Power distribution network probability interval power flow affine optimization method and system based on full-pure embedding

Abstract

The invention provides a power distribution network probability interval power flow affine optimization method and system based on full-pure embedding, and the method carries out the affine optimization of the power distribution network probability interval power flow through a full-pure embedding method, and builds an interval variable correlation model of a mixed box-ellipsoid set to describe the uncertainty between input variables. And the function of accurately simulating the influence of distributed photovoltaic access on the uncertainty power flow distribution of the power distribution network is realized. The full-pure embedding probability interval affine optimization power flow model has good completeness and higher conservative property when solving the power flow of the power distribution network, and is suitable for uncertainty power flow analysis in a relatively large fluctuation interval. The hybrid box type-ellipsoid correlation model not only can describe the independent fluctuation range of the power of each node, but also can capture the linear or weak nonlinear correlation between the nodes; the all-pure embedded power distribution network probability interval power flow model based on the evidence theory realizes organic unification of probability power flow and interval power flow.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution network optimization, and in particular relates to a distribution network probability interval power flow affine optimization method and system based on holomorphic embedding. Background Art

[0002] With the massive integration of intermittent renewable energy into distribution networks and the rapid growth of new loads, uncertainty is increasingly impacting power systems. Power flow calculation is a crucial foundation for power system analysis. Recent research has focused on how to address uncertainty in power flow calculations to analyze the impact of distributed energy sources such as photovoltaics and wind power on distribution network power flow distribution. Uncertainty power flow algorithms for distribution networks primarily include fuzzy power flow methods, interval power flow methods, and probabilistic power flow methods. The holomorphic embedded power flow method, a recursive power flow calculation method proposed in 2012, eliminates the need for repeated Jacobian matrix generation and involves only the computation of a system of linear equations. When a power flow solution exists for the system, the holomorphic embedded power flow method ensures convergence within the reliable domain.

[0003] Existing research has used a holomorphic embedding model to solve power flow problems in novel power systems, achieving enhanced conservatism in the calculation results. It also addresses existing affine power flow algorithms, such as reliance on initial values ​​and potential non-convergence in iterations. This demonstrates the holomorphic embedding method's superior conservatism and improved computational efficiency in power flow calculations. However, the output power of distributed energy resources in distribution networks can be correlated, and existing studies of probabilistic interval power flows in distribution networks based on holomorphic embedding have neglected the impact of correlations between input uncertainties on the probabilistic interval power flow results. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a distribution network probability interval power flow affine optimization method and system based on holomorphic embedding, which is used to accurately simulate the impact of distributed photovoltaic access on the uncertainty power flow distribution of the distribution network.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a distribution network probability interval power flow affine optimization method based on holomorphic embedding, comprising the following steps: S1: Initialization, input relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; S2: Establish an affine power flow model of the system's node voltage and power based on the relevant parameters of the distribution network; introduce an embedding factor to construct a holomorphic embedded affine optimization power flow model; S3: Based on the distributed photovoltaic output, a focal element model and multi-dimensional joint trust distribution are established, and the model is substituted into the holomorphic embedded affine optimization power flow model to obtain the holomorphic embedded probability interval affine optimization power flow model and solved; S4: Based on the correlation coefficient, an interval variable correlation model of the hybrid box-ellipsoid set is established and converted into affine constraints, which are then solved jointly in a holomorphic embedded probability interval affine optimization power flow model. S5: Obtain the probability boundary of the probability interval power flow solution of the distribution network based on evidence theory.

[0006] According to the above scheme, in step S2, the specific steps are: S21: For PV nodes, the absolute value of the node's affine voltage is obtained based on the node's given voltage value; for balanced nodes, the affine voltage of the node is obtained based on the node's given voltage value; an affine power flow model is established for the power system's node's affine power, affine voltage, branch series admittance, and node parallel branch admittance; S22: Introduce the embedding factor and construct a holomorphic embedding affine optimization power flow model.

