https://orcid.org/0000-0001-6561-6912
ABSTRACT
Climate change alters river runoff regimes, affecting the safe operation of hydropower stations. This study proposed an optimization scheduling and risk analysis framework for cascade hydropower under climate change using the Qingjiang cascade hydropower stations as a case study. The framework has three stages. Firstly, a hydrological model coupling GCMs with SWAT under CMIP5 scenarios is established to predict future runoff. Secondly, cascade hydropower optimization scheduling under climate change is performed using the POA (Progressive Optimization Algorithm). Thirdly, a risk assessment index system is established, including risks of insufficient power generation, insufficient output, and water abandonment. The POMR (Probability Optimization Method for the Risk) is applied to calculates power scheduling risks. Results show that the simulated annual average runoff at Changyang Station increases by 6.0, 8.7, and 13.2% under the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively. Annual power generation for the Qingjiang cascade is projected to rise by 6.2–16.5%, with increases of 5.2–12.9% during flood seasons and 7.5–19.9% in non-flood seasons. Comprehensive risk rates decline to 0.1767, 0.1706, and 0.1630 across the scenarios. This research provides scientific and technical support for managing water resources and operating the Qingjiang cascade under climate change.
HIGHLIGHTS
Proposed an optimization scheduling and risk analysis framework for cascade hydropower under climate change.
Coupled SWAT with GCMs to predict future runoff in the Qingjiang River Basin under CMIP5 scenarios.
Developed a cascade hydropower optimization scheduling model to analyze generation changes under various future climate scenarios.
Established a risk assessment index system (covering insufficient power generation, insufficient output, and water abandonment) and evaluated comprehensive risk rates for cascade dispatch under three scenarios.
ABBREVIATIONS
- SWAT
Soil and Water Assessment Tool
- SDSM
statistical downscaling model
- HRUs
hydrological response units
- GCM
global climate model
- RCP
representative concentration pathway
- CanESM2
The second generation Canadian Earth System Model
- DEM
digital elevation model
- NCEP
National Center for Environmental Prediction
- POMR
probability optimization method for the risk
- POA
progressive optimal algorithm
- AHP
analytic hierarchy process
- SBY
ShuiBuYa Hydropower station
- GHY
GeHeYan Hydropower station
- GBZ
GaoBaZhou HSydropower station
INTRODUCTION
Climate change and human activities are the primary drivers of water allocation and the hydrological cycle in river basins (He & James 2021; Mitiku et al. 2023). The combined influence of climate change and human activities has caused significant temporal, spatial, and quantitative changes in the hydrological cycle and water balance within river basins. These changes alter runoff patterns, impacting cascade reservoir operations and posing challenges for effective water resources management (Mohammed & Scholz 2017; Xue et al. 2022). Understanding hydrological processes and their spatiotemporal evolution under global change is crucial for adaptive water resources management (Xia et al. 2015; Brighenti et al. 2019; Wang et al. 2019a; Xu & Jiang 2022).
Research on hydrological cycles and spatiotemporal evolution under climate change has become a major focus in 21st-century water science. Pandey et al. (2019) used the Soil and Water Assessment Tool (SWAT) model to simulate the near-, medium-, and long-term changes in mean annual runoff under RCP4.5 and RCP8.5 scenarios in the Chamelia watershed of western Nepal, evaluating spatio-temporal distribution in water availability in response to climate change. Wang et al. (2017) taking the Ovens River in Australia as the research area, compared the effectiveness of four downscaling methods in analyzing the eco-hydrological response under climate change. Nilawar & Waikar (2019) used the Pedu-Muda Reservoir in Peninsular Malaysia as the study object and assessed climate change impacts on reservoir operations using multi-objective water storage optimization. Studies on regional hydrological response and reservoir dispatching under climate change provide valuable references for future water resource planning and management. Eum & Simonovic (2010) analyzed the sensitivity of large-, small-, and medium-sized reservoirs under different climate change scenarios. They concluded that large reservoirs are less sensitive than small and medium-sized reservoirs to climate change, and gave the optimal adaptive rule curves of the multi-purpose reservoirs. Ahmadi et al. (2015) established the optimal reservoir dispatching model considering future climate change. They formulated the dynamic optimal dispatching strategy to address climate change scenarios. The study showed that the adaptive dispatching strategies effectively balance power generation reliability and reservoir vulnerability.
Currently, the formulation of dispatching rules for the Qingjiang cascade is based on historical runoff data, which makes it challenging to adapt to the new climate change needs. This significantly affects the safe and stable operation of cascade reservoirs and their overall benefits. Therefore, this paper focuses on the Qingjiang River Basin in China and developed a SWAT model using spatial and observational data from the basin. Meteorological data for each station under different representative concentration pathway (RCP) scenarios, as outlined in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) (AR5) (2013), were simulated using the statistical downscaling model (SDSM) and the CanESM2 climate model. The calibrated SWAT model was then used to simulate monthly and daily runoff for the future period. Finally, a cascade co-generation dispatch model based on future climate change scenarios was developed and analyzed for risk. This study has significant theoretical and practical implications for the safe and effective use of cascade hydropower and water resources in the Qingjiang River Basin under climate change.
