Development of an Optimal Model for the Xiluodu-Xiangjiaba Cascade Reservoir System Considering the Downstream Environmental Flow

sustainability

Article Development of an Optimal Model for the Xiluodu-Xiangjiaba Cascade Reservoir System Considering the Downstream Environmental Flow

Lingquan Dai 1,2,* , Huichao Dai 2, Haibo Liu 3, Yu Wang 1, Jiali Guo 1, Zhuosen Cai 1 and Chenxi Mi 4 1 College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, China; [email protected] (Y.W.); [email protected] (J.G.); [email protected] (Z.C.) 2 China Three Gorges Corporation, Beijing 100038, China; [email protected] 3 China Yangtze Power Corporation, Yichang 443002, China; [email protected] 4 Helmholtz Centre for Environmental Research, Brueckstr 3a, D-39114 Magdeburg Germany; [email protected] * Correspondence: [email protected]; Tel.: +86-0717-6392298

Received: 11 December 2019; Accepted: 26 January 2020; Published: 29 January 2020

Abstract: To explore the influence of the Xiluodu-Xiangjiaba cascade reservoir system on the appropriate environmental flow (AEF) of the Jinsha River, a multiobjective optimal cascade reservoir model was established with the aim of maximizing power generation while minimizing the downstream degree of AEF alteration. The AEF was determined using the range of variability approach (RVA). The optimal model was solved using an improved version of NSGA-II called INSGA2-DS. Inflows in typical normal and dry years were selected for optimization. The results show that in a normal year, power generation can be increased by 1.28% compared with that under the current regular operation conditions by prioritizing the maximization of power generation, in which case the degree of AEF alteration will increase by 13.86%. In contrast, the degree of AEF alteration will decrease by 22.53% if ecological protection is prioritized, but power generation will decrease by 0.62%. Similarly, in a dry year, power generation can be increased by 1.76% compared with that under the current regular operation conditions to maximize economic benefit, in which case, the degree of AEF alteration will increase by 4.95%. By contrast, the degree of AEF alteration can be decreased by 13.70% if the objective is AEF minimization, but power generation will decrease by 0.48%. These research results provide useful information for the formulation of ecological operation schemes involving cascade reservoirs on the Jinsha River.

Keywords: lower reaches of the Jinsha River; ecological operation; multiobjective optimization; optimal model; INSGA2-DS

1. Introduction Among all renewable energy sources, hydropower is the most commonly used for electricity production, with the corresponding global capacity having increased by more than 30% between 2007 and 2015 [1,2]. In the past three decades, reservoirs and hydropower stations have been rapidly developed to provide clean energy and reduce greenhouse gas emissions in China [3,4]. One of the most prevalent ways to take full advantage of available hydropower resources is to build cascade reservoirs along a river [5,6]. Relative to the total revenue generated by the operation of independent reservoirs, synergistic beneﬁts can be achieved through the coordinated operation of cascade reservoirs [7]. Generally, the main objective of cascade reservoirs is to maximize energy and revenue yields [8,9]. However, this strategy has an adverse impact on downstream river ecosystems. In addition to

Sustainability 2020, 12, 966; doi:10.3390/su12030966 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 966 2 of 18 providing economic benefits, reservoirs also serve other purposes, including providing sufficient water for downstream habitats to maintain aquatic biodiversity, irrigation for agriculture, recreational opportunities, and domestic and industrial water supplies [10,11]. The Xiluodu-Xiangjiaba cascade reservoir system is located in the lower reaches of the Jinsha River [12]. The lower reaches of the Jinsha River are also a pivotal part of the “National Nature Conservation Zone of Rare Fishes” [13,14]. With its exceptional flow pattern, climate and natural environment, the conservation zone is home to abundant and diverse communities of aquatic organisms, among which fish resources are particularly abundant. The zone includes more than 70 types of rare and endemic fishes, such as Coreius guichenoti, Acipenser dabryanus, and the Chinese sucker fish [15,16]. After the cascade reservoir system started operation, the downstream flow changed greatly, especially during the impoundment period in September. These changes directly affected the habitats of rare fish species in the lower reaches at various spatial and temporal scales. The number of fish species and the average size of the fish have decreased, and juvenile populations have also been decreasing [17,18]. Flow is the main driving force affecting the physical habitat conditions of a river, which, in turn, are the main factors determining biological composition [19,20]. The water allocated for a river ecosystem must be within the range of the natural variability of the flow regime. In the absence of environmental constraints, the pursuit of economic benefits may lead to dramatic changes in the environmental flow regime, which will have a negative impact on human settlements, aquatic biodiversity, agriculture and recreational activities [21,22]. Thus, there is an urgent need to take effective measures to alleviate this problem. Many studies have shown that the appropriate environmental flow (AEF) for downstream areas can be maintained through reservoir optimization [23,24]. Zhang et al., established a multiobjective optimization model with the aim of maximizing the annual power generation while minimizing the degree of ecological change in the lower reaches of the Lancang River [25]; Takada et al. developed a method for constructing optimal operation curves considering environmental water supplies for the Dau Tieng Reservoir [26]; Sichilalu et al. presented an optimal control model for a wind-hydrokinetic powered pumpback operation of a hydropower plant with stringent regulatory requirements on downstream environmental flows [27]; Stuart et al. developed the building block method of environmental flows to enhance the abundance of juvenile Murray cod and promote population recovery [28]. Notably, several researchers have previously studied the optimization of the Xiluodu-Xiangjiaba cascade reservoir system. However, most of these researchers have focused on only a single objective, such as electricity production, impoundment, navigation, or sediment loading, and the flow has been considered only as a constraint condition [29]. In contrast to these previous approaches, efforts to achieve the ecological optimization of reservoirs must consider both economic and ecological objectives; nevertheless, these two types of objectives may conflict, with efforts to pursue the optimum for one objective inevitably reducing performance in terms of another objective [30,31]. To minimize the negative impact of cascade reservoir operations, a regulatory policy for the downstream environmental flow must be incorporated into the optimal policy, which typically reduces operational flexibility and therefore reduces revenue-generating capacity [32,33]. In the present study, the downstream AEF is considered as an objective function. Based on the river discharge, the AEF is determined using the range of variability approach (RVA). Then, an ecologically oriented optimization model was established to obtain an optimal curve that balances the economic and ecological requirements of the cascade reservoir system during impoundment. Finally, the model was optimized using an improved nondominated sorting genetic algorithm based on dominance strength (INSGA2-DS). The results of this study could provide useful information to help water conservancy institutions and policy makers improve the sustainable management of cascade reservoirs in the lower reaches of the Jinsha River. Sustainability 2020, 12, 966 3 of 18

2. Materials and Methods

2.1. Study Area The lower reaches of the Jinsha River (from Panzhihua to Yibin) represent some of the most Sustainability 2020, 12, 966 3 of 17 abundant river resources in China. Four cascade reservoirs, namely, the Wudongde (WDD), Baihetan (BHT),Baihetan Xiluodu (BHT), (XLD) Xiluodu and Xiangjiaba(XLD) and Xiangjiaba (XJB) Reservoirs, (XJB) Reservoirs, either are either under are construction under construction or have or been completed.have been (Figure completed.1). Xiluodu (Figure and 1). XiangjiabaXiluodu and were Xiangjiaba ﬁrst-phase were projects, first‐phase for whichprojects, impoundment for which beganimpoundment in 2013 and began 2012, respectively.in 2013 and The2012, installed respectively. capacities The ofinstalled these two capacities hydropower of these stations two are 12,600hydropower MW and 6000stations MW, are respectively 12,600 MW [and34,35 6000]. The MW, hydraulic respectively connection [34,35]. between The hydraulic the two connection reservoirs is tight,between forming the a two cascade reservoirs reservoir is tight, system forming with a e cascadeﬀective reservoir joint operation system conditions, with effective the joint main operation parameters of theseconditions, two reservoirs the main parameters are listed in of Table these1 .two reservoirs are listed in Table 1.