[0007] Furthermore, in step S22, the specific steps are: A holomorphic embedded affine optimization power flow model of the balancing node is established according to the given voltage magnitude and phase; The central value of affine voltage is introduced as the embedding value, and a holomorphic embedded affine optimization power flow model of PQ nodes under noise is established. The central value of affine reactive power is introduced as the embedding value, and a holomorphic embedding model of PV nodes under noise is established.

[0008] According to the above scheme, in step S3, the specific steps are: S31: Divide the fluctuation range of the distributed photovoltaic output active power and reactive power at the distribution network node into multiple sub-intervals and assign corresponding probabilities to them. Assuming that the sub-interval division principle is the same and the corresponding probabilities of the sub-intervals are also the same, a focal element model of the distributed photovoltaic output is constructed; S32: Establishing a trust distribution for the output active power of distributed photovoltaics; establishing a multi-dimensional joint trust distribution based on the number of distributed photovoltaic power stations in the distribution network; S33: Convert the distributed photovoltaic output active power and reactive power of each interval into affine form respectively, and substitute them into the holomorphic embedded affine optimization power flow model established in step S2 to obtain the holomorphic embedded probability interval affine optimization power flow model; S34: Calculate the affine solution of the unknown voltage and PV node reactive power, as well as the interval range of the node voltage amplitude and phase angle.

[0009] Furthermore, in step S34, the specific steps are: S341: Based on the principle that the coefficients of the same-order power series on both sides of the equation are equal, the holomorphic embedded probability interval affine optimization power flow model is organized into a system of linear equations, and the affine solution of the unknown voltage and PV node reactive power is obtained; S342: Taking the affine form of the node voltage amplitude and phase angle as the objective function, considering the node power constraint and voltage amplitude constraint, solve and output the interval range of the node voltage amplitude and phase angle.

[0010] Furthermore, in step S4, the specific steps are: S41: Establish an interval variable correlation model of a hybrid box-ellipsoid set based on the correlation coefficient, the expected value of the distributed photovoltaic active power and reactive power, the covariance matrix of the input interval, the total number of input intervals, and the upper and lower bounds of a certain input interval; S42: Obtain the constraints for solving the holomorphic embedded probability interval affine optimization power flow model considering the hybrid box-ellipsoid set correlation model; S43: adding the constraint conditions to the holomorphic embedded probability interval affine optimization power flow model of step S33, and solving the interval range of the output node voltage amplitude and phase angle.

[0011] Furthermore, in the step S4, the constraints include the affine expression of the active power of the node composed of the existing noise elements and their coefficients, as well as the slope of the parallelogram, the inclination angle of the ellipsoid, the constraint interval vectors of the parallelogram model and the ellipsoid model, the major and minor radii of the ellipse and the center values ​​of different input focal element intervals.

[0012] According to the above scheme, in step S5, the specific steps are: The trust function and likelihood function are calculated based on the active power of distributed photovoltaics and the probability corresponding to the sub-interval, and the probability boundary of the distribution network probability interval power flow solution is constructed.

[0013] A distribution network probabilistic interval power flow affine optimization system based on holomorphic embedding, The parameter acquisition submodule is used for initialization and input of relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; The model optimization submodule is used to establish an affine power flow model of the system's node voltage and power based on the relevant parameters of the distribution network; it introduces an embedding factor to construct a holomorphic embedded affine optimization power flow model; The interval modeling submodule is used to establish a focal element model and multi-dimensional joint trust distribution based on the distributed photovoltaic output, substitute it into the holomorphic embedded affine optimization power flow model to obtain the holomorphic embedded probabilistic interval affine optimization power flow model and solve it; The model parsing submodule is used to establish the interval variable correlation model of the mixed box-ellipsoid set based on the correlation coefficient, convert it into affine constraints, and solve it simultaneously in the holomorphic embedded probability interval affine optimization power flow model; The probability boundary submodule is used to obtain the probability boundary of the probability interval power flow solution of the distribution network based on evidence theory.

