A load supply risk assessment method based on affine analytic recursion

Abstract

The application provides a load supply risk assessment method based on affine analytic recursion, establishes a joint evidence structure body form of multi-dimensional uncertainty factors, and constructs a hypercube space of system input; based on affine arithmetic principles, reconstructs an affine model of load supply risk assessment, and defines approximate judgment conditions of repeated flow out-of-limit; constructs a variable step size repeated flow model based on affine analytic recursion, and obtains an affine analytic type flow expression of recursive solution; formulates a step size correction strategy of the affine analytic repeated flow method, and calculates load supply risks of the system under different load levels.

Description

Technical Field

[0001] This invention relates to the field of load supply risk assessment technology, and in particular to a load supply risk assessment method based on affine analytical recursion. Background Technology

[0002] Load supply risk assessment in distribution networks provides a deeper understanding of power supply capacity under different load levels, ensuring the safe and reliable operation of the distribution network. With the increasing penetration of distributed generation in distribution networks, the intermittency and randomness it brings make load supply risk assessment increasingly difficult. Therefore, evaluating load supply risk under the influence of uncertainties is of significant guiding importance for power system resource planning and allocation, network design and reconfiguration.

[0003] As a conventional method for assessing load supply risk, the repetitive power flow method obtains limit values ​​that meet system constraints by continuously increasing the system load and repeatedly performing power flow calculations. However, the repetitive power flow method requires a proportional and continuous increase in the load growth ratio until the constraints are no longer met, resulting in low calculation accuracy and problems of large computational load and low efficiency. As an evolution of the repetitive power flow method, the variable step size repetitive power flow method uses an automatic step size adjustment method to search forward step by step, which can select an appropriate load growth ratio according to the real-time operating conditions, effectively improving the assessment accuracy, while also having the advantage of reducing computational load, and has attracted widespread attention. However, when considering the uncertainties of the system, the existing variable step size affine repetitive power flow method based on forward and backward iteration, although it can judge and calculate the boundary values ​​of the result according to the constraints, is difficult to solve the problems of complex affine number operations, algorithm convergence dependence, and network universality.

[0004] To further consider the uncertainty of system input, the risk assessment of distribution network load supply is mainly based on methods such as Monte Carlo probabilistic power flow, optimization solutions, and affine forward-backward repeating power flow. However, the probabilistic repeating power flow method based on Monte Carlo simulation is difficult to directly determine the boundary changes of the objective function based on the constraints, requiring a large amount of random sampling and repeated calculations, which leads to a huge computational load. Although optimization solutions can solve the above problems well, the calculation process is relatively complex, which greatly affects the computational efficiency. In this regard, the affine forward-backward repeating power flow method is proposed, which can avoid the complex optimization process and suppress certain interval expansion, but it still requires setting appropriate initial values ​​to ensure computational convergence, and the algorithm has the limitation of only being applicable to radial networks.

[0005] Furthermore, the assessment of uncertainty in existing load supply risk is usually based on classical probability theory. While it can describe the random uncertainty brought about by natural conditions, when data is limited, constructing a probability model without a basis may ignore the uncertainty caused by the limited information available and lead to misleading results. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a load supply risk assessment method based on affine analytic recursion, so as to achieve a more accurate and efficient analysis of load supply risk levels.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a load supply risk assessment method based on affine analytical recursion, comprising the following steps:

[0008] Step 1: Establish a joint evidence structure for multidimensional uncertainty factors and construct a hypercube space for system input;

[0009] Step 2: Based on the principle of affine arithmetic, reconstruct the affine model for load supply risk assessment and define approximate judgment conditions for repeated power flow exceeding limits;

[0010] Step 3: Construct a variable-step-size repetitive power flow model based on affine analytic recursion to obtain the recursively solved affine analytic power flow expression;

[0011] Step 4: Develop a step size correction strategy for the affine analytical repetitive power flow method and calculate the load supply risk of the system under different load levels.

