A power quality optimization method for distribution transformer area based on photovoltaic inverter

Abstract

The application relates to the technical field of power system operation control, and discloses a distribution transformer area electric energy quality optimization method based on a photovoltaic inverter, which comprises the following steps: determining an inverter cluster connected through a shared neutral line and injecting a quadrature perturbation signal; identifying a voltage response sensitivity parameter and separating the voltage response sensitivity parameter into a common-mode sensitivity component and a differential-mode sensitivity component; calculating a common-mode voltage offset value from an original measurement deviation by using the common-mode component, and obtaining a corrected differential-mode deviation; establishing a reactive power optimization model with the minimum corrected differential-mode deviation as a target and containing a common-mode adjustment amplitude limiting constraint; solving the model, decomposing a total adjustment amount into common-mode and differential-mode shares, and issuing the execution in a combination mode of broadcasting and unicasting. The application can inhibit the neutral line potential cooperative drift, eliminate the control error caused by the voltage reference point fluctuation, and improve the accuracy and stability of the voltage regulation of the distribution transformer area.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and more specifically, to a method for optimizing power quality in distribution transformer areas based on photovoltaic inverters. Background Technology

[0002] With the implementation of photovoltaic development strategies such as county-wide promotion, a large number of household distributed photovoltaic systems have been connected to low-voltage distribution networks. Due to the randomness of photovoltaic power output and its mismatch with the spatiotemporal distribution of loads, power quality problems such as voltage exceeding limits at the distribution station terminals and three-phase voltage imbalance are easily caused. Currently, utilizing the remaining capacity of photovoltaic inverters for reactive power and voltage regulation is an economical and effective means to solve these problems. Its mainstream control modes include local voltage-reactive power droop control and communication-based centralized optimal power flow optimization.

[0003] Existing regulation methods typically treat low-voltage distribution networks as a three-phase balanced system. Even if three-phase imbalance is considered, the influence of neutral line impedance is often ignored during calculation and modeling, or the neutral point potential is assumed to be zero. Under this processing logic, the control system directly uses the collected phase voltage data as the basis for regulation, and only performs independent or decoupled control on the voltage drop of each phase conductor.

[0004] However, in practice, low-voltage distribution substations generally use a three-phase four-wire wiring system, and the grounding resistance at multiple points is not ideally zero. In scenarios where the proportion of single-phase residential photovoltaic installations is high and the installation locations are random, there is often a severe three-phase current imbalance within the substation area. When this unbalanced current flows through the neutral line, which has impedance, it causes the neutral line's potential to ground to rise or drift.

[0005] At this point, the phase-neutral voltage value collected by the inverter actually includes the combined effects of phase voltage drop and neutral potential shift. Existing technology, failing to distinguish between these two, often incorrectly identifies the global voltage fluctuation caused by neutral potential shift as a local voltage deviation on the phase line, thus directing the inverter to output incorrect reactive power. This misadjustment not only fails to eliminate voltage over-limits but may also exacerbate three-phase current imbalance, further pushing up the neutral potential, causing the control target to fail to converge, and even leading to repeated voltage oscillations in the distribution area. Summary of the Invention

[0006] This invention provides a method for optimizing power quality in distribution transformer areas based on photovoltaic inverters, which solves the technical problems mentioned in the background art.

[0007] This invention provides a method for optimizing power quality in distribution transformer areas based on photovoltaic inverters, comprising: Identify multiple photovoltaic inverters connected by a shared neutral line within the distribution transformer area, and control the photovoltaic inverters to inject mutually orthogonal reactive power disturbance signals; Based on the voltage response to the reactive power disturbance signal, the voltage reactive power sensitivity parameter is identified, and the voltage reactive power sensitivity parameter is separated into a common-mode sensitivity component characterizing the coordinated drift of the neutral line potential and a differential-mode sensitivity component characterizing the phase line voltage drop. Based on the common-mode sensitivity component, the common-mode voltage offset value caused by neutral line potential drift in the original voltage measurement deviation is calculated, and the common-mode voltage offset value is subtracted from the original voltage measurement deviation to generate the corrected differential-mode voltage deviation; A reactive power optimization model is established with the objective of minimizing the corrected differential-mode voltage deviation and including common-mode regulation amplitude limit constraints for the common-mode sensitivity component. The total reactive power regulation is obtained by solving the reactive power optimization model. The total reactive power regulation is decomposed into common-mode regulation and differential-mode regulation, and then sent to the photovoltaic inverter for execution.

[0008] The beneficial effects of this invention are as follows: By injecting orthogonal reactive power perturbation signals into photovoltaic inverters with shared neutral line connections, the common-mode sensitivity component characterizing the coordinated drift of the neutral line potential and the differential-mode sensitivity component characterizing the phase line voltage drop are identified and separated online. This allows for the elimination of common-mode interference caused by neutral line potential drift in voltage deviation calculations, and the establishment of an optimization model that includes common-mode regulation amplitude limits. This invention solves the voltage reference system distortion problem caused by neglecting the influence of neutral line impedance in traditional methods, eliminating the inverter's erroneous response to the neutral line potential and the risk of system oscillation. Thus, under conditions of severe three-phase load imbalance and high photovoltaic penetration, it achieves precise voltage management in distribution transformer areas, while significantly suppressing abnormal rises in the neutral line-to-ground potential, ensuring the safe and stable operation of the distribution network. Attached Figure Description

[0009] Figure 1 This is a flowchart of a power quality optimization method for distribution transformer areas based on photovoltaic inverters according to the present invention; Figure 2 This is a schematic diagram of a specific implementation scenario of the present invention. Detailed Implementation

[0010] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0011] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" indicate that the element or object preceding the term encompasses the elements or objects listed following the term and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0012] like Figure 1 As shown, a method for optimizing power quality in distribution transformer areas based on photovoltaic inverters includes: Identify multiple photovoltaic inverters connected by a shared neutral line within the distribution transformer area, and control the photovoltaic inverters to inject mutually orthogonal reactive power disturbance signals; Based on the voltage response to the reactive power disturbance signal, the voltage reactive power sensitivity parameter is identified, and the voltage reactive power sensitivity parameter is separated into a common-mode sensitivity component characterizing the coordinated drift of the neutral line potential and a differential-mode sensitivity component characterizing the phase line voltage drop. Based on the common-mode sensitivity component, the common-mode voltage offset value caused by neutral line potential drift in the original voltage measurement deviation is calculated, and the common-mode voltage offset value is subtracted from the original voltage measurement deviation to generate the corrected differential-mode voltage deviation; A reactive power optimization model is established with the objective of minimizing the corrected differential-mode voltage deviation and including common-mode regulation amplitude limit constraints for the common-mode sensitivity component. The total reactive power regulation is obtained by solving the reactive power optimization model. The total reactive power regulation is decomposed into common-mode regulation and differential-mode regulation, and then sent to the photovoltaic inverter for execution.

[0013] Preferably, multiple photovoltaic inverters connected via a shared neutral line within a distribution transformer area are identified, and the photovoltaic inverters are controlled to inject mutually orthogonal reactive power disturbance signals, including: Establish containing The collection of the aforementioned photovoltaic inverters The photovoltaic inverters mentioned above are all connected to the low-voltage side of the same distribution transformer area; Construct order is Adama matrix ,in ,and To meet The smallest integer from the Adamant matrix; Remove all elements from the middle The row, select the first Rows form an orthogonal coding matrix ,in Indicates the first The photovoltaic inverter mentioned above is in the first The encoded value at time n, and satisfying: ; in, Let be the transpose of the orthogonal encoding matrix. It is the identity matrix; Calculate the first The photovoltaic inverter mentioned above is in the first reactive power disturbance amplitude at each moment :

[0014] in, This is the preset upper limit of the absolute perturbation amplitude. This is the preset margin occupancy ratio coefficient. For the first The photovoltaic inverter mentioned above is in the first Normalized active power at any given moment; Generate the first The photovoltaic inverter mentioned above is in the first Injected reactive power at a given moment : ; in, For the first The photovoltaic inverter mentioned above is in the first The original reactive power command at each moment. This indicates that the synchronization time index is in accordance with the stated order. Take the mold.

[0015] The total number of photovoltaic inverters is the total number of photovoltaic inverters in the distribution transformer area that meet the conditions of shared neutral line and controllable reactive power output, which is collected through the distribution transformer area's accounting records.

[0016] The rated apparent power of the i-th inverter is the factory-calibrated apparent power rating of the i-th photovoltaic inverter, which can be obtained by reading the inverter's nameplate or retrieving parameters from the device's backend.

