Bi-level Programming Method Research Articles

Potential way to plan China's power system (2021–2050) for climate change mitigation

Planning power system (PS) towards renewable energy is crucial for reducing carbon dioxide (CO2) emission as well as mitigating climate change. However, the inherent uncertainty and hierarchical structure of PS pose intractable challenges to the planning process. This study develops a multi-GCM-based interval bi-level programming (MIBP) method that can balance two-level decision-making conflict between CO2-emisison reduction and system cost minimization. MIBP can also deal with uncertainties expressed as interval values in objective functions and constraints. Then, a MIBP-PS model is formulated to plan PS for China (2021–2050), where the upper-level objective is to minimize CO2 emission and the lower-level objective is to minimize the system cost. The major findings are: (i) the CO2 emission for PS would reach peak value before 2030 and then reduce by [10.2, 20.4]% in 2050, which is mainly owing to the curtailment of fossil fuel; (ii) compared with the conventional model, CO2 emission from MIBP-PS model could decrease by [3.1, 4.8]%, which shows the superiority of the developed model; (iii) the fossil-fuel power would be gradually replaced by renewable energy, and the proportion of coal-fired power would decrease by 38.8% by 2050, especially small coal-fired facilities (i.e., below 0.3 GW) should be gradually phased down.

Sustainable management of water-economy-ecology nexus through coupling bi-level fractional optimization with effluent-trading mechanism: A case study of Dongjiang watershed

Ecosystem deterioration and freshwater depletion due to population growth and rapid urbanization have posed great challenges in managing water-economy-ecology nexus (WEEN) for watersheds. The objective of this study is to develop a bi-level fuzzy fractional programming (BFFP) method to identify sustainable watershed WEEN strategies with considering effluent-trading program. The BFFP method improves traditional methods for WEEN management over handling the bi-level decision process, ratio-objectives and fuzzy environmental policies simultaneously. Then, through coupling BFFP with effluent-trading mechanism, a BFFP-WEEN model is firstly formulated and employed to the Dongjiang watershed in China, where ninety-nine scenarios are examined to reflect various policy implications and decision-makers’ preferences. Major findings are: (1) compared with non-trading, effluent-trading can effectively reduce pollution discharges (e.g., reducing 140.1×106 ton of Chemical Oxygen Demand and 79.5×106 ton of Ammonia-Nitrogen over the planning horizon), revealing that effluent-trading mechanism is beneficial to the improvement of ecological environment; (2) under the trading mechanism, trading ratio has significant effects on marginal benefit and water allocation (e.g., improving marginal benefit by 15.4% and saving 363.7×106 m3 of total water allocation under 1.03 of trading ratio); (3) in order to alleviate the deterioration of ecosystem, industrial water use should be limited firstly and the area of forest land should be expanded; for ensuring the ecosystem requirements, it is recommended to promote the reuse of reclaimed water and improve wastewater treatment/recycling technology. The major improvements in this study include: (1) the development of the BFFP approach to deal with hierarchical decision conflicts and optimize system efficiency under uncertain environmental policies, and (2) the application of BFFP-WEEN model with coupling the effluent-trading mechanism to generate desired strategies for synergistic management of WEEN, and help balance the conflicts among water shortage, ecological degradation, and economic development in watersheds.

Bilevel spatial–temporal aircraft taxiing optimization considering carbon emissions

Air transportation pollution is mainly caused by aircraft carbon emissions. One of the key methods for reducing aircraft carbon emissions is to optimize the taxiing route on the airport surface. In view of this, a bilevel spatial–temporal taxiing optimization model considering carbon emissions is proposed in this paper. A bilevel programming method is deployed in the model to minimize the carbon emissions, taxiing waiting time, and conflicts of aircraft, which not only facilitates environmentally friendly airport establishment but also improve airport operation efficiency. Particularly, the influence of taxiing conflicts and turning action are considered when calculating the carbon emissions in the paper, which provides a more effective subjective for the model. An iterative neighborhood search algorithm is proposed to solve the model. The operation data of Baiyun Airport in China are utilized to validate the model. The results indicate that, compared with the first-come first-serve (FCFS), the proposed model reduces the total carbon emissions of aircraft by 814 kg on the premise of no taxiing conflict or 2% of the total. Compared with tabu search, it can reduce carbon emissions by 375 kg. This study can provide a more environmentally friendly taxiing strategy for aircraft and reduce carbon emissions.

