A multi-time-scale source-load matching driven distribution network distributed photovoltaic reverse sending limit evaluation method and system

Abstract

The application provides a power distribution network distributed photovoltaic reverse sending limit evaluation method and system driven by multi-time scale source and load matching. In view of the voltage over-limit and power reverse sending problem caused by high proportion of distributed photovoltaic access to the power distribution network, multi-time scale characteristics are extracted as the explanatory variables of the photovoltaic reverse sending limit formation mechanism, and time series containing wind power, photovoltaic and load demand are constructed. The multi-dimensional time series is reduced by using the discretization-aggregation technology, and the limit combination scene of system operation is accurately extracted. A holomorphic embedded power flow model containing generation and load change direction scaling factor is constructed, the nonlinear power balance equation is converted into a holomorphic complex analytic function about the embedded variable, and the equivalent analytic expression of the node voltage is obtained by using the Maclaurin series expansion. By applying the voltage safety boundary condition to the analytic function, the maximum photovoltaic access capacity limit without voltage over-limit is directly solved and analyzed.

Description

Technical Field

[0001] This invention belongs to the field of distribution network operation analysis technology, specifically relating to a method and system for evaluating the backfeed limit of distributed photovoltaic power transmission in distribution networks driven by multi-timescale source-load matching. Background Technology

[0002] Against the backdrop of the global transition to clean and low-carbon energy, distributed renewable energy sources (including distributed wind power and distributed photovoltaics) are being massively integrated into distribution network systems. Wind and solar energy exhibit significant intermittent, fluctuating, and stochastic characteristics. The high proportion of distributed power generation has altered the traditional unidirectional power flow physical form of distribution networks, transforming them into complex active networks with multiple power sources. When the output of distributed power sources far exceeds the local load absorption capacity, severe power backflow will occur, leading to serious system operation problems such as voltage exceeding limits at the line ends and transformer and feeder overloads.

[0003] When assessing the capacity of a distribution network to accommodate distributed generation, multi-timescale characteristics play a decisive role as the core explanatory variable for the formation mechanism of the backfeeding limit. Current limit assessment methods are mainly divided into deterministic methods, stochastic methods, optimization-based methods, and time series methods. Deterministic methods cannot cover the uncertainties of modern power systems; stochastic methods (such as Monte Carlo simulations) and optimization methods have extremely high computational complexity when dealing with large-scale nonlinear networks with complex constraints, making it difficult to guarantee a globally optimal solution. Although time series methods can reflect the actual source-load matching situation, the massive amount of historical operating data brings a huge computational burden. More seriously, when approaching the photovoltaic backfeeding limit boundary, traditional iterative power flow algorithms based on Jacobian matrix inversion (such as the Newton-Raphson method) often face ill-conditioned convergence or even divergence problems due to the singularity of the system's Jacobian matrix, resulting in the inability to accurately locate the true backfeeding limit capacity point.

[0004] To address the aforementioned issues, this invention proposes a multi-timescale source-load matching driven method for assessing the backfeeding limit of distributed photovoltaic power grids. It utilizes discretization-aggregation technology to screen extreme operating scenarios and employs a directed scaling fully pure embedding method to obtain the equivalent analytical expression of node voltages through rigorous complex analytical mapping, thereby efficiently and accurately assessing the backfeeding limit capacity of the distribution network. Summary of the Invention

[0005] The purpose of this invention is to propose a method and system for assessing the limit of distributed photovoltaic backfeeding in distribution networks driven by multi-timescale source-load matching. This method solves the technical problems of non-convergence of iterative power flow algorithms at the limit boundary and the large amount of computation for long-time-series data in the existing technology, and significantly improves the computational efficiency and absolute accuracy of distribution network limit capacity assessment driven by multi-source heterogeneous data.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A multi-timescale source-load matching driven method for evaluating the backfeed limit of distributed photovoltaic power in distribution networks includes the following steps:

[0008] Step A: Collect power distribution network operation data and extract time series data of distributed wind power active power output, photovoltaic active power output and load demand at multiple time scales; the multi-time scale characteristics are directly used as the core explanatory variables for the formation mechanism of photovoltaic backfeed limit and participate in the limit capacity analysis.

