Boosting hydropower generation of mixed reservoirs for reducing carbon emissions by using a simulation–optimization framework

Reservoir joint operation is an important and efficient non-engineering measure for promoting renewable energy production, water resources management and carbon emissions reduction (Berga 2016; Kuriqi et al. 2019; Tamm & Tamm 2020; Wegner et al. 2020; Spanoudaki et al. 2022). As one of the important parameters of reservoir operation, the flood-limited water level (FLWL) is usually used to make a tradeoff between flood prevention and hydropower production (Zhou et al. 2014; Liu et al. 2015a, 2015b; Zhu et al. 2022a, 2022b, 2022c). The standard operation policy (SOP) of annual FLWL, in general, can allow ample storage capacity for flood prevention; however, it often gives rise to large spilled water and low impoundment water volume in the flood season (Li et al. 2014; Yazdi & Moridi 2018; Liu et al. 2022). Considering flood seasonality, the optimization of seasonal FLWLs is beneficial to largely facilitate the development and utilization of flood resources without lowering flood prevention standards, compared with the SOP of annual FLWL.

The optimal operation of FLWLs of reservoirs is a vital approach for satisfactorily balancing flood prevention and hydroelectricity needs (Yun & Singh 2008; Chen et al. 2017). In general, under the same hydrological conditions, the larger the value of the FLWL is set to be, the higher the reservoir flood risk will be. In contrast, the benefits of floodwater resources utilization such as hydropower generation (HG) and water supply will be decreased largely if the value of the FLWL is set to be low. Given the benefits and cost of hydraulic infrastructures, the annual FLWL is calculated by flood regulation simulation based on the annual maximum design floods corresponding to some critical return periods (Li et al. 2010). Since annual maximum design floods do not consider flood seasonality, a reservoir will adopt a small and single value of the annual FLWL resulting in a low floodwater resources utilization efficiency (Xiong et al. 2020). Hence, it is desired to conduct more intensive research on the optimization of seasonal FLWLs in consideration of the flood seasonality to boost hydropower output and floodwater utilization efficiency of reservoirs.

Recently, several studies have been conducted to improve floodwater operation and management without updating hydraulic infrastructures, from the perspectives of flood season segmentation and seasonal FLWL operation (Jiang et al. 2019; He et al. 2022). The flood season segmentation often divides the whole flood season into two or three sub-season segments, and then each sub-season will set an FLWL accordingly. For instance, genesis analysis (Singh et al. 2005), fractal theory (Fang et al. 2010), change-point analysis (Liu et al. 2010), the statistical method (Dhakal et al. 2015), entropy-based method (Singh 2011), fuzzy set analysis (Mu et al. 2022), and so on, have been applied for analyzing the flood seasonality to accomplish the season segmentation. Following up flood season segmentation, some researchers focus on determining seasonal FLWL operation schemes from the standpoint of risk–benefit analysis. The risk analysis model proposed by Zhou et al. (2015) can adequately assess the impact of the uncertainties consisting of hydrology input, water release capacity and reservoir storage capacity on the values of seasonal FLWLs by using the Monte Carlo simulation method. In comparison to the SOP of annual FLWL, Liu et al. (2015a, 2015b) constructed an optimization operation model to identify the seasonal FLWL scheme of the Three Gorges Reservoir (TGR) for three sub-season segments without increasing the reservoir flood prevention risk. In addition, the joint optimization operation of reservoirs and their floodplains is also an efficient approach for increasing the values of seasonal FLWLs to stimulate the comprehensive benefits of hydropower and floodwater resources (Xie et al. 2018). Kim et al. (2022) introduced a resilience framework to optimize reservoir hydropower operation for mitigating the power loss due to seasonal FLWL control. Wan et al. (2023) proposed a multi-objective synergistic decision-making method to optimize the FLWL scheme of the Xianghongdian Reservoir for making tradeoffs between HG benefits and flood prevention risk. The existing studies have been focusing on optimizing the seasonal FLWL schemes for single reservoir operation, whereas none of the studies have been carried out to optimize season FLWL schemes for mixed reservoirs. As known, with an increasing number of reservoirs, it is highly complex and challenging for researchers to model and optimize the seasonal FLWL management system, because more complicated hydraulic connections and more constraints and decision variables need to be considered in the model (Giuliani et al. 2021). Thus, it is crucial to explore the seasonal FLWL management system of mixed reservoirs for facilitating hydropower production expansion while stimulating floodwater resources utilization benefits.

