Integrated energy system probabilistic interval energy flow adaptive calculation method, device and medium

Abstract

This invention discloses an adaptive calculation method, apparatus, and medium for probabilistic interval energy flow in integrated energy systems. The method includes: establishing a probabilistic interval energy flow model for the integrated energy system; transforming the original problem into a two-stage low-rank approximation model solution based on low-rank approximation theory; constructing a single-variable function within the rank-one function using radial basis functions; adaptively selecting the rank of the low-rank approximation model based on cross-entropy theory; calculating the undetermined coefficients of the low-rank approximation model based on the selected rank; and rapidly obtaining the output response probability box based on the obtained low-rank approximation model. This invention is the first to apply low-rank approximation theory to the probabilistic interval energy flow calculation of integrated energy systems and utilizes radial basis functions to construct a rank-one function for the input variables, achieving a complex nonlinear approximation of the deterministic performance flow and improving the solution accuracy of the probabilistic interval energy flow problem in integrated energy systems. This invention can be widely applied to integrated energy systems.

Description

Technical Field

[0001] This invention relates to integrated energy systems, and more particularly to a method, apparatus, and medium for adaptive calculation of energy flow within a probability interval of an integrated energy system. Background Technology

[0002] To address climate change and promote sustainable development, the international community has set goals of reducing carbon emissions and transitioning to clean energy. Integrated energy systems are a crucial solution for achieving these goals. By organically combining various energy resources and energy-consuming equipment, and coordinating planning, optimizing operation, and economically dispatching resources, they aim to achieve efficient energy utilization and emission reduction.

[0003] Energy flow calculation is a fundamental technology used in the coordinated planning, optimized operation, and economic dispatch of integrated energy systems. It aims to calculate state parameters such as voltage or pressure at nodes and current or flow in branches within an integrated energy system based on limited known information. This not only assesses the real-time operating status of the system but also provides a basis for optimized dispatch, equipment location and capacity determination, and fault analysis, making it of significant importance. However, with the large-scale integration of renewable energy and the increasing diversification of energy-consuming equipment, uncertainties in integrated energy systems have also greatly increased, including uncertainties in renewable energy output and in electricity, gas, and heat loads. The increased uncertainty significantly affects the energy flow distribution of integrated energy systems; therefore, it is necessary to analyze it from the perspective of uncertain energy flow.

[0004] Currently, commonly used uncertain energy flow models mainly fall into two categories: probabilistic energy flow models and interval energy flow models, which consider a single input uncertainty. Probabilistic energy flow models describe the input uncertainty as a random variable, relying heavily on extensive historical data and accurate distribution fitting, making them difficult to implement. Interval energy flow models can describe the input uncertainty as an interval variable when data is limited, but their results are typically conservative. However, in practice, the uncertainty information available to operators often falls between these two extremes. Therefore, if a probabilistic energy flow model is used, calculations may be impossible due to missing data; conversely, if an interval energy flow model is used, a large amount of useful information will be discarded, failing to fully exploit the value of the data. In recent years, probabilistic interval energy flow models, which can fully utilize existing uncertainty information to consider both types of input uncertainties, have attracted attention.

[0005] Mathematically, probabilistic interval energy flow models involve the quantitative analysis of dual uncertainties. Current solution methods mainly fall into two categories: simulation methods based on two-layer Monte Carlo sampling and approximation methods based on polynomial chaotic expansions. Simulation methods based on two-layer Monte Carlo sampling perform two-layer Monte Carlo simulations, sampling the outer random variables and the inner interval variables separately, thus transforming the solution of probabilistic interval energy flow into a large number of deterministic energy flow calculations. Although this method can provide relatively accurate results, its solution time is long. Approximation methods based on polynomial chaotic expansions, on the other hand, assume a probability distribution for the interval variables, transforming them into random variables, and use orthogonal polynomial chaotic expansions of the input random variables to fit the output response of the probabilistic interval energy flow, thereby obtaining a surrogate model of the output response. However, this method is very sensitive to the dimensionality of the input variables and the order of the polynomial chaotic expansion, encountering the "curse of dimensionality" problem when dealing with probabilistic interval energy flow problems with high-dimensional input variables. Furthermore, approximation methods based on low-order polynomial chaotic expansions do not perform well in solving probabilistic interval energy flow problems involving complex nonlinearities. Therefore, further research is needed to explore new methods that enable rapid and accurate solutions to probabilistic interval energy flow problems with high-dimensional input variables and complex nonlinearities. Summary of the Invention

[0006] In order to at least partially solve one of the technical problems existing in the prior art, the purpose of this invention is to provide a method, device and medium for adaptive calculation of energy flow in a probability interval of an integrated energy system.

[0007] The technical solution adopted in this invention is:

[0008] An adaptive calculation method for probabilistic interval energy flow in a comprehensive energy system.

[0009] Includes the following steps:

[0010] Establish a probabilistic interval energy flow model for a comprehensive energy system;

[0011] The original problem is transformed into a two-stage low-rank approximation model for solution based on the low-rank approximation theory.

[0012] A radial function is used to construct a univariate function in the rank-one function, and the rank of the low-rank approximation model is adaptively selected based on the cross-entropy theory.

[0013] Based on the selected rank, the undetermined coefficients of the low-rank approximation model are calculated using the alternating least squares method;

[0014] The output response probability box is quickly obtained based on the obtained low-rank approximation model.

