Method for analyzing correlation between power grid investment cost and load curve characteristics

Abstract

The application provides a power grid investment cost and load curve characteristic correlation analysis method, first, taking power grid transmission line investment cost and generator set operation cost as an objective function, considering power balance and branch power upper and lower limit constraints, a power grid investment model is established; secondly, a Monte Carlo simulation method based on Latin hypercube sampling is proposed, the generation of the load curve is realized, and the load curve characteristics are extracted, the construction of the data set is completed, and data support is provided for analyzing the correlation between the power grid investment cost and the load characteristics; then, the training set input and the training set output of the model are constructed, and the XGBoost model is trained, and the nonlinear mapping relationship between the load curve characteristics and the power grid investment cost is constructed; finally, the weight of each load curve characteristic is calculated through the trained XGBoost model, and the size of the weight is sorted, and the influence degree of each load curve characteristic on the power grid investment cost is analyzed by comparing the weight size.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system planning, in particular to a method for analyzing the correlation between power grid investment cost and load curve characteristics. BACKGROUND

[0002] The traditional power grid investment strategy under the environment of high economic growth is no longer suitable for the current development situation. Under the joint guidance of multiple goals such as electricity price marketization reform, rural power grid upgrading and transformation, and state-owned enterprise quality improvement and efficiency increase, accurate investment and quality improvement and efficiency increase are the inevitable choice for the high-quality development of current power grid enterprises and the construction of new power systems. Therefore, in order to improve the efficiency of power grid investment and formulate a reasonable and effective power grid investment scheme, scholars have carried out a lot of research on power grid investment optimization.

[0003] Existing research mainly focuses on the construction of investment models and the design of optimization algorithms. However, in reality, the original intention of formulating a power grid investment scheme is to meet the electricity demand of users, so the load curve will directly affect the cost of power grid investment. The characteristics of the load curve represent the load curve of user electricity consumption. Therefore, in order to improve the efficiency of power grid investment, it is necessary to analyze the correlation between power grid investment cost and load curve characteristics, provide a reference for the formulation of electricity price policy, and fundamentally reduce the cost of power grid investment by optimizing the load curve. In order to analyze the correlation between power grid investment cost and load curve characteristics, the characteristics of the load curve need to be extracted. The traditional Monte Carlo simulation method mainly uses random sampling method to generate samples, which has the problems of difficulty in reflecting the original probability distribution of random variables, low sampling efficiency and poor robustness.

[0004] Therefore, in order to solve the above technical problems, it is necessary to propose a new technical means. SUMMARY

[0005] Therefore, the present application provides a method for analyzing the correlation between power grid investment cost and load curve characteristics, which provides a reference for the formulation of electricity price policy, and fundamentally reduces the cost of power grid investment by optimizing the load curve.

[0006] A method for analyzing the correlation between power grid investment cost and load curve characteristics, comprising the steps of:

[0007] S1. Building a power grid investment model:

[0008] Establishing an objective function:

[0009] ;

[0010] Wherein, F is the investment cost of power grid transmission line and the operation cost of generator set; c l , c gThese represent the investment cost per unit capacity of the line and the price quote for the g-th generator unit, respectively; N l N g These represent the total number of branches and the total number of generators in the system, respectively; L l T is the length of the l-th branch; l P is the capacity of the l-th branch; f,g,t Let g be the power of the g-th generator unit in time period t; T is the total number of time periods; and t is the time interval.

[0011] Establish constraints:

[0012] 1) Power balance constraints:

[0013]

[0014] Where t = 1, 2, ..., T; From(n) is the set of paths with node n as the first and last node; To(n) is the set of paths with node n as the last node; P l,t P represents the power of branch l during time period t; N represents the number of nodes connected to the load; P n,load,t Let be the load of the nth node in time period t;

[0015] 2) Branch power constraints:

[0016]

[0017] Where t=1,2,…,T; l=1,2,…,N l ;T l Let L be the capacity of branch l;

[0018] 3) Engine output upper and lower limit constraints:

[0019]

[0020] Where t=1,2,…,T; g=1,2,…,N g ;P f,g,max This represents the upper limit of the power output of the g-th generator unit.