[0009] Step B: Using discretization-aggregation technology, the time series data is normalized and distributed to a three-dimensional spatial grid divided according to a preset step size. The frequency of time series data points in each grid cell is counted. Based on the upper limit of the interval in the wind power active power output dimension and the photovoltaic active power output dimension, and the lower limit of the interval in the load demand dimension, the extreme degree of source and load corresponding to each non-empty grid cell is determined. Extreme boundary grid cells are extracted, and the combination of the wind power active power output interval, photovoltaic active power output interval and load demand interval corresponding to each extreme boundary grid cell constitutes an extreme operation combination dataset.

[0010] Step C: Sequentially take each extreme operating combination in the extreme operating combination dataset as the operating condition to be evaluated for the distribution network. Based on the upper limit of the wind power active power output range, the upper limit of the photovoltaic active power output range, and the lower limit of the load demand range in each extreme operating combination, determine the initial power generation, initial load power, and power change direction scaling factor of each node under the corresponding operating condition to be evaluated. For each operating condition to be evaluated, transform the nonlinear power balance equation of the distribution network into a complex analytical equation system with complex embedded variables as independent variables, and complete the construction of a fully embedded power flow model including the power change direction scaling factor.

[0011] Step D: For each operating condition to be evaluated, calculate the zero-order coefficients of the initial reference state when the complex embedded variable is zero. Use the Maclaurin series expansion method to express the voltage of each node and the reactive power generation as power series with respect to the complex embedded variable. Solve the coefficients of each order of the power series by recursion to generate the equivalent analytical expression of the voltage of each node with respect to the complex embedded variable under each operating condition to be evaluated.

[0012] Step E: Set the upper limit value of the voltage of the distribution network nodes. For each operating condition to be evaluated, solve for the positive real roots of the complex embedded variables corresponding to the modulus of the equivalent analytical expression of the voltage of each node when the modulus is equal to the upper limit value. Determine the minimum value among the positive real roots of each node under the same operating condition to be evaluated, and obtain the photovoltaic back-feed limit capacity corresponding to the operating condition to be evaluated. Compare the photovoltaic back-feed limit capacity corresponding to all extreme operating combinations in the extreme operating combination dataset, and determine the minimum value among them as the maximum back-feed limit capacity of the distributed photovoltaic system in the distribution network without exceeding the limit.

[0013] Preferably, the specific implementation of extracting extreme boundary mesh cells is as follows:

[0014] The specific implementation method for extracting extreme boundary mesh cells is as follows:

[0015] Along the direction of increasing active power output of wind power and photovoltaic power and decreasing load demand, all non-empty grid cells are traversed; if no other non-empty grid cell forms a dominant relationship with the traversed grid cell in three dimensions, the traversed grid cell is determined as an extreme boundary grid cell, and one or more extreme boundary grid cells are obtained.

[0016] For any two non-empty grid cells g and h, let the upper limit of the discrete interval of wind power active power output, the upper limit of the discrete interval of photovoltaic active power output, and the lower limit of the discrete interval of load demand corresponding to the g-th non-empty grid cell be respectively... , , Let the upper limit of the discrete interval of wind power active power output, the upper limit of the discrete interval of photovoltaic active power output, and the lower limit of the discrete interval of load demand corresponding to the h-th non-empty grid cell be respectively... , , When the following conditions are met:

[0017]

[0018]

[0019]

[0020] Furthermore, if at least one of the three inequalities is a strict inequality, it is determined that the non-empty grid cell h has a dominance relationship with the non-empty grid cell g in the extreme directions of the source load.

[0021] Preferably, the fully embedded power flow model includes the voltage magnitude constraint equation for the slack node, the complex analytical equation for the load node, and the complex analytical equation and voltage magnitude constraint equation for the generator node.

[0022] The voltage magnitude constraint equation of the balancing node is defined as follows:

[0023]

[0024] in, Representative node Regarding embedded variables The voltage complex analytic function, Representative node Given the reference voltage amplitude, Represents the set of balanced nodes;

[0025] The complex analytical equation of the load node is defined as follows:

[0026]

[0027] in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. Represents the elements of the nodal admittance matrix. Representative node Regarding complex embedded variables The voltage complex analytic function, Representative node The conjugate of the initial complex apparent power, Representative node Complex apparent power change conjugate, Representative node Regarding conjugate embedded variables The conjugate of the voltage complex analytic function, Represents the set of load nodes;