Bilevel Optimal Economic Dispatch of CNG Main Station Considering Demand Response

Compressed natural gas (CNG) main stations are critical components of the urban energy infrastructure for CNG distribution. Due to its high electrification and significant power consumption, researching the economic operation of the CNG main station in demand response (DR)-based electricity pricing environments is crucial. In this paper, the dehydration process is considered in the CNG main station energy consumption model to enhance its participation in DR. A bilevel economic dispatch model for the CNG main station is proposed, considering critical peak pricing. The upper-level and lower-level models represent the energy cost minimization problems of the pre-system and rear-system, respectively, with safety operation constraints. The bilevel programming model is solved using a genetic algorithm combined with a bilevel programming method, which has better efficiency and convergence. The proposed optimization scheme has better control performance and stability, reduces the daily electricity cost by approximately 21.04%, and decreases the compressor switching frequency by 50.00% without changing the CNG filling demand, thus significantly extending the compressor’s service life. Moreover, the average comprehensive power cost of processing one unit of CNG reduces 20.62%.

A bi-Level programming method for SPaT estimation at fixed-time controlled intersections using license plate recognition data

Signal phase and timing (SPaT) information is a necessary input for traffic performance evaluation. However, current SPaT estimation studies mainly focus on estimation of cycle length or green time of a certain movement, and are realized mostly by floating car data whose data quality significantly affects the estimation accuracy. As license plate recognition (LPR) systems are becoming a widely implemented and reliable data source in China, in this study, a SPaT estimation method is proposed using the LPR data for fixed-time controlled intersections. The SPaT estimation problem is formulated as a bi-level programming model to find the optimal match between the phase boundaries and the LPR passing time series in the study period. Evaluation is done with an empirical case and compared with an existing method, results show that the estimation accuracies of the phase duration can reach 90.0%, outperforming the existing method and demonstrating great potential for practical application.

Managing water-energy-carbon nexus in integrated regional water network planning through graph theory-based bi-level programming

The water-energy-carbon nexus (WECN) has raised the attentions in the past years due to the shortages of water and energy resources, climate change and their close connection. It is critical to study WECN in water network systems due to their energy- and carbon-intensive characteristics. In optimization of WECN in water network planning, decision makers with conflictive objectives may have different decision-making power levels. In this study, an integrated Graph Theory-Based Bi-Level Water Network Planning Model, named GraBiL is developed, which represents a methodological contribution to the challenge of quantitative interrelationships of WECN and hierarchical decision-making problem in regional-scale water network planning. The GraBiL model has improved upon the existing bi-level programming and graph theory-based method for solving spatial layout optimization in two-level decision-making problem. Two-level conflictive objectives including minimizing total system cost and maximizing energy saving are considered. Fuzzy uncertainties associated with water loads are quantified. The impacts of carbon emission control on total system economic costs, energy consumption and the optimal water network planning are effectively addressed. The results from a hypothetical case study indicate that enhanced overall satisfaction for meeting the two-level objectives can be achieved with the proposed GraBiL model. Optimal water network planning schemes including spatial layout under four representative carbon emission control scenarios are compared. The proposed model has provided insight into quantitative interrelationships of WECN, hierarchical decision-making, optimization of water network spatial layout and quantification of fuzzy uncertainty associated with water loads in regional-scale water network planning.

Interval-parameter bi-level programming for energy system management under uncertainty: Towards a deep-decarbonized and sustainable future in China

To reach the goal of carbon-neutral society, synergistic approaches based on mathematical models that are capable of planning energy system associated with complex uncertainty and hierarchical structure are desired. In this study, an interval-parameter bi-level programming (IBP) method that is effective for solving hierarchical decision-making problems with conflict objectives and uncertainty is developed. Then, an IBP based China's energy system model (abbreviated as IBP_CES) is formulated for mainland China during 2021–2050, where the higher-level objective of minimizing carbon dioxide (CO2) emission is given priority, following by the lower-level objective of minimizing system cost. Results from IBP_CES show that, although China's energy supply would still rely heavily on fossil fuels, the share of coal would decrease to 33.9% by 2050. Results also disclose that the national CO2 emission would reach the peak value during 2026-2030 and then decline rapidly due to development of renewable energy and promotion of carbon-treatment technology which is beneficial for government to achieve carbon neutrality goals. In addition, compared to the traditional single-level model, CO2 emission from IBP_CES can decrease by 5.9%, demonstrating that IBP_CES is more superior in energy system decarbonization. The findings can help decision makers to well understand the interactions and tradeoffs between climate mitigation and economic development, and provide effective information on clean, sustainable and deep-decarbonized development strategies.

