Linearization method of reversible pumped storage power station dispatching operation model

Abstract

The invention discloses a linearization method of a reversible pumped storage power station dispatching operation model. Comprising the following steps: sequentially carrying out linearization processing on a nonlinear part containing an absolute value in a reversible pumped storage power station dispatching operation model, carrying out linearization processing on a nonlinear part containing a quadratic term in a reservoir capacity curve, and carrying out linearization processing on an operation state constraint of a pumped storage reversible unit; and carrying out linearization processing on a pumped storage reversible unit power generation output function, carrying out linearization processing on a pumped storage reversible unit power generation output vibration area, and carrying out linearization processing on a part containing an extreme value function. According to the method, a complex scheduling model is integrally converted into a standard mixed integer linear programming model, so that an efficient commercial solver can be directly utilized for rapid solving, and the generation efficiency and stability of the pumped storage power station optimization scheduling scheme are remarkably improved on the premise of ensuring the model precision.

Description

Technical Field

[0001] This invention relates to a linearization method for the scheduling and operation model of a pumped storage power station, specifically a linearization method for the scheduling and operation model of a reversible pumped storage power station, belonging to the field of reservoir scheduling technology. Background Technology

[0002] Generally, the operation and scheduling of hydropower stations is a complex problem involving multiple factors and objectives. With the large-scale integration of new energy sources into the power grid, reversible pumped storage power stations, due to their bidirectional regulation capabilities, are crucial in peak shaving and valley filling and balancing fluctuations in the power grid. Specifically, the optimal scheduling of reversible pumped storage power stations aims to establish and solve mathematical models containing complex physical constraints. To effectively manage the power generation scheduling of reservoir groups, efficient mathematical models and optimization methods are needed. However, traditional methods typically employ nonlinear mathematical programming techniques such as dynamic programming and genetic algorithms, which face inherent challenges such as high model complexity, low solution efficiency, large result errors, and susceptibility to local optima. Therefore, transforming nonlinear models into efficiently solvable mixed-integer linear programming models has become an important research direction.

[0003] Existing technologies, such as the optimization analytical method and system for pumped storage power station scheduling disclosed in CN118539473B and the rapid operation simulation method for reversible hydropower stations considering unit vibration zone constraints disclosed in CN119227338A, both reflect this trend. The former proposes to linearize the objective function, constraints, and characteristic curves and use mixed-integer linear programming for solution; the latter uses unit aggregation and integer variable linear relaxation methods to specifically linearize vibration zone constraints to improve solution speed. However, these existing technologies still have obvious limitations: they either only focus on the overall linearization of the model without elaborating on the specific technical means for handling various nonlinear elements, or they only linearize specific constraints such as vibration zones, lacking a complete method that can systematically and meticulously coordinate the handling of all core nonlinear elements in the scheduling model. Specifically, existing technologies fail to provide a unified and accurate linearization transformation system for the nonlinear relationship between reservoir water level and capacity, the complex binary nonlinear characteristics between unit output, head, and flow rate, the mutually exclusive logical constraints of power generation and pumping operations, and common absolute value and extremum functions in the objective function. This results in linear models that either have insufficient approximations of key physical characteristics, affecting scheduling accuracy, or still suffer from solution efficiency bottlenecks due to incomplete linearization. Summary of the Invention

[0004] The purpose of this invention is to provide a linearization method for the scheduling and operation model of a reversible pumped storage power station in order to solve at least one of the above-mentioned technical problems. This linearization method utilizes systems engineering theory and modern computer technology to reduce the difficulty of solving complex nonlinear problems and improve the efficiency of solving them. Compared with traditional methods, this method can generate scheduling plans that meet scheduling principles more quickly, reduce solution errors, and has lower requirements for computing resources.

[0005] This invention achieves the above objective through the following technical solution: a linearization method for a reversible pumped storage power station scheduling and operation model, the linearization method comprising the following steps: S1. Linearize the nonlinear part containing absolute values ​​in the reversible pumped storage power station scheduling and operation model. S2. Linearize the nonlinear part of the reservoir capacity curve containing quadratic terms in the reversible pumped storage power station scheduling and operation model. S3. Linearize the operating state constraints of the reversible pumped storage units in the dispatch and operation model of the reversible pumped storage power station. S4. Linearize the power output function of the reversible pumped storage unit in the dispatch and operation model of the reversible pumped storage power station. S5. Linearize the vibration zone of the power generation output of the reversible pumped storage unit in the dispatch and operation model of the reversible pumped storage power station. S6. Linearize the part of the reversible pumped storage power station scheduling and operation model that contains the extreme value function.

