoidal curve is employed. Second, a backup migration operator through adopting a backup strategy to combine perturb operator and blended operator is presented. This operator can make the entire population fully exchange or share information and thus further strengthen the exploitation ability. Finally, both differential mutation and Lévy local search are embedded as mutation operator for MsEBBO using a similar backup strategy. Gaining from this mutation operator, MsEBBO can be accelerated to escape from local optima and perform efficient search within global range. Additionally, an effective repair technique is proposed to handle different constraints of ED problems. The performance of MsEBBO is tested on four ED problems with diverse complexities. Experimental results and comparisons with other recently reported ED solution methods confirm that MsEBBO is capable of yielding a good balance between exploration and exploitation, and obtaining competitive solution quality. Moreover, the sensitivity of MsEBBO to variations in population size is investigated as well.
Article
Modelling the effect of valve point loadings on the performance and cost of power generators for electricity dispatch problems is necessary. For the past 20 years, the development of computer based methods for the identification of optimal designs have been based on a single model, introduced by Walters and Sheble (1993) [1]. This model approximates the non-monotonic incremental cost curve using a sine function. This note explores the properties of this model, highlighting one critical deficiency for use within an automated optimization based design system and proposes a new model.
Article
Annual load forecasting is very important for the electric power industry. As influenced by various factors, an annual load curve shows a non-linear characteristic, which demonstrates that the annual load forecasting is a non-linear problem. Support vector regression (SVR) is proven to be useful in dealing with non-linear forecasting problems in recent years. The key point in using SVR for forecasting is how to determine the appropriate parameters. This paper proposes a hybrid load forecasting model combining differential evolution (DE) algorithm and support vector regression to deal with this problem, where the DE algorithm is used to choose the appropriate parameters for the SVR load forecasting model. The effectiveness of this model has been proved by the final simulation which shows that the proposed model outperforms the SVR model with default parameters, back propagation artificial neural network (BPNN) and regression forecasting models in the annual load forecasting.
Article
This paper proposes an enhanced augmented Lagrange Hopfield network (EALHN) for solving economic dispatch (ED) with piecewise quadratic cost functions. The EALHN is an augmented Lagrange Hopfield neural network (ALHN), a continuous Hopfield neural network with its energy function based on augmented Lagrangian function, enhanced by a heuristic search for determination of fuel type. The proposed EALHN solves the ED problem in two phases. In the first phase, a heuristic search based on the average production cost of generating units is used to determine the most suitable fuel type for each unit so that total maximum power generation from all units is sufficient for supplying to load demand. In the last phase, the ALHN is applied to find optimal solution corresponding to the chosen fuel types. The proposed method is tested on several systems with various load demands and the obtained test results are compared to those from many other methods in the literature. Test results have indicated that the proposed method is efficient and fast for the ED problems with multiple fuel types represented by quadratic cost functions.
Article
Unit commitment (UC) is one of the most important daily tasks that independent system operators or regional transmission organizations must accomplish in the electric power market. In the conventional UC problem, especially under a deregulated power system, the power schedule is usually taken as an energy schedule. However, this simplification may preclude the realization of the feasible energy delivery in real cases owing to the violation of ramping limits, as shown in the literature. If the power system integrates large-scale wind energy, the above “infeasible’’ energy delivery problem will be worsened, since wind power output will increase the variability of the “net-load” balanced by the thermal units. In this paper, a new UC model is provided that includes the consideration of “feasible” energy delivery under large-scale wind integration. The proposed model can give not only the optimal and feasible energy schedule to thermal units but also a precise ramping process for implementing this schedule. The problem is formulated as a mixed-integer linear programming problem; a 5-unit and a 36-unit system with 25% wind integration are used to test the proposed model. Finally, the numerical results support the conclusions above effectively.
Article
This paper presents an interactive fuzzy satisfying method based on evolutionary programming technique for short-term multiobjective hydrothermal scheduling. The multiobjective problem is formulated considering two objectives: (i) cost and (ii) emission. Assuming that the decision maker (DM) has fuzzy goals for each of the objective functions, evolutionary programming technique based fuzzy satisfying method is applied for generating a corresponding optimal noninferior solution for the DM’s goals. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. A multi-reservoir cascaded hydroelectric system with a nonlinear relationship between water discharge rate, net head and power generation is considered. The water transport delay between connected reservoirs is taken into account. Thermal plants with nonsmooth fuel cost and emission level function are also taken into consideration. Results of the application of the proposed method are presented.