98° E 99° E 100° E 101° E 102° E 103° E 104° E

Beijing China 30° N

Dadu River

Yangtze River Basin 29° N Pingshan Yibin . XLD XJB . 28° N 05010025 Km

XLD-XJB Legend BHT . 27° N Cascade . Dam (completed) reservoir . Dam (under construction) Panzhihua WDD City . Hydrological station 26° N

Middle reaches of Lower reaches of the Jinsha River the Jinsha River

FigureFigure 1. 1.Location Location of of the the Xiluodu-XiangjiabaXiluodu‐Xiangjiaba cascade cascade reservoir reservoir system. system.

TableTable 1. Main1. Main parameters parameters of of the the Xiluodu-Xiangjiaba Xiluodu‐Xiangjiaba cascaded cascaded hydropower hydropower stations. stations.

ParameterParameter Xiluodu Xiluodu Reservoir XiangjiabaXiangjiaba Reservoir Reservoir HeightHeight of dam of (m) dam (m)285.5 162.0 162.0 Dead waterDead waterlevel (m) level (m)540.0 370.0 370.0 NormalNormal water waterlevel (m) level (m)600.0 380.0 380.0 Flood limitFlood water limit waterlevel (m) level (m)560.0 370.0 370.0 InstalledInstalled capacity capacity (MW) (MW) 12600 6000 6000 Minimum output (MW) 6650 2000 Minimum output (MW) 6650 2000 Maximum output (MW) 12600 6000 Maximum output (MW) 12600 6000 Total capacity (108 m3) 126.7 51.6 8 3 TotalMinimum capacity (10 outﬂow m ) (m3/s) 126.71500 1500 51.6 Minimum outflow (m3/s) 1500 1500 2.2. Model Establishment 2.2. Model Establishment 2.2.1. Objective Functions 2.2.1. Objective Functions TheThe objectives objectives of of the the model model were to to maximize maximize total total hydropower hydropower generation generation and to and minimize to minimize the thedegree degree of of AEF AEF alteration. alteration. These These two two objectives objectives are are mutually mutually conflicting conﬂicting because because maximizing maximizing hydropowerhydropower production production requires requires increasing increasing the water level level in in the the reservoir, reservoir, while while minimizing minimizing the the degreedegree of AEFof AEF alteration alteration requires requires more more waterwater to be released released from from the the reservoir reservoir for for downstream downstream needsneeds [36 ][36] These These two two competing competing objectives objectives of of thethe systemsystem are are expressed expressed as as follows. follows. (1)(1) Maximizing Maximizing the the hydropower hydropower generation generation ofof the overall system system T XLD XJB f1 maxT (PPtt ) t (1) Xt 1 f = max (PXLD + PXJB) ∆t (1) (2) Minimizing the degree of AEF1 alteration t t · T t=1 1 XJB, out fQQQ2,,min (t AEF t ) / AEF t (2) T t1 XLD XJB where T is the total optimization period; t is the time step index; Pt and Pt are the outputs of the Xiluodu and Xiangjiaba hydropower stations, respectively, in the tth time step; t is the

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(2) Minimizing the degree of AEF alteration

T 1 X XJB,out f = min ( Q Q )/Q (2) 2 T t − AEF,t AEF,t t=1

XLD XJB where T is the total optimization period; t is the time step index; Pt and Pt are the outputs of the Xiluodu and Xiangjiaba hydropower stations, respectively, in the tth time step; ∆t is the length of a XJB,out time step; Qt is the release from the Xiangjiaba Reservoir in the tth time step; and QAEF,t is the downstream AEF. The detailed solution process is described in Section 3.2.

2.2.2. Constraint Conditions The operation constraints of a reservoir include constraints on the water level, water balance, output and outﬂow. The speciﬁc constraints considered in this study are as follows. (1) Restriction on the reservoir water level:

Zi,min Zi Zi,max (3) t ≤ t ≤ t i i,min i,max where Zt, Zt , and Zt are the actual, minimum, and maximum water levels, respectively, of reservoir i in time step t. (2) Water balance constraint:

Vi = Vi + (Ii QTi QSi ) ∆t (4) t+1 t t − t − t · i i + where Vt+1 and Vt are the capacities of reservoir i at the beginning of time steps t and t 1, respectively; i i i It is the inflow to reservoir i; QTt is the outflow from the turbines; and QSt is the spillway or outlet i i flow that cannot be utilized for power generation. Together, QTt and QSt reflect the total outflow from the reservoir. (3) Spatial transition flow constraint:

i+1 i+1 i i It = IPt + QTt + QSt (5)

i+1 where IPt denotes the inflow between power stations i and i + 1 generated by precipitation. This equation indicates that the total inflow to reservoir i + 1 consists of the inflow generated between reservoirs i and i + 1, and the total outflow from reservoir i. (4) Output constraint: Pi,min Pi Pi,max (6) t ≤ t ≤ t i,min i,max where Pt and Pt are the minimum and maximum outputs, respectively, of reservoir i. (5) Outflow constraint Qi,min Qi Qi,max (7) t ≤ t ≤ t i,min i,max where Qt and Qt are the minimum and maximum permitted outflows, respectively, of reservoir i. (6) Nonnegativity constraint: Vi, Qi, Pi 0 (8) t t t ≥ 2.2.3. Penalty Functions It is difficult to satisfy all constraints simultaneously. To this end, two methods can be used to address all constraints during the process of optimization [37]. The first method involves setting certain limits, such as reservoir water level limits, when generating the initial population and developing a new generation. The second method is to determine whether a condition is satisfied after performing the Sustainability 2020, 12, 966 5 of 18 necessary calculations and then to remove infeasible solutions by means of a penalty function [38,39]. Such a penalty function penalizes individuals based on violations of constraints. In this study, the penalty function approach was used to reduce the applicability of infeasible solutions in order to encourage the selection of feasible solutions. Initially, the extent of constraint violation is calculated as follows: c = max(C C, 0) 1 min − (9) c = max(C Cmax, 0) 2 − where c1 and c2 represent the constraint violations, C is a constraint, and Cmin and Cmax represent the allowable constraint scope of each solution. Thus, c can be expressed as follows:

c = (c1 + c2)/2 (10) where c represents the average extent of violation of constraint C. Then, the corresponding penalty value is calculated as follows: P = 1 + β (11)

XNC XNX β = c , i = 1, 2, , NX; j = 1, 2, , N (12) ji ··· ··· C j=1 i=1 ( 0 x f easible cji = ∈ cji x < f easible where P is the penalty value, β is the penalty parameter, NX is the number of genes, NC is the number of constraints, and cji is the penalty function for the jth constraint on the ith variable. When the objective is to determine the minimum value, the objective function value is multiplied by the penalty value: Fm = fm P (13) ∗ When the objective is to determine the maximum value, the objective function value is divide by the penalty value. Fm = fm/P (14)