MATERIALS AND METHODS
Study area
An overview map of the Qingjiang River Basin.
Schematic diagram of the Qingjiang cascade hydropower stations.
Methodology
The overall methodological framework adopted in this study.
SWAT model establishment and validation
This study used the SWAT model to simulate future runoff in the Qingjiang River Basin under different climate change scenarios. The SWAT model is a semi-distributed hydrological model based on ArcGIS, which simulates the impacts of climatic factors and subsurface changes on watershed hydrological responses (Malik et al. 2022). The model requires spatial data, including digital elevation model (DEM), land use, and soil data. The DEM data were sourced from the ASTER GDEM 30-m resolution digital elevation dataset. The land-use data were obtained from the 1:100,000 land-use dataset of 2015 provided by the Resource and Environment Science Data Center of the Chinese Academy of Sciences, while the soil data were derived from the soil raster maps of the China region clipped by the Harmonized World Soil Database, which was constructed by the International Institute for Applied Systems Analysis in Vienna and the Food and Agriculture Organization of the United Nations. The observational data mainly include meteorological and hydrological data. In this study, five meteorological stations – Jianshi, Lichuan, Enshi, Wufeng, and Yichang – were used to measure daily maximum and minimum temperatures, as well as precipitation, with data from 1961 to 2005. The calibration and validation of the SWAT model primarily relied on monthly and daily runoff data from the Changyang station, located at the outlet of the watershed, for the period from 1976 to 2005.
DEM, land-use types, and soils in the Qingjiang River Basin.
, 
, 
, and 
represent the observed runoff, simulated runoff, the average value of observed runoff, and the average value of simulated runoff (m3/s), respectively. When ENS > 0.5 and R2 > 0.6, the model's simulated runoff results are considered acceptable. The closer the values are to 1, the better the model fit (Liu et al. 2021).Monthly and daily hydrological runoff data from Changyang Station for the period 1976–2005 were selected for parameter calibration. The SWAT model's warm-up period was 1976–1977, the calibration period was 1978–1995, and the validation period was 1996–2005. There are 28 parameters related to runoff in the SWAT model. After conducting a sensitivity analysis on these parameters, the top 10 most sensitive parameters were selected for calibration, and the SUFI-2 algorithm in SWAT-CUP was used for model calibration (Brighenti et al. 2019).
Prediction of future climate scenarios based on SDSM
The construction of the SDSM model requires National Center for Environmental Prediction (NCEP) reanalysis data, historical meteorological data from the stations in the basin, and output factors from the GCM CanESM2. The NCEP reanalysis data consists of 26 predictors and measured meteorological data. The measured meteorological data include the daily maximum and minimum temperatures and daily precipitation from 1961 to 2005 at five meteorological stations in the basin.
The construction of the SDSM model consists of two parts (Dai et al. 2015). The first part involves establishing a multiple linear regression relationship between forecast factors and forecast quantities to define the model; the second part uses GCM data to input into the model, generating climate element data for the basin stations under different scenarios in the future period (Guo & Wang 2016). This includes data on the maximum and minimum temperatures and the daily precipitation series for each station in the Qingjiang River Basin.
This study selects the CanESM2 model from CMIP5. Previous research has examined hydrological predictions for the middle reaches of the Yangtze River Basin under climate change. For instance, Yu et al. (2018) utilized 54 climate change simulation ensembles to assess the hydrological response of the Yangtze River Basin to potential future climate changes. Hu et al. (2019) evaluated extreme summer precipitation in the middle reaches of the Yangtze using CMIP5 models. Wang et al. (2019b) investigated changes in extreme precipitation in the Yangtze River Basin under global warming targets of 1.5 and 2.0 °C using five global climate models. These studies have demonstrated that the RCP scenarios effectively simulate future climate change characteristics in the middle reaches of the Yangtze River. Therefore, the RCP scenarios are also applicable for runoff simulations in the Qingjiang River Basin under climate change. Furthermore, the CanESM2 model has demonstrated good performance in simulating climate change. It integrates carbon emissions and climate scenarios, encompassing multiple cyclical processes such as energy, matter, water vapor, and greenhouse gases (CO2) in the atmosphere-ocean-land system. The horizontal resolution of the large-scale climate factors output by CanESM2 is approximately 2.8° (Mahdaoui et al. 2023). Chu et al. (2015) and Su et al. (2020) evaluated the simulation ability of CMIP5 models in the Yangtze River Basin using various statistical measures. Based on the statistical evaluation of temperature simulations, CanESM2 ranked highly among the models with better-simulated temperature results. Huang et al. (2015) analyzed the simulation ability of the integrated spatial and temporal structure model for the 500 hPa height field in East Asia and found that CanESM2 is one of the best models for simulating the main modes of summer climate. In conclusion, the RCP scenario under the CanESM2 climate model is well-suited for application in the Qingjiang River Basin.
The SDSM downscaling model was applied to predict the future temperature and precipitation patterns in the Qingjiang River Basin. Taking 1961–2005 as the base period, data from the CanESM2 model under three climate scenarios were input into the SDSM model to generate daily maximum and minimum temperatures, as well as daily precipitation data for five weather stations in the Qingjiang River Basin under different future scenarios. The arithmetic mean method was used to calculate daily maximum and minimum temperatures (Abdulkerim 2022), while the Tyson polygon method was used to estimate the surface rainfall across the basin.