[0006] As a further technical solution of the present invention, in S1, linearizing the nonlinear part containing absolute values ​​specifically includes: S11. Express the linear polynomial in the absolute value using a single free variable X: ; in, For a single free variable, For linear polynomials in absolute value, , , ... These are polynomial coefficients. , , ... These are free variables in a polynomial; S12, Introducing auxiliary variables and express And the three have the following relationship: ; in, For the part to be linearized, , For linearization auxiliary variables; S13, will Using linearized auxiliary variables and The representation is as follows: ; S14. Determine the linearization auxiliary variables. and Boundary: ; This concludes the linearization process for the nonlinear part containing absolute values.

[0007] As a further technical solution of the present invention, in S2, the linearization process for the nonlinear part containing quadratic terms specifically includes: S21, The reservoir capacity curve satisfies the function And the function contains water level The quadratic term, where V represents the reservoir capacity and Z represents the water level; S22. Based on the degree of piecewise linear fitting, the water level is divided into... There are several intervals, namely: , ,…, ; S23, Introducing binary variables ,and ,Will and It is expressed as follows: ; in, 0-1 variables; S24. Introducing auxiliary variables ,and For binary variables Apply boundary constraints: ; This concludes the linearization process for the nonlinear part containing quadratic terms.

[0008] As a further technical solution of the present invention: In S3, the linearization processing of the operating state constraints of the pumped storage reversible unit specifically includes: S31. The operating state constraints of the reversible pumped storage unit in the dispatching and operation model of the reversible pumped storage power station are expressed as follows: ; in, This refers to the number of pumped storage reversible units. Index for pumped storage reversible units. Indicates time period, This is the state variable for the pumped-storage reversible generator unit, where 0 indicates it is not operating and 1 indicates it is operating. It is the state variable of the pumping operation of the pumped storage reversible unit, where 0 indicates no operation and 1 indicates operation. S32, Introducing an auxiliary binary variable and

[0009] ; S33, through the introduction of auxiliary binary variables and For situations where one or more pumped storage reversible units are generating electricity while other pumped storage reversible units cannot be in pumping mode, the following handling should be performed: ; Among them, if If it equals 1, then It must be equal to 0, and It also equals 0; S34, through the introduction of auxiliary binary variables and For situations where one or more pumped storage reversible units are pumping water while other pumped storage reversible units cannot generate electricity, the following handling should be applied: ; Among them, if If it equals 1, then It must be equal to 0, and If it equals 0, then Equal to 0; This concludes the linearization process for the operating state constraints of the pumped storage reversible unit.

[0010] As a further technical solution of the present invention, in S4, the linearization processing of the power output function of the pumped storage reversible unit specifically includes: S41. The power output function of a pumped-storage reversible unit is expressed as follows: ; in, To generate electricity for pumped-storage reversible units. For the density of water, This refers to the power generation efficiency of pumped storage reversible units. The headwater for generating electricity in pumped-storage reversible units. The flow rate used for power generation in pumped storage reversible units; S42. Introducing the triangulation method, based on the maximum and minimum net head values ​​of the pumped storage reversible unit throughout the entire dispatch range, three turbine performance curves are considered for each pumped storage reversible unit's power generation conditions, corresponding to low ( ),middle( ) and high ( The head of the pumped storage reversible unit is divided into J triangular sub-regions, forming a two-dimensional space based on the power output function of the pumped storage reversible unit. S43. Introducing binary variables

[0011] ; ; in, It is a binary variable, representing the first... Does the combination of the unit's power output, net head of power generation, and power generation flow rate occur in the [missing information] section? Within a triangle; S44. Set weight coefficients , indicating a time period Inner The first triangle The weight of each vertex; This concludes the linearization process for the power output function of the pumped storage reversible unit.

[0012] As a further technical solution of the present invention, the weighting coefficient The specific settings include: S441. Set weight coefficients Boundary constraints: ; Where u is the vertex index of the triangle; S442, Based on weighting coefficients For the The first triangle At the vertex The upper and lower boundaries of the net head for power generation in a pumped storage reversible unit are as follows: ; ; in, Indicates the first The first triangle At the vertex The net head of power generation from a Taiwanese pumped-storage reversible generator unit. It is a maximum constant; S443, Based on weighting coefficients For the The first triangle At the vertex The power generation flow of the pumped storage reversible unit is expressed as follows: ; in, Indicates the first Taiwan pumped storage reversible unit in the first The first triangle The power generation flow at each vertex; S444, Based on weighting coefficients For the The first triangle At the vertex The power generation flow of the pumped storage reversible unit is expressed as follows: ; in, Indicates the first The first triangle The vertex of the first vertex The power output of the pumped storage reversible unit.

