Water Resources Allocation Method and Model for Basin Multidimensional System Based on Marginal Benefit Optimization

Abstract

The present invention provides a copula stochastic fractional programming model and a water resource allocation method for the water resource allocation of a multi-dimensional system in a basin based on marginal benefit optimization. By examining the water resource allocation schemes under different probability combination scenarios, analyzing the complex relationship between water - power - arable land resource shortages and default risks, a series of schemes under different scenarios are proposed. At the same time, through fractional programming, the trade-off relationship between system efficiency and environmental default risks is deeply analyzed, providing suggestions for decision-making considering comprehensive environmental, economic, and system reliability factors.

Description

Technical Field

[0001] The present invention relates to the technical field of resource utilization, and particularly relates to a method for water resource allocation of a basin multi-dimensional system based on marginal benefit optimization. Background Art

[0002] As important resources for social and economic production, water, food, and energy are mutually restrictive and inseparable. Studying the correlation relationship and coordinated development level of the water resource - food - energy system is of great significance for promoting regional sustainable development. To meet the growing economic development and food demand, large-scale farmland irrigation and inefficient irrigation models have caused a large amount of water resources to be wasted. At the same time, to solve the power gap problem, the impoundment regulation of basin reservoir power stations has also led to a large amount of water resources being occupied, thus affecting the living and production activities in downstream areas. Water resource shortage will not only trigger food and energy supply crises, but also cause a series of ecological environment problems such as wetland degradation, lake shrinkage, and soil salinization. To ensure basin security and sustainable social and economic development, the comprehensive management of the water - food - energy correlation system is imminent.

[0003] There are many uncertainties and complexities in the basin water resource - energy - food multi-dimensional system. First, the processes of water resource allocation, energy production, and food production are interrelated, and any change in system elements will bring different system responses, thus triggering the joint risks of the basin multi-dimensional system. Second, affected by natural and social and economic conditions, the components of the water - energy - food correlation system and their relationships often have uncertainties. For example, the available water resources usually show a random distribution with runoff, and the random water resources will in turn cause changes in cultivated land area and hydropower production. These uncertain elements and their complex interactions exacerbate the competition among users and affect the accuracy and reliability of decision-making. However, existing stochastic programming can often only solve the single uncertainty of parameters and cannot quantitatively characterize the interaction of random parameters in the multi-dimensional system. In addition, different decision-makers often have different decision-making preferences, such as maximizing economic benefits and minimizing resource utilization. Most existing multi-objective optimization methods often require preset subjective weights and cannot effectively quantify system efficiency and balance the conflict between economic development and resource conservation. Therefore, the present application introduces the copula stochastic fractional programming method and applies it to the management and planning of the basin water resource multi-dimensional system to reflect and handle this uncertainty and complexity, optimize the system marginal benefit, and provide technical support for the generation of decision-making schemes. Summary of the Invention

[0004] To overcome the defects existing in the prior art, in view of the complex correlation relationship of the water, energy and food systems and the problem of low water resource utilization efficiency, the present invention studies the actual water resource allocation and water consumption in the agricultural, power and food production sectors, abstracts a mathematical model, and constructs a copula stochastic fractional programming model system to solve the problem of low utilization efficiency.

[0005] To solve the above technical problems, the present invention provides a copula stochastic fractional programming model for water resource allocation of a basin multi-dimensional system based on marginal benefit optimization. The specific model is as follows: objective function: optimization of water distribution marginal benefit.

[0006]

[0007] The constraint conditions are as follows.

