Identifying Explicit Formulation of Operating Rules for Multi-Reservoir Systems Using Genetic Programming

Operating rules have been widely used to handle the inflows uncertainty for reservoir long-term operations. Such rules are often expressed in implicit formulations not easily used by other operators and/or reservoirs directly. This study presented genetic programming (GP) to derive the explicit nonlinear formulation of operating rules for multi-reservoir systems. Steps in the proposed method include: (1) determining the optimal operation trajectory of the multi-reservoir system using the dynamic programming to solve a deterministic long-term operation model, (2) selecting the input variables of operating rules using GP based on the optimal operation trajectory, (3) identifying the formulation of operating rules using GP again to fit the optimal operation trajectory, (4) refining the key parameters of operating rules using the parameterization-simulation-optimization method. The method was applied to multi-reservoir system in China that includes the Three Gorges cascade hydropower reservoirs (Three Gorges and Gezhouba reservoirs) and the Qing River cascade hydropower reservoirs (Shuibuya, Geheyan and Gaobazhou reservoirs). The inflow and storage energy terms were selected as input variables for total output of the aggregated reservoir and for decomposition. It was shown that power energy term could more effectively reflect the operating rules than water quantity for the hydropower systems; the derived operating rules were easier to implement for practical use and more efficient and reliable than the conventional operating rule curves and artificial neural network (ANN) rules, increasing both average annual hydropower generation and generation assurance rate, indicating that the proposed GP formulation had potential for improving the operating rules of multi-reservoir system.     

耦合KL理论与调度特征的大规模水电站群优化调度降维方法

大规模水电站群优化调度计算效率是水电及电力系统运行面临的最棘手问题之一,是突破超百座水电站高维复杂系统求解的理论和技术障碍。本文提出一种耦合KL理论与调度特征的水电优化调度降维方法,通过对水电站群长系列调度样本进行主成分分析,识别调度过程中的库水位变化特征值与其对应的特征函数,采用KL理论将库水位描述为多个水位变化特征项的组合函数,引入Kullback-Leibler散度以根据问题特点确定调度特征项随机系数的概率分布及初始值;构建了两阶段逐步迭代寻优策略,通过动态搜索水位特征项的随机系数实现大规模水电站群优化调度的高效求解。提出的方法以云南电网超百座水电站群调度问题进行了验证,通过不同算例对方法的有效性、高效性、随机系数概率分布和参数敏感性进行了分析,与经典动态规划及其改进算法相比,KL方法在有效保持结果精度的条件下显著提高了计算效率。     

双层耦联遗传算法求解流域梯级水电站厂内经济运行问题研究

针对梯级水电站厂内经济运行调度模型约束条件多、求解复杂的问题,提出了一种基于遗传算法的双层耦联求解算法,该算法兼有机组负荷分配和机组组合双重优化的特点,可同时求得厂内经济运行优化调度模型的全局最优解.研制开发了基于此算法的梯级水电站厂内经济运行优化调度程序软件,并且已应用于某流域梯级水电站厂内经济运行实际调度计算中,取得了较高的工程应用价值.     

An Efficient Linearization Method for Long-Term Operation of Cascaded Hydropower Reservoirs

The hydropower reservoir operation is a challenging optimization problem due to the nonlinear factors, where the water head, reservoir storage, release, generating capacity, and water rate are interconnected. To solve such a difficult problem in an efficient and stable way based on mathematical programming, efficient linearization method with high accuracy is of vital importance. This paper simplifies the hydropower output as the function of average reservoir storage and release, and presents an efficient piecewise linearization method that concaves the hydropower output function with a series of planes, which transforms the original nonlinear problem into a linear programming one without introducing any integer variables. The presented method is applied to a long-term hydropower scheduling (LHS) problem with 7 cascaded reservoirs, and a nonlinear direct search procedure is then employed to search further. The performance is compared with that of another linearization method that uses special ordered sets of type two, case study shows that LHS using the presented linearization method runs much faster and obtains results very close to that of the latter one. The presented method, as a high performance exact algorithm, should be very promising in solving the real-world hydropower operation problems.     

Water Management of Irrigation Dams Considering Climate Variation: Case Study of Zayandeh-rud Reservoir, Iran

Dependency of reservoir operation on the climate variation occurs especially in regions, where agricultural demand has a significant share of the total water demands. The variability between demands that are based on annual climate conditions may be larger than the uncertainty associated with other explanatory variables in long-term operation of an irrigation dam. This paper proposed a rule curves to the water managers of the Zayandeh-rud reservoir in Iran in long-lead reservoir operation. A regional optimal allocation of water among different crops and irrigation units is developed. The optimal allocation model is coupled with a reservoir operating model, which is developed based on the certain hedging that deals with the available water and the water demands mutually. This coupled model is able to activate restrictions on allocating water to agricultural demands considering variation of inflow to the reservoir, variation of demands and the economic value of allocating water among different crops and irrigation units. The resulted rule curve is presented with a number of tables for more details and accuracy and a simple curve, which is more useful for operational purpose.     