In Equations (13) and (14), Fm is the penalized objective function, and fm is the objective function. Constraints can be divided into three categories: boundary constraints, soft constraints, and hard constraints. Boundary constraints (Equation (3)) limit the search space for the design task. Soft constraints (Equations (6) and (7)) are enforced by means of penalties, which will slightly reduce the applicability of solutions with low levels of violation and significantly reduce the applicability of solutions with high levels of violation; consequently, such constraints are not strictly related to certain levels of violation. The degree of violation of soft constraints will guide the optimization algorithm towards the feasible solution space during the search process. The constant coefficient of a penalty term cannot be set to too large a value because doing so would make an optimal fitness value difficult to obtain. During the calculation process, if various genes have reached their limiting conditions, then corresponding penalties must be imposed in accordance with the degrees of violation of these limits. Consequently, the fitness value will change rapidly. The penalty functions for the various limiting conditions are defined as described below. When Qt,i < 0, the corresponding solution is impossible, and the penalty function associated with the violation of this physical condition involves multiplying the obtained negative release value by the appropriate penalty value: cXLD = 1000.QXLD,out.cXLD 1t − t 1 (15) cXJB = 1000.QXJB,outcXJB 1t − t 1 where c1t represents the average extent of violation of the release constraint. Sustainability 2020, 12, 966 6 of 18

For ﬂood control of the Jinsha River, a penalty function is established based on the requirement XJB,out XJB,out,max that Qt > Qt . This penalty function is formulated as follows:

XJB XJB,out,max XJB,out c = (Q Q ).c t (16) 2t t − t 2 where c2t represents the average extent of violation of the release constraint. g g,min For power generation, we establish penalty functions based on the requirements that Qt < Qt min and Pt < Pt . These penalty functions are formulated as follows:

XLD,g XLD,g,min cXLD = (Q Q ).cXLD 3t t − t 3t (17) cXLD = (NXLD NXLD,min).cXLD 4t t − t 4t XJB,g XJB,g,min cXJB = (Q Q ).cXJB 3t t − g 3t (18) cXJB = (NXJB NXJB,min).cXJB 4t t − t 4t XLD XLD where c3t and c4t represent the average levels of violation of the turbine release and reservoir XLD,g XLD,g,max XJB XJB outflow constraints (Qt > Qt ), respectively, for the Xiluodu Reservoir and c3t and c4t represent the average levels of violation of the turbine release and reservoir release constraints XJB,g XJB,g,max (Qt > Qt ), respectively, for the Xiangjiaba Reservoir. To maintain the ecological base flow demand in the downstream area, if the reservoir release is less than the ecological base flow demand, we apply the following penalty function:

XJB XJB,out XJB,out,min c = (Q Q ).c t (19) 5t t − t 5 where c5t represents the average extent of violation of the release constraint associated with the minimum downstream environmental ﬂow. The penalty parameter β is the sum of all levels of constraint violation:

XNX = ( XLD + XJB + XJB + XLD + XJB + XLD + XJB + XJB) β c1t c1t c2t c3t c3t c4t c4t c5t (20) t=1

The coefficients defined in the above functions are mainly subjective, and several trial-and-error processes must be conducted to effectively obtain suitable solutions.

2.3. Model Solution The goal of a single-objective optimization problem is to obtain an optimal solution by searching for the minimum or maximum value of the objective function. However, in real life, most water resource optimization problems involve conflicting objectives, for which there is no efficient method of finding optimal solutions with multiple trade-offs. The goal of such a multiobjective problem is to find an optimal solution for all targets, also known as a Pareto-optimal solution. The nondominated sorting genetic algorithm II (NSGA-II) is a fast elite multiobjective algorithm that follows the NSGA framework [40–42]. This method has been effectively implemented to address various water management issues. However, this algorithm has many deficiencies when solving for the Pareto boundaries of high-dimensional multivariable and complex nonlinear multiobjective problems, such as an inability to identify pseudo-nondominated solutions, an unreasonable crowding distance formula, and high computational complexity. This paper uses an improved algorithm based on NSGA-II, namely, INSGA2-DS. The pseudodominated solutions in the nondominated solution set are selected by introducing the concept of a dominance intensity order, and a new crowding distance formula that considers the variance is adopted. For calculating the crowding distance, an adaptive elite retention strategy is Sustainability 2020, 12, 966 7 of 18 introduced to control the scale of elite retention, and other means are also adopted to speed up the calculation efficiency. The details of the improved algorithm are introduced as follows.

2.3.1. Fast Nondominated Sorting NSGA-II uses the fast nondominated sorting method to determine the nondominated level and sort by comparing the dominance relations between each pair of individuals. However, this method results in a large number of pseudo-nondominated solutions in the nondominated set, which reduces the convergence eﬃciency and solution quality. To remove these pseudo-nondominated solutions, a measure called the dominance intensity is introduced as follows:   Xm f (i) f min  k k  ξi =  −  (21)  f max f min  k=1 k − k where ξi is the dominance intensity of the ith member of the population, m is the number of subobjectives, max min and fk and fk are the maximum and minimum values, respectively, of the kth subobjective in the nondominated set.

2.3.2. Distribution Retention Method The concept of distribution here refers to the degrees of similarity and difference along the real Pareto boundary, reflecting the uniformity and diversity of the solution set. NSGA-II considers only the distances between neighboring individuals. However, individuals with different degrees of crowding distance with respect to different subobjectives cannot yield more genetic opportunities, and this situation is not conducive to maintaining the solution distribution. Therefore, a new crowding distance formula that considers the variance is introduced as follows:

 id  iD =    1   Pm i 2−   1 f i+1 f i 1 d  +1   m j − j− − m    j=1  (22)  m  = P i+1 i 1  id fj fj−  j=1 − where iD is the crowding distance obtained with the new method, id is the crowding distance in NSGA-II, i+1 i 1 and fj and fj− are the values of the jth subobjective for individuals i+1 and i-1, respectively. After the above calculations, each individual member of the population is associated with three parameters: a nondominated set rank (rank), a dominance intensity (ξ) and a crowding distance (iD). The priorities of these parameters are ordered as follows: rank (smaller is better) > iD (larger is better) > ξ (smaller is better).

2.3.3. Adaptive Elite Retention Strategy The elite retention scale of NSGA-II is a ﬁxed value, which is not conducive to solution set convergence. In the improved algorithm, an adaptive elite retention strategy is adopted. In the early stage of evolution, the elite retention scale is set to increase the diversity of the solutions. In the later stage of evolution, the elite retention scale is set to improve the convergence of the algorithm. The number of elites in the population of the gth generation, Eg, is calculated as follows:

Eg = P αg (23) × where αg is the impact factor for the number of gth-generation elites and P is the population size. The value of αg is adaptively and iteratively calculated as follows:

αg+1 = αg[1 + ln(ρ + 1)] (24) Sustainability 2020, 12, 966 8 of 18

where αg+1 is the impact factor for the number of (g+1)th-generation elites and ρ is the ratio of the number of solutions in the nondominated set in the gth-generation population to the total population size P. The improved algorithm, INSGA2-DS, consists of five main operations: initialization, crossover and mutation, fast nondominated sorting, implementation of elite crowding comparison operators, and termination and output of results. The loop structure of INSGA2-DS is shown in Figure2. Pt is the parent population, and Pc and Pm are the offspring populations. F , F , , F are solution classes. F is the best solution set among 1 2 ··· k 1 the parents and offspring, F is the second-best solution set, etc. Sustainability 2020, 12, 966 2 8 of 17

Nondominated sorting F Nondominated sorting F1 P Pt F2 2 Crowding distance sorting P F Pt 1 Fi

P Crossover Pc Crossover Rejected Mutation Mutation

P m F Fk

R F t t FigureFigure 2. 2. FlowchartFlowchart of of the the INSGA2 INSGA2-DS‐DS procedure. procedure.