[0014] A computer memory stores a computer program that can be executed by a computer processor. The computer program executes a distribution network probability interval power flow affine optimization method based on holomorphic embedding.

[0015] The beneficial effects of the present invention are: 1. The present invention's affine optimization method and system for distribution network probability interval power flow based on holomorphic embedding performs affine optimization on the distribution network probability interval power flow based on the holomorphic embedding method, and establishes a hybrid box-ellipsoid set interval variable correlation model to describe the uncertainty between input variables, thereby achieving the function of accurately simulating the impact of distributed photovoltaic access on the distribution network uncertainty power flow distribution.

[0016] 2. The holomorphic embedded probability interval affine optimization power flow model of the present invention has good completeness when solving the distribution network power flow, and is less conservative than the existing Taylor expansion affine power flow algorithm.

[0017] 3. During the solution process, even if the node input power fluctuation range increases, the range of the solution result of the holomorphic embedded probability interval power flow affine optimization method of the present invention is still smaller than the Taylor expansion affine power flow algorithm, and is more conservative. It is more suitable for uncertainty power flow analysis under larger fluctuation ranges than the Taylor expansion affine power flow algorithm.

[0018] 4. The hybrid box-ellipsoid correlation model of the present invention can not only describe the independent fluctuation range of the power of each node, but also capture the linear or weak nonlinear correlation between them; the holomorphic embedded distribution network probabilistic interval power flow model based on evidence theory realizes the organic unity of probabilistic power flow and interval power flow.

[0019] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0021] Figure 1 is a flow chart of an embodiment of the present invention.

[0022] Figure 2 3 is a comparison diagram of voltage amplitude simulation results of node 16 in different fluctuation ranges of the IEEE-33 node distribution network according to an embodiment of the present invention.

[0023] Figure 31 is a cumulative probability distribution diagram of the voltage phase angle of node 18 in the IEEE-33 node distribution network according to an embodiment of the present invention when the hybrid box-ellipsoid correlation is considered. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0025] Example 1 See also Figure 1 The specific steps of the affine optimization method for distribution network probability interval power flow based on holomorphic embedding are as follows: S1: Initialization, input relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; S2: Establish an affine power flow model of the system's node voltage and power based on the relevant parameters of the distribution network; introduce an embedding factor to construct a holomorphic embedded affine optimization power flow model; S3: Based on the distributed photovoltaic output, a focal element model and multi-dimensional joint trust distribution are established, and the model is substituted into the holomorphic embedded affine optimization power flow model to obtain the holomorphic embedded probability interval affine optimization power flow model and solved; S4: Based on the correlation coefficient, an interval variable correlation model of the hybrid box-ellipsoid set is established and converted into affine constraints, which are then solved jointly in a holomorphic embedded probability interval affine optimization power flow model. S5: Obtain the probability boundary of the probability interval power flow solution of the distribution network based on evidence theory.

[0026] Furthermore, in step S2, the specific steps are: S21: For PV nodes, the absolute value of the node's affine voltage is obtained based on the node's given voltage value; for balanced nodes, the affine voltage of the node is obtained based on the node's given voltage value; an affine power flow model is established for the power system's node's affine power, affine voltage, branch series admittance, and node parallel branch admittance; S22: Introduce the embedding factor and construct a holomorphic embedding affine optimization power flow model.

[0027] Furthermore, in step S22, the specific steps are: A holomorphic embedded affine optimization power flow model of the balancing node is established according to the given voltage magnitude and phase; The central value of affine voltage is introduced as the embedding value, and a holomorphic embedded affine optimization power flow model of PQ nodes under noise is established. The central value of affine reactive power is introduced as the embedding value, and a holomorphic embedding model of PV nodes under noise is established.