[0015] Furthermore, the expression for the probabilistic interval energy flow model of the integrated energy system is as follows:

[0016]

[0017] In the formula, P i Q i These represent the injected active power and reactive power at node i, respectively; U i δ represents the voltage magnitude at node i. ij G represents the phase difference between the voltages at nodes i and j; ij B ij , respectively, represent the conductance and susceptance of the elements corresponding to nodes i and j in the node admittance matrix; n is the number of nodes in the power system; the subscript p denotes a pipeline; f p,ij π represents the air flow rate of pipe ij. i π j The air pressures at nodes i and j are respectively; k ij Pipeline parameters (depending on various factors such as pipeline length, inner diameter, friction coefficient, and natural gas temperature); s p,ij Characterizing the direction of airflow in a pipe, if π i ≥π j , then s p,ij =1, if π i <π j , then s p,ij =-1; the subscript c indicates compressor; f c,ij H represents the air flow rate through compressor ij. c,ij The power consumed by the compressor; B c,ij Z c,ij The compressor parameters (which depend on factors such as compressor temperature, efficiency, and compression factor); τ c,ij The gas flow rate consumed by the gas turbine; α c β c γ c f is the energy conversion efficiency constant; j∈i represents all nodes directly connected to node i via pipes or compressors; i s represents the injection gas flow rate at node i; c,ij Let s be the compressor direction variable. If i is the compressor inlet node, then s c,ij =1, if it is an exit node, then s c,ij =-1; A is the node-pipe correlation matrix of the heat network; m is the flow vector of each heat network pipe; m q B represents the outflow vector of each node; h The loop-branch correlation matrix of the thermal network; h f For the pressure drop in the thermal network pipeline; K is the pipeline resistance coefficient vector; C p T is the specific heat capacity of the working fluid; s T represents the heating temperature vector for each node; r T represents the regeneration temperature vector for each node;o Φ represents the effluent temperature vector at each node (before mixing); Φ represents the heat load vector at each node; T start T end T a These represent the starting temperature vector, ending temperature vector, and ambient temperature vector of the thermal network pipe, respectively; λ is the thermal conductivity coefficient of the pipe; L is the length vector of the pipe; m out The flow vector of the pipe at the outflow node; m in T is the pipe flow vector flowing into the node; out T is the node-mixed temperature vector; in This is the temperature vector at the end of the input pipe;

[0018] Suppose that the input variables in a comprehensive energy system include m-dimensional random variables and n-dimensional interval variables, then the nonlinear relationship between the output variables and the input variables can be simplified as follows:

[0019] Z = f(X) R ,Y I (1)

[0020] In the formula, X R =[X1,L,X i ,L,X m ] T Y is an m-dimensional random variable; I =[Y1,L,Y i ,L,Y n ] T Z is an n-dimensional interval variable; f(·) is the output variable; f(·) is the functional relationship between the output and input variables determined by the energy flow equation.

[0021] Furthermore, the transformation of the original problem into a two-stage low-rank approximation model based on low-rank approximation theory includes:

[0022] Construct a first-stage low-rank approximation model of the relationship between input random variables, interval variables, and output variables;

[0023] Solve for the undetermined coefficients of the first-stage low-rank approximation model to obtain the first-stage low-rank approximation model;

[0024] Based on the first-stage low-rank approximation model, we obtain the input random variable samples and the corresponding output variable boundary value samples, and construct a second-stage low-rank approximation model regarding the relationship between the upper and lower boundary values ​​of the input random variables and the output variables.

[0025] Solve for the undetermined coefficients of the second-stage low-rank approximation model to obtain the second-stage low-rank approximation model;

[0026] Based on the obtained second-stage low-rank approximation model, the probability boxes of the output variables are obtained.

[0027] Furthermore, the construction of the first-stage low-rank approximation model regarding the relationship between the input random variable, the interval variable, and the output variable includes:

[0028] In the first-stage low-rank approximation, the output variable Z = f(x) R ,y I After rank-r regularization, a low-rank approximation surrogate model of the sum of expansions of a finite number of rank-1 functions is used to approximate the result, as shown below:

[0029]

[0030] In the formula, b l (l=1,2,L,r) are the normalized weight coefficients; r is the number of rank-1 functions, i.e., the rank, also called the rank of the expression; ω l For the multivariate input variable ξ i (including random variable x) R and interval variable y I The rank-one function of ) is expressed as follows:

[0031]

[0032] In the formula: Let r be the i-th univariate function of the l-th rank-one function; usually the value of r is small (less than 5), so the above formula represents a regular low-rank approximation.

[0033] The low-rank approximate rank-one function will Marginal distribution with input variables Orthogonal polynomial basis functions Expanding upwards, the low-rank approximation model of formula (2) is further expressed as:

[0034]

[0035] In the formula, p is the k-th order univariate polynomial in the i-th random input; i for The highest order; In the l-th rank-1 function The coefficient.

[0036] Further, the process of solving for the undetermined coefficients of the first-stage low-rank approximation model to obtain the first-stage low-rank approximation model includes:

[0037] A1. Input a set of size M C Input variable sample points ξ C and input variable sample points ξ C The corresponding output response sample point zC Let the rank r = 1;

[0038] A2. Solve the following minimization problem using the alternating least squares method to obtain the rank-one function ω. r Undetermined coefficients of univariate functions in each dimension of input

[0039]

[0040] In the formula, W is the space of the rank tensor; The approximation error in response to Z; ||·|| 2 The 2-norm of the residual after applying the new first-order tensor; subscript ξ C This indicates that in the experimental design sample set (ξ) C ,z C Minimize on );

[0041] A3. Solve the following minimization problem using the least squares method to obtain a newly solved first-order function ω. r The normalized weighting coefficient b of (ξ) r At the same time, it updates the existing weight coefficients (b1, b2, ..., b r-1 );

[0042]

[0043] A4. If the rank r is less than the preset value R, let the rank r = r + 1 and go to step A1; otherwise, go to step A5.

