Energy-Water-Carbon Nexus Optimization for the Path of Achieving Carbon Emission Peak in China Considering Multiple Uncertainties: A Case Study in Inner Mongolia

The Chinese government has launched a guideline for carbon emissions up to the peak (CEUP) in the 2030 target. The electric power sector has to make its own contributions to the national CO2 emissions mitigation target. In this study, a patron–client interactive optimized (PCIO) model is proposed to investigate the regional energy–water–carbon nexus optimization under the policy background of the CEUP target. Inner Mongolia, the largest energy base in China, which is also facing the prominent contradiction including the energy production and serious environmental problems, is chosen as a case study. Multiple uncertainties, including the fuel price uncertainty and output of the wind and solar power, are considered to make the optimization process more realistic. Results show that coal-fired power will gradually be substituted by the gas, wind, and solar power in Inner Mongolia to reach the CEUP target. The CO2 capture and storage technology and air-cooling systems will play important roles, especially under the strict water policy scenario. However, the achievement of the CEUP and water-saving target will be at the expense of high system costs. The PCIO model makes it possible for the decision-maker to make flexible strategies to balance the CEUP target and saving system costs. The results have demonstrated the validity of the PCIO model in addressing the hierarchical programming problems.


Introduction
China has announced to the world that in 2030, carbon emissions will reach their peak so that it can make effective contributions to the global CO 2 emissions target. This target is China's national pledge to reduce carbon emissions, which will further help China switch the extensive economy mode to the low-carbon economy mode. To achieve this target, all sectors should assume responsibility and undertake the corresponding systematic reduction in CO 2 emissions. The electric power industry is the major CO 2 emissions contributor in China, which is responsible for 44% of the total CO 2 emissions in 2015 [1]. This amount is 1.5 times higher than that in the United States (US) and 2.5 times higher than that in European Union (EU), while China's electricity consumption per capita only accounts for a quarter of that in the US and one-half of that in EU [2]. The electric power industry in China needs to make great efforts to optimize its structure further and improve the energy efficiency so that the CO 2 emissions up to the peak (CEUP) target could be achieved as scheduled.
Thermal power, especially coal-fired power, is still in the dominant position in China's electric power system (EPS). In 2017, the installed generating capacity rose by 7.6% to gional energy-water-carbon nexus optimization under the background of the CEUP target, and investigates the best tradeoffs in the regional EPS in China. Multiple uncertainties, including the fuel price and the output of the wind and solar, are taken into consideration in this study. Inner Mongolia, the largest energy base in China, is chosen as a case study to verify the availability and efficiency of the proposed PCIO model.

The Algorithm of PCIO Model
Bi-level programming (BLP) is a special kind of statical Stackelberg game with two decision-makers at two different levels [8], a case of two-person, non-zero-sum, and full information game. It has the superiority in tackling problems with a hierarchical framework and helps to get a compromised solution between two levels [20]. The patron-client interactive optimized (PCIO) model was formulated based on the framework of the BLP model. The patron (upper) level of the PCIO model is to maximize the renewable power penetration ratio in Inner Mongolia; The client (lower) level of the model is to minimize the system cost. A fuzzy satisfaction degree method [21] is introduced to solve the PCIO model. As the values of the decision variables and function of the patron (client) level will be the in-put parameters of the client (patron) level to build the triangle membership function, both levels will exert influences on the other level. Coupled with the carbon emission and water withdrawals restraints in two level, the proposed PCIO model is applied to optimize the energy-water-emissions nexus in Inner Mongolia. The flow chart of algorithm is shown in Figure 1.
The algorithm of the fuzzy satisfaction degree method for the PCIO model is shown below: The upper-level objective and its constraints: The lower-level objective and its constraints: s.t (x 1 , x 2 ) ∈ F 2 = {(x 1 , x 2 )|A 1 x 1 + A 2 x 2 ≤ b, x 1 and x 2 ≥ 0 } (4) Max λ x U 1 + P 1 − x 1 /P 1 ≥ λ is the optimized solution of Equation (3). P 1 is the maximum tolerances around x U 1 . f 1 / f 2 is the result when the optimized decision variables of Equation (3)/Equation (1) is put into Equation (1)/Equation (3). µ x 1 ,µ f 1 ( f 1 (x)) and µ f 2 ( f 2 (x)) are three membership functions, which is built to restrain the minimum acceptable degrees of satisfaction λ. If the upperlevel decision maker is satisfied with the solution in [22], a satisfactory solution is reached. Otherwise, new membership functions for the decision variables and the objective function will be generated and the computation process is repeated until a satisfactory solution is reached. (1) and (3) individually Have the optimized results obtained?