[0028] In step S3, the specific steps are: S31: Divide the fluctuation range of the distributed photovoltaic output active power and reactive power at the distribution network node into multiple sub-intervals and assign corresponding probabilities to them. Assuming that the sub-interval division principle is the same and the corresponding probabilities of the sub-intervals are also the same, a focal element model of the distributed photovoltaic output is constructed; S32: Establishing a trust distribution for the output active power of distributed photovoltaics; establishing a multi-dimensional joint trust distribution based on the number of distributed photovoltaic power stations in the distribution network; S33: Convert the distributed photovoltaic output active power and reactive power of each interval into affine form respectively, and substitute them into the holomorphic embedded affine optimization power flow model established in step S2 to obtain the holomorphic embedded probability interval affine optimization power flow model; S34: Calculate the affine solution of the unknown voltage and PV node reactive power, as well as the interval range of the node voltage amplitude and phase angle.

[0029] Furthermore, in step S34, the specific steps are: S341: Based on the principle that the coefficients of the same-order power series on both sides of the equation are equal, the holomorphic embedded probability interval affine optimization power flow model is organized into a system of linear equations, and the affine solution of the unknown voltage and PV node reactive power is obtained; S342: Taking the affine form of the node voltage amplitude and phase angle as the objective function, considering the node power constraint and voltage amplitude constraint, solve and output the interval range of the node voltage amplitude and phase angle.

[0030] Furthermore, in step S4, the specific steps are: S41: Establish an interval variable correlation model of a hybrid box-ellipsoid set based on the correlation coefficient, the expected value of the distributed photovoltaic active power and reactive power, the covariance matrix of the input interval, the total number of input intervals, and the upper and lower bounds of a certain input interval; S42: Obtain the constraints for solving the holomorphic embedded probability interval affine optimization power flow model considering the hybrid box-ellipsoid set correlation model; S43: adding the constraint conditions to the holomorphic embedded probability interval affine optimization power flow model of step S33, and solving the interval range of the output node voltage amplitude and phase angle.

[0031] Furthermore, in step S4, the constraints include the affine expression of the active power of the node composed of the existing noise elements and their coefficients, as well as the slope of the parallelogram, the inclination angle of the ellipsoid, the constraint interval vectors of the parallelogram model and the ellipsoid model, the major and minor radii of the ellipse and the center values ​​of different input focal element intervals.

[0032] In step S5, the specific steps are: The trust function and likelihood function are calculated based on the active power of distributed photovoltaics and the probability corresponding to the sub-interval, and the probability boundary of the distribution network probability interval power flow solution is constructed.

[0033] This embodiment performs an affine optimization method on the probability interval power flow of the distribution network based on the holomorphic embedding method, and establishes an interval variable correlation model of a hybrid box-ellipsoid set to describe the uncertainty between input variables, thereby achieving the function of accurately simulating the impact of distributed photovoltaic access on the distribution network uncertainty power flow distribution.

[0034] Example 2 The steps of this embodiment are the same as those of embodiment 1, except that each step is applied to a specific example IEEE-33 node distribution network. Specifically, the following steps are included: S1: Initialization, input relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; The 10th and 20th nodes of the IEEE-33 node distribution network are connected to the distributed photovoltaic power station 1 and the distributed photovoltaic power station 2, and their output power is kW; considering the correlation between the injected powers of the two distributed PV power stations, the correlation coefficient of the hybrid box-ellipsoid ensemble correlation model is set to -0.5.

[0035] S2: Establish an affine model of system node voltage and power and introduce embedding factors to construct a holomorphic embedded affine optimization power flow model. The specific steps are as follows: S21: Establish an affine power flow model for the power system: , , , Where: i is the i nodes; l For the l nodes; is the node affine power, ; and are the node affine active power and reactive power respectively. In this embodiment, the symbol “^” represents the uncertainty affine quantity; For nodes i Affine voltage of is the voltage value given to the node; Representation node i and l The admittance between is the series admittance of the branch in the system, For nodes i The parallel branch admittance of N Indicates the total number of system nodes; PQ 、 PV 、 PH Represent the collection of PQ nodes, PV nodes and balance nodes respectively.