[0017] The original active power of the i-th inverter at time k is the actual active power output of the i-th photovoltaic inverter at the k-th synchronization time, which can be acquired in real time through the inverter's own power acquisition module. The original reactive power command of the i-th inverter at time k is the reactive power basic execution command received by the i-th photovoltaic inverter at the k-th synchronization time, which can be acquired through the inverter's control communication port.

[0018] The order exponent of the Hadamard matrix is ​​the smallest integer that satisfies the condition that 2 raised to the power of the exponent is greater than or equal to the total number of photovoltaic inverters plus 1. The order of the Hadamard matrix is ​​2 raised to the power of the order exponent, which is the number of columns in the orthogonal coding matrix.

[0019] The orthogonal coding matrix is ​​a matrix formed by removing all rows of 1 from the Hadamard matrix and selecting the first rows representing the total number of photovoltaic inverters. The matrix elements are only negative 1s and 1s, and it is used to assign orthogonal coding sequences to each inverter. The element in the orthogonal coding matrix is ​​the element in the i-th row and k-th column, with a value of either negative 1 or 1, representing the orthogonal coding value of the i-th inverter at the k-th synchronization time.

[0020] The upper limit of absolute perturbation amplitude is the absolute maximum value set for the reactive power perturbation amplitude of the photovoltaic inverter, preferably 0.02 per unit. This value can ensure the accuracy of voltage response identification without affecting the normal operation of the inverter due to excessive perturbation.

[0021] The margin occupancy ratio coefficient is the proportion of the real-time reactive power margin that the reactive power disturbance amplitude of the photovoltaic inverter can occupy. It is preferably 0.2. This value can avoid the disturbance occupying too much reactive power margin and ensure the inverter's ability to regulate voltage changes.

[0022] The perturbation amplitude of the i-th inverter at time k is the actual reactive perturbation amplitude of the i-th photovoltaic inverter at the k-th synchronization time.

[0023] The synchronization time index is a unified time count identifier set for all photovoltaic inverters in the distribution area. It is used to achieve timing synchronization of perturbation injection and is uniformly issued by the distribution area control center.

[0024] The reactive power injected by the i-th inverter at time k is the actual reactive power executed by the i-th photovoltaic inverter after superimposing the reactive power perturbation signal at the k-th synchronization time.

[0025] Inverter clusters are defined based on three conditions: the low-voltage side of the same distribution transformer area, shared neutral line, and controllable reactive power output. During implementation, the neutral line connection of each inverter is first confirmed through the distribution topology diagram of the transformer area. Then, the reactive power regulation function is checked through the inverter's background control system. Inverters without controllable reactive power output capability are directly excluded, and only inverters that meet all conditions are retained to form a cluster.

[0026] Construct an Hadamard matrix of order 2 raised to the power of m, greater than or equal to the total number of inverters plus 1. After removing rows all containing 1s, generate an orthogonal coding matrix. This matrix must satisfy the orthogonality conditions that the transpose multiplied by the original matrix equals the order multiplied by the identity matrix, and the sum of the elements in each row is 0. In implementation, the Hadamard matrix is ​​generated recursively. The first-order matrix has a single element of 1, and the k-order matrix consists of four k-1 matrices: the top left and bottom right are k-1 matrices, and the top right and bottom left are negative k-1 matrices.

[0027] The amplitude of the disturbance is dynamically calculated based on the real-time reactive power margin of the inverter. At the same time, the dual constraints of the absolute upper limit and the margin ratio are introduced. In implementation, the real-time reactive power margin is first calculated from the rated apparent power and real-time active power of the inverter. Then, the reactive power margin is multiplied by the margin occupancy ratio coefficient. The calculation result is compared with the upper limit of the absolute disturbance amplitude, and the minimum value of the two is taken as the actual disturbance amplitude.

[0028] Under a unified synchronization time index, timing matching between perturbations and orthogonal codes is achieved by taking the time index modulo the matrix order. The perturbation amplitude is multiplied by the coded value to obtain the perturbation signal, which is then superimposed on the original reactive power command injection. During implementation, the distribution area control center issues a unified synchronization time index. Each inverter takes the time index modulo the Hadamard matrix order, retrieves the orthogonal coded value of the corresponding column, multiplies it by its own perturbation amplitude to obtain the perturbation signal, and then superimposes it on the original reactive power command.

[0029] The Hadamard matrix is ​​constructed using a recursive method. Specifically, the recursive rule is that a first-order Hadamard matrix has a single element of 1. To generate a k-order Hadamard matrix, four k-1 order Hadamard matrices need to be concatenated in the positions of top left, top right, bottom left, and bottom right. The top left and bottom right are the original k-1 order Hadamard matrices, and the top right and bottom left are negative k-1 order Hadamard matrices, thus generating any Hadamard matrix that meets the order requirement.

[0030] The preferred range for the upper limit of the absolute perturbation amplitude is 0.02 to 0.05 per unit, and the preferred range for the margin occupancy ratio coefficient is 0.1 to 0.3.

[0031] The synchronization time index achieves time synchronization between the distribution control center and all inverters through power line carrier communication. The maximum tolerance for communication delay in this communication method is 50 milliseconds.

[0032] When the inverter's reactive power margin is 0, the amplitude of the inverter's perturbation is set to 0 directly, and the injection of reactive power perturbation signals into the inverter is stopped. The reactive power margin is restored to a value greater than 0 after the real-time active power change of the inverter.

[0033] The inverter index numbers are assigned sequentially from the beginning to the end of the distribution area according to the inverter's electrical connection location within the distribution area. The numbers are consecutive positive integers. The first inverter at the beginning of the distribution area, which is closest to the transformer, is numbered 1. The numbers extend along the distribution line to the end, and the last inverter is numbered according to the total number of photovoltaic inverters.

[0034] The orthogonal coding matrix is ​​constructed uniformly by the distribution area control center and then distributed to the local storage module of each inverter via power line carrier communication. The storage format is a binary array.

[0035] The start and stop conditions for perturbation injection are set as follows: perturbation injection is started when the absolute value of the voltage deviation of the transformer area is greater than 0.01 per unit value, and perturbation injection is stopped when the absolute value of the voltage deviation of the transformer area is less than 0.005 per unit value and this state is maintained for 3 consecutive control cycles.

[0036] Preferably, the voltage reactive power sensitivity parameter is identified based on the voltage response to the reactive power disturbance signal, including: Collection of the first The photovoltaic inverter mentioned above is in the first The measured value of the point of common coupling voltage at each moment Calculate its normalized voltage value The voltage difference value is then processed by first-order differential and low-pass filtering to obtain a smoothed voltage difference value. : ; ; in, The preset voltage filtering coefficient, This represents the original voltage difference value; Based on length The sliding window, utilizing the most recent The voltage differential observation matrix is ​​constructed from the data at each time point. and reactive disturbance input matrix : ; ; in, For a moment A column vector consisting of the smoothed voltage differential values ​​of all the photovoltaic inverters. For a moment A column vector consisting of the normalized reactive power disturbance signals of all the photovoltaic inverters. The total number of the photovoltaic inverters. Let the order of the Adamant matrix be [value]. The voltage reactive power sensitivity parameters are estimated using the ridge regression algorithm. : ; in, These are the preset regularization parameters. It is the identity matrix. It is the transpose of the reactive disturbance input matrix.

[0037] The measured voltage at the point of common coupling of the i-th inverter at time k is the effective value of the line voltage collected at the point of common coupling of the i-th photovoltaic inverter at the k-th synchronization time.

[0038] The rated phase voltage of a distribution transformer area is the nominal rated phase voltage value of the distribution transformer area, which is the reference value for normalized calculation of voltage measurement values.

[0039] The normalized voltage value of the i-th inverter at time k is the ratio of the measured value of the common coupling voltage of the i-th inverter to the rated phase voltage of the transformer area.

[0040] The original voltage difference value of the i-th inverter at time k is the difference between the normalized voltage value of the i-th inverter at the current time and the previous time.

[0041] The voltage low-pass filter coefficient is used to smooth the original voltage difference value. It is preferably 0.7. This value can effectively filter out high-frequency noise in voltage measurement, while retaining the voltage response characteristics caused by reactive power disturbance, and will not cause the response signal to be distorted due to excessive filtering.

[0042] The smoothed voltage difference value of the i-th inverter at time k is the value of the original voltage difference value of the i-th inverter after low-pass filtering.

[0043] The voltage differential observation matrix is ​​a matrix constructed by extracting the smoothed voltage differential values ​​of all photovoltaic inverters in the distribution area through a sliding window.