隔河岩水电站实时运行负荷分配控制研究

针对隔河岩水电站机组自动控制方式下的实时运行负荷分配,从时间和空间两方面建立双目标实时负荷分配模型,并提出水电站不可调控区的判定及区内运行策略。在时间上采用机组优先顺序判定与开停机原则相结合的方法安排机组组合,用动态规划法求解空间目标、同时协调时间目标求得一组优化解,并根据少开停机、少穿越振动区等需要筛选合适的负荷分配方案。经隔河岩水电站模拟运行,节约了用水并减少了机组穿越振动区次数,效果显著。     

基于耗水率动态规划模型的水电站水库优化调度

目前水电站水库优化调度常侧重于提高算法的精度和计算的速度,往往忽视了优化调度模型本身的合理性和准确性。综合耗水率是衡量水电站经济运行情况的重要指标。基于耗水率动态规划模型的水电站水库优化调度方法,依据水电站长期运行的历史资料,采用水电站综合耗水率参数作为水电站水库优化计算的基础,使优化结果更符合水库经济运行的实际要求。     

Chaotic Evolutionary Algorithms for Multi-Reservoir Optimization

The water sharing dispute in a multi-reservoir river basin forces the water resources planners to have an integrated operation of multi-reservoir system rather than considering them as a single reservoir system. Thus, optimizing the operations of a multi-reservoir system for an integrated operation is gaining importance, especially in India. Recently, evolutionary algorithms have been successfully applied for optimizing the multi-reservoir system operations. The evolutionary optimization algorithms start its search from a randomly generated initial population to attain the global optimal solution. However, simple evolutionary algorithms are slower in convergence and also results in sub-optimal solutions for complex problems with hardbound variables. Hence, in the present study, chaotic technique is introduced to generate the initial population and also in other search steps to enhance the performance of the evolutionary algorithms and applied for the optimization of a multi-reservoir system. The results are compared with that of a simple GA and DE algorithm. From the study, it is found that the chaotic algorithm with the general optimizer has produced the global optimal solution (optimal hydropower production in the present case) within lesser generations. This shows that coupling the chaotic algorithm with evolutionary algorithm will enrich the search technique by having better initial population and also converges quickly. Further, the performances of the developed policies are evaluated for longer run using a simulation model to assess the irrigation deficits. The simulation results show that the model satisfactorily meets the irrigation demand in most of the time periods and the deficit is very less.     

Application Research of the Improved Overall Temporal and Spatial Economic Operation Model Based on Information Entropy in Large-Scale Hydropower Station

For the high dimensional and complex inner-plant economical operation problem of large hydropower station, an improved ant colony optimization with adaptive ability, inspiring ability and local search ability was proposed. Spatial optimal load distribution model and temporal unit commitment model was combined into an overall temporal and spatial economic operation model, in which an innovative ant colony model of multiple ant colonies, multiple outsets and multiple routes was adopted. Information entropy was applied to adjust the path selection strategy and pheromone updating strategy of ant colonies along with the change of its value during the iteration. Two inspiring factors were applied in the algorithm to guide the ant colonies to search for optimal paths in a more efficient and targeted way. Local search ability was guaranteed by local translation of unit start-stop points of the optimal solution in each iteration. In the optimal load distribution model, optimal distribution table was set in advance using dynamic programming, which only took account of the stable operation regions and avoided the cavitation and vibration areas for the security and stability of units. The proposed method is applied to the Three Gorges Hydroelectric plant. Compared with other methods under different water heads, this method shows optimized result under the premise of both calculation speed and stability.     