Power generation dispatching model of the Qingjiang cascade
The data required for optimal dispatching of the Qingjiang cascade hydropower stations include essential parameters such as the characteristic data of the cascade hydropower stations, the water level – storage capacity curve, the downstream water level – discharge relationship curve, unit characteristic parameters, and the unit flow characteristic curve, among others.
This study establishes a dispatching model to maximize the annual energy generation of the Qingjiang cascade hydropower stations.
is the total energy generation of the cascade hydropower stations during the total dispatch periods, 
is the number of power stations, 
is the output coefficient of the ith power station; 
,
are the power generation flow and water head of the ith power station during the period t, respectively; 
-number of hours in period t.Constraints:
- (1) Water balance constraintswhere(4)
and 
are the water storage capacities at the beginning and end of period t for the ith power station; 
is the inflow of the ith power station during period t; 
is abandoned water flow of the ith power station during period t;
is the length of time t. - (2) Reservoir storage constraintswhere(5)
, 
are the minimum and maximum storage capacity allowed for the ith power station during the period t, respectively. - (3) Flow capacity constraints of hydropower stationswhere(6)
, 
are the minimum and maximum generation references for the time period t at the ith power station, respectively. - (4) Power station output constraintswhere(7)
and 
are the minimum and maximum output limits of the ith power station in period t, respectively. - (5) Guaranteed output constraints of the cascade hydropower stationswhere(8)
is the minimum output limit that must be met by the cascade hydropower stations. - (6) Abandoned water loss output functionwhere(9)
are abandoned water flow and net water head of power generation during the time period t, respectively; 
is the function of the water consumption rate for power generation; Ω represents the set of time periods during which abandoned water loss occurs.
is the objective function value of the original optimization problem; M is the penalty factor associated with the number of iteration times; 
is the default value associated with the ith constraint, and p is the number of defaults.Power generation risk index system and POMR-based risk analysis method
This paper develops a power generation risk index system for the cascade hydropower stations and uses the probability optimization method for the risk (POMR) method to analyze the associated risks.
Risk index identification and assessment are essential tools for evaluating the impact of various uncertainties on the dispatch system. The primary risks in power station dispatching arise from factors such as hydrology, hydraulics, engineering conditions, human management, and other uncertainties. The Qingjiang cascade power generation risk indices include three key factors: the risk of insufficient output, the risk of insufficient power generation capacity, and the risk of water abandonment.
(1) The risk rate of insufficient output of the cascade stations
does not meet the predetermined output 
during a given time period is defined as the risk rate of insufficient output 
. For the entire dispatching period, if any time period exhibits insufficient capacity, the entire dispatching period is considered insufficient:
is the actual dispatched output for the ith period; 
represents the predetermined output (i.e. load requirement) for the ith period; T is the total number of time periods in the dispatching schedule. (2) Risk rate of insufficient power generation
fails to meet the target generation E0 during the dispatch period is defined as the risk rate of insufficient power generation:
(3) Risk rate of water abandonment
In the formula, 
is the abandoned water flow during the ith period; W0 is the amount of abandoned water generated by the original power generation plan; 
is the length of the ith time period; T is the number of dispatching periods.
and 
represent the subjective and objective weights of the jth evaluation index, respectively, and 
is the preference coefficient balancing subjective and objective weights. In this study, the preference coefficient u = 0.3 was selected, as the weights obtained from the objective weighting method provide more reliable references for determining the comprehensive weights of each evaluation metric compared to the subjective weighting method.The POMR method no longer assumes that risk only arises when an event fails to meet a fixed target. Instead, it treats the target space as a variable, calculates the risk curve under changing conditions, and identifies the corresponding risk and the risk measures generated at each point of the curve (Zhang et al. 2011). This method has been widely applied across various fields, including engineering design, decision analysis, and risk management. It helps decision-makers understand and assess the impact of uncertainty factors on risk and select optimal decision-making strategies to mitigate risk.
represent the factor set of the risk indicator variable, with 
as the variables to be determined, and the target space defined as 
. Assume that the system's loss remains constant when it produces damage under any conditions. The computational model of the risk indicator is expressed as follows:
Among them, 
.
Define 
as the set weights of the risk variables with corresponding weights 
, with the norm 
defined as: 
.
, determine the optimal scenario for the occurrence (or treatment) of the event while minimizing the comprehensive risk value, i.e.:
denote the feasible domain space.RESULTS AND DISCUSSION
Predicted changes in daily temperature and precipitation
When selecting the optimal forecasting factors for the Qingjiang River Basin, the strongest correlation was exhibited between the mean surface air temperature and the 500 hPa geopotential heights. The ENS values for the daily maximum and minimum temperatures at the meteorological stations in the Qingjiang River Basin ranged from 0.68 to 0.83 during the calibration period and from 0.84 to 0.90 during the validation period. The simulation results for daily maximum and minimum temperatures at each station are shown in Table 1. The results demonstrate that the SDSM model is effective in simulating air temperature, and the overall relative error of the daily maximum and minimum temperatures at each station is less than 0.2%, and the deviation is less than 0.05 °C.
