On-line emission and economic load dispatch using adaptive Hopfield neural network

This paper presents an adaptive Hopfield neural network (AHNN) based methodology, where the slope of the activation function is adjusted, for finding approximate Pareto solutions for the multi-objective optimization problem of emission and economic load dispatch (EELD). We have placed emphasis on finding solutions quickly, rather than the global Pareto solutions, so that our algorithm can be employed in large on-line power systems where variations in load are quite frequent. To enable faster convergence, adaptive learning rates have been developed by using energy function and applied to the slope adjustment method. The proposed algorithm has been tested on selected IEEE bus benchmark systems. The convergence of AHNN is found to be nearly 50% faster than the non-adaptive version.     

基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度和经济排放联合调度问题

电力生产装置运行中各种燃料的成本逐步增加,需要最小化成本函数以求解此类复杂经济负荷调度问题.鉴于此,提出一种基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度(economic load dispatch, ELD)问题和经济排放联合调度(combined economic emission dispatch, CEED)问题.为了提高蚱蜢算法(grasshopper optimization algorithm, GOA)性能,提出一种改进的混合蚱蜢算法(hybrid grasshopper optimization algorithm, HGOA),将重力搜索算子和鸽群搜索算子-地标算子加入GOA中,增强算法的搜索能力,平衡算法的勘探和开发.同时,为了更好地解决ELD和CEED问题中的约束问题,提出6个惩罚函数,包括2个V型函数、反正切函数、反正弦函数、线性函数和二次函数,并使用动态惩罚策略代替传统的固定值惩罚策略.选取3个ELD问题案例和4个CEED问题案例验证所提出方法的有效性,实验结果表明, HGOA相较于其他元启发式算法在求解质量上表现更好,且动态惩罚策略比固定值惩罚策略效果更...     

Quantum-behaved bat algorithm for many-objective combined economic emission dispatch problem using cubic criterion function

In this research, a quantum computing idea based bat algorithm (QBA) is proposed to solve many-objective combined economic emission dispatch (CEED) problem. Here, CEED is represented using cubic criterion function to reduce the nonlinearities of the system. Along with economic load dispatch, emissions of SO₂, NO_x, and CO₂ are considered as separate three objectives, thus making it a four-objective (many-objective) optimization problem. A unit-wise price penalty factor is considered here to convert all the objectives into a single objective in order to compare the final results with other previously used methods like Lagrangian relaxation (LR), particle swarm optimization, and simulated annealing. QBA is applied in six-unit power generation system for four different loads. The obtained results show QBA successfully solve many-objective CEED problem with greater superiority than other methods found in the literature in terms of quality results, robustness, and computational performance. In the end of this paper, a detailed future research direction is provided based on the simulation results and its analysis. The outcome of this research demonstrates that the inclusion of quantum computing idea in metaheuristic technique provides a useful and reliable tool for solving such many-objective optimization problem.

     

Recurrent neural network modeling combined with bilinear model structure

In this paper, we propose a neural network modeling scheme for nonlinear systems. The proposed architecture is a new combination of neural network and bilinear system model in which the terms of cross-products of input and output signals within the bilinear model are taken as the inputs into the neural network. Compared with the original bilinear system, this kind of network model possesses much more adjustable parameters to fulfill the system identification. Moreover, instead of the general back-propagation method an evolutionary computation called the differential evolution algorithm is presented to update the network parameters. This algorithm is with multiple direction searches toward the global optimal solution for given optimization problem. To show the feasibility of the proposed scheme, a nonlinear chemical process system of continuously stirred tank reactor is illustrated. Many simulations and examinations are considered to verify the robustness of the proposed neural network structure on the modeling performance, including different sets of initial conditions of the algorithm and model orders.     

Simulated annealing algorithm for combined economic and emission power dispatch using max/max price penalty factor

A new recurrent neural model for crack growth process of aluminium alloy is developed in this work. It is shown that a recurrent neural network with the feedback loops at the output layer is constructed to model the dynamic relationship between the crack growth and cyclic stress excitations of aluminium alloy. The output feedback loops in the neural model play the role of capturing the fine changes of crack growth dynamics. The Extreme Learning Machine is then used to uniformly randomly assign the input weights in a proper range and globally optimize both the output weights and feedback parameters, to ensure that the dynamics of crack growth under variable-amplitude loading can be accurately modeled. The simulation results with the averaged experimental data of the 2024-T351 aluminium alloy show that the excellent modeling and prediction performance of the recurrent neural model can be achieved for fatigue crack growth of aluminium alloys.     

Bee colony optimization for combined heat and power economic dispatch

This paper presents a novel optimization approach to the combined heat and power economic dispatch problem by using bee colony optimization algorithm. The algorithm is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The performance of the proposed algorithm is validated by illustration with a test system. The results of the proposed approach are compared with those of particle swarm optimization, real-coded genetic algorithm and evolutionary programing techniques. From numerical results, it is seen that bee colony optimization based approach is able to provide a better solution at a lesser computational effort.     