寺坪水电站优化调度模型

随着社会经济的快速发展,水资源供需矛盾日趋尖锐,如何合理调度有限的水资源已成为水资源管理中的现实而紧迫的任务。通过进一步研究水库调度的机理,采用非线性规划作为优化求解方法构建了水库优化调度模型,非线性规划结合了线性规划和动态规划各自的优点,并将水库调度中的各种因素融入数学模型中,较准确地计算模拟期间各种优化变量数值条件下的目标函数值,并比较得出最优值。之后,基于多目标思想,给出了一组Pareto前沿解集,通过寺坪水电站的应用,构建不同的目标函数,得到一系列决策方案,以便决策者选择偏好的决策方案。     

基于进制数的水电站机组优化运行算法

机组组合是水电站短期发电计划中一个重要的问题,合理的组合运行能带来显著的经济效益。采用进制数编码形式表示机组的运行状态,以给定的负荷为基础,对机组运行进行优化,存储运行状态少,且最优方案不受初始值的影响;采用M atlab语言编写了电站内全局的最优机组组合及机组间负荷的合理分配程序,并给出了计算程序。实例计算结果表明:利用进制数的优化算法在机组组合优化问题上是可行的,也是有效的,该算法的收敛性好且速度快,对多机组电站的经济运行具有较好的实用价值。     

Large scale reservoir operation by Constrained Particle Swarm Optimization algorithms

In this paper two adapted versions of Particle Swarm Optimization (PSO) algorithm are presented for the efficient solution of large scale reservoir operation problems with release volumes taken as the decision variables of the problem. In the first version, exploiting the sequential nature of the solution building procedure of the PSO, the continuity equation is used at each period to define a new set of bounds for the decision variable of the next period which satisfies storage volume constraints of the problem. Particles of the swarm are, therefore, forced to fly in the feasible region of the search space except for very rare cases and hence the name of the Partially Constrained Particle Swarm Optimization (PCPSO) algorithm. In the second, the periods of the operations are treated in a reverse order prior to the PCPSO search to define a new set of bounds for each storage volume such that partially constrained particles are not given any chance of producing infeasible solutions and, hence, the name of Fully Constrained Particle Swarm Optimization (FCPSO) algorithm. These methods are used here to solve two problems of water supply and hydropower operation of “Dez” reservoir in Iran and the results are presented and compared with those of the conventional unconstrained PSO and a genetic algorithm. Three cases of short, medium and long-term operations are considered to illustrate the efficiency and effectiveness of the proposed methods for the solution of large scale operation problems. The methods are shown to be superior to the original PSO and genetic algorithm in locating near optimal solutions and convergence characteristics. Proposed algorithms are also shown to be relatively insensitive to the swarm size and initial swarm compared to the original unconstrained PSO and genetic algorithm.     

Optimal Allocation of Flood Control Capacity for Multi-Reservoir Systems Using Multi-Objective Optimization Approach

Operation of multi-reservoir systems during flood periods is of great importance in the field of water resources management. This paper proposes a multi-objective optimization model with new formulation for optimal operation of multi-reservoir systems. In this model, the release rate and the flood control capacity of each reservoir is considered as decision variable and the resulting nonlinear non-convex multi-objective optimization problem is solved with ε-constraint method through the mixed integer linear programming (MILP). Objective functions of the model are minimizing the flood damage at downstream sites and the loss of hydropower generation. The developed model is used to determine optimal operating strategies for Karkheh multi-reservoir system in southwestern Iran. For this purpose, the model is executed in two scenarios based on “two-reservoir” and “six-reservoir” systems and for floods with return periods of 25 and 50 years. The results show that in two-reservoir system, flood damage is at least about 114 million dollars and cannot be mitigated any further no matter how hydropower generation is managed. But, in the case of developing all six reservoirs, optimal strategies of coordinated operation can mitigate and even fully prevent flood damage.     

Application of an Interior-Point Algorithm For Optimization of a Large-Scale Reservoir System

Optimization of a multi-reservoir system operation is challenging due to the non-linearity, stochasticity, and dimensionality involved in such a problem. In this research, a long-term planning model is presented for optimizing the operation of Iranian Karoon-Dez reservoir system using an interior-point algorithm. The system is the largest multi-purpose reservoir system in Iran with hydropower generation, water supply, and environmental objectives. The focus is on resolving the dimensionality of this problem while considering hydropower generation and water supply objectives. The weighting and constraints methods of multi-objective programming are used to assess the trade-off between water supply and hydropower objectives so as to find noninferior solutions. The computational efficiency of the proposed approach is demonstrated using historical data taken from Karoon-Dez reservoir system.     