Simulated statistics of daily maximum and minimum temperatures
| Site number | Site name | Average daily temperature | Measured average value/°C | Simulated mean value/°C | Relative error/% | Deviation/°C |
|---|---|---|---|---|---|---|
| 57447 | Enshi | Supreme | 20.94 | 20.94 | 0 | 0 |
| Lowest | 13.03 | 13.04 | 0.07 | 0.01 | ||
| 57445 | Jianshi | Supreme | 20.25 | 20.26 | 0.03 | 0.01 |
| Lowest | 11.91 | 11.91 | 0 | 0 | ||
| 57439 | Lichuan | Supreme | 17.18 | 17.19 | 0.06 | 0.01 |
| Lowest | 9.64 | 9.66 | 0.15 | 0.02 | ||
| 57458 | Wufeng | Supreme | 18.79 | 18.81 | 0.09 | 0.02 |
| Lowest | 9.74 | 9.73 | −0.11 | −0.01 | ||
| 57461 | Yichang | Supreme | 21.54 | 21.53 | −0.05 | −0.01 |
| Lowest | 13.49 | 13.50 | 0.07 | 0.01 |
| Site number | Site name | Average daily temperature | Measured average value/°C | Simulated mean value/°C | Relative error/% | Deviation/°C |
|---|---|---|---|---|---|---|
| 57447 | Enshi | Supreme | 20.94 | 20.94 | 0 | 0 |
| Lowest | 13.03 | 13.04 | 0.07 | 0.01 | ||
| 57445 | Jianshi | Supreme | 20.25 | 20.26 | 0.03 | 0.01 |
| Lowest | 11.91 | 11.91 | 0 | 0 | ||
| 57439 | Lichuan | Supreme | 17.18 | 17.19 | 0.06 | 0.01 |
| Lowest | 9.64 | 9.66 | 0.15 | 0.02 | ||
| 57458 | Wufeng | Supreme | 18.79 | 18.81 | 0.09 | 0.02 |
| Lowest | 9.74 | 9.73 | −0.11 | −0.01 | ||
| 57461 | Yichang | Supreme | 21.54 | 21.53 | −0.05 | −0.01 |
| Lowest | 13.49 | 13.50 | 0.07 | 0.01 |
When selecting the optimal prediction factors for precipitation in the Qingjiang River Basin, the strongest correlations were observed with 500 hPa relative humidity, sea level divergence, and 850 hPa divergence. The simulation accuracy for daily precipitation is lower than that for air temperature, which is attributed to the complexity and uncertainty involved in simulating precipitation (Tian et al. 2021). To mitigate error accumulation in precipitation simulations, which could lead to larger final errors, the monthly precipitation series were used to calculate the ENS values. The ENS for the calibration and validation periods ranged from 0.67 to 0.73. Table 2 shows the simulation results for annual precipitation at the stations in the Qingjiang River Basin. The simulated annual average precipitation in the basin tends to be higher than the corresponding observed values, and the relative errors range from 9 to 13%. The smallest relative error occurred at the Wufeng station, while the largest was observed at the Lichuan station.
Annual precipitation simulation statistics
| Site number | Site name | Measured annual average value/mm | Annual simulated mean value/mm | Relative error/% | Deviation/mm |
|---|---|---|---|---|---|
| 57447 | Enshi | 1,455.1 | 1,630.1 | 10.74 | 175.0 |
| 57445 | Jianshi | 1,435.7 | 1,626.8 | 11.75 | 191.1 |
| 57439 | Lichuan | 1,312.3 | 1,508.6 | 13.01 | 196.3 |
| 57458 | Wufeng | 1,391.4 | 1,534.2 | 9.31 | 142.8 |
| 57461 | Yichang | 1,147.5 | 1,270.3 | 9.67 | 122.8 |
| Site number | Site name | Measured annual average value/mm | Annual simulated mean value/mm | Relative error/% | Deviation/mm |
|---|---|---|---|---|---|
| 57447 | Enshi | 1,455.1 | 1,630.1 | 10.74 | 175.0 |
| 57445 | Jianshi | 1,435.7 | 1,626.8 | 11.75 | 191.1 |
| 57439 | Lichuan | 1,312.3 | 1,508.6 | 13.01 | 196.3 |
| 57458 | Wufeng | 1,391.4 | 1,534.2 | 9.31 | 142.8 |
| 57461 | Yichang | 1,147.5 | 1,270.3 | 9.67 | 122.8 |
Change in temperature and precipitation in the Qingjiang River Basin compared with the base period.
Change in temperature and precipitation in the Qingjiang River Basin compared with the base period.
According to Figure 5, under the three scenarios in the future scenarios, the increases in daily maximum temperature and daily minimum temperature compared with the base period are 0.90–1.80 and 1.36–2.36 °C, respectively. The increase in annual precipitation ranges from 7.0 to 12.4% compared with the base period.
Runoff simulation in the future
Simulation results of daily and monthly runoff during calibration and validation periods in the Qingjiang River Basin.
