Joint optimal flood control operation of large scale mixed reservoirs

With the reservoir construction gradually completed, joint operation of reservoir groups is an important measure to realize reservoir flood control potential,but when the river basin is large, the flood channel routing and time-lag cannot be simplified, in addition, the curse of dimensionality is very difficult for model solving With the expansion of the number of reservoirs. These factors restrict the application of joint operation of large scale mixed reservoirs.In this study, The DP-POA cyclic iterative algorithm which is based on large scale system decomposed-coordinating method was proposed to solve the optimal problem considering the flood routing and time-lag.The upper Yangtze River is selected as a case study. 6 reservoirs, including the Three Gorges Reservoir(TGR)、Xiangjiaba Reservoir(XJB)、Xiluodu Reservoir (XLD)、 Pubugou Reservoir (PBG)、Goupitan Reservoir (GPT) and Tingzikou Reservoir (TZK)are taken into accounts.Compared with current operation of reservoirs independent,results demonstrate that the method can effectively reduce the maximum operating water level of TGR and flood diversion in the lower reaches of the TGR. Therefore, the safety of the flood control points along the river has been largely improved based on the proposed method.


Introduction
Flood disaster is one of the most damaging natural disasters, due to its high frequency and enormous destruction strength [1]. Reservoir is an effective engineering measure for flood control and disaster reduction. Optimization techniques for planning, design, and management of complex water resources systems have longstanding use in water resources engineering [2]. such as linear programming [3], dynamic programming (DP) [4], nonlinear programming [5], and folded dynamic programming (FDP) [6]. A variety of common operating rules have been derived for single-purpose reservoirs in series and in parallel [7]. Labadie [8] discusses the technological challenges and rewards of integrated optimization of reservoir systems.
Flood management reservoirs regulate inflows to reduce downstream flood damages [9]. These methods have been applied to small scale reservoir groups and achieved effective results. However, with the increase of the number of reservoirs and the increase of catchment area, some factors that can be ignored in the small reservoir groups become more and more influential and cannot be ignored. First, The time required for the model calculation increases rapidly with the increase of the number of reservoirs so that it is eventually unacceptable, for example, DP cannot be applied to joint flood control of more than four reservoirs because of the dimension disaster problem ; Second, With the increase of river length, the phenomenon of flood peak attenuation and loss is more and more serious, and the propagation delay is also more and more long, so that these factors which can be ignored in small watershed area become very important ; Third, There are hydraulic connections between series reservoirs, so that many methods that can be applied to parallel reservoirs without hydraulic connections are not suitable for series reservoirs ; Last but not least, the increasing number of reservoirs and the complex hydraulic connections between reservoirs make it difficult to find feasible initial solutions, which have a great impact on the convergence of algorithms such as POA. These problems bring great challenges to the modeling and solving of the joint flood control operation of large-scale mixed reservoir group.
For the above problems, A DP-POA cyclic iterative algorithm based on large system decomposition and coordination theory is proposed. The upper Yangtze River is selected as a case study. 6 reservoirs, including the Three Gorges Reservoir(TGR) 、 Xiangjiaba Reservoir(XJB)、Xiluodu Reservoir (XLD)、Pubugou Reservoir (PBG) 、 Goupitan Reservoir (GPT) and Tingzikou Reservoir (TZK) are taken into accounts. Compared with current operation of reservoirs independent,results demonstrate that the method can effectively reduce the maximum operating water level of TGR and flood diversion in the lower reaches of the TGR. Therefore, the safety of the flood control points along the river has been largely improved based on the proposed method.

Methodology
As shown in Fig. 1,The algorithm includes the following steps : First, Simplify the series reservoirs into a virtual reservoir ; Second, establish joint flood control Operating model; Third, from upstream to downstream, from tributary to main stream, DP algorithm is used to calculate reservoir optimization one by one and obtain the initial solution of reservoir group joint operation ; Fourth, taking the DP algorithm as the initial solution, the POA algorithm considering phenomenon of flood peak attenuation and loss is used to solve the joint flood control model ;Fifth The calculation results of virtual reservoirs are decomposed into serial reservoirs.

