Seawater desalination plant two-stage robust scheduling method considering wind power uncertainty

Abstract

The invention discloses a two-stage robust scheduling method of a seawater desalination plant considering wind power uncertainty. The method comprises the following steps: 1) obtaining basic parameters of the seawater desalination plant; 2) constructing a seawater desalination plant model based on the basic parameters of the seawater desalination plant; 3) constructing a two-stage robust optimization model based on the seawater desalination plant model; and 4) solving the two-stage robust optimization model by adopting a column sum constraint generation algorithm to obtain an optimal scheduling scheme of the seawater desalination plant considering the wind power uncertainty. The scheduling scheme obtained by the invention corresponds to the worst scene. According to the invention, the conservative property of the scheduling scheme can be flexibly adjusted. According to the robust optimization method, wind power output uncertainty is considered, the unbalance amount caused by prediction errors in the real-time market is lower than that of a deterministic optimization method, and therefore the final operation cost is reduced, and the scheduling scheme obtained through the method has higher robustness and the capacity of resisting the real-time market electricity price fluctuation risk.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated energy systems, and in particular to a two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty. Background Art

[0002] Today, approximately 40% of the world's population faces the severe challenge of freshwater shortages. Against this backdrop, desalination technology has rapidly developed in countries with water scarcity. Desalination, which uses seawater to desalinate and produce fresh water, is a key means of addressing the global freshwater crisis. Desalination primarily utilizes reverse osmosis (RO) membrane desalination technology and thermal desalination technologies such as multi-stage flash evaporation and multi-effect distillation, with RO being the most widely used. Currently, global desalination capacity continues to grow, with an average annual growth rate of 6.8% over the past decade. More than 120 countries are now using desalination to supplement their fresh water needs.

[0003] Desalination is essentially an energy-intensive industry that trades energy for resources, and desalination costs remain high. Currently, the cost of RO desalination in my country generally ranges from 5 to 8 yuan per ton of water, with energy costs accounting for over 40% and energy consumption reaching 3 to 5 kWh per ton of water. Traditional desalination plants are mostly powered by large thermal power plants or the grid. With the advancement of the "dual carbon" goals, the high emissions associated with high energy consumption are also gaining attention. To achieve energy conservation and emission reduction in desalination, utilizing new energy sources is an effective solution. (In the Jiangsu Dafeng wind power RO desalination pilot project, the cost per ton of water has dropped to 3.65 yuan, and CO2 emissions per ton of water have been reduced by 1.6 kg compared to thermal power RO.)

[0004] However, the random output of wind power, a distributed renewable energy source, presents challenges to the operation and scheduling of desalination plants. Effectively addressing the uncertainty of wind power output and achieving reliable and economical operation has become a key issue in the economic scheduling of desalination plants. Current research on desalination plant operation and scheduling has not addressed methods specifically for addressing wind power uncertainty in desalination plants equipped with wind power. Summary of the Invention

[0005] The present invention aims to provide a two-stage robust scheduling method for a seawater desalination plant taking into account wind power uncertainty, comprising the following steps:

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

[0007] 2) Based on the basic parameters of the desalination plant, a seawater desalination plant model is constructed.

[0008] 3) Based on the desalination plant model, a two-stage robust optimization model is constructed.

[0009] 4) The column and constraint generation algorithm is used to solve the two-stage robust optimization model to obtain the optimal scheduling scheme of the seawater desalination plant considering the uncertainty of wind power.

[0010] Furthermore, the basic parameters of the seawater desalination plant include parameters of various equipment, time-of-use electricity purchase price, electricity sales price, summer wind power within the scheduling cycle, winter wind power within the scheduling cycle, and water load demand.

[0011] The equipment includes a water intake pump, a high-pressure pump, an RO unit, an energy storage device, and a wind turbine.

[0012] Furthermore, the constraints of the seawater desalination plant model include energy consumption equipment operation constraints, energy storage and water reservoir operation constraints, wind turbine operation constraints, power balance constraints, and model convexity processing constraints.

[0013] The energy consumption equipment operation constraints include water intake pump operation constraints and high-pressure pump operation constraints.

[0014] The high-pressure pump operation constraints include power constraints, working pressure constraints, ramp constraints, and RO unit start and stop times constraints.

[0015] The energy storage and water reservoir operation constraints include water reservoir operation constraints and energy storage equipment operation constraints.

[0016] The model convexity processing constraints include bilinear term processing constraints and absolute value constraints.

[0017] Furthermore, the water intake pump operation constraints are as follows:

[0018]

[0019] Where t represents time, are the water pump power, water flow rate, and head at the tth time period, respectively. ρ and g are the water density and gravity acceleration, respectively. Characterizes the working status of the water intake pump. and q In Water intake flow The upper and lower limits of η. In is the pump unit efficiency of the intake pump.

[0020] The power constraints are as follows:

[0021] q d,t =K d A d (p d,t -Δπ) (3)

[0022]

[0023] Where d represents the RO unit index, p d,t ,q d,t 、 They represent the working pressure, outlet flow rate, and high-pressure pump power of the dth RO unit in the tth period respectively. d 、A d are the permeability coefficient and membrane area of ​​the dth RO unit membrane, respectively. Δπ is the transmembrane osmotic pressure difference. and q d,t The water flow rate q d,t The upper and lower limits of I d,t Characterizes the operating status of the dth RO unit in the tth period. d and b d is the high pressure pump power coefficient. C sw is the feed seawater concentration. and High pressure pump power upper and lower limits. and p d,t The working pressure p d,t upper and lower limits. is the RO unit set. t RO Indicates the total power of the RO unit. t Indicates the total freshwater flow. S RO Indicates the lower limit of freshwater production within the scheduling period. represents the set of time periods within the scheduling cycle. Δt represents the scheduling time interval. R is the reverse osmosis recovery rate.

[0024] The operating pressure constraints are as follows:

[0025]

[0026] Where, and Δp d are the upper and lower limits of the net transmembrane pressure of the dth RO unit respectively.

[0027] The climbing constraints are as follows:

[0028]

[0029]

[0030] Where, Indicates the high-pressure pump power of the dth RO unit in the t-1th period. d,t-1 Characterizes the operating status of the dth RO unit in the t-1th period. is the upper limit of the climbing power of the dth RO unit. is the upper limit of the downward climbing power of the dth RO unit. It is the upper limit of the working pressure increment of the dth RO unit per unit time period. It is the upper limit of the working pressure reduction of the dth RO unit per unit time period. Indicates the upper limit of the total power of the dth RO unit. d,t-1 It represents the working pressure of the dth RO unit in the t-1th period. Indicates the total working pressure p of the dth RO unit d upper limit.

[0031] The constraints on the start and stop times of the RO unit are as follows:

[0032]

[0033] Where, is the single start-up and shutdown cost of the dth RO unit. M is the total cost of starting and stopping the dth RO unit in the tth period. RO is the maximum number of start and stop times allowed for the RO unit within the scheduling period. T is the total number of time periods within the scheduling period. d,t+1 Represents the operating status of the d-th RO unit in the t+1-th period.

[0034] The operating constraints of the water reservoir are as follows:

[0035]

[0036] Where, are the water levels of the clean water tank and product water tank in the tth period respectively. Respectively represent the water levels of the clean water tank and product water tank in the t-1 period. Pre is the ratio of the flow rate of pretreated seawater to the feed water flow rate. A is the water flow rate of the product pool. CLT 、A PRT They are the bottom areas of the clean water tank and the product water tank respectively. h CLT They are the upper and lower limits of the water level in the clear water tank respectively. h PRT They are the upper and lower limits of the product pool water level respectively.

[0037] The energy storage equipment operation constraints are as follows:

[0038]

[0039]

[0040] Where, is the energy storage device power in the tth period. is the energy storage device power in the t-1 period. EBE They are the upper and lower limits of the energy storage device’s power. CH ,η DCH are the charging and discharging efficiency of the energy storage device respectively. t CH 、P t DCH are the charging and discharging power of the energy storage device in the tth period respectively. Respectively represent the charging and discharging states of the energy storage device. P CH They are the upper and lower limits of the charging power of the energy storage equipment respectively. P DCH They are the upper and lower limits of the energy storage device discharge power respectively.

[0041] The wind turbine operation constraints are as follows:

[0042] 0≤P t CU ≤P t WT (29)

[0043] Where, P t WT 、P t CU They are the predicted power and curtailed power of the wind turbines in the desalination plant in the tth period respectively.

[0044] The power balance constraints are as follows:

[0045] P t WT +P t PR -P t CU +P t DCH =P t CH +P t RO +P t In +P t RP (30)

[0046]

[0047] Where, P t PR is the power purchased by the desalination plant from the distribution grid, P t RP The power sold by the desalination plant to the distribution grid. The upper limit of the power that a desalination plant can purchase from the distribution grid. The upper limit of the electricity power sold by the desalination plant to the distribution grid.