[0008] Constraint on the available water volume for each user:

[0009]

[0010] Constraint on the maximum hydropower production capacity of the basin:

[0011]

[0012] Constraint on the cultivated land area:

[0013]

[0014] Joint probability constraint:

[0015] C(1 - p 1 , 1 - p 2 , 1 - p 3 ) = 1 - p,

[0016] Food security constraint:

[0017]

[0018] Power security constraint:

[0019]

[0020] Reservoir water volume balance constraint:

[0021]

[0022] Reservoir storage capacity constraint:

[0023]

[0024] Water resource transmission and distribution power constraint:

[0025]

[0026] Water demand constraints of other departments:

[0027]

[0028] Among them, f is the optimal marginal benefit; AW ijt is the agricultural water allocation volume of crop j in region i at time t, HW nt is the hydropower water allocation volume of reservoir n at time t, OW ist is the water allocation volume of other water use department s; BA ijt , BH nt , BO ist are the unit water allocation benefits of the agricultural, hydropower and other water use departments at time t respectively; γ ijt is the water allocation efficiency of region i at time t, LF ijt is the leaching fraction of crop j in region i at time t, is the power generation per unit water consumption; TSA t is the total available water volume of the basin at time t, MHP t is the total hydropower generation capacity of the basin at time t, AA t is the maximum arable land area of the basin at time t; WPC ijt is the water demand per unit planting area of crop j in region i at time t; ED it is the minimum power demand of region i; YA ijt is the yield of crop j in region i at time t; FD it is the per capita food demand in region i at time t; PO it is the population quantity in region i at time t; EPW nt is the evaporation of reservoir n; HS nt is the water demand of reservoir n; HS nmin , HS nmax are the minimum reservoir capacity and the designed reservoir capacity respectively; ESW it is the power consumption per unit water allocation in region i at time t; OWD ist is the minimum water demand of water use department s in region i; MOW ist is the maximum water allocation of water use department s in region i; p is the joint probability, p 1 , p 2 and p 3 are the independent probabilities of the available quantity constraints of water resources, hydropower and arable land resources respectively.

[0029] Since the available quantity of water resources in the above model presents a normal distribution form, which in turn affects the random normal distributions of the arable land area and hydropower production volume, the normal distributions of the water resources, hydropower production volume and arable land area mentioned above respectively refer to the expected values of μ 1 , μ 2 , μ3 , with a standard deviation of σ 1 、σ 2 、σ 3 For the random probability distribution of σ, σ, σ, since the model is a non - linear model and difficult to solve, the inverse function φ of probability is introduced 1 -1 (1 - p 1 )、φ 2 -1 (1 - p 2 )、φ 3 -1 (1 - p 3 ), the and in the above model can be respectively transformed into linear constraints:

[0030]

[0031]

[0032]

[0033] Through the copula method of multi - variable joint distribution modeling, the marginal probability distributions of each constraint condition can be connected by the copula function C(φ 1 -1 (1 - p 1 ), φ 2 -1 (1 - p 2 ), φ 3 -1 (1 - p 3 )) to determine the joint probability distribution constraint of the system. According to the fractional programming algorithm, the parameter is introduced, and at the same time, the above linearized constraint conditions are introduced to reconstruct the linear model as follows:

[0034] Objective function: Optimization of the marginal benefit of water distribution

[0035]

[0036] Constraint conditions:

[0037] Fractional linearization constraint:

[0038]

[0039] 0 < r < 1

[0040] Constraint on the available water volume for each user:

[0041]

[0042] Constraint on the maximum hydropower production capacity of the river basin:

[0043]

[0044] Constraint on cultivated land area:

[0045]

[0046] Joint probability constraint:

[0047] C(φ 1 -1 (1 - p 1 ), φ 2 -1 (1 - p 2 ), φ 3 -1 (1 - p 3 )) = 1 - p

[0048] Food security constraint:

[0049]

[0050] Power security constraint:

[0051]

[0052] Reservoir water balance constraint:

[0053]

[0054] Reservoir storage capacity constraint:

[0055]

[0056] Water resource allocation for power constraint:

[0057]

[0058] Water demand constraint for other sectors:

[0059]

[0060] The optimal solution AW of the transformed model ijt * , HW nt * , OW ist * can be easily obtained. Then the variable AW of the original model ijt * = AW ijt ·r, HW nt * = HW nt·r, OW ist * = OW ist ·r。

[0061] The present invention also provides a method for water resources allocation using the above copula stochastic fractional programming model, which includes:

[0062] a. Conduct an investigation on the target, and determine the method of the model, the objective function of the model, and the system constraints according to the actual situation; the objective function includes: under the condition of limited available water resources, reasonably allocate water volume and water distribution benefits for each user in the basin multi-dimensional system; the system constraints include the water volume balance constraint, energy supply and demand balance constraint, reservoir safety constraint, food security constraint, and water demand constraints of each department in each period of the basin;

[0063] b. Collect the required data, obtain the input data through investigation yearbooks, government announcements, and literature, and process the original data through interpolation and extrapolation statistical methods to obtain continuous statistical data that meets the model calculation;

[0064] c. Select software and program for calculation. The calculation results include: fitting the available water resources volume, hydropower production volume, and arable land area in the basin according to the statistical data to obtain the random distribution, constructing the best copula function for the three types of random distribution functions, and determining different independent and joint probability level combination scenarios; substituting into the stochastic fractional model to calculate the water resources allocation volume for each user, the system marginal benefit, the hydropower production mode, and the food planting structure under different joint risk levels;

[0065] d. According to the calculation results, arrange the water resources allocation plan for each subsystem, and arrange production according to the power production and food planting modes obtained under different probability levels to achieve the optimal marginal benefit.

[0066] The present invention introduces fractional programming and uncertainty optimization technologies and applies them to the management planning of basin water resources and water environment, providing a scientific basis and technical support for the comprehensive decision-making of the basin, and providing strong technical support for the basin to adjust the industrial structure, optimize the marginal benefit of water use, reasonably plan the management of water resources and water environment, and formulate management measures and control schemes that conform to regional characteristics.

[0067] Advantages of the present invention

[0068] The present invention can not only effectively handle the complex correlation relationships among random uncertainties in the multi-dimensional system of a basin, but also optimize the marginal benefit and balance the conflict between resource utilization and economic development. By examining the water resource allocation schemes under different probability combination scenarios, analyzing the complex relationships among water - power - arable land resource shortages and default risks, a series of schemes under different scenarios are proposed. At the same time, through fractional programming, the trade-off relationship between system efficiency and environmental default risk is deeply analyzed, providing suggestions for decision-making considering comprehensive environmental, economic, and system reliability factors. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A framework diagram of a copula stochastic fractional programming model system;

[0070] Figure 2 The marginal benefit and water resource allocation quantity results of eight embodiments;

[0071] Figure 3 The hydropower production and water allocation quantity results in different periods. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] The following uses embodiments to elaborate in detail on the implementation manner of the present invention, so as to fully understand how the present invention uses technical means to solve technical problems and the implementation process of achieving technical effects and implement accordingly.

[0073] In the present invention, the developed copula stochastic fractional programming model is applied to the management of the multi-dimensional system of a basin, aiming to optimize the water resource utilization efficiency, balance the conflict between resource protection and economic development, and provide a trade-off analysis between the joint risks and marginal benefits of water - energy - food within the system, providing flexible decision-making schemes for managers. Through the comparative analysis of the simulation results of the expected value model and the chance-constrained programming model, it can be obtained that under the chance-constrained programming model, with different values of the probability level p, it can be used to describe the decision-making behaviors of decision-makers with different risk preferences.

[0074] In the multi-dimensional system of a basin, affected by factors such as temperature, precipitation, and evapotranspiration, the available water resources usually show a random distribution with runoff. The random water resource quantity will further cause changes in the arable land area and hydropower output, resulting in the water - energy - food system facing the risk of joint shortages. At the same time, with the increasing tension of the water resource supply - demand relationship, how to optimize the marginal benefit of water allocation and improve the sustainability of system management has become the key to solving the ecological crisis of the basin system. Therefore, a stochastic fractional programming method is needed to handle the randomness, complexity, and joint probability risk characteristics of the multi-dimensional management system of the basin, providing a practical water resource allocation scheme for decision-makers. The following uses the copula stochastic fractional programming method to study the water resource allocation system within three planning periods.