Solving the multi-objective economic emission dispatch problems using Fast Non-Dominated Sorting TVAC-PSO combined with EMA

In this study, the Fast Non-Dominated Time-Varying Acceleration Coefficient-Particle Swarm Optimization (TVAC-PSO) combined with Exchange Market Algorithm (EMA) is proposed to solve the economic emission dispatch problems consisting of Combined Heat and Power Economic Emission Dispatch (CHPEED) and Dynamic Economic Emission Dispatch (DEED) multi-objective optimization problems considering operational constraints. A two-stage approach has been used to select the Best Compromise Solutions (BCSs), as the best solution which minimizes the operational cost and emission, simultaneously. For this purpose, at the first stage, applying Fuzzy Clustering Mean (FCM), the obtained Pareto Optimal Front (POF) is divided into several separated clusters. Then, using the Technique for Order of Performance by Similarity to Ideal Solution (TOPSIS), a single BCS is selected among each cluster. At first, the superiority of the proposed algorithm is evaluated on a number of benchmark functions, as well as the 48-unit CHPED test case. Then, to demonstrate the ability of the proposed algorithm in solving the multi-objective problem by finding the POF, the presented method has been applied to three case studies, and the results are compared with other algorithms in this field. Furthermore, a new test case is presented to confirm the proposed algorithm’s performance. The results verify the proposed method’s superiority over other available techniques in the literature. One of the most important novelty of this study is solving a multi-objective DEED problem considering the Ramp Rate Limits (RRLs), Valve Point Loading Effect (VPLE), power transmission loss impact, Spinning Reserve Requirements (SRRs), Prohibited Operating Zones (POZs) and Multiple Fuel Units (MFUs) simultaneously, for the first time.     

An economic dispatch algorithm of combined cycle units

This paper presents a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle (CC) units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying the total demand and generating-capacity constraints. A CC unit presents multiple configurations or states, each state having its own unique cost curve. Therefore, in performing ED, we need to be able to shift between these cost curves. Moreover, the cost curve is not convex for some of these states. Hence, ED becomes a non-convex optimization problem, which is difficult to solve by conventional methods. In this paper we present a new technique, developed to find the global solution, that is based on the calculation of the infimal convolution. The paper includes the results for a case test and we compare our solution with other techniques.     

Differential evolution with Gaussian mutation for combined heat and power economic dispatch

This paper presents differential evolution with Gaussian mutation to solve the complex non-smooth non-convex combined heat and power economic dispatch (CHPED) problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. Differential evolution (DE) is a simple yet powerful global optimization technique. It exploits the differences of randomly sampled pairs of objective vectors for its mutation process. This mutation process is not suitable for complex multimodal optimization. This paper proposes Gaussian mutation in DE which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the simplicity of the structure of DE. The effectiveness of the proposed method has been verified on five test problems and three test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed differential evolution with Gaussian mutation-based approach is able to provide better solution.     

求解广义特征根问题的反馈神经网络方法

研究了广义特征根问题求解的神经网络方法,给出了求解该问题的一个时间连续性反馈网络模型,利用LaSalle不变原理分析并证明了该网络的拟全局收敛性,这是网络能够确切的求解广义特征根问题的保证．同时,该网络解决了已有的基于罚函数方法构造的特征根问题的神经网络存在的一些基本缺陷:其一,基于罚函数的网络模型所得到的解可能不是真解,甚至可能都不是可行解;其二,它们的共同缺陷是有一个需要调节的参数,但是参数的选择并没有一个可供参考的准则;其三,这些模型的稳定性无法保证．本文所提出的网络模型解决了这些问题,并且,此网络具有一个很好的特征就是在初始点选定在问题的可行解集的话,网络轨线将永远是可行的并收敛到一个广义特征向量．最后,数值模拟也表明这里所提出的网络的可靠性能,进一步证明了此网络可以很好地求解广义特征根问题．     

Recurrent neural network with attention mechanism for language model

Neural Computing and Applications - The rapid growth of the Internet promotes the growth of textual data, and people get the information they need from the amount of textual data to solve problems....     

智能水滴算法与SQP相混合的电力环境经济调度

电力环境经济调度对于降低发电过程中煤耗成本和污染气体排放有着重要意义。本文给出一种智能水滴算法（intelligent water drops,IWD）和序列二次规划（sequential quadratic programming,SQP）相混合求解电力环境经济调度问题的方法（IWD-SQP）。针对SQP全局搜索弱的缺点,将智能水滴算法应用于求解连续优化问题,同时将每次迭代过程中水滴所产生的解作为序列二次规划初始解进行微调以得到更好的解。将提出的方法应用于一个10机组测试系统进行实验,与其他方法求解考虑阀点效应的电力环境经济调度问题相比,验证了IWD-SQP的可行性和有效性。     

Symbiotic organisms search optimization algorithm for economic/emission dispatch problem in power systems

This paper presents symbiotic organisms search (SOS) algorithm to solve economic emission load dispatch (EELD) problem for thermal generators in power systems. The basic objective of the EELD is to minimize both minimum operating costs and emission levels, while satisfying the load demand and all equality–inequality constraints. In other research direction, this multi-objective problem is converted into single-objective function by using price penalty factor approach in order to solve it with SOS. The proposed algorithm has been implemented on various test cases, with different constraints and various cost curve nature. In order to see the effectiveness of the proposed algorithm, its results are compared to those reported in the recent literature. The results of the algorithms indicate that SOS gives good results in both systems and very competitive with the state of the art for the solution of the EELD problems.

