Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using the hybrid bacterial foraging-Nelder-Mead algorithm

In this paper, a new approach is proposed to solve the economic load dispatch (ELD) problem. Power generation, spinning reserve and emission costs are simultaneously considered in the objective function of the proposed ELD problem. In this condition, if the valve-point effects of thermal units are considered in the proposed emission, reserve and economic load dispatch (ERELD) problem, a non-smooth and non-convex cost function will be obtained. Frequency deviation, minimum frequency limits and other practical constraints are also considered in this problem. For this purpose, ramp rate limit, transmission line losses, maximum emission limit for specific power plants or total power system, prohibited operating zones and frequency constraints are considered in the optimization problem. A hybrid method that combines the bacterial foraging (BF) algorithm with the Nelder-Mead (NM) method (called BF-NM algorithm) is used to solve the problem. In this study, the performance of the proposed BF-NM algorithm is compared with the performance of other classic (non-linear programming) and intelligent algorithms such as particle swarm optimization (PSO) as well as genetic algorithm (GA), differential evolution (DE) and BF algorithms. The simulation results show the advantages of the proposed method for reducing the total cost of the system.     

基于粒子群算法的水电站中长期优化调度研究

以洪家渡水电站为例,探讨了粒子群算法在水电站中长期优化调度的应用方法及效果。实例计算结果表明,该算法可以求解复杂约束条件的非线性水库优化调度,精度高、收敛速度快,为解决水电站中长期优化调度问题提供了一种有效的方法。     

The influence of carbon dioxide trading scheme on economic dispatch of generators

This paper aims at probing into the topic of power units’ operation and dispatch based on Carbon Dioxide (CO₂) trading scheme. The trading cost of CO₂ emission is embedded into the traditional economic dispatch model, which will be solved by the New Particle Swarm Optimization (NPSO). By considering the CO₂ trading scheme, the influences of the various strategies for unit’s dispatch are simulated and analyzed in this paper. The proposed method, NPSO is developed in such a way that PSO with Constriction Factor (PSO-CF) algorithm is applied as a based level search. NPSO introduces two operators, “Random Particles” and “Fine-Tuning” into the PSO-CF algorithm to improve the drawback of searching global optimum and make the search method more efficient at the end of search. The efficiency and ability of NPSO is demonstrated by the six generating units. Simulation results indicated that reasonable solutions provide a practical and flexible framework for power sectors. They can be also used for generating alternatives and thus help decision makers to obtain the goals of minimal operation cost under their desired emission’s policies.     

A Statistical Approach to the Design of a Dispatchable Wind Power-Battery Energy Storage System

A scheme that allows the dispatch of steady and controllable level of power from a wind power generating station is proposed in this paper. The scheme utilizes two battery energy storage systems (BESSs) in which the generated wind power is used to charge one BESS, while the second BESS is used to discharge constant power into grid. The role of the two BESS interchanges when the discharging BESS reaches specified operating limit. With this scheme in mind and based on given wind speed statistics, charging characteristics of the BESS are studied, and a method to determine the expected charging time of the BESS to reach stipulated battery state of charge is developed. The expected BESS charging time, in turn, dictates the constant power level that can be dispatched to the grid through the discharging BESS. The corresponding discharge time is also determined using the developed method, the accuracy of which is validated experimentally. The proposed design procedure is then used to determine the minimum BESS capacity based on the expected wind power. Statistical likelihood of dispatchable power delivery achievable from the scheme is also obtained.      

考虑风电消纳能力单目标及多目标模糊机组组合模型及应用

从机组经济调度优化的角度入手,研究了风电消纳的合理应对方式。为使机组组合安排能在消纳更多风电的同时兼顾电力系统运行的安全、可靠性准则,并满足一定的经济性,分别以弃风电量、机组运行费用和机组运行风险度三方面为优化目标建立了机组组合的优化模型及这三者共同的多目标优化模型。利用粒子群算法及模糊多目标优化方法对模型进行求解,并将上述模型和算法应用于某10机算例的计算中。分析结果表明,该建模思路能为风电的有效接纳提供有益的指导。     

Multiobjective optimal dispatch of microgrid based on analytic hierarchy process and quantum particle swarm optimization

Owing to the rapid development of microgrids (MGs) and growing applications of renewable energy resources, multiobjective optimal dispatch of MGs need to be studied in detail. In this study, a multiobjective optimal dispatch model is developed for a standalone MG composed of wind turbines, photovoltaics, diesel engine unit, load, and battery energy storage system. The economic cost, environmental concerns, and power supply consistency are expressed via subobjectives with varying priorities. Then, the analytic hierarchy process algorithm is employed to reasonably specify the weight coefficients of the subobjectives. The quantum particle swarm optimization algorithm is thereafter employed as a solution to achieve optimal dispatch of the MG. Finally, the validity of the proposed model and solution methodology are confirmed by case studies. This study provides reference for mathematical model of multiojective optimization of MG and can be widely used in current research field.     

