A method for quantifying flexibility of a seawater desalination plant

Abstract

The application discloses a method for quantifying flexibility of a seawater desalination plant, comprising the following steps: 1) obtaining basic parameters of the seawater desalination plant; 2) modeling equipment units of the seawater desalination plant to obtain equipment unit models of the seawater desalination plant; 3) establishing operation constraint conditions of the seawater desalination plant according to the equipment unit models of the seawater desalination plant; 4) performing convex processing on non-convex operation constraints in the operation constraint conditions of the seawater desalination plant to obtain linear operation constraints of the seawater desalination plant; 5) establishing a two-stage robust optimization model according to the linear operation constraints of the seawater desalination plant; and 6) solving the two-stage robust optimization model to obtain time-varying power intervals of interactive power between the seawater desalination plant and a power distribution network, so as to quantify flexibility of the seawater desalination plant. The application obtains a quantified value of flexibility of the seawater desalination plant, has good feasibility and applicability, and can effectively evaluate flexibility of the seawater desalination plant under various working conditions, and is an important basis for efficient participation of the seawater desalination plant in demand response.

Description

Technical Field

[0001] This invention relates to the field of demand response and flexibility quantification of seawater desalination plants, specifically a method for quantifying the flexibility of seawater desalination plants. Background Technology

[0002] As the proportion of renewable energy generation increases, the randomness and volatility of renewable energy sources such as wind and solar will lead to a continuous rise in the demand for frequency regulation, voltage regulation, and peak shaving in the power system. Traditional regulation resources mainly consist of thermal power plants and hydropower plants on the generation side. However, due to the limited quantity and capacity of these resources, and the high costs and long time required for their upgrading and expansion, they cannot meet the increasing regulation demands of the new power system. Therefore, the enormous flexibility inherent in demand-side resources has become an important resource for the development of the power system.

[0003] Seawater desalination plants are energy-intensive and flexible in operation, making them ideal resources for electricity demand response. For decades, desalination capacity has seen continuous growth. A scientific and reasonable assessment of the flexibility of desalination plants helps the power grid improve electricity pricing and incentive mechanisms, and is also a prerequisite for deeply exploring and effectively utilizing this resource.

[0004] Current research on the flexibility of seawater desalination plants mainly focuses on characterizing the power regulation characteristics of desalination plants and their interaction and coordination models with energy systems. Most studies only focus on the qualitative analysis of the flexibility of desalination plants, and no studies have yet conducted a quantitative assessment of the flexibility of desalination plants. Summary of the Invention

[0005] The purpose of this invention is to provide a method for quantifying the flexibility of a seawater desalination plant, comprising the following steps:

[0006] 1) Obtain the basic parameters of the seawater desalination plant;

[0007] 2) Based on the basic parameters of the seawater desalination plant, model the equipment units of the seawater desalination plant to obtain the equipment unit model of the seawater desalination plant;

[0008] 3) Based on the equipment unit model of the seawater desalination plant, establish the operating constraints of the seawater desalination plant, which include non-convex constraints and integer variables;

[0009] 4) Make the non-convex operating constraints in the operating constraints of the seawater desalination plant convex to obtain the linear operating constraints of the seawater desalination plant.

[0010] 5) Based on the linear operation constraints of the seawater desalination plant, establish a two-stage robust optimization model;

[0011] 6) Solve the two-stage robust optimization model to obtain the time-varying power range of the interaction power between the desalination plant and the power distribution network, so as to quantify the flexibility of the desalination plant.

[0012] Furthermore, the basic parameters of the seawater desalination plant include the predicted wind power of the power distribution network, freshwater load, seawater osmotic pressure, and seawater concentration.

[0013] Furthermore, the seawater desalination plant equipment unit model includes a water intake pump model, a reverse osmosis unit model, and an energy storage device model.

[0014] Furthermore, the water intake pump model includes the water intake pump power equation;

[0015] The power equation for the water intake pump is shown below:

[0016] (1)

[0017] In the formula, the subscript t represents the time period t; , and These represent the water intake pump power, water intake flow rate, and head for the t-th time period, respectively. and These are the density of water and the acceleration due to gravity, respectively. To improve the operating efficiency of the water pump.

[0018] Furthermore, the reverse osmosis unit model includes a high-pressure pump power equation and a high-pressure pump flow calculation equation;

[0019] The power equation for the high-pressure pump is shown below:

[0020] (2)

[0021] In the formula, the subscript t represents the time period t; , and These are the operating pressure, outlet flow rate, and high-pressure pump power of the high-pressure pump reverse osmosis unit d, respectively. This refers to the transmembrane osmotic pressure difference. and Let be a constant, and take respectively , ; R represents the concentration of the feed seawater; R represents the reverse osmosis recovery rate.

[0022] The equation for calculating the flow rate of a high-pressure pump is shown below:

[0023] (3)

[0024] In the formula, K d A d These are the permeation coefficient and membrane area of ​​the reverse osmosis unit d, respectively.

[0025] Furthermore, the energy storage device model includes a battery model and a water storage tank model;

[0026] The battery model is shown below:

[0027] (4)

[0028] In the formula, and These refer to the charging and discharging power of the battery, respectively. and These refer to the charging and discharging efficiency of the battery, respectively. , The battery charge at time t and time t-1; and These are 0-1 variables representing the charging and discharging states of the battery, respectively. and These represent the initial and final values ​​of the battery charge within the scheduling cycle; T represents the total number of time periods in a scheduling cycle. , These are the lower and upper limits of the battery charging power, respectively. , These are the lower and upper limits of the battery's discharge power, respectively. The scheduling time interval; and These are the upper and lower limits of the battery's capacity, respectively.

[0029] The reservoir model is shown below:

[0030] (5)

[0031] In the formula, and The water levels in the clear water tank and the product water tank are respectively for time period t. and These represent the water levels in the clear water tank and the product water tank at time t-1, respectively. This represents the ratio of pretreated seawater to feed water flow rate. This refers to the water flow rate from the product's water tank. and These represent the bottom areas of the clear water tank and the product water tank, respectively; R is the reverse osmosis recovery rate. and These represent the initial and final values ​​of the water level in the clear water reservoir during the scheduling cycle; and These represent the initial and final values ​​of the product pool water level during the scheduling cycle; Let be the flow rate of the water intake pump in the t-th time period; , These are the upper and lower limits of the water level in the clear water pool; , These are the upper and lower limits of the water level in the product pool, respectively. The total freshwater production of all reverse osmosis units during time period t is given.

[0032] Furthermore, the operating constraints of the seawater desalination plant include intake pump flow constraints, high-pressure pump flow constraints, high-pressure pump power constraints, total water production constraints of the reverse osmosis unit, high-pressure pump operating pressure constraints, high-pressure pump start-stop frequency constraints, wind turbine operation constraints, and power balance constraints.