The innovative nature of this study is indebted to optimizing HG and flood prevention operation using an evolutionary algorithm with the simulation–optimization framework, and its application is, for the first time, to promote the new niche of floodwater utilization. The new contribution of this study is threefold: proposing a multi-objective optimization operation model of seasonal FLWLs of mixed reservoirs; integrating the NSGA-II and a simulation–optimization framework to reduce computation complexity and time caused by plenty of variables and constraints related to modeling the seasonal FLWL management system of mixed reservoirs; and utilizing the technique for order of preference by similarity to ideal solution (TOPSIS) to identify the best operation scheme of seasonal FLWLs from the perspective of multi-criteria decision-making analysis. The proposed approach is applied to a mixed reservoir system composed of the TGR and six other reservoirs located in the upstream Yangtze River of China.

Seven representative flood events, including 1956 and 2007 (first sub-season segment); 1954, 1981, and 1998 (second sub-season segment); and 1952 and 1964 (third sub-season segment), were utilized for calculating the design flood hydrographs corresponding to 5, 1 and 0.1% occurrence frequencies in accordance with the flood peak–flood volume magnification method (Xiao et al. 2009; Zhou et al. 2015). The design flood hydrographs of the TGR are taken as an example, which are displayed in Figure A1. The durations of the flood event are 30, 30 and 15 days in the first, second and third sub-season segments, respectively. The calculation time step is 1 day in each flood event. These data have been calibrated and provided by the Bureau of Hydrology, Changjiang Water Resources Commission. The lower and upper boundaries of seasonal FLWLs of the mixed reservoirs in the three sub-season segments are listed in Table 2. The lower boundaries of seasonal FLWLs are equal to the annual FLWLs of the reservoirs and the upper ones are referred to the previous study (Liu et al. 2015a, 2015b).

The multi-objective operation model is constructed to tackle seasonal FLWL management challenges by increasing hydroelectricity output while guaranteeing flood prevention safety.

In the flood season, the model (Figure 2(a)) is constructed to simultaneously accomplish four objectives for synergistically maximizing HG and alleviating flood prevention pressure, which are Objective 1: maximization of the HG of reservoirs; Objective 2: minimization of the peak streamflow (PF) of the flood control station, which is suitable for operating small–medium (occurrence frequency ≤5%) flood events; Objective 3: minimization of the final water level (WL) of the reservoir at the flood prevention period, which is suitable for operating large (1% < occurrence frequency ≤ 5%) flood events; Objective 4: minimization of the highest reservoir WL (HWL), which is suitable for operating extra-large (occurrence frequency ≤1%) flood events.

The physical constraints are listed below:

• (1)
  Reservoir water balance equation:

  

  (5)

  where and are the inflow and water release (i.e., discharge) of the ith reservoir at the tth time, respectively.
• (2)
  Reservoir discharge limitation:

  

  (6a)

  

  (6b)

  where f[·] represents the maximum reservoir water release corresponding to the reservoir WL and is the occurrence time of the maximal inflow (i.e., flood peak) of the ith reservoir in the flood event.
• (3)
  Reservoir WL limitation:

  

  (7)

  where and are the minimal and maximal WLs of the ith reservoir at the tth time, respectively.
• (4)
  Initial WL limitation:

  

  (8)

  where is the seasonal FLWL (=initial WL) of the ith reservoir.
• (5)
  Power generation limitation:

  

  (9)

  where and are the minimum and maximum power generation of the ith reservoir at the tth time, respectively.
• (6)
  Hydraulic connection limitation:

  

  (10)

  where is the lateral flow in the upstream of the ith reservoir at the tth time.
• (7)

  Flood routing constraint:

Owing to the fast development of cloud computing, such complex mathematical problems can be handled with less computation time and much more efficiency. As known, the NSGA-II optimization algorithm has the ability to combine simulation methods to tackle the multi-objective optimization operation model (Zhang et al. 2019; Gonzalez et al. 2020; Hatamkhani et al. 2020). Hence, this study fused the SOP-based flood prevention simulation into the standard NSGA-II optimization algorithm to boost the performance of the multi-objective and joint operation model of seasonal FLWLs (i.e., the simulation–optimization framework). Because the intelligent optimization algorithm cannot ensure that the initial population includes feasible operation policies, the NSGA-II would be easy to fall into the local minima. For the proposed simulation–optimization framework, feasible operation policies for reservoir flood prevention are first created by the SOP-based flood prevention simulation, and then the optimal solution is searched efficiently by integrating the feasible operation policies into the initial population of the NSGA-II. In other words, fusion of feasible operation policies into the NSGA-II can effectively facilitate the search for Pareto Frontier with far less computation time, and thus could increase the capability of escaping from local optimum to find global optimum. The simulation (SOP)–optimization (NSGA-II) structure executes the below calculation steps.

Step 1: Set the seasonal FLWL schemes and initialize a population N₀ of size NP using the SOP-based flood prevention simulation (Figure 3) for each reservoir. In Figure 3, before the time t₁ of raising WL, if the inflow is smaller than the reservoir water release capacity (see Equation (6b)), the reservoir water release is set to be the inflow, and thus the WL would maintain the seasonal FLWL. From the time t₁ up to the time t₂ (t₂ is the occurrence of the HWL), the inflow increases gradually to be larger than the water release capacity, then the reservoir would implement water release in accordance with the water release capacity as well as the WL would reach the maximum value at the time t₂ (reservoir discharge = reservoir inflow). After the time t₂, the WL decreases with the decline in reservoir inflow gradually.

Step 2: Compute the fitness values of the N₀; divide the initial population N₀ into various ranks by using the non-dominated sorting method; and then compute crowding distance values of the initial population N₀.

Step 3: Produce the offspring population corresponding to the next generation by using the hybrid of the crowded tournament selection operator and the elitism preservation strategy; integrate parent chromosomes to create a new offspring one by using the crossover operator with a probability of p₁; and increase genetic diversity of the population by using the mutation operator with a probability of p₂. Therefore, an offspring population A₀ of size NP would be constructed with the three genetic operators.

Step 4: For each generation j, calculate the fitness values of A_j; integrate A_j−1 and A_j into a temporary population B_j of size 2 × NP; divide the temporary population B_j into various ranks; and compute the crowding distance values of the temporary population B_j.

Step 5: Execute the crowed tournament selection operator to choose an N_j+1 of size NP from N_j; implement genetic operators to create an A_j+1 of size NP; and calculate the fitness values of N_j+1 and A_j+1.

Step 6: Repeat Steps 2–5 to decide whether the calculation would be terminated according to the stop criteria. When the number of iterations is smaller than the maximum iteration (K), then Steps 2–5 would be repeated. Otherwise, output the optimal solutions associated with decision variables.

In our case, the multi-objective operation model would be driven by a number of 3,780 datasets (=7 reservoirs × 45 days (first and third sub-season segments) × 2 representative flood events × 3 return periods + 7 reservoirs × 30 days (second sub-season segment) × 3 representative flood events × 3 return periods, consisting of 3,780 decision variables (i.e., water release variables) and 15,120 physical constraints (=4 equations × 3,780 water release variables). After executing the SOP-based flood prevention simulation, plenty of initial solutions would be provided to meet the requirements of 15,120 physical constraints, which means the capability of the NSGA-II for searching global optimum would be largely raised. The parameters of the used NSGA-II for achieving the Pareto frontier were set as NP = 100, K= 500, p₁= 0.8 and p₂= 0.1.

Some multi-criteria decision-making methods were employed to identify the best scheme among a large amount of alternatives (Sánchez-Lozano et al. 2016; Tamimi et al. 2021; Zhu et al. 2022a, 2022b, 2022c). Because the TOPSIS has the ability to offer an opportunity for stakeholders and decision-makers on assessing and pre-experiencing the consequences of various best solutions, it was adopted to identify the best operation scheme from the Pareto solutions (i.e., alternatives) by considering flood prevention safety and HG benefits. The calculation steps of the TOPSIS-based multi-criteria decision-making analysis are described below.

