Risk and benefit analysis of multifunctional reservoir staged operating Open Access

With continuous economic development and the increasingly harsh global climate, the conflict between the supply and demand of water resources is becoming increasingly prominent. Multipurpose reservoirs, as important water conservancy structures, are helpful for flood control and can accumulate floods during the flood season into water resources available during the nonflood season. The flood-limiting water level (FLWL) of the reservoir represents the combination of reservoir flood control and profitability and is the highest level of water allowed to be stored in a reservoir during the flood season; it also acts as the starting level for flood control and dispatch. The reservoir flood-limiting water level (FLWL), which is the highest water level that allows storage during the flood season and the starting water level of flood control operation, is considered to be the intersection between flood control measures and utilizable benefits (Hua et al. 2012). A reasonable FLWL setting can make full use of rain and flood resources and effectively alleviate the contradiction between reservoir flood controls and potential benefits.

At present, many reservoirs are still operating at a conservative single FLWL (Li et al. 2016), which results in a waste of rain and flood resources and a huge loss of economic benefits (Ding et al. 2015). Therefore, many reservoirs have adjusted the operation mode to staged operation (Zhang et al. 2018). Flood season staging is an important prerequisite for successful staged operations. The commonly used methods for flood season staging include qualitative and quantitative analysis methods (Jiang et al. 2012; Li et al. 2020).

As there are many uncertainties in the operation of reservoirs (Chen et al. 2015; Chen et al. 2017), the adoption of staged operation not only increases the profitability of reservoirs but also introduces many risks. It is an arduous task to quantitatively analyse reservoir flood control risks by adopting a staged operation approach (Pan et al. 2015). Therefore, many scholars have researched the comprehensive issues surrounding reservoir flood risks and utilizable benefits. Huang et al. (2018) proposed an entropy theory-based flood risk analysis method that can effectively evaluate the impact of various uncertainties on reservoir operation compared with traditional analysis methods. A nonstationary Monte Carlo risk analysis model was developed by Kyuhyun & Hamlet (2020) to study the risks associated with unsteady hydrologic regimes, and it was applied to the study of extreme runoff and embankment design of the Wabash Basin, USA. Dai et al. (2019) proposed a flood risk analysis based on an improved stochastic differential equation and used it to evaluate the influence of uncertainties such as reservoir inflow forecasts and storage capacity curves on flood control operations in the Three Gorges reservoir. Li et al. (2019) used the power generation benefit as a utilizable benefit analysis index to calculate the increased power generation capacity of the Bikou reservoir compared with the original design of dynamic control of the water level during the flood season. Fang et al. (2014) used industrial and agricultural water supply benefit-sharing coefficients to estimate the benefit of water supply after the implementation of dynamic controls on the FLWL in the Gaotang-Ahu reservoir.

The Chengbi River Basin is located in a monsoon climate area. Floods in the basin are mostly caused by rainstorms. However, the reservoir operates with a single low water level year round, resulting in a large amount of abandoned water, which cannot effectively solve the local seasonal water shortage problem and seriously affects the comprehensive benefit of the reservoir and the sustainable development of the local economy. In summary, although many achievements have been made by previous authors in the study of FLWLs, some problems remain to be solved. (1) In response to the issue of reservoir flood safety and utilizable benefit, previous studies have often analysed the two separately. For reservoirs, flood control risks and utilizable benefits are closely related and mutually constrained, so how to comprehensively consider the influence of both on the staged operation of reservoirs becomes a problem that needs to be solved. (2) Previous studies of the FLWL have been based on a single period of the flood season, whereas flood characteristics vary between periods of the flood season. Therefore, this study aims to select the optimal FLWL scheme for the staged operation of a multipurpose reservoir based on a synergistic analysis of risks and benefits, thereby maximizing the overall benefit of the reservoir.

The Chengbi River belongs to the Xijiang River system of the Pearl River Basin and is a tributary of the Qianjiang River section of the Xijiang River. The climate of the Chengbi River Basin is characterized by a subtropical monsoon climate, the average annual rainfall at the dam site is 1,560 mm, and rainfall during the flood season is extremely prone to forming catastrophic floods. Rainfall is unevenly distributed within the year, with the period ranging from May to September accounting for approximately 87% of the annual rainfall. Runoff from the basin is unevenly distributed within the year, with a maximum runoff of 1,350 m³/s during the flood season and a minimum runoff of 0.3 m³/s during the nonflood season, for a multiyear average runoff of 40.6 m³/s.