A Stackelberg game model with tax for regional air pollution control

The command-and-control regulation is likely inefficient and costly. This study investigates a regional pollution control scheme with tax (RPCST) under which the central government sets the tax rate under a given pollutant reduction quota and local governments determine their pollution removal rates based on the central government’s policy. First, a one-leader-multi-follower (OLMF) Stackelberg game model is formulated, in which the central government is the leader and the local governments are the followers. Then, a procedure based on bilevel programming and relaxation method is applied to solve the OLMF model. Finally, a case study analyzing the SO2 reduction of the Yangtze River Delta in China is conducted to demonstrate the effectiveness of the RPCST. The results show that RPCST works better than the current command-and-control scheme. Our analysis provides a guideline for governments to design optimal tax schemes to effectively solve the regional air pollution crisis.

Optimal energy storage planning for stacked benefits in power distribution network

Energy storage system (ESS) is regarded as an effective tool to promote energy utilization efficiency and deal with the operational risk of the power distribution network (PDN), which is caused by the inherent uncertainties of distributed energy resources and the surging of new loads from emerging energy sectors. Multiple benefits could be accrued by ESSs when providing various services to the PDN. However, investing in ESSs without a comprehensive cost-benefit analysis will underestimate the ESSs’ profitability and result in a suboptimal planning scheme. To this end, this paper proposes a bi-level ESS planning method considering the stacked benefits of ESSs. First, to facilitate the comprehensive cost-benefit analysis in the investment decision making process, systematic definitions and quantitative methods of ESS benefits are proposed to evaluate both the investment and operational benefits of ESSs properly. Novel ESS reserve model and load hosting capacity evaluation model are also developed to improve the accuracy of the benefit assessment. Second, a game theory based bi-level programming method is proposed to precisely capture the two-layer dynamic interaction structure of ESS planning using an easy-to-implement mathematical optimization-based formulation with global optimum guarantee. Specifically, the upper level optimizes the sites and sizes of ESSs for maximizing the stacked benefits, while the lower level economic dispatch model determines the optimal scheduling of the installed ESSs. Finally, to make the bi-level ESS planning problem tractable, it is reformulated as a single-level mathematical programming with equilibrium constraints by the duality-based reformulation. The linearization method is applied to further convert it into a mixed-integer programming problem that could be directly solved by commercial solvers. Numerical results verify that the proposed planning strategy could yield cost-effective results under different settings. Comprehensive cost-benefit analysis also indicates that transmission and distribution system upgrade deferral, reserve/regulation provision and energy arbitrage are the top-three applications for maximizing ESS benefits, and it is not always reasonable to keep investing in ESSs as their marginal benefits will decrease to zero with the increasing ESS investment.

A hybrid multi-objective bi-level interactive fuzzy programming method for solving ECM-DWTA problem

Electronic countermeasure (ECM) has become one of the most significant factors in modern warfare, in the course of combat, the electronic jamming allocation tasks need to be flexibly adjusted with the change of combat stage, which puts forward higher requirements for the modeling and solution method of this kind of problems. To solve the ECM dynamic weapon target assignment (ECM-DWTA) problem, a hybrid multi-target bi-level programming model is established. The upper level takes the sum of the electronic jamming effects in the whole combat stage as an optimization objective, and locally optimizes the ECM weapon (ECM-WP) assignment scheme in each stage. The lower level takes the importance expectation value of the target subjected to interference and combat consumption as double optimization objectives to globally optimize the ECM-WP assignment scheme. Focus on solving this complex model, a hybrid multi-objective bi-level interactive fuzzy programming algorithm (HMOBIF) is proposed, in this method, exponential membership function is used to describe the satisfaction degree of each level. When solving the multi-objective optimization problem composed of membership functions in the upper and lower levels, we use the MOEA/D algorithm to obtain the Pareto Front (PF) solution set, and then each solution in PF is evaluated and selected by the TOPSIS multi-criteria evaluation method. This local and global interactive optimization process of bi-level model is actually the process of executing observation-orientation-decision-action loop in practical combat. According to the current example, we conduct numerical simulation on the parameters in the model and obtain the parameter values suitable for the model solution. The computational experiments on different scale ECM-DWTA problems show that HMOBIF method is superior to four bi-level programming algorithms in terms of performance index, and can better solve ECM-DWTA problems.