[0012] In a preferred embodiment, the construction of the probability box model is specifically as follows: in the wind farms and photovoltaic power stations connected to the system, wind speed sequences and light intensity sequences are collected at fixed time intervals, the data are preprocessed, and the maximum likelihood estimation method is used to fit the corresponding distributions and obtain the parameter intervals.

[0013] Assume that the distribution parameter of photovoltaic output is α∈[α] during the evaluation period. min ,α max ], β∈[β min ,β max The shape parameter of the wind speed distribution is k∈[k min ,k max The scale parameter is c∈[c min ,c max The probability box boundaries for photovoltaic power output and wind speed are shown in the following equations:

[0014]

[0015]

[0016] In the formula, v is the wind speed, and P is the wind speed. PV They have contributed to the photovoltaic industry.

[0017] In a preferred embodiment, the evidence structure model is constructed as follows: assuming the system connects to N wind farms and M photovoltaic power stations, and the probability boxes are all divided into D focal elements; by combining the focal element intervals of wind speed and photovoltaic output, a Cartesian product model of the system input is constructed, which yields the corresponding multidimensional joint basic credibility.

[0018]

[0019] In the formula, v1, ..., v N P PV1 , ..., P PVN For each input factor, the focal interval is defined. The basic reliability of wind speed coke and photovoltaic power output coke are respectively.

[0020] The original uncertain input space is transformed into an (N+M)-dimensional hypercube domain, with a total of N focal elements. λ =D N+M Each focal element is substituted into the subsequent calculation model to obtain the same output results characterized by focal elements and corresponding basic credibility.

[0021] In a preferred embodiment, load supply risk refers to the percentage increase in the maximum load of the distribution network under different load levels, taking into account system operating constraints. The model calculation formula is as follows:

[0022]

[0023] In the formula, S is the maximum load that the system can supply; i0 S represents the initial load of node i; n represents the number of nodes; S id Assuming the load growth direction, this paper takes S. id =S i0 λ represents the load growth factor; B represents the distribution network assessment area;

[0024] The constraints include power flow constraints and node voltage constraints, namely

[0025]

[0026] In the formula, U i U represents the node voltage amplitude. min and U max These are the lower and upper voltage limits, respectively; I ij with I ij.max These are the current transmitted in branch ij and the maximum current allowed to pass through that branch, respectively.

[0027] The objective function is transformed into a single-variable optimization objective with the simultaneous increase factor of the load of all nodes as the variable, i.e., finding maxλ;

[0028] To directly obtain the interval boundary changes of the objective function based on the constraints, based on the principle of affine arithmetic, different noise elements are used to characterize the uncertainty of the λ interval and different DG inputs, and the noise element coefficients represent the degree of uncertainty; the affine model of the injected power at node i is as follows:

[0029]

[0030] In the formula, S i0 The power center value; ε λ To characterize the noise element in the λ interval; ε j The noise element characterizing the uncertainty of DG; S i λ For ε λ Noise element coefficient; S i DGj For ε j The noise element coefficients; the affine model of node voltage and branch current is similar;

[0031] As the load at each point increases synchronously, it can be assumed that the node voltage decreases and the branch current increases. Therefore, the main constraint condition for judging λ is to compare whether the minimum node voltage and the maximum branch current meet the requirements. The judgment value of the λ interval boundary is defined as shown in the following formula (7).

[0032]

[0033] In the formula, and This is the judgment value for the lower bound of the λ interval. and This is the judgment value for the upper bound of the λ interval;

[0034] Based on the above model, the multidimensional coulomb combination of DG input is substituted into the variable step size repetitive power flow calculation. By judging the critical point of the constraint condition, the load growth step size is adjusted, and the system power flow state is repeatedly calculated until the maximum value of λ that meets the system constraint condition under the input coulomb combination is obtained. Finally, the output results of each coulomb combination are integrated to obtain the probability box form of λ, whose upper and lower boundaries represent the maximum probability distribution and minimum probability distribution of load supply risk under different load levels, respectively.