[0013] As a further technical solution of the present invention, in S5, the linearization treatment of the power output vibration zone of the pumped storage reversible unit specifically includes: S51. The vibration zone constraints in the dispatch and operation model of a reversible pumped storage power station are represented as follows: ; in, This represents the power output of the i-th pumped storage reversible unit during time period t. , These are pumped storage reversible units. The upper and lower limits of the output force in the r-th vibration zone; S52. Pumped storage reversible generator units often have multiple vibration zones, dividing the output range into multiple discontinuous intervals. After considering the maximum and minimum technical output of the pumped storage reversible generator unit, the R vibration zones divide the output of the pumped storage reversible generator unit into R+1 safe operating zones. S53, Introducing Indicator Variables Used to indicate pumped storage reversible units exist The output at any moment is in the first A safe operating zone is defined, and indicator variable boundaries are set: ; S54. Utilizing the introduced indicator variables Boundary constraints are applied to the power generation output of pumped storage reversible units: ; in, , These represent pumped storage reversible units. No. The upper and lower limits of each safe operating zone, and satisfying , , , ; This concludes the linearization process for the power output vibration zone of the pumped storage reversible unit.

[0014] As a further technical solution of the present invention, in S6, the linearization processing of the part containing the extremum function specifically includes: S61. Linearize the maximum value function; S62. Linearize the minimum value function.

[0015] As a further technical solution of the present invention, in S61, the linearization process of the maximum value function specifically includes: S611. Express the maximum value function expression using a single free variable Y: ; Where Y is a single free variable, Let be a variable with index t, where t = 1, 2, ..., T. express The maximum value at index t; S612, Introducing binary auxiliary variables Boundary constraints are applied to the introduced single free variable Y: ; ; Where M is a local constant; S613, Regarding the introduced binary auxiliary variables Apply boundary constraints: ; This concludes the linearization process for the maximum value function.

[0016] As a further technical solution of the present invention, in S62, the linearization process of the minimum value function specifically includes: S621. Express the minimum value function expression using a single free variable Z: ; Where Z is a single free variable. Let be a variable with index t, where t = 1, 2, ..., T. express The minimum value at index t; S622, Introducing binary auxiliary variables Boundary constraints are applied to the introduced single free variable Z: ; ; Where M is a local constant; S623, Regarding the introduced binary auxiliary variables Apply boundary constraints: ; This concludes the linearization process for the minimum function.

[0017] The beneficial effects of this invention are: 1) This invention uses techniques from the fields of mathematics and surveying to linearize the nonlinear problem in reservoir scheduling, reducing the complexity of the problem. It transforms the complex reservoir scheduling model into a simple linear programming model or a mixed-integer linear programming model, which can be solved quickly using efficient commercial solvers. While ensuring the accuracy of the model, it significantly improves the generation efficiency and stability of the optimized scheduling scheme of pumped storage power stations. 2) Compared with traditional methods such as dynamic programming and genetic algorithms to directly solve nonlinear models, this invention can reduce the difficulty of solving, shorten the solution time, and obtain higher accuracy results. 3) This invention overcomes the one-sidedness and fragmentation of existing linearization techniques for pumped storage power station scheduling models, and provides a systematic, complete and refined linearization method. This method needs to be able to collaboratively overcome various nonlinear problems from the objective function to the physical model and then to the operating logic, including but not limited to absolute value terms, extremum functions, reservoir capacity quadratic curves, unit output binary nonlinear functions, mutually exclusive operating condition logic and vibration zone constraints. In this way, the complex original model is completely transformed into a rigorous, complete mixed integer linear programming model that can directly call efficient commercial solvers. Finally, while ensuring that the model accurately represents the actual operating characteristics of the power station, a qualitative improvement is achieved in the computational efficiency and solution stability of the scheduling scheme. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is the water level-reservoir capacity relationship curve for a hydropower station. Figure 3A piecewise linear approximation of the NHQ curve; Figure 4 This is a schematic diagram of the combined vibration zone of the generator unit; Figure 5 This diagram illustrates the effect of a pumped-storage power station in mitigating water level fluctuations. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Example 1, as Figure 1 As shown, this embodiment provides a linearization method for the scheduling and operation model of a reversible pumped storage power station. This linearization method is implemented based on the scheduling and operation model of the reversible pumped storage power station, and specifically includes: First, the nonlinear part containing absolute values ​​in the reversible pumped storage power station scheduling and operation model is linearized.

[0021] Linearization of the nonlinear part containing absolute values ​​specifically includes: 1) Represent the linear polynomial in the absolute value using a single free variable X: ; in, For a single free variable, For linear polynomials in absolute value, , , ... These are polynomial coefficients. , , ... These are free variables in a polynomial; 2) Introduce linearization auxiliary variables and express And the three have the following relationship: ; in, For the part to be linearized, , For linearization auxiliary variables; 3) Linearization auxiliary variables introduced in the process and The representation is as follows: ; 4) Determine the linearization auxiliary variable and Boundary: ; This concludes the linearization process for the nonlinear part containing absolute values.