[0044] A5. Output the solution results of the undetermined coefficients of the low-rank approximation model.

[0045] Further, the second-stage low-rank approximation model, which obtains input random variable samples and corresponding output variable boundary value samples based on the first-stage low-rank approximation model, and constructs a second-stage low-rank approximation model regarding the relationship between the upper and lower boundary values ​​of the input random variables and the output variables, includes:

[0046] In the second-stage low-rank approximation, the upper and lower boundary values ​​Z of the output variable are... U =f U (x R ) and Z D =f D (x R After rank-r regularization, a low-rank approximation surrogate model of the sum of expansions of a finite number of rank-1 functions is used to approximate the result, as shown below:

[0047]

[0048]

[0049] In the formula, b l (l=1,2,L,r) are the normalized weight coefficients; r is the number of rank-1 functions, i.e., the rank, also called the rank of the expression; ω l For a multivariate input random variable x R The rank-one function is expressed as follows:

[0050]

[0051] In the formula, Let r be the i-th univariate function of the l-th rank-one function; usually the value of r is small (less than 5), so the above formula represents a regular low-rank approximation;

[0052] The low-rank approximate rank-one function will Marginal distribution with input variables Orthogonal polynomial basis functions Expanding on the above, the low-rank approximation models of equations (7) and (8) are further expressed as:

[0053]

[0054]

[0055] In the formula: p is the k-th order univariate polynomial in the i-th random input; i for The highest order; In the l-th rank-1 function The coefficient;

[0056] The step of obtaining the probability box of the output variable based on the obtained second-stage low-rank approximation model includes:

[0057] A low-rank approximation model is obtained between the upper and lower boundary values ​​of the input random variable and the corresponding output variable. and Then, by generating a set of random variables x R samples Substitute each sample into the second-stage low-rank approximation model to quickly obtain the upper and lower boundary value samples of the output variable, and then construct its probability box.

[0058] Furthermore, the method of constructing a single-variable function in a rank-one function using a radial function includes:

[0059] Using radial basis functions to construct univariate functions of rank-one function As shown below:

[0060]

[0061] In the formula, h is the number of known input variable sample points; φ j λ is a radial basis function; j These are the undetermined coefficients of the radial basis functions;

[0062] The radial basis function φ j The Gaussian radial basis functions are as follows:

[0063]

[0064] In the formula, ||ξ i -ξ i,j || represents the radial distance from the input variable point to the known sample point; q i is a constant of the Gaussian radial basis function.

[0065] Furthermore, the adaptive selection of the rank of the low-rank approximation model based on cross-entropy theory includes:

[0066] B1. Using the trained low-rank approximation model, input N ξ A sample is used to quickly obtain an approximate response of the energy flow within the probability interval of the integrated energy system.

[0067] B2. Find and Cross-entropy:

[0068]

[0069] B3. Determine if the cross-entropy is less than the convergence condition η:

[0070]

[0071] B4. If the convergence condition is met, output the adaptive rank r and the corresponding response. Otherwise, let the rank r = r + 1 and repeat steps B1 to B3.

[0072] Another technical solution adopted in this invention is:

[0073] An adaptive energy flow calculation device for a probabilistic interval of an integrated energy system, comprising:

[0074] At least one processor;

[0075] At least one memory for storing at least one program;

[0076] When the at least one program is executed by the at least one processor, the at least one processor performs the method as described above.

[0077] Another technical solution adopted in this invention is:

[0078] A computer-readable storage medium storing a processor-executable program, which, when executed by a processor, performs the method described above.

[0079] The beneficial effects of this invention are as follows: This invention is the first to apply low-rank approximation theory to the calculation of probabilistic interval energy flow in integrated energy systems, and utilizes radial basis functions to construct a rank-one function of the input variables, achieving a complex nonlinear approximation of the deterministic performance flow, thus improving the solution accuracy of the probabilistic interval energy flow problem in integrated energy systems. Furthermore, a rank selection method based on cross-entropy theory for the low-rank approximation method is designed to achieve adaptive rank selection, ensuring the performance of the method and improving its adaptability. Attached Figure Description

[0080] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0081] Figure 1 This is a flowchart of a probabilistic interval energy flow adaptive calculation method for an integrated energy system according to an embodiment of the present invention;

[0082] Figure 2 This is a schematic diagram of the probability box of the output variable Z in an embodiment of the present invention. Detailed Implementation

[0083] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown 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 are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0084] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0085] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0086] Furthermore, in the description of this invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0087] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0088] To address existing technical problems, this invention, based on the probability interval energy flow calculation requirements of integrated energy systems, and using low-rank approximation, radial basis functions, and cross-entropy as fundamental theoretical tools, proposes an adaptive, fast, and accurate calculation method for probability interval energy flow in integrated energy systems based on an improved low-rank approximation. This method aims to solve the following three technical problems: 1) How to quickly and accurately calculate probability interval energy flow using the low-rank approximation method when there are high-dimensional input variables; 2) How to improve the low-rank approximation method to achieve higher fitting accuracy under complex nonlinear conditions; 3) The performance of the low-rank approximation method depends on the selection of parameters; how to improve the low-rank approximation method to achieve adaptive optimization and selection of appropriate parameters, thereby improving its adaptability.

