Efficient real coded genetic algorithm to solve the non-convex hydrothermal scheduling problem

A simple and efficient optimisation procedure based on real coded genetic algorithm is proposed for the solution of short-term hydrothermal scheduling problem with continuous and non-smooth/non-convex cost function. The constraints like load-generation balance, unit generation limits, reservoir flow balance, reservoir physical limitations and reservoir coupling are also considered. The effectiveness of the proposed algorithm is demonstrated on a multichain-cascaded hydrothermal system that uses non-linear hydro generation function, includes water travel times between the linked reservoirs, and considers the valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint-handling technique, which eliminates the need for penalty parameters. A simple strategy based on allowing infeasible solutions to remain in the population is used to maintain diversity. The same problem is also solved using binary coded genetic algorithm. The features of both algorithms are same except the crossover and mutation operators. In real coded genetic algorithm, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in binary coded genetic algorithm. The comparison of the two genetic algorithms reveals that real coded genetic algorithm is more efficient in terms of thermal cost minimisation for a short-term hydrothermal scheduling problem with continuous search space.     

A FAST ALGORITHM FOR OPTIMAL HYDROTHERMAL SCHEDULING WITH CASCADED AND INDEPENDENT HYDRO PLANTS

ABSTRACT

This paper presents a fast algorithm for solving the short-term hydrothermal scheduling problem in a power system consisting of cascaded plants with time delay and independent hydro plants. The operational planning of such problem is concerned with the determination of scheduling for hydro as well as thermal plants to meet the daily system demand with the objective of minimizing the total fuel cost of the thermal plants over the day subject to the relevant operating constraints associated with the thermal and hydro plants.

The algorithm employs a fast and simple alternating solution approach for hydrothermal scheduling in which the hydro subproblem is solved using the method of local variation while the associated thermal subproblem is solved through a judicious combination of Successive Linear Programming (SLP) method and Participation Factor method. Many computational features are incorporated in the solution algorithm exploiting the inherent characteristic of the complex hydrothermal scheduling problem.     

A genetic algorithm solution to the optimal short-term hydrothermal scheduling

This paper presents an algorithm for solving the hydrothermal scheduling through the application of genetic algorithm (GA). The hydro subproblem is solved using GA and the thermal subproblem is solved using lambda iteration technique. Hydro and thermal subproblems are solved alternatively. GA based optimal power flow (OPF) including line losses and line flow constraints are applied for the best hydrothermal schedule obtained from GA. A 9-bus system with four thermal plants and three hydro plants and a 66-bus system with 12 thermal plants and 11 hydro plants are taken for investigation. This proposed GA reduces the complexity, computation time and also gives near global optimum solution.     

计及节能减排的梯级水火电优化调度研究

针对梯级水电站与火电联合调度难度大、约束多的困难,考虑了节能、减排及梯级蓄能等三个目标,并引入模糊理论建立多目标水火电优化调度的模糊模型,采用最大化满意度指标法将多目标转化为单目标优化,然后通过遗传算法求解此问题。结果表明,相较于纯火电优化调度,梯级水火电调度能有效节约能源,减少污染气体排放;在此基础上多目标的水火优化调度比单目标的水火优化调度更能同时兼顾节能、减排及水电站的蓄能,达到社会综合效益最大化。     

Coevolutionary Algorithm Based on Lagrangian Method for Hydrothermal Generation Scheduling

The coevolutionary algorithm (CEA) based on the Lagrangian method is proposed for hydrothermal generation scheduling. The main purpose of hydrothermal generation scheduling is to minimize the overall operation cost and the constraints satisfied by scheduling the power outputs of all hydro and thermal units under study periods, given electrical load and limited water resource. In the proposed method, a genetic algorithm is successfully incorporated into the Lagrangian method. The genetic algorithm searches out the optimum using multiple-path techniques and possesses the ability to deal with continuous and discrete variables. Regardless of the objective function characteristic the genetic algorithm does not have to modify the design rules and possesses the ability to go over local solutions toward the global optimal solution. The genetic algorithm can improve the disadvantages of the traditional Lagrangian method, which updates Lagrange multipliers according to the degree of system constraint violation by the gradient algorithm, and further searches out the global optimal solution. The developed algorithm is illustrated and tested on a practical Taiwan power system. Numerical results show that the proposed CEA based on the Lagrangian method is a very effective method for searching out the global optimal solution.     

