Determination methodology for optimising the energy storage size for power system

A methodology for determining the optimal size of energy storage system (ESS) integrated with thermal power system is presented in this study. The optimal size is characterised by the rated stored energy and the maximum power rating of installed ESS for which the power system can achieve maximum revenue. Therefore the ESS cost formulation is conducted by analysing economic cost benefit measures considering life cycle of ESS. Since unit commitment (UC) scheduling is an important and integral part of power system cost optimisation, this study considers the operating schedule of thermal units (TU) while resolving ESS schedule. This proposed method uses tabu search (TS)-based evolutionary technique for solving this optimisation problem. TS is included in this algorithm to avoid re-evaluation of already evaluated ESS size which is powered by max priority heap and hash table data structure. The weekly schedule period is considered instead of daily to achieve more precise results. The proposed method is applied in two different power systems to determine the appropriate size of to be installed ESS. Experimental results reported that establishing the proposed method is an effective one to compute the optimal size of ESS for different sized power systems.     

Optimising the spinning reserve requirements considering failures to synchronise

System operators use spinning reserve (SR) to respond to unforeseen events such as generation outages and unforeseen load changes. The amount of SR that a system must carry is usually determined on the basis of deterministic criteria such as the capacity of the largest synchronised generating unit or a given percentage of the load. Several authors have argued that these deterministic criteria are sub-optimal. They have proposed various techniques to adjust the SR requirements considering the likelihood and the consequences of the failure of one or more of the generating units that are synchronised to the system. However, so far none of these approaches has considered explicitly in the optimisation the significant danger associated with the failure of generating units to synchronise with the system in a timely fashion. A three-state reliability model for generating units that takes into account not only the probability of failing while operating but also the probability of failing to synchronise is proposed. This model is then used in a cost/benefit analysis to estimate the SR requirements at each period of the optimisation horizon. Finally, a reserve-constrained unit commitment programme that enforces these requirements is used to find the optimal generation schedule. This optimal approach is compared with existing heuristic approaches on the basis of the IEEE-RTS system.     

Economic-emission load dispatch using binary successive approximation-based evolutionary search

A novel binary successive approximation-based evolutionary search strategy has been proposed to solve the economic-emission load dispatch problem by searching the generation pattern of committed units. Inequality constraints are taken care of during the search of a generation pattern. To meet the demand, a slack generator is introduced to compensate the perturbation of unmet load during the search. To determine the trade-off relationship between conflicting objectives in the non-inferior domain, the weighting method is exploited. Once the trade-off has been obtained, fuzzy set theory helps the decision maker to choose the optimal operating point over the trade-off curve and adjust the generation schedule in the most preferred manner. Generally the weights are regulated in a systematic manner, which is a time-consuming process. To reduce the time to arrive at the best compromising solutions, the weight pattern assigned to objectives are searched for more significant digits in a fixed number of iterations. Performance of the algorithm is investigated on economic load dispatch problems of different sizes and complexity having non-convex cost curves where conventional gradient-based methods are inapplicable. This technique has emerged as the useful optimisation tool for handling network losses, ramp rate limits, valve point loading and prohibited zone avoidance into account to determine the global optimal dispatch solution as well as optimal operating point in the noninferior domain for any number of the goals. The method is applied on various test systems and better results are achieved with reference to emission (Kg/h), however when compared with other techniques, the proposed method has lower performance with reference to losses (MW) and cost ($/h).     

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.     

Maclaurin series-based lagrangian method for economic dispatch with valve-point effect

Power utilities in general use Lagrangian method to solve economic dispatch (ED) problem for ease of implementation. This is possible only if the cost function of generating units is convex. Owing to valve-point effect exhibited by multi-valve steam turbines, the cost function is non-convex. The Maclaurin series-based Lagrangian method is proposed to solve complicated, non-convex and non-linear ED problems. In this method, the rectified sinusoid function is represented by Maclaurin sine series expansion and is solved using the Lagrangian method. The problem is solved iteratively using lambda iteration method. The proposed methodology is validated using IEEE 30-bus test system. In addition, the effectiveness of the new algorithm is demonstrated with 3, 13 and 40 generator test systems available in the literature. The results obtained substantiate the applicability of the proposed method for solving ED problems with non-smooth cost functions at par with stochastic search techniques generally used.     