[0044] The reactive power disturbance input matrix is ​​a matrix formed by extracting data from the normalized reactive power disturbance signals of all photovoltaic inverters in the distribution area through a sliding window. The matrix dimension is consistent with the voltage differential observation matrix.

[0045] The ridge regularization parameter is the regularization coefficient used for ridge regression estimation. It is preferably 0.0001. This value can effectively solve the matrix rank deficiency problem after multiplying the transpose of the reactive disturbance input matrix with itself, ensure the numerical stability of the voltage reactive sensitivity parameter matrix solution, and prevent the identification results from being biased due to excessive regularization.

[0046] The voltage reactive power sensitivity parameter matrix is ​​a matrix that characterizes the coupling relationship between the reactive power variation of the photovoltaic inverter and the voltage variation at the point of common coupling within the distribution area.

[0047] The measured voltage at the point of common coupling of the photovoltaic inverter is sequentially processed by first-order differential processing and low-pass filtering to generate a smoothed voltage differential value. In practice, the difference between the normalized voltage value of each inverter at adjacent synchronization moments is first calculated to obtain the original voltage differential value. Then, following the calculation method of first-order low-pass filtering, the smoothed voltage differential value of the previous moment is multiplied by the voltage low-pass filter coefficient, and the result of multiplying the original voltage differential value of the current moment by 1 and subtracting the voltage low-pass filter coefficient is added to obtain the smoothed voltage differential value of the current moment.

[0048] A sliding window mechanism with a length equal to the order of the Hadamard matrix is ​​employed to extract smoothed voltage differential and reactive power disturbance sequences, constructing voltage differential observation matrices and reactive power disturbance input matrices respectively. In implementation, a time series is first established for the smoothed voltage differential values ​​and reactive power disturbance signals of all photovoltaic inverters within the distribution area, indexed by synchronization time. Then, the window length is set to be exactly the same as the order of the Hadamard matrix, retaining only continuous data corresponding to the corresponding time within the window. These data are arranged with inverter numbers as rows and time as columns, forming two matrices with matched dimensions.

[0049] A ridge regularization term is introduced into the least squares estimation model. The voltage-reactive power sensitivity parameter matrix is ​​obtained by solving the model using the voltage differential observation matrix and the reactive power disturbance input matrix. In practice, the product of the transpose of the reactive power disturbance input matrix and itself is first calculated. This product is then added to the product of the ridge regularization parameter and the identity matrix to obtain a new matrix. The inverse of this new matrix is ​​then calculated. Finally, the voltage differential observation matrix is ​​multiplied by the transpose of the reactive power disturbance input matrix, and then multiplied by the inverse matrix to obtain the voltage-reactive power sensitivity parameter matrix. This method effectively avoids the matrix invertibility problem caused by equipment disconnection or zero disturbance amplitude, ensuring the validity of the identification results.

[0050] The voltage reactive power sensitivity parameters are identified solely by utilizing the voltage response after reactive power disturbance signals are injected into the photovoltaic inverter, eliminating interference from other factors such as load fluctuations and natural changes in photovoltaic output. During implementation, other operating conditions within the transformer area are kept relatively stable during the reactive power disturbance signal injection period, and the disturbance signal is a known signal that is actively injected. The voltage response is attributed only to changes in this disturbance signal, ensuring that the identified parameter matrix reflects only the coupling relationship between reactive power and voltage.

[0051] The voltage measurements at the point of common coupling (PCC) are normalized based on the rated phase voltage of the transformer substation before subsequent differential and filtering operations are performed. During implementation, the voltage measurements collected by each inverter are divided by the rated phase voltage of the transformer substation to obtain dimensionless normalized voltage values. This ensures comparability of voltage data from photovoltaic inverters of different capacities and connection locations, avoiding the impact of voltage dimension differences on subsequent matrix calculations and parameter identification.

[0052] The sliding window adopts a cycle-by-cycle sliding update method. After completing the data acquisition of voltage and reactive power disturbance signals in each control cycle, the oldest data in the window is removed, and the latest acquired data is added to the window. The length of the window is always equal to the order of the Hadamard matrix, ensuring the timeliness of matrix construction and the continuity of data.

[0053] The sampling frequency of the common coupling point voltage measurement is set to 10 times the control cycle.

[0054] The normalization reference for the reactive power disturbance sequence is the rated apparent power of the photovoltaic inverter. The dimensionless normalized reactive power disturbance signal is obtained by dividing the actual value of the reactive power disturbance signal of each inverter by its rated apparent power.

[0055] The update frequency of the voltage reactive power sensitivity parameter matrix is ​​matched with the order of the Adama matrix. Each time a full data update of a sliding window is completed, the sensitivity parameter matrix is ​​identified and updated.

[0056] Both the voltage differential observation matrix and the reactive power disturbance input matrix adopt a two-dimensional numerical array storage format, stored in row-major order. The rows correspond to the index number of the photovoltaic inverter, the columns correspond to the synchronization time index, and the stored values ​​are double-precision floating-point numbers.

[0057] Preferably, the voltage reactive power sensitivity parameter is separated into a common-mode sensitivity component characterizing the coordinated drift of the neutral line potential and a differential-mode sensitivity component characterizing the phase line voltage drop, including: Regarding the voltage reactive power sensitivity parameter Perform singular value decomposition: ; in, It is a left singular vector matrix. It is a right singular vector matrix. It is a diagonal matrix containing singular values, and the singular values ​​are arranged in descending order; Extract the first principal component, including the first singular value. First left singular vector and the first right singular vector and to and After symbol normalization, the common-mode space morphological vector is obtained. and common mode injection coefficient vector : ; ; in, For symbolic functions, For vectors The One element, This refers to the total number of the photovoltaic inverters; Calculate the common-mode sensitivity component And from the voltage reactive sensitivity parameter Subtract the common-mode sensitivity component from the middle The differential mode sensitivity component is obtained. : ; ; in, is the transpose of the common mode injection coefficient vector.

[0058] The left singular vector matrix is ​​obtained by performing singular value decomposition on the voltage reactive power sensitivity parameter matrix. The number of columns in the matrix is ​​the same as the total number of photovoltaic inverters, and each column represents a left singular vector. The right singular vector matrix is ​​obtained by performing singular value decomposition on the voltage reactive power sensitivity parameter matrix. The number of columns in the matrix is ​​the same as the total number of photovoltaic inverters, and each column represents a right singular vector. The singular value diagonal matrix is ​​obtained by performing singular value decomposition on the voltage reactive power sensitivity parameter matrix. The elements on the diagonal are singular values, and all other elements are 0.

[0059] The first singular value is the first element in the diagonal matrix of singular values, arranged in descending order; it is the largest singular value among all singular values. The first left singular vector is the column vector in the left singular vector matrix corresponding to the first singular value; it is the first column of the left singular vector matrix. The first right singular vector is the column vector in the right singular vector matrix corresponding to the first singular value; it is the first column of the right singular vector matrix.

[0060] The common-mode spatial morphology vector is a vector obtained by normalizing the first left singular vector and is used to characterize the spatial distribution characteristics of the neutral line potential drift within the transformer area.

[0061] The common-mode injection coefficient vector is a vector obtained by multiplying the first singular value with the first right singular vector after sign normalization. It is used to characterize the coupling relationship between reactive power injection and neutral line potential drift within the transformer area.

[0062] The i-th element of the first left singular vector is the element in the first left singular vector corresponding to the i-th photovoltaic inverter, which serves as the basis for determining the symbol normalization process.

[0063] The sign function is a mathematical function used to determine the sign of a numerical value. If the input value is positive, it outputs 1; if the input value is negative, it outputs -1; and if the input value is 0, it outputs 0.

[0064] The common-mode sensitivity component is a matrix obtained by multiplying the common-mode spatial morphology vector and the transpose of the common-mode injection coefficient vector. It is used to characterize the voltage-reactive coupling relationship corresponding to the neutral line potential cooperative drift.

[0065] The differential-mode sensitivity component is the residual matrix obtained by subtracting the common-mode sensitivity component from the voltage-reactive-mode sensitivity parameter matrix. It is used to characterize the voltage-reactive-mode coupling relationship corresponding to the phase line voltage drop.

[0066] Singular value decomposition (SVD) is performed on the voltage reactive power sensitivity parameter matrix. Only the first singular value and its corresponding first left and right singular vectors are extracted to represent the core coupling characteristics. In practice, the Jacobi algorithm is used to perform SVD on the voltage reactive power sensitivity parameter matrix, obtaining a left singular vector matrix, a right singular vector matrix, and a singular value diagonal matrix. After arranging the diagonal elements of the singular value diagonal matrix in descending order, only the first largest singular value and its corresponding column vectors in the left and right singular vector matrices are extracted. All other singular values ​​and vectors are discarded. This method, based on the low-rank characteristic of neutral line coupling in the transformer substation, accurately extracts common-mode coupling features.