Optimal Short Term Operation Planning of a Large Hydrothermal Power System Based on a Nonlinear Network Flow Concept

This paper presents a procedure for solving the short term generation scheduling problem for a large hydrothermal system that includes transmission limitations. The integrated system is divided into a hydro and a thermal subsystem. A reduced gradient algorithm is employed for the solution of the hydro subproblem. This algorithm is specialized to efficiently solve nonlinear network flow problems with additional constraints of non-netwrk type. The thermal subsystem is solved using a fast unit commitment and dispatch algorithm. A case study with the Swedish system is discussed.     

具有相同机组水火电调度问题的新算法

对Lagrangian松弛法求解水火电调度问题时由机同机级引起解震荡现象进行了研究。通过一个例子分析了震荡产生的根本原因。对此，在松弛函数中引入了惩罚项并采用了伪次梯度法来修正乘子。新算法在求解低层子问题时并不同时求解，使震荡现象在很大程度上得以克服，同时可大幅度地降低偶解对约束的违反程度。通过简单的例子和对一个包含两组机同机组的短期发电调度问题的计算表明，对偶解的约束违反程度明显地降低，解震荡明显地减弱且最后可行解的质量有显著的改善。     

Short-term hydrothermal scheduling using clonal selection algorithm

An efficient optimization procedure based on the clonal selection algorithm (CSA) is proposed for the solution of short-term hydrothermal scheduling problem. CSA, a new algorithm from the family of evolutionary computation, is simple, fast and a robust optimization tool for real complex hydrothermal scheduling problems. Hydrothermal scheduling involves the optimization of non-linear objective function with set of operational and physical constraints. The cascading nature of hydro-plants, water transport delay and scheduling time linkage, power balance constraints, variable hourly water discharge limits, reservoir storage limits, operation limits of thermal and hydro units, hydraulic continuity constraint and initial and final reservoir storage limits are fully taken into account. The results of the proposed approach are compared with those of gradient search (GS), simulated annealing (SA), evolutionary programming (EP), dynamic programming (DP), non-linear programming (NLP), genetic algorithm (GA), improved fast EP (IFEP), differential evolution (DE) and improved particle swarm optimization (IPSO) approaches. From the numerical results, it is found that the CSA-based approach is able to provide better solution at lesser computational effort.     

Multi objective stochastic microgrid scheduling incorporating dynamic voltage restorer

This paper focus on optimal scheduling of microgrid including thermal and electrical loads, renewable energy sources (solar and wind), combined heat and power (CHP), conventional energy sources (boiler and micro turbine), energy storage systems (thermal and electrical storages), and series flexible alternating current transmission system (FACTS) devices. Dynamic Voltage Restorer (DVR) is included in the line between the main network and the microgrid in order to achieve a higher power transfer to the upstream grid. In the proposed method, wind speed, solar radiation, and loads are modelled as uncertain parameters based on a stochastic approach. The problem is modelled as a linear, mixed integer, constrained, and multi objective optimization one aiming at minimizing cost and pollution at the same time. Also, a sensitivity analysis is proposed for studying the sensitive parameters in microgrid management. The proposed multi objective and stochastic problem is solved by using the augmented Epsilon-constraint method. All results and calculations are obtained by using GAMS24.1.3/CPLEX12.5.1. Finally, in order to confirm the results of the proposed method, final results are compared to the genetic algorithm method. Simulation results demonstrate the viability and effectiveness of the proposed scheduling method for microgrid.     

Scheduling of hydrothermal power systems

The authors present a method for scheduling hydrothermal power systems based on the Lagrangian relaxation technique. By using Lagrange multipliers to relax system-wide demand and reserve requirements, the problem is decomposed and converted into a two-level optimization problem. Given the sets of Lagrange multipliers, a hydro unit subproblem is solved by a merit order allocation method, and a thermal unit subproblem is solved by using dynamic programming without discretizing generation levels. A subgradient algorithm is used to update the Lagrange multipliers. Numerical results based on Northeast Utilities data show that this algorithm is efficient, and near-optimal solutions are obtained. Compared with previous work where thermal units were scheduled by using the Lagrangian relaxation technique and hydro units by heuristics, the new coordinated hydro and thermal scheduling generates lower total costs and requires less computation time     