[0035] In a preferred embodiment, the affine power flow model based on analytical recursion is constructed as follows:

[0036] Based on the principle of fully embedded systems, affine analytical models for node voltage and reactive power are constructed as follows:

[0037]

[0038]

[0039] In the formula, M i The number of noise elements is represented; j represents the j-th noise element; i represents the i-th node; n represents the n-th term.

[0040] The affine analytical power flow model of the power system is shown in equation (10);

[0041]

[0042] In the formula, N is the number of system nodes; Y ik Let be the element in the i-th row and k-th column of the nodal admittance matrix; the superscript "*" indicates complex conjugate operation; Indicates the affine injection power at node i; Active power is injected into node i via affine projection.

[0043] In a preferred embodiment, based on the system affine analytical power flow model, the recursive initial value is obtained as follows: For the following equation (10), substituting the initial state s = 0, we can obtain:

[0044]

[0045] The solution can be obtained from the following equation (11):

[0046]

[0047] Therefore, in the initial state, the affine center values ​​of the constant terms of the voltage and reactive power series and the noise element coefficients are all 0; this initial state corresponds to the grid being unloaded, all generators not generating power, and the reactive power output of the PV nodes being zero, which has practical physical significance.

[0048] In a preferred embodiment, the recursive relationship of the power series coefficients of the affine state variables is constructed as follows:

[0049] To eliminate fractions To simplify calculations, define auxiliary variables.

[0050]

[0051] Based on the principle that the coefficients of each power series are equal, it can be deduced that... The calculation formula:

[0052]

[0053] After introducing auxiliary variables, the recursive relationship between affine power series can be obtained by extracting the coefficients of the same power series on both sides of the equation. To simplify the calculation, the recursive relationship is decomposed into two parts: the real part and the imaginary part, as shown in the following equation (17):

[0054]

[0055]

[0056]

[0057] The recurrence relation can be simplified into a system of algebraic linear equations:

[0058]

[0059] In the formula, H is the recursion matrix; It is the coefficient vector of the nth-order affine power series to be determined; It is a known vector whose coefficients are calculated from an affine power series of order no greater than n-1.

[0060] The condition for the recursive convergence of the judgment (18) is defined as follows:

[0061]

[0062] In the formula, Let represent the k-th order affine power series coefficients of the i-th state variable; sup and inf represent the interval maximum and minimum values ​​of the affine series, respectively; {} represents the set; ξ is the convergence precision;

[0063] After the recursion converges, the coefficients of each power series of the state variables can be obtained, thereby enabling the solution of the explicit analytical expression of the state variables:

[0064]

[0065] In the formula: k is the number of recursion steps to convergence.

[0066] In a preferred embodiment, the step size correction strategy for constructing the variable step size repetitive power flow method is specifically as follows:

[0067] According to the following formula (20), the state quantity solution of the system under a certain load level under a certain combination of coke elements is known, and the injected current of each node under the operating condition can be obtained.

[0068]

[0069] In the formula: Inject a current matrix into the node; Y is the node voltage matrix; p The grounding branch admittance diagonal matrix;

[0070] Based on the network topology and Kirchhoff's current law, a coefficient matrix A is constructed to obtain the current of each branch under this operating condition.

[0071]

[0072] Combined with the following formula (7), determine the system's over-limit situation under this working condition; if the system over-limits, decrease the value of the over-limit boundary corresponding to λ; if no over-limits occur, continue to increase λ with the original step size; the step size correction strategy is shown in the following formula (23);

[0073]

[0074] In the formula: O1 and O2 are the change flag bit vector and the change step size flag bit vector, respectively, with an initial value of [1,1]. Each column corresponds to the interval boundary of the output state quantity, thereby adjusting the upper and lower limits of the λ interval. When a certain boundary of the judgment node voltage interval or current interval exceeds the limit, the corresponding position of O1 is 0, otherwise it is 1. When the state quantity exceeds the limit for the first time during the operation of a certain input focal element combination, the corresponding position of O2 is corrected to 0.5.

