Power system distribution robust optimization planning method based on Taylor formula solution

Abstract

The invention provides an electric power system distribution robust optimization planning method based on Taylor formula solution, and the method comprises the steps: constructing a wind and light prediction error fuzzy set with empirical distribution as a center and a Wasserstein distance as a radius through wind and light prediction error data; coupling the first-stage model and the second-stage model through scale factors and affine constraints based on the wind-solar prediction error fuzzy set, and constructing a two-stage distribution robust optimization model; the two-stage distribution robust optimization model is converted into a mixed integer linear model through multiple conversion processing modes, the model is solved, a distribution robust optimization scheme of the power system is planned according to a solving result, and the multiple conversion processing modes comprise piecewise linearization, a duality theory, McCormick Envelope and a Taylor formula. According to the method, the efficient solution of the two-stage distribution robust optimization model is realized, and the planning accuracy and the solution efficiency of the power system optimization scheme are improved.

Description

Technical Field

[0001] This application relates to the field of new energy power system optimization and dispatch technology, and in particular to a power system partial bar optimization planning method based on Taylor formula. Background Technology

[0002] The new power system, primarily based on wind and solar power generation, faces increasingly stringent requirements for safe operation, making it crucial to enhance the power supply capacity of high-proportion renewable energy systems. Against this backdrop, improving the accuracy of power forecasting for wind and solar power is a proactive measure, allowing power dispatching authorities to rationally plan power system operations based on wind and solar power forecast information.

[0003] Since prediction errors are unavoidable, this greatly increases the uncertainty of the scheduling plan and the additional cost of dealing with risks. Therefore, it is necessary to optimize the uncertainty in the scheduling plan.

[0004] In related technologies, stochastic optimization and robust optimization methods are commonly used to address the aforementioned uncertainties. However, both of these optimization methods have their drawbacks. For example, stochastic optimization requires determining the distribution characteristics of the variables, while robust optimization is overly conservative. Summary of the Invention

[0005] This application aims to at least partially address one of the technical problems in the related art.

[0006] Therefore, the first objective of this application is to propose a power system partial bar optimization planning method based on Taylor formula. This method achieves efficient solution of the two-stage partial bar optimization model, improving the accuracy and solution efficiency of power system optimization scheme planning.

[0007] The second objective of this application is to propose a power system partial bar optimization programming system based on Taylor formula.

[0008] The third objective of this application is to propose an electronic device.

[0009] The fourth objective of this application is to provide a computer-readable storage medium.

[0010] To achieve the above objectives, the first aspect of this application is to propose a partial bar optimization programming method for power systems based on Taylor's formula, comprising the following steps:

[0011] Using wind and solar prediction error data from new energy power systems, a fuzzy set of wind and solar prediction errors is constructed with the empirical distribution as the center and the Wasserstein distance as the radius.

[0012] Based on the fuzzy set of wind and solar prediction errors and the operating parameters of various generator sets, the first-stage model and the second-stage model in the sub-Brubar optimization are coupled through scaling factor and affine constraint to construct a two-stage sub-Brubar optimization model.

[0013] The two-stage sub-Blule bar optimization model is converted into a mixed integer linear model through various transformation processing methods, and the mixed integer linear model is solved. Based on the solution results, a sub-Blule bar optimization scheme for the power system is planned. The various transformation processing methods include piecewise linearization, duality theory, McCormick Envelope, and Taylor formula.

[0014] Optionally, the step of constructing a fuzzy set of wind and solar prediction errors using wind and solar prediction error data from the new energy power system, centered on an empirical distribution and with a Wasserstein distance as the radius, includes: constructing a sample set by treating the wind and solar prediction error data as random variables; calculating the empirical distribution as the center of the fuzzy set based on the sample set; determining the Wasserstein distance between the empirical distribution and the true distribution; and determining the radius of the fuzzy set based on the Wasserstein distance.

[0015] Optionally, determining the radius of the fuzzy set based on the Wasserstein distance includes: determining an expression for the support space comprising the empirical distribution and the true distribution, wherein the expression comprises the Wasserstein distance and the diameter of the support space; calculating the diameter of the support space using the mean of the sample set, and determining the radius of the fuzzy set using the diameter of the support space and the confidence level of the fuzzy set; after constructing the fuzzy set of wind and solar prediction errors, the method further includes: standardizing the sample set to limit the range of the support set.

[0016] Optionally, constructing the two-stage sub-Blule bar optimization model includes: determining the first-stage model based on the operating parameters of the various generator sets, and determining the second-stage model based on the fuzzy set of wind and solar prediction errors, wherein the second-stage model represents the adjustment cost of thermal power units to compensate for wind and solar prediction errors; determining various constraints of the two-stage sub-Blule bar optimization model in the new energy power system, wherein the various constraints include multiple thermal power unit constraints, multiple hydropower unit constraints, power balance equations, and power flow constraints; determining multiple constraints satisfied by the scaling factors of thermal power units and hydropower units to compensate for wind and solar prediction errors, and determining the affine constraints based on the scaling factors and the actual output of thermal power units and hydropower units.