Accurate estimation of cost function parameters for thermal power plants using a novel optimization approach

Accurate parameter estimation of the input-output characteristics in thermal power plants is an important issue in power system because these characteristics directly affect the economic dispatch calculations. Parameter estimation is an optimization problem in which the optimal values of the unknown parameters should be estimated by an optimization technique. By considering the valve-point effect, the parameter estimation will be more difficult since the fitness function of this optimization problem turns into a non-smooth and non-convex function in which finding the global optimal is a challenging task. In this paper, a recently proposed metaheuristic approach, crow search algorithm (CSA), is proposed for accurate estimation of the input-output characteristics of thermal power plants with and without valve-point effect. Simulation results show that CSA finds more promising results than least squares method (LSM), particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC).     

Reactive power dispatch in wind farms using particle swarm optimization technique and feasible solutions search

In this paper, an optimization method for the reactive power dispatch in wind farms (WF) is presented. Particle swarm optimization (PSO), combined with a feasible solution search (FSSPSO) is applied in order to optimize the reactive power dispatch, taking into consideration the reactive power requirement at point of common coupling (PCC), while active power losses are minimized in a WF. The reactive power requirement at PCC is included as a restriction problem and is dealt with feasible solution search. Finally an individual set point, particular for each wind turbine (WT), is found. The algorithm is tested in a WF with 12 WTs, taking into consideration different control options and different active power output levels.     

Multi-objective optimal droop control of solid oxide fuel cell based integrated energy system

Solid oxide fuel cell (SOFC) based integrated energy system (IES) is promising in the future low-carbon power generation market, due to the high efficiency and flexibility. However, it is challenging for the dynamic control design in dealing with the conflicting objectives in terms of fast power tracking and overall efficiency during the transient process of load response. To this end, this paper develops a multi-objective optimal droop control strategy for the real-time power dispatch of the IES. Firstly, a nonlinear implicit dynamic model consisting of SOFC, lithium-ion battery, photovoltaic array and DC-DC converter is developed. Then, a multi-objective optimization is formulated to balance the power tracking performance and transient efficiency. Non-dominated sorting genetic algorithm-II (NSGA-II) is adopted to search the optimal parameters for droop controller. Simulation results demonstrates that the electricity loss of the proposed method can be reduced by 96.26% with a slight compromise in power tracking performance.     

Maximum power point tracking of a proton exchange membrane fuel cell system using PSO-PID controller

Fuel cells output power depends on the operating conditions, including cell temperature, oxygen partial pressure, hydrogen partial pressure, and membrane water content. In each particular condition, there is only one unique operating point for a fuel cell system with the maximum output. Thus, a maximum power point tracking (MPPT) controller is needed to increase the efficiency of the fuel cell systems. In this paper an efficient method based on the particle swarm optimization (PSO) and PID controller (PSO-PID) is proposed for MPPT of the proton exchange membrane (PEM) fuel cells. The closed loop system includes the PEM fuel cell, boost converter, battery and PSO-PID controller. PSO-PID controller adjusts the operating point of the PEM fuel cell to the maximum power by tuning of the boost converter duty cycle. To demonstrate the performance of the proposed algorithm, simulation results are compared with perturb and observe (P&O) and sliding mode (SM) algorithms under different operating conditions. PSO algorithm with fast convergence, high accuracy and very low power fluctuations tracks the maximum power point of the fuel cell system.     

An analysis for the need of a battery energy storage system in tracking wind power schedule output

电池储能系统(battery energy storage system,BESS)在风储联合应用中具有多种功能,利用电池储能系统提高风电并网调度运行能力是当前研究的热点之一.文章基于我国北方某风电场历史运行数据与预测数据,依据预测误差评价指标和风电场预报考核指标的综合评价方法对风电场预测数据进行分析研究,归纳了预测误差的概率分布特征;提出利用电池储能系统提高风电跟踪计划出力能力,统计并量化出电池储能系统用于跟踪计划出力场合的作用范围;通过仿真验证电池储能系统在风储联合系统中提高风电跟踪计划出力控制策略的有效性和可行性.     