Bi-level convex optimization of eco-driving for connected Fuel Cell Hybrid Electric Vehicles through signalized intersections

Eco-driving for connected Fuel Cell Hybrid Electric Vehicles (FCHEVs) is a coupled problem of speed planning and energy management. To reduce the computational burden, bi-level optimization decouples and hierarchically solves the upper-level and lower-level subproblems. This paper proposes a bi-level convex approach for eco-driving of a connected FCHEV proceeding through multiple signalized intersections. On the upper level, the non-linear traffic light constraints are transformed into time-varying linear state constraints and the cost function becomes quadratic after using the average speed. On the lower level, model convexification is carried out for the fuel cell system and battery. Then the upper-level speed planning and lower-level energy management are sequentially solved by the MOSEK solver and the Alternating Direction Method of Multipliers (ADMM) algorithm. The results show that the proposed bi-level convex approach greatly reduces the computational cost while maintaining high energy efficiency, with only 6.59% computational time and almost the same fuel economy compared to the bi-level Dynamic Programming (DP) method.

An improved fuzzy sorting algorithm coupling bi-level programming for synergetic optimization of agricultural water resources: A case study of Fujian Province, China

The uneven allocation of water resources and the shortage of regional water resources pose great challenges to the economic development and regional development balance of the Fujian province. Optimizing the water allocation structure in different regions can effectively alleviate water pressure. In this study, a type-2 fuzzy bi-level programming (T2FBL) method is proposed to plan the agricultural water resource system in the Fujian province. This method uses an improved fuzzy sorting algorithm to deal with uncertain parameters in the system and combines the bi-level programming method to balance the trade-off between two levels of decision-makers, the uncertain information contained in the secondary membership function omitted in the interval type-2 fuzzy theory is considered in the new ranking algorithm. Multiple scenarios related to different food security needs and different risk indices are examined. The major findings are as follows: (i) With an average tolerance of 75%, the average gross agricultural output value under various scenarios increased (0.4% ∼ 7%) (average 3.89%) after optimization. (ii) The regional water allocation scheme under different food demands and different water availability scenarios is calculated, and the results show that prioritizing adjustments to the industrial water distribution structure of Fuzhou and Zhangzhou will greatly relieve the water pressure in the Fujian province. (iii) The relationship between the availability of system water resources and economic benefits is given through the calculation results of the T2FBL model. These findings can provide an in-depth understanding of the interaction between agricultural, industrial and tertiary industry water allocation and provide technical support for agricultural water resource planning issues.

Development of an integrated bi-level model for China’s multi-regional energy system planning under uncertainty

Climate change mitigation and renewable resources utilization are becoming particularly urgent for energy system management. In this study, a bi-level joint-probabilistic programming (BJPP) method is developed for planning multi-regional energy system under different mitigation policies and uncertainties. BJPP can handle leader–follower issues in decision-making process as well as examine the risk of violating joint-probabilistic constraints. Based on the BJPP method, a China’s multi-regional energy system (named as BJPP_CMES) model is formulated to provide optimal scheme for energy system planning of China over a long-term horizon (2021–2050) by synergistically minimizing carbon dioxide (CO2) emission and system cost. A series of scenarios associated with different carbon capture and storage (CCS) levels and violation risks of energy-demand constraints are examined. Results reveal that: (i) the share of non-fossil energy in China’s energy supply would keep increasing in 2021–2050, and the highest growth of the renewable supply would occur in Ningxia (rising 47.7%); (ii) Sichuan, Inner Mongolia, and Gansu would be the top three suppliers of renewable electricity; (iii) the CO2 emission of China would reach a peak of [44.3, 54.8] billion tonnes during the period of 2026–2030; Shandong, Inner Mongolia, and Shanxi would be main contributors of CO2 emission in the future; (iv) compared with the single-level model, the CO2 emission from the BJPP_CMES model would reduce by [2.7, 5.7]%; (v) among developed regions, the individual probability level of Jiangsu-Zhejiang-Shanghai is the most significant parameter for both CO2 emission and system cost. The findings are helpful for decision makers to optimize multi-regional energy system (MES) with a low-carbon and cost-effective manner, as well as to provide useful information for renewable energy utilization and regional sustainable development.