[0017] Optionally, the constraints of the plurality of thermal power units include: minimum start-up and shutdown time constraints, ramp-up and landslide constraints, and output constraints; the constraints of the plurality of hydropower units include: reservoir capacity constraints, power generation flow constraints, hydropower conversion equations, and output constraints.

[0018] Optionally, the step of converting the two-stage bibliometric optimization model into a mixed-integer linear model through various transformation processing methods includes: simplifying the thermal power unit operating cost in the first-stage model through piecewise linearization; establishing an initial linear model of the minimum start-up and shutdown time constraint using 0-1 variables, and transforming the initial linear model through scaling changes; substituting the transformed initial linear model into the continuous operating time formula and continuous shutdown time formula in the minimum start-up and shutdown time constraint to obtain the linearized model of the minimum start-up and shutdown time constraint; and performing McCormick Envelope approximation on the hydropower unit output equation, wherein performing McCormick Envelope approximation includes: linearizing the hydropower conversion equation by introducing multiple relaxation variables, and adding multiple constraints based on the multiple relaxation variables.

[0019] Optionally, the step of converting the two-stage sub-Bruker optimization model into a mixed-integer linear model through multiple transformation processing methods further includes: transforming the coupled second-stage model using duality theory to obtain a first transformed model; approximating the first transformed model to obtain a second transformed model; and combining the initial second-stage model and the second transformed model to obtain a third transformed model, wherein the scale factor of the thermal power unit included in the third transformed model has a value range between 0 and 1; and performing a Taylor expansion of the third transformed model at the scale factor of the thermal power unit equal to 0.5 using the Taylor formula to linearize the constraints of the third transformed model.

[0020] To achieve the above objectives, a second aspect of this application also proposes a power system partial bar optimization programming system based on Taylor's formula, comprising the following modules:

[0021] The first construction module is used to construct a fuzzy set of wind and solar prediction errors using wind and solar prediction error data in the new energy power system, with the empirical distribution as the center and the Wasserstein distance as the radius.

[0022] The second construction module is used to couple the first-stage model and the second-stage model in the sub-Brubar optimization based on the fuzzy set of wind and solar prediction errors and the operating parameters of various generator sets, through scaling factors and affine constraints, to construct a two-stage sub-Brubar optimization model.

[0023] The solution module is used to convert the two-stage sub-Blule bar optimization model into a mixed integer linear model through various transformation processing methods, solve the mixed integer linear model, and plan the sub-Blule bar optimization scheme of the power system based on the model solution results. The various transformation processing methods include piecewise linearization, duality theory, McCormick Envelope, and Taylor formula.

[0024] To achieve the above objectives, a third aspect of this application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the power system sub-Brow bar optimization planning method based on Taylor formula solution as described in any of the first aspects above.

[0025] To achieve the above objectives, the fourth aspect of this application also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the power system sub-bar optimization planning method based on Taylor formula as described in any one of the first aspects.

[0026] The technical solution provided by the embodiments of this application brings at least the following beneficial effects: This application constructs a new energy power system optimization model considering prediction error information of wind power generation and photovoltaic power generation, and constructs the prediction error information within a fuzzy set with Wasserstein distance as the radius. Furthermore, the two-stage sub-Blule optimization model is coupled through affine constraints and scaling factors to form a multi-stage decision-making process. Finally, through various transformation methods including piecewise linearization, duality theory, McCormick Envelope, and Taylor formula, the two-stage sub-Blule optimization model is transformed into a mixed-integer linear model, thereby avoiding the increase in the number of constraints in the transformed model as the number of samples increases, greatly reducing the computation time and solution difficulty of the model, and improving the solution speed. Therefore, this application can achieve efficient solution of the two-stage sub-Blule optimization model, thereby formulating accurate and reasonable sub-Blule optimization schemes for new energy power systems, improving the accuracy and solution efficiency of power system optimization scheme planning, facilitating efficient and accurate handling of uncertainties in new energy power systems, and making it easier to rationally arrange power system dispatch plans.

[0027] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0028] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0029] Figure 1 This is a flowchart of a power system partial bar optimization planning method based on Taylor formula proposed in an embodiment of this application;

[0030] Figure 2 This is a flowchart illustrating a conversion processing method proposed in an embodiment of this application;

[0031] Figure 3 Here is a flowchart of another conversion processing method proposed in the embodiments of this application;

[0032] Figure 4 This is a schematic diagram of a power system sub-Blu-ray bar optimization planning system based on Taylor formula proposed in an embodiment of this application. Detailed Implementation

[0033] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0034] It should be noted that, addressing the drawbacks of stochastic and robust optimization methods used in related embodiments to handle uncertainty, this application utilizes Distributed Robust Optimization (DRO) to balance the disadvantages of both stochastic and robust optimization through its ability to make informed decisions under uncertainty. Therefore, this application solves the constructed DRO model to obtain a DRO optimization planning scheme.