[0067] Sign normalization is performed on the first left singular vector and the first right singular vector to ensure that the sum of all elements of the first left singular vector is positive and that the sign of their product remains unchanged. In practice, the algebraic sum of all elements of the first left singular vector is first calculated. If the sum is negative, all elements of both the first left and first right singular vectors are multiplied by -1. If the sum is positive, the vectors remain unchanged. If the sum is 0, the vectors are processed according to a preset rule. This operation eliminates the sign uncertainty of singular value decomposition.

[0068] The first left singular vector after sign normalization is defined as the common-mode space morphological vector, and the product of the first right singular vector and the first singular value is defined as the common-mode injection coefficient vector. Their cross product is the common-mode sensitivity component. In practice, the first left singular vector after sign normalization is directly used as the common-mode space morphological vector. Then, the value of the first singular value is multiplied by each element of the first right singular vector after sign normalization to obtain the common-mode injection coefficient vector. Finally, the common-mode space morphological vector is used as a row matrix, and the common-mode injection coefficient vector is used as a column matrix for multiplication. The resulting matrix is ​​the common-mode sensitivity component. This definition method matches the essence of neutral line potential drift.

[0069] By subtracting the common-mode sensitivity component from the voltage reactive power sensitivity parameter matrix, the residual matrix is ​​used as the differential-mode sensitivity component, thus decoupling neutral line potential drift from phase line voltage drop. In practice, a matrix subtraction operation is performed between the voltage reactive power sensitivity parameter matrix and the common-mode sensitivity component, subtracting corresponding elements one by one. The resulting residual matrix is ​​the differential-mode sensitivity component. This matrix only reflects the coupling relationship between voltage drop in each phase conductor and reactive power injection, and is independent of neutral line potential drift, achieving complete separation of the two causes of voltage change. For example, if an element at a certain position in the voltage reactive power sensitivity parameter matrix is ​​0.02, the corresponding element in the common-mode sensitivity component is 0.015, and the corresponding element in the differential-mode sensitivity component is 0.005.

[0070] Singular value decomposition is implemented using the Jacobi algorithm, with the computational precision requirement being that the singular values ​​are retained to 6 decimal places, and each element of the left and right singular vectors is retained to 6 decimal places.

[0071] The threshold for determining the validity of the common-mode component is set as follows: the ratio of the first singular value to the sum of all singular values ​​is not less than 0.7. That is, when the ratio of the first singular value to the algebraic sum of all singular values ​​is greater than or equal to 0.7, the common-mode component is determined to be valid, and subsequent offset value calculation can continue. When the ratio is less than 0.7, the neutral line coupling characteristics of the station area are determined to be insignificant, the common-mode component can be ignored, and the original sensitivity parameters can be directly used.

[0072] When the sum of all elements of the first left singular vector is 0, the exception handling rule is to invert the first non-zero element of the first left singular vector and invert the corresponding element of the first right singular vector, so that the sum of the elements of the processed first left singular vector is positive, and the sign of the product remains unchanged, to avoid the failure of sign normalization due to the sum of elements being 0.

[0073] The numerical precision standard for matrix operations is set to use double-precision floating-point numbers for all matrix and vector operations, with an effective number of 15 to 17 bits.

[0074] The common-mode sensitivity components and differential-mode sensitivity components are stored in a two-dimensional numerical array format, in row-major order. The stored values ​​are double-precision floating-point numbers and are uniformly stored by the distribution area control center. During transmission, the matrix is ​​flattened into a one-dimensional array by row and sent to the local storage module of each photovoltaic inverter via power line carrier communication. The transmitted number system is decimal, with 6 significant bits retained.

[0075] Preferably, based on the common-mode sensitivity component, the common-mode voltage offset value caused by neutral line potential drift in the original voltage measurement deviation is calculated, including: According to the The photovoltaic inverter mentioned above is in the first Normalized voltage value at each moment Calculate the original voltage measurement deviation with dead-time characteristics. : ; in, and These are the preset lower and upper limits of the normalized voltage, respectively. This is the preset dead zone width; Construct a diagonal weighted matrix , of which diagonal elements Determined based on the degree of voltage exceedance: ; in, The preset weighted gain coefficients, This is a truncation function; Using the weighting matrix and the common mode space morphological vector Calculate the original voltage measurement deviation Common-mode offset projection coefficient in the common-mode direction : ; in, This is a column vector consisting of the original voltage measurement deviations of all the aforementioned photovoltaic inverters. is the transpose of the common-mode space morphological vector. To prevent small positive numbers from being divided by zero; Calculate the common-mode voltage offset value : ; Wherein, the common-mode voltage offset value It is a vector whose elements correspond to the common-mode voltage offset of each of the photovoltaic inverters.

[0076] The normalized lower voltage limit is a normalized safe operating lower limit value set for the voltage at the point of common coupling of a photovoltaic inverter. It is preferably 0.95 per unit value. This value meets the national standard requirements for voltage operation of low-voltage distribution networks and is a reasonable lower limit for voltage operation in the distribution area.

[0077] The normalized voltage upper limit is a normalized safe operating upper limit value set for the voltage of the photovoltaic inverter's point of common coupling. It is preferably 1.05 per unit value. This value meets the national standard requirements for low-voltage distribution network voltage operation and is a reasonable upper limit for the voltage operation of the distribution area.

[0078] The voltage dead zone width is the dead zone threshold set for the calculation of the original voltage measurement deviation. It is preferably 0.005 per unit. This value can prevent the inverter from generating meaningless adjustment commands due to small voltage fluctuations and reduce frequent equipment operation.

[0079] The original voltage measurement deviation of the i-th inverter at time k is the voltage deviation value with dead zone characteristic calculated by the i-th photovoltaic inverter at the k-th synchronization time based on the voltage measurement value at the point of common coupling and the voltage safe operating range.

[0080] The diagonal weighted matrix is ​​a diagonal matrix constructed based on the severity of voltage exceedance of each photovoltaic inverter. All off-diagonal elements of the matrix are 0, and the diagonal elements are the weight values ​​corresponding to each inverter.

[0081] The i-th diagonal element of the weighting matrix is ​​the weight value of the i-th photovoltaic inverter in the diagonal weighting matrix, which is used to characterize the severity of the inverter's voltage exceeding the limit.

[0082] The voltage over-limit weighted gain coefficient is a coefficient used to amplify the weight corresponding to the severity of voltage over-limit, and is preferably 2.

[0083] The common-mode offset projection coefficient is a scalar obtained by weighted projection of the original voltage measurement deviation onto the common-mode spatial morphology vector direction. It is used to characterize the drift intensity of the overall neutral line potential in the transformer area at the current moment.

[0084] The small positive number to prevent division by zero is a numerical stability constant set for the calculation of the common-mode offset projection coefficient, to avoid the denominator being zero during the calculation process. It is preferably 0.000001.

[0085] The common-mode voltage offset vector is a vector that characterizes the voltage offset caused by neutral line potential drift in the common coupling point voltage of each photovoltaic inverter in the distribution area. Its elements correspond to the common-mode voltage offset value of each inverter.

[0086] The common-mode voltage offset value of the i-th inverter at time k is the element corresponding to the i-th photovoltaic inverter in the common-mode voltage offset value vector, which is the specific offset in the voltage measurement value of the inverter caused by the neutral line potential drift.

[0087] Based on the measured voltage at the photovoltaic inverter's point of common coupling (PCC) and the preset safe operating voltage range, the original voltage measurement deviation with dead-zone characteristics is calculated. A non-zero deviation only occurs when the voltage exceeds the range of the safe operating range plus the dead-zone. During implementation, the normalized voltage value of the inverter is first obtained, and then it is determined whether this value is less than the lower limit of the normalized voltage plus the voltage dead-zone width. If so, the deviation is the lower limit of the normalized voltage minus this voltage value; if it is greater than the upper limit of the normalized voltage minus the voltage dead-zone width, the deviation is the upper limit of the normalized voltage minus this voltage value; otherwise, the deviation is 0.

[0088] A diagonal weighted matrix is ​​constructed based on the severity of voltage exceedance for each photovoltaic inverter. During implementation, the absolute value of the difference between the normalized voltage value of each inverter and 1 is first calculated. Then, this value is divided by 0.05 and input into the truncation function to limit the result to between 0 and 1. The result is then multiplied by the voltage exceedance weighting gain coefficient and 1 is added. The resulting value is the diagonal element of the weighted matrix, and the off-diagonal elements are all set to 0.