Ant colony optimisation algorithm for distribution-allocation problem in a two-stage supply chain with a fixed transportation charge

In a fixed charge transportation problem, each route is associated with a fixed charge (or a fixed cost) and a transportation cost per unit transported. The presence of the fixed cost makes the problem difficult to solve, thereby requiring the use of heuristic methods. In this paper, an algorithm based on ant colony optimisation is proposed to solve the distribution-allocation problem in a two-stage supply chain with a fixed transportation cost for a route. A numerical study on benchmark problem instances has been carried out. The results obtained for the proposed algorithm have been compared with that for the genetic algorithm-based heuristic currently available in the literature. It is statistically confirmed that the proposed algorithm provides significantly better solutions.     

Unit commitment in oligopolistic markets by nonlinear mixed variable programming

In the paper we consider the unit commitment problem in oligopolistic markets. The formulation of the problem involves both integer and continuous variables and nonlinear functions as well, thus yielding a nonlinear mixed variable programming problem. Our formulation takes into account all technical constraints for the generating units, such as ramp rate and minimum up and down time constraints, considers the uncertainty related to the selling prices and allows modeling their dependence on the total output of a producer. The objective function is the expected value of the revenue over the different scenarios minus a term which takes into account the risk related to the decision. To solve the problem we adopt a recently proposed method for mixed integer nonlinear programming problems and use a derivative free algorithm to solve the continuous subproblems. We report results for two operators: one managing a single unit and the other managing three units. Numerical results give evidence to the features of the modeling and show viability of the adopted algorithm.     

Tabu search for the redundancy allocation problem of homogenous series–parallel multi-state systems

This paper develops an efficient tabu search (TS) heuristic to solve the redundancy allocation problem for multi-state series–parallel systems. The system has a range of performance levels from perfect functioning to complete failure. Identical redundant elements are included in order to achieve a desirable level of availability. The elements of the system are characterized by their cost, performance and availability. These elements are chosen from a list of products available in the market. System availability is defined as the ability to satisfy consumer demand, which is represented as a piecewise cumulative load curve. A universal generating function technique is applied to evaluate system availability. The proposed TS heuristic determines the minimal cost system configuration under availability constraints. An originality of our approach is that it proceeds by dividing the search space into a set of disjoint subsets, and then by applying TS to each subset. The design problem, solved in this study, has been previously analyzed using genetic algorithms (GAs). Numerical results for the test problems from previous research are reported, and larger test problems are randomly generated. Comparisons show that the proposed TS out-performs GA solutions, in terms of both the solution quality and the execution time.     

计及网损的快速经济调度方法

若网损近似为常数,对机组费用曲线满足凸特性的经济调度可解析求解,而网损实际是随机组功率变动而变动的,使这一解析求解的方法不能直接使用。对此,借助网损与机组功率间存在的线性凸特性的规律,依据潮流方程,提出网损随机组功率变动的快速经济调度算法,该算法将网损变动的经济调度问题转化成网损不变经济调度可解析的序列组合,使其在单调有限次代数计算后获得经济调度最优解。     

A BEST-FIRST SEARCH STRATEGY FOR ENERGY RELAXATION IN MER HEAT EXCHANGER NETWORKS

The pinch design method efficiently generates a maximum energy recovery (MER) network which meets the utility targets for a given value of the minimum approach temperature difference. However, this MER design usually contains a significantly greater number of heat exchanger units than the theoretical minimum. Loop breaking and energy relaxation may be used to eliminate these additional units. At each stage of loop breaking, it has been recommended that the unit with the smallest heat load should be removed. However, this study shows that this heuristic can lead to suboptimal designs with respect to energy consumption. An alternative systematic method is presented which reduces the number of units such that the energy penalty is a minimum. A mixed integer non-linear program (MINLP) is formulated with the objective of minimizing the energy consumption for a given number of units. Subsequent loop-network interaction analysis helps in identifying the exchanger units which are good candidates for removal. A lower bound on the consequent energy penalty is also evaluated. These bounds are employed in a ‘best-first’ search strategy to solve the proposed model. On removal of the candidate unit/units, the resulting topology transforms the MINLP to a non-linear/linear program (NLP/LP) which is solved by conventional algorithms. A loop and path identification algorithm (LAPIT), based on graph theory, has been developed as an aid to these computations.     