[0022] Second, the nonlinear part of the reservoir capacity curve containing quadratic terms in the reversible pumped storage power station scheduling and operation model is linearized.

[0023] Linearization of the nonlinear part containing quadratic terms specifically includes: 1) The reservoir capacity curve satisfies the function And the function contains water level The quadratic term, where V represents the reservoir capacity and Z represents the water level; 2) Based on the degree of piecewise linear fit, the water level is divided into... There are several intervals, namely: , ,…, ; 3) Introducing binary variables ,and ,Will and It is expressed as follows: ; in, 0-1 variables; 4) Introduce auxiliary variables ,and For binary variables Apply boundary constraints: ; This concludes the linearization process for the nonlinear part containing quadratic terms.

[0024] Third, the operating state constraints of the pumped storage reversible units in the dispatch and operation model of the reversible pumped storage power station are linearized.

[0025] The linearization of the operating state constraints of pumped storage reversible units specifically includes: 1) The operating state constraints of the reversible pumped storage unit in the dispatch and operation model of the reversible pumped storage power station are expressed as follows: ; in, This refers to the number of pumped storage reversible units. Index for pumped storage reversible units. Indicates time period, This is the state variable for the pumped-storage reversible generator unit, where 0 indicates it is not operating and 1 indicates it is operating. It is the state variable of the pumping operation of the pumped storage reversible unit, where 0 indicates no operation and 1 indicates operation. 2) Introduce auxiliary binary variables and

[0026] ; 3) By introducing auxiliary binary variables and For situations where one or more pumped storage reversible units are generating electricity while other pumped storage reversible units cannot be in pumping mode, the following handling should be performed: ; Among them, if If it equals 1, then It must equal 0, then It should also equal 0; 4) By introducing auxiliary binary variables and For situations where one or more pumped storage reversible units are pumping water while other pumped storage reversible units cannot generate electricity, the following handling should be applied: ; Among them, if If it equals 1, then It must be equal to 0, and If it equals 0, then Equal to 0; This concludes the linearization process for the operating state constraints of the pumped storage reversible unit.

[0027] Fourth, the power output function of the reversible pumped storage unit in the dispatch and operation model of the reversible pumped storage power station is linearized.

[0028] The linearization of the power output function of pumped storage reversible units specifically includes: 1) The power output function of a pumped storage reversible unit is expressed as follows: ; in, To generate electricity for pumped-storage reversible units. For the density of water, This refers to the power generation efficiency of pumped storage reversible units. The headwater for generating electricity in pumped-storage reversible units. The flow rate used for power generation in pumped-storage reversible units. This formula represents the relationship between the power output of a pumped storage reversible unit and the net head of power generation and the flow rate used for power generation. Obviously, this function is a bivariate nonlinear function. 2) Introducing the triangulation method from metrology, based on the maximum and minimum net head of power generation for the pumped-storage reversible unit throughout the entire dispatch range, three turbine performance curves are considered for each pumped-storage reversible unit's power generation operating conditions, corresponding to low ( ),middle( ) and high ( The water head is calculated, and the two-dimensional space formed by the power output function of the pumped storage reversible unit is divided into J triangular sub-regions. 3) Introducing binary variables

[0029] ; ; in, It is a binary variable, representing the first... Does the combination of the power output, net head, and flow rate of the pumped storage reversible unit occur in the [missing information] section? Within a triangle; 4) Set weighting coefficients , indicating a time period Inner The first triangle The weight of each vertex; Weighting coefficient The specific settings include: 41) Set weighting coefficients Boundary constraints: ; Where u is the vertex index of the triangle; 42) Based on the weighting coefficients For the The first triangle At the vertex The upper and lower boundaries of the net head for power generation in a pumped storage reversible unit are as follows: ; ; in, Indicates the first The first triangle At the vertex The net head of power generation for a pumped storage reversible unit; It is a maximum constant; 43) Based on the weighting coefficients For the The first triangle At the vertex The power generation flow of the pumped storage reversible unit is expressed as follows: ; in, Indicates the first The pumped storage reversible unit was in the first The first triangle The power generation flow at each vertex; 44) Based on the weighting coefficients For the The first triangle At the vertex The power generation flow of the pumped storage reversible unit is expressed as follows: ; in, Indicates the first The first triangle The vertex of the first vertex Power generation output of the pumped storage reversible unit; This concludes the linearization process for the power output function of the pumped storage reversible unit.

[0030] Fifth, linearization is applied to the vibration zone of the reversible pumped storage unit's power output in the reversible pumped storage power station's dispatch and operation model.