[0075] Compared with existing technologies, this invention has the following advantages: First, it introduces a probability box model and divides and combines the probability box models for various uncertainties, transforming the original input uncertainty space into a hypercube domain composed of multi-dimensional focal elements to describe the objective and cognitive uncertainties of new energy output. Second, it constructs a load supply risk assessment model based on affine arithmetic and judges the boundary conditions of the output interval based on the noise element coefficient values ​​of the constrained affine variables, avoiding a large number of sampling operations and achieving efficient processing of interval variables to obtain the system load supply risk level considering uncertainties. Finally, it reconstructs a variable-step-size repetitive affine analytical power flow model, using the recursive relationship of the power series coefficients of state variables and a variable-step-size correction strategy to recursively calculate the load supply risk level under different load levels, overcoming the shortcomings of traditional algorithms in terms of convergence dependence and network universality. Faced with the increasingly complex uncertainties of new power systems, the method in this paper does not require a large number of random samples to describe uncertainties, nor does it require the selection of appropriate initial values ​​to ensure power flow convergence, thus achieving a more accurate and efficient analysis of load supply risk levels. Attached Figure Description

[0076] Figure 1 This is a flowchart of a preferred embodiment of the present invention. Detailed Implementation

[0077] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0078] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0079] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0080] A load supply risk assessment method based on affine analytic recursion, referencing Figure 1 Specifically, it includes the following steps:

[0081] Step 1: Collect the input wind speed and light intensity sequences, fit their distributions, and obtain the parameter ranges of the corresponding distributions. Establish probability box models separately, segmenting each model according to equal basic confidence levels, and combine them to form a joint evidence structure model with multi-dimensional input.

[0082] Step 2: Input the system network structure and initial parameters h and λ, and construct the initial power and voltage affine model of the system;

[0083] Step 3: Calculate the system input load by combining the initial power with the input coke element combination and the load growth percentage λ;

[0084] Step 4: Obtain the initial values ​​of voltage and reactive power recursion for the affine power flow according to equation (11);

[0085] Step 5: Calculate the coefficients of each power series of each state quantity of the affine power flow recursively according to equation (18);

[0086] Step 6: Determine whether the recursive convergence condition of equation (19) is met. If the convergence condition is not met, return to step 5 until the recursive convergence condition is met.

[0087] Step 7: Determine if the step size h is less than the threshold. If not, determine if the focal element interval boundary exceeds the limit, correct h and λ, and return to step 3.

[0088] Step 8: Determine if the number of focal elements is sufficient. If not, return to Step 2 and substitute the result into the next focal element model.

[0089] Step 9: Combine the output λ interval results of each focal element combination to construct a probability box model of λ. Specifically, the method for constructing the evidence structure of uncertainty factors includes:

[0090] (1) Probability box model of DG output

[0091] Considering the uncertainty of wind power and photovoltaic new energy output, the active power output of photovoltaic depends on the intensity of sunlight, which approximates a Beta distribution in the short term; while wind speed is the main factor determining the output power of wind farm. Usually, a two-parameter Weibull distribution can be used to fit the wind speed change in a region, so that the corresponding active power output of wind turbine can be obtained according to the input wind speed.

[0092] Due to limitations in information acquisition capabilities, distribution parameters exhibit a degree of uncertainty. Therefore, probability box models using upper and lower cumulative distribution functions as boundaries are often applied to comprehensively describe both objective and cognitive uncertainties. In wind farms and photovoltaic power stations connected to the system, wind speed and solar intensity sequences are collected at fixed time intervals. The data are preprocessed, and the maximum likelihood estimation method is used to fit the corresponding distributions and obtain the parameter intervals.

[0093] Assume that the distribution parameter of photovoltaic output is α∈[α] during the evaluation period. min ,α max ], β∈[β min ,β max The shape parameter of the wind speed distribution is k∈[k min ,k max The scale parameter is c∈[c min ,c max The probability box boundaries for photovoltaic power output and wind speed are shown in equations (1) and (2), respectively:

[0094]

[0095]

[0096] In the formula, v is the wind speed, and P is the wind speed. PV They have contributed to the photovoltaic industry.