[0033] The flow rate constraint for the water intake pump is shown below:

[0034] (6)

[0035] In the formula, Let be the flow rate of the water intake pump in the t-th time period; A 0-1 variable representing the working state of the water intake pump; and These are the upper and lower limits of the water intake pump flow rate, respectively;

[0036] The high-pressure pump flow constraint is shown below:

[0037] (7)

[0038] In the formula, q d,t I represents the high-pressure pump flow rate of the reverse osmosis unit d during time period t. d,t Let q be a 0-1 variable representing the operating state of reverse osmosis unit d during time period t; D is the set of reverse osmosis units; T is the set of time periods within the scheduling cycle; t The total freshwater production of all reverse osmosis units during time period t; , The upper and lower limits of the flow rate of the high-pressure pump in the reverse osmosis unit d are the limits of the high-pressure pump flow rate.

[0039] The power constraints of the high-pressure pump are as follows:

[0040] (8)

[0041] In the formula, and These represent the upper and lower power limits for the reverse osmosis unit d, respectively. The total power of all reverse osmosis desalination units during time period t; , The high-pressure pump power of reverse osmosis unit d during time period t and time period t-1; , The upper and lower limits of the high-pressure pump power for reverse osmosis unit d; The 0-1 variables characterizing the operating state of the reverse osmosis unit d during the t-1 time period;

[0042] The total permeate capacity constraint of the reverse osmosis unit is shown below:

[0043] (9)

[0044] In the formula, This represents the lower limit of freshwater production within the scheduling cycle. T is the scheduling time interval; T is the period.

[0045] The operating pressure constraints for the high-pressure pump are as follows:

[0046] (10)

[0047] In the formula, p d,t , The operating pressure of the reverse osmosis unit d during time period t and time period t-1; , These are the upper and lower limits of the operating pressure of the reverse osmosis unit d; and This refers to the upper limit of the increase or decrease in operating pressure per unit time period for the reverse osmosis unit; A 0-1 variable characterizing the operating state of the reverse osmosis unit d during time period t+1; , These are the lower and upper limits of the operating pressure difference for the reverse osmosis unit;

[0048] The constraints on the number of start-stop cycles of the high-pressure pump are as follows:

[0049] (11)

[0050] In the formula, , These are the single start-up and shutdown costs of reverse osmosis unit d and its total start-up and shutdown costs within time period t, respectively. This represents the maximum number of times the reverse osmosis unit can be started and stopped within the scheduling cycle.

[0051] The operating constraints of wind turbine units are as follows:

[0052] (12)

[0053] In the formula, and These are the predicted power and reduced power of the wind turbine units in the desalination plant, respectively.

[0054] The power balance constraints are as follows:

[0055] (13)

[0056] In the formula, To reduce the power exchange between the desalination plant and the power distribution network; To reduce the power exchange limit between the plant and the distribution network.

[0057] Furthermore, the steps for making the non-convex operating constraints in the operating constraints of a seawater desalination plant convex include:

[0058] 4.1) Processing the bilinear constraints in the non-convex operational constraints, we obtain:

[0059] (14)

[0060] In the formula, the subscript t represents the time period t; This indicates the auxiliary variable that replaces the bilinear term; , Let be a constant, and take values ​​of 2.05 × 10⁻⁶. -5 2.78×10 -7 ;

[0061] Processing the absolute value constraints in non-convex operation constraints yields:

[0062] (15)

[0063] In the formula, continuous variables This indicates an auxiliary variable that replaces the absolute value sign.

[0064] 4.2) Establish linear operating constraints for the seawater desalination plant, namely:

[0065] (16)

[0066] In the formula, x and I are the compact forms of continuous and 0-1 optimization variables, respectively; The interaction power vector between the desalination plant and the distribution network; A, b, C, d, E, F, g represent constraint coefficients;

[0067] The compact forms of continuous and 0-1 optimization variables x and I are shown below:

[0068] (17)

[0069] In the formula, This is the water intake flow vector; To reduce the power vector of the wind turbine units in the de-emphasis plant.

[0070] Furthermore, the two-stage robust optimization model includes an outer master problem, an outer subproblem, an inner master problem, and an inner subproblem.

[0071] The two-stage robust optimization model is shown below:

[0072] (18)

[0073] In the formula, , These are the upper and lower limits of the power interaction between the desalination plant and the power distribution network, respectively. Let T be a completely one vector; These are uncertain parameters; This represents taking the Hadamard product of two vectors; , They are vectors The upper and lower limits;

[0074] Among them, the uncertain parameters As shown below:

[0075] (19)

[0076] In the formula, U represents the set of uncertain parameters;

[0077] The outer principal problem in the two-stage robust optimization model is shown below:

[0078] (20)

[0079] In the formula, The uncertain parameter corresponding to the l-th worst-case scenario identified for the subproblem; k is the number of worst-case scenarios identified in the current iteration; l is the scenario index identifier;

[0080] The outer sub-problem in the two-stage robust optimization model is shown below:

[0081] (twenty one)

[0082] In the formula, , These are the upper and lower boundaries of the interval obtained from the outer master problem in the current iteration;

[0083] The inner principal problem in the two-stage robust optimization model is shown below:

[0084] (twenty two)

[0085] In the formula, m is the scene index identifier; p is the currently found binary variable scene; μ1, μ2, and λ are dual variables; The objective function value of the inner main problem; , , These are the uncertain parameters corresponding to the m-th scenario;

[0086] The inner sub-problems are as follows:

[0087] (twenty three)

[0088] In the formula, The worst-case scenario obtained by solving the inner principal problem. , The upper and lower boundaries of the interval are obtained for the inner master problem in the current iteration.

[0089] Furthermore, the steps to solve the two-stage robust optimization model include:

[0090] 6.1) Initialize the outer iteration parameters of the two-stage robust optimization model; set the initial iteration number to k=0, and initialize the uncertain parameters. or Let the objective function of the inner principal problem be... It is a constant, and can be taken as 1×10. 3 1×10 4 Etc., iterative convergence parameters ;

[0091] 6.2) Solve the outer principal problem of the two-stage robust optimization model to obtain the boundary of the power-optimal feasible region. ;

[0092] 6.3) Initialize the inner iteration parameters of the two-stage robust optimization model; set the initial iteration count to m=0, and set the initial binary variables. ;

[0093] 6.4) Substitute the boundary value of the optimal feasible region for power. Solve the inner principal problem of the two-stage robust optimization model to obtain the identified worst-case scenario. and objective function value Let the objective function of the inner principal problem be... ;

[0094] 6.5) Based on the worst-case scenario Solve the inner subproblems of the two-stage robust optimization model to obtain the optimal values ​​of the two variables. ;

[0095] 6.6) Determine the objective function of the inner main problem; if... Furthermore, if the inner sub-problem is infeasible, then the worst-case scenario becomes... End the inner loop, and Returning to the outer main problem, proceed to step 6.8).

