Data-driven robust optimization scheduling implementation method based on multi-affine strategy

Abstract

The application discloses a data-driven robust optimization scheduling implementation method based on a multi-affine strategy, obtains a scheduling strategy by establishing a two-stage robust optimization model and solving, adopts a self-organizing mapping neural network to cluster a wind power sample data set to obtain a multi-uncertainty set, and then solves the robust optimization model based on the multi-affine strategy, transforms the optimization model by adopting the multi-affine strategy, and combines a dual principle to convert the original optimization model into a linear programming problem for solving, so as to realize data-driven robust optimization scheduling. The application is based on a robust optimization method, improves the conservativeness of uncertainty factor modeling by establishing a multi-uncertainty set, and improves the economy of the obtained scheduling strategy by introducing the multi-affine strategy, can ensure the optimization model solving efficiency, effectively depicts the fluctuation range of the uncertainty factor, and improves the power grid operation efficiency while ensuring the power grid safety.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of power system dispatching, and particularly relates to a data-driven robust optimization dispatching implementation method based on a multi-affine strategy. BACKGROUND

[0002] With large-scale grid connection of renewable energy, a dispatching method based on uncertainty factors needs to be researched. With large-scale grid connection of renewable energy, the output uncertainty of renewable energy has a significant influence on power grid operation, and the random characteristics of renewable energy output need to be accurately described, and a reasonable dispatching strategy needs to be arranged to improve power grid operation efficiency. Meanwhile, the fluctuation of renewable energy output puts forward higher requirements for safe operation of the power grid, and sufficient backup of conventional thermal power units needs to be ensured to cope with large fluctuations in renewable energy output. Therefore, a dispatching method considering uncertainty factors needs to be researched. SUMMARY

[0003] The application proposes a data-driven robust optimization dispatching implementation method based on a multi-affine strategy to solve the problems that the uncertainty set modeling in the prior art is relatively conservative, and the economic efficiency of the dispatching strategy based on the affine strategy is poor. The method is based on a robust optimization method, improves the conservativeness of uncertainty factor modeling by establishing a multi-uncertainty set, and improves the economic efficiency of the obtained dispatching strategy by introducing a multi-affine strategy, so that the fluctuation range of the uncertainty factor can be effectively described while ensuring the efficiency of the optimization model, the safety of the power grid can be ensured, and the operation efficiency of the power grid is improved.

[0004] The application is implemented by the following technical scheme:

[0005] The application relates to a data-driven robust optimization dispatching implementation method based on a multi-affine strategy, a dispatching strategy is obtained by establishing a two-stage robust optimization model and solving, a self-organizing mapping neural network is used to cluster wind power sample data sets to obtain a multi-uncertainty set, and then a robust optimization model solving method based on a multi-affine strategy is used, the optimization model is transformed by using a multi-affine strategy, and the original optimization model is converted into a linear programming problem for solving in combination with a duality principle, so that data-driven robust optimization dispatching is implemented.

[0006] The two-stage robust optimization model is established, and specifically comprises: a first stage model, whose optimization target is the sum of the generation and standby costs of conventional units being minimum, and the constraint conditions required for establishing the first stage model are constructed according to the power balance constraint of the power system, the upper and lower limits of the output of the conventional units, the transmission power range constraint of the line, the standby range constraint of the conventional units and the climbing ability; and a second stage model, whose optimization target is the sum of the rescheduling cost of the conventional units, the wind curtailment cost and the load shedding cost being minimum, and the constraint conditions required for establishing the second stage model are constructed according to the power balance constraint of the power system, the transmission power range constraint of the line, the wind curtailment range and the load shedding range constraint, the rescheduling output range constraint of the conventional units and the climbing ability.

[0007] The objective function of the first stage model is the sum of the generation and standby costs of the conventional units being minimum, that is: Wherein, p G,j,t , r Gu,j,t and r Gd,j,t are the active output, positive standby and negative standby of the conventional unit j at time t; a G,j , b G,j and c G,j are the generation cost coefficients of the conventional unit j; d Gu,j and d Gd,j are the positive standby cost coefficient and negative standby cost coefficient of the conventional unit j; N G is the number of conventional units, and t is time.