[0035] The following description, with reference to the accompanying drawings, illustrates a power system sub-Blule bar optimization planning method and system based on Taylor formula solution, as proposed in the embodiments of this application.

[0036] Figure 1 This is a flowchart of a power system partial bar optimization planning method based on Taylor formula proposed in an embodiment of this application, as shown below. Figure 1 As shown, the method includes the following steps:

[0037] Step S101: Using wind and solar prediction error data from the new energy power system, construct a fuzzy set of wind and solar prediction errors with the empirical distribution as the center and the Wasserstein distance as the radius.

[0038] Specifically, this application proposes a new energy power system optimization model that considers prediction error information of wind power generation and photovoltaic power generation. The model uses a non-parametric estimation method to construct a fuzzy set of wind and solar prediction errors with the empirical distribution as the center and the Wasserstein distance as the radius.

[0039] It should be noted that due to the existence of wind power and photovoltaic prediction errors, the power system dispatch results are greatly biased. Therefore, this application establishes a fuzzy set of wind and photovoltaic prediction errors based on Wasserstein distance to take into account the wind power and photovoltaic prediction error information.

[0040] In one embodiment of this application, a fuzzy set of wind and solar prediction errors is constructed using wind and solar prediction error data from a new energy power system, centered on an empirical distribution and with a Wasserstein distance as the radius. This includes the following steps:

[0041] The first step is to construct a sample set by treating the wind and solar prediction error data as random variables.

[0042] Specifically, the actual collected wind and solar prediction error data are used as random variables ξ, and a sample set Φ = {ξ1, ξ2, ..., ξ} is constructed using the collected data. n}, where n is the number of samples in the sample set.

[0043] The second step is to calculate the empirical distribution based on the sample set as the center of the fuzzy set.

[0044] Specifically, using the constructed sample set, the empirical distribution is calculated using the following formula: Where N is the number of samples used in the empirical distribution. Then, the calculated empirical distribution value is used as the center of the constructed fuzzy set.

[0045] The third step is to determine the Wasserstein distance between the empirical distribution and the true distribution, and then determine the radius of the fuzzy set based on the Wasserstein distance.

[0046] Specifically, a fuzzy set X is constructed with the Wasserstein distance as the radius to estimate the true distribution P. The fuzzy set can be represented by the following formula:

[0047]

[0048] in, Denotes the total probability distribution on the support set Ξ; d w (P N P) represents the empirical distribution P N The Wasserstein distance between the true distribution P and the real distribution P can be expressed by the following formula (2):

[0049]

[0050] Wherein, parameter ξ n ξ and ξ respectively represent obeying P N and P-distributed random variables; E(d(ξ) n ,ξ)) represents expectation; ∏(P N ,P) represents P N The joint distribution of ξ and P; d(ξ) n The random variable ξ is defined as follows: n The distance between ξ and ξ can be taken as d(ξ) in this embodiment. n ,ξ)=||ξ n -ξ||; inf denotes the infimum function.

[0051] The process of determining the radius ε of the fuzzy set in this embodiment is described in detail below. In this embodiment, the radius of the fuzzy set is determined based on the Wasserstein distance, including the following steps:

[0052] The first step is to determine an expression for the support space that includes both the empirical distribution and the true distribution, where the expression includes the Wasserstein distance and the diameter of the support space.

[0053] Specifically, for a fuzzy set radius ε, there exists a set containing P. N The support space Ω of the P distribution satisfies the following formula (3):

[0054]

[0055] Where D is the diameter of the supporting space Ω.

[0056] The second step is to calculate the diameter of the support space using the mean of the sample set, and then determine the radius of the fuzzy set using the diameter of the support space and the confidence level of the fuzzy set.

[0057] Specifically, assuming the confidence level of the fuzzy set is γ, the radius ε of the fuzzy set can be calculated using the following formula:

[0058]

[0059] The diameter D can be calculated using the following formula (5):

[0060]

[0061] Where μ is the mean of the sample set.

[0062] Furthermore, after constructing the fuzzy set of wind and solar prediction errors, this embodiment also includes: standardizing the sample set to limit the range of the support set.

[0063] Specifically, the processing method in this embodiment is as follows: First, for the sample set Φ={ξ1,ξ2,......,ξ n The following formula is used for standardization:

[0064] ψ n =Σ -1 / 2 (ξ n -μ), n=1,2,3......,N (6)

[0065] Where Σ represents the sample variance.

[0066] The standardized sample set Ψ satisfies the following formula:

[0067] Ψ={ξ|-l≤ξ≤l} (7)

[0068] The value of the boundary l can be solved using the following formula:

[0069]

[0070] Therefore, after determining the value of the boundary l, the range of the original sample set can be determined through inverse transformation.

[0071] Step S102: Based on the fuzzy set of wind and solar prediction errors and the operating parameters of various generator sets, the first-stage model and the second-stage model in the sub-Brubar optimization are coupled through scaling factors and affine constraints to construct a two-stage sub-Brubar optimization model.

