Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to earlier studies, we model the on–off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas. Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper. Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement.     

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     

Short-term operation scheduling of a hydropower plant in the day-ahead electricity market

This paper presents a novel approach to solve the short-term operation scheduling problem of a hydropower plant that sells energy in a deregulated electricity market with the objective of maximizing its revenue. This paper proposes a nonlinear programming based scheduling model that determines both the optimal unit commitment (start-ups and shut-downs scheduling) and the generation dispatch of the committed units (hourly power output). The power generated by each hydro unit is considered as a nonlinear function of the water discharge and the volume of the associated reservoir. The dependence of the units’ operating limits (maximum and minimum water flows) on the actual gross head has been also taken into account in this model. The results from a case study are also presented to illustrate the application of the proposed approach in a real hydro plant.     

Optimal operation of reservoirs for electric generation

Several tests have been performed with a simple test system under special conditions in order to highlight the influence of several factors including water head, discount rate, inflow seasonality, and system design. According to the results, reservoirs should operate at the highest possible storage level in order to maximize the generation efficiency of their associated power plants. This conservative behavior is shown to be the most economic for generation purposes. On the other hand, in a cascade system, the water head factor has the effect of specializing the behavior of the reservoirs. Reservoirs in the upper part of the cascade should play a regulation role while in the lower part of the cascade they should operate as run-of-river plants. These results have been verified on an actual large-scale hydroelectric system, the Brazilian South-Southeast Interconnected Electric System, composed of 51 hydro plants and 31 reservoirs     

Experiences with mixed integer linear programming based approacheson short-term hydro scheduling

This paper describes experiences with mixed integer linear programming (MILP) based approaches on the short-term hydro scheduling (STHS) function. The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hydro units in a hydro-dominant system for a user-definable study period at each time step while respecting all system and hydraulic constraints. The problem can be modeled in detail for a hydro system that contains both conventional and pumped-storage units. Discrete and dynamic constraints such as unit startup/shutdown and minimum-up/minimum-down time limits are also included in the model for hydro unit commitment (HUC). The STHS problem is solved with a state-of-the-art package which includes an algebraic modeling language and a MILP solver. The usefulness of the proposed solution algorithm is illustrated by testing the problem with actual hydraulic system data. Numerical experiences show that the solution technique is computationally efficient, simple, and suitable for decision support of short-term hydro operations planning. In addition, the proposed approaches can be easily extended for scheduling applications in a deregulated environment     

A noise annealing neural network for hydroelectric generationscheduling with pumped-storage units

A new approach based on neural network is proposed for the hydroelectric generation scheduling with pumped-storage units at Taiwan power system. The purpose of hydroelectric generation scheduling is to determine the optimal amounts of generated powers for the hydro units in the system. To achieve an economical dispatching schedule for the hydro units including two large pumped-storage plants, a neural network is employed to reach a schedule in which total fuel cost of the thermal units over the study period is minimized. The neural network model presented can solve nonlinear constrained optimization problems with continuous decision variables. Incorporating the noise annealing concepts, the model is able to produce such a solution which is the global optimum of the original problem with probability close to 1. The proposed approach is applied to hydroelectric generation scheduling of Taiwan power system. It is concluded from the results that the proposed approach is very effective in reaching proper hydro generation schedules     

A coordinated approach for real-time short term hydro scheduling

The paper describes a coordinated approach to short-term hydroelectric power generation scheduling and dispatch that has been developed as a part of the Tasmanian Hydro Electric Commission's new energy management system, which is being delivered by Landis and Gyr Energy Management. Tasmania's hydroelectric power generation system consists of 40 reservoirs in six river catchments. The daily water release for each plant is scheduled using the HEC's mid-term operation policy     

A Hybrid Method for Optimal Scheduling of Short-Term Electric Power Generation of Cascaded Hydroelectric Plants Based on Particle Swarm Optimization and Chance-Constrained Programming