Robust single machine scheduling with uncertain release times for minimising the maximum waiting time

We study a single machine scheduling problem (SMSP) with uncertain job release times (JRTs) under the maximum waiting time (MWT) criterion. To deal with the uncertainty, a robust model is established to find an optimal schedule, which minimises the worst-case MWT (W-MWT) when JRTs vary over given time intervals. Although infinite possible scenarios for JRTs exist, we show that only n scenarios are needed for calculating the W-MWT, where n is the number of jobs. Based on this property, the robust (SMSP) with uncertain JRTs to minimise the W-MWT is formulated as a mixed integer linear programming problem. To solve large-size problem instances, an efficient two-stage heuristic (TSH) is proposed. In the first stage, n near-optimal schedules are obtained by solving n deterministic scenario-based SMSPs, and their W-MWTs are evaluated. To speed up the solution and evaluation process, a modified Gusfield’s heuristic is proposed by exploiting the inner connections of these SMSPs. To further improve the schedule obtained in the first stage, the second stage consists of a variable neighbourhood search method by combining both swap neighbourhood search and insert neighbourhood search. We also develop a method to calculate the lower bound of the proposed model so that we can evaluate the performance of the solutions given by the TSH. Experimental results confirm the robustness of schedules produced and advantages of the proposed TSH over other algorithms in terms of solution quality and run time.     

An augmented Lagrange programming optimization neural network for short-term hydroelectric generation scheduling

An approach based on augmented Lagrange programming neural networks is proposed for determining the optimal hourly amounts of generated power for the hydro-units in an electric power system. This methodology is based on the Lagrange multiplier theory in optimization and searches for solutions satisfying the necessary conditions of optimality in the state space. The equilibrium point of the network satisfies the Kuhn–Tucker condition for the problem. The equilibrium point of the network corresponds to the Lagrange solution of the problem. The proposed technique has been applied to a multi-reservoir cascaded hydro-electric system with a non-linear power generation function of water discharge rate and storage volume. The water transportation delay between connected reservoirs is also taken into account. Results obtained from this approach are compared with those obtained from the two phase optimization neural network and the conventional augmented Lagrange multiplier method. It is concluded from the results that the proposed method provides better results with respect to constraint satisfaction and is very effective in yielding optimal hydro-generation schedules.     

基于对偶四元数的单目视觉目标位姿测量

目的在机器人视觉应用领域中,为控制机器人能够完成焊接、搬运、跟踪等任务,需要确定摄像机与目标之间的相对位姿关系,提出一种目标位姿测量方法。方法利用单摄像机获取目标特征,坐标变换参数表示为对偶四元数的形式,同时计算旋转矩阵和平移向量,构建位置向量和方向向量的测量值与模型值之间的误差方程,利用Hopfield神经网络实现拉格朗日乘子法,求解目标位姿最优解。结果利用Matlab软件平台,选择SVD,DQ以及文中算法进行比较,仿真实验结果表明,基于Hopfield神经网络和对偶四元数的位姿测量算法计算出的位姿参数误差最小。随着测量点数量的增大,文中提出的算法精度更高。结论对偶四元数同时求解位姿变换矩阵的旋转分量和平移分量,可消除计算误差,基于Hopfield神经网络和拉格朗日乘子法,可快速准确地计算,并收敛至目标位姿最优解。     

Bacterial foraging optimisation: Nelder?Mead hybrid algorithm for economic load dispatch

A novel stochastic optimisation approach to solve constrained economic load dispatch problem using hybrid bacterial foraging (BF) technique is presented. in order to explore the search space for finding the local minima of the current location, the simplex algorithm called nelder-mead is used along with BF algorithm. the proposed methodology easily takes care of solving non-convex economic dispatch problems along with different constraints such as transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones. simulations were performed over various standard test systems with different number of generating units and comparisons are performed with other existing relevant approaches. the findings affirmed the robustness and proficiency of proposed methodology over other existing techniques.     

Rescheduling with controllable processing times for number of disrupted jobs and manufacturing cost objectives

We consider a machine rescheduling problem that arises when a disruption such as machine breakdown occurs to a given schedule. Machine unavailability due to a breakdown requires repairing the schedule as the original schedule becomes infeasible. When repairing a disrupted schedule a desirable goal is to complete each disrupted job on time, i.e. not later than the planned completion time in the original schedule. We consider the case where processing times of jobs are controllable and compressing the processing time of a job requires extra processing cost. Usually, there exists a nonlinear relation between the processing time and manufacturing cost. We solve a bicriteria rescheduling problem that trades off the number of on-time jobs and manufacturing cost objectives. We give a mixed-integer second-order cone programming formulation for the problem. We develop a heuristic search algorithm to generate efficient solutions for the problem. Heuristic algorithm searches solution space by moving and swapping jobs among machines. We develop cost change estimates for job moves and swaps so that the heuristic implements only promising moves and hence generates a set of efficient solutions in reasonably short CPU times.     