TheThe approach for usingusing INSGA2-DSINSGA2‐DS to to solve solve the the problem problem considered considered in in this this paper paper is is illustrated illustrated in inFigure Figure3. 3.

Generate offspring population No No

Yes Set the Generate the Is the reservoir water Is the reservoir water Crossover Mutation parameters initial population level constraint met? level constraint met?

Yes

Nondominated ranking of the Calculate the objective Combine the parent and combined population functions offspring populations

Calculate the crowding Generate a new population Max. number of Yes Terminate and generations reached? distance for all solutions using tournament selection generations reached? output the results

FigureFigure 3. 3. SolutionSolution process process for for using using INSGA2 INSGA2-DS‐DS to to optimize optimize cascade cascade reservoir reservoir operation. 2.3.4. Parameter Setting 2.3.4. Parameter Setting For this study, the INSGA2-DS optimization model was programmed based on MATLAB. The For this study, the INSGA2‐DS optimization model was programmed based on MATLAB. The population size was set to 30, the maximum number of iterations was 1500, the crossover probability population size was set to 30, the maximum number of iterations was 1500, the crossover probability was 0.75, the mutation probability was 0.01, and 30 Pareto-optimal schemes were obtained through the was 0.75, the mutation probability was 0.01, and 30 Pareto‐optimal schemes were obtained through corresponding calculations. the corresponding calculations.

3. Results and Discussion

3.1. Optimization Period and Typical Years In accordance with the typical operation and regulation of cascade reservoirs, the Xiluodu Reservoir operates at a limiting water level of 560.0 m during the flood season (from June 1 to September 10); then, it begins to store water on September 10, and the water level reaches 600.0 m at the end of September. The Xiangjiaba Reservoir operates at 370.0 m during the flood season and then also starts to store water on September 10 and the water level reaches 380.0 m at the end of September. However, recent research has shown that the flood control capacity of cascade reservoirs may somewhat decrease from the end of August to early September. Therefore, to improve the

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3. Results and Discussion

3.1. Optimization Period and Typical Years In accordance with the typical operation and regulation of cascade reservoirs, the Xiluodu Reservoir operates at a limiting water level of 560.0 m during the ﬂood season (from June 1 to September 10); then, it begins to store water on September 10, and the water level reaches 600.0 m at the end of September. The Xiangjiaba Reservoir operates at 370.0 m during the ﬂood season and then also starts to store water on September 10 and the water level reaches 380.0 m at the end of September.

However,Sustainability recent 2020, 12 research, 966 has shown that the flood control capacity of cascade reservoirs may somewhat9 of 17 decrease from the end of August to early September. Therefore, to improve the reservoir storage fill ratereservoir and reduce storage the fill impact rate and of water reduce storage the impact downstream, of water the storage impoundment downstream, time should the impoundment be advanced totime the should end of be August. advanced to the end of August. ConsideringConsidering bothboth the the downstream downstream environmental environmental flow flow requirements requirements and and the the calculation calculation time, time, we dividedwe divided the datathe data to be to analyzed be analyzed into subperiods.into subperiods. Reservoir Reservoir managers managers often often use cycles use cycles of 5 days of 5 when days makingwhen making operation operation plans during plans theduring impoundment the impoundment period. In period. terms ofIn calculationterms of calculation efficiency, eitherefficiency, 5 or 6either days 5 is or a suitable6 days is time a suitable interval; time therefore, interval; the therefore, entire period the entire of interest period was of interest divided was into divided 8 subperiods, into 8 withsubperiods, the first with subperiod the first being subperiod Aug. 21–25, being the Aug. second 21‐ subperiod25, the second being subperiod Aug. 26–31, being the thirdAug. subperiod26‐31, the beingthird subperiod Sep. 1–5, and being so Sep. on. 1‐ 5, and so on. TheThe optimaloptimal results results strongly strongly depend depend on on the the choice choice of the of the typical typical hydrological hydrological year, year, as inflows as inflows often varyoften widely vary widely among diamongfferent different regulatory regulatory years. Typical years. years Typical include years wet, include normal wet, and drynormal years. and In thisdry study,years. theIn this inflow study, to the the Xiluodu inflow Reservoirto the Xiluodu in wet Reservoir years is very in wet high, years in which is very case high, impoundment in which case has littleimpoundment effect on the has downstream little effect environmental on the downstream flow; thus, environmental we selected flow; a normal thus, year we and selected dry year a normal as the typicalyear and years dry of year interest. as the The typical Pingshan years hydrological of interest. The station Pingshan is a controlled hydrological station station in the is lower a controlled reaches ofstation the Jinsha in the River lower (Figure reaches1). of Based the Jinsha on the River daily average(Figure 1). flow Based data on of Pingshanthe daily average station from flow 1956 data to of 2007Pingshan (52 years), station the from total 1956 flows to during 2007 (52 the years), impoundment the total period flows forduring every the year impoundment were accumulated period and for rankedevery year in descending were accumulated order (Figure and ranked4). in descending order (Figure 4).

5.5

5.0 wet years normal years dry years

) 4.5 3 m 10 4.0 selected 3.5 dry year

3.0 selected normal year 2.5 Total inflow (×10 inflow Total

2.0 0 5 10 15 20 25 30 35 40 45 50 Order Figure 4.4. Diagram ranking each year by the total ﬂowflow during thethe impoundmentimpoundment period.period.

AccordingAccording toto the the definition definition of of typical typical hydrological hydrological years years in hydrology, in hydrology, the top the 25% top of 25% the ranked of the totalranked flows total correspond flows correspond to wet years, to wet the years, total flows the total ranked flows between ranked the between top 25% the and top 75% 25% correspond and 75% tocorrespond normal years, to normal and the years, total and flows the rankedtotal flows below ranked the top below 75% the correspond top 75% correspond to dry years. to dry Based years. on thisBased principle, on this principle, the typical the dry typical year (ranked dry year at (ranked 75%) and at the 75%) typical and the normal typical year normal (ranked year at 50%)(ranked were at selected50%) were from selected among from the among dry years the anddry theyears normal and the years, normal respectively. years, respectively. The inflows The to inflows the Xiluodu to the ReservoirXiluodu Reservoir in the corresponding in the corresponding typical years typical are years shown are in shown Figure 5in. Figure 5.

10000 Normal year Dry year 9000

8000 /s) 3 7000

6000 Inflow (m 5000

4000 12345678 5-day time intervals (interval number) Figure 5. Inflows to Xiluodu Reservoir in the different typical years.