[0028] The complex analytical equations and voltage magnitude constraint equations of the generator node are defined as follows:

[0029]

[0030]

[0031] in, Representative node Net active power in the initial state, Represents the imaginary unit. Representative node Reactive load in the initial state, Representative node The change in active power, Representative node The change in reactive load, Representative node Regarding complex embedded variables The holomorphic function of reactive power generation, Representative node The square of the given voltage amplitude, Represents the set of PV nodes;

[0032] The initial power parameters are defined as follows:

[0033]

[0034]

[0035]

[0036]

[0037] in, Represents the initial active power generation. Represents the initial active load. Represents the load growth coefficient. Represents the power generation growth coefficient. Represents the initial complex apparent power. This represents the initial reactive load.

[0038] Preferably, step D is as follows:

[0039] The zeroth-order complex coefficients of the complex analytic function of the voltage at each node and the zeroth-order real coefficients of the holomorphic function of reactive power generation are obtained when the value of the complex embedded variable is zero, and these are used as the initial values ​​for the recursion.

[0040] Expand the complex analytic functions of the voltage at each node and the holomorphic function of reactive power generation at the origin of the complex plane into Maclaurin series form:

[0041]

[0042]

[0043] in, Representative node The voltage complex analytic function, Represents the order of the series expansion. The first representing the voltage function Coefficients of order complex number, The first function representing reactive power generation real coefficients of order;

[0044] Introducing the reciprocal function of the voltage at each node :

[0045]

[0046] in, Representative node The complex analytic function of the reciprocal of voltage. The first function representing the reciprocal of voltage Coefficients of the complex order;

[0047] Using identities Strict polynomial convolution summation eliminates complex division operations, establishing a recursive relationship between the coefficients of the complex analytic function of voltage and the coefficients of the reciprocal function of voltage:

[0048] when hour: , The zeroth-order complex coefficients represent the reciprocal function of voltage. The zeroth-order complex coefficients of the voltage function;

[0049] when hour: , This represents the inner summation index number for the convolution calculation. The first function representing the reciprocal of voltage Coefficients of order complex number, The first representing the voltage function Coefficients of the complex order;

[0050] Substitute the Mclaurin series of the voltage complex analytic function, the Mclaurin series of the voltage reciprocal function, and the Mclaurin series of the reactive power holomorphic function into the holomorphic embedded power flow model to establish recursive update equations for the complex coefficients of the voltage complex analytic function and the real coefficients of the reactive power holomorphic function at each node.

[0051] Starting from the zeroth-order complex coefficients of the complex analytical function of each node voltage and the zeroth-order real coefficients of the holomorphic function of reactive power generation, the equivalent analytical expression of each node voltage with respect to the complex embedded variables is obtained by solving the recursive update equation step by step until the preset convergence tolerance is met.

[0052] Preferably, the step of calculating the maximum back-feed limit capacity of distributed photovoltaic without exceeding the limit based on the minimum positive real root specifically involves multiplying the minimum positive real root by the initial deployment baseline capacity to obtain the maximum back-feed limit capacity of distributed photovoltaic in the system at the current node location.

[0053] Preferably, the power distribution network operation data comes from a JSON format file containing multiple operation days.

[0054] Preferably, the three dimensions of the three-dimensional spatial grid correspond to the active power output of wind power, the active power output of photovoltaic power, and the active power of the load, respectively, and the preset step size is 0.01 pu.

[0055] A multi-timescale source-load matching driven distributed photovoltaic backfeed limit assessment system for distribution networks includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs any of the above-mentioned distributed photovoltaic backfeed limit assessment methods for distribution networks.

[0056] A computer-readable storage medium having computer instructions stored thereon, which, when executed, implement any of the above-described methods for assessing the backfeeding limits of distributed photovoltaic power distribution networks.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] This method uses multi-timescale features as direct explanatory variables for the backward limit formation mechanism. Through efficient parsing and discretization-aggregation processing of JSON files, it directly identifies extreme combinations with high evaluation value, eliminating the need for time-domain simulations of massive redundant scenarios. This method employs a non-iterative algorithm based on a holomorphic mapping mechanism, fundamentally eliminating the power flow divergence problem caused by the singularity of the Jacobian matrix at the limit critical point, ensuring 100% mathematical convergence of the limit solution, and possessing extremely high engineering application and patent commercialization value. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention;

[0060] Figure 2 A schematic diagram of the probability density distribution of the wind power and photovoltaic back-feed limit capacity of this invention;

[0061] Figure 3 This is a schematic diagram of the cumulative probability distribution of the wind power and photovoltaic backfeed limit capacity of the present invention. Detailed Implementation

[0062] The following is in conjunction with the appendix Figure 1-3 The technical solution of the present invention will be described in detail below.