The PCIO Model
The functions, decision variables and parameters are presented in Table 1. The detailed information of each variable and parameter are shown close to the PCIO model. The patron-level objective emphasizes the maximization of renewable power penetration during the planning periods in Inner Mongolia, which is stated as: where f rep denotes renewable power penetration in the electric power system. Pele jt denotes the amount of electricity generated by power conversion technology j. j = 1, 2, 3, and 4 represent coal-fired power, gas-fired power, wind power, and photovoltaic power, respectively. PRS jt denotes the pre-regulated installed capacity of the electricity schemes (MW). η jt denotes the binary variables to identify whether a capacity expansion action of power conversion technology j should be executed. YC jt denotes the expansion capacity for conversion technology j (MW). L jt is the utilization hours of conversion technology j (hour). Considering the relationship between the path of achieving the carbon emissions peak and the harmonious development of the local economy, constraints of the environmenteconomy performances are taken into account at the patron level: Coordinated constraints for the environment-economy performances [23]: where µ and µ min denote the optimal and the minimum regional harmonious development index, respectively, in which the predetermined value of µ min was 0.8 in this model [23]. Details about the synergetic relationship for the environmental and economic performances of the systems are presented as follows: Membership function µ e (ω 1 ) denotes the coordinated degree between electricity supply and demand: where ω 1 is defined as the ratio of total power generation to power generation amount in 2005, which is expressed as: Membership function µ c (ω 2 ) denotes the coordination degree between regional economic performance and carbon emissions level, stated as: where ω 2 is the ratio of carbon emissions to regional economic performance, presented as where R EO and R CO denote the reference coefficients for the carbon emissions and the economic cost of the systems. In this study, the carbon emissions and the economic cost of Inner Mongolia's electric power system in 2005 were chosen as the reference coefficients, respectively. R E and R C denote the actual value of carbon emissions and system cost in different years. Constraints for total CO 2 -emissions are as follows: where ERC jt denotes CO 2 -emissions rate by power conversion technology j in period t (tonne/MWh), µ jt is the CO 2 reduction efficiency through the CCS technology in period k (%). γ jt is the proportion of the thermal power plants with the CCS devices (%). DLC t is the CO 2 emission limit from the thermal power plants in period k. ECG jt is the excess CO 2 generated from power conversion technology j in period k (10 3 t)
where (1) the cost for purchasing energy and water withdrawals: (2) the operating cost for power generation: (3) the penalty for power shortage: Energies 2021, 14, 1067 7 of 21 (4) the cost for capacity expansion: (5) the revenue for electricity transmission: (6) the cost for CO 2 capture and storage: (7) the penalty for excess CO 2 emissions: where i denotes the type of energy, i = 1, 2 for coal and natural gas, respectively. AES it denotes the amount of energy supply from source i in period t (PJ), P it is the price of coal and natural gas in period t (10 6 RMB¥/PJ). CPW pt denotes the cost for water in period k (10 6 RMB¥/tonne), AWS pt is the number of water withdrawals in period t under the water supply policy scenario p (tonnes). p denotes the water supply policy (flexible and strict). WF jptk denotes the water withdrawal factor of different power generating technologies (m 3 /MWh). k is the type of cooling technologies, k=1,2,3 denotes the cycling cooling, one-through, and air-cooling system, respectively. δ jtk is the kth proportion of cooling technologies (%). BGC jt is the benchmark technology cost for CCS technology (RMB/MWh). FS jt denotes the financial subsidy in period t. (7) GOCE jt denotes the operating cost for excess CO 2 released from power conversion technology j in period t (10 6 RMB¥/tonne). The constraints for resource availability: TEL it and TW L pt denote total energy resource supply level to generate electricity in period t (tonne) and total water resource supply level to generate electricity in period t (tonne), respectively.
The constraints for energy supply and electricity generation: FTC it denotes the unit of electricity generation per unit of energy carrier for energy i (GWh/PJ). The constraints for power demand-supply balance: SD jt denotes power loss for power conversion technology j in each planning period, DEM th denotes the electricity demand in Inner Mongolia in each period (10 3 GWh).
The constraints for realizing CO 2 emissions peak: CEm 2005 denotes the CO 2 emissions of Inner Mongolia from the electricity industry in 2005 (10 3 tonne).
The mass balance for water withdrawals: WCE pjt denotes the water withdrawals per unit of electricity generation (tonne/GWh), TSW pt is the total water resource supplies underwater withdrawal policy p (tonne).
The constraints for expansion capital: YCC jt denotes the expansion cost for conversion technology j in period t (10 3 RMB¥/GW), EPP jt denotes the power plants expansion fees in period t (10 6 RMB ¥). The constraints for the interval-integer variables:

Measuring the Fuel Price
The fuel price here includes two kinds of fuels, coal and natural gas. We assumed that both of their prices p F followed the Geometric Brownian Motion [24]: where p F denotes the fuel prices; α F is the drift parameters; χ F is the variance parameter, and dz denotes the independent increments of the Wiener process.

Measuring the Output of Wind Power and PV
(1) The output of wind power It is well established that wind speed distribution follows the Weibull probability density function (PDF) [25,26]. The probability of wind speed v (m/s) following Weibull PDF with shape factor (k) and scale factor (c) is given by: The mean value of Weibull distribution is defined as: where gramma function Γ(x) is described as: In this study, the empirical values of the Weibull shape (k) and scale parameter (c) in three planning periods are different. In this way, the wind power output in three periods can be simulated. The function of wind speed (v) is described as: where v in , v r , and v out are the cut-in, rated, and cut-out wind speeds of the turbine, respectively. P wr is the rated output power of the wind turbine. The various speed values were v in = 3 m/s, v r = 16 m/s, and v out = 25 m/s. Figure 2 was obtained through Monte Carlo simulation by the sample size of 10,000.  (2) The output of solar power The output of the solar power depends on the solar irradiance (G), which follows the lognormal PDF [27]. The probability of solar irradiance (G) following lognormal PDF with mean μ and standard deviation σ is: Weibull fitting (2) The output of solar power The output of the solar power depends on the solar irradiance (G), which follows the lognormal PDF [27]. The probability of solar irradiance (G) following lognormal PDF with mean µ and standard deviation σ is: In this paper, µ = 6 σ = 0.6 and G = 483 W/m 2 were based on [28]. The mean of the lognormal distribution is defined as: The solar irradiance (G) to energy conversion for solar PV is given by [29] where G std is the solar irradiance in a standard environmental set as 800 W/m 2 . R c is a certain irradiance point set as 120 W/m 2 . P sr is the rated output power of the solar PV unit. Similarly, Figure 3 was obtained through Monte Carlo simulation by the sample size of 10,000 [28].

