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.     

Optimal reactive power dispatch using self-adaptive real coded genetic algorithm

In this paper, self-adaptive real coded genetic algorithm (SARGA) is used as one of the techniques to solve optimal reactive power dispatch (ORPD) problem. The self-adaptation in real coded genetic algorithm (RGA) is introduced by applying the simulated binary crossover (SBX) operator. The binary tournament selection and polynomial mutation are also introduced in real coded genetic algorithm. The problem formulation involves continuous (generator voltages), discrete (transformer tap ratios) and binary (var sources) decision variables. The stochastic based SARGA approach can handle all types of decision variables and produce near optimal solutions. The IEEE 14- and 30-bus systems were used as test systems to demonstrate the applicability and efficiency of the proposed method. The performance of the proposed method is compared with evolutionary programming (EP) and previous approaches reported in the literature. The results show that SARGA solves the ORPD problem efficiently.     

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.     

A diploid genetic approach to short-term scheduling ofhydro-thermal system

In this paper a diploid genotype based genetic algorithm (GA) is applied to solve the short-term scheduling of hydrothermal systems. The proposed genetic algorithm uses a pair of binary strings with the same length to represent a solution to the problem. The crossover operator is carried out by means of the separating and recombining technique, which is of the same effect of that of uniform crossover. The dominance mechanism in the algorithm is realized by a simple Boolean algebra calculation. Simulation results show that the proposed algorithm has a strong ability to maintain gene diversity in a limited population due to the diploid chromosomal structure accompanying the dominance mechanism. This ability improves the overall performance and avoids premature convergence. The model can concurrently tackle the requirements of power balance, water balance and water traveling time between cascaded power stations, which are more difficult for other approaches to manage. Several examples are used to verify the validity of the algorithm     

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.     

用改进遗传算法求解水火电力系统的有功负荷分配

水火电力系统的短期有功负荷分配在电力系统的经济运行中发挥着重要的作用，从本质上讲它是一个具有复杂约束条件的非线性大型动态优化问题，处理起来十分复杂，采用传统优化算法难以得到理想的结果。文中提出对决策变量直接采用浮点数编码技术，并根据给定的概率分布进行杂交操作和实施参数变异的改进遗传算法（RGA），用以求解此问题，最后用具体算例对该方法进行了验证。通过与二进制编码遗传算法所得结果进行对比分析，表明此法计算结果正确合理，收敛速度快，求解精度高。这也说明RGA不失为一种行之有效的优化方法，具有应用潜力。     

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.     

Multi-objective optimization of hydrothermal energy system considering economic and environmental aspects

Along with continuous global warming, the environmental problems, besides the economic objective, are expected to play more and more important role in the operation of hydrothermal power system. In this paper, the short-term multi-objective economic environmental hydrothermal scheduling (MEEHS) model is developed to analyze the operating approach of MEEHS problem, which simultaneously optimize energy cost as well as the pollutant emission effects. Meanwhile, transmission line losses among generation units, valve-point loading effects of thermal units and water transport delay between hydraulic connected reservoirs are taken into consideration in the problem formulation. In order to solve MEEHS problem, a new multi-objective cultural algorithm based on particle swarm optimization (MOCA-PSO) is presented in way of combining the cultural algorithm framework with particle swarm optimization (PSO) to carry though the evolution of population space. Furthermore, an effective constrain handling method is proposed to handle the operational constraints of MEEHS problem. The proposed method is applied to a hydrothermal power system consisting of four hydro plants and three thermal units for the case studies. Compared with several previous methods, the simulation solutions of MOCA-PSO with smaller fuel cost and lower emission effects proves that it can be an alternative method to deal with MEEHS problems. The obtained results demonstrate that the change of optimization objective leads to the shift of optimal operation schedules. Finally, the scheduling results of MEEHS problem offer enough choices to the decision makers. Thus, the operation with better performance of environment is achieved by more energy system cost.     

基于互补机制的水火电力系统短期节能发电调度

为充分提高水火电力系统联合运行的经济性,将减少非可再生能源的使用量及降低火电成本为主要目标的水火电力系统短期发电调度问题,转化为水力发电量最大、耗水量最小和火力发电燃料总耗量最小且具有时序的3个优化子问题。该优化模型不仅可确定水电的最佳放水策略和火电的最佳出力,还可描述水电和火电的互补作用,充分体现节能和效益的理念。针对水电系统具有强非线性的特点,采用改电磁学算法进行求解,对火电子系统则采用内点法进行求解。算例结果验证了该方法的有效性。     

A genetic algorithm solution approach to the hydrothermal coordination problem

In this paper, a genetic algorithm solution to the hydrothermal coordination problem is presented. The generation scheduling of the hydro production system is formulated as a mixed-integer, nonlinear optimization problem and solved with an enhanced genetic algorithm featuring a set of problem-specific genetic operators. The thermal subproblem is solved by means of a priority list method, incorporating the majority of thermal unit constraints. The results of the application of the proposed solution approach to the operation scheduling of the Greek Power System, comprising 13 hydroplants and 28 thermal units, demonstrate the effectiveness of the proposed algorithm.     

Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network

This paper proposes an improved priority list (IPL) and augmented Hopfield Lagrange neural network (ALH) for solving ramp rate constrained unit commitment (RUC) problem. The proposed IPL-ALH minimizes the total production cost subject to the power balance, 15 min spinning reserve response time constraint, generation ramp limit constraints, and minimum up and down time constraints. The IPL is a priority list enhanced by a heuristic search algorithm based on the average production cost of units, and the ALH is a continuous Hopfield network whose energy function is based on augmented Lagrangian relaxation. The IPL is used to solve unit scheduling problem satisfying spinning reserve, minimum up and down time constraints, and the ALH is used to solve ramp rate constrained economic dispatch (RED) problem by minimizing the operation cost subject to the power balance and new generator operating frame limits. For hours with insufficient power due to ramp rate or 15 min spinning reserve response time constraints, repairing strategy based on heuristic search is used to satisfy the constraints. The proposed IPL-ALH is tested on the 26-unit IEEE reliability test system, 38-unit and 45-unit practical systems and compared to combined artificial neural network with heuristics and dynamic programming (ANN-DP), improved adaptive Lagrangian relaxation (ILR), constraint logic programming (CLP), fuzzy optimization (FO), matrix real coded genetic algorithm (MRCGA), absolutely stochastic simulated annealing (ASSA), and hybrid parallel repair genetic algorithm (HPRGA). The test results indicate that the IPL-ALH obtain less total costs and faster computational times than some other methods.     

Binary fireworks algorithm for profit based unit commitment (PBUC) problem

The deregulation of electricity markets has transformed the unit commitment and economic dispatch problem in power systems from cost minimization approach to profit maximization approach in which generation company (GENCO)/independent power producer (IPP) would schedule the available generators to maximize the profit for the forecasted prices in day ahead market (DAM). The PBUC is a highly complex optimization problem with equal, in equal and bound constraints which allocates scheduling of thermal generators in energy and reserve markets with no obligation to load and reserve satisfaction. The quality of the solution is important in deciding the commitment status and there by affecting profit incurred by GENCO/IPPs. This paper proposes a binary coded fireworks algorithm through mimicking spectacular display of glorious fireworks explosion in sky. In deregulated market GENCO/IPP has the freedom to schedule its generators in one or more market(s) based on the profit. The proposed algorithm is tested on thermal unit system for different participation scenarios namely with and without reserve market participation. Results demonstrate the superiority of the proposed algorithm in solving PBUC compared to some existing benchmark algorithms in terms of profit and number of iterations.     

Integrating genetic algorithms, tabu search, and simulatedannealing for the unit commitment problem

This paper presents a new algorithm based on integrating genetic algorithms, tabu search and simulated annealing methods to solve the unit commitment problem. The core of the proposed algorithm is based on genetic algorithms. Tabu search is used to generate new population members in the reproduction phase of the genetic algorithm. A simulated annealing method is used to accelerate the convergence of the genetic algorithm by applying the simulated annealing test for all the population members. A new implementation of the genetic algorithm is introduced. The genetic algorithm solution is coded as a mix between binary and decimal representation. The fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the proposed algorithm, a simple short-term memory procedure is used to counter the danger of entrapment at a local optimum, and the premature convergence of the genetic algorithm. A simple cooling schedule has been implemented to apply the simulated annealing test in the algorithm. Numerical results showed the superiority of the solutions obtained compared to genetic algorithms, tabu search and simulated annealing methods, and to two exact algorithms     

处理梯级水电站复杂约束的短期水火电系统环境经济优化调度

首先建立采用迭代费用惩罚系数的单目标水火电系统环境经济优化调度模型;其次为解决梯级水电站由于时间耦合性和空间相关性而带来的同时处理发电流量约束、库容约束和动态水量平衡约束的难题,给出约束条件的启发式处理方法,使得在满足上述复杂约束的同时,更利于最优解的搜寻。对总装机容量为2 975 MW的水火电系统(包含一个含4水电机组的梯级水电站和3个火电机组)进行仿真计算,结果不仅表明了该启发式约束条件处理方法的可行性和有效性,而且对比进化算法和差分进化算法所得结果,每天的燃料费用分别降低了4 303.96$和1 311.96$,污染气体排放量分别减少8 231.37 lb和1 522.37 lb。     

