Low-carbon emission/economic power dispatch using the multi-objective bacterial colony chemotaxis optimization algorithm considering carbon capture power plant

To study the constrained emission/economic dispatch problem involving competing objectives in electric power systems with carbon capture system (CCS) technology, this paper proposes a multi-objective optimization approach based on bacterial colony chemotaxis (MOBCC) algorithm. In this algorithm, a Lamarckian constraint handling method based approach is improved to update the bacterial colony and the external archive. Finally, the optimization tests of the proposed algorithm are carried out in the IEEE 30-bus test system. Results demonstrate this approach has the advantage of dealing with highly non-linear and multi-objective functions of carbon capture thermal generator’s emission/economic dispatch problem.     

Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II

This paper presents nondominated sorting genetic algorithm-II for solving combined heat and power economic emission dispatch problem. The problem is formulated as a nonlinear constrained multi-objective optimization problem. Nondominated sorting genetic algorithm-II is proposed to handle economic emission dispatch as a true multi-objective optimization problem with competing and noncommensurable objectives. The proposed algorithm is illustrated for two test systems and the test results are compared with those obtained from strength pareto evolutionary algorithm 2.     

A security constrained environmental/economic power dispatch technique using F-MSG algorithm for a power system area including limited energy supply thermal units

A security constrained non-convex environmental/economic power dispatch problem for a lossy electric power system area including limited energy supply thermal units is formulated. An iterative solution method based on modified subgradient algorithm operating on feasible values (F-MSG) and a common pseudo scaling factor for limited energy supply thermal units are used to solve it. In the proposed solution method, the F-MSG algorithm is used to solve the dispatch problem of each subinterval, while the common pseudo scaling factor is employed to adjust the amount of fuel spent by the limited energy supply thermal units during the considered operation period. We assume that limited energy supply thermal units are fueled under take-or-pay (T-O-P) agreement.The proposed dispatch technique is demonstrated on IEEE 30-bus power system with six thermal generating units having non-convex cost rate functions. Two of the generating units are selected as gas-fired limited energy supply thermal units. Pareto optimal solutions for the power system, where the constraint on the amount of fuel consumed by the limited energy supply thermal units is not considered, are calculated first. Later on, the same Pareto optimal solutions for the power system, where the fuel constraint is considered, are recalculated, and the obtained savings in the sum of optimal total fuel cost and total emission cost are presented. The dispatch problem of the first subinterval of the test system was solved previously by means of differential evolution (DE), and a hybrid method based on combination of DE and biogeography based optimization (BBO) for the best cost and the best emission cases in the literature. The results produced by these methods are compared with those of produced by the proposed method in terms of their total cost rate, emission rate and solution time values. It is demonstrated that the proposed method outperforms against the evolutionary methods mentioned in the above in terms of solution time values especially when the exact model of the test system is considered.     

基于改进多目标海樽群算法的电力系统优化调度

文中提出了一种新的多目标海樽群优化算法,将其与等式约束修正技术和可行解占优约束处理技术相结合,用于求解高度约束的电力系统环境经济优化调度问题。该算法采用高斯采样策略和变异操作增强其寻优性能;通过一种改进的基于动态拥挤距离的非支配排序方法获得分布均匀的帕累托最优前沿;应用模糊集理论为决策者提供最佳折中解。在IEEE 30节点6机组标准测试系统上进行算例仿真,并与其它优化算法进行了对比。结果表明,所提算法在求解电力系统环境经济调度问题时具有更好的优化效果。     

Application of model predictive control to optimal dynamic dispatch of generation with emission limitations

Reducing emission from fossil-fueled electric power generating plants has received considerable attention in recent years in both regulated and deregulated power markets. Under regulated power systems, utilities solve the dynamic economic dispatch problem to determine the optimal scheduling of the committed unit's output at minimum fuel cost while satisfying a set of constraints. In this paper, we introduce the following problems where the emission effects are included in the mathematical model: (1) dynamic economic emission dispatch and (2) emission constrained dynamic economic dispatch. Under deregulated markets, the generation company can determine the optimal amounts of energy to be sold in the market by running profit-based dynamic economic dispatch problem to maximize its own profit. To take into account the emission limitations we introduced two problems: (1) profit-based dynamic economic emission dispatch problem and (2) profit-based emission constrained dynamic economic dispatch problem. In this paper we applied the model predictive control (MPC) approach proposed recently to the dynamic dispatch problems in both regulated and deregulated systems. The convergence and robustness of the MPC algorithms are demonstrated through the application of MPC to these problems with a six-unit system.     