Scenario Setting
This study mainly concerned three key time nodes in the path of achieving the carbon peak of China during the energy-water-carbon nexus optimization in Inner Mongolia, including 2021, 2025, and 2030. Different non-renewable and renewable technologies were taken into consideration to meet not only the electric power demand and the CO2 emissions mitigation target but also the water conservation goals. As the Chinese government announced that by 2020, China's CO2 emissions intensity targets would fall by 40%~45% based on 2005's level, by 2030, the CO2 emissions intensity targets would fall by 60%~65% based on 2005's level, and the carbon emissions peak of China would be achieved. In this study, we assumed that the upper bound of these targets could be achieved as scheduled. Three CO2 emissions mitigation scenarios were set based on this official statement in these planning periods. The CO2 emissions' intensity in 2005 was the baseline. For example, GHG intensity will decrease by 45% of that in 2005 in period t=1 (2021), and it will be 60% and 65% of the baseline in the next two periods, respectively. Meanwhile, three different electricity demand levels (low, medium, and high) with different occurrence probability Lognormal fitting

Scenario Setting
This study mainly concerned three key time nodes in the path of achieving the carbon peak of China during the energy-water-carbon nexus optimization in Inner Mongolia, including 2021, 2025, and 2030. Different non-renewable and renewable technologies were taken into consideration to meet not only the electric power demand and the CO 2 emissions mitigation target but also the water conservation goals. As the Chinese government announced that by 2020, China's CO 2 emissions intensity targets would fall by 40%~45% based on 2005's level, by 2030, the CO 2 emissions intensity targets would fall by 60%~65% based on 2005's level, and the carbon emissions peak of China would be achieved. In this study, we assumed that the upper bound of these targets could be achieved as scheduled. Three CO 2 emissions mitigation scenarios were set based on this official statement in these planning periods. The CO 2 emissions' intensity in 2005 was the baseline. For example, GHG intensity will decrease by 45% of that in 2005 in period t = 1 (2021), and it will be 60% and 65% of the baseline in the next two periods, respectively. Meanwhile, three different electricity demand levels (low, medium, and high) with different occurrence probability were designed to cover different electricity supply likelihoods. As Inner Mongolia is located in a typical semi-arid region with drought-stressed water resources, two possible water conservation policy scenarios were taken into account, including three main cooling technologies in each scenario. The mix of these scenarios will help investigate the energywater-carbon nexus during the achievement of the carbon emissions peak path in 2030. The detailed, flexible, and strict data were based on the national water intake standard: Water Quota Part I: Thermal Power (GB/T18916) [30] and Water Saving Enterprise: Thermal Power Industry (GB/T26925-2011) [31], which is shown in Table 2. The pre-regulated installation capacity of each power technology is presented in Table 3. The key parameters of the PCIO model are shown in Table 4.

The Uncertainty Simulation in Different Periods
(1) The fuel price prediction Figure 4 indicates that the fuel prices from 2015 to 2030 in Inner Mongolia showed an upward trend for both coal and natural gas. However, the performances of the coal price and natural gas were fairly different. Generally, the price of coal showed an increasing trend over the whole planning horizon, while they had relatively dramatic fluctuations under some scenarios. The highest coal price in Inner Mongolia would increase to 726.18 yuan/tonne in 2030. The variation of the natural gas price showed different performances before and after 2022. It showed that from 2015 to 2022, the natural gas price had an apparent increasing trend, while it showed fluctuations after 2022 until 2030, which means that uncertainty during the prediction process made it difficult to forecast the nature gas price after 2022. To make the price prediction of two fuels available for the PCIO model, the price values in each period using the mean value under 16 scenarios were adopted to avoid the predictive deviation.
(2) The output prediction of wind and solar power Figure 5 shows the output prediction results of the wind and solar power in four seasons under three planning periods. It indicates that both the output of wind and solar power showed seasonal variation. For wind power, the simulation result showed that spring and winter were the main seasons that generate power in Inner Mongolia. Meanwhile, the peak output of wind power varied at different times of the day. For example, in spring, the peak output of the wind power appeared from 5:00 to 9:00 am, while in winter, it appeared from 20:00 to 23:00. Through the adjustment of shape factor and scale factor in period t=2 and t=3, the output simulation in these two periods could be executed. It indicates that the output of the wind power in t=2 and t=3 showed similar performances. The peak output of solar power also varied at different times of the day and different seasons.  726.18 yuan/tonne in 2030. The variation of the natural gas price showed different performances before and after 2022. It showed that from 2015 to 2022, the natural gas price had an apparent increasing trend, while it showed fluctuations after 2022 until 2030, which means that uncertainty during the prediction process made it difficult to forecast the nature gas price after 2022. To make the price prediction of two fuels available for the PCIO model, the price values in each period using the mean value under 16 scenarios were adopted to avoid the predictive deviation.
(2) The output prediction of wind and solar power Figure 5 shows the output prediction results of the wind and solar power in four seasons under three planning periods. It indicates that both the output of wind and solar power showed seasonal variation. For wind power, the simulation result showed that spring and winter were the main seasons that generate power in Inner Mongolia. Meanwhile, the peak output of wind power varied at different times of the day. For example, in spring, the peak output of the wind power appeared from 5:00 to 9:00 am, while in winter, it appeared from 20:00 to 23:00. Through the adjustment of shape factor and scale factor in period t=2 and t=3, the output simulation in these two periods could be executed. It indicates that the output of the wind power in t=2 and t=3 showed similar performances. The peak output of solar power also varied at different times of the day and different seasons.