[0063] This invention proposes a multi-timescale source-load matching driven method for evaluating the backfeed limit of distributed photovoltaic power grids; the following provides a detailed description of the steps for implementing this invention:

[0064] Step 1: Discretization, aggregation, and extreme combination extraction of multidimensional time series

[0065] The collection of distribution network operation data relies on exporting a JSON file containing data for each operating day. This JSON file is then parsed to obtain the active power time series of wind power output, solar power output, and load. Let the wind power time series be... The photovoltaic power time series is The load power time series is .in, The sampling time represents the time series. Representative moment The active power of wind power, Representative moment Photovoltaic active power, Representative moment The load active power. These three sequences are normalized based on their historical maximum values. Let the historical maximum values ​​of wind power active power, photovoltaic active power, and load active power be respectively... , and Then the normalized time series are represented as follows:

[0066]

[0067]

[0068]

[0069] A fixed interval step size of 0.01 pu was set, and the normalized wind power active power output, photovoltaic active power output, and load demand were divided into discrete intervals according to the preset step size. A three-dimensional grid cell was formed by one discrete interval for wind power active power output, one discrete interval for photovoltaic active power output, and one discrete interval for load demand. The frequency of time series data points falling into each three-dimensional grid cell at the same sampling time was counted. Grid cells with a data point frequency greater than zero were defined as non-empty grid cells.

[0070] Let the discrete interval of wind power active power output corresponding to the g-th non-empty grid cell be . The corresponding discrete interval of photovoltaic active power output is The corresponding load demand discrete range is In this context, the superscript L represents the lower limit of the corresponding discrete interval, the superscript U represents the upper limit of the corresponding discrete interval, and g represents the index number of the non-empty grid cell.

[0071] The upper limit of the active power output range for wind power, the upper limit of the active power output range for photovoltaic power, and the lower limit of the load demand range are used to characterize the extreme source-load levels of the corresponding non-empty grid cells. For any two non-empty grid cells g and h, when simultaneously satisfying:

[0072]

[0073]

[0074]

[0075] Furthermore, if at least one of the above three inequalities is a strict inequality, it is determined that the non-empty grid cell h has a dominance relationship with the non-empty grid cell g in the extreme directions of the source load.

[0076] Traverse all non-empty mesh cells and identify mesh cells to which no other non-empty mesh cells form the aforementioned dominance relationship as extreme boundary mesh cells. When an extreme boundary contains only one non-empty mesh cell, one extreme operating combination is obtained; when an extreme boundary contains multiple non-dominant non-empty mesh cells, multiple extreme operating combinations are obtained.

[0077] The combinations of wind power active power output range, photovoltaic active power output range, and load demand range corresponding to each extreme boundary grid cell are respectively regarded as extreme operating combinations, and an extreme operating combination dataset is constructed:

[0078]

[0079] in, Let Q represent the q-th extreme running combination, where Q represents the total number of extreme running combinations.

[0080] The extreme operating combination dataset serves as the input for subsequent fully embedded power flow calculations. For any extreme operating combination, the upper limit of the wind power active power output range, the upper limit of the photovoltaic active power output range, and the lower limit of the load demand range in that extreme operating combination are used to form the corresponding operating condition to be evaluated. Based on the operating condition to be evaluated, the initial power generation, initial load power, and power change direction scaling factor of each node in the distribution network are determined.

[0081] Step 2: Construct a fully embedded power flow model with directional scaling

[0082] For including A distribution network system with n nodes, where the total set of nodes is defined as follows: The set of balanced nodes is The set of PQ nodes (load nodes) is The set of PV nodes (generator nodes) is The original nonlinear power balance equation for a power distribution network is defined as follows:

[0083]

[0084] in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. The first node in the system admittance matrix represents the... Line number Column elements, Representative node Complex voltage, Representative node The conjugate of the complex injected power, Representative node The conjugate of the complex voltage.