碳排放限制的混杂最优闭环微电网调度算法

针对微电网经济调度效率低下等问题,提出了一种碳排放限制的混杂最优闭环微电网调度算法。算法在考虑火力发电机组和多分布式发电聚合体组合调度的同时,以电网实际需求响应和碳排放限制作为约束条件,建立微电网经济调度模型;并将经济调度问题转化为混杂系统的最优控制,从而建立微电网经济调度与混杂系统最优控制序列的等价一致性;推导混杂系统获取满足贝尔曼方程的最优代价函数,借助神经网络逼近最优值获得最优闭环调度序列。仿真实验验证了本调度算法的闭环有效性,能在不同初始条件和外部扰动下依然获得最优调度序列,同时仿真结果证实降低碳排放限额或提高碳排放交易价格都有助于减少电网系统的总碳排放量。     

考虑大用户直购电的动态环境经济调度

动态环境经济调度在环境经济调度的基础上考虑发电机组的爬坡约束,增强了调度时段内各时段间机组出力的强耦合约束,如何有效地解决此类问题至关重要。另外,大用户直购电如何影响电网动态环境经济运行调度也具有一定研究价值。为此,对考虑大用户直购电的动态环境经济调度问题进行建模,并采用内点法多约束处理策略改进多目标细菌群体趋药性(MOBCC)优化算法进行求解,旨在从系统发电成本的角度研究大用户直购电对经济调度的影响。最后,通过仿真验证明所提方法的有效性,并对仿真结果进行分析总结,说明所采用方法对大用户直购电策略、电网调度影响分析具有一定指导意义。     

Application of pattern search method to power system valve-point economic load dispatch

Direct search (DS) methods are evolutionary algorithms used to solve constrained optimization problems. DS methods do not require any information about the gradient of the objective function at hand, while searching for an optimum solution. One of such methods is pattern search (PS) algorithm. This study presents a new approach based on a constrained pattern search algorithm to solve well-known power system economic load dispatch problem (ELD) with valve-point effect. For illustrative purposes, the proposed PS technique has been applied to various test systems to validate its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method has been assessed and investigated through comparison with results reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving power system economic load dispatch problem.     

Dynamic optical economic dispatch under system availability constraints

In this paper we have developed a dynamic optimal economic dispatch policy based on a stochastic availability model of large-scale power systems and a piece-wise constant incremental fuel cost model. Using these models the optimal economic dispatch under given system availability constraint is formulated as a dynamic nonlinear optimization problem. The random variations of demands, available generation capacities and available tie line capacities are considered as constraints in the problem. In order to solve the optimization problem an efficient algorithm based on the rule of merit-order loading has been developed. The algorithm allows large dimensionality of the system and randomness of the system parameters. The algorithm can also be easily implemented on a dispatch computer. In order to illustrate the effect of the proposed method on system generation economy and availability, an example is presented giving detailed numerical results which are very encouraging. As far as the authors know, such an economic dispatch problem which maintains the system availability index at the highest possible level (under the given system environment) has never been considered in the literature before.     

Control area performance improvement by extended securityconstrained economic dispatch

An algorithm for solving the extended security constrained economic dispatch (ESCED) problem with real-time economic dispatch grade speed and reliability is presented. The ESCED problem is formulated by adding a regulating margin and ramp rate constraints to the network security constrained economic dispatch problem previously solved by the CEDC algorithm. Starting with Newton's method to optimize the Lagrangian, the ESCED is developed by superimposing on Newton's method eight major components called tracking start initialization, hessian pre-elimination, implicit dual variable calculations, regulating margin sensitivity coefficient calculations, traumatic event evaluation, constraint relaxation, implicit ramp rate constraint implementation, and relaxed incremental cost calculations. Test results are also presented     

Environmental/economic power dispatch using a fuzzified multi-objective particle swarm optimization algorithm

The environmental issues that arise from the pollutant emissions produced by fossil-fueled electric power plants have become a matter of concern more recently. The conventional economic power dispatch cannot meet the environmental protection requirements, since it only considers minimizing the total fuel cost. The multi-objective generation dispatch in electric power systems treats economic and emission impact as competing objectives, which requires some reasonable tradeoff among objectives to reach an optimal solution. In this paper, a fuzzified multi-objective particle swarm optimization (FMOPSO) algorithm is proposed and implemented to dispatch the electric power considering both economic and environmental issues. The effectiveness of the proposed approach is demonstrated by comparing its performance with other approaches including weighted aggregation (WA) and evolutionary multi-objective optimization algorithms. All the simulations are conducted based on a typical test power system.     

Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED) with non-smooth cost function. Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using three different test systems. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.     

电网规划综合评判决策系统的设计与应用

提出了一种求解电力系统负荷经济分配问题的改进粒子群优化算法.该算法考虑了机组的爬坡约束、出力限制区约束、非光滑费用函数曲线等非线性特性,用保留可行解的方法处理负荷平衡约束条件,用自适应罚函数法处理爬坡和出力限制区约束条件,加快了算法的收敛速度,对不活动粒子的处理使算法避免了"早熟"现象.仿真计算表明,改进粒子群优化算法是一种求解负荷经济分配问题的有效方法.     