The Optimized Electricity Supply and Cooling Technologies
Optimized solutions for electricity supply scheme and cooling technologies in Inner Mongolia are presented in Figure 6. It indicates that the amount of coal-fired power showed a downward trend from t=1 to t=3, while the strict water withdrawals scenario further decreased the amount of coal-fired power generation compared with the flexible one. The average decreasing amplitude under each demand level would be 9%, 5%, and 4% in period t=1, t=2 and t=3, respectively. Gas-fired power, wind power, and solar power showed an increasing trend as time goes on to make up the power generation shortage because of the reduction in coal-fired power. Meanwhile, the electric power production from wind and solar power was larger in the strict water policy scenario than in the flexible one. The phenomena could be attributed to the fact that wind power and solar power consumed no water during the power generation process, so strict water withdrawals policy resulted in more wind and solar power instead of coal-fired and gasfired power in Inner Mongolia. The distribution of three cooling technologies of coal-fired and gas-fired power in different time periods under different water withdrawals policy and power demand levels is also presented in Figure 5. It indicates that the air-cooling system would play the most important role when the strict water withdrawals policy is executed in Inner Mongolia, especially when the power demand level was medium and high, it increased by 77.53% (medium power demand) and 82.17% (high power demand) when t=1, 69.50% and 71.56% when t=2 and 64.74% and 57.53% when t=3 for the coal-fired power. The phenomenon showed that the strict water policy would be a powerful push on the application of the air-cooling system for coal-fired power. The installation capacity of coal-fired power also showed that as time goes on, the air-cooling system will replace the dominant position of the cycling cooling system and one through system. In 2035, the installation capacity of coal-fired with air-cooling technology would reach 70.64 GWh (flexible scenario) and 116.37 GWh (strict scenario). Meanwhile, the one-through system would gradually be replaced by the other two cooling technologies.

Capacity Expansion
The CO2 emissions up to the peak (CEUP) target and water withdrawal policies in the planning periods may greatly impact the power sources structure in Inner Mongolia. We analyzed the distributions of the generation capacity of Inner Mongolia for each technology under four scenarios in 2030 and tried to find out the interactions between the capacity expansion schemes and environmental limits. In Figure 7, the 65% CO2 emissions reduction on the base of 2005 was the CO2 limit. The flexible and strict water withdrawal policies coupled with this CO2 reduction level was chosen to investigate the mixed impact of CO2 and water constraints on the capacity expansion in 2030. The box-and-whisker diagram shows different impacts from different scenarios on the capacity expansion in Inner Mongolia. The boundary closest to zero is the first quartile, the one closest to the top indicates the 75th percentile, and the line within the box marks the median, error bars above Figure 6. The optimized electric power generation and capture and storage technology (CCS) scheme (ACS, OTS, and CCS denote the air-cooling system, the one-through system, and the cycling cooling system, respectively).