Improving the System Performance in Terrestrial-Satellite Relay Networks by Configuring Aerial Relay

Driven by the massively growing applications in Internet of Things (IoT) and the new requirements of the six generation (6G) wireless network, the amount of terrestrial mobile devices (TMDs) and data traffic in wireless communications have increased explosively. Consequently, the integrated terrestrial-satellite relay networks (ITSRNs) have emerged to address the issue of the huge wireless traffic with limited allocated resources, which attracts extensive research attention to the field of IoT. Limited improvement of system throughput is realized by configuring terrestrial relays (TR) in the previous works. In this paper, by introducing an aerial relay (AR), we propose a novel structure of ITSRN and investigate the system throughput maximization and energy consumption minimization problems by jointly optimizing power allocation and AR altitude. Specifically, the system implementation includes two periods: satellite to relay (S-R) period and satellite to devices (S-D) period. To maximize the overall system throughput, we propose a joint optimization scheme of the power allocation and altitude of AR. Due to its non-convexity, a bilevel programming method is proposed to obtain the global optimal solution, where the closed-form expressions of power allocation and the optimal altitude of AR are derived. Subsequently, we investigate the energy consumption minimization problem during S-R period, which is formulated as a convex problem. We propose a low complexity algorithm and derive the optimal closed-form solution based on the rigorous mathematical analysis. The effectiveness of the proposed algorithms and solutions are verified by extensive simulations.

Planning a Water–Food–Energy–Ecology Nexus System toward Sustainability: A Copula Bi-level Fractional Programming Method

A copula bi-level fractional programming (CBFP) method is developed for planning the water–food–energy–ecology (WFEE) nexus system. CBFP has advantages in (i) dealing with ratio-objective problems, (ii) balancing the conflicts between hierarchical decision levels, and (iii) reflecting joint risks of correlated uncertain variables. Then, a CBFP–WFEE model is formulated to the Ili-Balkhash basin in Central Asia, in which 108 scenarios associated with different irrigation efficiencies, ecological-flow demands (EBW), and water–land resources have been examined. Solutions of water allocation, hydropower generation, and land-use pattern are obtained. Our major findings are as follows: (i) from 2021 to 2050, water allocation to livestock in East Kazakhstan would remarkably increase (by 40.9%) when water allocation to food is satisfied; (ii) hydropower generation would increase with the rising ecological flows and arable land resources; (iii) EBW is the key factor influencing the water inflow to the Balkhash Lake; (iv) the share of ecosystem water allocation would exceed 17.5% by 2050, and grassland area would rank in the first place of the ecosystem. Compared with conventional bi-level stochastic programming and single-level fractional programming models, the CBFP–WFEE model can achieve a higher ecosystem service value and higher efficiency of water–land resources, which can provide more feasible and sustainable alternatives for the WFEE nexus system. The obtained results can help balance the contradictions among water shortage, economic development, and ecology protection, as well as provide synergic management strategies for regional sustainability.

Business strategy for high-speed rail in the express delivery sector: A case study of China using a bilevel programming method

The aim of this paper is to identify a business strategy for high-speed rail (HSR), including market positioning and price strategy, in the Chinese express delivery market using a bilevel programming model. Three routes were selected for case studies. The results showed that parcels with a high value of time (VOT) are mostly distributed to self-owned airlines. Compared with highway and conventional rail transport, HSR is relatively competitive for parcels with high VOT in both long- and middle-distance transport and parcels with extremely high VOT in middle-distance transport. Highway transport is the dominant mode for parcels with extremely low VOT in both long-distance and middle-distance routes. The freight rate of HSR must be more than 30% lower than that of air to be more competitive. Additionally, a sensitivity analysis considering increased speed and relocation of parcel distribution centres was performed to identify factors that affect the competitiveness of HSR in the express delivery sector. The results showed that the competitiveness of HSR for parcels with high VOT is improved significantly in middle-distance routes when either measure is adopted. However, there is no remarkable change in the performance of HSR for long-distance parcel transport and parcels with low VOT.

Influence analysis of energy policies on comprehensive performance of CCHP system in different buildings

As an on-site energy supply system, combined cooling, heating and power (CCHP) system plays significant role. Thus, CCHP systems servicing four types of buildings were employed in this paper. Considering high initial investment and off-design operation, a multi-objective optimization model and a bi-level programming method integrated with operation and design were proposed. Nominal capacity configurations were optimized with no supportive policy. Then influence of capital subsidy and feed-in tariff policies to system comprehensive performance were illustrated. Results show that CCHP system servicing residential building could not achieve economic merits whatever energy policy was employed. CCHP system servicing hotel and hospital could realize better comprehensive performance than that of office. While the capacity of power generation unit was lower than 1.5 MW and capital subsidy was lower than 3000 ¥/kW, the capital subsidy policy had slight effect on system performance. For feed-in tariff policy, when feed-in tariff ratio (Esale/Egrid) was quite low, nearly no change on system performance would be obtained. And when the feed-in tariff ratio was relatively high, the energy and environment performance would decrease significantly. If feed-in tariff ratio was in a reasonable price range, this policy would have a positive effect on CCHP system with different building types.