The Chengbi River reservoir is located in the lower reaches of the Chengbi River, where it provides power generation, flood control, water supply, and other comprehensive utilization functions. The normal storage level of the reservoir is 185.00 m, and the design flood is 187.96 m, with a utilizable storage capacity of 560 million m³ and 210 million m³ for flood control. The dam is designed for a 1,000-year flood and calibrated for a 10,000-year flood, and is a multiyear regulation reservoir. The total installed capacity of the power station is 30 MW, with 4 sets of hydrogenerator sets installed, with a single capacity of 7.5 MW. The power station is a post-dam type plant, with an average multi-year power generation capacity of 125 million kWh; it supplies power to the Baise City grid and has a guaranteed output of 11.57 MW and an installed number of utilization hours of 4,496 h. The downstream reservoir dam involves the cities of Baise and Tian Yang, Tian Dong County, and other densely populated towns, Baise Airport and important industrial and mining enterprises. Downstream transportation facilities include the Nanning-Kunming railroad, Nanning-Longlin secondary highway, National Highway 324, and Bailong Expressway. The protected area has 250,000 mu of arable land and a population of 300,000.

The Chengbi River reservoir has four hydrologic stations with hydrologic data ranging from 1963 to 2019. The Pingtang station controls a catchment area of approximately 1,326 km², occupying 67% of the catchment area above the dam site, which is highly representative. The data from Pingtang station are observed and compiled in accordance with the relevant specifications, and the measured data are of good continuity and reliable quality. Therefore, the measured flow data from 1963 to 2019 at Pingtang Station were chosen for time-series pattern analysis in this paper. The location of the reservoir and hydrologic station of Pingtang is shown in Figure 1.

The paper adopted mathematical and statistical analyses for flood staging of the Chengbi River reservoir and used the seasonality index (Walsh & Lawler 1981) to verify the rationality of the staging. Second, the Monte Carlo stochastic simulation and rounding methods were used to simulate the flood flow series randomly for flood risk analysis, and the Spearman rank correlation coefficient was applied to analyse the sensitivity of risk influencing factors. Once again, the water consumption rate per unit of the electricity method was used to calculate the generation benefit of the staged operation. Finally, a fuzzy comprehensive evaluation model was established to preferably select the optimal FLWL schemes for different periods. This chapter introduces the Monte Carlo stochastic simulation method, the rounding method, the water consumption rate per unit of electricity method and the fuzzy comprehensive evaluation model.

The independent random sample simulation experiment is repeated to obtain a batch of sample data ⁠, and the probability distribution function of the objective function Y can be obtained when the number of samples is sufficient.

The increased utilizable benefit of the Chengbi River reservoir due to the implementation of the staged operation is mainly in the form of power generation and water supply benefits. However, the staged elevation of the FLWL has led to an increase in the utilizable capacity and a corresponding increase in the water supply capacity. However, since acting as a water supply is not the primary function of the Chengbi River reservoir, the value-added benefit of the water supply was not considered in the benefit analysis of staged operations in this paper.

The fuzzy comprehensive evaluation method was used to evaluate the FLWL preferences, with the following main steps (Wang & Qiao 2019).

• (1)

  Determination of a matrix of the relative merit of assessment indicators was performed as follows:

Tables 1 and 2 show the frequency of the measured maximum peak flow in each month and the measured maximum peak magnitude, respectively. As shown in Tables 1 and 2, the floods of the Chengbi River reservoir are clearly divided into three levels. The highest frequency and magnitudes of maximun floods occured from June to August, followed by September to October and the smallest from April to May. According to the principle of flood separation that months with a similar chance of flooding and flood magnitude should not be separated (Jiang & Cao 2005), the flood season of the Chengbi River reservoir is divided into three periods: April to May, June to August, and September to October.

The seasonality index for each period was obtained using the seasonality index formula (Walsh & Lawler 1981), and the results are shown in Figure 2. As shown in Figure 2 and Table 3, the seasonality before flood staging is significant, while the seasonality index for each period after staging is significantly lower. Therefore, it is reasonable to stage floods according to chronological and magnitude patterns.

The reservoir design standard was developed considering a thousand-year frequency, with a corresponding probability of flood failure of 0.1%. To achieve a certain accuracy, the number of simulations ⁠; that is, ⁠. Based on the measured peak flow information and the 100,000 peak flow of the random simulation using the rounding method, the statistical characteristic parameters of the measured and simulated series of incoming flow at each stage of the Chengbi River reservoir were calculated using the method of moments (Lei et al. 2017). The results of the calculations are shown in Tables 4 and 5. As shown in Tables 4 and 5, the statistical characteristics of the simulated flood series and the measured flood series are the same, and it can be considered that the randomly generated simulated storage flow has a certain degree of reliability and can be used for the Chengbi River reservoir flood adjustment calculation.