Sustainability 2020, 12, 966 9 of 17 reservoir storage fill rate and reduce the impact of water storage downstream, the impoundment time should be advanced to the end of August. Considering both the downstream environmental flow requirements and the calculation time, we divided the data to be analyzed into subperiods. Reservoir managers often use cycles of 5 days when making operation plans during the impoundment period. In terms of calculation efficiency, either 5 or 6 days is a suitable time interval; therefore, the entire period of interest was divided into 8 subperiods, with the first subperiod being Aug. 21‐25, the second subperiod being Aug. 26‐31, the third subperiod being Sep. 1‐ 5, and so on. The optimal results strongly depend on the choice of the typical hydrological year, as inflows often vary widely among different regulatory years. Typical years include wet, normal and dry years. In this study, the inflow to the Xiluodu Reservoir in wet years is very high, in which case impoundment has little effect on the downstream environmental flow; thus, we selected a normal year and dry year as the typical years of interest. The Pingshan hydrological station is a controlled station in the lower reaches of the Jinsha River (Figure 1). Based on the daily average flow data of Pingshan station from 1956 to 2007 (52 years), the total flows during the impoundment period for every year were accumulated and ranked in descending order (Figure 4).

5.5

5.0 wet years normal years dry years

) 4.5 3 m 10 4.0 selected 3.5 dry year

3.0 selected normal year 2.5 Total inflow (×10 inflow Total

2.0 0 5 10 15 20 25 30 35 40 45 50 Order Figure 4. Diagram ranking each year by the total flow during the impoundment period.

According to the definition of typical hydrological years in hydrology, the top 25% of the ranked total flows correspond to wet years, the total flows ranked between the top 25% and 75% correspond to normal years, and the total flows ranked below the top 75% correspond to dry years. Based on this principle, the typical dry year (ranked at 75%) and the typical normal year (ranked at 50%)Sustainability were 2020selected, 12, 966 from among the dry years and the normal years, respectively. The inflows 10to of the 18 Xiluodu Reservoir in the corresponding typical years are shown in Figure 5.

10000 Normal year Dry year 9000

8000 /s) 3 7000

6000 Inflow (m 5000

4000 12345678 5-day time intervals (interval number) Figure 5. InflowsInﬂows to to Xiluodu Xiluodu Reservoir Reservoir in in the the different diﬀerent typical years.

3.2. Determination of the Appropriate Environmental Flow The AEF concept was historically developed as a response to the degradation of aquatic ecosystems caused by human intervention [43,44]. The AEF is a crucial phenomenon in terms of electricity production and sustaining river integrity and is a key driver of ecological processes. Any flow disturbance may significantly affect and alter fluvial ecosystem dynamics [45,46]. More than 200 methods of determining environmental flows have been developed, and they can be classified into four principal groups: (1) hydrological methods [47,48], including the Tennant, 7Q10, flow duration curve (FDC), aquatic biological base flow, and RVA methods [49]; (2) hydraulic methods [50,51], including the wetted perimeter and R2CROSS methods; (3) habitat simulation methods [52], including the instream flow incremental methodology (IFIM), the physical habitat method, the weighted effective width method, and the minimum demand method for a biological space; and (4) holistic methods, including the building block method and benchmarking. Currently, most AEFs obtained via either hydrological or hydraulic methods are calculated as fixed values which do not reflect the temporal variations in the river flow demand. For example, in the FDC method, only the flow value at a cumulative frequency of either 90% or 95% on the daily flow process curve is taken as the AEF, which is an approach that lacks practical rationality. To obtain an AEF that considers the temporal variations in demand, in this paper, the RVA method was used to calculate the AEF for the lower reaches of the Jinsha River. We calculated the AEF based on the runoff data collected at the Pingshan station from 1956 to 2007. The RVA method is a comprehensive method for assessing changes in river hydrological regimes by considering the size, frequency and variation characteristics of river flows. The calculation formula is as follows:

Q = Qmean,t (Qmax,t Q ) (25) AEF,t − − min,t where QAEF,t is the AEF in time step t, Qmean,t is the mean annual flow in time step t, and Qmax,t and Qmin,t are the maximum and minimum threshold values, respectively, in time step t as calculated using the RVA method. The formulas for calculating the maximum and minimum threshold values are as follows: n o Qmax,t = max (1 + µ)Qmedian,t, Qmean,t + µQsd,t n o (26) Q = min (1 η)Q , Qmean,t µQ min,t − median,t − sd,t where η is a percentage that is generally equal to 17%; Qmedian,t is the median flow in time step t; µ is an integer greater than 0, usually taken to be 1.0; and Qsd,t is the standard variance corresponding to the average flow in time step t. The AEF results calculated are plotted in Figure6. Sustainability 2020, 12, 966 10 of 17

3.2. Determination of the Appropriate Environmental Flow The AEF concept was historically developed as a response to the degradation of aquatic ecosystems caused by human intervention [43,44]. The AEF is a crucial phenomenon in terms of electricity production and sustaining river integrity and is a key driver of ecological processes. Any flow disturbance may significantly affect and alter fluvial ecosystem dynamics [45,46]. More than 200 methods of determining environmental flows have been developed, and they can be classified into four principal groups: (1) hydrological methods [47,48] , including the Tennant, 7Q10, flow duration curve (FDC), aquatic biological base flow, and RVA methods [49]; (2) hydraulic methods [50,51], including the wetted perimeter and R2CROSS methods; (3) habitat simulation methods [52], including the instream flow incremental methodology (IFIM), the physical habitat method, the weighted effective width method, and the minimum demand method for a biological space; and (4) holistic methods, including the building block method and benchmarking. Currently, most AEFs obtained via either hydrological or hydraulic methods are calculated as fixed values which do not reflect the temporal variations in the river flow demand. For example, in the FDC method, only the flow value at a cumulative frequency of either 90% or 95% on the daily flow process curve is taken as the AEF, which is an approach that lacks practical rationality. To obtain an AEF that considers the temporal variations in demand, in this paper, the RVA method was used to calculate the AEF for the lower reaches of the Jinsha River. We calculated the AEF based on the runoff data collected at the Pingshan station from 1956 to 2007. The RVA method is a comprehensive method for assessing changes in river hydrological regimes by considering the size, frequency and variation characteristics of river flows. The calculation formula is as follows:

QQAEF, t mean , t QQ max, t min, t  (26)

where QAEF, t is the AEF in time step t , Qmean, t is the mean annual flow in time step t , and Qmax,t

and Qmin,t are the maximum and minimum threshold values, respectively, in time step t as calculated using the RVA method. The formulas for calculating the maximum and minimum threshold values are as follows:

QQQQmax,tmediantmeantsdtmax 1 , , ,  ,  (27) QQQQmin,tmediantmeantsdtmin 1 , , ,  ,

where  is a percentage that is generally equal to 17%; Qmedian, t is the median flow in time step t;  Q isSustainability an integer2020 greater, 12, 966 than 0, usually taken to be 1.0; and sdt, is the standard variance corresponding11 of 18 to the average flow in time step t . The AEF results calculated are plotted in Figure 6.