[0072] Specifically, this application constructs a two-stage sub-Brussels bar optimization model based on the fuzzy set obtained in the previous step. The two stages in this model are coupled through affine constraints and scaling factors, thus forming a multi-stage decision-making process. That is, based on the constructed fuzzy set of wind and solar prediction errors, a first-stage model and a second-stage model are first constructed, and then the first-stage model and the second-stage model are coupled through affine constraints and scaling factors to form a two-stage decision-making process.

[0073] In one embodiment of this application, a two-stage sub-Bruker optimization model is constructed, including the following steps:

[0074] The first step is to determine the first-stage model based on the operating parameters of various generator sets, and to determine the second-stage model based on the fuzzy set of wind and solar prediction errors. The second-stage model represents the adjustment cost of thermal power units to compensate for wind and solar prediction errors.

[0075] Specifically, the first-stage model constructed in this embodiment is shown in the following formula:

[0076]

[0077] Among them, F(P) g,t The operating cost of thermal power units; Start-up and shutdown costs; These are the start-up costs and shutdown costs of thermal power units, respectively; d g,t This indicates the operating status of the thermal power unit at time t; These represent the start-stop control states of the thermal power unit at time t; a g b g c g C2(ρ·r) represents the coal consumption coefficient. T The spinning reserve cost of the unit is denoted as ρ, where ρ and r represent the row vectors of the reserve capacity price and reserve capacity of thermal and hydropower units, respectively, and can be determined by the following formula: in, This indicates the cost of rotating reserve on thermal power units. This indicates the operating reserve cost of a thermal power unit. This refers to the rotating reserve cost of hydroelectric generating units. This indicates the operating reserve cost of the hydroelectric generator unit.

[0078] The second-stage model constructed in this embodiment is shown in the following formula:

[0079]

[0080] The model represents the adjustment cost of thermal power units to compensate for wind and solar forecast errors. Ψt ξ represents the total error in wind and solar forecasting. w,t ξ v,t These represent the prediction errors for wind power output and solar power output, respectively; α g,t This represents the scaling factor for thermal power units. It is understandable that the prediction error data at time t in this formula can be determined based on the constructed fuzzy set.

[0081] The second step is to determine the various constraints of the two-stage sub-Bruker optimization model in the new energy power system. These constraints include constraints on multiple thermal power units, constraints on multiple hydropower units, power balance equations, and power flow constraints.

[0082] The constraints determined in this step include: minimum start-up and shutdown time constraints, ramp-up and landslide constraints, and power output constraints; and multiple constraints for hydropower units include: reservoir capacity constraints, power generation flow constraints, hydropower conversion equations, and power output constraints.

[0083] Specifically, the constraints for thermal power units are shown in the following formulas:

[0084]

[0085] Among them, the above formulas (13) to (16) represent the minimum start-up and shutdown time constraints of thermal power units; This indicates the time that the thermal power unit has been running continuously at time t; This indicates the duration of continuous shutdown of the thermal power unit at time t; Indicates the minimum start-up time of a thermal power unit; The minimum downtime of the thermal power unit is represented; the above formulas (17) and (18) represent the ramp and landslide constraints of the thermal power unit, respectively: These represent the upper and lower limits of the output of the thermal power unit, respectively; P g,t This represents the planned output of the thermal power unit at time t; represent the ramp rate and landslide rate of thermal power unit g, respectively; the above formula (19) represents the output constraint of thermal power unit; These represent the upper and lower limits of the standby capacity of thermal power units, respectively.

[0086] The constraints of the hydropower unit are shown in the following formulas:

[0087] V h,0 =V ini (20)

[0088] V h,24 =V end (twenty one)

[0089]

[0090] P h,t =C h,1 (V h,t ) 2 +C h,2 (Q h,t ) 2 +C h,3 V h,t Q h,t +C h,4 V h,t +C h,5 Q h,t +C h,6 (twenty four)

[0091]

[0092] Among them, formulas (20) to (22) represent reservoir capacity constraints; formula (23) represents power generation flow constraints; formula (24) represents the hydropower conversion equation; and formula (25) represents the output constraints of the hydropower unit; V h,t Indicates the reservoir capacity; Q h,tThis represents the power generation flow rate of the hydroelectric generator unit at time t; These represent the upper and lower limits of power generation flow, respectively; C h,1 To C h,6 P represents the hydroelectric conversion coefficient; h,t This indicates the generating capacity of the hydroelectric power unit; These refer to the upper and lower rotating reserve capacities of the hydropower units, respectively.

[0093] The determined power balance equation is shown in the following formula:

[0094]

[0095] Among them, G, H, W, V, and I correspond to the node set containing all thermal power units, hydropower units, wind power, photovoltaic power stations, and 24 nodes, respectively.

[0096] The defined power flow constraints are shown in the following formulas:

[0097]

[0098] Among them, P ij,t δ represents the power flowing from node i to node j at time t; i δ j These represent the power angles at nodes i and j, respectively; x ij L represents the impedance between nodes i and j; i,t This represents the load output by node i at time t; n = 1, 2, 3, 4 represent the node set containing thermal power units, hydropower units, wind power and photovoltaic power stations in node i, respectively; Θ i This represents the set of nodes connected to node i.