[0048] The bilinear term processing constraints are as follows:

[0049]

[0050] Where, is an auxiliary variable.

[0051] The absolute value constraints are as follows:

[0052] ω d,t ≥I d,t+1 -I d,t (38)

[0053] ω d,t ≥-(I d,t+1 -I d,t ) (39)

[0054]

[0055] Where, ω d,t is a continuous variable. is the upper limit of the total start-up and shutdown cost of the d-th RO unit in the t-th period.

[0056] Furthermore, the desalination plant model is as follows:

[0057]

[0058] Where A, E, and F are the coefficient matrices of the constraint conditions. b and g are constant column vectors.

[0059] Among them, the optimization variables x and I are as follows:

[0060]

[0061] Where, P In ,q In are the water pump power and water flow rate respectively. d ,q d Respectively represent the working pressure and water flow rate of the RO unit. Indicates the 1st,...,nth D The outlet flow vector of each RO unit. P is the high pressure pump power of the RO unit. RO Indicates the total power of the RO unit. q indicates the total flow of fresh water. h CLT 、h PRT are the water levels of the clean water tank and product water tank respectively. CH 、P DCHE are the charging and discharging power of the energy storage device respectively. BE P is the power of the energy storage device. CU Cutting power for wind turbines in desalination plants. is an auxiliary variable. d is a continuous variable. is the total cost of starting and stopping the RO unit. PR 、P RP are the power purchased and sold by the desalination plant to the distribution network. WT Predict the power of wind turbines for desalination plants. In Characterizes the working status of the water intake pump. d Characterizes the operating status of the RO unit. CH , I DCH Respectively represent the charging and discharging states of the energy storage device.

[0062] Furthermore, in step 3), the steps of constructing a two-stage robust optimization model are as follows:

[0063] 3.1) Determine the operational objectives of the desalination plant as follows:

[0064]

[0065] Where, is the total operating cost of the desalination plant under pre-scheduling. OP 、C SU They are the operation and maintenance costs and start-up and shutdown costs of the RO system of the seawater desalination plant. BE 、C CU They are respectively the operation and maintenance costs of wind turbines / energy storage equipment and the penalty costs for wind curtailment. EX is the power interaction cost between the desalination plant and the distribution grid.

[0066] 3.2) Calculation: The deterministic optimization model for the economic dispatch problem of a seawater desalination plant without considering the uncertainty of wind power output is as follows:

[0067]

[0068] Where A, E, F, and C are the coefficient matrices of the constraints. b and g are constant column vectors. x and I are optimization variables. h is the coefficient matrix. is an uncertain variable.

[0069] 3.3) The uncertainty of wind power output is described by using a box uncertainty set, as shown below:

[0070]

[0071] Where t represents time, T is the total number of time periods in the scheduling cycle, U is the uncertainty set, and u is the uncertain variable. is the wind power forecast, ΔP t max is the maximum fluctuation of wind power, P t WT The predicted power of the wind turbine in the desalination plant in the tth period. R0 is a set of real numbers.

[0072] 3.4) Construct a two-stage robust optimization model as follows:

[0073]

[0074] The two-stage robust optimization model consists of two stages. The first stage is an outer minimization problem, i.e., the minimum operating cost of the system, with the optimization variable being I. The second stage is an inner maximum minimization problem, i.e., finding the worst-case scenario, with the optimization variables being u and x.

[0075] The two-stage robust optimization model is converted into a deterministic optimization model as follows:

[0076]

[0077] Where Ω(x,u) represents the feasible region. λ, γ, and π are all dual variables corresponding to the constraints in the second stage.

[0078] Furthermore, the operation and maintenance cost of the RO system of the seawater desalination plant is C OP , the start-up and shutdown costs of the RO system of the seawater desalination plant C SU , Wind turbine / energy storage equipment operation and maintenance costs C BE , Wind turbine / energy storage equipment wind curtailment penalty fee C CU , the power interaction cost C between the desalination plant and the distribution network EX As shown below:

[0079]

[0080] Where t represents time, Represents the time period set within the scheduling period. d represents the RO unit index, It is a collection of RO units. c BE 、c BW They are the operation and maintenance cost coefficients of the seawater desalination plant RO system, energy storage equipment, and wind turbine. CU It is the penalty cost coefficient for wind curtailment in desalination plants. The on-grid electricity price of wind power for seawater desalination plants. The electricity price that the desalination plant purchases from the distribution grid. d,t Indicates the water outlet flow rate of the RO unit. is the total cost of starting and stopping the RO unit. t CH 、P t DCH are the charging and discharging power of the energy storage device respectively. t WT Predict the power of wind turbines in desalination plants. t CU Reduce the power of wind turbines in desalination plants. t PR 、P t RP They are respectively the power purchased and sold by the desalination plant to the distribution network.

[0081] Furthermore, in step 4), the steps for solving the two-stage robust optimization model are as follows:

[0082] 4.1) Decompose the two-stage robust optimization model into a main problem and sub-problems as follows:

[0083]

[0084] Where MP is the main problem, subscript l is the iteration index, and k is the number of iterations. SU is the startup and shutdown cost of the RO system in a seawater desalination plant. SP is the subproblem, A, E, F, and C are the coefficient matrices of the constraints. b and g are constant column vectors. x and I are optimization variables. u is an uncertain variable. U is the uncertainty set. Ω(I,u) represents the feasible region. h is the coefficient matrix. η is an auxiliary variable.

[0085] 4.2) Initialize the number of iterations k = 1, set the upper bound UB = +∞ and the lower bound LB = -∞ of the optimal solution of the two-stage robust optimization model, and set the initial worst scenario value u k .

[0086] 4.3) Based on the worst scenario value u k , find the optimal solution set for the main problem [I k ,η k 、x1…x k ], and update the lower bound of the optimal solution LB=max{C SU +η k ,LB}, where I k 、x1…x k All are optimization variables. k is the auxiliary variable for the kth iteration.

[0087] 4.4) The optimal solution of the main problem I k Substitute into the subproblem and solve to get the worst scenario value u k+1 , and update the upper bound of the optimal solution UB=min{CSU +Q(I k ),UB}, where Q(I k ) is the output value of the sub-problem.

[0088] 4.5) Determine whether UB-UL≤ε holds. If so, output the optimal solution x k ,I k If not, go to step 4.6), where ε is the convergence parameter.

[0089] 4.6) Add variable constraints to the main problem, set the number of iterations k = k + 1, and return to step 4.3).

[0090] The variable constraints are as follows:

[0091]

[0092] Where x k+1 is the optimization variable at the k+1th iteration.

[0093] Further, solve the worst scenario value u k+1 When , the subproblem is converted into a single-layer optimization problem for solution, as shown below:

[0094]

[0095] sA T λ+E T γ+C T π=h

[0096] γ≤0 (54)

[0097] Where λ, γ, and π represent the dual variables of the corresponding constraints in the second stage. A, E, and F represent the coefficient matrices of the constraints. b and g represent constant column vectors. x and I are optimization variables. u represents an uncertain variable. U represents the uncertainty set. h represents the coefficient matrix.

[0098] Among them, the uncertainty set U is as follows:

[0099]

[0100] Where t represents time and T is the total number of time periods in the scheduling cycle. t WT Predict the power of the wind turbines in the desalination plant during the tth period. is the wind power forecast, ΔP t max is the maximum fluctuation of wind power, B t Indicates whether the parameter has reached the boundary value. W is an uncertain adjustment parameter. R0 is a set of real numbers.

[0101] Furthermore, the two-stage robust optimization model is solved using the Gurobi solver.

[0102] The technical effect of the present invention is unquestionable. The present invention proposes a two-stage robust scheduling method for seawater desalination plants that takes into account the uncertainty of wind power. The scheduling scheme obtained by this method corresponds to the worst scenario.

[0103] The uncertainty adjustment parameter set in the present invention distinguishes the two-stage robust optimization model from the deterministic optimization model. As the uncertainty adjustment parameter increases, the operating cost of the desalination plant also increases accordingly. The present invention can flexibly adjust the conservatism of the scheduling plan.