A novel strategy for optimal scheduling of short-term electric power generation of cascaded hydroelectric plants based on particle swarm optimization (PSO) and chance-constrained programming is presented to maximize the expected profit at a given risk level in this paper. Based on chance-constrained programming, in which some specified probability are given to simulate some uncertainties, such as water inflows, electricity prices, unit status, and so on. This paper proposes a model for short-term scheduling optimization of cascaded hydro plants, which includes uncertainties, spatial-temporal constraints among cascaded reservoirs, etc. A hybrid particle swarm optimization (HPSO), which is embedded with evolutionary algorithms, is presented to use for the solution of global optimization problems. Catastrophe theory, which is concerned with natural evolutionary or survival-of-the-fittest, is utilized as an indication of the premature converge of PSO, and the positions of particles are further adjusted in the search space according to chaos optimization. In this way, each particle competes and cooperates with its neighbors. The proof shows that HPSO is guaranteed to converge to the global optimization solution with probability one. The model presented is solved by a combination method of HPSO and Monte Carlo simulation. Finally, a numerical example is served for demonstrating the feasibility of the method developed.      

Effect of a pumped storage plant on the generation reliability of the Taiwan power system

A novel approach to the reliability analysis of a power system with both hydro and pumped storage plants is presented in this paper. The proposed method is based on the concept of peak shaving for the hydro and pumped storage units. Different values of the stored energy of the pumped storage units are employed to demonstrate their effect on the generation reliability of a power system. The proposed scheme has been applied successfully to the reliability analysis of Taiwan power system.     

梯级水电站联合优化发电调度

梯级水电站联合发电调度的优化模型的确定在整个电网经济、安全运行中起着非常重要的作用。文中提出一种新的梯级水电站群联合发电优化调度的调度准则——以单位水体发电电价最高优先发电,在此基础上建立梯级水电站群联合发电优化调度模型及其评价方法。首先建立基于四层水体的水库能的水电站发电模型,在此基础上提出单位水体发电电价的概念。建立优化调度模型时,将电力系统中的负荷变化和在电力市场机制下分时上网电价的影响因素考虑在内。该模型能较为客观地反映梯级水电站运行情况,能给系统调度员做出最佳调度决策提供一定的依据。优化仿真计算结果证明该调度准则具有可行性和适用性。     

Optimal dispatch of generating units of the Itaipu hydroelectricplant

This paper is concerned with the optimal dispatch of generating units of Itaipu, the world's largest hydroelectric plant in operation. Itaipu is a 12.6 GW hydro plant, located on the Parana river, in South America, composed of 18 identical 700 MW generating units. A dynamic programming model has been developed to optimize the number of generating units in operation at each hour of the day in order to attain the total generation scheduling of the plant in the most economic way. The model highlights the tradeoff between start-up/shut-down of generating units and hydro power efficiency, taking into account variations in tailrace elevation, penstock head losses and turbine-generator efficiencies. The methodology has been tested for a typical generation scheduling, and the results show that the number of the turbine-generator sets dispatched has a major influence on the overall hydroplant efficiency, and therefore it is a key aspect to be considered in the dispatch of hydro generating units. In the case of Itaipu, the economic benefits, in terms of greater power efficiency with respect to actual operation, are in the range of millions of dollars per year     

基于水电厂调峰运行的水火电混合经济调度

在改进单亲遗传算法的基础上,以火电机组运行费用最小化为目标函数,提出了求解方法。模型中计入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,以及水电系统中多级水库的水流延迟等因素。算例仿真计算的结果表明该方法求解精度高、收敛速度快,进一步验证了算法的正确性和有效性。     

Optimal operation and hydro storage sizing of a wind–hydro power plant

Ambitious targets for renewable power production have been defined for the electric power systems in Europe. The accomplishment of these targets requires the increase in renewable energy production, namely from wind power generation. However, the intermittent nature of wind creates several problems to the power system operation and new approaches based on the combined use of wind power and energy storage technologies need to be developed. In this paper, the concept of the combined use of wind power production and hydro storage/production is exploited, through the development of an operational optimisation approach applied to a wind generator park with little water storage ability. The optimisation model defines the operational strategy to be followed for the hours ahead by a pump station and an hydraulic generator embedded in a wind/hydro pumping facility, using the Portuguese energy remuneration rules. The proposed methodology leads to considerable yearly profits for the wind generator production.     