[0089] This invention first establishes a probabilistic interval energy flow model for a comprehensive energy system; second, based on the low-rank approximation theory, the problem of calculating the probabilistic interval energy flow is transformed into a problem of solving a two-stage low-rank approximation model of the input response; then, the undetermined coefficients of the low-rank approximation model are calculated using the alternating least squares method to obtain a two-stage low-rank approximation model of the output response; finally, the approximation accuracy and adaptability of the low-rank approximation method are further improved based on the radial basis function and cross-entropy methods.

[0090] like Figure 1 As shown, this embodiment provides an adaptive calculation method for energy flow within a probabilistic interval of an integrated energy system, including the following steps:

[0091] S1. Establish a probabilistic interval energy flow model for the integrated energy system.

[0092] This embodiment employs a probabilistic interval energy flow model for an integrated energy system, representing electricity load, gas load, and heat load demand as random variables, and wind power and photovoltaic output as interval variables. The integrated energy system used in this embodiment includes an electricity subsystem, a natural gas subsystem, and a heat subsystem, and its probabilistic interval energy flow model is as follows:

[0093]

[0094] In the formula, P i Q i These represent the injected active power and reactive power at node i, respectively; U i δ represents the voltage magnitude at node i. ij G represents the phase difference between the voltages at nodes i and j; ij B ij , respectively, represent the conductance and susceptance of the elements corresponding to nodes i and j in the node admittance matrix; n is the number of nodes in the power system; the subscript p denotes a pipeline; f p,ij π represents the air flow rate of pipe ij. i π j The air pressures at nodes i and j are respectively; k ij Pipeline parameters (depending on various factors such as pipeline length, inner diameter, friction coefficient, and natural gas temperature); s p,ij Characterizing the direction of airflow in a pipe, if π i ≥π j , then s p,ij =1, if π i <π j , then s p,ij =-1. The subscript 'c' indicates a compressor; f c,ij H represents the air flow rate through compressor ij. c,ij The power consumed by the compressor; B c,ij Z c,ij The compressor parameters (which depend on factors such as compressor temperature, efficiency, and compression factor); τ c,ij The gas flow rate consumed by the gas turbine; α c β c γ c f is the energy conversion efficiency constant; j∈i represents all nodes directly connected to node i via pipes or compressors; i s represents the injection gas flow rate at node i; c,ij Let s be the compressor direction variable. If i is the compressor inlet node, then s c,ij =1, if it is an exit node, then s c,ij =-1; A is the node-pipe correlation matrix of the heat network; m is the flow vector of each heat network pipe; m q B represents the outflow vector of each node;h The loop-branch correlation matrix of the thermal network; h f For the pressure drop in the thermal network pipeline; K is the pipeline resistance coefficient vector; C p T is the specific heat capacity of the working fluid; s T represents the heating temperature vector for each node; r T represents the regeneration temperature vector for each node; o Φ represents the effluent temperature vector at each node (before mixing); Φ represents the heat load vector at each node; T start T end T a These represent the starting temperature vector, ending temperature vector, and ambient temperature vector of the thermal network pipe, respectively; λ is the thermal conductivity coefficient of the pipe; L is the length vector of the pipe; m out The flow vector of the pipe at the outflow node; m in T is the pipe flow vector flowing into the node; out T is the node-mixed temperature vector; in This is the temperature vector at the end of the input pipe.

[0095] Assume the input variables in the integrated energy system consist of m-dimensional random variables and n-dimensional interval variables. In the above energy flow model, the nonlinear relationship between the output and input variables can be simplified as follows:

[0096] Z = f(X) R ,Y I (1)

[0097] In the formula, X R =[X1,L,X i ,L,X m ] T Y is an m-dimensional random variable; I =[Y1,L,Y i ,L,Y n ] T Z represents the n-dimensional interval variable; Z represents the system state such as node voltage and node pressure, i.e., the output variable, also known as the output response; f(·) is the functional relationship between the output and input variables determined by the energy flow equation.

[0098] However, since both random variables and interval variables exist in formula (1), there are many uncertain input factors, and there is a complex nonlinear relationship between input and output, making it difficult for existing methods to solve directly and quickly.

[0099] S2. Based on the low-rank approximation theory, the original problem is transformed into a two-stage low-rank approximation model for solution.

[0100] To quickly obtain the probability boxes of the output variables in a probabilistic interval energy flow model of an integrated energy system, this embodiment transforms the probabilistic interval energy flow calculation problem of an integrated energy system into a two-stage surrogate model solution problem based on low-rank approximation theory. In the first stage, the analytical expression of the relationship between the input random variables, interval variables, and output variables is constructed using the low-rank approximation method, avoiding a large amount of deterministic probabilistic interval energy flow calculation. The analytical expression of the output variables obtained in the first stage yields samples of the input random variables and their corresponding boundary value samples of the output variables. In the second stage, based on the above samples, the analytical expression of the relationship between the upper and lower boundary values ​​of the input random variables and the output variables is further constructed using the low-rank approximation method, thereby improving the efficiency of obtaining the probability boxes of the output variables. The fast calculation method of probabilistic interval energy flow of an integrated energy system based on low-rank approximation mainly includes the following steps S21 to S25:

[0101] S21. Construct a first-stage low-rank approximation model of the relationship between input random variables, interval variables and output variables.