[0104] The robust optimization method of the present invention takes into account the uncertainty of wind power output. The imbalance caused by prediction errors in the real-time market is lower than that of the deterministic optimization method, thereby reducing the final operating cost. The scheduling scheme obtained by using the present invention has stronger robustness and the ability to resist the risk of real-time market electricity price fluctuations. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 It is a flowchart of the solution process of the method of the present invention;

[0106] Figure 2 This is a structural flow chart of a seawater desalination plant according to the method of the present invention;

[0107] Figure 3 This is an energy flow diagram for a seawater desalination plant according to the method of the present invention;

[0108] Figure 4 It is the water load prediction diagram;

[0109] Figure 5 The results of the summer desalination plant scheduling are as follows;

[0110] Figure 6 Forecast / actual wind power for summer;

[0111] Figure 7 The results of winter desalination plant scheduling;

[0112] Figure 8 is the predicted / actual wind power in winter. DETAILED DESCRIPTION

[0113] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0114] Example 1:

[0115] See also Figures 1 to 8 , a two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty, including the following steps:

[0116] 1) Obtain the basic parameters of the desalination plant.

[0117] 2) Based on the basic parameters of the desalination plant, a seawater desalination plant model is constructed.

[0118] 3) Based on the desalination plant model, a two-stage robust optimization model is constructed.

[0119] 4) The column and constraint generation algorithm is used to solve the two-stage robust optimization model to obtain the optimal scheduling scheme of the seawater desalination plant considering the uncertainty of wind power.

[0120] Example 2:

[0121] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is shown in Example 1. Furthermore, the basic parameters of the seawater desalination plant include parameters of various equipment, time-of-use electricity purchase price, electricity sales price, summer wind power within the scheduling period, winter wind power within the scheduling period, and water load demand.

[0122] The equipment includes a water intake pump, a high-pressure pump, an RO unit, an energy storage device, and a wind turbine.

[0123] Example 3:

[0124] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is shown in any one of Examples 1 to 2. Furthermore, the constraints of the seawater desalination plant model include energy consumption equipment operation constraints, energy storage and water reservoir operation constraints, wind turbine operation constraints, power balance constraints, and model convex processing constraints.

[0125] The energy consumption equipment operation constraints include water intake pump operation constraints and high-pressure pump operation constraints.

[0126] The high-pressure pump operation constraints include power constraints, working pressure constraints, ramp constraints, and RO unit start and stop times constraints.

[0127] The energy storage and water reservoir operation constraints include water reservoir operation constraints and energy storage equipment operation constraints.

[0128] The model convexity processing constraints include bilinear term processing constraints and absolute value constraints.

[0129] Example 4:

[0130] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is shown in any one of Examples 1 to 3. Furthermore, the water intake pump operation constraints are as follows:

[0131]

[0132] Where t represents time, P t In 、 are the water pump power, water flow rate, and head at the tth time period, respectively. ρ and g are the water density and gravity acceleration, respectively. Characterizes the working status of the water intake pump. and q In Water intake flow The upper and lower limits of η. In is the pump unit efficiency of the intake pump.

[0133] The power constraints are as follows:

[0134] q d,t =K d A d (p d,t -Δπ) (3)

[0135]

[0136] Where d represents the RO unit index, p d,t ,q d,t 、 They represent the working pressure, outlet flow rate, and high-pressure pump power of the dth RO unit in the tth period respectively. d 、A d are the permeability coefficient and membrane area of ​​the dth RO unit membrane, respectively. Δπ is the transmembrane osmotic pressure difference. and q d,t The water flow rate q d,t The upper and lower limits of I d,t Characterizes the operating status of the dth RO unit in the tth period. d and b d is the high pressure pump power coefficient. C sw is the feed seawater concentration. and High pressure pump power upper and lower limits. and p d,t The working pressure p d,t upper and lower limits. is the RO unit set. t RO Indicates the total power of the RO unit. tIndicates the total freshwater flow. S RO Indicates the lower limit of freshwater production within the scheduling period. represents the set of time periods within the scheduling cycle. Δt represents the scheduling time interval. R is the reverse osmosis recovery rate.

[0137] The operating pressure constraints are as follows:

[0138]

[0139] Where, and Δp d are the upper and lower limits of the net transmembrane pressure of the dth RO unit respectively.

[0140] The climbing constraints are as follows:

[0141]

[0142] Where, Indicates the high-pressure pump power of the dth RO unit in the t-1th period. d,t-1 Characterizes the operating status of the dth RO unit in the t-1th period. is the upper limit of the climbing power of the dth RO unit. is the upper limit of the downward climbing power of the dth RO unit. It is the upper limit of the working pressure increment of the dth RO unit per unit time period. It is the upper limit of the working pressure reduction of the dth RO unit per unit time period. Indicates the upper limit of the total power of the dth RO unit. d,t-1 It represents the working pressure of the dth RO unit in the t-1th period. Indicates the total working pressure p of the dth RO unit d upper limit.

[0143] The constraints on the start and stop times of the RO unit are as follows:

[0144]

[0145] Where, is the single start-up and shutdown cost of the dth RO unit. M is the total cost of starting and stopping the dth RO unit in the tth period. RO is the maximum number of start and stop times allowed for the RO unit within the scheduling period. T is the total number of time periods within the scheduling period. d,t+1 Represents the operating status of the d-th RO unit in the t+1-th period.

[0146] The operating constraints of the water reservoir are as follows:

[0147]

[0148] Where, are the water levels of the clean water tank and product water tank in the tth period respectively. Respectively represent the water levels of the clean water tank and product water tank in the t-1 period. Pre is the ratio of the flow rate of pretreated seawater to the feed water flow rate. A is the water flow rate of the product pool. CLT 、A PRT They are the bottom areas of the clean water tank and the product water tank respectively. h CLT They are the upper and lower limits of the water level in the clear water tank respectively. h PRT They are the upper and lower limits of the product pool water level respectively.

[0149] The energy storage equipment operation constraints are as follows:

[0150]

[0151] Where, is the energy storage device power in the tth period. is the energy storage device power in the t-1 period. E BE They are the upper and lower limits of the energy storage device’s power. CH ,η DCH are the charging and discharging efficiency of the energy storage device respectively. t CH 、P t DCH are the charging and discharging power of the energy storage device in the tth period respectively. Respectively represent the charging and discharging states of the energy storage device. P CH They are the upper and lower limits of the charging power of the energy storage equipment respectively. P DCH They are the upper and lower limits of the energy storage device discharge power respectively.

[0152] The wind turbine operation constraints are as follows:

[0153] 0≤P t CU ≤P t WT (29)

[0154] Where, P t WT 、P t CU They are the predicted power and curtailed power of the wind turbines in the desalination plant in the tth period respectively.

[0155] The power balance constraints are as follows:

[0156] P t WT +P t PR -P t CU +P t DCH =P t CH +P t RO +P t In +P t RP (30)

[0157]

[0158] Where, P t PR is the power purchased by the desalination plant from the distribution grid, P t RP The power sold by the desalination plant to the distribution grid. The upper limit of the power that a desalination plant can purchase from the distribution grid. The upper limit of the electricity power sold by the desalination plant to the distribution grid.

[0159] The bilinear term processing constraints are as follows:

[0160]

[0161] Where, is an auxiliary variable.

[0162] The absolute value constraints are as follows:

[0163] ω d,t ≥I d,t+1 -I d,t (38)

[0164] ω d,t ≥-(I d,t+1 -I d,t ) (39)

[0165]

[0166] Where, ω d,t is a continuous variable. is the upper limit of the total start-up and shutdown cost of the d-th RO unit in the t-th period.

[0167] Example 5:

[0168] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is described in any one of Examples 1 to 4. Furthermore, the seawater desalination plant model is as follows:

[0169]

[0170] Where A, E, and F are the coefficient matrices of the constraint conditions. b and g are constant column vectors.

[0171] Among them, the optimization variables x and I are as follows:

[0172]

[0173] Where, P In ,q In are the water pump power and water flow rate respectively. d ,q d Respectively represent the working pressure and water flow rate of the RO unit. Indicates the 1st,...,nth D The outlet flow vector of each RO unit. P is the high pressure pump power of the RO unit. RO Indicates the total power of the RO unit. q indicates the total flow of fresh water. h CLT 、h PRT are the water levels of the clean water tank and product water tank respectively. CH 、P DCH E are the charging and discharging power of the energy storage device respectively. BE P is the power of the energy storage device. CU Cutting power for wind turbines in desalination plants. is an auxiliary variable. d is a continuous variable. is the total cost of starting and stopping the RO unit. PR 、P RP are the power purchased and sold by the desalination plant to the distribution network. WT Predict the power of wind turbines for desalination plants. In Characterizes the working status of the water intake pump. d Characterizes the operating status of the RO unit. CH , I DCH Respectively represent the charging and discharging states of the energy storage device.