9800

9500

9200 /s) 3 8900

8600 AEF (m AEF

8300

8000 12345678 Sustainability 2020, 12, 966 5-day time intervals (interval number) 11 of 17 FigureFigure 6. 6. AppropriateAppropriate environmental environmental flow flow (AEF) (AEF) in in the lower reaches of the Jinsha River. 3.3. Optimization Results 3.3. Optimization Results 3.3.1. Optimization Results for a Normal Year 3.3.1. Optimization Results for a Normal Year For the selected normal year, under the current regular operation policy, the total power For the selected normal year, under the current regular operation policy, the total power generated generated by the cascade reservoir system during the impoundment period is 16.011 billion kW∙h, byand the the cascade degree reservoir of AEF alteration system during is 11.76%. the impoundment The Pareto‐optimal period issolution 16.011 billiondistribution kW h, for and this the normal degree · ofyear AEF is shown alteration in Figure is 11.76%. 7. Three The Pareto-optimal typical optimal solution schemes distribution were selected for thisfor analysis normal year of the is shownreservoir in Figurewater levels7. Three and typical outflows: optimal scheme schemes 1 (minimum were selected degree for of analysis AEF alteration), of the reservoir scheme water 2 (an levels unbiased and outflows:optimal solution) scheme 1and (minimum scheme degree3 (maximum of AEF alteration),power generation). scheme 2 (anThe unbiasedred circle optimal represents solution) the andreference scheme scheme 3 (maximum (regular power operation). generation). To achieve The redthe circlemaximum represents power the generation, reference scheme we can (regular choose operation).scheme 3, in To which achieve power the maximumgeneration poweris increased generation, by 1.28% we canat the choose cost of scheme increasing 3, in whichthe degree power of generationAEF alteration is increased by 13.86%. by To 1.28% achieve at the the cost maximum of increasing ecological the degreebenefit, of scheme AEF alteration 1 can be selected, by 13.86%. in Towhich achieve the thedegree maximum of AEF ecological alteration benefit, is reduced scheme by 1 can22.53% be selected, with a in0.62% which reduction the degree in ofpower AEF alterationgeneration. is If reduced there is byno 22.53%demand with preference, a 0.62% we reduction can choose in power scheme generation. 2; while reducing If there is the no degree demand of preference,AEF alteration we can by choose6.38%, schemethis scheme 2; while can reducing also increase the degree power of generation AEF alteration by 0.89%. by 6.38%, The this details scheme of canthese also optimal increase results power are generation shown in Table by 0.89%. 2. The details of these optimal results are shown in Table2.

15.85

) Scheme 1

h 15.90 ꞏ 15.95 regular operation 16.00 (billion kW

n 16.05

16.10

16.15 Scheme 3

Power generatio 16.20 Scheme 2

16.25 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 Degree of AEF alteration (%)

Figure 7. ParetoPareto-optimal‐optimal distribution for a normal year.

Table 2. Optimal results under three typical schemes in normal year.

Power Degree of AEF Scheme Objective Generation Alteration (%) (billion kW∙h) Minimizing the degree of AEF Scheme 1 15.912 9.11% alteration Scheme 2 Unbiased 16.153 11.01% Maximizing the power Scheme 3 16.217 13.39% generation Reference Regular operation 16.011 11.76% scheme

Figure 8 shows the cascade reservoir water levels and outflows for these three optimal schemes in a normal year. Under all three optimal schemes, the water storage capacity in the first two periods (intervals 1 and 2) is increased compared with that under regular operation, and the water level is increased earlier to enhance power generation. The water level of the Xiangjiaba Reservoir in the fourth period (interval 4) reaches 379.86 m and 379.85 m under schemes 3 and 2, respectively, and then remains at 379.80‐379.90 m until the end of the water storage period under scheme 3. Considering the downstream environmental flow, under scheme 2, the outflow of the Xiangjiaba Reservoir is increased at the beginning of the seventh period (interval 7). To ensure that the downstream environmental water demand is met, in scheme 1, the outflow of the Xiangjiaba

Sustainability 2020, 12, 966 12 of 18

Table 2. Optimal results under three typical schemes in normal year.

Power Generation Degree of AEF Scheme Objective (Billion kW h) Alteration (%) · Scheme 1 Minimizing the degree of AEF alteration 15.912 9.11% Scheme 2 Unbiased 16.153 11.01% Scheme 3 Maximizing the power generation 16.217 13.39% Reference scheme Regular operation 16.011 11.76%

Figure8 shows the cascade reservoir water levels and outflows for these three optimal schemes in a normal year. Under all three optimal schemes, the water storage capacity in the first two periods (intervals 1 and 2) is increased compared with that under regular operation, and the water level is increased earlier to enhance power generation. The water level of the Xiangjiaba Reservoir in the fourth period (interval 4) reaches 379.86 m and 379.85 m under schemes 3 and 2, respectively, and then remains at 379.80-379.90 m until the end of the water storage period under scheme 3. Considering the Sustainability 2020, 12, 966 12 of 17 downstream environmental flow, under scheme 2, the outflow of the Xiangjiaba Reservoir is increased Reservoirat the beginning is maintained of the seventhas close period as possible (interval to the 7). AEF; To ensure thus, that the thereservoir downstream water level environmental is slowly increasedwater demand in the is fourth met, inand scheme fifth periods. 1, the outflow The Xiluodu of the XiangjiabaReservoir water Reservoir level is reaches maintained 595.37 as m close in the as 5thpossible period; to then, the AEF; the outflow thus, the is reservoir increased water in the level seventh is slowly and eighth increased periods in the to fourth meet the and downstream fifth periods. environmentalThe Xiluodu Reservoir flow demand. water level reaches 595.37 m in the 5th period; then, the outflow is increased in the seventh and eighth periods to meet the downstream environmental flow demand.

604 381 600 380 596 379 378 592 377 588 Regular operation 376 Regular operation 584 Scheme 1 Scheme 1 Water level (m) Water level Water level (m) Water level Scheme 2 375 Scheme 2 580 Scheme 3 374 Scheme 3 576 373 12345678 12345678 5-day time intervals (interval number) 5-day time intervals (interval number) (a) (b)

12000 12000 10000 10000 /s) /s) 3 8000 3 8000 6000 6000 Regular operation Regular operation Scheme 1 4000 Scheme 1 4000 Scheme 2 Outflow (m Outflow (m Outflow 2000 Scheme 2 2000 Scheme 3 Scheme 3 AEF 0 0 12345678 12345678 5-day time intervals (interval number) 5-day time intervals (interval number) (c) (d)

FigureFigure 8. 8. ReservoirReservoir water water levels levels and and outflows outflows under under different different typical typical schemes schemes in in a a normal normal year: year: (a) (a ) waterwater level level of of the the Xiluodu Xiluodu Reservoir; Reservoir; (b) (b) water water level level of of the the Xiangjiaba Xiangjiaba Reservoir; Reservoir; (c) (c) outflow outflow of of the the XiluoduXiluodu Reservoir; Reservoir; (d) (d) outflow outflow of of the the Xiangjiaba Xiangjiaba Reservoir. Reservoir.