[0021] 4) Engine set ramping constraints:

[0022]

[0023] Where t=1,2,…,T; g=1,2,…,N g ;r g,up r g,up These are the upper and lower limits for the generator set's ramp speed;

[0024] 5) Branch capacity upper and lower limit constraints:

[0025]

[0026] where l = 1, 2, …, N l ; and are the upper and lower limit values of the branch l capacity, respectively.

[0027] S2. Generate the load data based on the Monte Carlo simulation method of Latin hypercube sampling, and the specific steps include:

[0028] S21. Divide f i (x i ) into K equidistant intervals such as [0, 1 / K], [1 / K, 2 / K], …, [K-1 / K, 1]; where f i (x i ) is the probability distribution of the random variable x i , where i = 1, …, m; m is the number of random variables that need to be sampled.

[0029] S22. Sample a number from each equidistant interval of the probability distribution function f i (x i ) as a sampling point, and then obtain the sample value corresponding to the sampling point according to the inverse function of f i (x i ); repeat this step until all K intervals are extracted.

[0030] S23. Repeat step S22 until m groups of random variables are extracted to obtain a sample matrix H with order K x m.

[0031] S24. Shuffle the order of elements in each column of the sample matrix H, i.e., change the order of the sampling points of each random variable, to obtain K load curves.

[0032] S25. Input the K load curves obtained into the power grid investment model built respectively to obtain K power grid investment cost values, which are written in the form of a column vector and denoted as X out .

[0033] S3. Extract the load curve characteristics of each load curve to obtain a matrix of load curve characteristics corresponding to the K load curves, denoted as X in , with order K x n, where n is the number of types of load curve characteristics extracted.

[0034] S4. Train the XGBoost model: take the load curve characteristic matrix X in as the input of the XGBoost model, and take the power grid investment cost X out as the output of the XGBoost model to construct the nonlinear mapping relationship between the load curve characteristics and the power grid investment cost.

[0035] S5. Analyze the relevance between the grid investment cost and the load curve characteristics based on the trained XGBoost model:

[0036] Calculate the weight of each load curve characteristic based on the trained XGBoost model, and sort the weight size. Analyze the influence degree of each load curve characteristic on the grid investment cost by comparing the weight size.

[0037] Further, the load curve characteristics extracted in step S3 include:

[0038] Peak C1: the maximum value of the system total load in the load change period; waist value C2: the intermediate value of the system total load in the load change period; valley value C3: the minimum value of the system total load in the load change period; peak duration C4: the duration of the maximum value of the system total load in the load change period; waist duration C5: the duration of the intermediate value of the system total load in the load change period; valley duration C6: the duration of the minimum value of the system total load in the load change period; peak valley difference C7: the difference between the maximum value and the minimum value of the system total load in the load change period.

[0039] Further, the XGBoost model in step S4 is constructed as follows:

[0040] The prediction function is established as follows:

[0041]

[0042] Wherein, M is the number of decision trees in the model; X i is the i-th input sample; f m represents the prediction value of the m-th tree; represents the prediction value after the m-th iteration; is a set of decision trees;

[0043] The objective function is established as follows:

[0044]

[0045]

[0046] Wherein, K is the number of samples; l is the loss function; represents the prediction value of the sample; y i represents the true value of the sample; is the regularization term; T is the number of leaf nodes of each tree; , is the penalty coefficient; w is the weight of each leaf;

[0047] After t iterations, the model can be represented as:

[0048]

[0049] wherein, represents the prediction value after the tth iteration; represents the prediction value after the (t-1)th iteration; represents the prediction value of the tth tree;

[0050] The objective function can be represented as:

[0051]

[0052] wherein, is a regularization term;

[0053] The loss function in the objective function is expanded by Taylor expansion of 2nd order, and the objective function can be expressed as:

[0054]

[0055] wherein, , are the first and second derivatives of the loss function l, respectively, and are specifically represented as: ;

[0056] The constant quantity in the objective function is removed, and the objective function can be simplified as:

[0057]

[0058] All samples of the same leaf node are combined, and the objective function is rewritten as a function of the weight w of the leaf node, to obtain the final objective function:

[0059]

[0060] wherein, is the weight of the jth leaf node, I j is a sample set containing the jth leaf node;

[0061] The weight of the leaf node is obtained through the above steps, and the shape of the optimal tree is obtained by minimizing the objective function obj.