Simulation results of daily and monthly runoff during calibration and validation periods in the Qingjiang River Basin.
The daily maximum and minimum temperature and precipitation data from the CanESM2 climate model under three emission scenarios are downscaled using SDSM and input into the model database through ArcSWAT. The runoff of the Qingjiang River Basin under high, medium, and low emission scenarios from 2006 to 2100 is predicted.
The change of runoff between the base period and the different scenarios
| Months | Base period/(m3/s) | Future runoff/(m3/s) | Runoff variability/% | ||||
|---|---|---|---|---|---|---|---|
| RCP2.6 | RCP4.5 | RCP8.5 | RCP2.6 | RCP4.5 | RCP8.5 | ||
| 1 | 79 | 106 | 115 | 133 | 25.5 | 31.5 | 40.6 |
| 2 | 120 | 138 | 147 | 163 | 13.2 | 18.8 | 26.5 |
| 3 | 222 | 232 | 241 | 245 | 4.2 | 7.6 | 9.2 |
| 4 | 411 | 417 | 425 | 435 | 1.6 | 3.3 | 5.5 |
| 5 | 620 | 581 | 588 | 602 | −6.7 | −5.4 | −3.0 |
| 6 | 683 | 663 | 679 | 690 | −2.9 | −0.5 | 1.1 |
| 7 | 852 | 832 | 853 | 884 | −2.4 | 0.2 | 3.7 |
| 8 | 495 | 568 | 581 | 616 | 12.9 | 14.9 | 19.7 |
| 9 | 428 | 495 | 501 | 542 | 13.5 | 14.6 | 21.0 |
| 10 | 340 | 467 | 479 | 526 | 27.3 | 29.2 | 35.4 |
| 11 | 223 | 227 | 240 | 265 | 1.5 | 6.8 | 15.7 |
| 12 | 105 | 145 | 165 | 174 | 27.5 | 36.1 | 39.2 |
| Average value | 381 | 406 | 418 | 440 | 6.0 | 8.7 | 13.2 |
| Months | Base period/(m3/s) | Future runoff/(m3/s) | Runoff variability/% | ||||
|---|---|---|---|---|---|---|---|
| RCP2.6 | RCP4.5 | RCP8.5 | RCP2.6 | RCP4.5 | RCP8.5 | ||
| 1 | 79 | 106 | 115 | 133 | 25.5 | 31.5 | 40.6 |
| 2 | 120 | 138 | 147 | 163 | 13.2 | 18.8 | 26.5 |
| 3 | 222 | 232 | 241 | 245 | 4.2 | 7.6 | 9.2 |
| 4 | 411 | 417 | 425 | 435 | 1.6 | 3.3 | 5.5 |
| 5 | 620 | 581 | 588 | 602 | −6.7 | −5.4 | −3.0 |
| 6 | 683 | 663 | 679 | 690 | −2.9 | −0.5 | 1.1 |
| 7 | 852 | 832 | 853 | 884 | −2.4 | 0.2 | 3.7 |
| 8 | 495 | 568 | 581 | 616 | 12.9 | 14.9 | 19.7 |
| 9 | 428 | 495 | 501 | 542 | 13.5 | 14.6 | 21.0 |
| 10 | 340 | 467 | 479 | 526 | 27.3 | 29.2 | 35.4 |
| 11 | 223 | 227 | 240 | 265 | 1.5 | 6.8 | 15.7 |
| 12 | 105 | 145 | 165 | 174 | 27.5 | 36.1 | 39.2 |
| Average value | 381 | 406 | 418 | 440 | 6.0 | 8.7 | 13.2 |
Scatter plot of annual runoff under three future scenarios in the Qingjiang River Basin. (a) RCP2.6 (b) RCP4.5 (c) RCP8.5.
Scatter plot of annual runoff under three future scenarios in the Qingjiang River Basin. (a) RCP2.6 (b) RCP4.5 (c) RCP8.5.
In Table 3, the annual increase in runoff under the three emission scenarios is projected to be 6.0, 8.7, and 13.2%, respectively. However, under the RCP2.6 scenario, future runoff is expected to decrease from May to July. This trend is influenced by a variety of factors. For instance, some scholars, such as Yue (2023), propose that under future climate change, runoff in certain months of the Yangtze River Basin will decrease, leading to a reduction in the concentration of the annual distribution. Conversely, other researchers, such as Qin et al. (2019), predict an increase in the average monthly runoff in the upper reaches of the Yangtze River. These differing outcomes may stem from variations in the climate models and forecast scenarios used.
The underlying cause of this situation lies in the uncertainty of runoff prediction results. The uncertainty in research on the impact of climate change on runoff arises from multiple factors (Saddique et al. 2019), among which the uncertainties in climate models and climate prediction scenarios typically exert the greatest impact (Kay et al. 2009; Teng et al. 2012).
The trend line in Figure 7 indicates an upward trend, with the annual runoff of the basin increasing alongside rising emission concentration under different future scenarios. The results are consistent with previous research (Su et al. 2020). The fluctuations under the RCP8.5 scenario are more pronounced compared to those under the RCP2.6 and RCP4.5 scenarios. This is attributed to the greater variation in annual precipitation under the RCP8.5 scenario.