[0096] like If the inner subproblem is feasible, then stop the inner and outer iterations and output the interval. If the solution is complete, proceed to step 6.7; otherwise, go to step 7.

[0097] 6.7) Generate new variables And add the following constraints to the inner principal problem:

[0098] (twenty four)

[0099] Update m = m + 1, then proceed to step 6.4).

[0100] 6.8) Generate new variables And add the following constraints to the outer master problem:

[0101] (25)

[0102] In the formula, , The upper and lower boundaries of the interval obtained for the inner main problem;

[0103] Update k=k+1, then proceed to step 6.2.

[0104] It is worth noting that this invention first inputs the basic parameters of the seawater desalination plant, models each unit in the seawater desalination plant, establishes the constraints of the seawater desalination plant, performs convexification processing on the nonlinear constraints, and obtains the compact form of the linear constraints. Based on the linear operation constraints of the seawater desalination plant, a two-stage robust optimization model is established to quantify the flexibility of the seawater desalination plant, and the model is solved based on the nested column and constraint generation algorithm. The commercial solvers IPOPT and Gurobi are used to solve the model, and the time-varying interactive power range between the seawater desalination plant and the distribution network is obtained.

[0105] The technical effects of this invention are undeniable. This invention addresses the issue of quantifying the flexibility of seawater desalination plants by providing a method for quantifying the flexibility of seawater desalination plants. This method fully quantifies the flexibility of seawater desalination plants and can provide a basis for desalination plants to participate in demand response and for setting incentive electricity prices for distribution networks, thereby improving demand response efficiency. Attached Figure Description

[0106] Figure 1 This is a flowchart illustrating the solution process of the method of the present invention.

[0107] Figure 2 This is a flow chart of the reverse osmosis process in a seawater desalination plant according to the present invention.

[0108] Figure 3 This is a structural diagram of the seawater desalination plant of the present invention.

[0109] Figure 4 This is a comparison chart of the flexibility of desalination plants under two different scenarios. Detailed Implementation

[0110] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0111] Example 1:

[0112] See Figures 1 to 4 A method for quantifying the flexibility of a seawater desalination plant includes the following steps:

[0113] 1) Obtain the basic parameters of the seawater desalination plant;

[0114] 2) Based on the basic parameters of the seawater desalination plant, model the equipment units of the seawater desalination plant to obtain the equipment unit model of the seawater desalination plant;

[0115] 3) Based on the equipment unit model of the seawater desalination plant, establish the operating constraints of the seawater desalination plant, which include non-convex constraints and integer variables;

[0116] 4) Make the non-convex operating constraints in the operating constraints of the seawater desalination plant convex to obtain the linear operating constraints of the seawater desalination plant.

[0117] 5) Based on the linear operation constraints of the seawater desalination plant, establish a two-stage robust optimization model;

[0118] 6) Solve the two-stage robust optimization model to obtain the time-varying power range of the interaction power between the desalination plant and the power distribution network, so as to quantify the flexibility of the desalination plant.

[0119] Example 2:

[0120] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as in Example 1, further wherein the basic parameters of the seawater desalination plant include the predicted wind power of the power distribution network, freshwater load, seawater osmotic pressure, and seawater concentration.

[0121] Example 3:

[0122] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Embodiments 1-2, further comprising a water intake pump model, a reverse osmosis unit model, and an energy storage device model.

[0123] Example 4:

[0124] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of embodiments 1-3, further wherein the water intake pump model includes a water intake pump power equation;

[0125] The power equation for the water intake pump is shown below:

[0126] (1)

[0127] In the formula, the subscript t represents the time period t; , and These represent the water intake pump power, water intake flow rate, and head for the t-th time period, respectively. and These are the density of water and the acceleration due to gravity, respectively. To improve the operating efficiency of the water pump.

[0128] Example 5:

[0129] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-4, further wherein the reverse osmosis unit model includes a high-pressure pump power equation and a high-pressure pump flow calculation equation.

[0130] Example 6:

[0131] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-5, further wherein the high-pressure pump power equation is as follows:

[0132] (2)

[0133] In the formula, the subscript t represents the time period t; , and These are the operating pressure, outlet flow rate, and high-pressure pump power of the high-pressure pump reverse osmosis unit d, respectively. This refers to the transmembrane osmotic pressure difference. and Let be a constant, and take respectively , ; R represents the concentration of the feed seawater; R represents the reverse osmosis recovery rate.

[0134] Example 7:

[0135] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-6, further wherein the high-pressure pump flow rate calculation equation is as follows:

[0136] (3)

[0137] In the formula, K d A d These are the permeation coefficient and membrane area of ​​the reverse osmosis unit d, respectively.

[0138] Example 8:

[0139] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of embodiments 1-7, further wherein the energy storage device model includes a battery model and a water storage tank model;

[0140] Example 9:

[0141] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-8, further wherein the battery model is as follows:

[0142] (4)

[0143] In the formula, and These refer to the charging and discharging power of the battery, respectively. and These refer to the charging and discharging efficiency of the battery, respectively. , The battery charge at time t and time t-1; and These are 0-1 variables representing the charging and discharging states of the battery, respectively. and These represent the initial and final values ​​of the battery charge within the scheduling cycle; T represents the total number of time periods in a scheduling cycle. , These are the lower and upper limits of the battery charging power, respectively. , These are the lower and upper limits of the battery's discharge power, respectively. The scheduling time interval; and These are the upper and lower limits of the battery's capacity, respectively.

[0144] Example 10:

[0145] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-9, further wherein the reservoir model is shown below:

[0146] (5)

[0147] In the formula, and The water levels in the clear water tank and the product water tank are respectively for time period t. and These represent the water levels in the clear water tank and the product water tank at time t-1, respectively. This represents the ratio of pretreated seawater to feed water flow rate. This refers to the water flow rate from the product's water tank. and These represent the bottom areas of the clear water tank and the product water tank, respectively; R is the reverse osmosis recovery rate. and These represent the initial and final values ​​of the water level in the clear water reservoir during the scheduling cycle; and These represent the initial and final values ​​of the product pool water level during the scheduling cycle; Let be the flow rate of the water intake pump in the t-th time period; , These are the upper and lower limits of the water level in the clear water pool; , These are the upper and lower limits of the water level in the product pool, respectively. The total freshwater production of all reverse osmosis units during time period t is given.

[0148] Example 11:

[0149] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-10, further wherein the operating constraints of the seawater desalination plant include intake pump flow constraints, high-pressure pump flow constraints, high-pressure pump power constraints, total water production constraints of the reverse osmosis unit, high-pressure pump operating pressure constraints, high-pressure pump start-stop frequency constraints, wind turbine operation constraints, and power balance constraints.