Capacity Expansion
The CO 2 emissions up to the peak (CEUP) target and water withdrawal policies in the planning periods may greatly impact the power sources structure in Inner Mongolia. We analyzed the distributions of the generation capacity of Inner Mongolia for each technology under four scenarios in 2030 and tried to find out the interactions between the capacity expansion schemes and environmental limits. In Figure 7, the 65% CO 2 emissions reduction on the base of 2005 was the CO 2 limit. The flexible and strict water withdrawal policies coupled with this CO 2 reduction level was chosen to investigate the mixed impact of CO 2 and water constraints on the capacity expansion in 2030. The box-and-whisker diagram shows different impacts from different scenarios on the capacity expansion in Inner Mongolia. The boundary closest to zero is the first quartile, the one closest to the top indicates the 75th percentile, and the line within the box marks the median, error bars above and below the box indicate the 90th and 10th percentiles, respectively. Moreover, the dots above or below the error bars represent the 5th and 95th percentiles.
Results indicated that the capacity expansion of different technologies had different appearances in mixed scenarios. Take the coal-fired power as an example, the mid hinge turned into a lower level, which meant the average amount of capacity expansion decreased (nearly 20%~50% reduction), and the dispersion of the distribution mainly aggregated on the low-capacity level (less than 30 GW for the coal-fired power) when the CO 2 limit and water constraints were taken into account. The performance of the average amount of the capacity expansion for the CO 2 limit and that coupled with the flexible water was approximately the same, although their distribution was different. When the strict water limit was involved, the average amount of capacity expansion showed the lowest level, which was just less than 10 GW. It indicated that the strict water policy dramatically reduced the capacity expansion amount of coal-fired power. For the gas-fired power, the skewness of gas-fired turned to a higher level (increased by 40%) when the CO 2 limit was taken into account. Moreover, the capacity expansion would be further promoted when the water limits were present, especially for the strict one.
The other two technologies show the same performance as the gas-fired power, which was in the presence of CO 2 limit, the amount of capacity expansion would be promoted, and water limits would further increase the amount of capacity expansion. The reason can be attributed to the fact that coal-fired power has higher CO 2 emissions and water withdrawals for cooling. The joint constraints from the CO 2 emissions limit and water withdrawals limit will lead to a substantial reduction in CO 2 and water withdrawals. Gas-fired and the other two technologies with fewer water withdrawals and emissions will have a large potential to make up the capacity gap when the amount of coal-fired power decrease.

The CO2 Emissions and Water Withdrawals
The installation level of CCS devices, the amount of CO2 emissions, and the CO2 reduction levels in Inner Mongolia are shown in Figure 8. It indicates that more CCS devices were acquired under the flexible water withdrawals scenario than the strict one. Compared with the flexible scenario, almost 10.19%, 15.78%, and 27.98% fewer CCS devices were required under the strict water scenario when the power demand level was low, medium, and high, respectively. The result indicates that strict water policy not only helps to decrease the water withdrawals but also indirectly leads to the CO2 emissions' mitigation because of the reduction in the thermal power (coal-fired and gas-fired) installations.