[0062] Further, the weight of each load curve feature is calculated in step S5, and the calculation method is as follows:

[0063]

[0064] wherein, is the weight of the load curve feature m, is the degree used by the load curve feature m, is the total number of splits.

[0065] The present application has the following beneficial effects:

[0066] 1. The traditional Monte Carlo simulation method mainly adopts a random sampling method for sample generation, however, the random sampling method has problems of being difficult to reflect the original probability distribution of random variables, low sampling efficiency and poor robustness; the present application proposes a Monte Carlo simulation method based on Latin hypercube sampling, which can ensure that the sampling values cover the entire distribution interval of the random variables, realize the generation of the load curve, extract the load curve features, complete the construction of the data set, and provide data support for analyzing the correlation between the power grid investment cost and the load characteristics;

[0067] 2. The present application proposes a power grid investment cost and load curve feature correlation analysis method based on the XGBoost algorithm, first, the training set input and the training set output of the model are constructed, then the XGBoost model is trained, the nonlinear mapping relationship between the load curve features and the power grid investment cost is constructed, finally, the trained XGBoost model is analyzed to obtain the influence degree of each load curve feature on the power grid investment cost, which provides a reference for the formulation of electricity price policy, and further reduces the power grid investment cost by optimizing the load curve. BRIEF DESCRIPTION OF DRAWINGS

[0068] The present application will be further described below in conjunction with the drawings and examples:

[0069] Figure 1 The present application will be further described below in conjunction with the drawings and examples: DETAILED DESCRIPTION

[0070] The present application will be further described below in conjunction with the drawings and examples:

[0071] A power grid investment cost and load curve feature correlation analysis method, comprising the steps of:

[0072] S1. Build a power grid investment model:

[0073] The present application uses a direct current flow model commonly used in the industry to model the power grid investment planning problem. The power grid transmission line investment cost and the generator set operation cost are taken as the objective function, the power balance and the upper and lower limits of branch power are considered as constraints, and the following power grid investment planning model is established:

[0074] Establish the objective function:

[0075] ;

[0076] Where, F is the investment cost of power grid transmission line and the operation cost of generator unit; c l , c g are the investment cost per unit line and per unit capacity, respectively; N l , N g are the total number of branches and the total number of units in the system, respectively; L l is the length of the lth branch; T l is the capacity of the lth branch; P f,g,t is the power of the gth generator unit in the tth time interval; T is the total number of time intervals; is the time interval;

[0077] The constraint conditions are established as follows:

[0078] 1) Power balance constraint:

[0079]

[0080] Where, t = 1, 2, …, T; From(n) is the line set with node n as the first end node; To(n) is the line set with node n as the last end node; P l,t is the power of the lth branch in the tth time interval; N is the number of nodes connected to the load; P n,load,t is the load of the nth node in the tth time interval;

[0081] 2) Branch power constraint:

[0082]

[0083] Where, t = 1, 2, …, T; l = 1, 2, …, N l ; T l is the capacity of the lth branch;

[0084] 3) Upper and lower limits of generator unit output constraint:

[0085]

[0086] Where, t = 1, 2, …, T; g = 1, 2, …, N g ; P f,g,max is the upper limit of the power of the gth generator unit;

[0087] 4) Generator unit ramping constraint:

[0088]

[0089] Where, t = 1, 2, …, T; g = 1, 2, …, N g ; r g,up , r g,up are the upper and lower limit values of the generator unit ramping, respectively;

[0090] 5) Branch capacity upper and lower bound constraints:

[0091]

[0092] where l = 1, 2, …, N l ; and are the upper and lower bound values of the capacity of branch l, respectively;

[0093] S2. The load data is generated based on the Latin hypercube sampling Monte Carlo simulation method, which can obtain sufficient samples and accurately depict the mapping relationship between the grid investment cost and the load curve characteristics, providing data support for subsequent model training. The specific steps include:

[0094] S21. f i (x i ) is divided into K equidistant intervals such as [0, 1 / K], [1 / K, 2 / K], …, [K-1 / K, 1]; where f i (x i ) is the probability distribution of random variable x i , and its value range is [0, 1], where i = 1, …, m; m is the number of random variables that need to be sampled;