[0036] S22: Introducing embedding factors to construct a holomorphic embedding affine optimization power flow model; For the balancing node in the power system, its voltage magnitude and phase are given values, so the holomorphic embedding model of the balancing node is:

[0037] Where: s is an auxiliary variable, which is a complex number. s = x +j y ; The voltage value given to the equilibrium node.

[0038] The holomorphic embedding model of a PQ node is:

[0039]

[0040] Where: n Indicates the n order term; is the affine voltage The central value of j Indicates the j Noise element; represents the noise element; is the total number of noise elements.

[0041] The holomorphic embedding model of the PV node is:

[0042]

[0043]

[0044] Where: is the affine reactive power The center value of .

[0045] S3: Establish a distributed photovoltaic output focal element model and multi-dimensional joint trust distribution, and transform the probability interval power flow model based on the focal element model into a holomorphic embedded probability interval affine optimization power flow model; the specific steps are: S31: In this embodiment, the distribution network node i Distributed photovoltaic output active power at and reactive power The fluctuation range of is divided into multiple sub-intervals and assigned corresponding probabilities. Here, it is assumed that the sub-interval division principle is the same and the probabilities corresponding to the sub-intervals are also the same, so as to construct the focal element model of the input variable; S32: Establishing the output active power of distributed photovoltaics Trust distribution:

[0046] Where: for The number of focal elements divided by the basic trust distribution; The interval radius is equal; m is the probability corresponding to the subinterval.

[0047] Assume that there is n distributed photovoltaic power stations, then the multi-dimensional joint trust distribution is:

[0048] S33: Each interval Convert to affine form Substitute into the holomorphic embedded affine optimization power flow model established in step S2, where , and The intervals The upper and lower bounds of Represents the noise element, for the reactive power range Using the same processing method, we can obtain the distribution network probabilistic interval power flow model based on holomorphic embedding:

[0049] Where: and Node i The load active and reactive power requirements at affine, where , ; and Node i The maximum and minimum values ​​of the load active power demand; and Node i The maximum and minimum values ​​of the reactive power demand of the load.

[0050] S34: Calculate the affine solution of the unknown voltage and PV node reactive power, as well as the range of node voltage amplitude and phase angle; the specific steps are: S341: According to the principle that the coefficients of the same power series on both sides of the equation are equal, the above holomorphic embedded probability interval power flow model is organized into a linear equation system, that is, the solution form of the power series coefficients is:

[0051] Where: is a known constant matrix; The unknown to be solved n A vector of coefficients of the power series of order; For the previous 1~ n -The known vector calculated from the coefficient of the 1st order power series; Solve to obtain the affine solution of unknown voltage and PV node reactive power:

[0052]

[0053] S342: Using the affine form of the node voltage amplitude and phase angle as the objective function, considering the node power constraint and voltage amplitude constraint, solve and output the interval range of the node voltage amplitude and phase angle:

[0054]

[0055] Where: and Node i The lower and upper bounds of the active power at and Node i The lower and upper bounds of reactive power at and Node i The lower and upper bounds of the voltage amplitude at .

[0056] S4: Based on the correlation coefficient, an interval variable correlation model of the hybrid box-ellipsoid set is established, which is converted into affine constraints and solved simultaneously in the holomorphic embedded probability interval affine optimization power flow model. The specific steps are as follows: S41: Assumptions is a column vector of input intervals, then the hybrid box-ellipsoid set correlation model is expressed as:

[0057]

[0058]

[0059]

[0060] Where: represents the correlation coefficient matrix; Indicates the i The input interval and j Correlation coefficient of the input interval; It is a vector composed of the expected values ​​of distributed photovoltaic active power and reactive power; ; is the covariance matrix of the input interval; n Indicates the total number of input intervals; and Respectively i The upper and lower bounds of the input interval.