[0075] The method for water resources allocation in a river basin system based on the copula stochastic fractional programming model of the present invention is carried out according to the following steps:

[0076] a. Conduct an investigation on the target system, and determine the method of the model, the objective function of the model, and system constraints according to the actual situation; the objective function includes: under the condition of limited available water resources, reasonably allocating water volume and water distribution benefits among users in the multi-dimensional river basin system; the system constraints include water volume balance constraints, energy supply and demand balance constraints, reservoir safety constraints, food security constraints, and water demand constraints of each department in each period of the river basin;

[0077] b. Collect the required data, obtain the input data through investigation yearbooks, government announcements, and literature, and process the original data through interpolation and extrapolation statistical methods to obtain continuous statistical data that conforms to model calculations;

[0078] c. Select software and program for calculation. The results of the calculation include: fitting the available water resources volume, hydropower production volume, and arable land area in the river basin according to the statistical data to obtain their random distributions, constructing the best copula function for the three types of random distribution functions, and determining different combinations of independent and joint probability levels; substituting into the stochastic fractional model to calculate the water resources allocation volume of each user, the system marginal benefit, the hydropower production mode, and the food planting structure under different combined risk levels;

[0079] d. According to the calculation results, arrange the water resources allocation plan for each subsystem, and arrange production according to the power production and food planting modes obtained under different probability levels to achieve the optimal marginal benefit.

[0080] The following table is the basic data.

[0081] Table 1 Joint probability values

[0082] Table 2 Model input data

[0083] Table 1 Joint probability values

[0084]

[0085] Table 2 Model input data

[0086]

[0087] Table 1 represents the distributions of 8 joint probability examples based on the copula function. Among them, the joint random probability levels are 0.01, 0.10, 0.15, and 0.20. Each joint probability level corresponds to 4 combinations of independent probability levels, totaling 8 sets of scenario examples. Table 2 shows the upper limit values of water resources, cultivated land area, and hydropower production corresponding to 8 joint probability levels, which are used in the copula stochastic fractional programming model. Assuming ten joint probability levels, detailed results of the water resource shortage situation and the water resource allocation obtained by different sectors at the corresponding probability levels can be obtained. At the same time, the corresponding marginal benefits and the changing trends of the water allocation for each user can be explored when the joint probability level changes from high to low, providing a measure of the water resource allocation under the multi-dimensional risks of the system for water resource managers.

[0088] The results of this copula stochastic fractional programming show that different default probability levels and their combinations will lead to different marginal benefits and water resource allocation patterns. Figure 2 They are the marginal benefits and water allocations for 8 examples. Among them, the lowest marginal benefit and the lowest water allocation both occur in the S1 scenario of the example, which are 1.43 $ / m 3 and 0.55×10 12 m 3 (joint probability p = 0.01); the highest marginal benefit and the highest water allocation both appear in the S8 scenario of the example, which are 1.47 $ / m 3 and 0.65×10 12 m 3 (p = 0.20). Generally speaking, as the joint default probability increases, the marginal benefit will increase, and vice versa. This is mainly because as p increases, the default risk of the water - energy - food correlation system increases, thus expanding the decision - making space and being more conducive to optimizing the marginal benefit. However, this also corresponds to a decrease in the reliability level of the system decision - making. In addition, different default probability levels will also change the water allocation structure of the agricultural and power sectors. From the perspective of the proportion of water allocation for each user, agriculture is the main water - consuming user in the basin. As the default probability decreases, the proportion of agricultural water resources will decrease from 62.9% in the S8 example to 56.4% in the S1 example. Specifically, as the independent default risk level p 1 decreases, the proportion of water allocation for animal husbandry will decrease, and the proportion of water allocation for cash crops will increase. This is because animal husbandry has the characteristics of high feeding costs and large water requirements. In the case of water shortage, more water will be allocated to the cultivation of cash crops to avoid a large amount of waste. Figure 3 They are the hydropower generation and their water allocations for each period. With the soaring of energy demand and the increase in power generation capacity, the power generation will increase throughout the planning period. For example, in the S5 scenario, the hydropower output in the basin will increase from 245.6×10 12 kWh in the t = 1 period to 255.9×10 12kWh (t = 3), and the water allocation for hydropower generation will increase by 0.6% over time.