[0102] In the first-stage low-rank approximation, the output variable Z = f(x) R ,y I After rank-r regularization, it can be approximated by a low-rank approximation surrogate model of the expansion sum of a finite number of rank-1 functions, as shown below:

[0103]

[0104] In the formula: b l (l=1,2,L,r) are the normalized weight coefficients; r is the number of rank-1 functions, i.e., the rank, also called the rank of the expression; ω l For the multivariate input variable ξ i (including random variable x) R and interval variable y I The rank-one function of ) can be expressed as follows:

[0105]

[0106] In the formula: Let r be the i-th univariate function of the l-th rank-one function. Typically, the value of r is small (less than 5), therefore the above expression represents a regular low-rank approximation.

[0107] The traditional low-rank approximate rank-one function will Marginal distribution with input variables Orthogonal polynomial basis functions Expanding upwards, the low-rank approximation model of equation (2) can be further expressed as:

[0108]

[0109] In the formula: p is the k-th order univariate polynomial in the i-th random input; i for The highest order; In the l-th rank-1 function The coefficient.

[0110] S22. Solve for the undetermined coefficients of the first-stage low-rank approximation model to obtain the first-stage low-rank approximation model.

[0111] This embodiment efficiently solves for the undetermined coefficients of the first-stage low-rank approximation model for determining the rank using the alternating least squares method. The specific process is as follows:

[0112] Step 1: Input a set of data of size M C Input variable sample points ξ C and its corresponding output response sample point z C Let the rank r = 1;

[0113] Step 2: Solve the following minimization problem using the alternating least squares method to obtain the rank-one function ω. r Undetermined coefficients of univariate functions in each dimension of input

[0114]

[0115] In the formula: W is the space of the rank tensor; The approximation error in response to Z; ||·|| 2 The 2-norm of the residual after applying the new first-order tensor; subscript ξ C This indicates that in the experimental design sample set (ξ) C ,z C Minimize on ).

[0116] Step 3: Solve the following minimization problem using the least squares method to obtain the newly solved first-order function ω. r The normalized weighting coefficient b of (ξ) r At the same time, it updates the existing weight coefficients (b1, b2, ..., b r-1 ).

[0117]

[0118] Step 4: If the rank r is less than the preset value R, set the rank r = r + 1 and go to step 1; otherwise, go to step 5.

[0119] Step 5: Output the solution results of the undetermined coefficients of the low-rank approximation model.

[0120] S23. Based on the first-stage low-rank approximation model, obtain the input random variable samples and their corresponding output variable boundary value samples, and construct the second-stage low-rank approximation model regarding the relationship between the upper and lower boundary values ​​of the input random variables and the output variables.

[0121] Similar to the first stage, in the second stage low-rank approximation, the upper and lower boundary values ​​Z of the output variable are... U =f U (x R ) and Z D =f D (x R After rank-r regularization, it can be approximated by a low-rank approximation surrogate model of the expansion sum of a finite number of rank-1 functions, as shown below:

[0122]

[0123]

[0124] In the formula: b l (l=1,2,L,r) are the normalized weight coefficients; r is the number of rank-1 functions, i.e., the rank, also called the rank of the expression; ω l For a multivariate input random variable x R The rank-one function can be expressed as follows:

[0125]

[0126] In the formula: Let r be the i-th univariate function of the l-th rank-one function. Typically, the value of r is small (less than 5), therefore the above expression represents a regular low-rank approximation.

[0127] Similar to the first stage, the low-rank approximate rank-one function will Marginal distribution with input variables Orthogonal polynomial basis functions Expanding upwards, the low-rank approximation models of equations (7) and (8) can be further expressed as:

[0128]

[0129]

[0130] In the formula: p is the k-th order univariate polynomial in the i-th random input; i for The highest order; In the l-th rank-1 function The coefficient.

[0131] S24. Solve for the undetermined coefficients of the second-stage low-rank approximation model to obtain the second-stage low-rank approximation model.

[0132] This embodiment efficiently solves for the undetermined coefficients of the first-stage low-rank approximation model for determining the rank using the alternating least squares method. The specific process is as follows:

[0133] Step 1: Input a set of data of size M C Input variable sample points ξ C and its corresponding output response sample point z C Let the rank r = 1;

[0134] Step 2: Solve the following minimization problem using the alternating least squares method to obtain the rank-one function ω. r Undetermined coefficients of univariate functions in each dimension of input

[0135]

[0136] In the formula: W is the space of the rank tensor; The approximation error in response to Z; ||·|| 2 The 2-norm of the residual after applying the new first-order tensor; subscript ξ C This indicates that in the experimental design sample set (ξ) C ,z C Minimize on ).

[0137] Step 3: Solve the following minimization problem using the least squares method to obtain the newly solved first-order function ω. r The normalized weighting coefficient b of (ξ) r At the same time, it updates the existing weight coefficients (b1, b2, ..., b r-1 ).

[0138]

[0139] Step 4: If the rank r is less than the preset value R, set the rank r = r + 1 and go to step 1; otherwise, go to step 5.

[0140] Step 5: Output the solution results of the undetermined coefficients of the low-rank approximation model.

[0141] S25. Based on the obtained second-stage low-rank approximation model, quickly obtain the probability boxes of the output variables.

[0142] This embodiment obtains a low-rank approximation model between the upper and lower boundary values ​​of the input random variable and its corresponding output variable. and Then, by generating a set of random variables x R samples Substituting each sample into the second-stage LRA model allows for the rapid acquisition of upper and lower boundary value samples of the output variable, thereby constructing its probability box.