[0089] The common-mode offset projection coefficient is calculated by weighted projection of the original voltage measurement deviation onto the direction of the common-mode spatial morphology vector. In practice, the transpose of the common-mode spatial morphology vector is first multiplied by the weighting matrix, and the result is then multiplied by the original voltage measurement deviation vector to obtain the numerator. Next, the transpose of the common-mode spatial morphology vector is multiplied by the weighting matrix, and the result is multiplied by the common-mode spatial morphology vector again, with a small positive number added to prevent division by zero to obtain the denominator. The numerator divided by the denominator is the projection coefficient. This calculation method can quantify the overall neutral line potential drift intensity while also considering the priority of voltage exceedances.

[0090] The common-mode voltage offset value is obtained by multiplying the common-mode offset projection coefficient by the common-mode spatial morphology vector. In practice, the value of the projection coefficient is multiplied by each element of the common-mode spatial morphology vector one by one. The resulting vector is the common-mode voltage offset value vector. Each element corresponds to the voltage offset of an inverter caused by neutral line potential drift. This method can convert the global neutral line drift intensity into the individualized offset value of each inverter, achieving precise isolation.

[0091] The quantification standard for the severity of voltage over-limit is the absolute value of the difference between the normalized inverter voltage value and 1. The larger the value, the more severe the over-limit. When the value is greater than 0.05, it is judged as a severe over-limit, and the cutoff function outputs 1, and the weight reaches the maximum value. When the value is less than or equal to 0.05, the weight is calculated according to the actual ratio, so as to achieve a linear correspondence between the degree of over-limit and the weight.

[0092] The weighting matrix is ​​updated at the same frequency as the control cycle of the transformer area. In each control cycle, the diagonal elements are recalculated based on the latest voltage measurement values ​​of each inverter, and the weighting matrix is ​​updated to ensure that the matrix can reflect the voltage over-limit status of each inverter in real time.

[0093] When multiple inverters exceed their voltage limits simultaneously, there is no additional priority in the weight allocation. Each inverter is assigned a weight based on the severity of its voltage limit exceedance. If there are inverters with the same degree of voltage limit exceedance, the weights are assigned sequentially according to the inverters' index numbers without changing the weight values.

[0094] The mapping relationship between the common-mode offset projection coefficient and the actual neutral line-to-ground potential is the projection coefficient multiplied by the rated phase voltage of the transformer area, which is the actual drift value of the neutral line-to-ground potential. This mapping relationship can realize the quantification of the projection coefficient, making it easier for operators to judge the actual degree of neutral line drift.

[0095] The upper limit constraint for the common-mode voltage offset value is that the absolute value of the value does not exceed 0.05 per unit. When the calculated common-mode voltage offset value exceeds this range, it is truncated to the boundary value of the range to avoid excessive offset value due to abnormal calculation.

[0096] The original voltage measurement deviation vector is stored in a one-dimensional numerical array. The deviation values ​​of each photovoltaic inverter are stored in the order of their index numbers, and the stored values ​​are double-precision floating-point numbers.

[0097] The calculation result of the common mode offset projection coefficient is limited to the range of -0.1 to 0.1 per unit. If the calculation result exceeds this range, it is determined that the operating status of the transformer area is abnormal, the subsequent offset value calculation is suspended, and an abnormal voltage alarm signal for the transformer area is issued to remind the operator to check the fault.

[0098] Preferably, subtracting the common-mode voltage offset value from the original voltage measurement deviation to generate the corrected differential-mode voltage deviation includes: Calculate the first The photovoltaic inverter mentioned above is in the first The corrected differential voltage deviation at each moment : ; in, For the first The original voltage measurement deviation of the photovoltaic inverter. For the first The common-mode voltage offset value of the photovoltaic inverter; The correction of differential mode voltage deviation satisfy: ; in, The vector formed by the original voltage measurement deviation. The common-mode offset projection coefficient is... The common mode space morphology vector.

[0099] The corrected differential-mode voltage deviation is obtained by subtracting the original voltage measurement deviation of each photovoltaic inverter from its corresponding common-mode voltage offset value element by element. In practice, the inverters are indexed one-to-one. The original voltage measurement deviation of the i-th inverter is subtracted from its common-mode voltage offset value, and the result is the corrected differential-mode voltage deviation for that inverter. After all inverters have completed this calculation, they are arranged by their indexes to obtain the corrected differential-mode voltage deviation vector.

[0100] The corrected differential-mode voltage deviation characterizes only the effective voltage control demand caused solely by phase voltage drops after eliminating the influence of neutral potential drift. During implementation, a subtraction operation is performed element-by-element to completely eliminate the global common deviation caused by neutral potential drift in the original voltage measurement deviation. The remaining corrected differential-mode voltage deviation is only related to the impedance voltage drop of each phase conductor. Subsequent reactive power optimization is only performed on this effective deviation, avoiding erroneous reactive power responses from the inverter to neutral potential drift. For example, if the neutral potential drift causes all inverters in a distribution area to have a common-mode offset of 0.006 per-unit in their original voltage measurement deviations, after this offset, the corrected differential-mode voltage deviation of each inverter only reflects the actual situation of its own phase voltage drop, providing an accurate basis for subsequent precise adjustments.

[0101] The processing rule when the corrected differential mode voltage deviation is zero is as follows: when the calculated result of the corrected differential mode voltage deviation of a certain inverter is 0, the inverter does not need to perform reactive power regulation. The current original reactive power command remains unchanged. Subsequent reactive power optimization regulation is only carried out for inverters with non-zero corrected differential mode voltage deviation to avoid meaningless adjustment actions that cause grid fluctuations.

[0102] The numerical range constraint for correcting differential mode voltage deviation is that the absolute value does not exceed 0.05 per unit. When the calculated absolute value of the corrected differential mode voltage deviation exceeds this range, the inverter voltage data is determined to be abnormal. The corrected differential mode voltage deviation is truncated to the corresponding boundary value, and the voltage measurement data of the inverter is marked to remind staff to check for equipment or communication faults.

[0103] The numerical calculation precision requirement for element-by-element subtraction is to use double-precision floating-point numbers and retain 6 decimal places during the calculation.

[0104] The positive and negative values ​​of the differential mode voltage deviation correction correspond to a clear reactive power adjustment direction. When the differential mode voltage deviation correction is positive, it indicates that the inverter's point of common coupling voltage is too low, and capacitive reactive power needs to be output to raise the voltage. When the differential mode voltage deviation correction is negative, it indicates that the inverter's point of common coupling voltage is too high, and inductive reactive power needs to be output to lower the voltage. This adjustment direction is consistent with the reactive voltage adjustment law of the low-voltage distribution network, ensuring the effectiveness of the adjustment action.

[0105] The storage and operation format of the corrected differential mode voltage deviation vector is a one-dimensional numerical array. The corrected differential mode voltage deviation values ​​of each photovoltaic inverter are stored in the order of their index numbers, and the stored values ​​are double-precision floating-point numbers.

[0106] Preferably, a reactive power optimization model is established with the objective of minimizing the corrected differential-mode voltage deviation and including common-mode regulation amplitude limits for the common-mode sensitivity component, comprising: Construct a system based on total reactive power regulation For a quadratic programming model with decision variables, its objective function is... Defined as: ; in, The corrected differential-mode voltage deviation vector is... The differential mode sensitivity component, For weighted matrices, The common-mode excitation penalty coefficient, Let be the transpose of the common mode injection coefficient vector. This is the three-phase equilibrium penalty coefficient. For the predicted first Average phase voltage This is the predicted total average of the three-phase voltages. To relax the penalty coefficient, These are slack variables; Set the constraints for the quadratic programming model: (1) Common-mode adjustment amplitude limit constraint: ; in, The preset upper limit of the equivalent voltage offset of the common mode is used to limit the neutral line-to-ground potential drift caused by reactive power regulation; (2) Voltage safety constraints (including relaxation variables): ; in, For the current voltage vector, and These are the upper and lower limits of the voltage. It is a non-negative slack variable. The common mode space morphological vector; (3) Capacity constraints: ; in, and The first The current reactive and active power of the photovoltaic inverter; (4) Climbing constraint: ; in, For the allowable rate of change of reactive power, To control the cycle.

[0107] The total reactive power regulation vector is a vector that serves as the decision variable in the quadratic programming model. Its elements are the reactive power regulation of each photovoltaic inverter, which is obtained by solving the optimization model.

[0108] The reactive power regulation of the i-th inverter is the element corresponding to the i-th photovoltaic inverter in the total reactive power regulation vector. It is the reactive power value that needs to be regulated by the inverter and is obtained by solving the optimization model.

