Qin Liu,Guo-hu Fng,*,Hong-in Sun,Xue-wen Wu

aCollege of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210098,China

bCanal Irrigation Management in Jiangsu Province,Huaian 223000,China

cCollege of Computer and Information Engineering,Hohai University,Nanjing 210098,China

Joint optimization scheduling for water conservancy projects in complex river networks

Qin Liua,Guo-hua Fanga,*,Hong-bin Sunb,Xue-wen Wuc

aCollege of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210098,China

bCanal Irrigation Management in Jiangsu Province,Huaian 223000,China

cCollege of Computer and Information Engineering,Hohai University,Nanjing 210098,China

In this study,we simulated water flow in a water conservancy project consisting of various hydraulic structures,such as sluices,pumping stations,hydropower stations,ship locks,and culverts,and developed a multi-period and multi-variable joint optimization scheduling model for flood control,drainage,and irrigation.In this model,the number of sluice holes,pump units,and hydropower station units to be opened were used as decision variables,and different optimization objectives and constraints were considered.This model was solved with improved genetic algorithms and veri fied using the Huaian Water Conservancy Project as an example.The results show that the use of the joint optimization scheduling led to a 10%increase in the power generation capacity and a 15%reduction in the total energy consumption.The change in the water level was reduced by 0.25 m upstream of the Yundong Sluice,and by 50%downstream of pumping stations No.1,No.2,and No.4.It is clear that the joint optimization scheduling proposed in this study can effectively improve power generation capacity of the project,minimize operating costs and energy consumption,and enable more stable operation of various hydraulic structures.The results may provide references for the management of water conservancy projects in complex river networks.

Complex river network;Water conservancy project;Hydraulic structure;Flow capacity simulation;Scheduling model;Optimal scheduling

1.Introduction

Water use conflict often occurs in plain areas with complex river networks and a prosperous economy due to the large population and high water demand.The construction of water conservancy projects consisting of sluices,pumping stations, hydropower stations,ship locks,and culverts makes it possible to reallocate water resources in a more rational and efficient manner.Optimizing the operation of these hydraulic structures of the water conservancy project is expected to guarantee flood control safety,satisfy water demands for different purposes, minimize operating costs and energy consumption,and improve water use efficiency.However,this is by no means a trivial task,and technical challenges to optimizing the joint operation of individual hydraulic structures of water conservancy projects remain.

Multi-objective optimal operation of the water conservancy project has been a topic of considerable interest,and a number of flood control models have been proposed in recent years (Liu et al.,2008;Wu et al.,2014;Zheng et al.,2008).For instance,Lin and Su(1996)proposed a flood control model foroptimal dispatching of multi-sluice water conservancy projects in plain areas based on hydrological and hydraulic characteristics and sluice performance.In this model,the openingclosing sequence of sluices,the number of sluice holes to be opened,and the duration of opening were optimized using discrete differential dynamic programming.Moradi-Jalal et al. (2004)used a genetic algorithm(GA)to automatically determine the minimal cost of pumping stations in consideration of target hydraulic performance requirements.Gu(2006)proposed an intelligent operation-aided decision-making model for sluices using an arti ficial neural network and an unsteady flow mathematical model to achieve intelligent control of sluices.Li et al.(2010)proposed a one-dimensional unsteady flow numerical model for river networks with multiple sluices and weirs with consideration of both sluice operation and flood discharge,and the solution for special river sections was obtained through the bi-directional iterating internal boundary control method.Chen et al.(2013)proposed a hydrodynamic model for plain river networks using the Saint-Venant equation,and the joint operation of water-logging, flood,and tidewater gate-pumps was simulated in the Linhong District of Lianyungang City based on the boundary runoff.

Models for other optimization objectives,such as improvement of water quality(Jiang et al.,2011;Zhou et al., 2013), flow-mass transport in tidal river networks(Song et al.,2014),and water distribution(Shi et al.,2010),have also been proposed in previous studies.The optimized operation rules of sluices in river networks have been studied with the river network mathematical models,arti ficial neural networks,and genetic algorithms(Gu et al.,2014).However, most of these models have considered a single sluice or pumping station as the scheduling target,and water flow simulation,improvement of water quality,and optimal flood control as the optimization objectives.In addition to sluices and pumping stations,there are many other hydraulic structures,such as hydropower stations,ship locks,and culverts, which are jointly used for flood control,drainage,irrigation, power generation,and shipping.These hydraulic structures constitute a complex open system that is closely related to the speci fic natural and socio-economic environment,and,from a mathematical perspective,is characterized by high dimensionality,nonlinearity,time variation,uncertainty,and multiple objectives.