Step 6: Rank all the alternatives (i.e., Pareto solutions) in accordance with the value of the close degree and select the best operation solution of seasonal FLWLs corresponding to the largest close degree.

The Pareto frontiers of HG (O1: HG) versus flood prevention operation (O2: PF, O3: WL, O4: HWL) from the NSGA-II corresponding to the first, second, and third sub-season segments are presented in Figures A2, 4(a -i) and A3, respectively. It is noted that the position of the SOP solution is far away from the Pareto frontiers of HG and flood prevention operation. The indicator values of the O1 (O2) of the Pareto solutions are larger (smaller) than those of the SOP solution. Taking the design flood with the 20-year return period based on the 1956 representative flood event (shown in FigureA2(a)), for example, the HG (O1: HG) and peak flow (O2: PF) of the Chenglingji flood control point using the SOP solution are 122 × 10⁸ kW h and 50,658 m³/s, respectively, while the HG (O1: HG) of the Pareto solutions ranges from 127 to 135 × 10⁸ kW h with smaller values of the O2 (≤50,000 m³/s). In addition, the values of the O1 raise with the decline in the O2 and the increase of the O3 and the O4.

There is a synergistic relationship between HG (O1) and the PF of the flood control station (O2), while the final WL of the reservoir at the flood prevention period (O3) and the HWL (O4) are competitive with the O1 and the O2. Overall, the Pareto solutions of the NSGA-II have the ability to counterbalance hydroelectricity production and flood prevention operation simultaneously to respond to various magnitudes (i.e., small–medium, large, and extra-large) of flood events.

The TOPSIS was utilized to determine the best operation scheme from the Pareto solutions for identifying seasonal FLWLs comprehensively considering multi-criteria of the HG, PF, WL, HWL and URS indicators. The decision-making analysis results are summarized in Table 3.

In comparison to the annual FLWLs (Table 1), for the first sub-season segment (pre-flood season), the minimal and maximal increasing values of the seasonal FLWLs for the seven mixed reservoirs are 6.51 and 9.53 m (TGR), 2.79 and 5.30 m (JY), 3.00 and 5.60 m (ZS), 0.93 and 1.65 m (DJ), 1.92 and 3.34 m (FT), 1.57 and 3.74 m (WQX), and 1.39 and 2.46 m (ZX). For the second sub-season segment (main-flood season), the minimal and maximal increasing values of the seasonal FLWLs for the seven mixed reservoirs are 1.53 and 4.18 m (TGR), 0.55 and 3.00 m (JY), 0.35 and 2.21 m (ZS), 0.13 and 0.85 m (DJ), 0.29 and 1.86 m (FT), 0.62 and 1.70 m (WQX), and 0.53 and 1.88 m (ZX). For the third sub-season segment (post-flood season), the minimal and maximal increasing values of the seasonal FLWLs for the seven mixed reservoirs are 4.36 and 8.24 m (TGR), 2.97 and 6.87 m (JY), 2.46 and 5.93 m (ZS), 0.76 and 1.65 m (DJ), 1.64 and 2.66 m (FT), 1.69 and 4.77 m (WQX), and 1.55 and 2.56 m (ZX). It is easy to find that the increments of seasonal FLWLs in the first and third sub-season segments are significantly higher than the increment of seasonal FLWLs in the third sub-season segment. That is to say, the first and third sub-season segments have more tremendous potential for developing flood resources without increasing the flood risk compared with the second sub-season segment.

For the same sub-season segment, in general, as the magnitude of design floods increases, the increment in seasonal FLWL decreases. Take the first sub-season segment (pre-flood season) for example, with respect to the design flood corresponding to the 1956 representative flood event, the seasonal FLWL of the TGR has declined from 154.26 to 151.51 m with the increase of return period from 20 to 1,000 years. The minimal (maximal) seasonal FLWL of the TGR in the second sub-season segment is 146.53 m (149.18 m), while for the first sub-season segment (the third one), the minimal and maximal seasonal FLWLs of the TGR are 151.51 and 154.53 m (149.36 and 153.24 m), respectively. From the perspectives of the three sub-season segments, because the magnitude of the design floods in the second sub-season segment is larger than that of the other two segments, the increment in seasonal FLWL of the second sub-season segment is getting smaller accordingly.