[0085] To eliminate nonlinearity and ensure convergence, complex embedding variables are introduced. The equations are then transformed into holomorphic function forms according to node type:

[0086] For the slack node, the voltage amplitude constraint equation is:

[0087]

[0088] in, Represents a balance node Regarding embedded variables The voltage complex analytic function, Represents a balance node Given the reference voltage amplitude, This represents the set of balanced nodes.

[0089] For the PQ node, considering the growth direction of distributed generation grid connection, the equation is:

[0090]

[0091] in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. Represents the elements of the nodal admittance matrix. Representative node Regarding embedded variables The voltage complex analytic function, Representative node The conjugate of the complex apparent power at the initial load level Represents a complex number embedded variable. Representative node The conjugate of the complex apparent power change, Representative node Regarding conjugate embedded variables The conjugate of the voltage complex analytic function, Represents the set of PQ nodes.

[0092] For a PV node, the holomorphic embedding equations for its active and reactive power are:

[0093]

[0094]

[0095] in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. Represents the elements of the nodal admittance matrix. Representative node Regarding embedded variables The voltage complex analytic function, Representative node Net active power in the initial state, Represents the imaginary unit. Representative node Reactive load in the initial state, Represents a complex number embedded variable. Representative node The change in active power, Representative node The change in reactive load, Representative node Regarding embedded variables The holomorphic function of reactive power generation, Representative node Regarding conjugate embedded variables The conjugate of the voltage complex analytic function, Representative node The square of the given voltage amplitude, Represents the set of PV nodes.

[0096] The initial power parameter is defined as follows:

[0097]

[0098]

[0099]

[0100]

[0101] in, Represents the initial net active power. Represents the initial active power generation. Represents the initial active load. Represents the load growth coefficient. Represents the power generation growth coefficient. Represents the initial complex apparent power. This represents the change in apparent power as a complex number. This represents the change in active power. Represents the change in reactive load. This represents the initial reactive load.

[0102] Step 3: Maclaurin series expansion and recursive solution

[0103] Voltage complex analytic function With reactive power generation holomorphic function Expanding at the origin of the complex plane, it takes the form of an absolutely convergent Maclaurin series:

[0104]

[0105]

[0106] in, Representative node The voltage complex analytic function, Represents the order of the series expansion. The first representing the voltage function Coefficients of order complex number, Represents a complex number embedded variable. Representative node The holomorphic function of reactive power generation, The first function representing reactive power generation Real coefficients of order.

[0107] Introducing the reciprocal function of voltage To avoid complex division:

[0108]

[0109] in, Representative node The complex analytic function of the reciprocal of voltage. Representative node The voltage complex analytic function, Represents the order of the series expansion. The first function representing the reciprocal of voltage Coefficients of order complex number, This represents a complex number embedded variable.

[0110] identity Expanded into the following series product relationship:

[0111]

[0112] in, This represents the order of the series expansion. The first function representing the reciprocal of voltage Coefficients of order complex number, Represents a complex number embedded variable. The first representing the voltage function Coefficients of order complex.

[0113] By making the coefficients of the same order equal on both sides of the identity, we obtain a strict recursive relation:

[0114] when hour:

[0115]

[0116] in, The zeroth-order complex coefficients represent the reciprocal function of voltage. The zeroth-order complex coefficients of the voltage function.

[0117] when hour:

[0118]

[0119] in, The first function representing the reciprocal of voltage Coefficients of order complex number, This represents the inner summation index number for the convolution calculation. The first function representing the reciprocal of voltage Coefficients of order complex number, The first representing the voltage function Coefficients of order complex number, The zeroth-order complex coefficients of the voltage function.

[0120] Substituting the coefficients of each order into the nonlinear holomorphic embedding model of the system, the recursive system equations for each order of coefficients are extracted as follows:

[0121] For the equilibrium node:

[0122]

[0123] in, Represents a balance node The voltage function Coefficients of order complex number, Represents the order, This represents the set of balanced nodes.

[0124] For PQ nodes:

[0125]

[0126] in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. Represents the elements of the nodal admittance matrix. Representative node The voltage function Coefficients of order complex number, Represents the initial apparent power conjugate. The first conjugate of the reciprocal function of voltage Order coefficient, Represents the conjugate of apparent power change. The first conjugate of the reciprocal function of voltage Order coefficient, Represents the set of PQ nodes.