[0008] The objective function is a quadratic function, which is converted into a series of linear functions by using the piecewise linearization method. For the jth unit, the operation cost function at time t is converted into a linear constraint, which is specifically: Wherein, W G,j,t is a newly introduced cost variable; and are the i-th set of linearization coefficients, and the superscript indicates the number of linear function segments; d is the number of segments, and the objective function of the first stage model is updated as:

[0009] The constraint conditions required for establishing the first stage model include the power balance constraint of the power system, the upper and lower limits of the output of the conventional units, the transmission power range constraint of the line, the standby range constraint of the conventional units and the climbing ability, and specifically comprises: Wherein, N R and N L are the number of wind turbines and the number of loads respectively; p R,i,t and p L,k,t are the predicted active output of the wind turbine i and the active demand of the load k at time t; p G,j,min and p G,j,maxrespectively are the lower and upper limits of the conventional unit j output; F l is the maximum transmission power of line l; π G,lj R,li L,lk respectively are the power transmission distribution factors between conventional unit j, wind turbine i, load k and line l; R Gu,j Gd,j respectively are the maximum positive reserve range and the maximum negative reserve range of conventional unit j; p G,j,ramp is the maximum ramping power of conventional unit j.

[0010] The objective function of the second stage model is the sum of the conventional unit rescheduling cost, the wind power curtailment cost and the load shedding cost, i.e. min (a wherein p Gu,j,t Gd,j,t respectively are the upward and downward rescheduling output of conventional unit j at time t; p Rc,i,t Lc,k,t respectively are the wind power curtailment power of wind turbine i and the load shedding power of load k at time t; c Gu,j Gd,j respectively are the cost coefficients of conventional unit j rescheduling; c Rc,i Lc,k respectively are the wind power curtailment cost coefficient of wind turbine i and the load shedding cost coefficient of load k.

[0011] The constraint conditions required to be considered when constructing the second stage model include the power system power balance constraint, the line transmission power range constraint, the wind power curtailment range and load shedding range constraint, the conventional unit rescheduling output range constraint and the ramping ability, specifically: -p G，j，ramp ≤(p G，j，t+1 +p Gu，j，t+1 -p Gd，j，t+1 )-(p G，j，t +p Gu，j，t -p Gd，j，t )≤p G，j，ramp , wherein: is the output prediction error of wind turbine i at time t; η Rc,i Lc,k respectively are the maximum wind power curtailment proportion of wind turbine i and the maximum load shedding proportion of load k.

[0012] The two-stage economic dispatch problem considering wind power prediction error constructed can be expressed as the following abstract mathematical problem: min (a T x+b T y), s.t. Ax≤c, ​​​​​​​​Wherein: x is the first stage decision variable, including pG, rGu, rGd, WG; y is the second stage decision variable, including pGu, pGd, pRc, pLc; a, b, A, c, B, C, D, d are corresponding coefficient matrixes; It is a specific implementation scenario of wind power prediction error.

[0013] The clustering processing specifically includes: for each sub data set, firstly, the sample data is subjected to decorrelation processing by using principal component analysis method, then the probability density function is fitted by using kernel density estimation method, and finally, multiple uncertainty sets are established.

[0014] The multiple uncertainty sets are established by using self-organizing mapping algorithm to process a large amount of wind power output historical data to obtain a plurality of sub data sets, and then using principal component analysis and kernel density estimation method to analyze the data of each data set to establish uncertainty sets, specifically including:

[0015] 1) The original wind power output data set is clustered by using self-organizing mapping algorithm to obtain N sub data sets.

[0016] 2) For each sub data set, principal component analysis and kernel density estimation method are used to establish uncertainty sets.

[0017] 3) Finally, N uncertainty sets are obtained: U i ={ξ|H i ξ≤h i}, i∈{1,..., N}, wherein: U i is the i-th uncertainty set, ξ is the wind power output prediction error, H i and h i are the coefficient matrixes of the i-th uncertainty set.

[0018] The two-stage robust optimization model based on multiple uncertainty sets is:

[0019]

[0020] The multiple affine strategy is introduced to transform the optimization model, that is, for each sub uncertainty set, when the actual wind power output prediction error belongs to the range of the uncertainty set, the unit rescheduling output, the wind power prediction error, the wind power prediction error and the wind power prediction error satisfy: Wherein: are the affine coefficients between the w-th sub uncertainty set unit rescheduling positive output, unit rescheduling negative output, load shedding power and wind power prediction error and wind power prediction error.