Cost/environmentally compromised dispatch for cascaded hydrothermal system using artificial bee colony algorithm

This paper evaluates the robustness of the artificial bee colony (ABC) algorithm while allocating optimal power generation in a hydrothermal power system at the level of minimum fuel cost and minimum pollutant emission impacts on the environment subjected to physical and technical constraints. The hydrothermal scheduling (HTS) is devised in a bi‐objective framework so as to optimize both objectives of fuel cost and emission release, individually and simultaneously subjected to a verity of intricate equality and inequality constraints. Initially, all feasible solutions are obtained through random search, and then the ABC algorithm is used for the exploration and exploitation processes together in the search space, thereby discovering the optimal hourly schedule of power generation in the hydrothermal system. Meanwhile, a dependent hydro‐discharge computation handles the equality constraints; especially, the reservoir end volume and slack thermal generating unit for each sub‐interval handle the power balance equality constraint. The performance of the proposed approach is illustrated on a multi‐chain interconnected hydrothermal power system with due consideration of the water transport delay between connected reservoirs and transmission loss of system load. The results obtained from the proposed technique are compared with those of other techniques. The results demonstrate that the ABC algorithm is feasible and efficient for solving the HTS problem. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

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.     

综合环境保护及峰谷电价的水火电短期优化调度

为了使电力市场环境中的发电侧能够实现节能环保且高收益的发电目标,对机组出力变化与分时电价波动之间的关系进行了研究,构建了一种新的水火电短期优化调度模型,该模型以实现电力市场条件下最大发电收益为目标,同时综合考虑了峰谷分时电价和环境保护成本对发电侧经济效益的影响,还考虑了梯级水电站群的蓄水量、下泄流量、机组出力等约束条件,由此得出机组的优化调度方案。针对传统优化算法难以处理高维梯级水电站优化调度多约束条件的缺陷,利用微分进化算法对此优化模型进行求解,仿真计算结果证明了该模型的合理性和算法的有效性。     

Teaching learning based optimization for short-term hydrothermal scheduling problem considering valve point effect and prohibited discharge constraint

This article presents a novel teaching learning based optimization (TLBO) to solve short-term hydrothermal scheduling (HTS) problem considering nonlinearities like valve point loading effects of the thermal unit and prohibited discharge zone of water reservoir of the hydro plants. TLBO is a recently developed evolutionary algorithm based on two basic concept of education namely teaching phase and learning phase. In first phase, learners improve their knowledge or ability through the teaching methodology of teacher and in second part learners increase their knowledge by interactions among themselves. The algorithm does not require any algorithm-specific parameters which makes the algorithm robust. Numerical results for two sample test systems are presented to demonstrate the capabilities of the proposed TLBO approach to generate optimal solutions of HTS problem. To test the effectiveness, three different cases namely, quadratic cost without prohibited discharge zones; quadratic cost with prohibited discharge zones and valve point loading with prohibited discharge zones are considered. The comparison with other well established techniques demonstrates the superiority of the proposed algorithm.     

Thermal unit commitment using binary/real coded artificial bee colony algorithm

This paper presents a binary/real coded artificial bee colony (BRABC) algorithm to solve the thermal unit commitment problem (UCP). A novel binary coded ABC with repair strategies is used to obtain a feasible commitment schedule for each generating unit, satisfying spinning reserve and minimum up/down time constraints. Economic dispatch is carried out using real coded ABC for the feasible commitment obtained in each interval. In addition, non-linearities like valve-point effect, prohibited operating zones and multiple fuel options are included in the fuel cost functions. The effectiveness of the proposed algorithm has been tested on a standard ten-unit system, on IEEE 118-bus test system and IEEE RTS 24 bus system. Results obtained show that the proposed binary ABC is efficient in generating feasible schedules.     

Optimal Thermal Unit Commitment Integrated with Renewable Energy Sources Using Advanced Particle Swarm Optimization

This paper presents a methodology for solving generation planning problem for thermal units integrated with wind and solar energy systems. The renewable energy sources are included in this model due to their low electricity cost and positive effect on environment. The generation planning problem also known by unit commitment problem is solved by a genetic algorithm operated improved binary particle swarm optimization (PSO) algorithm. Unlike trivial PSO, this algorithm runs the refinement process through the solutions within multiple populations. Some genetic algorithm operators such as crossover, elitism, and mutation are stochastically applied within the higher potential solutions to generate new solutions for next population. The PSO includes a new variable for updating velocity in accordance with population best along with conventional particle best and global best. The algorithm performs effectively in various sized thermal power system with equivalent solar and wind energy system and is able to produce high quality (minimized production cost) solutions. The solution model is also beneficial for reconstructed deregulated power system. The simulation results show the effectiveness of this algorithm by comparing the outcome with several established methods. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.