In this study,we simulated water flow in a water conservancy project consisting of sluices,pumping stations,hydropower stations,ship locks,and culverts,and developed a joint optimization scheduling model for flood control,drainage,and irrigation.In the model,the number of sluice holes,pump units,and hydropower station units to be opened were used as decision variables,and different optimization objectives and constraints were considered.The model was solved with improved genetic algorithms.In addition,a joint optimization scheduling system with a frame structure of system generalization-hydraulic simulation-optimization operation, which can provide technical support for scienti fic decisionmaking and management of flood control,drainage,and irrigation in complex river networks,was proposed.

2.Model establishment

2.1.Model characteristics

A necessary prerequisite for the establishment of a joint optimization scheduling model for water conservancy projects in complex river networks is simulation of the hydraulic connections between river networks and hydraulic structures. The optimal opening-closing sequence of sluices and the number of sluice holes,pump units,and hydropower station units to be opened in each calculation period are determined through the system analysis method.The joint optimization of the operation of these hydraulic structures of the water conservancy project aims to guarantee flood control safety, satisfy water demands for different purposes,minimize operating costs and energy consumption,and improve water use efficiency.In short,the joint optimization scheduling should contribute to achieving the maximum overall benefits of the water conservancy project.The multi-period and multivariable joint optimization scheduling proposed in this paper has the following characteristics:

(1)It combines hydraulic calculation for annular river networks and the optimal operation scheduling of various hydraulic structures of the water conservancy project.

(2)Waterconservancy projects in complex rivernetworks are highly susceptible to human impacts.In addition,the inflow of lower cascades depends almost entirely on the outflow of the upper cascade,resulting in complex boundary conditions and difficulty in the generalization of river networks.

(3)Hydraulic structures for different purposes scattered in complex river networks are interdependent and interact with one another.Thus,the subsystem constituted by neighboring hydraulic structures is not independent.

(4)As the water level and flow rate change with boundary conditions and scheduling modes,the joint optimization scheduling isa dynamic problemthatchanges temporally and spatially.

(5)Equal consideration is given to flood control,drainage, irrigation,water supply,power generation,and shipping.The interdependence and tensions between these functions need to be well considered.

(6)The ultimate aim of the joint optimization scheduling is to achieve the maximum potential of the water conservancy project.However,significant technical challenges remain, since the joint optimization scheduling problem,from a mathematical perspective,is a high-dimensional nonlinear programming problem with complex constraint conditions, and the solution must meet global convergence and timeliness.

2.2.Model generalization

A water conservancy project in complex river networks is essentially an open complex system,and thus it is necessary to take into account the comprehensive functions of the project, water exchange conditions,and arrangement of and relationship between different hydraulic structures in the generalization of the project.In this study,the project was generalized into a river network subsystem and a hydraulic structuresame as Eq.(6).In contrast,if inflow is insufficient and thus there is a need to use pumps,the minimization of the power generation capacity of the water conservancy project in the scheduling period can be regarded as a non-constrained objective function,while drainage,water supply,and shipping can be regarded as constraint conditions.Then,the objective function can be expressed as

whereFis the total electricity consumption of the water conservancy project in the scheduling period(kW·h),N2is the number of pumping stations,ρ is the density of water(kg/m3),is the pumping flow of theith pumping station in thetth periodis the time-averaged lift of theith pumping station in thetth period(m),is the performance efficiency of theith pumping station in thetth period,ηmotis the motor efficiency and equal to 0.94(Chen et al.,2010;Feng et al., 2011),and ηintis the transmission efficiency of the direct connection unit and equal to 1.0.are related to current decision variables.

2.4.2.Decision variables

In this joint optimization scheduling,sluices,pumping stations,hydropower stations,ship locks,and culverts are used as the optimization targets,and the number of sluice holes,pump units,and hydropower station units to be opened as the decision variables.Assuming that there areTscheduling periods andmdecision variables,a multi-dimensional decision variable,can be obtained,whereisthevalue oftheithdecisionvariableinthetth period.

2.4.3.Constraint conditions

In this joint optimization scheduling,both common constraints related tothe hydraulic calculationand the properties of hydraulic structures,and speci fic constraints related to different scheduling models(i.e.,FCSM,DSM,and ISM)are considered (Liu,2006).The eight common constraints are as follows:

(1)Constraints on flow rates and water levels of nodes without water storage capacity

In the simulation of river flow,a river junction is usually generalized into a node with a negligible area.Thus,the node has no water storage capacity,and the discharge and dynamic boundary conditions must be satis fied:

whereQijis the discharge converged at theith node from thejth river(m3/s);Aiis the water storage area of theith node(m2);Z0iis the average water level of theith node (m2);N0is the number of rivers converged at theith node; andZjiis the water level at the cross-section of thejth river connected to theith node(m),and the cross-section is nearest theith node.

(2)Hydraulic constraints for sluice

The hydraulic connection of sluices is usually expressed by the discharge through the sluice:

whereQLis the discharge through the sluice(m3/s).