[0095] S22. Sample a number from each equidistant interval of the probability distribution function f i (x i ) as a sampling point, generally select the midpoint of the interval as the sampling point, and then obtain the sample value corresponding to the sampling point according to the inverse function of f i (x i ); repeat the step until all K intervals are extracted;

[0096] S23. Repeat step S22 until m groups of random variables are extracted to obtain a sample matrix H with order K x m;

[0097] S24. Shuffle the order of elements in each column of the sample matrix H, i.e. change the order of the sampling points of each random variable, to obtain K load curves, which can reduce the correlation between random variables and thus reduce the influence on the calculation results;

[0098] S25. Input the K load curves obtained into the grid investment model built to obtain K grid investment cost values, which are written in the form of a column vector and denoted as X out ;

[0099] S3. Extract the load curve characteristics of each load curve to obtain a matrix of load curve characteristics corresponding to the K load curves, denoted as X in , with order K x n, where n is the number of extracted load curve characteristics;

[0100] S4. Train the XGBoost model: the load curve feature matrix X in is the input of the XGBoost model, and the grid investment cost X out is the output of the XGBoost model, and a nonlinear mapping relationship between the load curve features and the grid investment cost is constructed.

[0101] S5. Analyze the correlation between the grid investment cost and the load curve features based on the trained XGBoost model:

[0102] Based on the trained XGBoost model, the weight of each load curve feature is calculated, and the size of the weight is sorted. By comparing the size of the weight, the influence degree of each load curve feature on the grid investment cost is analyzed.

[0103] In this embodiment, the load curve features extracted in step S3 include:

[0104] Peak C1: the maximum value of the system total load in the load change period; waist value C2: the intermediate value of the system total load in the load change period; valley value C3: the minimum value of the system total load in the load change period; peak duration C4: the duration of the maximum value of the system total load in the load change period; waist duration C5: the duration of the intermediate value of the system total load in the load change period; valley duration C6: the duration of the minimum value of the system total load in the load change period; peak valley difference C7: the difference between the maximum value and the minimum value of the system total load in the load change period; and n = 7.

[0105] In this embodiment, since there is a complex correlation between the grid investment cost and the load curve features, it is difficult to directly construct a physical model. However, the method of machine learning has the characteristics of not needing to construct a physical model and strong nonlinear fitting ability. Therefore, an XGBoost model is constructed to analyze the correlation between the grid investment cost and the load curve features, and the construction process is as follows:

[0106] The prediction function is established as follows:

[0107]

[0108] where M is the number of decision trees in the model; X i is the i-th input sample; f m represents the prediction value of the m-th tree; represents the prediction value after the m-th iteration; is a set of decision trees;

[0109] The objective function is established as follows:

[0110]

[0111]

[0112] where K is the number of samples; l is the loss function; represents the predicted value of the sample; y i represents the true value of the sample; is the regularization term; T is the number of leaf nodes of each tree; , is the penalty coefficient; w is the weight of each leaf node;

[0113] Since the tree model generated by XGBoost model in each iteration is obtained by fitting the prediction residual of the model in the last iteration, after t iterations, the model can be represented as:

[0114]

[0115] where, represents the predicted value after the tth iteration; represents the predicted value after the (t-1)th iteration; represents the predicted value of the tth tree;

[0116] The objective function can be represented as:

[0117]

[0118] where, is the regularization term;

[0119] The loss function in the objective function is expanded by Taylor expansion of the second order, and the objective function can be expressed as:

[0120]

[0121] where, , are the first and second derivatives of the loss function l, respectively, and are specifically represented as: ;

[0122] The constant quantity in the objective function is removed, which can be simplified as:

[0123]

[0124] The above formula is the sum of all sample loss values. Since the samples ultimately converge to a leaf node, all samples in the same leaf node are combined, and the objective function is rewritten as a function of the leaf node weight w, and the final objective function is obtained:

[0125]

[0126] wherein, is the weight of the jth leaf node, I j denotes the sample set containing the jth leaf node;

[0127] The weight of the leaf node is obtained through the above steps, and the shape of the optimal tree is obtained by minimizing the objective function obj.

