Abstract:The integration of different energy resources from traditional power systems presents new challenges for real-time implementation and operation. In the last decade, a way has been sought to optimize the operation of small microgrids (SMGs) that have a great variety of energy sources (PV (photovoltaic) prosumers, Genset CHP (combined heat and power), etc.) with uncertainty in energy production that results in different market prices. For this reason, metaheuristic methods have been used to optimize the decision… Show more
“…With this purpose, the CE-CMAES algorithm was applied to solve the problem. To prove its effectiveness, the results of CE-CMAES were compared with 11 algorithms participating in the 2020 competition on "Evolutionary Computation in the Energy Domain: Smart Grid Applications" [36,38]. The MATLAB™ codes of the participating algorithms are available at http://www.gecad.isep.ipp.pt/ERM-competitions/2020-2 (accessed on 18 June 2022).…”
Section: Case Study and Results Analysismentioning
The increased penetration of renewables in power distribution networks has motivated significant interest in local energy systems. One of the main goals of local energy markets is to promote the participation of small consumers in energy transactions. Such transactions in local energy markets can be modeled as a bi-level optimization problem in which players (e.g., consumers, prosumers, or producers) at the upper level try to maximize their profits, whereas a market mechanism at the lower level maximizes the energy transacted. However, the strategic bidding in local energy markets is a complex NP-hard problem, due to its inherently nonlinear and discontinued characteristics. Thus, this article proposes the application of a hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem. The proposed CE-CMAES uses cross entropy for global exploration of search space and covariance matrix adaptation evolution strategy for local exploitation. The CE-CMAES prevents premature convergence while efficiently exploring the search space, thanks to its adaptive step-size mechanism. The performance of the algorithm is tested through simulation in a practical distribution system with renewable energy penetration. The comparative analysis shows that CE-CMAES achieves superior results concerning overall cost, mean fitness, and Ranking Index (i.e., a metric used in the competition for evaluation) compared with state-of-the-art algorithms. Wilcoxon Signed-Rank Statistical test is also applied, demonstrating that CE-CMAES results are statistically different and superior from the other tested algorithms.
“…With this purpose, the CE-CMAES algorithm was applied to solve the problem. To prove its effectiveness, the results of CE-CMAES were compared with 11 algorithms participating in the 2020 competition on "Evolutionary Computation in the Energy Domain: Smart Grid Applications" [36,38]. The MATLAB™ codes of the participating algorithms are available at http://www.gecad.isep.ipp.pt/ERM-competitions/2020-2 (accessed on 18 June 2022).…”
Section: Case Study and Results Analysismentioning
The increased penetration of renewables in power distribution networks has motivated significant interest in local energy systems. One of the main goals of local energy markets is to promote the participation of small consumers in energy transactions. Such transactions in local energy markets can be modeled as a bi-level optimization problem in which players (e.g., consumers, prosumers, or producers) at the upper level try to maximize their profits, whereas a market mechanism at the lower level maximizes the energy transacted. However, the strategic bidding in local energy markets is a complex NP-hard problem, due to its inherently nonlinear and discontinued characteristics. Thus, this article proposes the application of a hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem. The proposed CE-CMAES uses cross entropy for global exploration of search space and covariance matrix adaptation evolution strategy for local exploitation. The CE-CMAES prevents premature convergence while efficiently exploring the search space, thanks to its adaptive step-size mechanism. The performance of the algorithm is tested through simulation in a practical distribution system with renewable energy penetration. The comparative analysis shows that CE-CMAES achieves superior results concerning overall cost, mean fitness, and Ranking Index (i.e., a metric used in the competition for evaluation) compared with state-of-the-art algorithms. Wilcoxon Signed-Rank Statistical test is also applied, demonstrating that CE-CMAES results are statistically different and superior from the other tested algorithms.
“…Brute or exhaustive search algorithm is a set of instruction used to find optimal solution by examining all possible solution combinations. This search process is not that new at all, it has been applied in several optimization problems to search for the most deemed optimal solution [12,23,25].…”
“…Also, in [26] static and dynamic predictor weighting strategies were implemented and tested to improve the analog ensemble performance for wind power forecasting at on and offshore wind farms by using a brute force search procedure with error minimization over all possible predictor combinations. Usually, the general basic algorithm that follows an exhaustive or brute force search require two main stages: namely, Listing all the possible candidate solutions in a systematic way, and checking for the optimal solution and reporting it [12]. While the main disadvantage of brute exhaustive technique being its requirement for massive computational resources in order to find solutions in very large search spaces and which may sometimes makes it slow and infeasible [27], a drawback which can be addressed by using the search space reduction and algorithm parallelization strategies such as using parallel CPU-GPU computing structure.…”
“…However, although both the stochastic population-based evolutionary and greedybased search heuristic procedures are often more efficient than brute exhaustive search, they may sometimes not guarantee to achieve of global optimum [6,7], whereas greedy and its variant implementation, such as the greedy randomized adaptive search which have been used by (8) may face a hill climbing problem, the evolutionary extremums may be caused by its population-based stochastic search heuristic implementation which may probabilistically select at that one time from a very unfit initialized genes chromosomes of the creature being optimized [9], among other things. As such, as observed in [10], the surprising outstanding successes of the systematic brute force-based exhaustive search counterpart in producing optimal WVE models configuration sets with predictive performances similar to those created by evolutionary-based optimization procedures in conjunction with its theoretical guarantee for finding an optimal solution through a search across systematic search spaces [11], it may become imperative to implement the brute exhaustive search procedures, as given the required high computational effort is available, it guarantees exhaustion of all candidate solutions combinations [11,12], for optimality search problems, such as this of finding the appropriate weights for the most accurate WVE, at a reasonable efficiency tradeoff when the deemed global optima solution estimations has been defined as a key requirement, that is, must occur.…”
Other than the individual machine learning models' capabilities, the weighted voting ensemble (WVE) technique relies on appropriate weight assignment in order to significantly realize prediction performance improvement. Often evolutionary global or grid local search heuristics are being applied for such a challenging optimization task. However, these techniques do not guarantee optimal solution finding. In turn, the surprising outstanding successes of brute exhaustive search procedure in producing similar results shed light on its significance and the need to exploit its possible weights solutions search space(s) with corresponding sizes as a key determinant factor for implementing a successful brute search procedure for finding optimal WVE solution with a trade-off the computational efficiency. This paper formulates an asymptotically WVE weights domain constraints optimal 1EX(-)Z + initial term-based arithmetic sequences initialization function, and then a computational multi-precision search space-based generation algorithm is developed to find optimal WVE solution as part of the brute exhaustive search procedure. It took 45 minutes for a proposed algorithm to generate 133,192 combinations and find the optimal solution in weights space of precision 0.01.
“…The authors of [28] solved the reactive power optimization problem by using an adaptive differential evolution method. Several heuristic algorithms were utilized for parallel computing in solving bidding problems in local energy markets in [29]. A parallel particle swarm optimization was used in [30] to maximize the profits of the industrial customers that provide operational services to the power grid.…”
The optimum penetration of distributed generations into the distribution grid provides several technical and economic benefits. However, the computational time required to solve the constrained optimization problems increases with the increasing network scale and may be too long for online implementations. This paper presents a parallel solution of a multi-objective distributed generation (DG) allocation and sizing problem to handle a large number of computations. The aim is to find the optimum number of processors in addition to energy loss and DG cost minimization. The proposed formulation is applied to a 33-bus test system, and the results are compared with themselves and with the base case operating conditions using the optimal values and three popular multi-objective optimization metrics. The results show that comparable solutions with high-efficiency values can be obtained up to a certain number of processors.
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