一种基于分步遗传算法的多无人清洁车区域覆盖路径规划方法

为了解决不规则区域内多无人清洁车区域覆盖路径的全局规划问题,提出一种基于分步遗传算法的区域覆盖方法。 首 先,将目标区域依据清洁车大小进行栅格化,将多车辆区域覆盖路径规划问题转化为多旅行商(MTSP)问题。 然后,使用分步 遗传算法求解多旅行商问题:第 1 步采用模糊 c 均值聚类方法将求解多旅行商问题转化为求解多个单旅行商(TSP)问题;第 2 步使用了分步遗传算法对每个单旅行商问题进行求解,并使用杂草入侵算法中子父代共存的思想对遗传算法的选择机制进行 改进。 最后,分别在模拟的校园场景和小区场景中进行仿真实验。 实验结果表明,在两个场景中提出的方法能够实现多无人清 洁车完成区域路径覆盖,提出的分步遗传算法比分组遗传算法收敛速度更快;在校园场景中,提出的分步遗传算法相比于分组 遗传算耗时减少 54%,最优解路径长度减少 38%;在小区场景中,提出的分步遗传算法相比于分组遗传算耗时减少 55%,最优 解路径长度减少 44%。     

A Fast Production Scheduler for Generation Expansion Planning in a Hydro-Thermal System

A fast production scheduling algorithm suitable for generation expansion studies is described in this paper. It can handle several independent rivers, thermal plants, pumped storage plants, import, export, and internal non-firm markets. Inflows and load are deterministic and a one-reservoir limit is imposed on each river. The scheduling problem is formulated as a generalized network problem which is efficiently solved by an adaption of the simplex method. The algorithm is part of a program developed by Hydro-Québec to conduct preliminary evaluations of alternative expansion plans. The program and the scheduling algorithm are presented.     

电动汽车充放电与风力/火力发电系统的协同优化运行

提出一种通过控制规模化电动汽车的充放电,使其能够与现有的风力/火力发电系统协同运行的优化调度策略。针对传统含电动汽车的电力系统优化模型没有考虑电动汽车用户成本,实用性不高的缺陷,建立了包含电网运行经济性、电动汽车用户成本、CO2排放、最小弃风量的多目标优化模型;提出了将改进的NSGA-II遗传算法和加权尺度法相结合的智能优化算法。应用该算法,求出多目标动态优化模型的帕累托前沿,获得了最符合实际的电力系统综合优化调度方案。对所提出的多目标优化调度方法进行了仿真计算,结果证明,采用所提优化策略可以获得最佳的火电、风电与电动汽车之间的出力方案。该方案符合实际,在合理的电动汽车用户成本范围内可有效地降低电网运行成本、风力发电弃风量和大气碳排放量,应用价值较高。     

基于正弦余弦算法的NoC测试规划研究

如何实现多约束条件下测试时间优化是目前片上网络(NoC)测试中亟待解决的问题。提出一种基于正弦余弦算法(SCA)的NoC测试规划优化方法。采用专用TAM的并行测试方法,在满足功耗、引脚约束的条件下,建立测试规划模型,对NoC进行测试。通过群体围绕最优解进行正弦、余弦的波动,以及多个随机算子和自适应变量进行寻优,达到最小化测试时间的目的。在ITC’02 test benchmarks测试集上进行对比实验,结果表明相比粒子群优化(PSO)算法,提出的算法能够获得更短的测试时间。     

A Joint Smart Generation Scheduling Approach for Wind Thermal Pumped Storage Systems

Abstract

Energy storage plays a crucial role in the development of smart grids with high wind power penetration. Pumped storage is an effective solution for smoothing wind power fluctuation and reducing the operating cost for a wind thermal power system. The joint generation scheduling of power systems with mixed wind power, pumped storage, and thermal power is a challenging problem. This article proposes a novel two-stage generation scheduling approach for this problem in the contexts of smart grids. Through optimization, a day-ahead thermal unit commitment and pumped storage schedule are provided; then, in real time, the pumped storage schedule is updated to mitigate the wind power forecasting error and hence avoid the curtailment of wind power generation. The proposed model aims to reduce the total operating cost, accommodate uncertain wind power as much as possible, and smooth the output fluctuation faced by thermal units, while making the system operate in a relatively reliable way. A binary particle swarm optimization algorithm for solving the proposed model and the pumped storage schedule update algorithm are also presented. The model and algorithm are tested on a ten-generator test system.     