3.3.2. Optimization Results for a Dry Year 3.3.2. Optimization Results for a Dry Year For the selected typical dry year, under the regular operation scheme, the total power generated For the selected typical dry year, under the regular operation scheme, the total power generated by the cascade reservoir system during the impoundment period is 12.156 billion kW h, and the by the cascade reservoir system during the impoundment period is 12.156 billion kW∙h,· and the degree of AEF alteration is 27.30%. The Pareto-optimal distribution for this dry year is shown in degree of AEF alteration is 27.30%. The Pareto‐optimal distribution for this dry year is shown in Figure9. Again, three typical optimal schemes are selected, namely, scheme 1 (minimum degree of Figure 9. Again, three typical optimal schemes are selected, namely, scheme 1 (minimum degree of AEF alteration), scheme 2 (unbiased optimal solution), and scheme 3 (maximum power generation), AEF alteration), scheme 2 (unbiased optimal solution), and scheme 3 (maximum power generation), to analyze the reservoir water levels and outﬂows. To maximize power generation, we can choose to analyze the reservoir water levels and outflows. To maximize power generation, we can choose scheme 3, which increases power generation by 1.76% while increasing the degree of AEF alteration by 4.95%. To minimize the degree of AEF alteration, we can choose scheme 1, which reduces the degree of AEF alteration by 13.70% while decreasing power generation by 0.48%. If there is no demand preference, scheme 2 can increase power generation by 1.08% while decreasing the degree of AEF alteration by 7.51%. The details of the optimal results are shown in Table 3.

Sustainability 2020, 12, 966 13 of 18

scheme 3, which increases power generation by 1.76% while increasing the degree of AEF alteration by 4.95%. To minimize the degree of AEF alteration, we can choose scheme 1, which reduces the degree of AEF alteration by 13.70% while decreasing power generation by 0.48%. If there is no demand preference, scheme 2 can increase power generation by 1.08% while decreasing the degree of AEF alterationSustainability by 2020 7.51%., 12, 966 The details of the optimal results are shown in Table3. 13 of 17

12.05 Scheme 1 h) 12.10 ꞏ

12.15 regular operation 12.20

12.25

12.30 Scheme 3

12.35 Scheme 2 Power generation (billion kW 12.40 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 Degree of the AEF alteration (%)

Figure 9. ParetoPareto-optimal‐optimal distribution for a dry year.

Table 3. Optimal results under three typical schemes in aa drydry year.year.

Power Generation Degree of the AEF Scheme Objective Power (billion kW h)DegreeAlteration of the AEF (%) Scheme Objective Generation · Alteration (%) Scheme 1 Minimizing the degree of AEF alteration(billion kW∙h) 12.098 23.56% Scheme 2 Unbiased 12.287 25.25% Minimizing the degree of AEF SchemeScheme 1 3 Maximizing the power generation12.098 12.37023.56% 28.65% Reference schemealteration Regular operation 12.156 27.30% Scheme 2 Unbiased 12.287 25.25% Maximizing the power FigureScheme 10 3 shows the cascade reservoir water levels and12.370 outflows for these three28.65% optimal schemes in a dry year. Due to the smallgeneration inflow in dry years, the differences between the optimal schemes Reference are smaller than those forRegular a normal operation year. Under scheme 3,12.156 which prioritizes raising27.30% the water level, the Xiangjiabascheme Reservoir water level reaches 379.83 m in the fourth period and then remains above 379.00 m. The Xiluodu Reservoir water level reaches 599.36 m in the sixth period, and the water level is thenFigure decreased 10 shows to 594.52 the mcascade in the seventh reservoir period water to maintainlevels and a hydraulic outflows headfor these difference three for optimal power generation.schemes in Ina dry scheme year. 1, Due the outflow to the small of the inflow Xiluodu in Reservoir dry years, begins the differences to be increased between in the the fifth optimal period toschemes meet the are demand smaller forthan the those downstream for a normal environmental year. Under flow. scheme Compared 3, which to thoseprioritizes in scheme raising 3, thethe averagewater level, outflows the Xiangjiaba of the Xiluodu Reservoir Reservoir water in level the fifthreaches and 379.83 sixth periods m in the in fourth scheme period 1 are increasedand then byremains 775.46 above m3/s 379.00 and 817.27 m. The m3 Xiluodu/s, respectively. Reservoir In water both scheme level reaches 1 and 599.36 scheme m 2, in the the water sixth period, level of and the Xiluoduthe water Reservoir level is then is reduced decreased in the to seventh 594.52 m period in the so seventh that the period outflow to is maintain as close asa hydraulic possible to head the AEFdifference of the for downstream power generation. river. In scheme In scheme 1, the 1, averagethe outflow outflow of the to XiangjiabaXiluodu Reservoir in the seventh begins period to be isincreased 8481.55 in m 3the/s, whereasfifth period in scheme to meet 2,the it demand is 8616.98 for m the3/s todownstream meet the downstream environmental AEF flow. demand Compared in the dryto those season. in scheme 3, the average outflows of the Xiluodu Reservoir in the fifth and sixth periods in scheme 1 are increased by 775.46 m3/s and 817.27 m3/s, respectively. In both scheme 1 and scheme 2, the water level of the Xiluodu Reservoir is reduced in the seventh period so that the outflow is as close as possible to the AEF of the downstream river. In scheme 1, the average outflow to Xiangjiaba in the seventh period is 8481.55 m3/s, whereas in scheme 2, it is 8616.98 m3/s to meet the downstream AEF demand in the dry season.

604 381 600 380 596 379 378 592 377 588 Regular operation 376 Regular operation 584 Scheme 1 Scheme 1 Water level (m) Water level Scheme 2 (m) Water level 375 Scheme 2 580 Scheme 3 374 Scheme 3 576 373 12345678 12345678 5-day time intervals (interval number) 5-day time intervals (interval number) (a) (b)

Sustainability 2020, 12, 966 13 of 17

12.05 Scheme 1 h) 12.10 ꞏ

12.15 regular operation 12.20

12.25

12.30 Scheme 3

12.35 Scheme 2 Power generation (billion kW 12.40 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 Degree of the AEF alteration (%) Figure 9. Pareto‐optimal distribution for a dry year.

Table 3. Optimal results under three typical schemes in a dry year.

Power Degree of the AEF Scheme Objective Generation Alteration (%) (billion kW∙h) Minimizing the degree of AEF Scheme 1 12.098 23.56% alteration Scheme 2 Unbiased 12.287 25.25% Maximizing the power Scheme 3 12.370 28.65% generation Reference Regular operation 12.156 27.30% scheme

Figure 10 shows the cascade reservoir water levels and outflows for these three optimal schemes in a dry year. Due to the small inflow in dry years, the differences between the optimal schemes are smaller than those for a normal year. Under scheme 3, which prioritizes raising the water level, the Xiangjiaba Reservoir water level reaches 379.83 m in the fourth period and then remains above 379.00 m. The Xiluodu Reservoir water level reaches 599.36 m in the sixth period, and the water level is then decreased to 594.52 m in the seventh period to maintain a hydraulic head difference for power generation. In scheme 1, the outflow of the Xiluodu Reservoir begins to be increased in the fifth period to meet the demand for the downstream environmental flow. Compared to those in scheme 3, the average outflows of the Xiluodu Reservoir in the fifth and sixth periods in scheme 1 are increased by 775.46 m3/s and 817.27 m3/s, respectively. In both scheme 1 and scheme 2, the water level of the Xiluodu Reservoir is reduced in the seventh period so that the outflow is as close as possible to the AEF of the downstream river. In scheme 1, the average outflow to Xiangjiaba inSustainability the seventh2020 period, 12, 966 is 8481.55 m3/s, whereas in scheme 2, it is 8616.98 m3/s to meet the downstream14 of 18 AEF demand in the dry season.