[0089] In summary, in the multi-dimensional management system of water resources - energy - food in the set basin, the marginal benefit of system water allocation can be significantly improved, and the water resource demands of each user are competitively met. The system joint and independent probabilities present the risks of violating the constraints of the available amounts of water resources, electricity, and arable land resources. The results show that different joint probabilities correspond to the risks of violating different resource shortages, leading to different marginal benefits and water resource allocation patterns.

[0090] Implementing this intellectual property right first and foremost as described above does not set restrictions on other forms of implementing such new products and / or new methods. Those skilled in the art will use this important information to modify the above content to achieve similar implementation scenarios. However, all modifications or adaptations based on the new products of the present invention are within the reserved rights.

[0091] As described above, it is only a preferred embodiment of the present invention and not a limitation in other forms. Any person skilled in the relevant art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes, and adaptations made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A construction method of a copula stochastic fractional programming model for water resources allocation in a multi-dimensional basin system based on marginal benefit optimization, Characterized in that: The model is specifically: Objective function: Optimization of water distribution marginal benefit, The constraints are as follows, Available water volume constraint for each user: Maximum hydropower production capacity constraint of the basin: Cultivated land area constraint: Joint probability constraint: C(1 - p 1 , 1 - p 2 , 1 - p 3 ) = 1 - p, Food security constraint: Power security constraint: Reservoir water balance constraint: Reservoir storage capacity constraint: Water resource transmission and distribution power constraint: Water demand constraint for other departments: Among them, f is the optimal marginal benefit; AW ijt is the agricultural water allocation volume of crop j in region i at time t, HW nt is the hydropower water allocation volume of reservoir n at time t, OW ist is the water allocation volume of other water use department s; BA ijt 、BH nt 、BO ist are the unit water allocation benefits of agriculture, hydropower and other water use departments at time t respectively; γ ijt is the water allocation efficiency of region i at time t, LF ijt is the leaching fraction of crop j in region i at time t, is the electricity generation per unit of water consumption; TSA t is the total available water volume of the basin at time t, MHP t is the total hydropower generation capacity of the basin at time t, AA t is the maximum arable land area of the basin at time t; WPC ijt is the water requirement per unit planting area of crop j in region i at time t; ED it is the minimum electricity demand of region i; YA ijt is the yield of crop j in region i at time t; FD it is the per capita food demand in region i at time t; PO it is the population quantity of region i at time t; EPW nt is the evaporation of reservoir n; HS nt is the water requirement of reservoir n; HS nmin 、HS nmax are the minimum reservoir capacity and the designed reservoir capacity respectively; ESW it is the unit water allocation power consumption in region i at time t; OWD ist is the minimum water requirement of water use department s in region i; MOW ist is the maximum water allocation volume of water use department s in region i; p is the joint probability, p 1 ,p 2 and p 3 are the independent probabilities of the availability constraints of water resources, hydropower and arable land resources respectively.

2. A method for water resources allocation using the copula stochastic fractional programming model described in claim 1, Characterized in that, It includes: a. Conduct an investigation on the objective, and determine the objective function and system constraints of the model according to the actual situation; The objective function includes: Under the condition of limited available water resources, reasonably allocate water volume and water distribution benefits for each user in the multi-dimensional basin system; The system constraints include water balance constraints in each period of the basin, energy supply and demand balance constraints, reservoir safety constraints, food security constraints, and water demand constraints for each department; b. Collect the required data, obtain the input data through investigation yearbooks, government announcements, and literature, and process the original data through interpolation and extrapolation statistical methods to obtain continuous statistical data that conforms to model calculations; c. Select software and program for calculation. The results of the calculation include: Fit the random distributions of the available water resources volume, hydropower production volume, and arable land area in the basin according to the statistical data, construct the best copula function for the three types of random distribution functions, and determine different independent and joint probability level combination scenarios; Substitute into the random distribution model to calculate the water resources allocation volume for each user, the system marginal benefit, the hydropower production mode, and the food planting structure under different joint risk levels; d. According to the calculation results, arrange the water resources allocation plan for each subsystem, and arrange production according to the power production and food planting modes obtained under different probability levels to achieve the optimal marginal benefit.

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