Operating model
Based on the flood control demand and the flood control capability of the basin, the integrated flood control model of reservoir group is established.

Objective function
The joint flood control operation of large-scale reservoir often involves multiple objectives.(1) the excess flood capacity of flood control points is the least;(2) the maximum adjusted flood level of the reservoir is lowest to reduce flood risk;(3) minimum sum of squares of flow at flood control points;(4) minimum sum of squares of outflow of reservoir. The above four objectives are combined to be one objective by using weight method, The final objective function is shown below: where F is Objective function value;i is the number reservoir;N is the total number of reservoir;t is operating period number;j is the number of flood control points;M is the total number of flood control points;

Constraints
(1) The lowest and the highest water level constraints: (2) The water balance constraint: where , (3) The minimum outflow and the outflow capacity constraints: where ,  control points, and t q Δ is the inflow in the interval zones between the ith reservoir and the flood control point downstream. m ax j q is the allowed maximum discharge for the jth flood control point downstream.

Flood channel routing
This paper uses Muskingum method to calculate flood routing : Xiluodu reservoir and Xiangjiaba reservoir are located in the lower reaches of the jinsha river, Their aim is to ensure that Yibin,Luzhou and Chongqing meet flood control standards，and cooperate with the three gorges reservoir to reduce flood losses in the middle and lower reaches of the Yangtze river; Pubugou reservoir is located in Dadu River which is the tributary of the Minjiang River, Flood control aim of Pubugou reservoir is to ensure that Chengkun railway meet flood control standards and cooperate with other reservoirs to reduce flood losses of river basin; Tingzikou reservoir is located in Jialing River, Flood control aim of Pubugou reservoir is to ensure that Langzhou meet flood control standards and cooperate with other reservoirs to reduce flood losses of river basin; Goupitan reservoir is located in Wujiang River, Flood control aim of Goupitan reservoir is to ensure that Sinan meet flood control standards and cooperate with other reservoirs to reduce flood losses of river basin. The specific parameters of the reservoir are shown in table 1.
The flood control standardof flood control points is shown in table 2. The goal of reservoir group operation is shown below.
(1) Ensure the safety of the reservoirs, this target translates into a water level constraint; (2) Ensure Yibin, Luzhou, Chengkun railway, Langzhong,sinan, and Chongqing meet flood control standards.In other word, When the flow is lower than the designed flow, the flow after regulation shall not exceed the safe flow; (3) The jingjiang river does not divide flood when the peak flow below 100-year design flood; (4) Minimize excess flooding in the Chenglingji area. (5) Minimize the maximum flood operation level of the Three Gorges Reservoir; (6) Minimize the the sum of squared outflow the reservoirs; (7) Minimize the the sum of squared flow the flood control points.

Results
The method proposed is used to operate the 50-year design flood ,100-year design flood , 1000-year design flood,with selecting 1954, 1980, 1969, 1981, 1998and 2010 to be typical flood hydrograph. The results show that:   (1) The maximum operating water level of all reservoirs is below the safe water level; (2)Yibin, Luzhou, Chengkun railway, Langzhong,sinan, Jinjiang and Chongqing have achieved flood control standards; (3) Compare to existing methods, The method proposed in this paper greatly reduces the excess flood volume in the chenglingji area; (4) It significantly lowered the maximum operating water level of the three gorges reservoir,this helps to reduce flood risk.

CONCLUSIONS
This paper focuses on the joint flood control operation of large-scale mixed reservoir group, The DP-POA cyclic iterative algorithm which is based on large scale system decomposed-coordinating method was proposed.,and this method was applied to the joint flood control of reservoirs on the upper reaches of the Yangtze river. Compared with current operation of reservoirs independent,results demonstrate that the method can effectively reduce the maximum operating water level of TGR and flood diversion in the lower reaches of the TGR. Therefore, the safety of the flood control points along the river has been largely improved based on the proposed method.