[0150] Example 12:

[0151] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-11, further wherein the intake pump flow constraint is as follows:

[0152] (6)

[0153] In the formula, Let be the flow rate of the water intake pump in the t-th time period; A 0-1 variable representing the working state of the water intake pump; and These are the upper and lower limits of the water intake pump flow rate, respectively;

[0154] Example 13:

[0155] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-12, further wherein the high-pressure pump flow constraint is as follows:

[0156] (7)

[0157] In the formula, q d,t I represents the high-pressure pump flow rate of the reverse osmosis unit d during time period t. d,t Let q be a 0-1 variable representing the operating state of reverse osmosis unit d during time period t; D is the set of reverse osmosis units; T is the set of time periods within the scheduling cycle; t The total freshwater production of all reverse osmosis units during time period t; , The upper and lower limits of the flow rate of the high-pressure pump in the reverse osmosis unit d are the limits of the high-pressure pump flow rate.

[0158] Example 14:

[0159] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-13, further wherein the high-pressure pump power constraint is as follows:

[0160] (8)

[0161] In the formula, and These represent the upper and lower power limits for the reverse osmosis unit d, respectively. The total power of all reverse osmosis desalination units during time period t; , The high-pressure pump power of reverse osmosis unit d during time period t and time period t-1; , The upper and lower limits of the high-pressure pump power for reverse osmosis unit d; The 0-1 variables characterizing the operating state of the reverse osmosis unit d during the t-1 time period;

[0162] Example 15:

[0163] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-14, further wherein the total water production capacity constraint of the reverse osmosis unit is as follows:

[0164] (9)

[0165] In the formula, This represents the lower limit of freshwater production within the scheduling cycle. T is the scheduling time interval; T is the period.

[0166] Example 16:

[0167] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-15, further wherein the high-pressure pump operating pressure constraint is as follows:

[0168] (10)

[0169] In the formula, p d,t , The operating pressure of the reverse osmosis unit d during time period t and time period t-1; , These are the upper and lower limits of the operating pressure of the reverse osmosis unit d; and This refers to the upper limit of the increase or decrease in operating pressure per unit time period for the reverse osmosis unit; A 0-1 variable characterizing the operating state of the reverse osmosis unit d during time period t+1; , The working pressure difference of the reverse osmosis unit (i.e., operating state I) d,t The lower and upper limits of the difference between the operating pressure of the reverse osmosis unit and the transmembrane osmotic pressure;

[0170] Example 17:

[0171] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-16, further wherein the high-pressure pump start-up and shutdown frequency constraints are as follows:

[0172] (11)

[0173] In the formula, , These are the single start-up and shutdown costs of reverse osmosis unit d and its total start-up and shutdown costs within time period t, respectively. This represents the maximum number of times the reverse osmosis unit can be started and stopped within the scheduling cycle.

[0174] Example 18:

[0175] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-17, further wherein the operating constraints of the wind turbine units are as follows:

[0176] (12)

[0177] In the formula, and These are the predicted power and reduced power of the wind turbine units in the desalination plant, respectively.

[0178] Example 19:

[0179] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-18, further wherein the power balance constraints are as follows:

[0180] (13)

[0181] In the formula, To reduce the power exchange between the desalination plant and the power distribution network; To reduce the power exchange limit between the plant and the distribution network.

[0182] Example 20:

[0183] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-19, further comprising the step of making non-convex operating constraints in the operating constraints of the seawater desalination plant convex, including:

[0184] 1) Processing the bilinear constraints in the non-convex operation constraints, we obtain:

[0185] (14)

[0186] In the formula, the subscript t represents the time period t; This indicates the auxiliary variable that replaces the bilinear term; , Let be a constant, and take respectively ;

[0187] Processing the absolute value constraints in non-convex operation constraints yields:

[0188] (15)

[0189] In the formula, continuous variables This indicates an auxiliary variable that replaces the absolute value sign.

[0190] 2) Establish linear operating constraints for the seawater desalination plant, namely:

[0191] (16)

[0192] In the formula, x and I are the compact forms of continuous and 0-1 optimization variables, respectively; The interaction power vector between the desalination plant and the distribution network; A, b, C, d, E, F, g represent constraint coefficients;

[0193] The compact forms of continuous and 0-1 optimization variables x and I are shown below:

[0194] (17)

[0195] In the formula, This is the water intake flow vector; To reduce the power vector of the wind turbine units in the de-emphasis plant.

[0196] Example 21:

[0197] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-20, further wherein the two-stage robust optimization model includes an outer principal problem, an outer sub-problem, an inner principal problem, and an inner sub-problem;

[0198] Example 22:

[0199] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-21, further comprising the following two-stage robust optimization model:

[0200] (18)

[0201] In the formula, , These are the upper and lower limits of the power interaction between the desalination plant and the power distribution network, respectively. Let T be a completely one vector; These are uncertain parameters; This represents taking the Hadamard product of two vectors; , They are vectors The upper and lower limits;

[0202] Among them, the uncertain parameters As shown below:

[0203] (19)

[0204] In the formula, U represents the set of uncertain parameters;

[0205] Example 23:

[0206] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-22, further wherein the outer principal problem in the two-stage robust optimization model is as follows:

[0207] (20)

[0208] In the formula, The uncertain parameter corresponding to the l-th worst-case scenario identified for the subproblem; k is the number of worst-case scenarios identified in the current iteration; l is the scenario index identifier;

[0209] Example 24:

[0210] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-23, further wherein the outer sub-problem in the two-stage robust optimization model is as follows:

[0211] (twenty one)

[0212] In the formula, , These are the upper and lower boundaries of the interval obtained from the outer master problem in the current iteration;

[0213] Example 25:

[0214] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-24, further wherein the inner principal problem in the two-stage robust optimization model is as follows:

[0215] (twenty two)

[0216] In the formula, m is the scene index identifier; p is the currently found binary variable scene; μ1, μ2, and λ are dual variables; The objective function value of the inner main problem; , , These are the uncertain parameters corresponding to the m-th scenario;

[0217] Example 26:

[0218] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-25, further comprising the following inner-level sub-problems in the two-stage robust optimization model:

[0219] (twenty three)

[0220] In the formula, The worst-case scenario obtained by solving the inner principal problem. , The upper and lower boundaries of the interval are obtained for the inner master problem in the current iteration.

[0221] Example 27:

[0222] A method for quantifying the flexibility of a seawater desalination plant, with technical content identical to any one of Examples 1-26, further comprising the following steps for solving the two-stage robust optimization model:

[0223] 1) Initialize the outer iteration parameters of the two-stage robust optimization model; set the initial iteration count to k=0 and initialize the uncertain parameters. or Let the objective function of the inner principal problem be... For a sufficiently large number, 1 × 10 can be taken. 3 1×10 4 Iterative convergence parameters ;

[0224] 2) Solve the outer principal problem of the two-stage robust optimization model to obtain the boundary of the power-optimal feasible region. ;

[0225] 3) Initialize the inner iteration parameters of the two-stage robust optimization model; set the initial iteration count to m=0, and set the initial binary variables. ;

[0226] 4) Substitute the boundary value of the optimal feasible region for power. Solve the inner principal problem of the two-stage robust optimization model to obtain the identified worst-case scenario. and objective function value Let the objective function of the inner principal problem be... ;

[0227] 5) Based on the worst-case scenario Solve the inner subproblems of the two-stage robust optimization model to obtain the optimal values ​​of the two variables. ;

[0228] 6) Determine the objective function of the inner main problem; if... Furthermore, if the inner sub-problem is infeasible, then the worst-case scenario becomes... End the inner loop, and Return to the outer main problem and proceed to step 8).