Comparison results of the best solutions acquired from the TOPSIS and the SOP solution on the five evaluation indicators in the three sub-season segments are displayed in Figures A4, 5(a -i) and A5, respectively.

The improvement rates of the five evaluation indicators obtained from the best solutions over those of the SOP solution are listed in Table 4. For all the design floods, it is found that the HG, PF and HWL indicators of the best solutions are better than those of the SOP solution with the minimal and maximal improvement rates of 0.47 and 10.26%, −4.42 and −0.06%, and −1.41 and −0.42%, respectively. This indicates that the seasonal FLWL scheme of the best solutions can improve the HG of reservoirs without increasing the flood control risk. For the first and third sub-season segments, the HWL of the best solutions is larger than that of the SOP solution because of the higher seasonal FLWLs. In addition, the URS of the best solutions is larger than that of the SOP solution for most design floods.

In summary, compared with the annual FLWL scheme (i.e., the SOP solution), the proposed seasonal FLWL schemes (i.e., the best solutions), without lowering the flood prevention standard, enhance the joint operation of mixed reservoirs to accomplish at least 620 million kW h (4.2% improvement), 80 million kW h (0.5% improvement) and 171 million kW h (2.0% improvement) in hydropower production corresponding to the first, second and third sub-season segments, meanwhile bringing down 487, 63 and 134 million kg in CO₂ emissions accordingly.

The seasonal FLWL is a crucial parameter that is used to guide reservoir operation to counterbalance the hydroelectricity production and flood prevention in different sub-season segments. The novelty of this study was to develop a multi-objective operation model of seasonal FLWLs which fused the SOP-based simulation into the NSGA-II, which was first applied to produce the Pareto solutions for trading off the demands from HG and flood prevention in seven reservoirs in the Yangtze River. Based on plenty of Pareto solutions generated from the proposed simulation–optimization framework, the TOPSIS was utilized to aptly identify the best one for seasonal FLWL management. The main conclusions are drawn below.

• (1)

  Compared with the SOP solution, the Pareto solutions could efficiently make a tradeoff among the maximization of the hydroelectricity output (O1), the minimization of the PF of the flood control station (O2), the minimization of the final WL of the reservoir at the flood prevention period (O3) and the minimization of the HWL (O4), to skillfully cope with small–medium, large and extra-large flood events.

• (2)

  In comparison to the annual FLWL scheme (i.e., the SOP solution) of the seven reservoirs, the best solution obtained from the TOPSIS could increase the FLWL values of the seven reservoirs from 1.39 up to 6.51 m in the first sub-season segment, from 0.13 up to 1.53 m in the second sub-season segment and from 0.76 up to 4.36 m in the third sub-season segment, without increasing the flood prevention risk.

• (3)

  The proposed seasonal FLWL schemes not only could boost the reservoir operation to attain 868 million kW h/year (5.1% improvement) in average hydroelectricity output but also could decrease 681 million kg in CO₂ emissions during the flood season.

It is worth noting that the developed multi-objective optimization operation model of seasonal FLWLs in this study is aimed at efficiently counterbalancing hydropower production and flood prevention operation, meanwhile reducing CO₂ emissions associated with the use of fossil energy.

In the future, it will be interesting to conduct the research on the flood pre-discharge operation of reservoirs by integrating accurate and reliable flood forecasting information to validate the feasibility and transferability of the proposed methods.

This work was partially funded by the National Key Research and Development Program of China (2021YFC3200303) and the Research Council of Norway (FRINATEK Project 274310, KLIMAFORSK Project 302457). The authors would like to thank the editors and anonymous reviewers for their valuable and constructive comments related to this manuscript.

YH contributed to data curation, writing of the original draft preparation, software, and visualization. SG contributed to the conceptualization, methodology, writing of the original draft preparation, and supervision. YZ contributed to the conceptualization, methodology, reviewing and editing the writing, and supervision. DZ contributed to data curation, software, visualization, investigation, and validation. HC contributed to reviewing and editing the writing, visualization, and investigation. LX contributed to reviewing and editing the writing, investigation, and validation. JL contributed to data curation, visualization, and investigation. C-YX contributed to reviewing and editing the writing, investigation, and validation.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.