[0021] The matrix form corresponding to the multiple affine strategy is: y=M i ξ+mi wherein: M i , m i are the coefficient matrix of the affine strategy in the ith sub-uncertainty set respectively.

[0022] The combination of the dual principle converts the original optimization model into a linear programming problem, and specifically includes:

[0023] ① After introducing the multi-affine strategy, the original two-stage robust optimization model becomes: objective function s.t. Ax≤c, wherein: the robust constraint (CM i +D)ξ≤d-Bx-Cm i , U i ={ξ|H i ξ≤h i}, i∈{1,..., N}, and the robust constraint is equivalent to: H i T π i =(CM i +D) T , π i ≥0, π i is the dual variable; the dual problem equivalent to the inner maximization problem of the objective function is: H i T v i =(b T M i ) T , v i ≥0, v i is the dual variable; the converted linear programming model is: The constraint conditions include the converted constraint above and Ax≤c.

[0024] ② Introducing new variables to transform the inner maximization problem in the objective function: wherein: Z is the newly introduced variable; the constraint conditions include the converted constraint above, Ax≤c, and Z≥h i T v i +b T m i , The transformed model is a linear programming model.

[0025] The solving adopts, but is not limited to, the CPLEX solver to calculate and obtain the optimal scheduling strategy.

[0026] Technical effects

[0027] Compared with the prior art, the application can accurately depict the fluctuation characteristics of uncertain factors; meanwhile, a robust optimization model solving method based on a multi-affine strategy is proposed, and based on the scheduling strategy obtained by solving, the power grid operation efficiency can be effectively improved while ensuring safety. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 is a flowchart of the application;

[0029] Figure 2 is a system schematic diagram of the application;

[0030] Figure 3 is an embodiment effect schematic diagram. DETAILED DESCRIPTION

[0031] This embodiment takes the IEEE 118 node system as an example: in the IEEE 118 node system, there are a total of 186 transmission lines and 54 generator units, and in this embodiment, the 54 generator units all have rescheduling capability. Four wind turbine generators are connected to node 15, node 49, node 59 and node 90 respectively, and the predicted output of each is 300 MW. The load data used in this embodiment is derived from an actual power grid, and the wind power data is derived from four wind farms in Gansu region. The load power and the output of the wind turbine generator are scaled according to the load of the IEEE 118 node system.

[0032] As shown in Figure 1 , the embodiment relates to a data-driven robust optimization scheduling implementation method based on a multi-affine strategy, a deterministic optimization model is established according to the power grid safety constraints, the unit operation constraints, the wind curtailment and the load shedding constraints; a multi-uncertainty set is established according to the renewable energy output prediction error; a two-stage robust optimization model based on uncertainty factors is established based on the deterministic optimization model and the multi-uncertainty set; the model is converted into a linear programming problem by using the multi-affine strategy and the duality principle, and a scheduling strategy is obtained by solving.

[0033] As shown in Figure 2 , the embodiment relates to a data-driven robust optimization scheduling system for implementing the above method, comprising: a deterministic optimization model modeling module, a multi-uncertainty set modeling module, a two-stage robust optimization model modeling module and a solving module, wherein: the deterministic optimization model modeling module and the multi-uncertainty set modeling module respectively establish a deterministic optimization model and a multi-uncertainty set according to the power grid data and the renewable energy data, and output to the two-stage robust optimization model modeling module, the two-stage robust optimization model modeling module further establishes a robust optimization scheduling model based on uncertainty factors, and the scheduling strategy is calculated through the solving module.

[0034] Through specific practical experiments in the IEEE 118-bus system, based on system parameters, load, and wind power data, the above method was used to obtain the results shown in Table 1 and... Figure 3 The results are shown.

[0035] Table 1

[0036]

[0037] Table 1 compares the mean total operating cost, the mean operating cost of the first stage, the mean operating cost of the second stage, and the standard deviation of the total operating cost for the three methods. The table shows that the first-stage operating cost of this method is significantly lower than that of the single affine strategy method, while the second-stage operating costs of the two methods are very close. Regarding the total operating cost, the average cost of this method is lower than that of the single affine strategy method, and the standard deviation of this method is basically the same as that of the single affine strategy method. This is because this method, while ensuring the reliability of the scheduling scheme, reduces conservatism by employing a multi-affine strategy approach, thereby improving the system's operating efficiency.