[0031] Linearization of the power output vibration zone of pumped storage reversible units specifically includes: 1) The vibration zone constraints in the dispatch and operation model of a reversible pumped storage power station are represented as follows: ; in, This represents the power output of the i-th pumped storage reversible unit during time period t. , These are pumped storage reversible units. The upper and lower limits of the output force in the r-th vibration zone; 2) Pumped storage reversible generators often have multiple vibration zones, which divide the output range into multiple discontinuous intervals. After considering the maximum and minimum technical output of the pumped storage reversible generator, the R vibration zones divide the output of the pumped storage reversible generator into R+1 safe operating zones. 3) Introduce indicator variables Used to indicate pumped storage reversible units exist The output at any moment is in the first A safe operating zone is defined, and indicator variable boundaries are set: ; 4) Utilize the introduced indicator variables Boundary constraints are applied to the power output of pumped storage reversible units: ; in, , These represent pumped storage reversible units. No. The upper and lower limits of each safe operating zone, and satisfying , , , ; This concludes the linearization process for the power output vibration zone of the pumped storage reversible unit.

[0032] Sixth, linearize the part of the reversible pumped storage power station scheduling and operation model that contains the extreme value function.

[0033] Linearization of the part of the function containing extrema specifically includes: 1) Linearize the maximum value function.

[0034] 11) Express the maximum value function expression using a single free variable Y: ; Where Y is a single free variable, Let be a variable with index t, where t = 1, 2, ..., T. express The maximum value at index t; 12) Introduce binary auxiliary variables Boundary constraints are applied to the introduced single free variable Y: ; ; Where M is a local constant; 3) Regarding the introduced binary auxiliary variables Apply boundary constraints: ; This concludes the linearization process for the maximum value function.

[0035] 2) Linearize the minimum function.

[0036] 21) Express the minimum value function using a single free variable Z: ; Where Z is a single free variable. Let be a variable with index t, where t = 1, 2, ..., T. express The minimum value at index t; 22) Introducing binary auxiliary variables Boundary constraints are applied to the introduced single free variable Z: ; ; Where M is a local constant; 23) Regarding the introduced binary auxiliary variables Apply boundary constraints: ; This concludes the linearization process for the minimum function.

[0037] Example 2, as Figures 2 to 5 As shown, this embodiment provides a linearization method based on the constraints of a reservoir scheduling and operation model. This linearization method specifically includes: Step 1: Perform the following linearization process on the absolute value component of the load deviation constraint in the reservoir scheduling and operation model: Step 1.1: Express the linear polynomial in the absolute value using a single free variable: ; Where t is the time period number, t=1,2,…,T; T is the total number of time periods; For the t-th time period, the th Power generation output of the Taiwanese generator unit; For the t-th time period, the th Pumping power of the unit; The duration of a unit of time period; Let t be the net load for time period t.

[0038] Step 1.2: Introduce auxiliary variables and express And the three have the following relationship: ; in, For the part to be linearized, , This is an auxiliary variable for linearization.

[0039] Step 1.3, Using the auxiliary variables introduced in step 1.2, the expression is as follows: ; Step 1.4: Determine the boundaries of the auxiliary variables introduced in Step 1.2: ; Step 1.5: This concludes the linearization process in Step 1.

[0040] Step 2: Perform the following linearization process on the nonlinear parts containing quadratic terms, such as the reservoir capacity curve, in the reservoir scheduling and operation model: Step 2.1: The reservoir capacity curve satisfies the function And the function contains water level Quadratic terms, such as Figure 2 As shown.

[0041] Step 2.2: Based on the degree of piecewise linear fitting, divide the water level into... There are several intervals, namely: , ,…, The interval divisions are shown in Table 1:

[0042] Step 2.3: Introduce binary variables ,and ,Will and It is expressed as follows: ; in, It is a 0-1 variable.

[0043] Step 2.4: Introduce auxiliary variables ,and Regarding the variables introduced in step 2.3 Apply boundary constraints: ; Step 2.5: This concludes the linearization process in Step 2.

[0044] Step 3: Perform the following linearization processing on the unit operating state constraints in the pumped storage model during reservoir scheduling and operation: Step 3.1, the operating state constraints of pumped storage power station units in the reservoir scheduling and operation model are represented as follows: ; in, This refers to the number of generating units in a pumped storage power station. For unit indexing; Indicates a time period; It is the state variable for the generator unit's power generation; 0 indicates that it is not running, and 1 indicates that it is running. It is a state variable for the pumping operation of the unit, where 0 indicates that it is not running and 1 indicates that it is running.

[0045] Step 3.2: Introduce auxiliary binary variables and

[0046] ; Step 3.3: Using the auxiliary variables introduced in Step 3.2, the following processing is performed on the situation in Step 3.1 where one or more units are generating electricity while other units cannot be in pumping state: ; Among them, if If it equals 1, then due to step 3.2, It must be equal to 0, and Then it should also equal 0.