[0128] Further, the weight of each load curve feature is calculated in step S5, and the calculation method is as follows:

[0129]

[0130] wherein, is the weight of the load curve feature m, is the number of times used by the load curve feature m, is the total number of splits.

[0131] In this embodiment, in order to verify the effectiveness of the proposed correlation analysis method, the IEEE-30 and IEEE-118 node systems are used, and the daily load curve of the maximum load day is selected as the model input; the investment cost c of the unit line unit capacity l = 1 × 10 5 6 yuan, the time interval t = 1, the total time interval T = 24, the sample number K = 5000, of which 4000 is the training sample and 1000 is the test sample.

[0132] Three kinds of power grid investment cost and load curve feature correlation analysis methods are compared, which are M0, M1 and M2, wherein:

[0133] M0: the method proposed in the present application, but not using Latin hypercube sampling method for sampling, but using random sampling method for sampling;

[0134] M1: the method proposed in the present application, but not using XGBoost algorithm, but using GBDT algorithm;

[0135] M2: the method proposed in the present application;

[0136] The accuracy of the obtained model is verified in the IEEE-30 and IEEE-118 node systems using M0-M2 three methods respectively, taking 1000 samples as test samples, and the average relative error results are shown in Table 1 and Table 2;

[0137]

[0138]

[0139] As shown in Table 1, the average relative errors of M0 and M1 are increased by 2.81% and 3.08% respectively compared with M2. Thus, it can be obtained that the samples generated by random sampling are difficult to reflect the distribution characteristics of the load curve, resulting in higher error of the model trained by the load curve generated by the method, and the Latin hypercube sampling solves the problem and reduces the average relative error of the model. In addition, through the above analysis, it can be known that the XGBoost algorithm has higher accuracy than the traditional GBDT algorithm, and since the XGBoost algorithm adds regularity in the loss function, the algorithm is not prone to overfitting, so it has higher accuracy.

[0140] To further demonstrate the practicability of the method proposed in the application, Table 2 shows the running conditions of M0-M2 in the IEEE-118 node system, and the analysis can obtain that the average relative errors of M0 and M1 are increased by 4.36% and 4.27% respectively compared with M2. The obtained results are consistent with the analysis of Table 1, which illustrates the effectiveness of the method M2 proposed in the application.

[0141] In the embodiment, in order to analyze the influence of each load characteristic on the investment cost of the power grid and provide a theoretical reference for the formulation of the electricity price policy, Table 3 and Table 4 respectively give the importance analysis results of each load characteristic based on the M2 model in the IEEE-30 and IEEE-118 node systems;

[0142]

[0143] As can be seen from Table 3 and Table 4, the peak load curve C1 has the greatest influence on the investment cost of the power grid. The reason for causing this phenomenon is that the maximum capacity that the line needs to bear mainly depends on the peak value of the load. Therefore, the greater the peak value is, the higher the investment cost of the power grid is. It can be concluded that when the electricity price policy is formulated, it is necessary to formulate a policy that can reduce the peak load of the user, so as to reduce the investment cost of the power grid.

[0144] Finally, it should be explained that the above embodiments are only used to illustrate the technical solutions of the application but not limit the application. Although the application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the application can be modified or replaced equivalently without departing from the purpose and scope of the application, and all of them should be covered in the scope of the claims of the application.