[0099] The third step is to determine the multiple constraints that the scaling factors of thermal power units and hydropower units satisfy to compensate for wind and solar forecasting errors, and to determine the affine constraints based on the scaling factors and the actual output of thermal power units and hydropower units.

[0100] Specifically, the scaling factor determined in this step satisfies several constraints, as shown in the following formulas:

[0101] 0≤α g,t ≤1 (31)

[0102] 0≤α h,t ≤1 (32)

[0103]

[0104] Where, α g,t α h,t These represent the proportional factors used by thermal power units and hydropower units to compensate for errors in wind and solar forecasts, respectively.

[0105] The affine constraints determined in this step are shown in the following formula:

[0106] Ρ g,t =P g,t -α g,t Ψ t (36)

[0107] Ρ h,t =P h,t -α h,t Ψ t (37)

[0108] Among them, P g,t , P h,t These represent the actual output of thermal power units and hydropower units, respectively.

[0109] Step S103: The two-stage sub-Blule bar optimization model is converted into a mixed integer linear model through various transformation processing methods, and the mixed integer linear model is solved. Based on the solution results, a sub-Blule bar optimization scheme for the power system is planned. Among these methods, piecewise linearization, duality theory, McCormick Envelope, and Taylor formula are used.

[0110] Specifically, to achieve efficient solution of the two-stage sub-Brussels bar optimization model obtained in the previous step, this step first transforms the two-stage model into a mixed-integer linear model through various processing methods, including piecewise linearization, duality theory, McCormick envelope, and Taylor formula, to improve the solution speed. It is understandable that, as mentioned above, the model constructed in the previous step considers various constraints in the power system, forming a mixed nonlinear integer programming model, which significantly increases the solution speed and difficulty. Therefore, this application transforms the two-stage model into a mixed-integer linear model to achieve efficient solution of the two-stage sub-Brussels bar optimization model. The process of transforming the two-stage sub-Brussels bar optimization model and various constraints is described in detail below.

[0111] To more clearly illustrate the specific implementation of this application in converting a two-stage sub-Bruker optimization model into a mixed-integer linear model through various conversion processing methods, the following example illustrates a conversion method proposed in one embodiment of this application. Figure 2 This is a flowchart illustrating a conversion processing method proposed in an embodiment of this application, as shown below. Figure 2 As shown, the method includes the following steps:

[0112] Step S201: The operating cost of thermal power units in the first-stage model is simplified by using piecewise linearization.

[0113] Specifically, the operating cost of thermal power units is piecewise linearized. The operating cost of thermal power units in the objective function of the first-stage model can be expressed by the following formula: This formula can be simplified by using piecewise linearization to reduce the solution time of the model. The specific simplification formulas used are shown below:

[0114]

[0115] Among them, P g,t(n) P represents g,t The sequential statistics; m represents the number of segments into which the operating cost function is piecewise linearized; This represents the output value of thermal power units sorted from the mth segment to the (m-1)th segment; This represents the slope value of the sorting from the m-th segment to the (m-1)-th segment.

[0116] Step S202: Establish an initial linear model with minimum start-stop time constraints using 0-1 variables, and transform the initial linear model by scaling.

[0117] Specifically, when linearizing the minimum start-stop time constraints, a mixed integer linear model is first established using 0-1 variables for the minimum start-stop time constraints of the thermal power units shown in formulas (13) to (16) above. The resulting initial linear model is shown in the following formula:

[0118]

[0119] Then, the model is transformed by scaling. First, define the scaling transformation model as shown in the following formula:

[0120]

[0121] The initial linear model is then transformed using a scaling transformation model to obtain the following formula:

[0122]

[0123] This formula represents the initial linear model after the transformation.

[0124] Step S203: Substitute the transformed initial linear model into the continuous running time formula and continuous downtime formula in the minimum start-stop time constraint to obtain the linearized model of the minimum start-stop time constraint.

[0125] Specifically, substituting the above formula (42) into the continuous running time formula and continuous downtime formula in the minimum start-stop time constraint, i.e. the above formulas (13) and (14), we can obtain the following formula:

[0126]

[0127] This formula represents the linearized model of the minimum start-stop time constraint.

[0128] Step S204: Perform McCormick Envelope approximation on the hydropower unit output equation. The McCormick Envelope approximation includes: linearly transforming the hydropower conversion equation by introducing multiple relaxation variables, and adding multiple constraints based on multiple relaxation variables.

[0129] Specifically, the McCormick envelope approximation is applied to the hydropower unit output equation. For the aforementioned hydropower conversion equation, i.e., formula (24), the nonlinear constraints are transformed into linear constraints, thereby simplifying the solution time of the model. Specifically, during the simplification, the slack variables shown in the following formula are first introduced:

[0130]

[0131] These slack variables can transform formula (24) into the following formula:

[0132]

[0133] Furthermore, the following constraints are added as shown in each of the formulas:

[0134]

[0135] This allows for the linearization of multiple constraints on the model, facilitating subsequent solutions.