[0174] Example 6:

[0175] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is described in any one of Examples 1 to 5. Furthermore, in step 3), the steps for constructing a two-stage robust optimization model are as follows:

[0176] 3.1) Determine the operational objectives of the desalination plant as follows:

[0177]

[0178] Where, is the total operating cost of the desalination plant under pre-scheduling. OP 、C SU They are the operation and maintenance costs and start-up and shutdown costs of the RO system of the seawater desalination plant. BE 、C CU They are respectively the operation and maintenance costs of wind turbines / energy storage equipment and the penalty costs for wind curtailment. EX is the power interaction cost between the desalination plant and the distribution grid.

[0179] 3.2) Calculation: The deterministic optimization model for the economic dispatch problem of a seawater desalination plant without considering the uncertainty of wind power output is as follows:

[0180]

[0181] Where A, E, F, and C are the coefficient matrices of the constraints. b and g are constant column vectors. x and I are optimization variables. h is the coefficient matrix. is an uncertain variable.

[0182] 3.3) The uncertainty of wind power output is described by using a box uncertainty set, as shown below:

[0183]

[0184] Where t represents time, T is the total number of time periods in the scheduling cycle, U is the uncertainty set, and u is the uncertain variable. is the wind power forecast, ΔP t max is the maximum fluctuation of wind power, P t WT The predicted power of the wind turbine in the desalination plant in the tth period. R0 is a set of real numbers.

[0185] 3.4) Construct a two-stage robust optimization model as follows:

[0186]

[0187] The two-stage robust optimization model consists of two stages. The first stage is an outer minimization problem, i.e., the minimum operating cost of the system, with the optimization variable being I. The second stage is an inner maximum minimization problem, i.e., finding the worst-case scenario, with the optimization variables being u and x.

[0188] The two-stage robust optimization model is converted into a deterministic optimization model as follows:

[0189]

[0190] Where Ω(x,u) represents the feasible region. λ, γ, and π are all dual variables corresponding to the constraints in the second stage.

[0191] Example 7:

[0192] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is shown in any one of Examples 1 to 6. Furthermore, the operation and maintenance cost C of the RO system of the seawater desalination plant is OP , the start-up and shutdown costs of the RO system of the seawater desalination plant C SU , Wind turbine / energy storage equipment operation and maintenance costs C BE , Wind turbine / energy storage equipment wind curtailment penalty fee C CU , the power interaction cost C between the desalination plant and the distribution network EX As shown below:

[0193]

[0194] Where t represents time, Represents the time period set within the scheduling period. d represents the RO unit index, It is a collection of RO units. c BE 、c BW They are the operation and maintenance cost coefficients of the seawater desalination plant RO system, energy storage equipment, and wind turbine. CU It is the penalty cost coefficient for wind curtailment in desalination plants. The on-grid electricity price of wind power for seawater desalination plants. The electricity price that the desalination plant purchases from the distribution grid. d,t Indicates the water outlet flow rate of the RO unit. is the total cost of starting and stopping the RO unit. t CH 、P t DCH are the charging and discharging power of the energy storage device respectively. t WT Predict the power of wind turbines in desalination plants. t CU Reduce the power of wind turbines in desalination plants. t PR 、P t RP They are respectively the power purchased and sold by the desalination plant to the distribution network.

[0195] Example 8:

[0196] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is described in any one of Examples 1 to 7. Furthermore, in step 4), the steps for solving the two-stage robust optimization model are as follows:

[0197] 4.1) Decompose the two-stage robust optimization model into a main problem and sub-problems as follows:

[0198]

[0199] Where MP is the main problem, subscript l is the iteration index, and k is the number of iterations. SU is the startup and shutdown cost of the RO system in a seawater desalination plant. SP is the subproblem, A, E, F, and C are the coefficient matrices of the constraints. b and g are constant column vectors. x and I are optimization variables. u is an uncertain variable. U is the uncertainty set. Ω(I,u) represents the feasible region. h is the coefficient matrix. η is the auxiliary variable, which is the value of the objective function in the second stage of the optimal solution.

[0200] 4.2) Initialize the number of iterations k = 1, set the upper bound UB = +∞ and the lower bound LB = -∞ of the optimal solution of the two-stage robust optimization model, and set the initial worst scenario value u k .

[0201] 4.3) Based on the worst scenario value u k , find the optimal solution set for the main problem [I k ,η k 、x1…x k ], and update the lower bound of the optimal solution LB=max{C SU +η k ,LB}, where I k 、x1…x k All are optimization variables. k is the auxiliary variable at the kth iteration, that is, the value of the objective function of the second stage in the optimal solution of the Kth iteration.

[0202] 4.4) The optimal solution of the main problem I k Substitute into the subproblem and solve to get the worst scenario value u k+1 , and update the upper bound of the optimal solution UB=min{C SU +Q(I k ),UB}, where Q(I k ) is the output value of the sub-problem, that is, the objective function value of the second stage.

[0203] 4.5) Determine whether UB-UL≤ε holds. If so, output the optimal solution x k ,I k If not, go to step 4.6), where ε is the convergence parameter.

[0204] 4.6) Add variable constraints to the main problem, set the number of iterations k = k + 1, and return to step 4.3).

[0205] The variable constraints are as follows:

[0206]

[0207] Where x k+1 is the optimization variable at the k+1th iteration.

[0208] Example 9:

[0209] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty. The main technical content is shown in any one of Examples 1 to 8. Further, the worst scenario value u is solved. k+1 When , the subproblem is converted into a single-layer optimization problem for solution, as shown below:

[0210]

[0211] sA T λ+E T γ+C T π=h

[0212] γ≤0 (54)

[0213] Where λ, γ, and π represent the dual variables of the corresponding constraints in the second stage. A, E, and F represent the coefficient matrices of the constraints. b and g represent constant column vectors. x and I are optimization variables. u represents an uncertain variable. U represents the uncertainty set. h represents the coefficient matrix.

[0214] Among them, the uncertainty set U is as follows:

[0215]

[0216] Where t represents time and T is the total number of time periods in the scheduling cycle. t WT Predict the power of the wind turbines in the desalination plant during the tth period. is the wind power forecast, ΔP t max is the maximum fluctuation of wind power, B t Indicates whether the parameter has reached the boundary value. W is an uncertain adjustment parameter. R0 is a set of real numbers.

[0217] Example 10:

[0218] A two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty, the main technical content of which is shown in any one of Examples 1 to 9. Furthermore, the two-stage robust optimization model is solved using a Gurobi solver.

[0219] Example 11:

[0220] See also Figures 1 to 8 , a two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty, including the following steps:

[0221] 1) Input the basic parameters of the desalination plant;

[0222] 2) Model the desalination plant equipment units based on basic parameters;

[0223] 3) Based on the above basic model, a two-stage robust optimization model for a seawater desalination plant is established considering the uncertainty of wind power;

[0224] 4) Solve the above-mentioned overall model of the seawater desalination plant and obtain the optimal operation plan of the seawater desalination plant.

[0225] The specific implementation steps are as follows:

[0226] (1) Basic parameters

[0227] The basic parameters of a desalination plant include equipment parameters, time-of-use electricity purchase and sales prices, wind power output in summer and winter during the dispatch cycle, and water load demand. Detailed parameters are given in the following example.

[0228] (2) Equipment Model

[0229] 1. Water Intake Pump Operation Constraints

[0230] The intake pump and high-pressure pump are the most energy-consuming equipment in the RO desalination plant. Assuming the head of the intake pump is fixed, its operating constraints are:

[0231]

[0232] Where: P t In 、 and are the water pump power, water flow rate and head in the tth period respectively; ρ and g are the water density and gravity acceleration respectively. is a 0-1 variable representing the working status of the water intake pump (1 means running); and q In They are In the following text, the subscript t represents the t-th period, and the upper and lower underscores represent the upper and lower limits of the corresponding variables.

[0233] 2. High-pressure pump operation constraints

[0234] 1. Power model

[0235] The power consumed by the high-pressure pump is related to the working pressure, feed seawater concentration, reverse osmosis recovery rate and osmotic membrane parameters, namely:

[0236] q d,t =K d A d (p d,t -Δπ) (3)

[0237]

[0238] Where: p d,t ,q d,t and are the working pressure, outlet flow rate and high-pressure pump power of RO unit d respectively; K d 、A d are the permeability coefficient and membrane area of ​​the dth RO unit membrane respectively; Δπ is the transmembrane osmotic pressure difference; a d and b d is the high-pressure pump power coefficient; C sw is the feed seawater concentration; I d,t is a 0-1 variable representing the operating status of the RO unit d (1 indicates operation).

[0239] Assuming that the reverse osmosis module consists of d RO units connected in parallel, the total power and total fresh water production satisfy:

[0240]

[0241]

[0242] Where: is the set of RO units (d is 3 in this paper), is the time period set within the scheduling period (this paper considers day-ahead scheduling, P t RO and q t are the total power of RO unit and the total flow of fresh water respectively; S RO is the lower limit of freshwater production within the scheduling period; Δt is the scheduling time interval (Δt=1h).