The typical 1,000-year design flood was amplified by the peak flow control multiplier amplification method, and 100,000 incoming flood process lines were obtained for each of the main and later flood seasons. The FLWL of each scheme was used as the starting level for flood regulation, and the electrical algorithm was used to calculate the simulated inflow flood of the Chengbi River reservoir. According to the flood regulation calculation results, the risk control index was 188.87 m higher than the original design flood level of the reservoir, and the risk rate of the reservoir under different FLWL schemes was calculated by the Monte Carlo stochastic simulation method. See Tables 6 and 7 and Figure 3 for the calculation results. As shown in Figure 3, the gradual elevation of the FLWL increases the risk rate at which the maximum reservoir flood regulation level exceeds the original annual design level. The flood risk varies from 0.0910 to 0.1204% when the FLWL of the main flood season is raised from 185.00 to 187.00 m. Considering that reservoir staging should be operated in a manner that does not increase the flood risk, a flood risk rate of no more than 0.1% was considered reasonable for the FLWL scheme. Accordingly, the FLWL adjustment of the Chengbi River reservoir should not exceed 185.50 m during the main flood season and should not exceed 187.50 m during the later flood season.

The volume increase by raising the was calculated according to the relationship between the water level and reservoir capacity by the linear interpolation method. The water consumption rate per unit of electricity corresponding to each FLWL could be obtained according to the ‘Chengbi River Reservoir Operating Manual’. The results of using the water consumption rate per unit of electrical energy formula (5) to calculate the value-added power generation benefit of each stage of the Chengbi River reservoir after implementing staged operations are shown in Table 8 and Figure 4.

As shown in Figure 4, the power generation benefit of the Chengbi River reservoir increases with the elevation of the FLWL. When the FLWL in the main flood season is raised from 185.00 to 187.00 m, the power generation benefit increases from 0 to 983 kWh. The power generation benefit increases from 0 to 2,203 kWh when the FLWL of the later flood season is raised from 185.00 to 189.00 m.

Before using the fuzzy comprehensive evaluation model, the evaluation index system was established first. The adjustment of the reservoir FLWL involves the flood control risk as well as the utilizable benefit. For the flood risk, the probability of the water level exceeding the design flood was selected as the risk assessment objective in this paper. For the utilizable benefit, the value-added reservoir generation benefit was selected as the benefit assessment objective. The specific evaluation index system framework is shown in Figure 5.

Based on the results of the calculation of the risks and benefit of the staged raising of the FLWL in the Chengbi River reservoir, the eigenvalues of each indicator for the main and later flood seasons in the Chengbi River reservoir can be obtained, as shown in Tables 9 and 10.

The relationship between the FLWL adjustment schemes of the main and later flood seasons and the relative optimal membership degree are shown in Tables 11 and 12.

The tables show that the FLWL corresponding to the maximum value of the relative optimal membership degree of 0.6001 during the main flood season is 185.50 m, so 185.50 m is the optimum value for raising the FLWL during the main flood season of the Chengbi River reservoir. The FLWL corresponding to the maximum value of 0.5242 of the relative optimal membership degree in the later flood season is 187.50 m, so 187.50 m is the optimal value for raising the FLWL during the later flood season of the Chengbi River reservoir.

The FLWL is considered a combination of benefits and flood control measures, and reasonable regulation of the FLWL will increase the utilization of water resources. Since construction, many reservoirs have been operated at a single FLWL, resulting in a large amount of abandoned water and the inability to make full use of flood resources. Therefore, many reservoirs have to start exploring the issue of adjusting the FLWL. This paper presents a comprehensive analysis of the flood control risks and benefits of raising the FLWL of the reservoir, thereby revealing the changes in flood control risk and power generation benefit under different FLWL schemes. A fuzzy comprehensive evaluation model was also established by combining the operation of the reservoir to preferably select the best FLWL for the main and later flood seasons of the reservoir under different preferences, providing an important basis for the staged operation of the Chengbi River reservoir.

Based on the temporal distribution pattern and flood magnitude distribution pattern presented by the flood of the reservoir in Tables 2 and 3, the flood season is divided into three periods, which is consistent with the results of most flood staging studies in China (Chen et al. 2019; Jiang et al. 2019). However, the length and onset of the flood season vary slightly, mainly in relation to the spatial and temporal distribution characteristics of precipitation in China. There is a large difference in precipitation between the northern and southern regions, with less precipitation and shorter flood periods in the north and more precipitation and longer flood periods in the south. As seen from Figures 3 and 4, raising the FLWL not only increases the utilizable benefit but also increases the risk of flood control for the reservoir. This is because raising the FLWL increases not only the hydraulic capacity and amount of water stored but also the probability of reservoir failure. Therefore, when determining the FLWL, it is necessary to consider the flood risk and benefit of the reservoirs to ensure that the flood risk does not exceed the design standard and the FLWL is raised as much as possible to maximize the benefit. Most rivers in China are characterized by seasonal variations in the size and timing of floods, and the characteristics of floods are different during each stage of the flood season, requiring FLWL adjustments to be made in periods according to the characteristics of the flood in each stage. Most reservoir FLWL studies have not considered staged FLWL control decision studies but only considered adjusting the FLWL in the main or later flood season (Liu et al. 2007; Lyu et al. 2019). This study considers three periods, the preflood season, main flood season, and later flood season, and adjusts the FLWL according to the incoming water characteristics, thereby greatly increasing the flexibility of reservoir operating and the power generation benefits, making more effective and efficient use of rainfall and flood resources in each period.