[0038] At the same time, from Figure 3 As can be seen from (a), when considering the risk and reliability of the optimization method based on the quartile, the quartile of this method is significantly smaller than that of the single affine strategy method, which means that this method can achieve better scheduling results.

[0039] like Figure 3 As shown in (b), the total operating costs of our method and the single affine strategy method are compared in 100 out-of-sample experiments. The 45-degree reference line in the figure signifies that the total operating costs of the two methods are equal, and points falling above the reference line indicate that the total operating cost of our method is lower than that of the single affine strategy method. It is clear from the figure that the data points in the out-of-sample experiments all fall above the reference line, meaning that our method can effectively improve the system's operating efficiency.

[0040] In summary, this invention establishes a deterministic optimization model based on the constraints of power grid and generator unit operation, and uses self-organizing mapping, principal component analysis, and kernel density estimation methods to establish multiple uncertainty sets, accurately characterizing the stochastic characteristics of wind power output, and establishing a two-stage robust optimization model based on uncertainty. By employing multiple affine strategies and the duality principle, the optimization model is transformed into an easily solvable linear programming problem. By establishing multiple uncertainty sets and adopting multiple affine strategies, the power grid's operating efficiency can be effectively improved while ensuring safe operation of the power grid.

[0041] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A data-driven robust optimization scheduling implementation method based on multiple affine strategies, characterized in that, By establishing a two-stage robust optimization model and solving it, the scheduling strategy is obtained. The wind power sample dataset is clustered using a self-organizing mapping neural network to establish multiple uncertain sets. Then, a robust optimization model based on multiple affine strategies is used to solve the problem. By transforming the optimization model using multiple affine strategies and combining the duality principle, the original optimization model is transformed into a linear programming problem for solution, thus realizing data-driven robust optimization scheduling. The establishment of multiple uncertainty sets refers to: processing a large amount of historical wind power output data using a self-organizing map algorithm to obtain several subsets of data; then analyzing the data in each subset using principal component analysis and kernel density estimation methods to establish uncertainty sets separately, specifically including: 1) The self-organizing map algorithm is used to cluster the original wind power output dataset to obtain N sub-datasets; 2) For each subset of data, principal component analysis and kernel density estimation are used to establish an uncertainty set; 3) Finally, N uncertain sets are obtained: , where: U i For the i-th uncertain set, H represents the wind power output prediction error. i h i Let be the coefficient matrix of the i-th uncertain set; The two-stage robust optimization model is as follows: ; The constructed two-stage economic dispatch problem considering wind power forecasting errors is represented by the following abstract mathematical problem: Where: x is the decision variable for the first stage, including the active power output of conventional units, positive and negative reserves pG, rGu, rGd, and cost variable WG; y is the decision variable for the second stage, including the upward and downward readjustment output of conventional units pGu, pGd, and the wind curtailment power and load shedding power of wind turbines pRc, pLc; a, b, A, c, B, C, D, d are the corresponding coefficient matrices; This refers to a specific scenario for wind power prediction errors.

2. The data-driven robust optimization scheduling implementation method based on multi-affine strategy according to claim 1, characterized in that, The establishment of the two-stage robust optimization model specifically includes: establishing a first-stage model, whose optimization objective is to minimize the sum of conventional unit generation and reserve costs, and constructing the constraints to be considered for the first-stage model based on power system power balance constraints, upper and lower limits of conventional unit output constraints, line transmission power range constraints, conventional unit reserve range constraints, and ramp-up capability; establishing a second-stage model, whose optimization objective is to minimize the sum of conventional unit rescheduling costs, wind curtailment costs, and load shedding costs, and constructing the constraints to be considered for the second-stage model based on power system power balance constraints, line transmission power range constraints, wind curtailment range and load shedding range constraints, conventional unit rescheduling output range constraints, and ramp-up capability.