[0229] like If the inner subproblem is feasible, then stop the inner and outer iterations and output the interval. The solution process is now complete.

[0230] If the situation is otherwise, proceed to step 7).

[0231] 7) Generate new variables And add the following constraints to the inner principal problem:

[0232] (twenty four)

[0233] Update m = m + 1, then proceed to step 4).

[0234] 8) Generate new variables And add the following constraints to the outer master problem:

[0235] (25)

[0236] In the formula, , The upper and lower boundaries of the interval obtained for the inner main problem;

[0237] Update k=k+1, then proceed to step 2.

[0238] Example 28:

[0239] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of Examples 1-27, and further, the tools for solving the two-stage robust optimization model include IPOPT and Gurobi.

[0240] Example 29:

[0241] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of embodiments 1-28, further wherein the flexibility of the seawater desalination plant is characterized by the time-varying power range of its interaction power with the power distribution network, and a two-stage robust optimization model is used to solve it.

[0242] Example 30:

[0243] A method for quantifying the flexibility of a seawater desalination plant includes the following steps;

[0244] 1) Obtain the basic parameters of the seawater desalination plant;

[0245] Furthermore, the basic parameters of the seawater desalination plant include wind power forecast, freshwater load, seawater osmotic pressure, and seawater concentration.

[0246] 2) Based on the basic parameters of the seawater desalination plant, model the equipment units of the seawater desalination plant to obtain the equipment unit model of the seawater desalination plant;

[0247] The desalination plant equipment unit model includes a water intake pump model, a reverse osmosis unit model, and an energy storage device model.

[0248] The water intake pump model includes the water intake pump power equation;

[0249] The power equation for the water intake pump is shown below:

[0250] (1)

[0251] In the formula, the subscript t represents the time period t; , and These represent the water intake pump power, water intake flow rate, and head for the t-th time period, respectively. and These are the density of water and the acceleration due to gravity, respectively.

[0252] The reverse osmosis unit model includes the high-pressure pump power equation and the high-pressure pump flow calculation equation.

[0253] The power equation for the high-pressure pump is shown below:

[0254] (2)

[0255] In the formula, the subscript t represents the time period t; , and These are the operating pressure, outlet flow rate, and high-pressure pump power of the high-pressure pump reverse osmosis unit d, respectively. This refers to the transmembrane osmotic pressure difference. and Let be a constant, and take respectively , ; R represents the concentration of the feed seawater; R represents the reverse osmosis recovery rate.

[0256] The equation for calculating the flow rate of a high-pressure pump is shown below:

[0257] (3)

[0258] In the formula, K d and A d These represent the permeation coefficient and membrane area of ​​the RO unit d-permeable membrane, respectively.

[0259] The energy storage device model includes a battery model and a water storage tank model;

[0260] The battery model is shown below:

[0261] (4)

[0262] In the formula, and These refer to the charging and discharging power of the battery, respectively. and These refer to the charging and discharging efficiency of the battery, respectively. Battery charge; and These are 0-1 variables representing the charging and discharging states of a battery. Take 1 as charging. Take 1 as discharge); and These represent the initial and final values ​​of the battery charge within the scheduling cycle; T represents the total number of time periods in a scheduling cycle; the underscores and superscripts indicate the upper and lower limits of the corresponding variables.

[0263] The reservoir model is shown below:

[0264] (5)

[0265] In the formula, and These are the water levels in the clear water tank and the product water tank, respectively. This represents the ratio of pretreated seawater to feed water flow rate. This refers to the water flow rate from the product's water tank. and These represent the bottom areas of the clear water tank and the product water tank, respectively; R is the reverse osmosis recovery rate. and These represent the initial and final values ​​of the water level in the clear water reservoir during the scheduling cycle; and These represent the initial and final values ​​of the product pool water level during the scheduling cycle.

[0266] 3) Based on the equipment unit model of the seawater desalination plant, establish the operating constraints of the seawater desalination plant containing non-convex constraints and integer variables;

[0267] The operational constraints include intake pump flow rate constraints, high-pressure pump flow rate constraints, high-pressure pump power constraints, total water production constraints of the reverse osmosis unit, high-pressure pump operating pressure constraints, high-pressure pump start-stop frequency constraints, wind turbine operation constraints, and power balance constraints.

[0268] The flow rate constraint for the water intake pump is shown below:

[0269] (6)

[0270] In the formula, Let be the power of the water intake pump in the t-th time period; A 0-1 variable representing the working state of the water intake pump (1 indicates operation); and These are the upper and lower limits of the water intake pump flow rate, respectively;

[0271] The high-pressure pump flow constraint is shown below:

[0272] (7)

[0273] In the formula, q d,t I represents the high-pressure pump flow rate of the reverse osmosis unit d during time period t. d,t The variable q represents the 0-1 values ​​(1 indicates operation) characterizing the operating state of the reverse osmosis unit d; the underscores and superscripts indicate the upper and lower limits of the corresponding variables; D is the set of reverse osmosis units, and T is the set of time periods within the scheduling cycle (considering day-ahead scheduling, T={1,2,…,24}); t The total freshwater production of all reverse osmosis units during time period t;

[0274] The power constraints of the high-pressure pump are as follows:

[0275] (8)

[0276] In the formula, and These represent the upper / lower power limits for the reverse osmosis unit d, respectively. The total power of all reverse osmosis desalination units at time t;

[0277] The total permeate capacity constraint of the reverse osmosis unit is shown below:

[0278] (9)

[0279] In the formula, S RO This represents the lower limit of freshwater production within the scheduling cycle. For scheduling time interval ( =1h);

[0280] The operating pressure constraints for the high-pressure pump are as follows:

[0281] (10)

[0282] In the formula, p d,t The working pressure of the RO unit d is given by equation 2. Equation 2 indicates that in order to ensure that water molecules can pass through the semipermeable membrane, the working pressure of the RO unit must be greater than the transmembrane osmotic pressure, but must not exceed a certain limit to maintain the service life of the semipermeable membrane. and This represents the upper limit of the operating pressure increment / decrease per unit time period for the RO unit;

[0283] The constraints on the number of start-stop cycles of the high-pressure pump are as follows:

[0284] (11)

[0285] In the formula, , These are the single start-up and shutdown costs of RO unit d and its total start-up and shutdown costs within time period t, respectively. This represents the maximum number of times the RO unit can be started and stopped within the scheduling cycle.