[0097] (2) Evidence Structure Model of Multidimensional DG Input

[0098] Assuming the system connects to N wind farms and M photovoltaic power plants, and each probability box is divided into D focal elements, combining the focal element intervals of wind speed and photovoltaic output, a Cartesian product model of the system input can be constructed to obtain the corresponding multidimensional joint basic reliability.

[0099]

[0100] In the formula, v1, ..., v N P PV1 , ..., P PVN For each input factor, the focal interval is defined. The basic reliability of the wind speed coke element and the photovoltaic output coke element are respectively.

[0101] Equation (3) transforms the original input uncertainty space into an (N+M)-dimensional hypercube domain, with a total of N focal elements. λ =D N +M Each focal element is substituted into the subsequent calculation model to obtain output results that are also characterized by focal elements and their corresponding basic credibility.

[0102] Specifically, constructing a load supply risk assessment model based on affine arithmetic includes:

[0103] Load supply risk refers to the percentage increase in the maximum load of the distribution network under different load levels, taking into account system operating constraints. The model calculation formula is as follows:

[0104]

[0105] In the formula, S is the maximum load that the system can supply; i0 S represents the initial load of node i; n represents the number of nodes; S id Assuming the load growth direction, this paper takes S. id =S i0 λ represents the load growth factor; B represents the distribution network assessment area.

[0106] The constraints include power flow constraints and node voltage constraints, namely

[0107]

[0108] In the formula, U i U represents the node voltage amplitude. min and U max These are the lower and upper voltage limits, respectively; I ij with I ij.max These are the current transmitted in branch ij and the maximum current allowed to pass through that branch, respectively.

[0109] Optimizing equation (4) can transform the objective function into a single-variable optimization objective with the simultaneous increase factor of the load of all nodes as the variable, i.e., finding maxλ.

[0110] To directly obtain the interval boundary changes of the objective function based on the constraints, different noise elements are used, based on the principle of affine arithmetic, to characterize the uncertainty of the λ interval and different DG inputs, with the noise element coefficients representing the degree of uncertainty. The affine model for the injected power at node i is as follows:

[0111]

[0112] In the formula, S i0 The power center value; ε λ To characterize the noise element in the λ interval; ε j The noise element characterizing the uncertainty of DG; Si λ For ζ λ Noise element coefficient; S i DGj For ζ j The noise element coefficients; the affine model of node voltage and branch current is similar.

[0113] As the load at each point increases synchronously, it can be assumed that the node voltage decreases and the branch current increases. Therefore, the constraint condition for judging λ is mainly to compare whether the minimum node voltage and the maximum branch current meet the requirements. The judgment value of the λ interval boundary is defined as shown in equation (7).

[0114]

[0115] In the formula, and This is the judgment value for the lower bound of the λ interval. and This is the judgment value for the upper bound of the λ interval.

[0116] Based on the above model, the multidimensional coulomb combinations of DG inputs are substituted into the variable-step repetitive power flow calculation. By judging the critical point of the constraint conditions, the load growth step size is adjusted, and the system power flow state is repeatedly calculated until the maximum value of λ that meets the system constraint conditions under the input coulomb combination is obtained. Finally, the output results of each coulomb combination are integrated to obtain the probability box form of λ, whose upper and lower boundaries represent the maximum and minimum probability distributions of load supply risk under different load levels, respectively. Under a certain load level, when the probability of supply risk is high, measures need to be adjusted as soon as possible to avoid the risk.

[0117] Specifically, the variable step-size repetitive power flow method based on affine analytic recursion includes:

[0118] (1) Affine power flow model based on analytical recursion

[0119] Based on the principle of fully embedded systems, affine analytical models for node voltage and reactive power are constructed as follows:

[0120]

[0121]

[0122] In the formula, M i The number of noise elements is represented by ; j represents the j-th noise element; i represents the i-th node; and n represents the n-th term.