It is worth noting that there are many uncertainties in reservoir flood risk analysis. In this paper, the effects of observation errors in the reservoir storage capacity curve and outflow error factors on the calculated flood risk are considered, and Monte Carlo stochastic simulation is used to perform 1,000 random simulations of the design flood process considering the two factors, followed by sensitivity analysis using the Spearman rank correlation method (the results are shown in Schedules 1 and 2). The Spearman rank correlation coefficients for the observation errors of the reservoir storage capacity curve and the outflow error are −0.778 and −0.079, respectively. The correlation between the two risk factors and the operation risk is weak, and the sensitivity of the observation errors of the reservoir storage capacity curve is stronger than that of the outflow error. The sensitivity coefficients of both are less than 0. Both show a negative correlation with water level changes, indicating that the maximum water level of the reservoir will increase when the reservoir capacity and the downstream flow are reduced.

The novelties of this paper are as follows. (1) To solve the problem of the abandonment of a large amount of water during the flood season due to the operation of the reservoir at a single flood level year round, a staged operation model was adopted. The flood season of the reservoir was divided into roughly three periods and the flood risks and benefits of raising the FLWL in such stages were considered. (2) Based on the actual operation of the reservoir, a fuzzy comprehensive evaluation model was established. The risk and benefit were synergistically analysed to optimize the optimal FLWL scheme within each stage of the reservoir, thereby providing support for the future operation of the reservoir and the effective use of water resources.

In this study, the flood season was divided into three periods based on the chronological pattern of the annual maximum flood flow and the magnitude of the flood in the Chengbi River reservoir. According to the results of flood staging, the flood risk and power generation benefit of each FLWL scheme in the main and later flood seasons of the reservoir were considered comprehensively; the most suitable FLWL for each stage was preferentially selected using a fuzzy comprehensive evaluation model, and the results of the study are as follows.

• (1)

  The reservoir inflow of the Chengbi River reservoir can be divided into the preflood season, main flood season, and later flood season according to their chronological patterns, with the preflood season covering April to May, the main flood season covering June to August and the later flood season covering September to October. The staging results were verified using seasonal indices, and the results were found to be reasonable. The seasonality index was used to validate the staging results, and it was found that the seasonality index decreased significantly after staging, indicating the reasonableness of the staging.

• (2)

  Raising the FLWL to 185.50 m during the main flood season has an associated flood risk of 0.095% and increases the power generation benefit by 2.16 million kWh. The later flood season raises the FLWL to 188.50 m, with a flood risk of 0.099% and an additional 18.97 million kWh of power generation.

• (3)

  The design flood process considering the observation errors of the reservoir storage capacity curve and reservoir outflow errors in the process of reservoir operation is performed for flood regulation calculation, and the Spearman rank correlation coefficient is selected to determine the sensitivity of each risk factor. The results show that these two factors show a weak negative correlation with the maximum water level, and the sensitivity of the observation errors of the reservoir storage capacity curve is greater than that of the outflow error.

• (4)

  According to the fuzzy comprehensive evaluation results, the optimal FLWL of the reservoir is 185.50 m in the main flood season and 187.50 m in the later flood season. The significance of raising the FLWL in the preflood season is not influential, so the FLWL in the preflood season should be kept at 185.00 m.

The authors are grateful for the support of the National Natural Science Foundation of China (51969004 and 51579059), the National Key Research and Development Program of China (2017YFC1502405,2016YFC0401303), the Guangxi Natural Science Foundation of China (22017GXNSFAA198361), and the Innovation Project of Guangxi Graduate Education (YCBZ2019022).

Chongxun Mo: Conceptualization, Methodology, Software. Yifan Wu: Data curation, Writing-Original draft preparation. Yuli Ruan: Visualization, Investigation. Shutan Zhao: Supervision. Juliang Jin: Writing-Reviewing and Editing.

Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions. We will conduct further research on this aspect in the future. The existing research data will be gradually developed in the subsequent papers, and it is only temporarily confidential at present.

There is no conflict of interest or competition among authors.

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