Energy-Efficient Resource Allocation for NOMA-MEC Networks With Imperfect CSI

The combination of non-orthogonal multiple access (NOMA) and multi-access edge computing (MEC) can significantly improve the system performance including communication coverage, spectrum efficiency, etc. In this article, we focus on energy-efficient resource allocation for a multi-user multi-BS NOMA-MEC network with imperfect channel state information (CSI), where each user can upload its tasks to multiple base stations (BSs) for remote executions. We propose an optimization scheme, including task assignment, power allocation and user association, to minimize energy consumption. Specifically, we transform the probabilistic problem into a non-probabilistic one. To efficiently solve this nonconvex energy minimization problem, we first investigate the one-user two-BS case and derive the optimal closed-form expressions of task assignment and power allocation via the bilevel programming method. Subsequently, based on the derived optimal solution, we propose a low complexity algorithm for the user association in the multi-user multi-BS scenario. Simulations demonstrate that the proposed algorithm can yield much better performance than the conventional OMA scheme and the identical results with lower complexity from the exhaustive search with the small number of BSs.

Location optimization of a competitive distribution center for urban cold chain logistics in terms of low-carbon emissions

Owing to the fast economic and social development in Wuhan, the demand for cold chain logistics is increasing rapidly. Currently, the scale of the existing distribution centers cannot fully meet this demand, so building new ones would seem necessary. Research rarely considers consumer choice from the perspective of competition between new and existing cold chain distribution centers, and the low-carbon concept is rarely considered when a competitive site is selected. This paper therefore puts forward a model to assist the decision-making process regarding the choice of location where cold chain logistics facilities might be sited. Based on a bi-level programming method, this model is constructed where the upper level of government aims to determine an optimal location and scale for a cold chain distribution center as well as a rational trading policy regarding carbon emissions to minimize the total social cost of the whole logistics system. The lower level adopts the demand user equilibrium model, which considers the demands of logistics users when choosing between new and existing cold chain distribution centers, so as to minimize the cost incurred by each logistics user. We use the cloud particle swarm optimization algorithm to solve the model and decide a suitable location for a new center in Wuhan, the principal city in the Hubei Province, in China. The study reveals that: (1) The high demand is equivalent to the high number of new distribution centers; (2) The high attractiveness of these centers is equal to their high total scale; (3) Changes in carbon emissions trading prices have an impact on the scale, total carbon emissions, and total social cost of new cold chain distribution centers; (4) The carbon emissions quota policy has an impact on the scale of the location chosen for a new cold chain distribution center, total carbon emissions, and total social costs. This article provides a scientific basis regarding decisions concerning the location of new cold chain distribution centers by the government, and provides some ideas for energy conservation improvement and carbon emissions reduction by the whole society.

Synergetic management of energy-water nexus system under uncertainty: An interval bi-level joint-probabilistic programming method

Synergic management of energy-water nexus (EWN) system is essential for coping with the dilemma of joint shortage of energy and water and supporting socio-economic sustainable development. The system is full of multiple uncertainties, making deterministic analysis methods infeasible. In this study, an interval bi-level joint-probabilistic programming (IBJP) approach is first developed through incorporating bi-level programming (BP) and interval joint-probabilistic programming (IJP) within a framework. IBJP has advantages in balancing the tradeoff between two-level decision makers under uncertainty, tackling uncertainties expressed as joint probabilities and interval values, and examining the risk of violating joint-probabilistic constraints. Then, the developed method is applied to planning China’s EWN system over a long-term planning horizon (2021–2050). Multiple scenarios related to different groups of constraint-violation levels for violating electricity demand and/or water availability constraints are examined. Results reveal that uncertainties associated with joint and individual probabilities have effects on the synergic management of EWN system. Results also disclose that limited water resource can promote electricity generation structure toward a low water-intensity, clean and sustainable pattern, in which the share of clean energy would increase to 66.25% by 2050 and the corresponding water withdrawal would save 41.20%.