[0127] For PV nodes:

[0128]

[0129]

[0130] in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. Represents the elements of the nodal admittance matrix. Representative node The voltage function Coefficients of order complex number, Represents the initial active power. Represents the imaginary unit. Represents the initial reactive load. The first reciprocal of the voltage Order coefficient, The first function representing reactive power generation Order coefficient, Represents the 0th order coefficient of the reciprocal conjugate of the voltage. Represents the 0th order coefficient of the reactive power generation function. Represents the change in active power. Represents the change in reactive load. The first reciprocal of the voltage Order coefficient, Represents the convolution sum index. The first function representing reactive power generation Order coefficient, The first reciprocal of the voltage Order coefficient, The first representing the voltage function Order coefficient, The first representing the voltage conjugate function Order coefficient, Represents the set of PV nodes.

[0131] The initial load level (i.e.,) is solved using the Newton-Raphson method. Reference state under ) and Then, the above recursive equations are solved step by step until the preset convergence tolerance is met, thereby obtaining the complete analytical polynomials of each node.

[0132] Step 4: Backfeed Limit Assessment and Capacity Determination

[0133] Obtain the equivalent analytical expression for each node under each extreme combination. To avoid power quality problems caused by voltage exceeding limits, safety operation guidelines for the distribution network are applied. The maximum permissible voltage reference limit for the system is set to... Let the modulus of the equivalent polynomial be always equal to this limit:

[0134]

[0135] in, Representative node The voltage function Coefficients of order complex number, Represents a complex number embedded variable (for finding the target real root). This represents the per-unit value of the upper limit of voltage.

[0136] Using algebraic root-finding algorithms to find the smallest positive real root of the equation in the real number field This serves as the root of the full-load index. This root corresponds to the scaling factor at which the system reaches the critical voltage limit-over-limit state. Multiply by the initial deployment baseline capacity (fixed at) This allows for the precise determination of the maximum backfeed capacity (in kilowatts) of the distributed photovoltaic system at that node location, providing an absolutely accurate control margin benchmark for the distribution network dispatching end.

[0137] The actual verification process is provided below:

[0138] 1. Validation scheme and data source settings

[0139] This invention was validated on a standard IEEE 33-node distribution network system. The system's base capacity was strictly calibrated to a set value of 10,000 kW, and the base voltage was 12.66 kV. To obtain highly representative time-series matching characteristics and highlight the effectiveness of multi-timescale characteristics as the core explanatory variables of the backfeeding limit mechanism, simulated white noise data was not used as the experimental data source. Instead, a JSON file containing data from each operating day of the Wan Hong real low-voltage distribution area was exported as the sole experimental data source, covering a total of 35,040 data points with a high-resolution sampling time step of 15 minutes throughout the year. Node 1 was set as the balancing node with a reference voltage of 1.0 pu, and the upper limit of the safe voltage for all nodes in the network was set to a predetermined 1.05 pu.

[0140] 2. Comparative Analysis and Verification of Invention Effects

[0141] When processing multivariate time series extracted from JSON data files, the setting of the step size (Bin Width) has a decisive impact on the computation speed and accuracy. Table 1 shows the comparison of the results of backfeed limit capacity calculations for the same extreme combinations using the discretization-aggregation technique and the fully pure embedding analytical method (HEM) proposed in this patent, as well as the traditional iteration-dependent Newton-Raphson method (NR).

[0142] Table 1: Comparison of backfeed limit calculation results under different discrete interval step sizes (benchmark point: 10872 kW)

[0143]

[0144] Discussion of actual effects:

[0145] 1. Eliminating non-convergence defects: Traditional NR algorithm frequently encounters singularities in the Jacobian matrix near the voltage limit point (1.05 pu), leading to iterative divergence. The HEM of this invention, employing complex analytic series mapping, guarantees 100% convergence mathematically and can accurately capture deterministic capacity values ​​approaching the physical limit point.

[0146] 2. Improved computational efficiency: As shown in Table 1, when the distance step size is set to 0.01 pu, this method locks in 10 extreme scenarios. Compared with the traditional method of scanning point by point for 35040 full-time points, the HEM calculation time of this invention is only 0.4082 seconds, which is nearly a quarter of the traditional NR method, while the error is controlled within 0.92%, accurately determining the single-node photovoltaic backfeed limit capacity as 10768 kW.