     

Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch

This paper proposes an improved multi-objective differential evolutionary algorithm named multi-objective hybrid differential evolution with simulated annealing technique (MOHDE-SAT) to solve dynamic economic emission dispatch (DEED) problem. The proposed MOHDE-SAT integrates the orthogonal initialization method into the differential evolution, which enlarges the population diversity at the beginning of population evolution. In addition, modified mutation operator and archive retention mechanisms are used to control convergence rate, and simulated annealing technique and entropy diversity method are utilized to adaptively monitor the population diversity as the evolution proceeds, which can properly avoid the premature convergence problem. Furthermore, the MOHDE-SAT is applied on the thermal system with a heuristic constraint handling method, and obtains more desirable results in comparison to those alternatives established recently. The obtained results also reveal that the proposed MOHDE-SAT can provide a viable way for solving DEED problems.     

Recurrent neural network training with feedforward complexity

This paper presents a training method that is of no more than feedforward complexity for fully recurrent networks. The method is not approximate, but rather depends on an exact transformation that reveals an embedded feedforward structure in every recurrent network. It turns out that given any unambiguous training data set, such as samples of the state variables and their derivatives, we need only to train this embedded feedforward structure. The necessary recurrent network parameters are then obtained by an inverse transformation that consists only of linear operators. As an example of modeling a representative nonlinear dynamical system, the method is applied to learn Bessel's differential equation, thereby generating Bessel functions within, as well as outside the training set.     

An effective cuckoo search algorithm for large-scale combined heat and power economic dispatch problem

Neural Computing and Applications - This paper develops an effective cuckoo search algorithm (ECSA) for searching optimal solutions for the problem of combined heat and power economic dispatch. The...     

自适应差分进化算法及对动态环境经济调度问题应用

为了应对动态环境经济调度(DEED)问题的高维性和大规模约束性,提出了一种自适应多目标差分进化算法(ADEA)。设计自适应差分交叉模块,提出改进的current to best/1交叉策略提高种群的多样性,有效地提高传统进化算法的探索与开采能力,提出一种修补策略处理功率平衡约束和爬坡率约束。为了验证该方法的有效性,数值仿真将ADEA应用于10机系统进行测试,并与同类算法展开比较,仿真结果表明ADEA具有较好的收敛能力,获得的Pareto前沿具有较好的均匀性和延展性,通过模糊决策获得的最好折中解能为电力系统调度人员提供较为合理的调度方案。     

Recurrent neural network approach for cyclic job shop scheduling problem

While cyclic scheduling is involved in numerous real-world applications, solving the derived problem is still of exponential complexity. This paper focuses specifically on modelling the manufacturing application as a cyclic job shop problem and we have developed an efficient neural network approach to minimise the cycle time of a schedule. Our approach introduces an interesting model for a manufacturing production, and it is also very efficient, adaptive and flexible enough to work with other techniques. Experimental results validated the approach and confirmed our hypotheses about the system model and the efficiency of neural networks for such a class of problems.     

An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch

Economic dispatch is carried out at the energy control center to find out the optimal output of thermal generating units such that power balance criterion is met, unit operating limits are satisfied and the fuel cost is minimized. With growing environmental awareness and strict government regulations throughout the world, it has become essential to optimize not only the total fuel cost but also the harmful emissions, both, under static as well as dynamic conditions. The static environment economic dispatch finds the optimal output of generating units for a fixed load demand at a given time, while the dynamic environmental economic dispatch schedules the output of online generators with changing power demands over a certain time period (normally one day) so as to minimize these two conflicting objectives, simultaneously. In this paper, the price penalty factor approach is employed for simultaneous minimization of cost and emission. The generator ramp rate constraints, non-convex and discontinuous nature of cost function and the large number of generators in practical power plants, make this problem very difficult to solve. Here, a fuzzy ranking approach is employed to identify the solution which offers the best compromise between cost and emission objectives.     

Recurrent neural network as a linear attractor for pattern association

We propose a linear attractor network based on the observation that similar patterns form a pipeline in the state space, which can be used for pattern association. To model the pipeline in the state space, we present a learning algorithm using a recurrent neural network. A least-squares estimation approach utilizing the interdependency between neurons defines the dynamics of the network. The region of convergence around the line of attraction is defined based on the statistical characteristics of the input patterns. Performance of the learning algorithm is evaluated by conducting several experiments in benchmark problems, and it is observed that the new technique is suitable for multiple-valued pattern association.