[0286] The operating constraints of wind turbine units are as follows:

[0287] (12)

[0288] In the formula, and These are the predicted power and reduced power of the wind turbine units in the desalination plant, respectively.

[0289] The power balance constraints are as follows:

[0290] (13)

[0291] In the formula, To reduce the interaction power between the plant and the distribution network (injection into the distribution network is positive); To reduce the power exchange limit between the plant and the distribution network.

[0292] 4) The non-convex operating constraints of the seawater desalination plant are made convex to obtain the linear operating constraints of the seawater desalination plant;

[0293] The aforementioned constraint convexity technique mainly handles bilinear constraints and absolute value constraints.

[0294] The bilinear constraint is handled using the McCormick envelope, as shown below:

[0295] (14)

[0296] In the formula, the subscript t indicates time t; This indicates the auxiliary variable that replaces the bilinear term;

[0297] The handling of absolute value constraints is as follows:

[0298] (15)

[0299] In the formula, continuous variables This indicates an auxiliary variable that replaces the absolute value sign.

[0300] The convexized operational constraints can be expressed in a compact form as follows:

[0301] (16)

[0302] In the formula, x and I are the compact forms of continuous and 0-1 optimization variables, respectively.

[0303] 5) Based on the linear operation constraints of the seawater desalination plant, a two-stage robust optimization model is established to quantify the flexibility of the seawater desalination plant, and the model is solved based on a nested column and constraint generation algorithm.

[0304] The flexibility of a seawater desalination plant is characterized by the time-varying power range of its interaction power with the power distribution network, and a two-stage robust optimization model is used to solve it.

[0305] The two-stage robust optimization model is divided into inner and outer dual-layer principal and sub-problems;

[0306] The two-stage robust optimization model is shown below:

[0307] (17)

[0308] In the formula, , These are the upper and lower limits of the power interaction between the desalination plant and the power distribution network, respectively. Let T be a completely one vector; These are uncertain parameters; This represents taking the Hadamard product of two vectors; , They are vectors The upper and lower limits;

[0309] The uncertain parameters are as follows:

[0310] (18)

[0311] The outer main problem is as follows:

[0312] (19)

[0313] In the formula, The uncertain parameter is the l-th worst-case scenario identified for the subproblem, while the known parameter is k; k is the number of worst-case scenarios identified in the current iteration; l is the scenario index identifier.

[0314] The outer sub-problem is shown below:

[0315] (20)

[0316] In the formula, , These are the upper and lower boundaries of the interval obtained from the outer main problem in the current iteration, which are known values ​​in the subproblems;

[0317] The inner main problem is as follows:

[0318] (twenty one)

[0319] In the formula, m is the scene index identifier; p is the currently found binary variable scene; As dual variables;

[0320] The inner sub-problems are as follows:

[0321] (twenty two)

[0322] In the formula, The worst-case scenario obtained from solving the inner master problem is a known value.

[0323] The inner-layer iterative problem mainly deals with integer variables to achieve a smooth transformation of the outer-layer subproblems.

[0324] The steps to solve the two-stage robust optimization model include:

[0325] 1) Initialize outer iteration parameters. Set the initial iteration count to k=0 and initialize the uncertain parameters. or Let the objective function of the inner principal problem be... For sufficiently large numbers, we can take Iterative convergence parameters ;

[0326] 2) Solve the outer principal problem to obtain the boundary of the optimal feasible region. ;

[0327] 3) Initialize the inner iteration parameters. Set the initial iteration count to m=0, and set the initial binary variables. ;

[0328] 4) Substitute the optimal boundary obtained in step 2) Solve the inner principal problem to obtain the worst-case scenario identified. and objective function value ,make ;

[0329] 5) Obtained from solving the inner master problem Solve the inner subproblem to obtain the optimal value of the two variables. ;

[0330] 6) Determine if Furthermore, if the inner sub-problem is infeasible, then the worst-case scenario becomes... End the inner loop, and Return to the outer main problem and proceed to step 8); if If the inner subproblem is feasible, then stop the inner and outer iterations and output the interval. The solution process ends here; otherwise, proceed to step 7).

[0331] 7) Generate new variables And add the following constraints to the inner principal problem:

[0332] (twenty three)

[0333] Update m = m + 1, then proceed to step 4).

[0334] 8) Generate new variables And add the following constraints to the outer master problem:

[0335] (twenty four)

[0336] Update k=k+1, then proceed to step 2.

[0337] Tools for assessing the flexibility of desalination plants include IPOPT and Gurobi.

[0338] Example 31:

[0339] A method for quantifying the flexibility of a seawater desalination plant, with the same technical content as any one of embodiments 1-30, further comprising an energy storage unit and an equipment unit; the energy storage unit comprising a battery, a clear water tank, and a product water tank; the equipment unit comprising a wind turbine generator set, a water intake pump, a high-pressure pump, and a reverse osmosis unit; and the seawater desalination plant also being equipped with wiring to enable interaction with the power grid.

[0340] Example 32:

[0341] A verification experiment of the method for quantifying the flexibility of seawater desalination plants described in Examples 1-31 is as follows:

[0342] 1) Identify the various equipment units of the seawater desalination plant, including the clear water tank, product water tank, storage batteries, intake pumps, reverse osmosis unit, and wind turbine generator set. (See attached...) Figure 2 As shown, seawater is first pumped into a clear water tank for pretreatment by an intake pump. After flocculation and sedimentation, it enters a reverse osmosis unit for desalination. The high-pressure pump in the reverse osmosis unit pressurizes the water to achieve salt-water separation. Finally, the desalinated freshwater enters a product water tank to supply the water load. The seawater desalination plant is equipped with clear water tanks and product water tanks to allow for flexible control of water production plans.

[0343] As attached Figure 3 The diagram shows the structure of a seawater desalination plant. The power busbar is connected to the power grid, batteries, wind turbine generators, and energy-consuming equipment of the desalination plant. The desalination plant is primarily powered by a wind farm, but in emergencies, it can be powered by the distribution network, allowing the plant's wind power to be fed into the grid.

[0344] 2) Using the method of this invention, the flexibility of a seawater desalination plant can be quantified:

[0345] 2.1) Input basic data

[0346] Input the basic parameters of the seawater desalination plant, including: wind power forecast, freshwater load, seawater osmotic pressure, and seawater concentration.

[0347] The predicted wind power and freshwater load are given in Table 1; the seawater osmotic pressure and seawater concentration are given in Table 2.

[0348] Table 1 Wind power and freshwater load during the dispatch cycle

[0349]

[0350] Table 2 Seawater Parameters

[0351]

[0352] 2.2) Establishing the operational constraints of a seawater desalination plant and its compact form after convexity.