[0143] The purpose of probability interval energy flow calculation is to obtain the probability distribution and confidence interval of the output variable, that is, the probability boxes (p-boxes) defined by the upper and lower boundaries of the output variable, such as... Figure 2 As shown.

[0144] Maximum probability distribution F of output variable max (Z) and the minimum probability distribution F min (Z) represents the probability distributions of its lower and upper boundaries, respectively. Figure 2 It can be seen that the fluctuation range of the output variable Z is the region enclosed by the maximum and minimum probability distributions. In the probability-interval energy flow, the event Z of the output variable exceeding the limit... <Z limit The probability of occurrence is the interval [Pr min ,Pr max Therefore, compared to probabilistic energy flow calculation, the advantage of probabilistic interval energy flow is that, for example, when the probability distribution of injected power at certain nodes in the system is difficult to obtain accurately, it can be regarded as an interval variable, thereby enabling the estimation of the maximum and minimum probabilities of the output variable exceeding its limit.

[0145] S3. Construct a single-variable function in the rank-one function using radial functions.

[0146] Single-variable functions that are traditionally approximated by low-rank functions as rank-one functions The low-order expansion of orthogonal polynomials used in the approximation method yields poor approximation results for probability interval energy flow models with complex nonlinearities. Furthermore, the accuracy and computational efficiency of the low-rank approximation method are highly dependent on the appropriate selection of the rank r. On the one hand, a higher rank results in a better approximation of the low-rank model and a more accurate output response probability box; on the other hand, a higher rank increases the computational burden, affecting the performance of the method. To address these issues, this section, building upon step S2, further improves the low-rank approximation method based on radial basis functions and cross-entropy theory. This allows the low-rank approximation method to obtain more accurate probability interval energy flow results and enables adaptive optimization of the low-rank approximation rank, improving the adaptability of the method.

[0147] The specific steps for constructing the rank-one function based on radial basis functions are as follows:

[0148] Radial basis functions (RBFs) have the ability to approximate any continuous function with arbitrary precision. To address the issue of poor approximation performance of traditional low-rank approximation rank-one functions for complex nonlinear models, this embodiment uses RBFs to construct univariate functions of rank-one functions. As shown below:

[0149]

[0150] In the formula, h is the number of known input variable sample points; φ j λ is a radial basis function; j These are the undetermined coefficients of the radial basis function. Commonly used radial basis functions include linear radial basis functions, cubic radial basis functions, spline radial basis functions, and Gaussian radial basis functions. Since the Gaussian radial basis function is more suitable for models with high nonlinearity, this embodiment uses the Gaussian radial basis function, as shown below:

[0151]

[0152] In the formula, ||ξ i -ξ i,j || represents the radial distance from the input variable point to the known sample point; q i is a constant of the Gaussian radial basis function.

[0153] S4. Adaptively select the rank of the low-rank approximation model based on cross-entropy theory.

[0154] To find a suitable rank, this embodiment uses cross-entropy as the convergence metric for low-rank approximation. It quantifies the difference in output response probability distributions between the low-rank approximation model with rank r and the low-rank approximation model with rank r-1, and designs an adaptive optimization method for the rank. Cross-entropy is a mathematical method that quantitatively measures the difference between two probability distributions. As the rank r increases, the response output of the low-rank approximation model with rank r-1... The closer to output The higher the similarity between two distributions, the smaller the cross-entropy. The specific steps of the low-rank approximate rank adaptive selection method based on cross-entropy are as follows:

[0155] Step 1: Using the trained low-rank approximation model, input N ξ A sample is used to quickly obtain an approximate response of the energy flow within the probability interval of the integrated energy system.

[0156] Step 2: Find and cross-entropy

[0157]

[0158] Step 3: Determine if the cross-entropy is less than the convergence condition η

[0159]

[0160] Step 4: If the convergence condition is met, output the adaptive rank r and the corresponding response. Otherwise, let the rank r = r + 1, and repeat steps one through three.

[0161] Combining steps S2 and S3, the flowchart of the adaptive fast calculation method for probabilistic interval energy flow of the integrated energy system based on the improved low-rank approximation is as follows: Figure 1 As shown.

[0162] S5. Calculate the undetermined coefficients of the low-rank approximation model based on the selected rank.

[0163] S6. Quickly obtain the output response probability box based on the obtained low-rank approximation model.

[0164] In summary, compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0165] (1) This invention is the first to apply the low-rank approximation method to the calculation of probabilistic interval energy flow problems in integrated energy systems. The output response is represented as the sum of expansions of a finite number of r rank-one functions through rank-r regular decomposition, and the undetermined coefficients of each rank-one function are solved using alternating least squares. The advantage of this method is that the number of coefficients to be solved is linearly related to the number of input variables, effectively solving the dimensionality curse problem faced by traditional approximation methods based on polynomial chaotic expansion when dealing with probabilistic interval energy flow problems containing high-dimensional input variables.

[0166] (2) This invention, for the first time, designs a two-stage low-rank approximation method to improve the efficiency of probabilistic interval energy flow calculation for integrated energy systems. In the first stage, the low-rank approximation method is used to construct an analytical expression between the input random variables, interval variables, and output response, avoiding a large amount of deterministic calculation. Through the analytical expression of the output response obtained in the first stage, samples of the input random variables and their corresponding output response boundary values ​​can be obtained. In the second stage, the low-rank approximation method is further used to construct an analytical expression of the relationship between the upper and lower boundary values ​​of the input random variables and the output response, thereby improving the efficiency of obtaining the probability box of the output response.

