Differential evolution combined with clonal selection for dynamic economic dispatch

Dynamic economic load dispatch (DELD) is one of the most important steps in power system operation. Various optimisation algorithms for solving the problem have been developed; however, due to the non-convex characteristics and large dimensionality of the problem, it is necessary to explore new methods to further improve the dispatch results and minimise the costs. This article proposes a hybrid differential evolution (DE) algorithm, namely clonal selection-based differential evolution (CSDE), to solve the problem. CSDE is an artificial intelligence technique that can be applied to complex optimisation problems which are for example nonlinear, large scale, non-convex and discontinuous. This hybrid algorithm combines the clonal selection algorithm (CSA) as the local search technique to update the best individual in the population, which enhances the diversity of the solutions and prevents premature convergence in DE. Furthermore, we investigate four mutation operations which are used in CSA as the hyper-mutation operations. Finally, an efficient solution repair method is designed for DELD to satisfy the complicated equality and inequality constraints of the power system to guarantee the feasibility of the solutions. Two benchmark power systems are used to evaluate the performance of the proposed method. The experimental results show that the proposed CSDE/best/1 approach significantly outperforms nine other variants of CSDE and DE, as well as most other published methods, in terms of the quality of the solution and the convergence characteristics.

A hybrid harmony search with arithmetic crossover operation for economic dispatch

Economic dispatch (ED) problems often exhibit non-linear, non-convex characteristics due to the valve point effects. Further, various constraints and factors, such as prohibited operation zones, ramp rate limits and security constraints imposed by the generating units, and power loss in transmission make it even more challenging to obtain the global optimum using conventional mathematical methods. Meta-heuristic approaches are capable of solving non-linear, non-continuous and non-convex problems effectively as they impose no requirements on the optimization problems. However, most methods reported so far mainly focus on a specific type of ED problems, such as static or dynamic ED problems. This paper proposes a hybrid harmony search with arithmetic crossover operation, namely ACHS, for solving five different types of ED problems, including static ED with valve point effects, ED with prohibited operating zones, ED considering multiple fuel cells, combined heat and power ED, and dynamic ED. In this proposed ACHS, the global best information and arithmetic crossover are used to update the newly generated solution and speed up the convergence, which contributes to the algorithm exploitation capability. To balance the exploitation and exploration capabilities, the opposition based learning (OBL) strategy is employed to enhance the diversity of solutions. Further, four commonly used crossover operators are also investigated, and the arithmetic crossover shows its efficiency than the others when they are incorporated into HS. To make a comprehensive study on its scalability, ACHS is first tested on a group of benchmark functions with a 100 dimensions and compared with several state-of-the-art methods. Then it is used to solve seven different ED cases and compared with the results reported in literatures. All the results confirm the superiority of the ACHS for different optimization problems.

A biogeography-based optimization algorithm with mutation strategies for model parameter estimation of solar and fuel cells

Mathematical models are useful tools for simulation, evaluation, optimal operation and control of solar cells and proton exchange membrane fuel cells (PEMFCs). To identify the model parameters of these two type of cells efficiently, a biogeography-based optimization algorithm with mutation strategies (BBO-M) is proposed. The BBO-M uses the structure of biogeography-based optimization algorithm (BBO), and both the mutation motivated from the differential evolution (DE) algorithm and the chaos theory are incorporated into the BBO structure for improving the global searching capability of the algorithm. Numerical experiments have been conducted on ten benchmark functions with 50 dimensions, and the results show that BBO-M can produce solutions of high quality and has fast convergence rate. Then, the proposed BBO-M is applied to the model parameter estimation of the two type of cells. The experimental results clearly demonstrate the power of the proposed BBO-M in estimating model parameters of both solar and fuel cells.

An efficient harmony search with new pitch adjustment for dynamic economic dispatch

A simple yet efficient harmony search (HS) method with a new pitch adjustment rule (NPAHS) is proposed for dynamic economic dispatch (DED) of electrical power systems, a large-scale non-linear real time optimization problem imposed by a number of complex constraints. The new pitch adjustment rule is based on the perturbation information and the mean value of the harmony memory, which is simple to implement and helps to enhance solution quality and convergence speed. A new constraint handling technique is also developed to effectively handle various constraints in the DED problem, and the violation of ramp rate limits between the first and last scheduling intervals that is often ignored by existing approaches for DED problems is effectively eliminated. To validate the effectiveness, the NPAHS is first tested on 10 popular benchmark functions with 100 dimensions, in comparison with four HS variants and five state-of-the-art evolutionary algorithms. Then, NPAHS is used to solve three 24-h DED systems with 5, 15 and 54 units, which consider the valve point effects, transmission loss, emission and prohibited operating zones. Simulation results on all these systems show the scalability and superiority of the proposed NPAHS on various large scale problems.

An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models

Clean and renewable energy generation and supply has drawn much attention worldwide in recent years, the proton exchange membrane (PEM) fuel cells and solar cells are among the most popular technologies. Accurately modeling the PEM fuel cells as well as solar cells is critical in their applications, and this involves the identification and optimization of model parameters. This is however challenging due to the highly nonlinear and complex nature of the models. In particular for PEM fuel cells, the model has to be optimized under different operation conditions, thus making the solution space extremely complex. In this paper, an improved and simplified teaching-learning based optimization algorithm (STLBO) is proposed to identify and optimize parameters for these two types of cell models. This is achieved by introducing an elite strategy to improve the quality of population and a local search is employed to further enhance the performance of the global best solution. To improve the diversity of the local search a chaotic map is also introduced. Compared with the basic TLBO, the structure of the proposed algorithm is much simplified and the searching ability is significantly enhanced. The performance of the proposed STLBO is firstly tested and verified on two low dimension decomposable problems and twelve large scale benchmark functions, then on the parameter identification of PEM fuel cell as well as solar cell models. Intensive experimental simulations show that the proposed STLBO exhibits excellent performance in terms of the accuracy and speed, in comparison with those reported in the literature.

Enhanced durability of Li-O2 batteries employing vertically standing Ti nanowire array supported cathodes

Ti nanowire arrays vertically standing on Ti foam prepared by a facile corrosion method were used as self-supported Li-O₂ battery cathodes. The batteries exhibited enhanced durability at high rate current densities (e.g. cycling 640 times at 5 A g^-1).