3. The data-driven robust optimization scheduling implementation method based on multi-affine strategy according to claim 2, characterized in that, The objective function of the first-stage model is to minimize the sum of the generation and standby costs of conventional generating units, i.e.: ,in: These represent the active power output, positive reserve, and negative reserve of conventional unit j at time t. Let be the power generation cost coefficient for conventional unit j; These are the positive and negative reserve cost coefficients for conventional unit j, respectively; N G t represents the number of conventional generating units; t represents time. The objective function is a quadratic function, which is transformed into a series of linear functions using a piecewise linearization method; for the j-th unit, its operating cost function at time t is transformed into a linear constraint, specifically: ,in: This is a newly introduced cost variable; Let be the linearization coefficients of the i-th group, whose superscript indicates the number of linear function segments; d is the number of segments. Then the objective function of the first-stage model is updated as follows: ; The constraints to be considered when constructing the first-stage model include: power system power balance constraints, upper and lower limits of conventional unit output constraints, line transmission power range constraints, conventional unit reserve range constraints, and ramping capability, specifically: in: These refer to the number of wind turbine units and the number of loads, respectively. These represent the predicted active power output of wind turbine i and the active power demand of load k at time t, respectively. These are the lower and upper limits of the output of conventional generating units, respectively. This represents the maximum transmission power of line l. These are the power transmission distribution factors between conventional unit j, wind turbine i, load k, and line l, respectively. These represent the maximum positive reserve range and the maximum negative reserve range for conventional generating units, respectively. This is the maximum ramping power for a conventional unit.

4. The data-driven robust optimization scheduling implementation method based on multi-affine strategy according to claim 2, characterized in that, The objective function of the second-stage model is to minimize the sum of conventional unit rescheduling costs, wind curtailment costs, and load shedding costs, i.e.: ,in: These represent the upward and downward readjustments of the output of the conventional unit j at time t, respectively. Let i be the wind curtailment power of wind turbine i and the load shedding power of load k at time t, respectively. These are the cost coefficients for rescheduling conventional unit j; These are the wind curtailment cost coefficient for wind turbine i and the load shedding cost coefficient for load k, respectively. The constraints to be considered when constructing the second-stage model include: power system power balance constraints, line transmission power range constraints, wind curtailment and load shedding range constraints, conventional unit rescheduled output range constraints, and ramp-up capability, specifically: ,in: Let be the output prediction error of wind turbine i at time t; These represent the maximum wind curtailment ratio of wind turbine i and the maximum load shedding ratio of load k, respectively.

5. The data-driven robust optimization scheduling implementation method based on multi-affine strategy according to claim 1, characterized in that, The clustering process specifically includes: for each subset of data, firstly, principal component analysis is used to decorrelate the sample data, then kernel density estimation is used to fit the probability density function, and finally, a multi-uncertain set is established.

6. The data-driven robust optimization scheduling implementation method based on multi-affine strategy according to claim 4, characterized in that, The aforementioned transformation of the optimization model using a multi-affine strategy refers to the following: for each subset of uncertainty, when the actual wind power output prediction error falls within the range of that subset, the rescheduled power output, curtailed power, load shedding power, and wind power prediction error satisfy the following relationship: These are the affine coefficients between the positive output of the w-th sub-uncertain centralized unit rescheduled, the negative output of the unit rescheduled, the load shedding power, and the wind curtailment power and wind power prediction error, respectively.

7. The data-driven robust optimization scheduling implementation method based on multi-affine strategy according to claim 1, characterized in that, The matrix form corresponding to the multi-affine strategy is as follows: ,in: , These are the coefficient matrices of the affine strategy in the i-th sub-uncertainty set; The method of transforming the original optimization model into a linear programming problem by incorporating the duality principle includes: ① After introducing a multi-affine strategy, the original two-stage robust optimization model becomes: objective function Among them: robust constraints Robust constraints are equivalent to: Let these be the dual variables; the dual problem equivalent to the objective function and its inner maximization problem is: The variables are dual variables; the transformed linear programming model is: The constraints include the transformed constraints mentioned above and ; ② Introduce new variables to transform the inner maximization problem in the objective function: Where: Z is the newly introduced variable; constraints include the constraints after the above transformation, The transformed model is a linear programming model.

8. A data-driven robust optimization scheduling implementation system based on a multi-affine strategy according to any one of claims 1 to 7, characterized in that, include: The system comprises a deterministic optimization modeling module, a multi-uncertainty set modeling module, a two-stage robust optimization modeling module, and a solution module. Specifically, the deterministic optimization modeling module and the multi-uncertainty set modeling module establish deterministic optimization models and multi-uncertainty sets based on grid data and renewable energy data, respectively, and output them to the two-stage robust optimization modeling module. The two-stage robust optimization modeling module further establishes a robust optimization scheduling model based on uncertainty factors, and the scheduling strategy is calculated by the solution module.

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