(3)Constraints on the number of sluice holes to be opened

The number of sluice holes to be opened provides an allowable set of decision variables and the range for each dimensional vector of multi-dimensional decision variables. The constraint can be expressed as

(4)Constraints on design discharge through sluices

The sluice discharge can be calculated by Eq.(9),which should not exceed the design discharge through the sluice:

(5)Constraints on opening modes of sluices

The opening modes of sluices(i.e.,alternate opening or symmetrical opening from the middle)often have many constraints and technical limitations in order to avoid adverse conditions.

(6)Constraints on the number of units to be opened

The number of units(for pumping or hydropower stations)to be opened provides an allowable set of the decision variables and the range for each dimensional vector of multi-dimensional decision variables.The constraints can be expressed as

(7)Constraints on water level

The water level at any calculation section throughout the scheduling period must be higher than the bottom elevation of the section in order to prevent zero flow in the river and ensure the effectiveness of the hydrodynamic model:

(8)Other constraints

Other constraints include the water head of the pumping or hydropower stations,output,flow capacity,and the minimum water level required by shipping.

Specific constraints can be set for each scheduling mode (i.e.,FCSM,DSM,and ISM),such as the characteristic water level of key sluices,which needs to be determined in accordance with actual conditions.

3.Model solution

3.1.Improved genetic algorithm

A genetic algorithm is a heuristic search that mimics the process of natural selection and is routinely used to generate useful solutions to optimization problems.In a genetic algorithm,a population of candidate solutions to an optimization problem evolves toward better solutions.The evolution starts from a population of randomly generated individuals and is an iterative process.The more fit individuals are stochastically selected from the current population,and then modified to form a new generation. Commonly,the algorithm terminates when either a maximum number of generations has been produced or a satisfactory fitness level has been reached for the population(Wang and Cao,2002).In order to improve the calculation efficiency, precision,and stability,and make the genetic algorithm more suitable for large system problems,the genetic algorithm is improved in terms of the following three aspects:(1)Population size and diversity:A number of randomly generated new individuals are added into the population,and the more fit individuals of the father,offspring,and randomly generated population are selected to breed a new generation, allowing for a broader exploration of the optimal solution.(2) Crossover and mutation probabilities:The probabilities of crossover(Pc)and mutation(Pm)are fixed in the conventional genetic algorithm(CGA).Instead of using fixed values ofPcandPm,the adaptive genetic algorithm(AGA)proposed by Wang and Cao(2002)can adaptively adjustPcandPmdepending on the fitness of the solutions.In this case,highfitness individuals have higherPcandPmvalues to be selected than low-fitness individuals.(3)Evolution strategies: A generation replacement scheme with an elitist strategy is used in this study,which allows for the survival of the best solutions of each generation.

3.2.Solution steps

Fig.2.Flowchart of joint optimization scheduling model.

Fig.5.Optimization scheduling results for different hydraulic station in typical periods from 2002 to 2012.

Fig.6.Optimization scheduling results for different pumping stations in typical periods from 2002 to 2012.

The multi-period and multi-variable joint optimization scheduling model is solved by the improved genetic algorithm, as shown in Fig.2.the Yundong Sluice and pumping station No.3 are used as water level boundary conditions in the joint optimization scheduling model,and this is consistent with the conventional scheduling. These results indicate that the water levelis better controlled by the joint optimization scheduling,making it convenient for the control and maintenance of the system.

Fig.7.Characteristic water levels upstream of Yundong Sluice and downstream of pumping stations No.1,No.2,and No.4 for Huaian Water Conservancy Project in typical periods from 2002 to 2012.

5.Conclusions

In this study,we simulated water flow in a water conservancy project consisting of sluices,pumping stations,hydropower stations,ship locks,and culverts,and developed a multi-period and multi-variable joint optimization scheduling model for flood control,drainage,and irrigation.In the model,the number of sluice holes,pump units,and hydropower station units to be opened were used as decision variables,and different optimization objectives and constraints were considered.The model was solved by improved genetic algorithms and verified using the Huaian Water Conservancy Project as an example.The results show that this joint optimization scheduling model is capable of(1)leading to a 10% increase in the power generation capacity and a 15%reduction in the total power consumption;(2)providing a more stable operation for various hydraulic structures;and(3) improving water use efficiency without additional facilities and costs.However,hydrological forecasting was not considered in this study,and more studies are therefore warranted to investigate the joint optimization scheduling of water conservancy projects based on upstream real-time hydrological forecasts.

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Received 18 April 2016;accepted 21 August 2016

Available online 14 March 2017

This work was supported by the Water Conservancy Science and Technology Project of Jiangsu Province(Grant No.2012041)and the Jiangsu Province Ordinary University Graduate Student Research Innovation Project (Grant No.CXZZ13_0256).

*Corresponding author.

E-mail address:hhufgh@126.com(Guo-hua Fang).

Peer review under responsibility of Hohai University.

http://dx.doi.org/10.1016/j.wse.2017.03.008

1674-2370/?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).

?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).