[0147] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A multi-timescale source-load matching driven method for evaluating the backfeed limit of distributed photovoltaic power in distribution networks, characterized in that, Includes the following steps: Step A: Collect power distribution network operation data and extract time series data of distributed wind power active power output, photovoltaic active power output and load demand at multiple time scales; Step B: Using discretization-aggregation technology, the time series data is normalized and distributed to a three-dimensional spatial grid divided according to a preset step size. The frequency of time series data points in each grid cell is counted. Based on the upper limit of the interval in the wind power active power output dimension and the photovoltaic active power output dimension, and the lower limit of the interval in the load demand dimension, the extreme degree of source and load corresponding to each non-empty grid cell is determined. Extreme boundary grid cells are extracted, and the combination of the wind power active power output interval, photovoltaic active power output interval and load demand interval corresponding to each extreme boundary grid cell constitutes an extreme operation combination dataset. Step C: Sequentially take each extreme operating combination in the extreme operating combination dataset as the operating condition to be evaluated for the distribution network. Based on the upper limit of the wind power active power output range, the upper limit of the photovoltaic active power output range, and the lower limit of the load demand range in each extreme operating combination, determine the initial power generation, initial load power, and power change direction scaling factor of each node under the corresponding operating condition to be evaluated. For each operating condition to be evaluated, transform the nonlinear power balance equation of the distribution network into a complex analytical equation system with complex embedded variables as independent variables, and complete the construction of a fully embedded power flow model including the power change direction scaling factor. Step D: For each operating condition to be evaluated, calculate the zero-order coefficients of the initial reference state when the complex embedded variable is zero. Use the Maclaurin series expansion method to express the voltage of each node and the reactive power generation as power series with respect to the complex embedded variable. Solve the coefficients of each order of the power series by recursion to generate the equivalent analytical expression of the voltage of each node with respect to the complex embedded variable under each operating condition to be evaluated. Step E: Set the upper limit value of the voltage of the distribution network nodes. For each operating condition to be evaluated, solve for the positive real roots of the complex embedded variables corresponding to the modulus of the equivalent analytical expression of the voltage of each node when the modulus is equal to the upper limit value. Determine the minimum value among the positive real roots of each node under the same operating condition to be evaluated, and obtain the photovoltaic back-feed limit capacity corresponding to the operating condition to be evaluated. Compare the photovoltaic back-feed limit capacity corresponding to all extreme operating combinations in the extreme operating combination dataset, and determine the minimum value among them as the maximum back-feed limit capacity of the distributed photovoltaic system in the distribution network without exceeding the limit.

2. The method for assessing the backfeed limit of distributed photovoltaic power in distribution networks according to claim 1, characterized in that, The specific implementation method for extracting extreme boundary mesh cells is as follows: Along the direction of increasing active power output of wind power and photovoltaic power and decreasing load demand, all non-empty grid cells are traversed; if no other non-empty grid cell forms a dominant relationship with the traversed grid cell in three dimensions, the traversed grid cell is determined as an extreme boundary grid cell, and one or more extreme boundary grid cells are obtained. For any two non-empty grid cells g and h, let the upper limit of the discrete interval of wind power active power output, the upper limit of the discrete interval of photovoltaic active power output, and the lower limit of the discrete interval of load demand corresponding to the g-th non-empty grid cell be respectively... , , Let the upper limit of the discrete interval of wind power active power output, the upper limit of the discrete interval of photovoltaic active power output, and the lower limit of the discrete interval of load demand corresponding to the h-th non-empty grid cell be respectively... , , When the following conditions are met: Furthermore, if at least one of the three inequalities is a strict inequality, it is determined that the non-empty grid cell h has a dominance relationship with the non-empty grid cell g in the extreme directions of the source load.

