Dynamic coordination and control technology of the operating water level during flood season and its application in Xiluodu-Xiangjiaba-Three Gorges cascade reservoirs

To satisfy the increasing multi-objective scheduling requirements in flood season of the Xiluodu-Xiangjiaba Three Gorges multi-function cascade reservoir system located in the lower reaches of Jinsha River and the upper reaches of Yangze River, and simultaneously solve the key technical problems of the resource utilization of floods by joint optimal scheduling of cascade reservoirs. This paper explorers and presents a scientific solution of joint dynamic control of the reservoirs’ operating water level during flood season that suitable for the flood resources comprehensive utilization of the large-scale cascade reservoirs in the Yangtze River Basin. Specifically, the solution is composed of a dynamic control mode for the operating water level of the cascade reservoir during the main flood season (ie, forecast and pre-impounding, grade regulating, and staged discharge control), a phased release theory of the flood control capacity at the end of flood season and a risk analysis model for the decision of the cascade reservoir scheduling. These new technical solutions were successfully applied to the 2016-2019 scheduling practices of the XiluoduXiangjiaba Three Gorges cascade reservoir system, the world’s largest multi-function multi-reservoir system that operation and management by the China Three Gorges Corporation (CTG). The comprehensive benefits of the cascade reservoir in flood control, power generation, shipping, ecology, and the water supply during reservoir impounding and falling periods have been significantly improved, including greatly reducing downstream flood * Corresponding author: zhang_song2@ctg.com.cn © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). E3S Web of Conferences 346, 02003 (2022) https://doi.org/10.1051/e3sconf/202234602003 Sharing Water: Multi-Purpose of Reservoirs and Innovations

pressure, increasing power generation and water supply, improving navigation condition, promoting fish reproduction. Meanwhile, it also verifies that these new technologies are scientific, practical, universal and have a broad application prospect.

Introduction
The Xiluodu-Xiangjiaba -Three Gorges-Gezhouba cascade hydropower stations, developed by China Three Gorges Corporation and put into operation on the main stream of Yangtze River, is the largest watershed cascade hydropower system around the world. Among the system, Xiangjiaba and Xiluodu, located at the lower reaches of Jinsha River, are the key power generation spot of the West-East Electricity Transmission Project in China and they have been put into operation since 2012 and 2013, respectively. The Three Gorges Project (TGP) is the backbone controlling project for harnessing and developing the Yangtze River. The TGP entered into the cofferdam power generation period after its first generating unit was put into operation in 2003 and has began the experimental storage period of 175m since 2008. The Gezhouba hydropower station that 38km downstream away of the TGP has been constructed and put into operation since 1981. It has become the shipping and counter regulating reservoir for the TGP. Over the past few decades, after the construction and operation of a large number of controlling hydropower stations with large reservoir capacity and good regulation performance in the main and tributaries of the Yangtze River, the unified dispatching pattern of large-scale hydropower stations in the upper and middle reaches of the Yangtze River has started to form. In recent years, by means of exploitation research and practical applications of the unified optimized dispatching for the giant cascade hydropower stations, China Three Gorges Corporation has fully conducted the initial comprehensive organization and implementation of the Xiluodu-Xiangjiaba -Three Gorges-Gezhouba cascade hydropower stations for combined flood control, impounding, waning and ecological dispatching in 2017. However, from the layer of technology, the unified dispatching of these four hydropower stations are merely the simple combination for the subsystem optimization of the Xiluodu-Xiangjiaba and the Three Gorges-Gezhouba cascade hydropower systems. The dispatching calculation method for each single hydropower station from upstream to downstream was still used within the subsystems, which can never be called as the true "unified optimization dispatching". The purpose of this research is to solve the above problem and answer the question of how to deal with the relationship of flood control, power generation, shipping and water resources utilization in the joint multiobjective dispatching, continue to progress and further enhance the general economic operation level of cascade hydropower system.

Overview of the Cascade Hydropower System
The Jinsha River Hydropower Base ranks the first place at the "Planning of Thirteen Hydropower Bases in China", which is the largest hydropower base in China, as well as the main force of the West-East Electricity Transmission Project. Wudongde, Baihetan, Xiluodu and Xiangjiaba are the four world-class giant cascade hydropower stations planned at the lower reaches of Jinsha River. The total installed capacity of the four stations is 4.21 million kW, which is the equivalent of two of the TGP, and its designed annual power generation is about 184.3 billion kW•h. The Xiluodu and Xiangjiaba hydropower stations are the latter two level cascade hydropower stations, have been constructed and put into operation separately in 2012 and 2013. The Xiluodu hydropower station locates at the main stream of Jinsha River flows through Leibo County of Sichuan Province and Yongshan County of Yunnan Province. The upper part connects the flow from the Baihetan and the latter part is with the Xiangjiaba. The main purpose of the hydropower station is to generate power and control flood. In addition, there are comprehensive utilization benefits such as sediment blocking, improving navigation conditions in reservoir area and lower reaches. The Xiangjiaba hydropower station is the lowest one of the cascade hydropower stations development on the main stream of Jinsha River. The left bank of the dam locates in Yibin County of Sichuan Province and the right bank Shuifu County of Yunnan Province. The upper part of the dam is 156.6km away from the Xiluodu river course and the latter part 33km away from Yibin City. Also, it is 700km away from Yichang. The hydropower station mainly generates electricity, improves shipping conditions, takes flood control and irrigation into account, and has the function of reverse regulation of Xiluodu hydropower station. The TGP locates in Sandouping, Yichang, Hubei Province and about 44km far away from the Yichang station on the lower reach. It is the essential key project of harnessing and developing the Yangtze River and also is of comprehensive benefits such as flood control, power generation, shipping and water resources utilization. The Gezhouba hydropower station locates at the lower reach about 38km away from the Three Gorges, whose dispatching mission is to reverse-regulate the unsteady flow process discharged from the daily regulation of the TGP to give full play to the power generation benefits under the conditions of ensuring the safety and unimpeded navigation. The geographical location of the study cascade hydropower stations is shown as Fig. 1. The designed characteristic parameters of each hydropower station are listed in Table  1.  For the Xiluodu-Xiangjiaba-Three Gorges-Gezhouba cascade hydropower stations, the optimized objective function is to maximize the total power generation or the total power benefit of the system during the dispatching period, written as Eq. (1), Eq. (2): , , , , , , where E, B = the total power generation and the total power benefit of the cascade hydropower system during the dispatching period, respectively, kW