Article
Despite the uncertainty surrounding the design of a mechanism which is ultimately accepted by nations worldwide, the necessity to implement regulations to curb emissions of greenhouse gases on a global scale is consensual. The electricity sector plays a fundamental role in this puzzle and countries may soon have to revise their operating policy directives in order to make them compatible with additional constraints imposed by such regulations. We present a modeling approach for greenhouse gas emissions quotas which can be incorporated into a stochastic dual dynamic programming algorithm, commonly used to solve the hydro-thermal scheduling problem. Our approach is flexible and capable of accommodating a detailed representation of emissions and related constraints. A case study based on the Guatemalan power system exemplifies the potential effects of considering these restrictions.
Article
This paper presents the principle of bushing shield size, position and its covering material determination, based on the optimization algorithm. An optimization procedure has been carried out using a differential evolution (DE) algorithm combined with a solver of the software tool EleFAnT, which is used for solving computationally expensive parametrically-written bushing FEM model. The goal of this research is to accelerate the optimization process, respectively to reduce the computational cost by introducing the Kriging metamodeling.
Article
In this paper, a new approach is proposed to solve the economic load dispatch (ELD) problem. Power generation, spinning reserve and emission costs are simultaneously considered in the objective function of the proposed ELD problem. In this condition, if the valve-point effects of thermal units are considered in the proposed emission, reserve and economic load dispatch (ERELD) problem, a non-smooth and non-convex cost function will be obtained. Frequency deviation, minimum frequency limits and other practical constraints are also considered in this problem. For this purpose, ramp rate limit, transmission line losses, maximum emission limit for specific power plants or total power system, prohibited operating zones and frequency constraints are considered in the optimization problem. A hybrid method that combines the bacterial foraging (BF) algorithm with the Nelder–Mead (NM) method (called BF–NM algorithm) is used to solve the problem. In this study, the performance of the proposed BF–NM algorithm is compared with the performance of other classic (non-linear programming) and intelligent algorithms such as particle swarm optimization (PSO) as well as genetic algorithm (GA), differential evolution (DE) and BF algorithms. The simulation results show the advantages of the proposed method for reducing the total cost of the system.
Conference Paper
This paper presents a novel differential evolution algorithm for optimization of state-of-the-art real world industry challenges. The algorithm includes the self-adaptive jDE algorithm with one of its strongest extensions, population reduction, and is now combined with multiple mutation strategies. The two mutation strategies used are run dependent on the population size, which is reduced with growing function evaluation number. The problems optimized reflect several of the challenges in current industry problems tackled by optimization algorithms nowadays. We present results on all of the 22 problems included in the Problem Definitions for a competition on Congress on Evolutionary Computation (CEC) 2011. Performance of the proposed algorithm is compared to two algorithms from the competition, where the average final best results obtained for each test problem on three different number of total function evaluations allowed are compared.
Article
Export Date: 18 July 2012, Source: Scopus, CODEN: APEND, doi: 10.1016/j.apenergy.2011.06.009, Language of Original Document: English, Correspondence Address: Georgilakis, P.S.; Electric Power Division, School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), GR 15780 Athens, Greece; email: pgeorg@power.ece.ntua.gr, References: Georgopoulou, C.A., Giannakoglou, K.C., Metamodel-assisted evolutionary algorithms for the unit commitment problem with probabilistic outages (2010) Appl Energy, 87, pp. 1782-1792;
Article
a b s t r a c t Short-term hydrothermal coordination (STHTC) is a very complicated optimization problem. It is a dynamic large-scale non-linear problem and requires solving unit commitment and economic power load dispatch problems. From this perspective, many successful and powerful optimization methods and algorithms have been employed to solve this problem. These optimization methodologies and techniques are widely diverse and have been the subject of ongoing enhancements over the years. This paper presents a survey of literature on the various optimization methods applied to solve the STHTC problem. A review and a methodology-based classification of most of the publications on the topic are presented.