A new honey bee mating optimization algorithm for non-smooth economic dispatch

The non-storage characteristics of electricity and the increasing fuel costs worldwide call for the need to operate the systems more economically. Economic dispatch (ED) is one of the most important optimization problems in power systems. ED has the objective of dividing the power demand among the online generators economically while satisfying various constraints. The importance of economic dispatch is to get maximum usable power using minimum resources. To solve the static ED problem, honey bee mating algorithm (HBMO) can be used. The basic disadvantage of the original HBMO algorithm is the fact that it may miss the optimum and provide a near optimum solution in a limited runtime period. In order to avoid this shortcoming, we propose a new method that improves the mating process of HBMO and also, combines the improved HBMO with a Chaotic Local Search (CLS) called Chaotic Improved Honey Bee Mating Optimization (CIHBMO). The proposed algorithm is used to solve ED problems taking into account the nonlinear generator characteristics such as prohibited operation zones, multi-fuel and valve-point loading effects. The CIHBMO algorithm is tested on three test systems and compared with other methods in the literature. Results have shown that the proposed method is efficient and fast for ED problems with non-smooth and non-continuous fuel cost functions. Moreover, the optimal power dispatch obtained by the algorithm is superior to previous reported results.     

孤岛运行模式下的微网经济负荷分配

研究了微网孤岛运行模式下的经济负荷分配问题,即在满足系统约束条件下如何优化微网中各微电源的出力,使微网的目标成本最小.建立了微网孤岛运行模式的经济负荷分配数学模型,然后采用改进粒子群优化算法对微网的经济负荷分配进行了研究.最后通过算例验证了数学模型与优化算法的正确性与自效性.     

Solving the economic dispatch problem with a modified quantum-behaved particle swarm optimization method

In this paper, a modified quantum-behaved particle swarm optimization (QPSO) method is proposed to solve the economic dispatch (ED) problem in power systems, whose objective is to simultaneously minimize the generation cost rate while satisfying various equality and inequality constraints. The proposed method, denoted as QPSO-DM, combines the QPSO algorithm with differential mutation operation to enhance the global search ability of the algorithm. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zones, and nonsmooth cost functions are considered when the proposed method is used in practical generator operation. The feasibility of the QPSO–DM method is demonstrated by three different power systems. It is compared with the QPSO, the differential evolution (DE), the particle swarm optimization (PSO), and the genetic algorithm (GA) in terms of the solution quality, robustness and convergence property. The simulation results show that the proposed QPSO–DM method is able to obtain higher quality solutions stably and efficiently in the ED problem than any other tested optimization algorithm.     

Implementation of repowering optimization for an existing photovoltaic‐pumped hydro storage hybrid system: A case study in Sichuan,China

For a remote area or an isolated island, where the grid has not extended, a standalone hybrid energy system can provide cheap and adequate power for local users. However, with the development of society, the load demand will increase and the original system cannot completely meet the load demand. This situation occurs in Xiaojin, Sichuan, China. The existing photovoltaic‐pumped hydro storage (PV‐PHS) hybrid system in this area as the original system cannot completely meet the load requirements at present. The term “repowering” aims to maximize the reliability of power supply and the utilization of the PV‐PHS hybrid energy system that differs from traditional planning optimization to build all components. The repowering strategy is to integrate wind turbines (WTs) and battery into the original system. For the repowering system, a power management strategy is proposed to determine the operating modes of the PHS and battery. Three objectives, which are minimizing percentage of the demand not supplied, levelized cost of energy, and curtailment rate of renewable energy, are considered in the optimization model. Simulation is conducted by single‐objective, biobjective, and triobjective particle swarm optimization (PSO) techniques. For the single‐objective optimization, the comparison of PSO and genetic algorithm (GA) is made. For the double‐objective optimization, multiobjective PSO (MOPSO) is compared with weighted sum approach (WSA), and fuzzy satisfying method is utilized to find the win‐win solution. The results reveal that the repowering strategy can help to achieve maximum reliability of power supply after load demand increases significantly, and the battery plays an important role in such a hybrid system.     