The CO 2 Emissions and Water Withdrawals
The installation level of CCS devices, the amount of CO 2 emissions, and the CO 2 reduction levels in Inner Mongolia are shown in Figure 8. It indicates that more CCS devices were acquired under the flexible water withdrawals scenario than the strict one. Compared with the flexible scenario, almost 10.19%, 15.78%, and 27.98% fewer CCS devices were required under the strict water scenario when the power demand level was low, medium, and high, respectively. The result indicates that strict water policy not only helps to decrease the water withdrawals but also indirectly leads to the CO 2 emissions' mitigation because of the reduction in the thermal power (coal-fired and gas-fired) installations. With the help of the CCS devices, the CO 2 emissions showed a decreasing trend in Inner Mongolia as time goes on to realize the target of reaching the CO 2 emissions peak of China in 2030. For example, the amount of CO 2 emissions was 10,015 × 10 10 tonne in t=1, 9634 × 10 10 tonne in t=2, and 8635 × 10 10 tonne in t=3 when the power demand level was low, while when the power demand level was high, the CO 2 emission was 14795 × 10 10 tonne, 12,689 × 10 10 tonne, and 11158 × 10 10 tonne in t=1,2, and 3, respectively. Meanwhile, the CO 2 reduction through the CCS devices showed an increasing trend as time goes on. Higher power demand led to more CO 2 emissions reduction to meet the CO 2 emissions criteria.
The water withdrawals and system cost are shown in Figure 9. It indicates that the strict water policy had an apparent effect on the reduction in water withdrawals than the flexible water policy. For example, the water withdrawals decreased by 41.02%, 48.28%, and 59.07% in t=1,2, and 3 when the power demand was low. The system cost showed an increasing trend as time goes on, and the result also showed that increasing power demand level led to an increase in the system cost. The system cost under the flexible water withdrawal policy led to an average level of 16.32%, 13.76%, and 7.36% reduction than that under the strict policy when the demand level was low, medium, and high. The reason can be attributed to the fact that on the one hand, more air-cooling technologies will take the place of the once-through or the cycling cooling system to reach the water reduction target, which may result in higher system cost; on the other hand, more renewable power technologies, whose water consumption can even be neglected but with higher fixed investment fees, will be applied instead of the thermal power technologies, especially the coal-fired power under the strict water policy, which will further lead to the increase in the system cost. Although the thermal power showed a decreasing trend as time goes on, more CCS devices were still necessary to achieve the more and more strict CO2 emissions target, and this was the third sector, which led to the increase in the system cost. Generally, under the triple constraints of power demand, water policy, and carbon emissions mitigation, more system costs should be invested to help reach the synergetic energy-economy-environment goals in the EPS of Inner Mongolia.  The water withdrawals and system cost are shown in Figure 9. It indicates that the strict water policy had an apparent effect on the reduction in water withdrawals than the flexible water policy. For example, the water withdrawals decreased by 41.02%, 48.28%, and 59.07% in t=1,2, and 3 when the power demand was low. The system cost showed an increasing trend as time goes on, and the result also showed that increasing power demand level led to an increase in the system cost. The system cost under the flexible water withdrawal policy led to an average level of 16.32%, 13.76%, and 7.36% reduction than that under the strict policy when the demand level was low, medium, and high. The reason can be attributed to the fact that on the one hand, more air-cooling technologies will take the place of the once-through or the cycling cooling system to reach the water reduction target, which may result in higher system cost; on the other hand, more renewable power technologies, whose water consumption can even be neglected but with higher fixed investment fees, will be applied instead of the thermal power technologies, especially the coal-fired power under the strict water policy, which will further lead to the increase in the system cost. Although the thermal power showed a decreasing trend as time goes on, more CCS devices were still necessary to achieve the more and more strict CO 2 emissions target, and this was the third sector, which led to the increase in the system cost. Generally, under the triple constraints of power demand, water policy, and carbon emissions mitigation, more system costs should be invested to help reach the synergetic energy-economy-environment goals in the EPS of Inner Mongolia. 2021, 14, x FOR PEER REVIEW 5 of 23 Figure 9. The water withdrawals and system cost.