[0109] The objective function of the quadratic programming model is a function used to measure the reactive power optimization effect. It consists of a weighted sum of three parts and is the optimization objective of the optimization model. It is calculated by correcting the differential voltage deviation and each penalty term.

[0110] The common-mode excitation penalty coefficient is a coefficient used to penalize the projection amplitude of the total reactive power regulation in the direction of the common-mode injection coefficient vector. It is preferably 5. This value can effectively suppress the common-mode regulation amplitude, avoid the aggravation of neutral line potential drift, and at the same time, it will not excessively restrict the voltage control effect of differential-mode regulation.

[0111] The three-phase balance penalty coefficient is a coefficient used to penalize the dispersion of the three-phase voltage average. It is preferably 1. This value can take into account the three-phase balance regulation on the basis of precise voltage management, and will not affect the core goal of voltage regulation due to excessive pursuit of three-phase balance.

[0112] The predicted average voltage of phase φ is the average voltage of each phase calculated based on the differential-mode sensitivity component, the common-mode sensitivity component, and the total reactive power regulation, which characterizes the predicted operating level of the phase voltage.

[0113] The predicted three-phase voltage average is the arithmetic mean of the predicted voltage averages of the three phases, representing the overall predicted voltage level of the distribution transformer area.

[0114] The slack variable penalty coefficient is a coefficient used to penalize slack variables in voltage safety constraints. It is preferably 10000. This value is a large penalty coefficient, which can minimize the triggering of slack variables and ensure the effectiveness of voltage safety constraints. Only a small number of violations are allowed under extreme operating conditions.

[0115] Relaxation variables are non-negative variables introduced to ensure that voltage safety constraints can be met under extreme operating conditions. They are divided into undervoltage relaxation variables (s). - and overpressure slack variable s + .

[0116] The upper limit of the common mode equivalent voltage offset is an absolute value limit set for the common mode excitation, preferably 0.01 per unit. This value can effectively limit the neutral line-to-ground potential drift caused by reactive power regulation, which meets the operational safety requirements of low-voltage distribution transformer areas.

[0117] Undervoltage relaxation variables are non-negative relaxation variables introduced in voltage safety constraints to cope with extreme undervoltage conditions, and are used to appropriately relax the lower voltage limit constraint.

[0118] Overvoltage relaxation variables are non-negative relaxation variables introduced in voltage safety constraints to cope with extreme overvoltage conditions, and are used to appropriately relax the upper limit of voltage constraints.

[0119] The current voltage vector is a vector composed of the normalized voltage values ​​of each photovoltaic inverter at the current moment, representing the real-time voltage status of each inverter in the distribution area.

[0120] The current reactive power of the i-th inverter is the actual reactive power output of the i-th photovoltaic inverter at the current moment.

[0121] The current active power of the i-th inverter is the actual active power output of the i-th photovoltaic inverter at the current moment.

[0122] The permissible reactive power change rate is the maximum reactive power regulation value set for the i-th photovoltaic inverter per unit time, preferably 0.1 per unit per second. This value matches the actual reactive power regulation rate of the photovoltaic inverter, avoiding grid voltage oscillations caused by excessively fast regulation.

[0123] The control cycle duration is the time interval between the distribution transformer area performing a reactive power optimization calculation and issuing an adjustment command, preferably 2 seconds.

[0124] A quadratic programming model is constructed with the total reactive power regulation as the decision variable. The objective function is the weighted sum of the squared error term for correcting differential-mode voltage deviation, the common-mode excitation penalty term, and the three-phase voltage mean dispersion penalty term. In implementation, the difference between the corrected differential-mode voltage deviation and the product of the differential-mode sensitivity component and the total reactive power regulation is first calculated, then multiplied by the weighting matrix, and the square of the L2 norm is calculated and halved to form the first part. Next, the square of the product of the transpose of the common-mode injection coefficient vector and the total reactive power regulation is calculated, multiplied by the common-mode excitation penalty coefficient, and halved to form the second part. Then, the sum of the squares of the differences between the predicted voltage mean of each phase and the overall three-phase mean is calculated, multiplied by the three-phase balance penalty coefficient, and halved to form the third part. Finally, the product of the relaxation variable and the relaxation penalty coefficient is added, and the objective function is obtained by summing all parts, achieving multi-objective collaborative optimization.

[0125] A common-mode regulation amplitude limit constraint is set, and the dot product of the common-mode injection coefficient vector and the total reactive power regulation is used as the common-mode excitation quantity, limiting its absolute value to not exceeding the upper limit of the common-mode equivalent voltage deviation. In implementation, the product of each element of the common-mode injection coefficient vector and the corresponding element of the total reactive power regulation is first calculated, and then all products are added together to obtain the common-mode excitation quantity. If the absolute value of this value exceeds the preset upper limit, the optimization model will automatically adjust the total reactive power regulation quantity to bring the dot product result back within the limit range, directly suppressing neutral line potential drift from an optimization perspective.

[0126] The voltage safety constraint introduces two non-negative relaxation variables, undervoltage and overvoltage, and sets a large penalty coefficient. In practice, when the reactive power margin of the transformer area is insufficient to meet the voltage safety requirements, the model will introduce a very small relaxation variable to appropriately relax the voltage constraint. At the same time, because the relaxation penalty coefficient is large, the value of the relaxation variable will be kept as small as possible to ensure that the voltage operates within a range close to the safety range and avoid the model having no solution under extreme conditions.

[0127] The inverter capacity constraint is transformed into a normalized second-order cone form, meaning the square of the sum of the inverter's current reactive power and reactive power regulation does not exceed 1 minus the square of the current active power. In implementation, both the inverter's active and reactive power are first normalized to between 0 and 1. Then, constraints are set according to this quadratic inequality to ensure the convexity of the constraints, enabling the quadratic programming model to have a globally optimal solution and avoiding poor regulation performance caused by local optima.

[0128] The ramp constraint limits the rate of change of total reactive power regulation to no more than the allowable value. In implementation, the ratio of the absolute value of the total reactive power regulation to the control cycle is limited to not exceeding the inverter's allowable rate of reactive power change. This ensures that the inverter's reactive power regulation rate matches its hardware performance, preventing repeated voltage oscillations in the distribution area due to excessively rapid regulation. For example, if the allowable rate of reactive power change is 0.1 per unit per second, the control cycle is 2 seconds, and the absolute value of reactive power regulation for a single inverter does not exceed 0.2 per unit.

[0129] The predicted voltage is obtained by adding the current voltage, the product of the differential-mode sensitivity component and the total reactive power regulation, and the product of the common-mode spatial morphology vector and the common-mode excitation. In practice, this calculation method is consistent with the separation logic of the sensitivity component, and takes into account the influence of differential-mode regulation and common-mode regulation on the voltage, so as to ensure the accuracy of the predicted voltage and provide a reliable basis for voltage safety constraints.

[0130] The quadratic programming model is solved using the interior point method. During implementation, the convergence accuracy is set to 0.0001, meaning that when the absolute value of the gradient of the objective function is less than this value, the solution is considered converged, and the optimal solution for the total reactive power regulation is obtained.

[0131] The predicted average voltage of phase φ is calculated using the arithmetic mean method. During implementation, the predicted voltage values ​​of all photovoltaic inverters connected to that phase in the distribution area are first added together, and then divided by the number of inverters in that phase to obtain the average voltage of that phase. The total average voltage of the three phases is the sum of the average voltage values ​​of the three phases divided by 3.

[0132] When multiple constraints conflict in a quadratic programming model, the priority order is: voltage safety constraint is higher than capacity constraint, capacity constraint is higher than ramp constraint, ramp constraint is higher than common mode regulation amplitude limit constraint. During implementation, the model will prioritize satisfying the high-priority constraints. Under the premise that the high-priority constraints are satisfied, the values ​​of the low-priority constraints will be optimized to ensure the safe operation of the transformer area voltage as the primary goal.

[0133] The maximum allowable value of the slack variable is set to 0.02 per unit. Even if the distribution area is under extreme operating conditions, the values ​​of the undervoltage and overvoltage slack variables cannot exceed this value to avoid serious voltage overruns in the distribution area due to excessive slack variables and to ensure the safe operation of the distribution network.

[0134] The mapping relationship between the upper limit of the equivalent voltage deviation of the common mode and the actual neutral line to ground potential is the upper limit of the equivalent voltage deviation of the common mode multiplied by the rated phase voltage of the transformer area, which is the maximum allowable drift value of the neutral line to ground potential. For example, if the upper limit of the equivalent voltage deviation of the common mode is 0.01 per unit and the rated phase voltage of the transformer area is 220 volts, then the maximum allowable drift value of the neutral line to ground potential is 2.2 volts.