[0047] Step 3.4: Using the auxiliary variables introduced in Step 3.2, the following processing is performed on the situation in Step 3.1 where one or more units are pumping water and other units cannot be generating electricity, as per the unit operation status constraints: ; Among them, if If it equals 1, then due to step 3.2, It must be equal to 0, and If it equals 0, then It equals 0.

[0048] Step 3.5: The linearization of the content described in Step 3 is now complete. The results of the relevant variables are shown in Table 2.

[0049] Step 4: Perform the following linearization process on the output function of the pumped storage generator unit in the reservoir scheduling and operation model: Step 4.1, the output function of the pumped storage generator unit is expressed as follows: ; in, To provide power to hydroelectric generating units; The density of water; The power generation efficiency of the generator set; The head of the water turbine unit; This represents the power generation reference flow rate of the hydropower unit. The formula in this step expresses the relationship between the power output of the hydropower unit, the generating head, and the generating flow rate. Clearly, this function is a bivariate nonlinear function, and its relationship is shown in Table 3:

[0050] Step 4.2: Introducing the triangulation method from metrology, based on the maximum and minimum net head values ​​of the unit throughout the entire scheduling range, three turbine performance curves are considered for each unit, corresponding to low ( =270m), Middle ( ) and high ( The net head of the water source is also considered. Upper limits for power generation and hydroelectric flow are demarcated with dashed lines. Each performance curve is approximated by two linear segments, and then the two-dimensional space of the hill map is divided into nine triangular sub-regions, such as... Figure 3 As shown.

[0051] Step 4.3: Introduce binary variables

[0052] ; ; in, It is a binary variable, representing the first... Does the combination of the unit's power output, net head, and power generation flow rate occur in the [missing information]? Within a triangle.

[0053] Step 4.4: Set weighting coefficients , indicating a time period Inner The first triangle The weight of each vertex.

[0054] Step 4.4.1: Set boundary constraints for weighting coefficients: ; Where u is the vertex index of the triangle.

[0055] Step 4.4.2: Adjust the weighting coefficients according to the weighting coefficients in step 4.4.1. The first triangle At the vertex The water head setting of the trolley unit has upper and lower boundaries: ; ; in, Indicates the first The first triangle At the vertex The water head of the tandem unit; It is a maximum constant.

[0056] Step 4.4.3: Adjust the weighting coefficients according to the weighting coefficients in step 4.4.1. The first triangle At the vertex The power generation flow of the unit is expressed as follows: ; in, Indicates the first The unit was in the first The first triangle The power generation flow at each vertex.

[0057] Step 4.4.4: Adjust the weighting coefficients according to the weighting coefficients in step 4.4.1. The first triangle At the vertex The power generation flow of the unit is expressed as follows: ; in, Indicates the first The first triangle The vertex of the first vertex The power output of the Taiwanese generator unit.

[0058] Step 4.5: This concludes the linearization process in Step 4.

[0059] Step 5: Perform the following linearization processing on the unit vibration zone in the reservoir scheduling and operation model: The vibration zones of the unit are shown in Table 4:

[0060] Step 5.1, the vibration zone constraints in the reservoir operation model are represented as follows: ; in, This represents the power output of the i-th generating unit during time period t; , The units The upper and lower limits of the output in the r-th vibration zone.

[0061] Step 5.2: Large hydropower units often have multiple vibration zones. The output range is divided into multiple discontinuous intervals. Considering the unit's maximum and minimum technical output, the R vibration zones divide the unit's output into R+1 safe operating zones, such as... Figure 4 As shown.

[0062] Step 5.3: Introduce indicator variables Used to indicate generator set exist The output at any moment is in the first A safe operating zone is defined, and indicator variable boundaries are set: ; Step 5.4: Utilize the indicator variables introduced in Step 5.3 Boundary constraints are applied to the generator output of the unit: ; in, , They represent the generating units. No. The upper and lower limits of each safe operating zone, and satisfying , , , .

[0063] Step 5.5: This concludes the linearization process in step 5.

[0064] Step 6: Linearize the load peak-valley difference in the reversible pumped storage power station dispatching and operation model as follows: Step 6.1: First, linearize the maximum value function: Step 6.1.1: Represent the maximum value function expression using a single free variable Y: ; Where Y is a single free variable, The equivalent load for time period t is the total system load minus wind and solar power output.

[0065] Step 6.1.2: Introduce binary auxiliary variables Apply boundary constraints to the single free variable Y introduced in step 6.1.1: ; ; Where M is a local constant.