[0061] S42: The constraints for solving the holomorphic embedded probability interval affine optimization power flow model considering the hybrid box-ellipsoid set correlation model are obtained as follows:

[0062] Where: Indicates the j The affine expression of the active power of each node is composed of the existing noise elements and their coefficients, that is, ; is the slope of the parallelogram; is the tilt angle of the ellipsoid; and are the constraint interval vectors of the parallelogram model and the ellipsoid model respectively; and are the major and minor radii of the ellipse respectively; and Represents the center value of different input focal element intervals.

[0063] S43: adding the constraint conditions to the optimization model in step S3, and solving the interval range of the node voltage amplitude and phase angle.

[0064] S5: Calculate the probability boundary of the distribution network probability interval power flow solution based on evidence theory; the specific steps are: Assume that the active power of distributed photovoltaic is ,make , is the probability corresponding to the subinterval, the trust function and likelihood function The calculation formula is:

[0065]

[0066] Table 1 shows the node voltage amplitude, phase angle, and branch active and reactive power solution errors of the Monte Carlo method using the solution method of this embodiment and the Taylor expansion affine power flow method in an IEEE-33 node distribution network. Table 1 Comparison of solution errors

[0067] It can be seen that the average error of the solution results of the holomorphic embedding affine optimization power flow algorithm in this embodiment is smaller than that of the Taylor expansion affine power flow algorithm, indicating that the holomorphic embedding affine optimization power flow algorithm has better performance and is less conservative. Taking the error of the IEEE-33 node distribution network simulation results as an example, the errors of the node voltage amplitude and phase angle solutions of the holomorphic embedding affine optimization power flow algorithm are much smaller than those of the Taylor expansion affine power flow algorithm, with average errors of -0.0393% and -4.7596%, respectively. The errors of the branch active power and reactive power solutions of the holomorphic embedding affine optimization power flow algorithm are slightly smaller than those of the Taylor expansion affine power flow algorithm, with average errors of -0.0081% and -0.0138%, respectively.

[0068] Figure 2The following figure compares the voltage amplitude simulation results of node 16 in the IEEE-33 node distribution network under different fluctuation ranges. It can be seen that as the fluctuation range of the injected power increases, the interval range of the solution result of the holomorphic embedded affine optimization power flow algorithm is significantly smaller than that of the Taylor expansion affine power flow algorithm, indicating that the holomorphic embedded affine optimization power flow algorithm has better performance and is more suitable for uncertainty power flow analysis under larger fluctuation ranges.

[0069] Figure 3 The cumulative probability distribution of the voltage phase angle at node 18 in an IEEE-33-node distribution network considering hybrid box-ellipsoid correlation is shown. Four focal element partitioning scenarios are considered: 2 focal elements, 4 focal elements, 8 focal elements, and 16 focal elements. It can be seen that the probability interval range of the variable to be determined decreases with the increase in the number of focal element intervals, and the cumulative trust function curve and cumulative likelihood function curve tend to be smooth. This shows that the holomorphic embedded distribution network probabilistic interval power flow model achieves an organic unification of probabilistic power flow and interval power flow, and the hybrid box-ellipsoid correlation model can both describe the independent fluctuation range of each node power and capture the linear or weak nonlinear correlations between them.

[0070] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0071] Example 3 This embodiment is used to implement the principle of the above method embodiment to construct a distribution network probability interval power flow affine optimization system based on holomorphic embedding, including a parameter acquisition submodule, a model optimization submodule, an interval modeling submodule, a model analysis submodule and a probability boundary submodule.

[0072] The parameter acquisition submodule is used for initialization and input of relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; The model optimization submodule is used to establish an affine power flow model of the system's node voltage and power based on the relevant parameters of the distribution network; it introduces an embedding factor to construct a holomorphic embedded affine optimization power flow model; The interval modeling submodule is used to establish a focal element model and multi-dimensional joint trust distribution based on the distributed photovoltaic output, substitute it into the holomorphic embedded affine optimization power flow model to obtain the holomorphic embedded probabilistic interval affine optimization power flow model and solve it; The model parsing submodule is used to establish the interval variable correlation model of the mixed box-ellipsoid set based on the correlation coefficient, convert it into affine constraints, and solve it simultaneously in the holomorphic embedded probability interval affine optimization power flow model; The probability boundary submodule is used to obtain the probability boundary of the probability interval power flow solution of the distribution network based on evidence theory.