Economic dispatch using particle swarm optimization: A review

Electrical power industry restructuring has created highly vibrant and competitive market that altered many aspects of the power industry. In this changed scenario, scarcity of energy resources, increasing power generation cost, environment concern, ever growing demand for electrical energy necessitate optimal economic dispatch. Practical economic dispatch (ED) problems have nonlinear, non-convex type objective function with intense equality and inequality constraints. The conventional optimization methods are not able to solve such problems as due to local optimum solution convergence. Meta-heuristic optimization techniques especially particle swarm optimization (PSO) has gained an incredible recognition as the solution algorithm for such type of ED problems in last decade. The application of PSO in ED problem, which is considered as one of the most complex optimization problem has been summarized in present paper.     

Optimal coordination of wind-hydro-thermal based on water complementing wind

The increasing integration of wind power into the existing power system demands for effective strategies to deal with wind intermittency and uncertainty. Relying solely on thermal power to cover wind uncertainty will sacrifice the operating efficiency and economy of thermal generators. In view of this, the adjustable hydropower is preferred for complementing wind fluctuation and uncertainty and the coordinated dispatch problem of wind-hydro-thermal power is established. Based on a newly designed water supplementing wind strategy, the original complex problem is decomposed into wind-hydro subproblem and thermal subproblem. A novel stochastic constraint related to wind power uncertainty is proposed and handled according to stochastic programming theory. By introducing the concept of expected breed rate and elitist preservation strategy, the particle swarm optimization (PSO) algorithm is improved and combined with the exterior penalty function method for solving the complete optimization problem. Optimal generation scheduling schemes that can make full use of wind energy and ensure efficient and economic operating of thermal generators are obtained by the proposed approach. Meanwhile the coordinating operation of wind, hydro and thermal power under different water resources and wind penetrations respectively are revealed and discussed.     

Power flow control of grid connected hybrid renewable energy system using hybrid controller with pumped storage

This paper presents a grid-connected HRES using a hybrid controller with PHS for optimal power flow control and minimizing the production cost. The novelty of the proposed approach is the joined execution of the SSA and CSA named as SSA-CS are apparently a very new metaheuristic algorithm. Moreover, the proposed method is the cost-effective power production of the microgrids and effective utilization of renewable energy sources without wasting the available energy. Here, the energy sources in particular PV system, WT, MT and battery with PHS are utilized to generate the power of the MG system. In the proposed approach, the required power demand of the energy system is predicted by the ANN technique. After that, the production cost minimization is done in view of the anticipated load demand by utilizing the optimization approaches to be a specific SSA-CS algorithm. The result of the proposed approach is actualized in the MATLAB/Simulink working platform. The performance of the proposed approach is examined by comparing the current methodologies such as SSA and PSO with the proposed SSA-CS approach. The simulation results show that the proposed method generates maximum power and furthermore the proposed framework has less production cost in light of the power demand.     

直流孤岛及弱联系方式下动态无功备用优化

针对直流孤岛及弱联系方式下系统经历大扰动后所面临的稳态电压波动问题,提出一种基于灵敏度的应对稳态电压波动的动态无功备用优化方法,该方法首先根据潮流方程获得节点电压和发电机的无功变化量及计及直流无功变化的电压变化量,然后基于推导得到的灵敏度矩阵,建立无功备用优化模型,以无功备用最大为目标,若干运行条件为约束,求解直流孤岛及弱联系方式下的动态无功备用方案。算例分析结果表明,所提方法可有效提高系统的总无功备用,减少直流孤岛运行模式下节点电压的波动范围,保障系统安全运行。     

Jaya algorithm-based energy management system for battery- and ultracapacitor-powered ultralight electric vehicle

To improve the driving performance of the electric vehicles, batteries or ultracapacitors (UCs) are frequently preferred in the energizing systems. In hybrid structures with multiple supply sources, an energy management system (EMS) is needed to improve the system efficiency, and to provide the optimum power sharing between a battery and a UC. The purpose of this study is to investigate the effectiveness of the Jaya optimization method for the urban use of the EMS of an ultralight electric vehicle powered by battery/UC. The performance of the proposed method is compared with dynamic programming (DP) that is one of the global optimization methods and particle swarm optimization (PSO) that is one of the other heuristic methods for real-time applications. The simulation results show that Jaya-EMS approached 3.1% to the DP, which yields the optimum result with respect to the total energy loss. In addition, the proposed method yields a loss of less than 1.9% from the PSO-EMS. If all the above situations are considered, the proposed EMS method has less lossy alternative solution for the real-time applications.