基于改进遗传算法的小型水电站短期优化调度

针对小型水电站在丰水期的短期优化调度问题,提出了短期优化调度的数学模型和基于改进遗传算法的工程实现方法,并通过实例仿真及对仿真结果的详细分析,说明了该算法的有效性,对小型水电站短期优化调度有一定的指导意义。     

Optimal Operation of Reservoir Systems using Simulated Annealing

A stochastic search technique, simulated annealing (SA), is used to optimize the operation of multiple reservoirs. Seminal application of annealing technique in general to multi-period, multiple-reservoir systems, along with problem representation and selection of different parameter values used in the annealing algorithm for specific cases is discussed. The search technique is improved with the help of heuristic rules, problem-specific information and concepts from the field of evolutionary algorithms. The technique is tested for application to a benchmark problem of four-reservoir system previously solved using a linear programming formulation and its ability to replicate the global optimum solution is examined. The technique is also applied to a system of four hydropower generating reservoirs in Manitoba, Canada, to derive optimal operating rules. A limited version of this problem is solved using a mixed integer nonlinear programming and results are compared with those obtained using SA. A better objective function value is obtained using simulated annealing than the value from a mixed integer non-linear programming model developed for the same problem. Results obtained from these applications suggest that simulated annealing can be used for obtaining near-optimal solutions for multi-period reservoir operation problems that are computationally intractable.     

Multi-Objective Operating Rules for Danjiangkou Reservoir Under Climate Change

The natural variations of climatic system, as well as the potential influence of human activity on global warming, have changed the hydrologic cycle and threatened current water resources management. And the conflicts between different objectives in reservoir operation may become more and more challenging because of the impact of climate change. This study aims at deriving multi-objective operating rules to adapt to climate change and alleviate the conflicts. By combining the reservoir operation function and operating rule curves, an adaptive multi-objective operation model was proposed and developed. The optimal operating rules derived both by dynamic programming and NSGA-II method were compared and discussed. The projection pursuit method was used to select the best operating rules. The results demonstrate that the reservoir operating rules obtained by NSGA-II can increase the power generation and water supply yield and reliability, and the rules focusing on water supply can significantly increase the reservoir annual water supply yield (by 18.7 %). It is shown that the proposed model would be effective in reservoir operation under climate change.     

Design-Operation of Multi-Hydropower Reservoirs: HBMO Approach

To illustrate and test the applicability and performance of the innovative honey-bee mating optimization (HBMO) algorithm in highly non-convex hydropower system design and operation, two problems are considered: single reservoir and multi-reservoir. Both hydropower problems are formulated to minimize the total present net cost of the system, while achieving the maximum possible ratio for generated power to installed capacity. The single hydropower reservoir problem is approached by the developed algorithm in 10 different runs. The first feasible solution was generated initially and later improved significantly and solutions converged to a near optimal solution very rapidly. In the application of the proposed algorithm to a five-reservoir hydropower system with 48 periods and a total of 230 decision variables, in early mating flights, the first feasible solution was identified and the results converged to a near optimal solution in later mating flights. In the case of the multi-reservoir problem, an efficient gradient-based nonlinear-programming solver (LINGO 8.0) failed to find a feasible solution and for the single hydropower reservoir design problem it performed much worse than the proposed algorithm.     

基于改进遗传算法的生态友好型水库调度

以锦屏梯级水库为案例,从系统工程论的角度出发,将梯级水库作为物理系统,以年发电量为目标函数,建立了梯级水库调度优化模型。为减少水库调度对河道生态系统的影响,在鱼类栖息地模拟的研究基础上,引入目标物种的生态需水过程对调度模型进行动态约束,并采用改进的遗传算法进行求解。研究得到了满足目标鱼类生态需水条件下发电量最大的梯级水库调度策略,并对生态流量满足程度与工程效益损失之间的定量响应关系进行了研究,提出了折中方案选择的基本原则。     

Reservoir flood control operation model incorporating multiple uncontrolled water flows

This study presents a weighted pre‐emptive goal programming model formulation for coordinated reservoir operation, with easy inclusion of uncontrolled water flows. The model is combined with a multiple water inflows forecasting model, and can be used for real time reservoir operation. Water flow routing from various upstream sites is accounted by with a single compact equation. Integration of controlled and uncontrolled water flows in the optimization model simplifies the operation model, resulting in accurate computation of the downstream water flow. Multiple objectives with water storage and flow variables are used to derive optimal regulation for a reservoir system under flood conditions. For real time operations, the model can be used to determine optimal water release rates for a current period, on the basis of an optimal water release schedule for an operating horizon (T). The model is applied to the flood control operation of reservoirs in the Narmada River Basin (India), with three controlled and three uncontrolled water flows affecting the downstream flow at Hoshangabad. Reservoir water storage and downstream control point flows are zoned, with prioritized objectives used to derive the optimal water release rates. Model applications to the 1999 flood event in the Narmada River Basin with observed and forecasted inflows illustrates that, if water inflows were known through a forecasting technique well in advance, the coordinated operation of the reservoirs could substantially reduce the peak water flows at the control points. The study also indicates that uncontrolled channel flows at the damage site were sufficiently high to cause flooding at the damage site.