The Optimized Penetration and Satisfaction Degree
The optimized result of renewable energy penetration and satisfaction degree of the system is shown in Table 5. The renewable penetration showed an increasing trend as time goes on, and the strict water withdrawal policy led to a higher renewable penetration rate in each planning period. For example, in t=2, the renewable penetration rate under the strict water policy was 3.58% more than that under the flexible one. However, the satisfaction degree of the system, which implies that each part of the system has reached its best balance, had different performances. The supreme satisfaction degree (λ=0.9523) appeared in t=2 under the strict water withdrawal policy, which means that the renewable penetration rate and the system cost achieved the optimal tradeoff under the CO2 emissions reduction level in the period t=2. The satisfaction degree helps quantize the overall system satisfaction level. Decision-makers can evaluate and adjust their optimized strategies based on the satisfaction degree.

Conclusion
This study proposed a patron-client interactive optimized (PCIO) model to investigate the energy-water-carbon nexus optimization in Inner Mongolia under the policy background of 2030 CO2 emissions up to the peak target in China, concerning the uncertainty of fuel price and output of the wind and solar power. PICO model not only had the ability to tackle problems with the hierarchical relationship and achieved the proper tradeoffs between maximizing the renewable power penetration and minimizing the system cost but also synergistically dealt with multiple optimized targets, including the power supply and capacity expansion schemes, water consumption control through the combination of different cooling techniques and CO2 emissions mitigation target with the CCS device.

The Optimized Penetration and Satisfaction Degree
The optimized result of renewable energy penetration and satisfaction degree of the system is shown in Table 5. The renewable penetration showed an increasing trend as time goes on, and the strict water withdrawal policy led to a higher renewable penetration rate in each planning period. For example, in t=2, the renewable penetration rate under the strict water policy was 3.58% more than that under the flexible one. However, the satisfaction degree of the system, which implies that each part of the system has reached its best balance, had different performances. The supreme satisfaction degree (λ=0.9523) appeared in t=2 under the strict water withdrawal policy, which means that the renewable penetration rate and the system cost achieved the optimal tradeoff under the CO 2 emissions reduction level in the period t=2. The satisfaction degree helps quantize the overall system satisfaction level. Decision-makers can evaluate and adjust their optimized strategies based on the satisfaction degree.

Conclusions
This study proposed a patron-client interactive optimized (PCIO) model to investigate the energy-water-carbon nexus optimization in Inner Mongolia under the policy background of 2030 CO 2 emissions up to the peak target in China, concerning the uncertainty of fuel price and output of the wind and solar power. PICO model not only had the ability to tackle problems with the hierarchical relationship and achieved the proper tradeoffs between maximizing the renewable power penetration and minimizing the system cost but also synergistically dealt with multiple optimized targets, including the power supply and capacity expansion schemes, water consumption control through the combination of different cooling techniques and CO 2 emissions mitigation target with the CCS device.
The optimized results indicated that the coal-fired power showed a downward trend during the whole planning horizon under the CEUP target in Inner Mongolia. Gas-fired and renewable power will continuously substitute the place of coal-fired power in this region. The strict water withdrawal policy further exacerbated the substitution effect of the coalfired power by wind and solar power, with an average level of 9%, 5%, and 4% in three periods. To achieve both the CEUP and water-saving target, the CCS device and the aircooling system will play gradually important roles in Inner Mongolia's EPS, especially in the strict water withdrawal scenario, even when the coal-fired power decreases as time goes on. However, these targets will be achieved at the expense of high system costs, which may increase the financial burden of the local government of Inner Mongolia. The PICO model makes it possible to make reasonable tradeoffs between maximizing the renewable energy proportion and minimizing the system costs through the quantized satisfaction degree. Decision-makers can make flexible strategies through the adjustment of the membership function of the PICO model.
As Inner Mongolia is a major energy supply province, which shoulders the responsibility of transferring the electric power resource to other regions (mainly to the Jing-Jin-Hebei region), the potential impacts on the local energy-water-carbon nexus when transmitting energy to other regions should also be taken into consideration. Meanwhile, wind and solar power generation curtailment may also be core concerns with respect to the CEUP target in Inner Mongolia, which will also be investigated in our future studies.