[0353] Based on the unit models and constraints of the seawater desalination plant listed above, the non-convex constraints are further convexized to establish a compact form of the linear operation constraints of the seawater desalination plant.

[0354] 2.3) Establish and solve a two-stage robust optimization model.

[0355] Based on the above model, establish internal and external dual-layer main and sub-problems, and solve the flexibility of the seawater desalination plant according to the solution steps.

[0356] 2.4) Experimental Results

[0357] Two case studies are presented for a seawater desalination plant to verify the effectiveness and superiority of the method of the present invention.

[0358] Case 1: Baseline scenario, parameters are given in Table 1 and Table 2.

[0359] Case 2: The wind power output was modified to the typical daily wind power output in summer, while the other parameters remained the same as in Case 1.

[0360] (a) Interval feasibility verification

[0361] The power values ​​for 24 time periods were uniformly sampled within the intervals obtained in the two examples, resulting in 100,000 decision combinations. The obtained scenarios were then substituted into the original problem to verify whether any decision combination within the interval is feasible, as shown in Table 3.

[0362] Table 3. Feasibility of decision combinations for interaction power within the desired interval under two examples.

[0363]

[0364] It is evident that all samples drawn under both examples are feasible, indicating that the desired interval has good feasibility and the proposed method has good applicability to various examples.

[0365] (b) Interval rationality analysis

[0366] As attached Figure 4 As shown, the desalination plant's energy absorption capacity is relatively consistent across different seasons under varying wind power outputs, while its energy transmission capacity decreases significantly during the summer. The upper boundary of the interval exhibits a trend of lower output during the day and a sharp increase at night, consistent with the changing trend of wind power output. The lower boundary of the interval also shows significant fluctuations, and when wind power is relatively abundant (periods 19-24), the system's power transmission capacity is significantly enhanced, while its power absorption capacity decreases. The above analysis demonstrates that the interval proposed in this invention is reasonable and effective.

[0367] This invention provides a quantitative value for the flexibility of seawater desalination plants, demonstrating good feasibility and applicability. It can effectively assess the flexibility of seawater desalination plants under various operating conditions and serves as an important basis for their efficient participation in demand response.

Claims

1. A method for quantifying the flexibility of a seawater desalination plant, characterized in that, Includes the following steps: Step 1) Obtain the basic parameters of the seawater desalination plant; Step 2) Based on the basic parameters of the seawater desalination plant, model the equipment units of the seawater desalination plant to obtain the equipment unit model of the seawater desalination plant; Step 3) Based on the equipment unit model of the seawater desalination plant, establish the operating constraints of the seawater desalination plant, which include non-convex constraints and integer variables; Step 4) Make the non-convex operating constraints in the seawater desalination plant convex to obtain the linear operating constraints of the seawater desalination plant. Step 5) Establish a two-stage robust optimization model based on the linear operation constraints of the seawater desalination plant; Step 6) Solve the two-stage robust optimization model to obtain the time-varying power range of the interaction power between the desalination plant and the power distribution network, so as to quantify the flexibility of the desalination plant. The basic parameters of the seawater desalination plant include the predicted wind power of the power distribution network, freshwater load, seawater osmotic pressure, and seawater concentration. The two-stage robust optimization model includes an outer master problem, an outer subproblem, an inner master problem, and an inner subproblem. The two-stage robust optimization model is shown below: （18） In the formula, , These are the upper and lower limits of the power interaction between the desalination plant and the power distribution network, respectively. Let T be a completely one vector; These are uncertain parameters; This represents taking the Hadamard product of two vectors; , They are vectors The upper and lower limits; x and I are the compact forms of continuous and 0-1 optimization variables, respectively; A, b, C, d, E, F, and g represent constraint coefficients; To reduce the interactive power vector between the desalination plant and the distribution network; The compact forms of continuous and 0-1 optimization variables x and I are shown below: （17） In the formula, This is the water intake flow vector; To reduce the power vector of the wind turbine units in the de-emphasis plant; To measure the power of the water pump; This refers to the water intake flow rate; The outlet flow rate of the high-pressure pump reverse osmosis unit d; The operating pressure of the high-pressure pump reverse osmosis unit d; The high-pressure pump power of the reverse osmosis unit d is the high-pressure pump power. This refers to the power of the high-pressure pump; , These are the water levels in the clear water tank and the product water tank, respectively. , Provides charging and discharging power for the battery; Battery charge; An auxiliary variable to replace the bilinear term; An auxiliary variable used to replace the absolute value sign; The total cost of starting and stopping the reverse osmosis unit d; A 0-1 variable representing the working state of the water intake pump; A 0-1 variable characterizing the operating state of the reverse osmosis unit d; , A 0-1 variable representing the charging and discharging state of a battery; Among them, the uncertain parameters As shown below: （19） In the formula, U represents the set of uncertain parameters; The outer principal problem in the two-stage robust optimization model is shown below: （20） In the formula, The uncertain parameter corresponding to the l-th worst-case scenario identified for the subproblem; k is the number of worst-case scenarios identified in the current iteration; l is the scenario index identifier; The outer sub-problem in the two-stage robust optimization model is shown below: （21） In the formula, , These are the upper and lower boundaries of the interval obtained from the outer master problem in the current iteration; The inner principal problem in the two-stage robust optimization model is shown below: （22） In the formula, m is the scene index identifier; p is the currently found binary variable scene; As dual variables; The objective function value of the inner main problem; , , These are the uncertain parameters corresponding to the m-th scenario; The inner sub-problems are as follows: （23） In the formula, The worst-case scenario obtained by solving the inner principal problem; , The upper and lower boundaries of the interval are obtained for the inner master problem in the current iteration.

2. The method for quantifying the flexibility of a seawater desalination plant according to claim 1, characterized in that, The desalination plant equipment unit model includes a water intake pump model, a reverse osmosis unit model, and an energy storage device model.

3. The method for quantifying the flexibility of a seawater desalination plant according to claim 2, characterized in that, The water intake pump model includes the water intake pump power equation; The power equation for the water intake pump is shown below: （1） In the formula, the subscript t represents the time period t; , and These represent the water intake pump power, water intake flow rate, and head for the t-th time period, respectively. and These are the density of water and the acceleration due to gravity, respectively. To improve the operating efficiency of the water pump.

4. The method for quantifying the flexibility of a seawater desalination plant according to claim 2, characterized in that, The reverse osmosis unit model includes the high-pressure pump power equation and the high-pressure pump flow calculation equation. The power equation for the high-pressure pump is shown below: （2） In the formula, the subscript t represents the time period t; , and These are the operating pressure, outlet flow rate, and high-pressure pump power of the high-pressure pump reverse osmosis unit d, respectively. This refers to the transmembrane osmotic pressure difference. and It is a constant; R represents the concentration of the feed seawater; R represents the reverse osmosis recovery rate. The equation for calculating the flow rate of a high-pressure pump is shown below: （3） In the formula, K d , A d are the permeation coefficient and membrane area of the reverse osmosis unit d, respectively.