The optimal dispatching schemes of the Qingjiang cascade under climate change
The optimization principle of the progressive optimal algorithm (POA) is that the optimal path is locally optimal for each pair of decision sets defined by their initial and terminal values. By applying this principle, a complex sequential decision problem can be decomposed into a series of two-stage extremum problems, thereby simplifying the original problem (Wang et al. 2024).
Qingjiang cascade hydropower stations output process diagram. (a) SBY (b) GHY (c) GBZ
Qingjiang cascade hydropower stations output process diagram. (a) SBY (b) GHY (c) GBZ
Figure 8 shows that the output of the Qingjiang cascade hydropower stations increases with higher emission concentrations. Under the RCP2.6 scenario, monthly output decreases from May to July compared to the base period, while output increases in other months. In the RCP4.5 scenario, output in May and June remains similar to the base period, except for a decrease in July at GHY, with output increasing in other months. Under the RCP8.5 scenario, all future monthly outputs, except for SBY in May, exceed the base period. The decline in output during certain months is associated with reduced runoff under specific scenarios.
Table 4 presents the multi-year average power generation of the Qingjiang cascade under different scenarios in flood season and non-flood season.
Optimized dispatch results of the Qingjiang cascade in the different scenarios
| Power station | Period/scenario | Multi-year average electricity generation/billion kW·h | Flood season power generation/billion kW·h | Non-flood season power generation/billion kW·h |
|---|---|---|---|---|
| SBY | Base period | 45.43 | 28.21 | 17.22 |
| RCP2.6 | 49.75 | 30.46 | 19.29 | |
| RCP4.5 | 53.23 | 32.54 | 20.69 | |
| RCP8.5 | 56.41 | 33.94 | 22.47 | |
| GHY | Base period | 31.19 | 18.64 | 12.55 |
| RCP2.6 | 31.98 | 18.95 | 13.03 | |
| RCP4.5 | 32.55 | 19.31 | 13.24 | |
| RCP8.5 | 33.87 | 19.86 | 14.01 | |
| GBZ | Base period | 9.34 | 3.89 | 5.45 |
| RCP2.6 | 9.52 | 3.97 | 5.55 | |
| RCP4.5 | 9.61 | 4.06 | 5.55 | |
| RCP8.5 | 9.84 | 4.18 | 5.74 | |
| Qingjiang cascade | Base period | 85.96 | 50.74 | 35.22 |
| RCP2.6 | 91.25 | 53.38 | 37.87 | |
| RCP4.5 | 95.39 | 55.91 | 40.48 | |
| RCP8.5 | 100.12 | 57.98 | 42.22 |
| Power station | Period/scenario | Multi-year average electricity generation/billion kW·h | Flood season power generation/billion kW·h | Non-flood season power generation/billion kW·h |
|---|---|---|---|---|
| SBY | Base period | 45.43 | 28.21 | 17.22 |
| RCP2.6 | 49.75 | 30.46 | 19.29 | |
| RCP4.5 | 53.23 | 32.54 | 20.69 | |
| RCP8.5 | 56.41 | 33.94 | 22.47 | |
| GHY | Base period | 31.19 | 18.64 | 12.55 |
| RCP2.6 | 31.98 | 18.95 | 13.03 | |
| RCP4.5 | 32.55 | 19.31 | 13.24 | |
| RCP8.5 | 33.87 | 19.86 | 14.01 | |
| GBZ | Base period | 9.34 | 3.89 | 5.45 |
| RCP2.6 | 9.52 | 3.97 | 5.55 | |
| RCP4.5 | 9.61 | 4.06 | 5.55 | |
| RCP8.5 | 9.84 | 4.18 | 5.74 | |
| Qingjiang cascade | Base period | 85.96 | 50.74 | 35.22 |
| RCP2.6 | 91.25 | 53.38 | 37.87 | |
| RCP4.5 | 95.39 | 55.91 | 40.48 | |
| RCP8.5 | 100.12 | 57.98 | 42.22 |
As shown in Table 4, flood season power generation at SBY and GHY exceeds that of the non-flood season, with power generation increasing as emission concentration rises. The average multi-year increase in power generation for the Qingjiang cascade ranges from 6.2 to 16.5%. The increase in flood season power generation ranges from 5.2 to 12.9%, while the increase in non-flood season power generation ranges from 7.5 to 19.9%.
Since the GBZ Power Station is a runoff power station with limited regulation and storage capacity, the water head in the non-flood season is higher than in the flood season. The flood season power generation period lasts five months, from May to September, while the non-flood season lasts seven months, from October to April. As a result, the non-flood season has a longer power generation period. Although the flow is higher in the flood season, the power generation during the non-flood season remains higher after calculation. Chen et al. (2010) also observed that the power generation at GBZ Power Station is greater during the non-flood season than in the flood season.
Table 5 shows the results of the multi-year average water level and annual water abandonment of the Qingjiang cascade hydropower stations in the base period and different scenarios.