[0243] 2. Work stress model

[0244] To ensure that water molecules can pass through the semipermeable membrane, the operating pressure of the RO unit must be greater than the transmembrane osmotic pressure. However, excessive operating pressure will affect the service life of the semipermeable membrane. Therefore, there are the following constraints:

[0245]

[0246] Where: and Δp d They are the upper and lower limits of the net transmembrane pressure of RO unit d respectively.

[0247] 3. Climbing constraints

[0248] Sudden changes in the operating pressure or power of the RO unit will reduce the service life of the osmotic membrane. Therefore, this paper considers the following ramp constraints:

[0249]

[0250] Where: and are the upper / lower climbing power limits of RO unit d respectively; and The upper limit of the working pressure increase / decrease of the RO unit per unit time period; t = 2,…,24.

[0251] 4. Start and stop frequency constraints

[0252] Frequent start and stop of the RO unit will affect the service life of the osmotic membrane and increase power loss. This paper uses the following constraints to limit the number of start and stop times of the RO unit:

[0253]

[0254] Where: are the single start-stop cost of RO unit d and the total start-stop cost in time period t; MRO is the maximum allowed start-stop times of RO unit in the scheduling period.

[0255] 3. Reservoir Operation Constraints

[0256] The clean water tank stores pre-treated seawater, and the product water tank stores post-treated desalinated water. The operating constraints of the two are similar:

[0257]

[0258]

[0259] Where: and are the water levels of the clean water tank and the product water tank respectively; r Pre is the ratio of the flow rate of pretreated seawater to feed water; A is the water flow rate of the product pool; CLT 、A PRT are the bottom areas of the clean water tank and the product water tank respectively; R is the reverse osmosis recovery rate; Formula (22) indicates that the water level of the reservoir at the end of the scheduling period must be restored to the initial water level.

[0260] IV. Energy Storage Equipment Operation Constraints

[0261] The operating constraints of energy storage equipment are as follows:

[0262]

[0263] Where: P t CH and P t DCH are the charging and discharging power of the energy storage device respectively; η CH and η DCH are the charging and discharging efficiency of the energy storage device respectively; The power of the energy storage device; and are 0-1 variables representing the charging and discharging states of the energy storage device ( Take 1 for charging, (1 is taken for discharge), formula (25) is the mutual exclusion constraint of charge / discharge state; formula (28) is the power constraint of energy storage equipment at the end of the period.

[0264] 5. Wind turbine operation constraints

[0265] The desalination plant is equipped with wind turbines, and the wind power meets the following constraints:

[0266] 0≤P t CU ≤P t WT (29)

[0267] Where: P t WT and P t CU The predicted power and curtailed power are for the wind turbines in the desalination plant respectively.

[0268] 6. Power Balance Constraints

[0269] The desalination plant studied in this paper is an electric energy producer and consumer, and has electric energy interaction with the distribution network. The power balance constraint is:

[0270] P t WT +P t PR -P t CU +P t DCH =P t CH +P t RO +P t In +P t RP (30)

[0271] Where: P t PR P is the power purchased by the desalination plant from the distribution network, t RP The power sold by the desalination plant to the distribution network must meet the following constraints:

[0272]

[0273] Where: It is the power limit for purchasing and selling electricity between the desalination plant and the distribution network.

[0274] Since Equation (5) contains bilinear terms, Equations (16) to (17) are non-convex terms with absolute value signs, and Equations (2), (11) to (17), and (25) to (27) contain integer variables representing the start / stop status of the water intake pump and RO unit, and the charge / discharge status of the energy storage device, the optimal scheduling problem of the desalination plant is a MINLP problem. It is necessary to convexify the bilinear terms and absolute value constraints in the model separately to transform the original problem into a MILP problem.

[0275] 7. Processing of bilinear terms

[0276] The power equation of the high-pressure pump contains the bilinear term q d,t p d,t , this paper uses McCormick envelope to process it and introduces auxiliary variables By replacing the bilinear terms, Equation (5) can be transformed into the following linear constraints:

[0277]

[0278] Equations (34) to (37) are McCormick envelope constraints.

[0279] 8. Processing of Absolute Value Constraints

[0280] Introducing the continuous variable ω d,t By replacing the absolute value symbol, equations (16) and (17) can be transformed into the following set of linear constraints:

[0281] ω d,t ≥I d,t+1 -I d,t (38)

[0282] ω d,t ≥-(I d,t+1 -I d,t ) (39)

[0283]

[0284] Formulas (38) to (39) can ensure that the variable ω d,tNot less than ±(I d,t+1 -I d,t ), eliminating the absolute value sign and transforming the model into a linear constraint form.

[0285] After convexification, the constraints of the desalination plant are summarized as follows:

[0286] 1. Energy consumption equipment (water intake pump, high-pressure pump) operation constraints (Equations (1) to (4), (6) to (15))

[0287] 2. Energy storage and reservoir operation constraints (Equations (18) to (28))

[0288] 3. Wind turbine operation constraints (Equation (29))

[0289] 4. Power balance constraints (Equations (30) to (32))

[0290] 5. Model Convexity Constraints (Equations (33) to (41))

[0291] The above model can be further expressed in the following compact form:

[0292]

[0293] In formula (42), A, E, and F represent the coefficient matrices in the constraints, and b and g are the corresponding constant column vectors.

[0294] Where x and y are optimization variables, and the specific expression is

[0295]

[0296] The vector with subscript d contains the corresponding variables of all RO units, starting with q d For example, it is expressed as:

[0297]

[0298] Where: For nth D The outlet flow vector of each RO unit.

[0299] (3) Two-stage robust optimization model for seawater desalination plants considering wind power uncertainty

[0300] Based on the basic model of the above desalination plant, a two-stage robust optimization model is established.

[0301] The operating goal of a seawater desalination plant is to minimize the daily operating cost, as shown in the formula:

[0302]

[0303] Where: is the total operating cost of the desalination plant under pre-scheduling; C OP 、C SU are the operation and maintenance costs and start-up and shutdown costs of the RO system of the desalination plant; C BE 、C CU are the operation and maintenance costs of wind turbines / energy storage equipment and the penalty costs for wind curtailment; C EX is the power interaction cost between the desalination plant and the distribution network. The sub-item costs are expressed as follows:

[0304]

[0305] Where: c BE 、c BW are the operation and maintenance cost coefficients of the desalination plant RO system, energy storage equipment and wind turbine respectively; c CU Penalty cost coefficient for wind curtailment in desalination plants; They are the on-grid electricity price of wind power of the desalination plant and the electricity purchase price from the distribution network.

[0306] When the uncertainty of wind power output is not considered, the deterministic optimization model of the economic dispatch problem of the above desalination plant can be obtained, and its compact form can be expressed as

[0307]

[0308] h is the corresponding coefficient matrix in the objective function. The first row of the constraints in the compact model is the equality constraint in the optimization model, the second row is the equality constraint, and the third row represents the predicted value of wind power output power.

[0309] Desalination plant optimization scheduling models that don't consider uncertainty often rely on deterministic optimization scheduling models based on forecasts. However, this approach relies on the accuracy of the forecasts. However, the numerous uncertainties inherent in actual power systems make forecast accuracy difficult to guarantee, making uncertainty management crucial.

[0310] The box uncertainty set is used to describe the uncertainty of wind power output and load power.

[0311]

[0312] in, is the wind power forecast, ΔP t max The maximum fluctuation of wind power. The actual wind power output varies within this fluctuation range and is not affected by the wind power output and load power distribution probability function. It can be determined according to previous prediction deviations and actual operating experience.

[0313] The purpose of the two-stage robust optimization model thus constructed is to find the most economically optimal scheduling solution when the uncertain variable u changes towards the worst scenario within the uncertainty set U. It has the following form:

[0314]

[0315] The model is mainly divided into two stages. The outer minimization problem is the first stage, which represents the minimum operating cost of the system, and the optimization variable is I; the inner layer is the maximum minimization problem, which aims to find the worst scenario, and the optimization variables are u and x.

[0316] Ω(I,u) represents the feasible domain of the optimization variable x. Given a set of uncertain variables (I,u), its feasible domain will also change. At this time, the two-stage robust optimization model is converted into a deterministic optimization model. The specific expression is

[0317]

[0318] Where λ, γ, and π represent the dual variables under the corresponding constraints in the second-stage minimization problem.

[0319] (4) Model solution

[0320] For the above two-stage robust optimization model, the column and constraint generation (C&CG) algorithm is adopted to solve it. The original problem is decomposed into a main problem and sub-problems. When solving the main problem, constraints and variables related to the sub-problems are continuously added to obtain a more compact lower bound value. By alternately solving the main problem and sub-problems, the upper and lower bounds of the optimal solution are continuously converged, and the optimal solution is obtained.