Claims

1. A method for analyzing the correlation between grid investment cost and load curve characteristics, characterized in that, The method comprises the steps of: S1. Building a power grid investment model: Establishing an objective function: ； Where F is the investment cost of transmission line and the operation cost of generator unit; c l , c g are the investment cost per unit length and per unit capacity of transmission line and the bid of the gth generator unit, respectively; N l , N g are the total number of branches and the total number of units in the system, respectively; L l is the length of the lth branch; T l is the capacity of the lth branch; P f,g,t is the power of the gth generator unit in the tth time interval; T is the total number of time intervals;△t is the time interval; t = 1, 2, …, T; g = 1, 2, …, N g ; l = 1, 2, …, N l ; Establishing constraint conditions: 1) Power balance constraint: Wherein, From(n) is the line set with node n as the head node; To(n) is the line set with node n as the tail node; P l,t is the power of branch l in time period t; N is the number of nodes connected to the load; P n,load,t is the load of the nth node in time period t; 2) Branch power constraint: where T l is the capacity of branch l; 3) Engine set output upper and lower limit constraint: P f,g,max is the power upper limit value of the gth generator set; 4) Engine set climbing constraint: Wherein, r g,up , r g,down are the upper and lower limits of the generator set climbing respectively; 5) Branch capacity upper and lower limit constraint: wherein, , are respectively the upper and lower limit values of the branch l capacity; S2. Based on the Latin hypercube sampling Monte Carlo simulation method, the load data is generated, and the specific steps include: S21. f i (x i ) is divided into K equidistant intervals [0, 1 / K], [1 / K, 2 / K], …, [K-1 / K, 1]; wherein f i (x i ) is a probability distribution of a random variable x i , wherein i = 1, …, m; m is the number of random variables that need to be sampled; S22. Sample one number from each equidistant interval of the probability distribution function f i (x i ) as a sampling point, and then obtain the sample value corresponding to the sampling point according to the inverse function of f i (x i ); repeat the step until K intervals are all extracted; S23. Repeat step S22 until m sets of random variables are extracted, and obtain a sample matrix H with an order of K*m; S24. Shuffle the arrangement order of each column element of the sample matrix H, that is, change the order of the sampling points of each random variable, and obtain K load curves; S25. The K load curves obtained are respectively input into the built power grid investment model to obtain K power grid investment cost values, which are written in the form of a column vector and denoted as X out ; S3. Extracting the load curve features of each load curve to obtain a matrix of load curve features corresponding to the K load curves, denoted as X in , with an order of K x n, where n is the number of types of extracted load curve features; S4. Train the XGBoost model: the load curve feature matrix X in is input to the XGBoost model, the grid investment cost X out is output of the XGBoost model, a nonlinear mapping relationship between the load curve features and the grid investment cost is constructed; S5. Based on the trained XGBoost model, the correlation between the power grid investment cost and the load curve characteristics is analyzed: Based on the trained XGBoost model, the weight of each load curve characteristic is calculated, and the size of the weight is sorted, and the influence degree of each load curve characteristic on the power grid investment cost is analyzed by comparing the weight size.

2. The method of claim 1, wherein: The load curve characteristics extracted in step S3 include: Peak C1: The maximum value of the total load of the system in the load change period; waist value C2: The intermediate value of the total load of the system in the load change period; valley value C3: The minimum value of the total load of the system in the load change period; peak duration C4: The duration of the maximum value of the total load of the system in the load change period; waist value duration C5: The duration of the intermediate value of the total load of the system in the load change period; valley value duration C6: The duration of the minimum value of the total load of the system in the load change period; peak valley difference C7: The difference between the maximum value and the minimum value of the total load of the system in the load change period.

3. The method of claim 1, wherein: The XGBoost model in step S4 has the following construction process: The prediction function is established as follows: where M is the number of decision trees in the model; X i is the i-th input sample; f m represents the prediction value of the m-th tree; represents the prediction value of the sample; is the set of decision trees; The objective function is established as follows: where K is the number of samples; l is the loss function; y i represents the true value of the sample; T is the number of leaf nodes of each tree; w is the weight of each leaf; After t iterations, the model is represented as: wherein, predicates a prediction value after the tth iteration; predicates a prediction value after the (t-1)th iteration; predicates a prediction value of the tth tree; The objective function is represented as: The loss function in the objective function is expanded by Taylor series of 2 times, and the objective function is expressed as: wherein, , are the first and second derivatives of the loss function l, respectively, and are given by: ； The objective function is simplified by removing the constant quantity, to: Combining all samples of the same leaf node together, and rewriting the objective function as a function of the leaf node weight w, we obtain the final objective function: wherein, is the weight of the jth leaf node, I j is the set of samples containing the jth leaf node; Through the above steps, the weight of the leaf node is obtained, and the shape of the best tree is obtained by minimizing the objective function obj.

4. The method of claim 3, wherein: The weight of each load curve characteristic in step S5 is calculated in the following manner: wherein is the weight of the load curve characteristic m, is the number of times the load curve characteristic m is used, is the total number of splits.

Images