Short-term hydrothermal generation scheduling model using a genetic algorithm

A new model to deal with the short-term generation scheduling problem for hydrothermal systems is proposed. Using genetic algorithms (GAs), the model handles simultaneously the subproblems of short-term hydrothermal coordination, unit commitment, and economic load dispatch. Considering a scheduling horizon period of a week, hourly generation schedules are obtained for each of both hydro and thermal units. Future cost curves of hydro generation, obtained from long and mid-term models, have been used to optimize the amount of hydro energy to be used during the week. In the genetic algorithm (GA) implementation, a new technique to represent candidate solutions is introduced, and a set of expert operators has been incorporated to improve the behavior of the algorithm. Results for a real system are presented and discussed.     

Hybrid Chemical Reaction Optimization Approach for Combined Economic Emission Short-term Hydrothermal Scheduling

—This article presents the hybridization of a newly developed, novel, and efficient chemical reaction optimization technique and differential evolution for solving a short-term hydrothermal scheduling problem. The main objective of the short-term scheduling is to schedule the hydro and thermal plants generation in such a way that minimizes the generation cost. However, due to strict government regulations on environmental protection, operation at minimum cost is no longer the only criterion for dispatching electrical power. The idea behind the environmentally constrained hydrothermal scheduling formulation is to estimate the optimal generation schedule of hydro and thermal generating units in such a manner that fuel cost and harmful emission levels are both simultaneously minimized for a given load demand. In this context, this article proposes a hybrid chemical reaction optimization and differential evolution approach for solving the multi-objective short-term combined economic emission scheduling problem. The effectiveness of the proposed hybrid chemical reaction optimization and differential evolution method is validated by carrying out extensive tests on two hydrothermal scheduling problems with incremental fuel-cost functions taking into account the valve-point loading effects. The result shows that the proposed algorithm improves the solution accuracy and reliability compared to other techniques.     

A decentralized scheduling method for flowshop problems with resource constraints

In this paper, we propose a decentralized scheduling method for flowshop scheduling problems with resource constraints using the Lagrangian decomposition and coordination approach. When a flowshop scheduling problem with resource constraints is decomposed into machine‐level subproblems, the decomposed problem becomes very difficult to solve so as to obtain the optimal solution, even when the production sequence of operations is given. In this study, the decomposed subproblems are solved by a simulated annealing algorithm combined with dynamic programming. By decomposing the problem into single machine subproblems, the changeover cost can easily be incorporated in the objective function. In order to reduce the computation time, a heuristic algorithm for calculating the starting times of operations is also proposed. The performance of the proposed method is compared with that of the simulated annealing method by which the schedule of the entire machine is successively improved. Numerical results have shown that the proposed method can generate better solutions than the conventional method. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(1): 44–51, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10364     

Optimal short-term scheduling for a large-scale cascaded hydrosystem

This paper describes a short term hydro generation optimization program that has been developed by the Hydro Electric Commission (HEC) to determine optimal generation schedules and to investigate export and import capabilities of the Tasmanian system under a proposed DC interconnection with mainland Australia. The optimal hydro scheduling problem is formulated as a large scale linear programming algorithm and is solved using a commercially-available linear programming package. The selected objective function requires minimization of the value of energy used by turbines and spilled during the study period. Alternative formulations of the objective function are also discussed. The system model incorporates the following elements: hydro station (turbine efficiency, turbine flow limits, penstock head losses, tailrace elevation and generator losses), hydro system (reservoirs and hydro network: active volume, spillway flow, flow between reservoirs and travel time), and other models including thermal plant and DC link. A valuable by-product of the linear programming solution is system and unit incremental costs which may be used for interchange scheduling and short-term generation dispatch     

基于免疫遗传算法的超短期发电计划优化

超短期发电计划优化在电力系统调度运行中发挥着越来越重要的作用,但由于其是一个非线性整数约束优化问题,数学模型复杂,很难从理论上找到全局最优解。针对电力系统发电计划优化问题,引入免疫遗传算法,很好地解决了遗传算法局部收敛的问题,实现了群体收敛性和个体多样性间的动态平衡调整,能快速准确求解,及时调整超短期发电计划方案,从而达到安全经济环保调度,优化资源配置的效果。