Multi-year average water level and annual water abandonment under different scenarios of the Qingjiang cascade hydropower stations
| Period/scenario | Multi-year average water level/m | Annual water abandonment/billion m3 | ||||
|---|---|---|---|---|---|---|
| SBY | GHY | SBY | GHY | GBZ | Qingjiang cascade | |
| Base period | 383.73 | 195.43 | 0.32 | 0.55 | 4.98 | 5.85 |
| RCP2.6 | 384.63 | 196.37 | 0.53 | 0.71 | 5.54 | 6.78 |
| RCP4.5 | 385.07 | 196.68 | 0.62 | 0.89 | 6.32 | 7.83 |
| RCP8.5 | 386.24 | 197.12 | 0.81 | 1.28 | 7.64 | 9.73 |
| Period/scenario | Multi-year average water level/m | Annual water abandonment/billion m3 | ||||
|---|---|---|---|---|---|---|
| SBY | GHY | SBY | GHY | GBZ | Qingjiang cascade | |
| Base period | 383.73 | 195.43 | 0.32 | 0.55 | 4.98 | 5.85 |
| RCP2.6 | 384.63 | 196.37 | 0.53 | 0.71 | 5.54 | 6.78 |
| RCP4.5 | 385.07 | 196.68 | 0.62 | 0.89 | 6.32 | 7.83 |
| RCP8.5 | 386.24 | 197.12 | 0.81 | 1.28 | 7.64 | 9.73 |
As shown in Table 5, the average annual water level at SBY under RCP2.6, RCP4.5, and RCP8.5 scenarios exhibits an increasing trend, with the largest increase observed under the RCP8.5 scenario, where the average annual water level rises by 2.51 m. Similarly, the average annual water level at GHY also shows an upward trend across all three scenarios, with the greatest increase under the RCP8.5 scenario, where the average annual water level increases by 1.69 m. Additionally, the annual water abandonment for the Qingjiang cascade under three discharge scenarios increases by 0.93, 1.98, and 3.88 billion m3, respectively, compared with the base period.
Power generation dispatch risk indicators analysis
The weights of three-generation dispatch risk indicators under different climate change scenarios for the Qingjiang cascade are determined using the entropy weighting method. The objective weights for the risk rate of insufficient system output, the risk rate of insufficient power generation, and the risk rate of water abandonment are presented in Table 6.
The weights of risk indicators for generation dispatch for future climate change scenarios
| Weights | Future scenarios | Insufficient power generation | Insufficient output | Risk of water abandonment |
|---|---|---|---|---|
| Objective | RCP2.6 | 0.3521 | 0.2954 | 0.3525 |
| RCP4.5 | 0.3418 | 0.2858 | 0.3724 | |
| RCP8.5 | 0.3285 | 0.2711 | 0.4004 | |
| Subjective | 0.3119 | 0.1976 | 0.4904 | |
| Comprehensive | RCP2.6 | 0.3400 | 0.2661 | 0.3939 |
| RCP4.5 | 0.3328 | 0.2593 | 0.4078 | |
| RCP8.5 | 0.3235 | 0.2491 | 0.4274 |
| Weights | Future scenarios | Insufficient power generation | Insufficient output | Risk of water abandonment |
|---|---|---|---|---|
| Objective | RCP2.6 | 0.3521 | 0.2954 | 0.3525 |
| RCP4.5 | 0.3418 | 0.2858 | 0.3724 | |
| RCP8.5 | 0.3285 | 0.2711 | 0.4004 | |
| Subjective | 0.3119 | 0.1976 | 0.4904 | |
| Comprehensive | RCP2.6 | 0.3400 | 0.2661 | 0.3939 |
| RCP4.5 | 0.3328 | 0.2593 | 0.4078 | |
| RCP8.5 | 0.3235 | 0.2491 | 0.4274 |
The subjective weights of insufficient power generation, insufficient output, and water abandonment risk are 0.3119, 0.1976, and 0.4904, respectively. The maximum characteristic root is λ = 3.0537, with a consistency index 
and a random consistency index RI = 0.58. The consistency ratio 
, when 
, indicates that the inconsistency of matrix A is within the permissible range. The matrix demonstrates satisfactory consistency, passes the consistency check, and can be used as a weight vector derived from the normalized feature vector. Therefore, the subjective weight vector was obtained using the hierarchical analysis method 
.
From Table 6 it can be observed that, under the three climate change scenarios, the weights assigned to the water abandonment risk rate, calculated through a combination of subjective and objective methods, accounted for the largest proportion. This was followed by the risk rate of insufficient power generation, while the weight of the risk rate of insufficient system output represented the smallest proportion.
Based on the established power generation risk index system, a quantitative calculation and analysis of power generation scheduling risks using the POMR method was conducted. The risk rates for the power generation dispatching risk index under future climate change scenarios are presented in Table 7.