[0073] Each sub-module is mainly used to implement each step of the method embodiment, which will not be described in detail here.

[0074] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0075] This embodiment also includes a processor, a communication interface, a memory, and a communication bus; wherein the processor, the communication interface, and the memory communicate with each other via the communication bus; the memory stores a computer program, and when the program is executed by the processor, the processor executes the steps of the distribution network probability interval power flow affine optimization method based on holomorphic embedding.

[0076] This embodiment also provides a computer-readable storage medium having executable instructions stored thereon. When the instructions are executed by a processor, the processor implements a distribution network probability interval power flow affine optimization method based on holomorphic embedding.

[0077] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware.

[0078] Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0079] This application is described with reference to the flowcharts of the method and computer program product according to Example 1 of the application and the block diagram of the device (system) according to Example 3. It should be understood that each process or block in the flowchart or block diagram, as well as combinations of processes or blocks in the flowchart or block diagram, can be implemented by computer program instructions.

[0080] These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce the instructions for implementing the process Figure 1 a process or multiple processes or boxes Figure 1 A probabilistic interval power flow affine optimization system for distribution networks based on holomorphic embedding of functions specified in a box or multiple boxes.

[0081] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes or boxes Figure 1 The function specified in one or more boxes.

[0082] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes or boxes Figure 1 The steps of the affine optimization method for the probabilistic interval power flow of distribution networks based on holomorphic embedding are specified in a box or multiple boxes.

[0083] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A distribution network probability interval power flow affine optimization method based on holomorphic embedding, characterized by: The following steps are involved: S1: Initialization, input relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; S2: Establish an affine power flow model of the system's node voltage and power based on the relevant parameters of the distribution network; introduce an embedding factor to construct a holomorphic embedded affine optimization power flow model; S3: Based on the distributed photovoltaic output, a focal element model and multi-dimensional joint trust distribution are established, and the model is substituted into the holomorphic embedded affine optimization power flow model to obtain the holomorphic embedded probability interval affine optimization power flow model and solved; S4: Based on the correlation coefficient, an interval variable correlation model of the hybrid box-ellipsoid set is established and converted into affine constraints, which are then solved jointly in a holomorphic embedded probability interval affine optimization power flow model. S5: Obtain the probability boundary of the probability interval power flow solution of the distribution network based on evidence theory.

2. The affine optimization method for distribution network probability interval power flow based on holomorphic embedding according to claim 1 is characterized in that: In the step S2, the specific steps are: S21: For PV nodes, the absolute value of the node's affine voltage is obtained based on the node's given voltage value; for balanced nodes, the affine voltage of the node is obtained based on the node's given voltage value; an affine power flow model is established for the power system's node's affine power, affine voltage, branch series admittance, and node parallel branch admittance; S22: Introduce the embedding factor and construct a holomorphic embedding affine optimization power flow model.

3. The affine optimization method for distribution network probability interval power flow based on holomorphic embedding according to claim 2 is characterized in that: In the step S22, the specific steps are: A holomorphic embedded affine optimization power flow model of the balancing node is established according to the given voltage magnitude and phase; The central value of affine voltage is introduced as the embedding value, and a holomorphic embedded affine optimization power flow model of PQ nodes under noise is established. The central value of affine reactive power is introduced as the embedding value, and a holomorphic embedding model of PV nodes under noise is established.