梯级水电站多目标模糊优化调度模型及其求解方法

根据梯级水电站不仅具有电力联系而且具有水力联系的运行特点,提出一种以年发电量和一级水电站耗水量为优化目标的梯级水电站多目标长期优化调度模型.通过定义各目标的隶属度函数,将多目标优化问题模糊化;采用最大模糊满意度法将多目标优化问题转化为单目标非线性规划问题;应用协调粒子群算法(CPSO)求解单目标优化问题.仿真验证了模型的正确性和求解方法的可行性,为梯级水电站优化调度提供了一种新颖有效的途径.     

Differential evolution technique-based short-term economic generation scheduling of hydrothermal systems

This paper presents differential evolution (DE)-based optimization technique for solving short-term economic generation scheduling of hydrothermal systems. A multi-reservoir cascaded hydrothermal system with non-linear relationship between water discharge rate, power generation and net head is considered here. The water transport delay between the connected reservoirs is also taken into account. Several equality and non-equality constraints on thermal units as well as hydro units and the effect of valve-point loading are also included in the problem formulation. The effectiveness of the proposed method is demonstrated on two test systems comprising of hydro and thermal units. Convergence characteristic of the proposed technique has been found to be quite satisfactory. The results obtained by the proposed technique are compared with other evolutionary methods. It is seen that the proposed technique is capable of producing encouraging solutions.     

Proposal of a simplified method for integrating reduction of effective power of pumped storage into a generation system planning method

Pumped storage hydropower stations are extensively used as peaking and reserve power plants. The current trend in this area is to increase their power output relative to the capacity of reservoirs, which results in a shorter maximum duration of full‐power operation while availability of the energy required for the pumping becomes less evident. This increases the possibility of reducing the effective power of pumped storage units in the case of a tight supply–demand balance in the power system. Although many studies have examined a role of pumped storage in generation systems, few studies have explicitly dealt with the power reduction. This paper proposes a new linear programming model that incorporates the reduction of effective power of pumped storage. The proposed model makes it possible to easily incorporate the power reduction in computations by employing hypothetical daily load curves and dispatching loads to the curves. The model also includes LNG combined cycle power generation plants that are now being intensively implemented. The developed model is applied to a power system model. The sample study reveals that the reduction of effective power considerably varies from season to season and the reduction highly affects the optimal generation mix, that is, the optimal share of pumped storage. © 2001 Scripta Technica, Electr Eng Jpn 134(4): 50–61, 2001     

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。     

梯级水电系统组合优化调度方法研究

文章提出两种基于Ｌａｇｒａｎｇｅ松驰技术的梯级水电系统优化调度算法,能够综合处理离散运行区间,最小启停机时间等离散约束、水库间的水力耦合网络约束以及水头影响。基于实际系统数据的数值仿真,表明了该算法的有效性和实用性。     

求解水电站日负荷优化分配的混合整数非线性规划模型

考虑水电调度复杂非线性关系,提出水电站日负荷优化分配的混合整数非线性规划(MINLP)模型。采用多项式拟合技术处理MINLP模型中的水位、库容、流量、出力等多变量耦合函数关系,分析确定了适合的多项式阶数和描述方式,构建了水位与库容、尾水位与出库流量的一元四次多项式,提出表征机组出力的水头和发电流量二元二次拟合方法,得到了水头—流量—出力关系三维拟合曲面,可以满足变化水头下机组出力的精细化计算要求。最后,采用成熟的MINLP求解器实现高效计算。提出的模型通过溪洛渡18台机组日负荷分配问题得到验证,从模型应用复杂度和结果精度两方面与经典混合整数线性规划(MILP)模型进行比较,表明MINLP模型应用便捷且精度较高,与实际耗水量的误差较MILP模型减少91%,更能反映水电站实际情况。     

基于进化捕食策略法的风-水-火电短期负荷分配优化

考虑负荷与风电的不确定性,建立了基于机会约束规划的风-水-火电短期负荷分配优化模型。为了更好地权衡局部搜索与全局搜索性能,应用进化捕食策略法求解水-火电短期优化调度与风-水-火电短期负荷分配问题。算例结果表明,与其他算法相比,进化捕食策略法在水-火电短期优化调度中能够搜索到更优的解,同时基于机会约束规划的优化方法为系统旋转备用容量的合理设置提供了依据。