5. The method for quantifying the flexibility of a seawater desalination plant according to claim 2, characterized in that, The energy storage device model includes a battery model and a water storage tank model; The battery model is shown below: （4） In the formula, and These refer to the charging and discharging power of the battery, respectively. and These refer to the charging and discharging efficiency of the battery, respectively. , The battery charge at time t and time t-1; and These are 0-1 variables representing the charging and discharging states of the battery, respectively. and These represent the initial and final values ​​of the battery charge within the scheduling cycle; T represents the total number of time periods in a scheduling cycle. , These are the lower and upper limits of the battery charging power, respectively. , These are the lower and upper limits of the battery's discharge power, respectively. The scheduling time interval; and These are the upper and lower limits of the battery's capacity, respectively. The reservoir model is shown below: （5） In the formula, and The water levels in the clear water tank and the product water tank are respectively for time period t. and These represent the water levels in the clear water tank and the product water tank at time t-1, respectively. This represents the ratio of pretreated seawater to feed water flow rate. This refers to the water flow rate from the product's water tank. and These represent the bottom areas of the clear water tank and the product water tank, respectively; R is the reverse osmosis recovery rate. and These represent the initial and final values ​​of the water level in the clear water reservoir during the scheduling cycle; and These represent the initial and final values ​​of the product pool water level during the scheduling cycle; Let be the flow rate of the water intake pump in the t-th time period; , These are the upper and lower limits of the water level in the clear water pool; , These are the upper and lower limits of the water level in the product pool, respectively. The total freshwater production of all reverse osmosis units during time period t is given.

6. The method for quantifying the flexibility of a seawater desalination plant according to claim 1, characterized in that, The operational constraints of the seawater desalination plant include intake pump flow constraints, high-pressure pump flow constraints, high-pressure pump power constraints, total water production constraints of the reverse osmosis unit, high-pressure pump operating pressure constraints, high-pressure pump start-stop frequency constraints, wind turbine operation constraints, and power balance constraints. The flow rate constraint for the water intake pump is shown below: （6） In the formula, Let be the flow rate of the water intake pump in the t-th time period; A 0-1 variable representing the working state of the water intake pump; and These are the upper and lower limits of the water intake pump flow rate, respectively; The high-pressure pump flow constraint is shown below: （7） In the formula, q d,t I represents the high-pressure pump flow rate of the reverse osmosis unit d during time period t. d,t Let q be a 0-1 variable representing the operating state of reverse osmosis unit d during time period t; D is the set of reverse osmosis units; T is the set of time periods within the scheduling cycle; t The total freshwater production of all reverse osmosis units during time period t; , The upper and lower limits of the flow rate of the high-pressure pump in the reverse osmosis unit d are the limits of the high-pressure pump flow rate. The power constraints of the high-pressure pump are as follows: （8） In the formula, and These represent the upper and lower power limits for the reverse osmosis unit d, respectively. The total power of all reverse osmosis desalination units during time period t; , The high-pressure pump power of reverse osmosis unit d during time period t and time period t-1; , The upper and lower limits of the high-pressure pump power for reverse osmosis unit d; The 0-1 variables characterizing the operating state of the reverse osmosis unit d during the t-1 time period; The total permeate capacity constraint of the reverse osmosis unit is shown below: （9） In the formula, This represents the lower limit of freshwater production within the scheduling cycle. T is the scheduling time interval; T is the period. The operating pressure constraints for the high-pressure pump are as follows: （10） In the formula, , The operating pressure of the reverse osmosis unit d during time period t and time period t-1; , These are the upper and lower limits of the operating pressure of the reverse osmosis unit d; and This refers to the upper limit of the increase or decrease in operating pressure per unit time period for the reverse osmosis unit; The variable is a 0-1 variable representing the operating state of the reverse osmosis unit d during time period t+1; , These are the lower and upper limits of the operating pressure difference for the reverse osmosis unit; The constraints on the number of start-stop cycles of the high-pressure pump are as follows: （11） In the formula, , These are the single start-up and shutdown costs of reverse osmosis unit d and its total start-up and shutdown costs within time period t, respectively. This represents the maximum number of times the reverse osmosis unit can be started and stopped within the scheduling cycle. The operating constraints of wind turbine units are as follows: （12） In the formula, and These are the predicted power and reduced power of the wind turbine units in the desalination plant, respectively. The power balance constraints are as follows: （13） In the formula, To reduce the power exchange between the desalination plant and the power distribution network; To reduce the power exchange limit between the plant and the distribution network.

7. The method for quantifying the flexibility of a seawater desalination plant according to claim 1, characterized in that, The steps for making non-convex operating constraints in the operating constraints of a seawater desalination plant convex include: Step 1) Process the bilinear constraints in the non-convex operation constraints to obtain: （14） In the formula, the subscript t represents the time period t; This indicates the auxiliary variable that replaces the bilinear term; , It is a constant; Processing the absolute value constraints in non-convex operation constraints yields: （15） In the formula, continuous variables This indicates an auxiliary variable that replaces the absolute value sign. Step 2) Establish linear operating constraints for the seawater desalination plant, namely: （16）。 8. The method for quantifying the flexibility of a seawater desalination plant according to claim 1, characterized in that, The steps to solve a two-stage robust optimization model include: Step 1) Initialize the outer iteration parameters of the two-stage robust optimization model; set the initial iteration number to k=0 and initialize the uncertain parameters. or Let the objective function of the inner principal problem be... The constant is the iterative convergence parameter. ;constant The value is 1×10 3 Or 1×10 4 ; Step 2) Solve the outer principal problem of the two-stage robust optimization model to obtain the boundary of the power-optimal feasible region. ; Step 3) Initialize the inner iteration parameters of the two-stage robust optimization model; set the initial iteration count to m=0, and set the initial binary variables. ; Step 4) Substitute the boundary value of the optimal feasible region for power. Solve the inner principal problem of the two-stage robust optimization model to obtain the identified worst-case scenario. and objective function value Let the objective function of the inner principal problem be... ; Step 5) Based on the worst-case scenario Solve the inner subproblems of the two-stage robust optimization model to obtain the optimal values ​​of the two variables. ; Step 6) Determine the objective function of the inner main problem; if... Furthermore, if the inner sub-problem is infeasible, then the worst-case scenario becomes... End the inner loop, and Return to the outer main problem and proceed to step 8). like If the inner subproblem is feasible, then stop the inner and outer iterations and output the interval. The solution process ends here; otherwise, proceed to step 7. Step 7) Generate new variables And add the following constraints to the inner principal problem: （24） Update m = m + 1, then proceed to step 4). Step 8) Generate new variables And add the following constraints to the outer master problem: （25） In the formula, , The upper and lower boundaries of the interval obtained for the inner main problem; Update k=k+1, then proceed to step 2.

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