4. The method for affine optimization of distribution network probability interval power flow based on holomorphic embedding according to claim 1 is characterized in that: In the step S3, the specific steps are: S31: Divide the fluctuation range of the distributed photovoltaic output active power and reactive power at the distribution network node into multiple sub-intervals and assign corresponding probabilities to them. Assuming that the sub-interval division principle is the same and the corresponding probabilities of the sub-intervals are also the same, a focal element model of the distributed photovoltaic output is constructed; S32: Establishing a trust distribution for the output active power of distributed photovoltaics; establishing a multi-dimensional joint trust distribution based on the number of distributed photovoltaic power stations in the distribution network; S33: Convert the distributed photovoltaic output active power and reactive power of each interval into affine form respectively, and substitute them into the holomorphic embedded affine optimization power flow model established in step S2 to obtain the holomorphic embedded probability interval affine optimization power flow model; S34: Calculate the affine solution of the unknown voltage and PV node reactive power, as well as the interval range of the node voltage amplitude and phase angle.

5. The method for affine optimization of distribution network probability interval power flow based on holomorphic embedding according to claim 4 is characterized in that: In the step S34, the specific steps are: S341: Based on the principle that the coefficients of the same-order power series on both sides of the equation are equal, the holomorphic embedded probability interval affine optimization power flow model is organized into a system of linear equations, and the affine solution of the unknown voltage and PV node reactive power is obtained; S342: Taking the affine form of the node voltage amplitude and phase angle as the objective function, considering the node power constraint and voltage amplitude constraint, solve and output the interval range of the node voltage amplitude and phase angle.

6. The affine optimization method for distribution network probability interval power flow based on holomorphic embedding according to claim 5 is characterized in that: In the step S4, the specific steps are: S41: Establish an interval variable correlation model of a hybrid box-ellipsoid set based on the correlation coefficient, the expected value of the distributed photovoltaic active power and reactive power, the covariance matrix of the input interval, the total number of input intervals, and the upper and lower bounds of a certain input interval; S42: Obtain the constraints for solving the holomorphic embedded probability interval affine optimization power flow model considering the hybrid box-ellipsoid set correlation model; S43: adding the constraint conditions to the holomorphic embedded probability interval affine optimization power flow model of step S33, and solving the interval range of the output node voltage amplitude and phase angle.

7. The affine optimization method for distribution network probability interval power flow based on holomorphic embedding according to claim 6 is characterized in that: In step S4, the constraints include the active power affine expression of the node composed of existing noise elements and their coefficients, as well as the slope of the parallelogram, the inclination angle of the ellipsoid, the constraint interval vectors of the parallelogram model and the ellipsoid model, the major and minor radii of the ellipse, and the center values ​​of different input focal element intervals.

8. The method for affine optimization of distribution network probability interval power flow based on holomorphic embedding according to claim 1 is characterized in that: In the step S5, the specific steps are: The trust function and likelihood function are calculated based on the active power of distributed photovoltaics and the probability corresponding to the sub-interval, and the probability boundary of the distribution network probability interval power flow solution is constructed.

9. A distribution network probabilistic interval power flow affine optimization system based on holomorphic embedding, characterized by: The parameter acquisition submodule is used for initialization and input of relevant parameters of the distribution network, distributed photovoltaic output and correlation coefficient; The model optimization submodule is used to establish an affine power flow model of the system's node voltage and power based on the relevant parameters of the distribution network; it introduces an embedding factor to construct a holomorphic embedded affine optimization power flow model; The interval modeling submodule is used to establish a focal element model and multi-dimensional joint trust distribution based on the distributed photovoltaic output, substitute it into the holomorphic embedded affine optimization power flow model to obtain the holomorphic embedded probabilistic interval affine optimization power flow model and solve it; The model parsing submodule is used to establish the interval variable correlation model of the mixed box-ellipsoid set based on the correlation coefficient, convert it into affine constraints, and solve it simultaneously in the holomorphic embedded probability interval affine optimization power flow model; The probability boundary submodule is used to obtain the probability boundary of the probability interval power flow solution of the distribution network based on evidence theory.

10. A computer memory, characterized in that: A computer program executable by a computer processor is stored therein, and the computer program executes the distribution network probability interval power flow affine optimization method based on holomorphic embedding as described in any one of claims 1 to 8.

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