[0123] The affine analytical power flow model of the power system is shown in equation (10).

[0124]

[0125] In the formula, N is the number of system nodes; Y ik Let be the element in the i-th row and k-th column of the nodal admittance matrix; the superscript "*" indicates complex conjugate operation; Indicates the affine injection power at node i; Active power is injected into node i via affine projection.

[0126] (2) Solving for initial values ​​using recursion

[0127] Substituting equation (10) into the initial state s = 0, we get:

[0128]

[0129] According to equation (11), the solution can be obtained:

[0130]

[0131] Therefore, in the initial state, the affine center values ​​of the constant terms of the voltage and reactive power series, as well as the noise element coefficients, are all 0. This initial state corresponds to the power grid being unloaded, all generators not generating power, and the reactive power output of the PV nodes being zero, which has practical physical significance.

[0132] (3) Recurrence relation of power series coefficients of affine state variables

[0133] To eliminate fractions To simplify calculations, define auxiliary variables.

[0134]

[0135] Based on the principle that the coefficients of each power series are equal, it can be deduced that... The calculation formula:

[0136]

[0137] After introducing auxiliary variables, substitute equations (8) and (9) into equation (10) respectively. By extracting the coefficients of the same power series on both sides of the equation, the recursive relationship between affine power series can be obtained. To simplify the calculation, the recursive relationship is decomposed into two parts: the real part and the imaginary part, as shown in equations (15)-(17).

[0138]

[0139]

[0140]

[0141] The recurrence relation can be simplified into a system of algebraic linear equations:

[0142]

[0143] In the formula, H is the recursion matrix; It is the coefficient vector of the nth-order affine power series to be determined; It is a known vector whose coefficients are calculated from an affine power series of order no greater than n-1.

[0144] The condition for the recursive convergence of the judgment (18) is defined as follows:

[0145]

[0146] In the formula, denoted by k, the coefficients of the k-th order affine power series of the i-th state variable; sup and inf represent the maximum and minimum values ​​of the affine series in the interval, respectively; {} represents the set; ξ is the convergence precision.

[0147] After the recursion converges, the coefficients of each power series of the state variables can be obtained, thereby enabling the solution of the explicit analytical expression of the state variables:

[0148]

[0149] In the formula: k is the number of recursion steps to convergence.

[0150] (4) Step size correction strategy

[0151] According to equation (20), the state variables of the system under a certain load level under a certain combination of foci elements are known, and the injected current of each node under this operating condition can be obtained.

[0152]

[0153] In the formula: Inject a current matrix into the node; Y is the node voltage matrix; p This is the diagonal matrix of the grounding branch admittance.

[0154] Based on the network topology and Kirchhoff's current law, a coefficient matrix A is constructed to obtain the current of each branch under this operating condition.

[0155]

[0156] Combined with equation (7), determine the system's limit-crossing status under this operating condition. If the system exceeds the limit, decrease the value of the limit-crossing boundary corresponding to λ; if no limit-crossing occurs, continue to increase λ with the original step size. The step size correction strategy is shown in equation (23).

[0157]

[0158] In the formula: O1 and O2 are the change flag bit vector and the change step size flag bit vector, respectively, with an initial value of [1,1]. Each column corresponds to the interval boundary of the output state quantity, thereby adjusting the upper and lower limits of the λ interval. When a certain boundary of the judgment node voltage interval or current interval exceeds the limit, the corresponding position of O1 is 0, otherwise it is 1. When the state quantity exceeds the limit for the first time during the operation of a certain input focal element combination, the corresponding position of O2 is corrected to 0.5.