Constraint Conditions
The combined power generation calculation of the cascade hydropower stations includes runoff regulation calculation and hydraulic energy calculation.

Solving Algorithm
An improved LSSDC-DDDP method was used to solve the model (see Fig. 2 and Fig. 3): (1) Large system decomposition coordination (LSSDC) method, using decomposition and coordination mechanism to decompose the optimization problem of cascade reservoir large system into a series of simple sub-optimization problems, so as to achieve the reduction and decoupling of complex problems. (2) Through the feasible domain decomposition mechanism of decision variables, discrete differential dynamic programming (DDDP) divides the huge solution space of the subsystem into many subspaces, realizing the change of computational complexity from exponential growth to linear growth.

Constraint Handling
In most applications of the DDDP, the penalty function method has been the most popular approach in handling inequality and equality constraints. In this approach, a penalty term that is proportional to the constraint violation of a solution is added to the objective function to form the penalized function.

Calculating Time Intervals
The dispatching time length for the optimization models is one year, calculating unit of which is about 10 days and 36 periods of time in general.

Inflow Setting
The inflow of the optimized dispatching model adopts the actual inflow data from 2015 to 2017 of cascade hydropower stations (basically includes the dispatching influence from reservoirs put into operation in the upper reaches of Yangtze River), see Table 2. Frequency of year 80% 53% 49% 91% 79% 68%

Starting Water Level
Under different working conditions calculation of the optimized dispatching for cascade hydropower stations (control strategy of inflow plus water level of ten days), the starting dispatching water level of each reservoir at the beginning of the year is Table 3.    In order to analyze difference between calculation results of models for the maximizing power generation MaxE and the maximizing power generation benefit MaxB, two types of models have been adopted to conduct the optimized dispatching calculation of cascade hydropower station combined generation concerning the actual inflow in 2017, the optimized dispatching process of these two models could be referred to Fig. 4. From Fig. 4, we can see that calculation results to these two models are completely the same. The reason is that as for the Xiluodu-Xiangjiaba-the Three Gorges-Gezhouba cascade hydropower station, the price of electricity on the grid in power production decreases in turn from top to bottom and "the generation efficiency" also decreases accordingly that the unit price benefit and generation efficiency of power station are of the same significance and in the same order so that the optimal decision-making process of the two optimization models under the current electricity price situation is basically equivalent.  Table 5, from Table 5 we can see: (1) With the full installation of Xiluodu and Xiangjiaba cascade hydropower station was completed in 2014, the optimized power generation of cascade hydropower station during 2015 to 2017 is more than the actual power generation on average. In terms of scheduling process diagram, the actual scheduling process is basically consistent with the model optimization process.
(2) The optimized power generation of the Three Gorges is lower than the actual power generation on average. The main reason of which is that the ten days water level control scheme is adopted in the calculation is conservative. In flood season, the operating water

Conclusion
(1) As for the Xiluodu-Xiangjiaba-the Three Gorges-Gezhouba cascade hydropower station, due to the price of power generation tends to be decreasing from upstream hydropower stations to downstream hydropower stations, the "power generation efficiency" tends to be falling and generation efficiency of power station are of the same significance and in the same order so that the optimal decision-making process of the two optimization models under the current electricity price situation is basically equivalent.
(2) Adopt the established optimized dispatching model, 1 billion kW•h, 1.9 billion kW•h and 4.4 billion kW•h have been able to be augmented separately in 2015, 2016 and 2017.
(3) In the optimized model application research, the calculation unit is ten days. While the flood season dispatching setting of the cascade hydropower station includes the control of water level, there are much more uncertainty within the flood season inflow process, flood control situation upstream and downstream of the cascade hydropower station and flood control scheduling strategies. For a further step, flood dispatching data in actual flood season of recent years is needed to draw up unified regulations for flood season to calculate the combined power generation of cascade reservoirs in typical annual flood season and optimize the augmented dispatching power generation.