[0135] The principle for adjusting the weights of the objective function is as follows: when the voltage in the transformer area is severely out of bounds, the common-mode excitation penalty coefficient and the three-phase balance penalty coefficient should be appropriately reduced to ensure the priority of voltage regulation; when the three-phase imbalance in the transformer area is severe, the three-phase balance penalty coefficient should be appropriately increased; when the neutral line potential drift in the transformer area is severe, the common-mode excitation penalty coefficient should be appropriately increased to achieve dynamic adjustment of the weights.

[0136] Preferably, the process involves solving the reactive power optimization model to obtain the total reactive power regulation, decomposing the total reactive power regulation into a common-mode regulation share and a differential-mode regulation share, and sending this to the photovoltaic inverter for execution, including: Calculate the first Common-mode excitation scalar at time 1 : ; in, Let be the transpose of the common mode injection coefficient vector. This refers to the total reactive power regulation. Calculate the common-mode adjustment share and the differential adjustment share : ; ; in, To prevent tiny positive numbers with a denominator of zero; Will Broadcast to all the aforementioned photovoltaic inverters, The first in element Send to the The aforementioned photovoltaic inverter; No. The photovoltaic inverter calculates the local target reactive power value. : ; in, This represents the current reactive power. The first common mode injection coefficient vector One element; No. The photovoltaic inverter generates reactive power and executes commands. : ; in, The limiting function is based on the inverter capacity. To control the cycle, For the first The reactive response time constant of the photovoltaic inverter.

[0137] The common-mode excitation scalar at time k is obtained by multiplying the transpose of the common-mode injection coefficient vector with the total reactive power regulation vector. It is used to characterize the degree of neutral line potential drift caused by the total reactive power regulation.

[0138] The common-mode regulation component vector at time k is obtained by multiplying the common-mode excitation scalar with the normalized common-mode injection coefficient vector, representing the component in the total reactive power regulation used to induce neutral line potential drift.

[0139] The common-mode regulation share of the i-th inverter at time k is the element corresponding to the i-th photovoltaic inverter in the common-mode regulation share vector, which is the common-mode component in the total reactive power regulation of the inverter.

[0140] The differential mode regulation share vector at time k is the vector obtained by subtracting the common mode regulation share vector from the total reactive power regulation vector, representing the component of the total reactive power regulation used to improve the phase line voltage drop.

[0141] The differential mode regulation share of the i-th inverter at time k is the element corresponding to the i-th photovoltaic inverter in the differential mode regulation share vector, which is the differential mode component in the total reactive power regulation of the inverter.

[0142] The local target reactive power value of the i-th inverter at time k is the reactive power regulation target value calculated by the inverter combining the original reactive power command, its own differential mode regulation share, and common mode regulation share.

[0143] The reactive power response time constant of the i-th inverter is a parameter characterizing the dynamic characteristics of reactive power regulation of the photovoltaic inverter, reflecting how quickly the inverter tracks reactive power commands.

[0144] The reactive power execution command of the i-th inverter at time k is the final reactive power adjustment command obtained after the local target reactive power value has been processed by first-order inertial filtering and amplitude limiting.

[0145] The amplitude limiting function is used to limit the reactive power execution command within the rated capacity range of the inverter. When the input value is outside the range, the output value is the boundary value; when the input value is within the range, the output value is the original value.

[0146] The exponential function is used for first-order inertial filtering calculations and has a base of the natural constant.

[0147] The current time synchronization index is a time identifier used to synchronize the command execution timing between the distribution area control center and all photovoltaic inverters, and it is uniformly issued by the distribution area control center.

[0148] Data packets are the data carriers that transmit control information from the regional control center to the photovoltaic inverter. They are divided into broadcast data packets and unicast data packets. Broadcast data packets contain synchronization indexes and common-mode excitation scalars, while unicast data packets contain the differential-mode regulation share of the corresponding inverter.

[0149] The common-mode excitation scalar is obtained by projecting the total reactive power regulation onto the common-mode injection coefficient vector. This scalar is then used to synthesize the common-mode regulation share with the normalized common-mode injection coefficient vector. The differential-mode regulation share is obtained by subtracting the common-mode regulation share from the total reactive power regulation. In practice, each element of the common-mode injection coefficient vector is first divided by the product of the vector's transpose and itself, and a small positive number is added to prevent division by zero, thus normalizing the vector. Then, the common-mode excitation scalar is multiplied by each normalized element to obtain the common-mode regulation share vector. Finally, the differential-mode regulation share vector is obtained by subtracting the elements of the common-mode regulation share vector from the corresponding elements of the total reactive power regulation vector.

[0150] A broadcast communication method is used to send data packets containing synchronization indexes and common-mode excitation targets to all photovoltaic inverters, while a unicast communication method is used to send data packets containing the corresponding differential-mode regulation share to each inverter individually. In practice, the distribution center sends common-mode related data through the broadcast channel of power line carrier communication, which can be received by all inverters. Then, a unique communication address is assigned to each inverter through the unicast channel, and the differential-mode regulation share of that inverter is sent separately to avoid data confusion.

[0151] The photovoltaic inverter reconstructs its local target reactive power value by combining the received common-mode excitation scalar, the locally stored common-mode injection coefficient vector elements, and the differential-mode regulation component with its own original reactive power command. In practice, the inverter first retrieves its corresponding common-mode injection coefficient vector element from the local storage module, multiplies it by the common-mode excitation scalar, divides by the product of the transpose of the common-mode injection coefficient vector and itself, and adds a small positive number to prevent division by zero, thus obtaining its own common-mode regulation component. Then, the original reactive power command is added to the common-mode regulation component and the received differential-mode regulation component to obtain the local target reactive power value.

[0152] The photovoltaic inverter sequentially performs first-order inertial filtering and amplitude limiting processing on the local target reactive power value to generate the final reactive power execution command. During implementation, the reactive power execution command from the previous moment is first multiplied by the ratio of the negative control period of the natural constant to the reactive power response time constant raised to a power of 1. Then, the result of subtracting the previous execution command from the local target reactive power value is multiplied by 1 and subtracted from the aforementioned exponent. These two results are added together to complete the filtering. The filtered result is then input into the amplitude limiting function to restrict the reactive power within the inverter's rated reactive power range, thus obtaining the execution command.

[0153] Both broadcast and unicast communications use the power line carrier communication protocol, which is suitable for the communication environment of low-voltage power distribution networks and does not require additional communication lines. The transmission baud rate of broadcast data packets is 1200 bits per second, and the transmission baud rate of unicast data packets is 2400 bits per second, ensuring the stability and efficiency of data transmission. The data packet verification method adopts cyclic redundancy check, and the check bit length is 16 bits.

[0154] When a photovoltaic inverter fails to receive a broadcast or unicast data packet within 50 milliseconds, the abnormal handling rule is to maintain the reactive power execution command of the previous moment unchanged, and at the same time send a communication fault feedback signal to the distribution area control center. After the control center receives fault signals from at least 3 inverters, it resends the corresponding data packet to ensure the timeliness of the inverter's adjustment command.

[0155] The initial value setting rule for the first-order inertial filter is that when the photovoltaic inverter participates in regulation for the first time, the initial value of the reactive power execution command is the current actual reactive power value of the inverter, which is obtained in real time by the inverter's own power acquisition module. This ensures the continuity of the filter calculation and avoids voltage fluctuations caused by sudden changes in the initial value.

[0156] The specific limiting range of the amplitude limiting function is from the negative real-time reactive power margin of the inverter to the positive real-time reactive power margin of the inverter. The real-time reactive power margin is calculated from the current active power of the inverter and is 1 minus the square root of the square of the normalized active power. This ensures that the executed command does not exceed the actual adjustment capacity of the inverter and avoids inverter protection shutdown due to command over-limit.

[0157] The local target reactive power value and reactive power execution instructions of the i-th inverter are stored in a single-precision floating-point format in the inverter's local storage module. The storage address is allocated according to the inverter's index number, and each value occupies 4 bytes of storage space.

[0158] The timing matching rule for the issuance and execution of reactive power execution commands is that all photovoltaic inverters execute the new reactive power execution command at the time corresponding to the current time synchronization index in the broadcast data packet. When the control center issues the data packet, it sets the synchronization index to the third control cycle after the data packet is sent, so as to reserve enough time for all inverters to receive and parse the data packet, and ensure that the adjustment actions of all inverters in the distribution area are synchronized.