3. The method for assessing the backfeed limit of distributed photovoltaic power in distribution networks according to claim 1, characterized in that, The fully embedded power flow model includes the voltage magnitude constraint equation for the slack node, the complex analytical equation for the load node, and the complex analytical equation and voltage magnitude constraint equation for the generator node. The voltage magnitude constraint equation of the balancing node is defined as follows: in, Representative node Regarding embedded variables The voltage complex analytic function, Representative node Given the reference voltage amplitude, Represents the set of balanced nodes; The complex analytical equation of the load node is defined as follows: in, Represents the total number of nodes in the system. Represents the node index number. Represents the target node index number. Represents the elements of the nodal admittance matrix. Representative node Regarding complex embedded variables The voltage complex analytic function, Representative node The conjugate of the initial complex apparent power, Representative node Complex apparent power change conjugate, Representative node Regarding conjugate embedded variables The conjugate of the voltage complex analytic function, Represents the set of load nodes; The complex analytical equations and voltage magnitude constraint equations of the generator node are defined as follows: in, Representative node Net active power in the initial state, Represents the imaginary unit. Representative node Reactive load in the initial state, Representative node The change in active power, Representative node The change in reactive load, Representative node Regarding complex embedded variables The holomorphic function of reactive power generation, Representative node The square of the given voltage amplitude, Represents the set of PV nodes; The initial power parameters are defined as follows: in, Represents the initial active power generation. Represents the initial active load. Represents the load growth coefficient. Represents the power generation growth coefficient. Represents the initial complex apparent power. This represents the initial reactive load.

4. The method for assessing the backfeed limit of distributed photovoltaic power in distribution networks according to claim 3, characterized in that, Step D is as follows: The zeroth-order complex coefficients of the complex analytic function of the voltage at each node and the zeroth-order real coefficients of the holomorphic function of reactive power generation are obtained when the value of the complex embedded variable is zero, and these are used as the initial values ​​for the recursion. Expand the complex analytic functions of the voltage at each node and the holomorphic function of reactive power generation at the origin of the complex plane into Maclaurin series form: in, Representative node The voltage complex analytic function, The order of the series expansion. The first representing the voltage function Complex coefficients of order 1 The first function representing reactive power generation real coefficients of order; Introducing the reciprocal function of the voltage at each node : in, Representative node The complex analytic function of the reciprocal of voltage. The first function representing the reciprocal of voltage Coefficients of the complex order; Using identities Establish the recursive relationship between the coefficients of the complex analytic function of voltage and the coefficients of the reciprocal function of voltage: when hour: , The zeroth-order complex coefficients represent the reciprocal function of voltage. Represents the 0th-order complex coefficients of the voltage function; when hour: , This represents the inner summation index number for the convolution calculation. The first function representing the reciprocal of voltage Complex coefficients of order 1 The first representing the voltage function Coefficients of the complex order; Substitute the Mclaurin series of the voltage complex analytic function, the Mclaurin series of the voltage reciprocal function, and the Mclaurin series of the reactive power holomorphic function into the holomorphic embedded power flow model to establish recursive update equations for the complex coefficients of the voltage complex analytic function and the real coefficients of the reactive power holomorphic function at each node. Starting from the zeroth-order complex coefficients of the complex analytical function of each node voltage and the zeroth-order real coefficients of the holomorphic function of reactive power generation, the equivalent analytical expression of each node voltage with respect to the complex embedded variables is obtained by solving the recursive update equation step by step until the preset convergence tolerance is met.

5. The method for assessing the backfeed limit of distributed photovoltaic power in distribution networks according to claim 1, characterized in that, The specific method for calculating the maximum back-feed limit capacity of distributed photovoltaic without exceeding the limit based on the minimum positive real root is as follows: multiply the minimum positive real root by the initial deployment baseline capacity to obtain the maximum back-feed limit capacity of distributed photovoltaic in the system at the current node location.

6. The method for assessing the backfeed limit of distributed photovoltaic power in distribution networks according to claim 1, characterized in that, The power distribution network operation data comes from a JSON format file containing multiple operating days.

7. The method for assessing the backfeed limit of distributed photovoltaic power in distribution networks according to claim 1, characterized in that, The three dimensions of the three-dimensional spatial grid correspond to the active power output of wind power, the active power output of photovoltaic power, and the active power of the load, respectively, and the preset step size is 0.01 pu.

8. A multi-timescale source-load matching driven distributed photovoltaic backfeed limit assessment system for distribution networks, characterized in that, It includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the distribution network distributed photovoltaic backfeed limit assessment method as described in any one of claims 1-7.

9. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the instruction is executed, it implements the distribution network distributed photovoltaic backfeed limit assessment method as described in any one of claims 1 to 7.

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