[0167] (3) This invention is the first to apply radial basis functions to low-rank approximation theory and construct a rank-one function based on radial basis function expansion. Radial basis functions have excellent approximation properties for nonlinear functions and can overcome the shortcomings of traditional methods that construct rank-one functions based on low-order expansion of orthogonal polynomials, which have poor approximation effects on complex nonlinear models, thus obtaining more accurate results.

[0168] (4) This invention is the first to apply cross-entropy theory to low-rank approximation theory, and designs an adaptive parameter selection method for low-rank approximation algorithms based on cross-entropy. This solves the problem of the dependence of low-rank approximation algorithm performance on parameter selection. Compared with the traditional method of empirically setting the rank, the adaptive selection method of this invention can automatically optimize the selection of the low-rank approximation rank according to the actual situation, thereby improving the adaptability of the algorithm.

[0169] (5) The integrated energy system probability interval energy flow model constructed by this invention can make reasonable use of the information of system uncertainty factors. The improved low-rank approximation algorithm designed can efficiently and accurately realize the calculation of the integrated energy system probability interval energy flow. It is suitable for the operation and scheduling requirements of the integrated energy system under the background of large-scale access of new energy, and can bring good social and economic benefits.

[0170] The present invention also provides a probabilistic interval energy flow adaptive calculation device for an integrated energy system, comprising:

[0171] At least one processor;

[0172] At least one memory for storing at least one program;

[0173] When the at least one program is executed by the at least one processor, the at least one processor performs the following: Figure 1 The method shown.

[0174] This embodiment provides a probabilistic interval energy flow adaptive calculation device for an integrated energy system. It can execute the probabilistic interval energy flow adaptive calculation method for an integrated energy system provided in the method embodiment of the present invention. It can execute any combination of implementation steps of the method embodiment and has the corresponding functions and beneficial effects of the method.

[0175] This application also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform... Figure 1 The method shown.

[0176] This embodiment also provides a storage medium storing instructions or programs that can execute the adaptive calculation method for probabilistic interval energy flow of a comprehensive energy system provided in the method embodiment of the present invention. When the instructions or programs are run, any combination of implementation steps of the method embodiment can be executed, and the method has the corresponding functions and beneficial effects.

[0177] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0178] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0179] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0180] 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.

[0181] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), 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). Furthermore, computer-readable media can even 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 computer memory.

[0182] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in 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.

[0183] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, 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.

[0184] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0185] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A probabilistic interval adaptive calculation method for energy flow in a comprehensive energy system, characterized in that, Includes the following steps: Establish a probabilistic interval energy flow model for a comprehensive energy system; The original problem is transformed into a two-stage low-rank approximation model for solution based on the low-rank approximation theory. A radial function is used to construct a univariate function in the rank-one function, and the rank of the low-rank approximation model is adaptively selected based on the cross-entropy theory. Calculate the undetermined coefficients of the low-rank approximation model based on the selected rank; The output response probability box is quickly obtained based on the obtained low-rank approximation model; The transformation of the original problem into a two-stage low-rank approximation model based on low-rank approximation theory includes: Construct a first-stage low-rank approximation model of the relationship between input random variables, interval variables, and output variables; Solve for the undetermined coefficients of the first-stage low-rank approximation model to obtain the first-stage low-rank approximation model; Based on the first-stage low-rank approximation model, we obtain the input random variable samples and the corresponding output variable boundary value samples, and construct a second-stage low-rank approximation model regarding the relationship between the upper and lower boundary values ​​of the input random variables and the output variables. Solve for the undetermined coefficients of the second-stage low-rank approximation model to obtain the second-stage low-rank approximation model; Based on the obtained second-stage low-rank approximation model, the probability boxes of the output variables are obtained; The method of constructing a single-variable function in a rank-one function using a radial function includes: Using radial basis functions to construct univariate functions of rank-one function As shown below: （12） In the formula, h The number of known input variable sample points; These are radial basis functions; These are the undetermined coefficients of the radial basis functions; The radial basis function The Gaussian radial basis functions are as follows: （13） In the formula, The radial distance from the input variable point to the known sample point; is a constant of the Gaussian radial basis function.

2. The adaptive calculation method for probabilistic interval energy flow in a comprehensive energy system according to claim 1, characterized in that, The expression for the probabilistic interval energy flow model of the integrated energy system is as follows: In the formula, , They are nodes i The injected active power and reactive power; For nodes i The voltage amplitude; For nodes i , j Phase difference of voltage; , These are the nodal admittance matrices. i , j The electrical conductance and susceptance of the element corresponding to the node; n This represents the number of nodes in the power system; the subscript p indicates a pipeline. For pipelines i - j airflow rate; , They are nodes i , j air pressure; For pipeline parameters; Characterizing the direction of airflow in a pipe, if ,but ,like ,but The subscript 'c' indicates a compressor. For flow through the compressor i - j airflow rate; The power consumed by the compressor; , These are compressor parameters; The gas flow rate consumed by the gas turbine; , , The energy conversion efficiency constant; Indicates connection to nodes via pipes or compressors. i All directly connected nodes; For nodes i The injection gas flow rate; For compressor direction variable, if i If it is the compressor inlet node, then If it is an exit node, then ; A This represents the node-pipe correlation matrix of the thermal network. For each heating network pipeline flow vector; This represents the outflow vector for each node. B h The loop-branch correlation matrix of the thermal network; h f For pressure drop in heating network pipelines; K This represents the vector of pipe resistance coefficients. The specific heat capacity of the working fluid; This represents the heating temperature vector for each node; This represents the regeneration temperature vector for each node; This represents the outflow temperature vector for each node; The heat load vector for each node; , , These represent the starting temperature vector, ending temperature vector, and ambient temperature vector of the thermal network pipeline, respectively; λ is the thermal conductivity coefficient of the pipeline. L The length vector of the pipe; The pipe flow vector for the outflow node; This represents the pipeline flow vector flowing into the node; The node-mixed temperature vector; This is the temperature vector at the end of the input pipe; Assume the input variables in the integrated energy system include m dimensional random variables and n For a variable with a given interval, the non-linear relationship between the output and input variables can be simplified as follows: （1） In the formula, for m 3D random variable; for n 3D interval variables; Z For output variables; f (·) represents the functional relationship between the output and input variables determined by the energy flow equation.

