The Method For High-Dimensional Hydropower System Operations Based On Random Sampling

In recent years,China has witnessed a very rapid hydropower development.Large quantities of cascaded hydropower systems,which are characterized with huge installed capacity,many reservoirs and dense distribution range,have been put into operation.Optimal operations of hydropower plants are among the most important and challenging tasks for large hydropower producers and power grid dispatching organizations.In recent decades,this problem has attracted increasing attention from researchers because many large hydropower reservoirs have been put into operation worldwide and bear major responsibilities in their respective power systems,particularly in some hydropower-rich countries.Chinese hydropower resources are the most abundant and concentrated in the southwest.As is well known,hydropower systems involve complex hydraulic relations among upstream and downstream hydropower plants and electrical connections among plants on different rivers as well as various equality and inequality operation conditions and constraints,most of which are highly nonlinear and nonconvex.Therefore,the rapid expansion of the scale of hydropower systems in hydropower-rich countries is leading to a serious challenge called“curse of dimensionality” regarding the optimal operations of high-dimensional hydropower systems.As the computational time and storage memory grow exponentially with the plant number,we need to explore more efficient optimal methods.Based on the hydropower system in the southwest of China,this paper studies the “Curse of dimensionality” of large-scale hydropower system dispatching,and proposes two methods to be applied under different conditions.The main content and conclusions are summarized as follows:(1)The most commonly method used for hydropower dispatching is dynamic planning and its optimization algorithm.In order to find the idea of dimensionality reduction,We respectively analyzed four representative methods,DP,DDDP,POA,SDP,and obtained the growth mode of their calculation amount with the increase of the number of hydropower stations based on the principle of the methods.As the number of hydropower stations participating in the calculation increases,the combination of states and decision-making in a single period will increase exponentially.(2)The first method named FRS.Its efficient to alleviate the dimensionality challenge.A random sampling(RS)technique is exploited to select representative water level states at each period by considering discrepant weights for different solution ranges.The RS can dynamically adjust sampling size and times with the selected samples.Moreover,acceptability and reliability parameters are introduced into the RS optimization to ensure a reasonable reliability level of the results.A feasible region identification(FRI)method is well designed to narrow the search range by transforming various operation constraints into equivalent water level limits and integrating them with water level range got from hundreds of simulation calculations.Furthermore,this method can use the water levels obtained in last iteration to dynamically update feasible regions during the calculation process.Three case studies involving a large-scale hydropower system with 21 plants are presented to verify the validity,efficiency,and sensitivity of the proposed method.Compared to dynamic programming(DP),discrete differential dynamic programming(DDDP)and progressive optimality algorithm(POA),the method requires only 0.85%,1.27% and 3.14% of the computational effort to produce almost the same results.Moreover,a sensitivity analysis indicates that the reliability parameter in this method has a larger impact on the computational time than other parameters.(3)The second method,FP-SDP,is based on SDP and uses feasible region identification technology to reduce the decision-making scope and state scope.Compared with the FRS,the feasible region identification technology used in this method not only used in decision-making scope but also used in state scope.Compared with the results of SDP,it is shown that reducing some useless states does not affect the quality of scheduling rules,and can improve computing efficiency.The SDP method can meet the needs of parallel technology at multiple levels.In order to make better use of the advantages of parallel technology,reduce the computing time required for task control and communication and avoid unnecessary resource idleness,the initial water level of the period is selected for parallelism.The results show that the scheduling rules obtained by FP-SDP can obtain better results compared with DP.Compared with SDP,FP-SDP can save dozens of times of calculation time,so FP-SDP is more dominant in the calculation of scheduling rules.