604 381 600 380 596 379 378 592 377 588 Regular operation 376 Regular operation 584 Scheme 1 Scheme 1 Water level (m) Water level Scheme 2 (m) Water level 375 Scheme 2 580 Scheme 3 374 Scheme 3 576 373 12345678 12345678 Sustainability 20205-day, 12 ,time 966 intervals (interval number) 5-day time intervals (interval number) 14 of 17 (a) (b) 12000 12000 10000 Regular operation 10000

/s) Scheme 1 /s) 3 3 8000 Scheme 2 8000 Scheme 3 6000 6000 4000 4000

Outflow (m Outflow (m Outflow Regular operation AEF 2000 2000 Scheme 1 Scheme 2 Scheme 3 0 0 12345678 12345678 5-day time intervals (interval number) 5-day time intervals (interval number) (c) (d)

Figure 10. Reservoir water levels and outflows under different optimal schemes in a dry year: (a) water Figure 10. Reservoir water levels and outflows under different optimal schemes in a dry year: (a) level of the Xiluodu Reservoir; (b) water level of the Xiangjiaba Reservoir; (c) outflow of the Xiluodu water level of the Xiluodu Reservoir; (b) water level of the Xiangjiaba Reservoir; (c) outflow of the Reservoir; (d) outflow of the Xiangjiaba Reservoir. Xiluodu Reservoir; (d) outflow of the Xiangjiaba Reservoir. 3.4. Discussion 3.4. Discussion In the above analysis, operation optimization was performed for a typical normal hydrological yearIn and the a typicalabove analysis, dry year, operation and three optimization different optimal was schemes performed and for their a typical levels ofnormal optimization hydrological were yearinvestigated and a typical for each dry typical year, and year. three For thedifferent typical optimal normal schemes year, the and diff erencestheir levels among of optimization the different wereoptimal investigated schemes are for more each obvious typical dueyear. to For the the larger typical inflow normal to the year, reservoirs. the differences When the among maximum the differentpower generation optimal schemes is sought, are the more water obvious level of due each to reservoirthe larger increases inflow to quickly the reservoirs. and then, When once the maximumhighest water power level generation is reached, is it sought, is maintained the water at this level level of each for power reservoir generation. increases Therefore, quickly and the rangethen, onceof outflow the highest fluctuation water is level large, is leadingreached, to it an is maintained increase in the at this environmental level for power flow. generation. By contrast, Therefore, when the theenvironmental range of outflow flow is prioritizedfluctuation to is minimize large, leading the degree to an of AEFincrease alteration, in the the environmental stability of the flow. outflow By contrast,must be maintained, when the environmental resulting in a relatively flow is prioritized slow rise in to the minimize reservoir the water degree levels of and,AEF consequently, alteration, the a stabilityreduction of in the the outflow total power must generation be maintained, of the resulting cascade reservoirin a relatively system. slow rise in the reservoir water levelsFor and, the consequently, typical dry year, a reduction because the in incomingthe total power flow is generation generally lower of the than cascade the environmental reservoir system. flow, the diForfferences the typical among dry the year, various because optimal the incoming schemes areflow smaller is generally than those lower in than the typical the environmental normal year. flow,In the the regular differences operation among scheme, the various the reservoir optimal water schemes levels are rise smaller slowly. than When those the in the power typical generation normal year.is sought, In the the regular corresponding operation optimal scheme, scheme the reservoir still gives water priority levels to rise increasing slowly. the When reservoir the power water generationlevels as soon is assought, possible, the whereascorresponding when theoptimal goal is scheme to minimize still gives the degree priority of AEFto increasing alteration, the reservoircorresponding water optimal levels as scheme soon as is possible, designed whereas to improve when the the ecological goal is to benefit minimize of the the cascade degree reservoir of AEF alteration,system by reducingthe corresponding the water levelsoptimal during scheme a certain is designed period. to In improve general, thethe optimal ecological schemes benefit obtained of the cascadehere are reasonablyreservoir system consistent by withreducing actual the operations. water levels During during real operation, a certain the period. manager In general, can choose the a optimalsuitable schemeschemes in obtained accordance here with are specific reasonably needs. consistent with actual operations. During real operation, the manager can choose a suitable scheme in accordance with specific needs. 4. Conclusions 4. Conclusions This paper establishes an optimal model for the impoundment period of the Xiangjiaba-Xiluodu cascadeThis reservoir paper systemestablishes considering an optimal both economic model andfor ecological the impoundment benefits, where period the AEF of of the Xiangjiabadownstream‐Xiluodu river is cascade determined reservoir using system the RVA considering method. Inboth the economic proposed and method, ecological the improved benefits, whereINSGA2-DS the AEF algorithm of the downstream is used as a viableriver is means determined of determining using the the RVA optimal method. reservoir In the scheduling proposed method,by balancing the improved objectives INSGA2 related to‐DS human algorithm needs, is used water as management a viable means and of river determining ecological the protection. optimal reservoir scheduling by balancing objectives related to human needs, water management and river ecological protection. When the optimization is focused on maximizing economic benefit in a normal hydrological year and a dry year, the level of power generation can be increased by 1.28% and 1.76%, respectively, but the degree of change in the AEF is simultaneously increased by 13.86% and 4.95%, respectively (compared to the current regular operation scheme). Conversely, when the optimization is focused on ecological needs, the degree of AEF alteration can be reduced by 22.53% and 13.70%, respectively, while power generation is reduced by 0.62% and 0.48%, respectively. In addition, the wide distribution of the Pareto fronts produced using the proposed optimization techniques provides decision makers with considerable flexibility in establishing appropriate rules for reservoir operations by balancing human and ecological needs. The results not only verify the effectiveness of the proposed method but also provide a quantitative relationship between power generation and the degree of AEF alteration as well as operational references.

Sustainability 2020, 12, 966 15 of 18

When the optimization is focused on maximizing economic benefit in a normal hydrological year and a dry year, the level of power generation can be increased by 1.28% and 1.76%, respectively, but the degree of change in the AEF is simultaneously increased by 13.86% and 4.95%, respectively (compared to the current regular operation scheme). Conversely, when the optimization is focused on ecological needs, the degree of AEF alteration can be reduced by 22.53% and 13.70%, respectively, while power generation is reduced by 0.62% and 0.48%, respectively. In addition, the wide distribution of the Pareto fronts produced using the proposed optimization techniques provides decision makers with considerable flexibility in establishing appropriate rules for reservoir operations by balancing human and ecological needs. The results not only verify the effectiveness of the proposed method but also provide a quantitative relationship between power generation and the degree of AEF alteration as well as operational references.

Author Contributions: Conceptualization, L.D. and H.D.; methodology, L.D. and Y.W.; software, Z.C. and C.M.; validation, L.D. and Z.C.; formal analysis, L.D.; investigation, J.G. and Z.C.; resources, H.D. and H.L.; data curation, L.D. and Z.C.; writing-original draft preparation, L.D.; writing—review and editing, L.D., C.M. and J.G.; supervision, H.D. and H.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (51809150), the China Postdoctoral Science Foundation (2019T120119), the CRSRI Open Research Program (CKWV2019725/KY), and the Three Gorges Follow-up Research Project (2017HXXY-05). Acknowledgments: The authors wish to acknowledge China Yangtze Power Corporation for the use of various facilities in carrying out this research. Many thanks are due to the anonymous referees for their detailed and helpful comments. In addition, the authors appreciate the review and editorial comments of the reviewers, and the editor. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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