An effective hybrid immune algorithm for solving the distributed permutation flow-shop scheduling problem

In this article, an effective hybrid immune algorithm (HIA) is presented to solve the distributed permutation flow-shop scheduling problem (DPFSP). First, a decoding method is proposed to transfer a job permutation sequence to a feasible schedule considering both factory dispatching and job sequencing. Secondly, a local search with four search operators is presented based on the characteristics of the problem. Thirdly, a special crossover operator is designed for the DPFSP, and mutation and vaccination operators are also applied within the framework of the HIA to perform an immune search. The influence of parameter setting on the HIA is investigated based on the Taguchi method of design of experiment. Extensive numerical testing results based on 420 small-sized instances and 720 large-sized instances are provided. The effectiveness of the HIA is demonstrated by comparison with some existing heuristic algorithms and the variable neighbourhood descent methods. New best known solutions are obtained by the HIA for 17 out of 420 small-sized instances and 585 out of 720 large-sized instances.     

A bi-objective model for robust yard allocation scheduling for outbound containers

This article examines the yard allocation problem for outbound containers, with consideration of uncertainty factors, mainly including the arrival and operation time of calling vessels. Based on the time buffer inserting method, a bi-objective model is constructed to minimize the total operational cost and to maximize the robustness of fighting against the uncertainty. Due to the NP-hardness of the constructed model, a two-stage heuristic is developed to solve the problem. In the first stage, initial solutions are obtained by a greedy algorithm that looks n-steps ahead with the uncertainty factors set as their respective expected values; in the second stage, based on the solutions obtained in the first stage and with consideration of uncertainty factors, a neighbourhood search heuristic is employed to generate robust solutions that can fight better against the fluctuation of uncertainty factors. Finally, extensive numerical experiments are conducted to test the performance of the proposed method.     

求解考虑顺序相关调整时间的双边装配线平衡问题的变邻域搜索算法

为有效解决带有顺序相关调整时间的双边装配线平衡问题,提出了一种简单高效的变邻域搜索算法。该算法通过将优先关系约束融入到交换、插入、交叉、变异等算子中,分别得到4个不同的邻域结构来保证搜索过程中解的可行性,避免过多重复邻域解的生成。4个邻域结构的搜索空间依次变大,以增强算法搜索能力。同时,结合装配线的特点,提出基于作业序列的编码和解码方式,在解码过程中,优先选择空闲时间较多的边,引入启发式目标加快算法收敛。分配结束后,对装配线末端的工作站组进行局部调整。通过将该算法先后用于求解无/有顺序相关调整时间的双边装配线平衡第一类问题,并与已有的算法进行对比,验证了所提的变邻域搜索算法的优越性和有效性。     

A Stock Location Model for Dual Address Order Picking Systems

A model is formulated to evaluate alternative stock levels and item locations for dedicated storage warehouses where storage and retrieval transactions are interleaved to economize on travel of the order picking vehicle. The model can be used to measure the order picking and inventory cost effects of warehouse layouts representing alternatives to application of economic lot sizing and cube per order index storage assignment. A simple, sequential search heuristic is proposed for generating such alternative warehouse layouts and applied to a sample problem.     

Iterated beam search for the combined car sequencing and level scheduling problem

The level scheduling problem is concerned with the final stage of a multi-stage just-in-time production system so that different models of a product are evenly distributed in a discrete production sequence, thereby making the problem practically an unconstrained optimisation problem. The car sequencing problem, on the other hand, is a constraint satisfaction problem based on a number of options constricting the final assembly schedule. The combined car sequencing and level scheduling problem aims to find the optimal production schedule that evenly distributes different models over the planning horizon and satisfies all option constraints. This paper proposes a parametric iterated beam search algorithm for the combined problem that can be used either as a heuristic or as an exact optimisation method. The paper includes a computational study based on a 54-instance test bed that proves the effectiveness of the proposed algorithm.