[0136] Furthermore, the two-stage sub-Bruker optimization model is transformed and solved.

[0137] The following example illustrates the specific conversion process of the DRO model using another conversion method proposed in one embodiment of this application. Figure 3 Here is a flowchart of another conversion processing method proposed in this application embodiment, such as... Figure 3 As shown, the method includes the following steps:

[0138] Step S301: The coupled second-stage model is transformed using duality theory to obtain the first transformed model.

[0139] Specifically, the two-stage split-Bruker model obtained in step S102 is denoted by the following formula:

[0140]

[0141] As can be seen from this formula, if the second-stage model is not considered, the objective function of the split-bulk model is a simple planning problem. However, the existence of the second-stage model complicates the solution. Therefore, this application uses duality theory to transform the model. The second-stage model is first denoted as follows:

[0142]

[0143] Using duality theory, this model can be transformed into the following formula:

[0144]

[0145] Formula (51) can be further transformed into the following formula:

[0146]

[0147] This formula represents the first transformation model.

[0148] Step S302: The first conversion model is approximated to obtain the second conversion model, and the initial second-stage model and the second conversion model are combined to obtain the third conversion model, wherein the value range of the proportional factor of the thermal power unit included in the third conversion model is between 0 and 1.

[0149] Specifically, although the objective function of the split-bar model is easier to solve after the transformation in step S301, the difficulty of solving the model gradually increases as the number of constraints increases with the number of samples. Therefore, this embodiment further approximates the first transformation model as shown in the following formula:

[0150]

[0151] Combining formula (53) (i.e., the second transformation model) and formula (11) (i.e., the initial second-stage model), the second-stage model can be transformed into the third transformation model shown in the following formula:

[0152]

[0153] In formula (54), the scaling factor α of the thermal power unit is... g,t The value ranges from 0 to 1.

[0154] Step S303: Use Taylor's formula to perform Taylor expansion on the third conversion model at the point where the scale factor of the thermal power unit is equal to 0.5, so as to linearize the constraints of the third conversion model.

[0155] Specifically, due to α in the above formula (54) g,tThe value range of is between 0 and 1, and the coefficient of the quadratic term is much smaller than the coefficient of the linear term. Therefore, in the embodiments of this application, the Taylor formula can be used to convert formula (54) in... A Taylor expansion is performed at the point, thus linearizing the constraints of formula (54) as shown in the following formula:

[0156]

[0157] Therefore, the embodiments of this application convert the nonlinear sub-bar optimization model into a mixed integer linear programming model. Obviously, the number of constraints in the converted model will not increase with the increase of the number of samples, which greatly reduces the computation time and difficulty of solving the model.

[0158] Furthermore, by solving the transformed mixed-integer linear programming model, a partial Brussels bar optimization planning scheme for the power system can be obtained. The obtained partial Brussels bar optimization planning scheme for the power system can address the uncertainty problem in the dispatch plan of the new energy power system, and improve the rationality and accuracy of the dispatch plan based on wind power and photovoltaic forecast information.

[0159] In summary, the power system partial Blule bar optimization planning method based on Taylor's formula in this application constructs a new energy power system optimization model that considers prediction error information of wind power generation and photovoltaic power generation, and constructs the prediction error information within a fuzzy set with Wasserstein distance as the radius. Furthermore, the two-stage partial Blule bar optimization model is coupled through affine constraints and scaling factors to form a multi-stage decision-making process. Finally, through various transformation methods including piecewise linearization, duality theory, McCormick Envelope, and Taylor's formula, the two-stage partial Blule bar optimization model is transformed into a mixed-integer linear model, thereby avoiding the increase in the number of constraints in the transformed model with the increase in the number of samples, significantly reducing the computation time and solution difficulty of the model, and improving the solution speed. Therefore, this application can achieve efficient solution of the two-stage partial Blule bar optimization model, thereby formulating accurate and reasonable partial Blule bar optimization schemes for new energy power systems, improving the accuracy and solution efficiency of power system optimization scheme planning, facilitating efficient and accurate handling of uncertainties in new energy power systems, and enabling reasonable scheduling of power system dispatch plans.

[0160] To implement the above embodiments, this application also proposes a power system partial bar optimization programming system based on Taylor formula. Figure 4 This is a schematic diagram of a power system partial bar optimization programming system based on Taylor formula proposed in an embodiment of this application, as shown below. Figure 4 As shown, the system includes: a first building module 100, a second building module 200, and a solution module 300.

[0161] The first construction module 100 is used to construct a fuzzy set of wind and solar prediction errors using wind and solar prediction error data in the new energy power system, with the empirical distribution as the center and the Wasserstein distance as the radius.

[0162] The second construction module 200 is used to construct a two-stage sub-Brubar optimization model by coupling the first-stage model and the second-stage model in the sub-Brubar optimization with scaling factors and affine constraints based on the fuzzy set of wind and solar prediction errors and the operating parameters of various generator sets.