[0321] By decoupling the original problem and adding the optimal and feasible cutting plane constraints of the sub-problems on the basis of the main problem constraints, the main problem is obtained as

[0322]

[0323] In the formula, l represents the current number of iterations, x l 、u l They represent the values ​​of the subproblems after l iterations.

[0324] After decoupling, the sub-problem is in the form of

[0325]

[0326] Given Ω(x,u), the subproblem is a deterministic optimization problem. However, it is difficult to solve the two-layer optimization problem. Through dual transformation, the inner layer min is converted to max and merged with the outer layer max to convert it into a single-layer optimization problem. The following problem is obtained after the transformation:

[0327]

[0328] st A T λ+E T γ+C T π=h

[0329] γ≤0 (53)

[0330] According to the relevant conclusions of linear optimization theory and extreme point method, when the dual problem of (53) obtains the optimal solution, the uncertain parameter u will take the value of a certain extreme point in its uncertain set U. In other words, when the dual problem of (53) obtains the optimal solution, the uncertain parameter will take the value at the boundary value of its value interval. By introducing the uncertain adjustment parameter, the uncertain set can be rewritten as follows:

[0331]

[0332] Where B t Takes -1 or 1, which indicates whether the parameter has reached the boundary value. W is an uncertain adjustment parameter, whose value is 0…T. It can be used to adjust the robustness of the optimal solution of the model. When the value is larger, the model is more conservative, and when the value is smaller, it will be more risky. W When is 0, the uncertain parameters will not exist and the model will be converted to a deterministic optimization model. At this point, the subproblem has become a max single-layer optimization model.

[0333] Through a series of derivation and transformation, the two-stage robust optimization model is finally transformed into the main problem (51) and the sub-problem (53). The column and constraint generation algorithm (C&CG) is used to iteratively solve the main problem and the sub-problems, and finally the optimal solution is obtained.

[0334] C&CG algorithm steps:

[0335] At the beginning, we first set a set of worst-case scenario values, then solve the main problem, obtain the optimal solution of the main problem and substitute it into the sub-problem, solve the sub-problem to obtain a new set of worst-case scenarios, and at the same time substitute the constraints corresponding to the scenario into the main problem, and continuously alternately iterate the solution, so that the upper and lower bounds of the optimal solution of the original problem continue to converge, and finally the optimal solution is obtained.

[0336] The specific steps for solving the problem are as follows.

[0337] Step 1: Set a set of worst-case scenario values, set the upper and lower bounds of the optimal solution of the objective function UB = +∞, UL = -∞, the number of iterations k = 1, and the convergence parameter ε = 0.005;

[0338] Step 2: Obtain the optimal solution of the main problem by solving the main problem (I k ,η k 、x1…x k ), update the lower bound of the optimal solution of the objective function

[0339]

[0340] Step 3: Solve the I obtained from the main problem k Substitute into the subproblem and get the worst scenario u k+1 , update the upper bound of the objective function

[0341]

[0342] Step 4: Determine whether the upper and lower bounds of the optimal solution of the objective function converge. If UB-UL≤ε is satisfied, stop the iteration and output the optimal solution x k ,I k Otherwise, add the following constraints:

[0343] η≥h T x k+1

[0344] Ax k+1 +b=0

[0345] Ex k+1 +FI+g≤0

[0346]

[0347] Let k = k + 1, return to step 2 and continue iterating until the convergence condition is met.

[0348] In summary, the Gurobi solver is used to solve the model and obtain the optimization results.

[0349] Example 12:

[0350] The two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty, the main technical content is shown in Example 11, and further, as shown in the attached Figure 2As shown in the figure, seawater first enters the clear water tank through the water intake pump for pretreatment. After flocculation, sedimentation and other treatments, it enters the reverse osmosis unit for desalination treatment. The high-pressure pump of the reverse osmosis unit is pressurized to achieve salt-water separation, and the concentrated brine enters the concentrated brine tank; the desalinated fresh water enters the product water tank to supply the water load; the seawater desalination plant is equipped with clear water tanks and product water tanks to achieve flexible regulation of water production plans.

[0351] (1) Input basic data

[0352] As mentioned above, input the basic parameters of the desalination plant. Among them, the purchase / sale electricity price is shown in Table 1; the wind power in summer and winter during the dispatch period is shown in Table 2; the water load demand is shown in the attached Figure 4 shown.

[0353] Table 1 Purchase / sale electricity prices

[0354]

[0355] Table 2 Wind power in summer and winter during the dispatch period

[0356] Time Summer wind power / kW Winter wind power / kW 1 88.25 459.38 2 129.95 342.22 3 162.45 261.96 4 150.13 274.81 5 99.37 279.53 6 135.87 258.54 7 23.52 312.35 8 31.57 390.25 9 102.77 330.37 10 74.99 124.99 11 68.64 126.48 12 24.43 121.71 13 4.18 142.83 14 11.70 172.67 15 4.12 210.70 16 19.81 162.64 17 18.51 274.65 18 0 402.30 19 82.37 470.42 20 274.78 317.10 21 527.83 178.41 22 563.22 136.14 23 675.35 122.11 24 768.61 197.04

[0357] (2) Model establishment and solution

[0358] As mentioned above, a two-stage robust optimization model of a seawater desalination plant considering the uncertainty of wind power is established, with Equation (49) as the objective function, and then the Gurobi solver is called in Yalmip to solve and obtain the optimization results.

[0359] (3) Experimental results

[0360] A three-pronged analysis of desalination plant scenarios verifies the effectiveness and superiority of the present invention. First, assuming a wind power uncertainty parameter of 12, the economic dispatch results of the desalination plant are analyzed. Example 1 is set up as follows: Scenario A: Two-stage robust optimal dispatch of a desalination plant under winter wind power conditions; Scenario B: Two-stage robust optimal dispatch of a desalination plant under summer wind power conditions.

[0361] Furthermore, to verify that the scheduling scheme derived from the robust optimization model of the present invention corresponds to the worst-case scenario, Example 2, based on the summer scenario, was set up as follows: Scheme A: A two-stage robust optimization model with the wind power uncertainty parameter set to 12 hours; Scheme B: A deterministic optimization scheme with the 10-21 hour period as the minimum of the wind power processing prediction interval; Scheme C: A deterministic optimization scheme with the 1-9 and 22-24 hour periods as the minimum of the wind power processing prediction interval; Scheme D: The same two-stage robust optimization model with the wind power output and wind power uncertainty parameter set to 12 hours.

[0362] On the other hand, to verify that the optimization method proposed in this invention can flexibly adjust the conservatism of the scheduling scheme, Example 3 is set up as follows based on the summer scenario: Scheme A: The wind power uncertainty parameter is set to 0; Scheme B: The wind power uncertainty parameter is set to 12; Scheme C: The wind power uncertainty parameter is set to 24.

[0363] On the other hand, in order to verify that the scheduling scheme obtained by the optimization method proposed in the present invention has stronger robustness and the ability to resist the risk of real-time market electricity price fluctuations, the prediction error is taken as 10%. Example 4 is set up as follows based on the summer scenario: Scheme A: a two-stage robust optimization model with an uncertain wind power parameter of 12; Scheme B: a deterministic optimization model.

[0364] Calculation example 1

[0365] First, we analyze two scenarios for desalination plant scheduling in two seasons. Table 3 below shows the various costs and energy consumption of the desalination plant under the two scenarios.

[0366] Table 3 Cost and energy consumption of Example 1

[0367] plan A B Total cost / yuan 7914.5 8795.83 RO system operation and maintenance cost / yuan 6691.7 6691.7 High-pressure pump start-up and shutdown cost / yuan 15.75 15.75 Electricity purchase cost / yuan 910.88 1855 Electric energy storage operation and maintenance cost / yuan 74 73.96 Wind turbine operation and maintenance cost / yuan 159 98.42 Wind curtailment penalty / yuan 0 0 Electricity sales profit / yuan 0 2.17 Desalination plant energy consumption / kWh 7423.67 7436.19

[0368] An analysis of Plan A shows that wind power output reaches a severe level in periods 3, 4, 6, 9-11, and 19-24. Due to the low wind power output throughout the day, the desalination plant needs to purchase electricity from the distribution network at the beginning of the day to meet its own power consumption. As the electricity price reaches the normal price, the desalination plant chooses to purchase more electricity for energy storage to hedge against peak electricity prices and reduce total costs. The electricity price is higher in the period 11-19, and the electricity in the energy storage equipment is used first, and electricity purchase is avoided as much as possible. As night falls, wind power output increases sharply. At this time, the wind power basically covers the energy consumption of the desalination plant, so there is basically no need to purchase electricity to meet its own power needs. Energy storage charging is carried out in the period 23-24 to restore the energy storage to its initial capacity. An analysis of Plan B shows that the wind power output is in severe conditions in periods 1, 2, 8, 9, and 14-21 respectively. In winter, the wind power output is large throughout the day. In the initial period of the day, since the electricity price is at the valley hour, more electricity will be purchased to offset the peak electricity price and reduce the total cost. When the water load reaches a high level throughout the day, the desalination plant consumes a lot of energy. At this time, the electricity in the energy storage will be used first to meet its own needs. In the period 22-24, the wind power output cannot meet the energy consumption needs of the desalination plant. At this time, the electricity price is at the valley hour, so a large amount of electricity will be purchased to meet its own needs and restore the energy storage to the initial power.