[0159] The common-mode injection coefficient vector is broadcast from the regional control center to the local storage module of all photovoltaic inverters after each sensitivity parameter update. The storage period is consistent with the sensitivity parameter update period, ensuring that the vector stored locally by the inverter is completely synchronized with the vector in the control center, thus avoiding adjustment errors caused by parameter inconsistencies.

[0160] like Figure 2 As shown, Figure 2 This is a schematic diagram of a specific implementation scenario for this solution, including: distribution transformer, mortgaged busbar, photovoltaic inverter, and shared neutral line.

[0161] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A method for optimizing power quality in distribution transformer areas based on photovoltaic inverters, characterized in that, include: Identify multiple photovoltaic inverters connected by a shared neutral line within the distribution transformer area, and control the photovoltaic inverters to inject mutually orthogonal reactive power disturbance signals; Based on the voltage response to the reactive power disturbance signal, the voltage reactive power sensitivity parameter is identified, and the voltage reactive power sensitivity parameter is separated into a common-mode sensitivity component characterizing the coordinated drift of the neutral line potential and a differential-mode sensitivity component characterizing the phase line voltage drop. Based on the common-mode sensitivity component, the common-mode voltage offset value caused by neutral line potential drift in the original voltage measurement deviation is calculated, and the common-mode voltage offset value is subtracted from the original voltage measurement deviation to generate the corrected differential-mode voltage deviation; A reactive power optimization model is established with the objective of minimizing the corrected differential-mode voltage deviation and including common-mode regulation amplitude limit constraints for the common-mode sensitivity component. The total reactive power regulation is obtained by solving the reactive power optimization model. The total reactive power regulation is then decomposed into common-mode regulation and differential-mode regulation, and sent to the photovoltaic inverter for execution.

2. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 1, characterized in that, Identify multiple photovoltaic inverters connected via a shared neutral line within the distribution transformer area, and control the photovoltaic inverters to inject mutually orthogonal reactive power disturbance signals, including: Inverters connected to the low-voltage side bus of the same distribution transformer area and having controllable reactive power output capability are divided into an electrical subsystem connected by a shared neutral line, and an index number is assigned to each photovoltaic inverter in the electrical subsystem. Construct an Adama matrix that satisfies the orthogonality condition, and select the row vectors in the Adama matrix after removing all row vectors that are positive one as the orthogonal encoding sequence assigned to each photovoltaic inverter, wherein the order of the Adama matrix is ​​greater than or equal to the total number of photovoltaic inverters plus one. Based on the current apparent power and active power of each photovoltaic inverter, the reactive power margin at the current moment is calculated, and based on the reactive power margin and the preset perturbation safety limit, the reactive disturbance amplitude of each photovoltaic inverter is determined. Under a unified synchronization time index, the reactive power disturbance amplitude is multiplied by the element value of the corresponding time in the orthogonal coding sequence to obtain the reactive power disturbance signal, and the reactive power disturbance signal is superimposed on the original reactive power command of the photovoltaic inverter for injection.

3. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 2, characterized in that, Based on the voltage response to the reactive power disturbance signal, identify the voltage reactive power sensitivity parameters, including: Collect the common coupling point voltage measurement value of each photovoltaic inverter in multiple consecutive control cycles, and perform first-order differential processing and low-pass filtering smoothing on the common coupling point voltage measurement value to generate a smooth voltage differential sequence. Extract the reactive power disturbance signal injected by each of the photovoltaic inverters in the consecutive multiple control cycles to generate a reactive power disturbance sequence; Using a sliding window mechanism, the smoothed voltage difference sequence and the reactive power disturbance sequence with a length equal to the order of the Adama matrix are extracted to construct the voltage difference observation matrix and the reactive power disturbance input matrix, respectively. A least squares estimation model containing a ridge regularization term is constructed. The least squares estimation model is solved using the voltage difference observation matrix and the reactive power disturbance input matrix to obtain the voltage reactive power sensitivity parameters.

4. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 3, characterized in that, The voltage reactive power sensitivity parameter is separated into a common-mode sensitivity component characterizing the coordinated drift of the neutral line potential and a differential-mode sensitivity component characterizing the phase line voltage drop, including: The voltage reactive power sensitivity parameter is subjected to singular value decomposition. The singular values ​​are arranged in descending order, and the first singular value, the corresponding first left singular vector, and the first right singular vector are extracted. Perform sign normalization on the first left singular vector and the first right singular vector to ensure that the sum of all elements of the first left singular vector is positive, and keep the sign of the product of the first left singular vector and the first right singular vector unchanged. The first left singular vector after symbol normalization is used as the common mode space morphological vector, the product of the first right singular vector after symbol normalization and the first singular value is used as the common mode injection coefficient vector, and the product of the common mode space morphological vector and the common mode injection coefficient vector is used as the common mode sensitivity component. The common-mode sensitivity component is subtracted from the voltage reactive sensitivity parameter, and the resulting residual matrix is ​​used as the differential-mode sensitivity component.

5. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 4, characterized in that, Based on the common-mode sensitivity component, the common-mode voltage offset value caused by neutral line potential drift in the original voltage measurement deviation is calculated, including: Based on the current common coupling voltage measurement value of each photovoltaic inverter and the preset safe voltage operating range, the original voltage measurement deviation with dead zone characteristics is calculated, and a non-zero deviation is generated only when the common coupling voltage measurement value exceeds the safe voltage operating range; A weighted matrix is ​​constructed based on the severity of voltage exceedance for each photovoltaic inverter. The original voltage measurement deviation is projected in a weighted manner onto the direction of the common-mode spatial morphology vector to calculate the common-mode offset projection coefficient, which characterizes the overall potential drift intensity of the neutral line at the current moment. The common-mode offset projection coefficient is multiplied by the common-mode spatial shape vector to obtain the common-mode voltage offset value.

6. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 5, characterized in that, Subtracting the common-mode voltage offset value from the original voltage measurement deviation to generate the corrected differential-mode voltage deviation includes: The original voltage measurement deviation of each photovoltaic inverter is subtracted element by element from the corresponding common-mode voltage offset value to obtain the corrected differential-mode voltage deviation; the corrected differential-mode voltage deviation represents the effective voltage control requirement caused only by the phase line voltage drop after eliminating the influence of neutral line potential cooperative drift.

7. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 6, characterized in that, A reactive power optimization model is established with the objective of minimizing the corrected differential-mode voltage deviation and including common-mode regulation amplitude limits for the common-mode sensitivity component, including: Construct a quadratic programming model with total reactive power regulation as the decision variable; The objective function of the quadratic programming model is defined, and the objective function consists of a weighted sum of three parts: The first part is the weighted error square term between the corrected differential voltage deviation and the predicted voltage regulation calculated based on the differential sensitivity component and the total reactive power regulation; The second part is a penalty term for the projection amplitude of the total reactive power regulation in the direction of the common mode injection coefficient vector; The third part is the penalty term for the dispersion of the three-phase voltage mean; The constraints of the quadratic programming model are set, and the constraints include: Voltage safety constraint: Limits the predicted point of common coupling voltage to within a preset voltage safety operating range; Capacity constraint: The apparent power of each of the photovoltaic inverters is limited to not exceeding its rated capacity; Climbing constraint: Limits the rate of change of the total reactive power regulation; Common-mode regulation amplitude limit constraint: Calculate the inner product of the common-mode injection coefficient vector and the total reactive power regulation as the common-mode excitation amount, and limit the absolute value of the common-mode excitation amount to be less than or equal to the preset upper limit of the common-mode equivalent voltage offset.

8. The method for optimizing power quality in distribution transformer areas based on photovoltaic inverters according to claim 7, characterized in that, Solving the reactive power optimization model yields the total reactive power regulation, which is then decomposed into a common-mode regulation share and a differential-mode regulation share, and sent to the photovoltaic inverter for execution, including: The total reactive power regulation is projected onto the common-mode injection coefficient vector direction to obtain the common-mode excitation quantity; The common-mode regulation share is synthesized using the common-mode excitation amount and the normalized common-mode injection coefficient vector, and the differential-mode regulation share is obtained by subtracting the common-mode regulation share from the total reactive power regulation amount. A data packet containing the current synchronization index and the common-mode excitation quantity is sent to all photovoltaic inverters using broadcast communication, and a data packet containing the corresponding component of the differential-mode regulation share is sent to each photovoltaic inverter using unicast communication. Each of the photovoltaic inverters uses the received common-mode excitation, the locally stored common-mode injection coefficient vector elements, and the components of the differential-mode adjustment share to reconstruct and generate a local target reactive power value; Each of the photovoltaic inverters performs first-order inertial filtering and amplitude limiting on the local target reactive power value to generate the final reactive power execution command.

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