[0163] The solver module 300 is used to convert the two-stage sub-Bruker optimization model into a mixed-integer linear model through various transformation processing methods, solve the mixed-integer linear model, and plan the sub-Bruker optimization scheme of the power system based on the model solution results. The various transformation processing methods include piecewise linearization, duality theory, McCormick envelope, and Taylor formula.

[0164] Optionally, in one embodiment of this application, the determining module 200 is specifically used for: obtaining multiple positive trends of each influencing factor under the current working conditions through a positive prediction model, and combining the positive trends corresponding to all influencing factors into multiple positive trend groups, and combining the multiple positive trend groups into a positive trend matrix; calculating the weight normalized value of each element in the positive trend matrix based on the normalized calculation formula, and forming a weight normalization matrix with all the calculated weight normalized values; using each element in the weight normalization matrix, calculating the positive index of each positive trend group according to the index calculation formula; and by comparing the positive indicators, selecting the target positive trend group with the largest positive index from the multiple positive trend groups, and taking the factor group corresponding to the target positive trend group as the optimal factor group.

[0165] Optionally, in one embodiment of this application, the first construction module 100 is specifically used to: construct a sample set by using the wind and solar prediction error data as random variables; calculate the empirical distribution as the center of the fuzzy set based on the sample set; determine the Wasserstein distance between the empirical distribution and the true distribution, and determine the radius of the fuzzy set based on the Wasserstein distance.

[0166] Optionally, in one embodiment of this application, the first construction module 100 is specifically used to: determine an expression for the support space that includes the empirical distribution and the true distribution, wherein the expression includes the Wasserstein distance and the diameter of the support space; calculate the diameter of the support space using the mean of the sample set, and determine the radius of the fuzzy set using the diameter of the support space and the confidence level of the fuzzy set; and standardize the sample set to limit the range of the support set.

[0167] Optionally, in one embodiment of this application, the second construction module 200 is specifically used for: determining a first-stage model based on the operating parameters of various generator sets, and determining a second-stage model based on the fuzzy set of wind and solar prediction errors, wherein the second-stage model represents the adjustment cost of thermal power units to compensate for wind and solar prediction errors; determining multiple constraints of the two-stage sub-Bruker optimization model in the new energy power system, wherein the multiple constraints include multiple thermal power unit constraints, multiple hydropower unit constraints, power balance equations, and power flow constraints; determining multiple constraints satisfied by the scaling factors of thermal power units and hydropower units to compensate for wind and solar prediction errors, and determining affine constraints based on the scaling factors and the actual output of thermal power units and hydropower units.

[0168] Optionally, in one embodiment of this application, the solution module 300 is specifically used to: simplify the thermal power unit operating cost in the first-stage model through piecewise linearization; establish an initial linear model of minimum start-up and shutdown time constraints using 0-1 variables, and transform the initial linear model through scaling; substitute the transformed initial linear model into the continuous operating time formula and continuous shutdown time formula in the minimum start-up and shutdown time constraints to obtain a linearized model of the minimum start-up and shutdown time constraints; and perform McCormick Envelope approximation on the hydropower unit output equation, wherein performing McCormick Envelope approximation includes: linearly transforming the hydropower conversion equation by introducing multiple relaxation variables, and adding multiple constraints based on multiple relaxation variables.

[0169] Optionally, in one embodiment of this application, the solution module 300 is specifically used to: transform the coupled second-stage model through duality theory to obtain a first transformed model; approximate the transformation of the first transformed model to obtain a second transformed model, and combine the initial second-stage model and the second transformed model to obtain a third transformed model, wherein the scale factor of the thermal power unit included in the third transformed model is in the range of 0 to 1; and perform Taylor expansion of the third transformed model at the scale factor of the thermal power unit being equal to 0.5 using Taylor formula to linearize the constraints of the third transformed model.

[0170] It should be noted that the explanation of the above-described embodiment of the power system partial bar optimization planning method based on Taylor formula also applies to the system in this embodiment, and will not be repeated here.

[0171] In summary, the power system partial bar optimization planning system based on Taylor formula in this application can efficiently solve the two-stage partial bar optimization model, thereby formulating accurate and reasonable partial bar optimization schemes for new energy power systems. This improves the accuracy and solution efficiency of power system optimization scheme planning, which is beneficial for efficiently and accurately dealing with uncertainties in new energy power systems and facilitates the reasonable arrangement of power system dispatching plans.

[0172] To implement the above embodiments, this application also proposes an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the power system sub-bar optimization planning method based on Taylor formula solution as described in any of the first aspects above.

[0173] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the power system sub-Blu-ray optimization planning method based on Taylor formula solution as described in any one of the first aspect embodiments above.

[0174] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0175] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0176] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0177] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0178] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0179] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it includes one or a combination of the steps of the method embodiments.