3. The adaptive calculation method for probabilistic interval energy flow in a comprehensive energy system according to claim 1, characterized in that, The construction of the first-stage low-rank approximation model regarding the relationship between input random variables, interval variables, and output variables includes: In the first stage of the low-rank approximation, the output variable After order r Regular decomposition is approximated by a low-rank approximation surrogate model of the sum of expansions of a finite number of rank-one functions, as shown below: （2） In the formula, These are the normalized weighting coefficients; r The number of rank-one functions; For multivariate input variables The rank-one function is expressed as follows: （3） In the formula: For the first l The rank-1 function of the first i Single-variable function; The low-rank approximate rank-one function will Marginal distribution with input variables Orthogonal polynomial basis functions Expanding upwards, the low-rank approximation model of formula (2) is further expressed as: （4） In the formula, For the first i The nth random input k A single-variable polynomial of order 1; for The highest order; For the first l In a rank-1 function The coefficient.

4. The adaptive calculation method for probabilistic interval energy flow in a comprehensive energy system according to claim 1, characterized in that, The process of solving for the undetermined coefficients of the first-stage low-rank approximation model to obtain the first-stage low-rank approximation model includes: A1. Input a set of sizes. M C Input variable sample points ξ C and input variable sample points ξ C Corresponding output response sample points z C Let the rank r= 1; A2. Solve the following minimization problem using the alternating least squares method to obtain the rank-one function. ω r Undetermined coefficients of univariate functions in each dimension of input ; （5） In the formula, W The space of a rank tensor; In response Z Approximation error; || || 2 The 2-norm of the residual after applying the new first-order tensor; subscript ξ C Indicates the experimental design sample set ( ξ C , z C Minimize on ); A3. Solve the following minimization problem using the least squares method to obtain a newly solved first-order function. ω r ( ξ Normalized weighting coefficients b r At the same time, the existing weight coefficients are updated. b 1, b 2, , b r-1 ); （6） A4. If the rank r Less than the preset value R Let the rank r=r+1 Proceed to step A1; otherwise, proceed to step A5. A5. Output the solution results of the undetermined coefficients of the low-rank approximation model.

5. The adaptive calculation method for probabilistic interval energy flow in a comprehensive energy system according to claim 1, characterized in that, The process involves obtaining input random variable samples and corresponding output variable boundary value samples based on the first-stage low-rank approximation model, and constructing a second-stage low-rank approximation model regarding the relationship between the upper and lower boundary values ​​of the input random variables and the output variables. This includes: In the second-stage low-rank approximation, the upper and lower boundary values ​​of the output variable are... and After order r Regular decomposition is approximated by a low-rank approximation surrogate model of the sum of expansions of a finite number of rank-one functions, as shown below: （7） （8） In the formula, These are the normalized weighting coefficients; r The number of rank-one functions; For multivariate input random variables The rank-one function is expressed as follows: （9） In the formula, For the first l The rank-1 function of the first i Single-variable function; The low-rank approximate rank-one function will Marginal distribution with input variables Orthogonal polynomial basis functions Expanding upwards, the low-rank approximation models of equations (7) and (8) are further expressed as: （10） （11） In the formula: For the first i The nth random input k A single-variable polynomial of order 1; for The highest order; For the first l In a rank-1 function The coefficient; The step of obtaining the probability box of the output variable based on the obtained second-stage low-rank approximation model includes: A low-rank approximation model is obtained between the upper and lower boundary values ​​of the input random variable and the corresponding output variable. and Then, by generating a set of random variables samples Substitute each sample into the second-stage low-rank approximation model to quickly obtain the upper and lower boundary value samples of the output variable, and then construct its probability box.

6. The adaptive calculation method for probabilistic interval energy flow in a comprehensive energy system according to claim 1, characterized in that, The adaptive selection of the rank of the low-rank approximation model based on cross-entropy theory includes: B1. Using the trained low-rank approximation model, input... A sample is used to quickly obtain an approximate response of the energy flow within the probability interval of the integrated energy system. ; B2. Find and Cross-entropy: B3. Determine if the cross-entropy is less than the convergence condition. : B4. If the convergence condition is met, output the adaptive rank. r and corresponding response Otherwise, let the rank be... r=r+1 Repeat steps B1 to B3.

7. A probabilistic interval energy flow adaptive calculation device for an integrated energy system, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of claims 1-6.

8. A computer-readable storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to perform the method as described in any one of claims 1-6.

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