Risk rate of power generation dispatching risk index under future climate change scenarios
| Future scenarios | Insufficient power generation | Insufficient output | Risk of water abandonment | Comprehensive risk rate |
|---|---|---|---|---|
| RCP2.6 | 0.1358 | 0.1528 | 0.2281 | 0.1767 |
| RCP4.5 | 0.1054 | 0.1374 | 0.2449 | 0.1706 |
| RCP8.5 | 0.0561 | 0.1072 | 0.2764 | 0.1630 |
| Future scenarios | Insufficient power generation | Insufficient output | Risk of water abandonment | Comprehensive risk rate |
|---|---|---|---|---|
| RCP2.6 | 0.1358 | 0.1528 | 0.2281 | 0.1767 |
| RCP4.5 | 0.1054 | 0.1374 | 0.2449 | 0.1706 |
| RCP8.5 | 0.0561 | 0.1072 | 0.2764 | 0.1630 |
Radar chart of risk indicators for generation dispatch under future climate change scenarios. (a) Insufficient power generation; (b) insufficient system output; (c) water abandoned.
Radar chart of risk indicators for generation dispatch under future climate change scenarios. (a) Insufficient power generation; (b) insufficient system output; (c) water abandoned.
Radar chart of comprehensive risk ratios for generation dispatch under future climate change scenarios.
Radar chart of comprehensive risk ratios for generation dispatch under future climate change scenarios.
Regarding the risk rate of insufficient power generation (Figure 9(a)), the risk rate under the RCP2.6 scenario is higher than that of the RCP4.5 and RCP8.5 scenarios, with the lowest risk rate observed in the RCP8.5 scenario. For the risk rate of insufficient system output (Figure 9(b)), the risk rate under the RCP2.6 scenario is slightly higher than that of the RCP4.5 and RCP8.5 scenarios, with the lowest rate again found in the RCP8.5 scenario. In terms of the risk rate of abandoned water (Figure 9(c)), the risk rate under the RCP8.5 scenario is higher than that of the RCP2.6 and RCP4.5 scenarios, with the RCP2.6 scenario exhibiting the lowest risk rate of abandoned water.
Figure 10 shows that the comprehensive risk rates for power generation under the Qingjiang cascade climate change scenarios are 0.1767, 0.1706, and 0.1630, respectively. The comprehensive risk rate under the RCP2.6 scenario is slightly higher than that under the RCP4.5 and RCP8.5 scenarios, with the lowest risk rate observed under the RCP8.5 scenario. In the future climate scenario, the average annual runoff in the Qingjiang River Basin is expected to increase. As emission concentration rises, the comprehensive risk of power generation decreases. This indicates that at low emission concentrations, greater attention should be paid to the power generation risks of reservoirs. Measures such as extending the runoff forecast lead time, improving the accuracy of the runoff forecast, and implementing pre-storage and pre-release of reservoirs based on the forecasted inflows should be prioritized. Additionally, joint optimal scheduling and compensatory regulation among hydropower stations can also be employed to mitigate these risks.
CONCLUSIONS
This study proposed a comprehensive framework for optimizing cascade hydropower scheduling while addressing risks associated with climate change. The framework integrated the SWAT model with GCMs to predict future runoff. The cascade hydropower optimization scheduling model was established, and the POA algorithm ensured an efficient solution to the model. A risk assessment index system, encompassing insufficient power generation, insufficient output, and water abandonment, was established, while the POMR method offered quantitative risk analysis. Taking the Qingjiang cascade hydropower stations as a case study, the main conclusions are as follows:
(1) The SWAT model exhibited strong predictive performance, with NSE and R² values exceeding 0.70 in both the calibration and validation phases. Future runoff is projected to increase by 6.0, 8.7, and 13.2% under the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively. This increase in runoff creates opportunities for enhanced hydropower generation, especially during non-flood seasons.
(2) Power generation across all scenarios is expected to increase, with annual average growth ranging from 6.2 to 16.5%. Notably, the non-flood season exhibited higher growth rates, between 7.5 and 19.9%, compared to the flood season. However, the increase in water availability also leads to higher water abandonment, with annual increases of 0.93, 198, and 388 million m³ under RCP2.6, RCP4.5, and RCP8.5, respectively.
(3) The risk analysis revealed that higher emission concentration reduced the overall comprehensive risk rate. Although RCP8.5 was associated with the highest water abandonment risk, it resulted in the lowest risks of insufficient power generation and output, resulting in a lower overall risk rate of 0.1630 compared to 0.1767 (RCP2.6) and 0.1706 (RCP4.5).
Based on the latest climate change model CMIP6, deep analyzing the impact of uncertainty factors on runoff simulation and developing adaptive scheduling strategies will be our further research focus.
ACKNOWLEDGEMENT
This research is supported by the Hubei Key Laboratory of Intelligent Yangtze and Hydroelectric Science Open Fund (242202000903), the National Natural Science Foundation of China (Grant No. 52179018), the Hubei Province Natural Science Foundation (General Program) (2023AFB594), major scientific and technological projects of the Ministry of Water Resources of China (SKS-2022003), and the Discipline Innovation and Talent Introduction Base of Hydraulic Engineering.
AUTHOR CONTRIBUTIONS
Y.L. contributed to the conception and framework of the study; R.H. analyzed the data and wrote the main manuscript text; H.M. constructed the model and prepared the tables and figures; S.S. and J.G. writing-review and editing; H.Z. and C.L. provided the relevant data for the study; Y.W. provided constructive advice. All authors reviewed the results and approved the final version of the manuscript.
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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