[0369] In summary, the correctness and effectiveness of the two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty proposed in this invention are verified through examples.

[0370] Calculation example 2

[0371] Three deterministic optimization schemes for desalination plant scheduling are solved. Table 4 below shows the total cost of the desalination plant under the four schemes.

[0372] Table 4 Cost of each solution in Example 2

[0373] plan A B C D Total cost / yuan 8795.83 8590.23 8606.72 8795.83

[0374] Table 4 shows that although the period in which the wind power output reaches the minimum of the forecast interval in Scheme 2 includes all peak-price periods, and the period in which the wind power output reaches the minimum of the forecast interval in Scheme 3 includes all off-peak-price periods, both scenarios are still not the worst-case scenario, and the day-ahead operating costs are lower than those obtained by the robust optimization model. Only in Scheme 4, when the time periods selected for both scenarios are exactly the same, does the operating cost obtained by the deterministic optimization model match that of the two-stage robust optimization model.

[0375] In summary, the calculation examples verify that the scheduling scheme obtained by the two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty proposed in this invention corresponds to the worst scenario.

[0376] Calculation example 3

[0377] Solve the three solutions of Example 3. Table 5 below shows the operating costs of the seawater desalination plant under the three solutions.

[0378] Table 5 Operating costs of seawater desalination plants under different uncertain regulation parameters

[0379] plan A B C Total cost / yuan 8530.41 8795.83 8826.28

[0380] As shown in Table 5, when the uncertainty adjustment parameter is equal to 0, the two-stage robust optimization model is equivalent to deterministic optimization. As the uncertainty adjustment parameter increases, the desalination plant's operating costs also increase accordingly. In other words, the more the desalination plant considers the uncertainty it faces when formulating its day-ahead scheduling plan, the more conservative the resulting plan, and the higher the corresponding operating costs. This increase in operating costs is primarily due to the desalination plant's increased electricity purchases from the distribution network and decreased electricity sales, as shown in Table 6. A larger uncertainty adjustment parameter means a greater number of periods in which wind power output reaches the minimum value of the forecast interval. Consequently, the desalination plant's surplus / surplus power also increases / decreases accordingly, resulting in a higher total electricity purchase.

[0381] Table 6 Electricity purchase / sale of desalination plants under different uncertain regulation parameters

[0382] plan A B C Power purchased / kWh 3856.42 4248.31 4339.39

[0383] In summary, the example demonstrates that the two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty proposed in this invention can flexibly adjust the conservatism of the scheduling scheme.

[0384] Calculation example 4

[0385] Assuming that the purchase / sale price in the real-time market is 1.5 / 0.5 times the price in the corresponding period in the day-ahead market, the final operating costs of the robust optimization method and the deterministic optimization method under different wind power forecast errors are shown in Table 7.

[0386] Table 7 Comparison of optimization methods under different prediction errors

[0387] plan A B Day-ahead operating cost / yuan 8795.83 8530.41 Balance cost / yuan 555.70 892.00 Total cost / yuan 9351.53 9422.41

[0388] The day-ahead scheduling scheme obtained using the deterministic optimization method in Table 7 has lower operating costs than the robust optimization method. This does not necessarily mean that the deterministic optimization method is superior to the robust method. This scheme corresponds to the dispatch plan submitted by the desalination plant in the day-ahead market. However, the imbalance between the planned power generation and consumption and the actual power generation and consumption the following day caused by forecast errors must be compensated by the desalination plant in the real-time market. The purchase and sale prices in the real-time market are generally higher or lower than those in the day-ahead market, which ultimately increases the desalination plant's transaction costs. Because the robust optimization method accounts for wind power output uncertainty, the imbalance caused by forecast errors in the real-time market is lower than that in the deterministic optimization method, thereby reducing the final operating costs.

[0389] In summary, the example shows that the scheduling scheme obtained by the two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty proposed in this invention has stronger robustness and the ability to resist the risk of real-time market electricity price fluctuations.

Claims

1. A two-stage robust scheduling method for seawater desalination plants considering wind power uncertainty, characterized by: The following steps are involved: 1) Obtain basic parameters of the desalination plant; 2) Based on the basic parameters of the desalination plant, a seawater desalination plant model is constructed. 3) Based on the desalination plant model, a two-stage robust optimization model is constructed; 4) The column and constraint generation algorithm is used to solve the two-stage robust optimization model to obtain the optimal scheduling scheme of the seawater desalination plant considering the uncertainty of wind power.

2. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 1 is characterized in that: The basic parameters of the desalination plant include equipment parameters, time-of-use electricity purchase price, electricity sales price, summer wind power within the dispatching cycle, winter wind power within the dispatching cycle, and water load demand; The equipment includes a water intake pump, a high-pressure pump, an RO unit, an energy storage device, and a wind turbine.

3. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 1 is characterized in that: The constraints of the desalination plant model include energy consumption equipment operation constraints, energy storage and water reservoir operation constraints, wind turbine operation constraints, power balance constraints, and model convexity processing constraints; The energy consumption equipment operation constraints include water intake pump operation constraints and high pressure pump operation constraints; The high-pressure pump operation constraints include power constraints, working pressure constraints, ramp constraints, and RO unit start and stop times constraints; The energy storage and water reservoir operation constraints include water reservoir operation constraints and energy storage equipment operation constraints; The model convexity processing constraints include bilinear term processing constraints and absolute value constraints.

4. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 3 is characterized in that: The water intake pump operation constraints are as follows: Where t represents time, P t In 、 are the water pump power, water flow rate, and head at the t-th period respectively; ρ and g are the water density and gravity acceleration respectively; Characterize the working status of the water intake pump; and q In Water intake flow The upper and lower limits of η In The pump unit efficiency of the water intake pump; The power constraints are as follows: q d,t =K d A d (p d,t -Δπ) (3) Where d represents the RO unit index, p d,t ,q d,t 、 They represent the working pressure, outlet flow rate, and high-pressure pump power of the dth RO unit in the tth period respectively; K d 、A d are the permeability coefficient and membrane area of ​​the dth RO unit membrane respectively; Δπ is the transmembrane osmotic pressure difference; and q d,t The water flow rate q d,t Upper and lower limits of I d,t Characterizes the operating status of the dth RO unit in the tth period; a d and b d is the high-pressure pump power coefficient; C sw is the feed seawater concentration; and High pressure pump power Upper and lower limits; and p d,t The working pressure p d,t Upper and lower limits; is the RO unit set; P t RO Indicates the total power of the RO unit; q t represents the total freshwater flow; S RO Indicates the lower limit of freshwater production within the scheduling period; represents the time period set within the scheduling cycle; Δt represents the scheduling time interval; R is the reverse osmosis recovery rate; The operating pressure constraints are as follows: Where, and Δ p d are the upper and lower limits of the net transmembrane pressure of the dth RO unit respectively; The climbing constraints are as follows: Where, I represents the high-pressure pump power of the d-th RO unit in the t-1th period; d,t-1 Characterizes the operating status of the dth RO unit in the t-1th period; is the upper limit of the climbing power of the dth RO unit; is the upper limit of the downward climbing power of the dth RO unit; The upper limit of the working pressure increment per unit time period of the dth RO unit; The upper limit of the working pressure reduction per unit time period of the dth RO unit; Indicates the upper limit of the total power of the dth RO unit; p d,t-1 represents the working pressure of the dth RO unit in the t-1th period; Indicates the total working pressure p of the dth RO unit d Upper limit of The constraints on the start and stop times of the RO unit are as follows: Where, is the single start-up and shutdown cost of the dth RO unit; is the total cost of starting and stopping the dth RO unit in the tth period; M RO is the maximum number of start and stop times allowed for the RO unit within the scheduling period; T is the total number of time periods within the scheduling period; I d,t+1 Characterizes the operating status of the dth RO unit in the t+1th period; The operating constraints of the water reservoir are as follows: Where, are the water levels of the clean water tank and product water tank in the tth period respectively; Respectively represent the water levels of the clean water tank and product water tank in the t-1th period; r Pre is the ratio of the flow rate of pretreated seawater to feed water; A is the water flow rate of the product pool; CLT 、A PRT are the bottom areas of the clean water tank and product water tank respectively; h CLT are the upper and lower limits of the water level in the clear water tank respectively; h PRT They are the upper and lower limits of the product pool water level respectively; The energy storage equipment operation constraints are as follows: Where, is the energy storage device power in the tth period; is the energy storage device power in the t-1 period; E BE are the upper and lower limits of the energy storage device’s power respectively; η CH ,η DCH are the charging and discharging efficiency of energy storage equipment respectively; P t CH 、P t DCH are the charging and discharging power of the energy storage device in the tth period respectively; Respectively characterize the charging and discharging states of the energy storage device; P CH They are the upper and lower limits of the charging power of the energy storage equipment respectively; P DCH They are the upper and lower limits of the energy storage device discharge power respectively; The wind turbine operation constraints are as follows: 0≤P t CU ≤P t WT (29) Where, P t WT 、P t CU The predicted power and curtailed power of the wind turbines in the desalination plant in the tth period are respectively; The power balance constraints are as follows: P t WT +P t PR -P t CU +P t DCH =P t CH +P t RO +P t In +P t RP (30) Where, P t PR is the power purchased by the desalination plant from the distribution grid, P t RP The power sold by the desalination plant to the distribution grid; A cap on the power that desalination plants can purchase from the distribution grid; The upper limit of the power that the desalination plant can sell to the distribution grid; The bilinear term processing constraints are as follows: Where, is an auxiliary variable; The absolute value constraints are as follows: oh d,t ≥I d,t+1 -I d,t (38) ω d,t ≥-(I d,t+1 -I d,t ) (39) Where, ω d,t is a continuous variable; is the upper limit of the total start-up and shutdown cost of the d-th RO unit in the t-th period.

5. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 1 is characterized in that: The desalination plant model is shown below: Where A, E, and F are coefficient matrices of constraints; b and g are constant column vectors; Among them, the optimization variables x and I are as follows: Where, P In ,q In are the water pump power and water flow rate respectively; p d ,q d Respectively represent the working pressure and water flow rate of the RO unit; Indicates the 1st,...,nth D The outlet flow vector of each RO unit; is the high-pressure pump power of the RO unit; P RO represents the total power of the RO unit; q represents the total flow of fresh water; h CLT 、h PRT are the water levels of the clean water tank and the product water tank respectively; P CH 、P DCH are the charging and discharging power of the energy storage device respectively; E BE is the power of the energy storage device; P CU Cutting power for wind turbines at desalination plants; is an auxiliary variable; ω d is a continuous variable; is the total start-up and shutdown cost of the RO unit; P PR 、P RP are the power purchased and sold by the desalination plant to the distribution network; P WT Predicting the power of wind turbines in desalination plants; In Characterizes the working status of the water pump; I d Characterizes the operating status of the RO unit; I CH , I DCH Respectively represent the charging and discharging states of the energy storage device.

6. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 1 is characterized in that: In step 3), the steps for constructing a two-stage robust optimization model are as follows: 3.1) Determine the operational objectives of the desalination plant as follows: Where, is the total operating cost of the desalination plant under pre-scheduling; C OP 、C SU are the operation and maintenance costs and start-up and shutdown costs of the RO system of the seawater desalination plant; C BE 、C CU are wind turbine / energy storage equipment operation and maintenance costs, and wind curtailment penalty costs; C EX is the power interaction cost between the desalination plant and the distribution grid; 3.2) Calculation: The deterministic optimization model for the economic dispatch problem of a seawater desalination plant without considering the uncertainty of wind power output is as follows: Where A, E, F, and C are the coefficient matrices of the constraints; b and g are constant column vectors; x and I are optimization variables; and h is the coefficient matrix. is an uncertain variable; 3.3) The uncertainty of wind power output is described by using a box uncertainty set, as shown below: Where t represents time, T is the total number of time periods in the scheduling cycle; U is the uncertainty set; u is the uncertain variable; P t pre is the wind power forecast, ΔP t max is the maximum fluctuation of wind power, P t WT For the tth period Predicted power of wind turbines in seawater desalination plants; R0 is a set of real numbers; 3.4) Construct a two-stage robust optimization model as follows: The two-stage robust optimization model consists of two stages. The first stage is the outer minimization problem, i.e., the minimum operating cost of the system, with the optimization variable I; the second stage is the inner maximum minimization problem, i.e., finding the worst scenario, with the optimization variables u and x. The two-stage robust optimization model is converted into a deterministic optimization model as follows: Where Ω(x,u) represents the feasible region; λ, γ, and π all represent the dual variables corresponding to the constraints in the second stage.

7. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 6 is characterized in that: The operation and maintenance cost of the RO system of the seawater desalination plant is C OP , the start-up and shutdown costs of the RO system of the seawater desalination plant C SU , Wind turbine / energy storage equipment operation and maintenance costs C BE , Wind turbine / energy storage equipment wind curtailment penalty fee C CU , the power interaction cost C between the desalination plant and the distribution network EX As shown below: Where t represents time, represents the time period set within the scheduling cycle; d represents the RO unit index, is a collection of RO units; c BE 、c BW are the operation and maintenance cost coefficients of the seawater desalination plant RO system, energy storage equipment, and wind turbine respectively; c CU The penalty cost coefficient for wind curtailment in desalination plants; The on-grid tariff for wind power generated by desalination plants; is the electricity price purchased by the desalination plant from the distribution grid; d,t Indicates the water flow rate of the RO unit; is the total start-up and shutdown cost of the RO unit; P t CH 、P t DCH are the charging and discharging power of the energy storage device respectively; P t WT Predict the power of wind turbines in seawater desalination plants; P t CU Reduce the power of wind turbines in desalination plants; t PR 、P t RP They are respectively the power purchased and sold by the desalination plant to the distribution network.

8. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 1, characterized in that: In step 4), the steps for solving the two-stage robust optimization model are as follows: 4.1) Decompose the two-stage robust optimization model into a main problem and sub-problems as follows: Where MP is the main problem, subscript l is the iteration index, k is the number of iterations; C SU is the start-up and shutdown cost of the RO system of the seawater desalination plant; SP is the subproblem, A, E, F, and C are the coefficient matrices of the constraint conditions; b and g are constant column vectors; x and I are optimization variables; u is an uncertain variable; U is an uncertainty set; Ω(I,u) represents the feasible region; h is the coefficient matrix; η is an auxiliary variable; 4.2) Initialize the number of iterations k = 1, set the upper bound UB = +∞ and the lower bound LB = -∞ of the optimal solution of the two-stage robust optimization model, and set the initial worst scenario value u k ; 4.3) Based on the worst scenario value u k , find the optimal solution set for the main problem [I k ,η k 、x1…x k ], and update the lower bound of the optimal solution LB=max{C SU +η k ,LB}, where I k 、x1…x k All are optimization variables; η k is the auxiliary variable at the kth iteration; 4.4) The optimal solution of the main problem I k Substitute into the subproblem and solve to get the worst scenario value u k+1 , and update the upper bound of the optimal solution UB=min{C SU +Q(I k ),UB}, where Q(I k ) is the output value of the sub-problem; 4.5) Determine whether UB-UL≤ε holds. If so, output the optimal solution x k ,I k If not, proceed to step 4.6), where ε is the convergence parameter; 4.6) Add variable constraints to the main problem, set the number of iterations k = k + 1, and return to step 4.3); The variable constraints are as follows: Where x k+1 is the optimization variable at the k+1th iteration.

9. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 8, characterized in that: Solve the worst scenario value u k+1 When , the subproblem is converted into a single-layer optimization problem for solution, as shown below: Where λ, γ, and π are all dual variables corresponding to the constraints in the second stage; A, E, and F are all coefficient matrices of the constraints; b and g are all constant column vectors; x and I are both optimization variables; u is an uncertain variable; U is an uncertainty set; and h is a coefficient matrix. Among them, the uncertainty set U is as follows: Where t represents time, T is the total number of time periods in the scheduling cycle; P t WT The predicted power of the wind turbine in the desalination plant in the tth period; P t pre is the wind power forecast, ΔP t max is the maximum fluctuation of wind power, B t Indicates whether the uncertainty parameter takes the boundary value; Γ W is an uncertain adjustment parameter; R0 is a real number set.

10. The two-stage robust scheduling method for a seawater desalination plant considering wind power uncertainty according to claim 1, characterized in that: The two-stage robust optimization model is solved using the Gurobi solver.

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