[0180] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0181] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A partial bar optimization programming method for power systems based on Taylor's formula, characterized in that, Includes the following steps: Using wind and solar prediction error data from new energy power systems, a fuzzy set of wind and solar prediction errors is constructed with the empirical distribution as the center and the Wasserstein distance as the radius. Based on the fuzzy set of wind and solar prediction errors and the operating parameters of various generator sets, the first-stage model and the second-stage model in the sub-Brubar optimization are coupled through scaling factor and affine constraint to construct a two-stage sub-Brubar optimization model. The two-stage sub-Blule bar optimization model is converted into a mixed integer linear model through various transformation processing methods, and the mixed integer linear model is solved. Based on the solution results, a sub-Blule bar optimization scheme for the power system is planned. The various transformation processing methods include piecewise linearization, duality theory, McCormick Envelope, and Taylor formula.

2. The method according to claim 1, characterized in that, The method of utilizing wind and solar prediction error data from new energy power systems to construct a fuzzy set of wind and solar prediction errors centered on an empirical distribution and with a Wasserstein distance as the radius includes: The wind and solar prediction error data are used as random variables to construct a sample set; The empirical distribution is calculated based on the sample set and used as the center of the fuzzy set. Determine the Wasserstein distance between the empirical distribution and the true distribution, and determine the radius of the fuzzy set based on the Wasserstein distance.

3. The method according to claim 2, characterized in that, Determining the radius of the fuzzy set based on the Wasserstein distance includes: Determine an expression for the support space that includes the empirical distribution and the true distribution, wherein the expression includes the Wasserstein distance and the diameter of the support space; The diameter of the support space is calculated using the mean of the sample set, and the radius of the fuzzy set is determined using the diameter of the support space and the confidence level of the fuzzy set. After constructing the fuzzy set of wind and solar prediction errors, the method further includes: The sample set is standardized to limit the range of the support set.

4. The method according to claim 1, characterized in that, The constructed two-stage sub-Bruker optimization model includes: The first stage model is determined based on the operating parameters of the various generator sets, and the second stage model is determined based on the fuzzy set of wind and solar prediction errors, wherein the second stage model represents the adjustment cost of thermal power units to compensate for wind and solar prediction errors; The two-stage sub-Bruker optimization model is applied to various constraints in the new energy power system. These constraints include constraints on multiple thermal power units, constraints on multiple hydropower units, power balance equations, and power flow constraints. The proportional factors that thermal power units and hydropower units satisfy to compensate for wind and solar forecasting errors are determined, and the affine constraints are determined based on the proportional factors and the actual output of the thermal power units and hydropower units.

5. The method according to claim 4, characterized in that, The constraints of the multiple thermal power units include: minimum start-up and shutdown time constraints of thermal power units, ramp-up and landslide constraints of thermal power units, and output constraints of thermal power units. The constraints of the multiple hydropower units include: reservoir capacity constraints, power generation flow constraints, hydropower conversion equations, and hydropower unit output constraints.

6. The method according to claim 5, characterized in that, The process of converting the two-stage sub-Bruker optimization model into a mixed-integer linear model through various transformation methods includes: The operating cost of thermal power units in the first stage model is simplified by using a piecewise linearization method. An initial linear model of the minimum start-stop time constraint is established using 0-1 variables, and the initial linear model is transformed by scaling. Substitute the transformed initial linear model into the continuous running time formula and continuous downtime formula in the minimum start-stop time constraint to obtain the linearized model of the minimum start-stop time constraint. The McCormick Envelope approximation is applied to the hydropower unit output equation. The McCormick Envelope approximation includes: linearly transforming the hydropower conversion equation by introducing multiple relaxation variables, and adding multiple constraints based on the multiple relaxation variables.

7. The method according to claim 6, characterized in that, The process of converting the two-stage sub-Bruker optimization model into a mixed-integer linear model through multiple transformation methods also includes: By using duality theory, the coupled second-stage model is transformed to obtain the first transformed model; The first conversion model is approximated to obtain the second conversion model. The second conversion model is then combined with the initial second-stage model to obtain the third conversion model. The ratio factor of the thermal power unit included in the third conversion model is between 0 and 1. The Taylor expansion of the third conversion model is performed at a scaling factor of 0.5 for the thermal power unit using the Taylor formula to linearize the constraints of the third conversion model.

8. A power system partial bar optimization programming system based on Taylor's formula, characterized in that, Includes the following modules: The first construction module is used to construct a fuzzy set of wind and solar prediction errors using wind and solar prediction error data in the new energy power system, with the empirical distribution as the center and the Wasserstein distance as the radius. The second construction module is used to couple the first-stage model and the second-stage model in the sub-Brubar optimization based on the fuzzy set of wind and solar prediction errors and the operating parameters of various generator sets, through scaling factors and affine constraints, to construct a two-stage sub-Brubar optimization model. The solution module is used to convert the two-stage sub-Blule bar optimization model into a mixed integer linear model through various transformation processing methods, solve the mixed integer linear model, and plan the sub-Blule bar optimization scheme of the power system based on the model solution results. The various transformation processing methods include piecewise linearization, duality theory, McCormick envelope, and Taylor formula.

9. An electronic device, comprising: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the power system partial bar optimization planning method based on Taylor formula as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the power system partial bar optimization planning method based on Taylor formula as described in any one of claims 1-7.

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