Article
This paper presents a study on optimization of a fixed bed tri-reformer reactor (TR). This reactor has been used instead of conventional steam reformer (CSR) and auto thermal reformer (CAR). A theoretical investigation has been performed in order to evaluate the optimal operating conditions and enhancement of methane conversion, hydrogen production and desired H2/CO ratio as a synthesis gas for methanol production. A mathematical heterogeneous model has been used to simulate the reactor. The process performance under steady state conditions was analyzed with respect to key operational parameters (inlet temperature, O2/CH4, CO2/CH4 and steam/CH4 ratios). The influence of these parameters on gas temperature, methane conversion, hydrogen production and H2/CO ratio was investigated. Model validation was carried out by comparison of the reforming model results with industrial data of CSR. Differential evolution (DE) method was applied as a powerful method for optimization. Optimum feed temperature and reactant ratios (CH4/CO2/H2O/O2) are 1100Â K and 1/1.3/2.46/0.47 respectively. The optimized TR has enhanced methane conversion by 3.8% relative to industrial reformers in a single reactor. Methane conversion, hydrogen yield and H2/CO ratio in optimized TR are 97.9%, 1.84 and 1.7 respectively. The optimization results of tri-reformer were compared with the corresponding predictions from process simulation software operated at the same feed conditions.
Article
This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA-PS-SQP algorithm is very efficient in solving power system economic dispatch problem.
Article
This paper presents a novel approach for daily Volt/Var control in distribution systems using Distributed Generation (DG) units. The impact of DG units on Volt/Var control is significant in a distribution network with radial configuration and small X/R ratio. In this paper, a price-based approach is adopted to determine the optimum active and reactive power dispatch for the DG units, the reactive power contribution of the capacitor banks, and the tap settings of the transformers in a day in advance. A fuzzy adaptive particle swarm optimization (FAPSO) method is used to solve the daily Volt/Var control which is a non-linear mixed-integer problem. A mathematical expression of the proposed method and its effectiveness using simulation results are provided.
Article
This paper presents the development of a method to determine the value of forecasting (for load, wind power, etc.) in electricity-generation. An adaptive unit commitment (UC) strategy has been developed for this aim. An electricity generator faces demand with a given uncertainty. Forecasts are made to meet this load at the lowest cost. The adaptive UC strategy can be described as follows. Each hour, the generating company constructs a new forecast for a fixed number of hours. We assume that the first forecasted hour is in fact predicted correctly. For these forecasted hours, an optimal UC schedule is determined (given the on/off states of power plants for the current hour). The solution for the first hour (i.e., the one that was predicted correctly) is retained, and a new forecast is made. A 15,000Â MW power system is used in a 168 hour (one-week) schedule. The UC problems presented in this work are solved through a Mixed-Integer Linear Programming (MILP) approach. In the first case, the effect of limited (correct) forecasting is investigated. Forecasts are made 100% correctly, but the UC scheme is built modularly and compared with the reference case, where the UC problem is solved for the one-week problem as a whole. Depending on the number of forecasted hours, solutions differ by up to 0.5% with the reference case. In a second case, when a certain error is imposed on the forecasts made (up to 5%), the deviations from the optimal solution become larger and amount in certain cases to almost 1%.
Article
Unit Commitment (UC) is a term used for the strategic choice whereby the available power plants have to be on-line every time. Most UC models described in the literature are specifically designed for the power utilities. They are typical short-term models for relatively small power-systems. Apart from practical use in the utilities themselves, UC is also implemented in the broader context of electricity-generation modelling. For these purposes, however, the power systems can be much larger and the time scale more extended. Since UC is only a minor part of these models, the calculation time dedicated to UC has to be limited, thereby possibly sacrificing somewhat on accuracy. Two methods are compared. Unit Decommitment (UD), which is considered completely accurate and Advanced Priority Listing, which is less accurate but also less complicated. Simulations demonstrate that UD is slightly more accurate (0.03-0.6%), but takes much more calculation time (5-10 times more) than Advanced Priority Listing.
Chapter
Differential Evolution (DE) algorithms belong to Evolutionary Algorithms (EAs). They are widely used for optimizing continuous functions. In this chapter we present a self-adaptive differential evolution algorithm which uses (1) a self-adaptive mechanism on control parameters F and CR, (2) more strategies during the mutation operation, (3) a population size (NP) reduction mechanism during the evolutionary process, and (4) the ε constrained method. The performance of our algorithm is reported over the set of twenty four CEC2006 constrained benchmark functions.