[0066] Step 6.1.3: The binary auxiliary variable introduced in step 6.1.2 Apply boundary constraints: ; Step 6.1.4: This concludes the linearization process in Step 6.1.

[0067] Step 6.2: First, linearize the minimum function: Step 6.2.1: Express the minimum value function expression using a single free variable Z: ; Z is a single free variable.

[0068] Step 6.2.2: Introduce binary auxiliary variables Apply boundary constraints to the single free variable Z introduced in step 6.2.1: ; ; Where M is a local constant.

[0069] Step 6.2.3: The binary auxiliary variable introduced in step 6.2.2... Apply boundary constraints: ; Step 6.2.4: This concludes the linearization of the content described in Step 6.2, with the following result: Figure 5 .

[0070] Working Principle: The various nonlinear constraints and objective functions inherent in the scheduling and operation of reversible pumped-storage power stations are gradually transformed into linear or mixed-integer linear constraints, thereby constructing a fully linearized optimization model that can be efficiently solved. The linearization process proceeds sequentially as follows: linearization of the nonlinear components containing absolute values; linearization of the nonlinear components containing quadratic terms, such as the reservoir capacity curve; linearization of the unit operating state constraints; linearization of the pumped-storage generator output function; linearization of the unit vibration zone; and linearization of the components containing extrema functions. All these linearization steps are not performed in isolation, but are organically connected and synergistically acted upon through shared key variables such as unit state variables and output variables, collectively transforming the original nonlinear mixed-integer programming model into a standardized and clearly structured mixed-integer linear programming model.

[0071] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0072] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A linearization method for a reversible pumped storage power station scheduling and operation model, characterized in that, The linearization method includes the following steps: S1. Linearize the nonlinear part containing absolute values ​​in the reversible pumped storage power station scheduling and operation model. S2. Linearize the nonlinear part of the reservoir capacity curve containing quadratic terms in the reversible pumped storage power station scheduling and operation model. S3. Linearize the operating state constraints of the reversible pumped storage units in the dispatch and operation model of the reversible pumped storage power station. S4. Linearize the power output function of the reversible pumped storage unit in the dispatch and operation model of the reversible pumped storage power station. S5. Linearize the vibration zone of the power generation output of the reversible pumped storage unit in the dispatch and operation model of the reversible pumped storage power station. S6. Linearize the part of the reversible pumped storage power station scheduling and operation model that contains the extreme value function.

2. The linearization method according to claim 1, characterized in that, In S1, the linearization process for the nonlinear part containing absolute values ​​specifically includes: S11. Express the linear polynomial in the absolute value using a single free variable X: ； in, For a single free variable, For linear polynomials in absolute value, , , ... These are polynomial coefficients. , , ... These are free variables in a polynomial; S12. Introduce linearization auxiliary variables. and express And the three have the following relationship: ； in, For the part to be linearized, , For linearization auxiliary variables; S13, will Using the linearized auxiliary variable and The representation is as follows: ； S14. Determine the linearization auxiliary variable. and Boundary: ； This concludes the linearization process for the nonlinear part containing absolute values.

3. The linearization method according to claim 1, characterized in that, In S2, the linearization process for the nonlinear part containing quadratic terms specifically includes: S21, The reservoir capacity curve satisfies the function And the function contains water level The quadratic term, where V represents the reservoir capacity and Z represents the water level; S22. Based on the degree of piecewise linear fitting, the water level is divided into... There are several intervals, namely: , ,…, ; S23, Introducing binary variables ,and ,Will and It is expressed as follows: ； in, 0-1 variables; S24. Introducing auxiliary variables ,and For the binary variable Apply boundary constraints: ； This concludes the linearization process for the nonlinear part containing quadratic terms.

4. The linearization method according to claim 1, characterized in that, In S3, the linearization of the operating state constraints of pumped storage reversible units specifically includes: S31. The operating state constraints of the reversible pumped storage unit in the dispatching and operation model of the reversible pumped storage power station are expressed as follows: ； in, This refers to the number of pumped storage reversible units. Index for pumped storage reversible units. Indicates time period, This is the state variable for the pumped-storage reversible generator unit, where 0 indicates it is not operating and 1 indicates it is operating. It is the state variable of the pumping operation of the pumped storage reversible unit, where 0 indicates no operation and 1 indicates operation. S32, Introducing an auxiliary binary variable and : ； S33, through the introduction of the aforementioned auxiliary binary variable and For situations where one or more pumped storage reversible units are generating electricity while other pumped storage reversible units cannot be in pumping mode, the following handling should be performed: ； Among them, if If it equals 1, then It must be equal to 0, and It also equals 0; S34, through the introduction of the aforementioned auxiliary binary variable and For situations where one or more pumped storage reversible units are pumping water while other pumped storage reversible units cannot generate electricity, the following handling should be applied: ； Among them, if If it equals 1, then It must be equal to 0, and If it equals 0, then Equal to 0; This concludes the linearization process for the operating state constraints of the pumped storage reversible unit.

