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.     

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     

Hydrothermal self-scheduling problem in a day-ahead electricity market

This paper addresses the self-scheduling problem of determining the unit commitment status for power generation companies before submitting the hourly bids in a day-ahead market. The hydrothermal model is formulated as a deterministic optimization problem where expected profit is maximized using the 0/1 mixed-integer linear programming technique. This approach allows precise modelling of non-convex variable cost functions and non-linear start-up cost functions of thermal units, non-concave power-discharge characteristics of hydro units, ramp rate limits of thermal units and minimum up and down time constraints for both hydro and thermal units. Model incorporates long-term bilateral contracts with contracted power and price patterns, as well as forecasted market hourly prices for day-ahead auction. Solution is achieved using the homogeneous interior point method for linear programming as state of the art technique, with a branch and bound optimizer for integer programming. The effectiveness of the proposed model in optimizing the generation schedule is demonstrated through the case studies and their analysis.     

水火电力系统短期节能与经济发电优化调度

选取节能和经济两个决策目标,建立水火电力系统发电多目标优化调度模型,寻求满足决策目标的最优调度方案。根据水力发电和火力发电的能耗特性,引入同等装机容量技术条件下水煤转换系数的概念,建立了水火电力系统联合发电能耗模型以及火电综合成本模型,并选取水火电力系统发电等效总煤耗最小作为节能调度的目标,选取火电厂发电综合成本最小作为经济调度的目标,对含有梯级水电站群和多个火电厂的大区域性电力系统进行多目标优化调度。以一个具有8个梯级水电站和8个火电厂的水火电力系统为例进行仿真,其结果证明所建的节能与经济发电优化调度模型能够在增加发电量的同时,提高水资源利用率,节约煤炭资源,降低火电成本,创造良好的发电效益和经济效益。     

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.     

Short-term hydrothermal scheduling through evolutionary programming technique

An efficient short-term hydrothermal scheduling algorithm based on the evolutionary programming (EP) technique is proposed. In the algorithm, the thermal generating units in the system are represented by an equivalent unit. The power balance constraints, total water discharge constraint, reservoir volume constraints and the constraints on the operation limits of the equivalent thermal and hydro units are fully taken into account. The effectiveness of the proposed algorithm is demonstrated through an example system and the results are compared with those obtained by the classical gradient search and simulated annealing (SA) approaches. Numerical results show that the proposed EP approach provides a cheaper schedule even than the SA approach and hence, has more powerful ability to achieve the global optimum solution than the SA approach.     

Short term hydro–wind–thermal scheduling based on particle swarm optimization technique

Hydro–wind–thermal scheduling is one of the most important optimization problems in power system. An aim of the short term hydrothermal scheduling of power systems is to determine the optimal hydro, wind and thermal generations in order to meet the load demands over a scheduled horizon of time while satisfying the various constraints on the hydraulic, wind and thermal power system network. In this paper we present optimal hourly schedule of power generation in a hydro–wind–thermal power system applying PSO technique. The simulation results inform that the proposed PSO approach appears to be the powerful to minimize fuel cost and it has better solution quality and good convergence characteristics than other techniques.     

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.     

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.     

河南电网AGC水火电联调试验研究

在华中网调对各省调的联络线电量考核办法由区域控制偏差(ACE)模式转变为控制性能标准(CPS)模式的背景下,由于河南电网的水电机组较少,因而水火电自动发电控制(AGC)机组的协调控制成为一个有待解决的问题。提出了2种控制模式,并进行了水火电联调试验研究。根据试验结果,对2种控制模式及其不同应用方案的特性和效果进行分析比较,在此基础上提出水火电机组同时投运时的合理控制方案,并针对联调试验中出现的问题,确定需要进一步开展的工作。     

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.     

基于遗传算法的水火电混合电力系统短期发电计划优化

在改进传统遗传算法的基础上 ,提出了水火电混合电力系统短期发电计划优化问题的数学模型和求解方法。模型计及了水电机组的发电流量、净水头和输出功率间的非线性关系 ,水电系统中多级水库的水流延迟等因素。算例表明本算法能更有效地达到或接近全局最优解 ,对编制大型水火电混合电力系统的日调度计划有实用价值。     

Power generation scheduling for multi-area hydro-thermal systemswith tie line constraints, cascaded reservoirs and uncertain data

The authors propose an approach to the short-term generation scheduling of hydro-thermal power systems (GSHT). The objective of GSHT is to minimize the total operation cost of thermal units over the scheduling time horizon. To solve the problem within a reasonable time, the problem is decomposed into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. A probabilistic method is employed in considering load forecasting errors and forced outages of generating units to satisfy system reliability requirements. For the hydro subsystem, network flow concepts are adopted to coordinate water use over the entire study time span and the reduced gradient method is used to overcome the linear characteristic of the network flow method to obtain the optimal solution. Three case studies for the proposed method are presented     

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.     

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 new long-term hydro production scheduling method for maximizingthe profit of hydroelectric systems

This paper presents a new long-term hydrothermal production scheduling method. The proposed method maximizes the profit of hydroelectric plants, based on the monthly energy requirement of the system, instead of minimizing the production cost of thermal units. It is shown that different forms of composite thermal marginal costs will lead to the same hydro production schedule. Thus a linear marginal cost, the simplest form, is sufficient for long-term hydrothermal scheduling. A linear hydro marginal profit is also sufficient for this purpose. An immediate conclusion is that an actual composite thermal cost function, which is complicated by thermal unit availability, may not be needed for the long-term optimal hydrothermal scheduling. Due to this simplification, traditional long and mid-term hydrothermal scheduling, a complicated problem, becomes easier to solve. The method can be used by the owners of independent hydro plants in a region for long-term hydroelectric scheduling under both deregulation and competition. A case study shows that the model allocates successfully and efficiently the hydroelectric resources to peak demand periods with negligible computation time     

An efficient method for optimal scheduling of fixed head hydro andthermal plants

An efficient and optimal method for scheduling thermal plants in coordination with fixed-head hydro units is presented. The method linearizes the coordination equation and solves for the water availability constraint separately from unit generation. Once the water constraint Lagrange multiplier is determined, the unit output can be computed easily. Case studies with various systems are presented and discussed     

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.     

Active power based distance protectionscheme in the presence of seriescompensators

This paper presents opposition-based differential evolution to determine the optimal hourly schedule of power generation in a hydrothermal system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Opposition-based differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based differential evolution (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. The effectiveness of the proposed method has been verified on two test problems, two fixed head hydrothermal test systems and three hydrothermal multi-reservoir cascaded hydroelectric test systems having prohibited operating zones and thermal units with valve point loading. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based differential evolution based approach is able to provide better solution.     

Opposition-based differential evolution for hydrothermal power system

This paper presents opposition-based differential evolution to determine the optimal hourly schedule of power generation in a hydrothermal system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Opposition-based differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based differential evolution (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. The effectiveness of the proposed method has been verified on two test problems, two fixed head hydrothermal test systems and three hydrothermal multi-reservoir cascaded hydroelectric test systems having prohibited operating zones and thermal units with valve point loading. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based differential evolution based approach is able to provide better solution