Claims

1. A load supply risk assessment method based on affine analytic recursion, characterized in that... Includes the following steps: Step 1: Establish a joint evidence structure for multidimensional uncertainty factors and construct a hypercube space for system input; Step 2: Based on the principle of affine arithmetic, reconstruct the affine model for load supply risk assessment and define approximate judgment conditions for repeated power flow exceeding limits; Step 3: Construct a variable-step-size repetitive power flow model based on affine analytic recursion to obtain the recursively solved affine analytic power flow expression; Step 4: Calculate the load supply risk of the system under different load levels; In step 2, load supply risk refers to the percentage increase in the maximum load of the distribution network under different load levels, taking into account system operating constraints. The model calculation formula is as follows: （4） In the formula, S is the maximum load that the system can supply; i0 S represents the initial load of node i; n represents the number of nodes; S id Assuming the load growth direction, this paper takes S. id =S i0 λ represents the load growth factor; B represents the distribution network assessment area; The constraints include power flow constraints and node voltage constraints, namely （5） In the formula, U i U represents the node voltage amplitude. min and U max These are the lower and upper voltage limits, respectively. I ij with I ij.max These are the current transmitted in branch ij and the maximum current allowed to pass through that branch, respectively. The objective function is transformed into a single-variable optimization objective with the simultaneous increase factor of the load of all nodes as the variable, i.e., finding maxλ; To directly obtain the interval boundary changes of the objective function based on the constraints, based on the principle of affine arithmetic, different noise elements are used to characterize the uncertainty of the λ interval and different DG inputs, and the noise element coefficients represent the degree of uncertainty; the affine model of the injected power at node i is as follows: （6） In the formula, S i0 This is the center value of power; Ɛ λ To characterize the noise element in the λ interval; S i λ For λ Noise element coefficient; S i DGj For j The noise element coefficients; the affine model of node voltage and branch current is similar; As the load at each point increases synchronously, it can be assumed that the node voltage decreases and the branch current increases. Therefore, the constraint condition for determining λ mainly involves comparing whether the minimum node voltage and the maximum branch current meet the requirements. The judgment value for the boundary of the λ interval is defined as follows: As shown; （7） In the formula, U-min,i and I-min,ij are the judgment values ​​of the lower bound of the λ interval, and U+min,i and I+min,ij are the judgment values ​​of the upper bound of the λ interval. Based on the above model, the multidimensional coulomb combination of DG input is substituted into the variable step size repetitive power flow calculation. By judging the critical point of the constraint condition, the load growth step size is adjusted, and the system power flow state is repeatedly calculated until the maximum value of λ that meets the system constraint condition under the input coulomb combination is obtained. Finally, the output results of each coulomb combination are integrated to obtain the probability box form of λ, whose upper and lower boundaries represent the maximum probability distribution and minimum probability distribution of load supply risk under different load levels, respectively.

2. The load supply risk assessment method based on affine analytic recursion according to claim 1, characterized in that, The specific steps for constructing the probability box model are as follows: In the wind farms and photovoltaic power stations connected to the system, wind speed sequences and light intensity sequences are collected at fixed time intervals, and the data are preprocessed. The maximum likelihood estimation method is used to fit the corresponding distributions and obtain the parameter intervals. Assume that during the evaluation period, the distribution parameter of photovoltaic output is α∈[α]. min , α max ], β∈[β min , β max The shape parameter of the wind speed distribution is k∈[k min , k max The scale parameter is c∈[c min , c max Then the probability box boundaries of photovoltaic power output and wind speed are respectively as shown in the equation. , As shown: （1） （2） In the formula, v is the wind speed, and P is the wind speed. PV They have contributed to the photovoltaic industry.

3. The load supply risk assessment method based on affine analytic recursion according to claim 1, characterized in that, The specific steps for constructing the evidence structure model are as follows: Assuming the system connects to N wind farms and M photovoltaic power stations, and each probability box is divided into D focal elements; by combining the focal element intervals of wind speed and photovoltaic output, a Cartesian product model of the system input can be constructed to obtain the corresponding multidimensional joint basic credibility. （3） In the formula, v1, ..., v N P PV1 , ..., P PVN For each input factor, the focal interval is defined. The basic reliability of wind speed coke and photovoltaic power output coke are respectively. The original uncertain input space is transformed into an (N+M)-dimensional hypercube domain, with a total of N focal elements. λ =D N+M ; Each focal element is substituted into the subsequent calculation model to obtain the same output results characterized by focal elements and corresponding basic credibility.