Combined economic and emission dispatch problems using biogeography-based optimization

In this work, biogeography-based optimization (BBO) is presented for solving different constrained economic load dispatch (ELD) problems combined with economic emission aspects in power system. Nonlinear characteristics of generators like valve point discontinuities, ramp rate limits and prohibited operating zones are considered in the problem. The simulation results show that the proposed BBO algorithm based solutions prove to be the best near-global optimal as compared to the solutions based on Newton–Raphson, Tabu search, genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA), fuzzy logic controlled genetic algorithm (FCGA), particle swarm optimization (PSO) and differential evolution (DE).     

Dynamic environmental economic dispatch using multiobjective differential evolution algorithm with expanded double selection and adaptive random restart

The dynamic environmental economic dispatch (DEED) model is presented in this paper, in which the fuel cost and emission effect over a certain period of time are optimized as conflicting objectives. It is a high dimensional, nonlinear constrained multiobjective optimization problem when generators’ valve point effect, ramp rate limits and power load variation are considered. This paper proposes a modified adaptive multiobjective differential evolution (MAMODE) algorithm to solve the problem. In MAMODE, expanded double selection and adaptive random restart operators are proposed to modify the evolutionary processes for avoiding premature and a dynamic heuristic constraint handling (DHCH) approach is introduced to deal with the complicated constraints. The DHCH can lessen infeasible solutions gradually. To illustrate the effectiveness of the method, four cases based on three test power systems are studied. The simulation result indicates that the DEED can be solved quickly. Comparison of numerical results demonstrates the proposed method has higher performance.     

基于免疫遗传算法的环境经济负荷调度

介绍以目标函数为抗原,以问题解为抗体,利用进化策略进行群体更新的免疫遗传算法。讨论环境经济负荷调度多目标函数优化问题,给出利用免疫遗传算法解决这一问题的主要步骤。利用一个含有5个电力生产单元的燃煤电力系统模型验证了该算法的可行性和有效性。并与遗传算法和Hop fie ld神经网络进行比较分析,证实了该算法解决该类问题的优化性和快速收敛性。     

Modeling for Dynamic Economic Emission Dispatch Under Uncertainty

This article presents a new model to solve the dynamic economic emission dispatch problem incorporating uncertainties in the process of power generation. Besides the classic dynamic economic emission dispatch factors, the constraints of both reliability and efficiency are especially considered to restrain the disturbances of uncertainties. Accordingly, the penalty and reserve cost function together with the penalty and reserve emission function are added in the multi-objective function, respectively. To obtain some quantitative results, the characterizations of the different sources of uncertainty are discussed based on statistical theory, and this optimization problem is numerically solved by the improved particle swarm optimization algorithm. Eventually, the simulation results demonstrate that improving the level of reliability will increase the operation costs and emissions of the power system, while increasing the level of efficiency will decrease the operation costs and emissions of the power system. Furthermore, there seems to be no significant linear correlation among the economic and environmental costs and the proportion of wind power generation under the requirements of reliability and efficiency.     

基于启发式线性规划的大规模安全约束调度快速求解方法

提升大规模安全约束经济调度优化模型的求解性能是开展大电网跨省区电力电量全局优化平衡的前提与基础。首先分析问题的物理特性,通过并行计算求解不考虑机组爬坡约束的分时段约束松弛模型。基于对松弛解的分析获得可用于指导安全约束经济调度模型改进的有用信息,以约束剔除和约束增加的方式提出了基于启发式线性规划的大规模安全约束经济调度快速求解方法。将所提算法运用于新英格兰10机扩展系统和中国实际电网,验证了所提算法的正确性和有效性。     

基于改进MOBCC算法的热电联合系统经济环境调度

热电联产因其节能减排作用成为综合能源系统的重要组成部分,对于热电联合系统经济环境调度问题,采用基于帕累托支配的改进MOBCC算法求解,改进MOBCC算法在收敛性、解集的多样性和时间效率上具有优越的性能.采用基于约束违反指数的约束处理方法处理约束条件,并采用基于目标满意度与目标权重之间关系的多目标决策方法选择最优折衷解....     

An Improved Particle Swarm Optimization for the Combined Heat and Power Dynamic Economic Dispatch Problem

—This study presents a novel improved particle swarm optimization algorithm to solve the combined heat and power dynamic economic dispatch problem. This problem is formulated as a challenging non-convex and non-linear optimization problem considering practical characteristics, such as valve-point effects, transmission losses, ramp-rate limits, mutual dependency of power and heat, spinning reserve requirements, and transmission security constraints. The proposed method combines classical particle swarm optimization with a chaotic mechanism, time-variant acceleration coefficients, and a self-adaptive mutation scheme to prevent premature convergence and improve solution quality. Moreover, multiple efficient constraint handling strategies are employed to deal with complex constraints. The effectiveness of the proposed improved particle swarm optimization for solving the combined heat and power dynamic economic dispatch problem is validated on three different test systems, and the results are compared with those of other variants of particle swarm optimization as well as other methods reported in the literature. The numerical results demonstrate the superiority of improved particle swarm optimization in solving the combined heat and power dynamic economic dispatch problem while strictly satisfying all the constraints.