5. The linearization method according to claim 1, characterized in that, In S4, the linearization of the power output function of the pumped storage reversible unit specifically includes: S41. The power output function of a pumped-storage reversible unit is expressed as follows: ； in, To generate electricity for pumped-storage reversible units. For the density of water, This refers to the power generation efficiency of pumped storage reversible units. The headwater for generating electricity in pumped-storage reversible units. The flow rate used for power generation in pumped storage reversible units; S42. Introduce the triangulation method. Based on the maximum and minimum net head values ​​of the pumped storage reversible unit within the entire dispatch range, consider three turbine performance curves for each pumped storage reversible unit's power generation operation, corresponding to low net head, medium net head, and high net head, respectively. Divide the two-dimensional space formed by the power output function of the pumped storage reversible unit into J triangular sub-regions. S43. Introducing binary variables : ； ； in, It is a binary variable, representing the first... Does the combination of the power output, net head, and flow rate of the pumped storage reversible unit occur in the [missing information] section? Within a triangle; S44. Set weight coefficients , indicating a time period Inner The first triangle The weight of each vertex; This concludes the linearization process for the power output function of the pumped storage reversible unit.

6. The linearization method according to claim 5, characterized in that, The weighting coefficient The specific settings include: S441. Set weight coefficients Boundary constraints: ； Where u is the vertex index of the triangle; S442, Based on weighting coefficients For the The first triangle At the vertex The upper and lower boundaries of the net head for power generation in a pumped storage reversible unit are as follows: ； ； in, Indicates the first The first triangle At the vertex The net head of power generation from a Taiwanese pumped-storage reversible generator unit. It is a maximum constant; S443, Based on weighting coefficients For the The first triangle At the vertex The power generation flow of the pumped storage reversible unit is expressed as follows: ； in, Indicates the first Taiwan pumped storage reversible unit in the first The first triangle The power generation flow at each vertex; S444, Based on weighting coefficients For the The first triangle At the vertex The power generation flow of the pumped storage reversible unit is expressed as follows: ； in, Indicates the first The first triangle The vertex of the first vertex The power output of the pumped storage reversible unit.

7. The linearization method according to claim 1, characterized in that, In S5, the linearization process for the power output vibration zone of pumped storage reversible units specifically includes: S51. The vibration zone constraints in the dispatch and operation model of a reversible pumped storage power station are represented as follows: ； in, This represents the power output of the i-th pumped storage reversible unit during time period t. , These are pumped storage reversible units. The upper and lower limits of the output force in the r-th vibration zone; S52. Based on the fact that there are multiple vibration zones in the power generation of pumped storage reversible units, the output range is divided into multiple discontinuous intervals. After considering the maximum and minimum technical output of the pumped storage reversible unit, the R vibration zones divide the output of the pumped storage reversible unit into R+1 safe operation zones. S53, Introducing Indicator Variables Used to indicate pumped storage reversible units exist The output at any moment is in the first A safe operating zone is established, and indicator variables are set. Boundary: ； S54. Utilizing the introduced indicator variables Boundary constraints are applied to the power output of pumped storage reversible units: ； in, , These represent pumped storage reversible units. No. The upper and lower limits of each safe operating zone, and satisfying , , , ; This concludes the linearization process for the power output vibration zone of the pumped storage reversible unit.

8. The linearization method according to claim 1, characterized in that, In S6, the linearization process for the part containing the extrema function specifically includes: S61. Linearize the maximum value function; S62. Linearize the minimum value function.

9. The linearization method according to claim 8, characterized in that, In S61, the linearization of the maximum value function specifically includes: S611. Express the maximum value function expression using a single free variable Y: ； Where Y is a single free variable, Let be a variable with index t, where t = 1, 2, ..., T. express The maximum value at index t; S612, Introducing binary auxiliary variables Boundary constraints are applied to the introduced single free variable Y: ； ； Where M is a local constant; S613, Regarding the introduced binary auxiliary variables Apply boundary constraints: ； This concludes the linearization process for the maximum value function.

10. The linearization method according to claim 8, characterized in that, In S62, the linearization of the minimum function specifically includes: S621. Express the minimum value function expression using a single free variable Z: ； Where Z is a single free variable. Let be a variable with index t, where t = 1, 2, ..., T. express The minimum value at index t; S622, Introducing binary auxiliary variables Boundary constraints are applied to the introduced single free variable Z: ； ； Where M is a local constant; S623, Regarding the introduced binary auxiliary variables Apply boundary constraints: ； This concludes the linearization process for the minimum function.

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