4. The load supply risk assessment method based on affine analytic recursion according to claim 1, characterized in that, The affine power flow model based on analytical recursion is constructed as follows: Based on the principle of fully embedded systems, affine analytical models for node voltage and reactive power are constructed respectively: （8） （9） In the formula, M i The number of noise elements is represented by ; j represents the j-th noise element; i represents the i-th node of the system; n represents the n-th term; Ɛ j Noise element characterizing the uncertainty of DG; The affine analytical power flow model of the power system is as follows: As shown; （10） In the formula, N is the number of system nodes; Y ik Let be the element in the i-th row and k-th column of the nodal admittance matrix; the superscript "*" indicates complex conjugate operation; Indicates the affine injection power at node i; Active power is injected into node i via affine projection.

5. The load supply risk assessment method based on affine analytic recursion according to claim 1, characterized in that, Based on the system affine analytical power flow model, the specific method for obtaining the recursive initial values ​​is as follows: For the formula Substituting the initial state s=0, we get: （11） according to Solution: （12） Therefore, in the initial state, the affine center values ​​of the constant terms of the voltage and reactive power series and the noise element coefficients are all 0; this initial state corresponds to the grid being unloaded, all generators not generating power, and the reactive power output of the PV nodes being zero, which has practical physical significance.

6. The load supply risk assessment method based on affine analytic recursion according to claim 1, characterized in that, The recursive relationship for the power series coefficients of affine state variables is constructed as follows: To eliminate the fraction 1 / V* i(s) * To simplify calculations, define auxiliary variables. : （13） Based on the principle that the coefficients of each power series are equal, it can be deduced that... The calculation formula: （14） After introducing auxiliary variables, the recurrence relation between affine power series can be obtained by extracting the coefficients of the same power series on both sides of the equation. To simplify the calculation, the recurrence relation is decomposed into two parts: the real part and the imaginary part, as shown in the following equation. As shown: （15） （16） （17） The recurrence relation can be simplified into a system of algebraic linear equations: （18） In the formula, H is the recursion matrix; It is the coefficient vector of the nth-order affine power series to be determined; It is a known vector whose coefficients are calculated from an affine power series of order no greater than n-1. Define the judgment expression The condition for recursive convergence is: （19） In the formula, Let represent the k-th order affine power series coefficients of the i-th state variable; sup and inf represent the maximum and minimum values ​​of the affine series interval, respectively; {} denotes a set; For convergence accuracy; After the recursion converges, the coefficients of each power series of the state variables can be obtained, thereby enabling the solution of the explicit analytical expression of the state variables: （20） In the formula: k is the number of recursion steps to convergence.

7. The load supply risk assessment method based on affine analytic recursion according to claim 6, characterized in that, The specific step size correction strategy for constructing the variable step size repetitive power flow method is as follows: According to the formula Given the state variables of the system under a specific load level with a certain combination of foci elements, the injected current of each node under this operating condition can be obtained. （21） In the formula: Inject a current matrix into the node; The node voltage matrix; The grounding branch admittance diagonal matrix; Based on the network topology and Kirchhoff's current law, a coefficient matrix A is constructed to obtain the current of each branch under this operating condition. ; （22） Combined Determine if the system exceeds the limits under the given operating condition; if the system exceeds the limits, decrease the value of the limit boundary corresponding to λ; if no limit exceeds the limits, continue to increase λ with the original step size; the step size correction strategy is as follows: As shown; （23） In the formula: O1 and O2 are the change flag bit vector and the change step size flag bit vector, respectively, with an initial value of [1,1]. Each column corresponds to the interval boundary of the output state quantity, thereby adjusting the upper and lower limits of the λ interval. When a certain boundary of the judgment node voltage interval or current interval exceeds the limit, the corresponding position of O1 is 0, otherwise it is 1. When the state quantity exceeds the limit for the first time during the operation of a certain input focal element combination, the corresponding position of O2 is corrected to 0.5.

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