A data-driven adaptive droop voltage control method

Abstract

The present application relates to power distribution network voltage control technical field, disclose a kind of data-driven adaptive droop voltage control method, comprising, S1, obtain photovoltaic output and the time series data of load demand, and carry out normalization processing;S2, extract multiple typical operating day scenarios using clustering algorithm;S3, establish the optimal voltage control model with the minimum voltage deviation minimization and reactive power cost minimization as target;And construct voltage-reactive sample data set;S4, using bayesian information criterion-segmented linear regression algorithm, fitting to obtain segmented linear droop control curve;S5, the droop control curve is deployed to local controller, and the reactive power instruction that should be output is obtained by inquiring or calculating droop control curve, and the instruction is executed to realize the distributed voltage control of communication dependence-free.The present application has the advantages of realizing inverter-based reactive power personalized adjustment, not relying on communication facilities, improving the stability and regulation efficiency of distribution network.

Description

Technical Field

[0001] This invention relates to the field of distribution network voltage control technology, and in particular to a data-driven adaptive droop voltage control method. Background Technology

[0002] The application of distributed energy resources (DERs) is becoming increasingly widespread, especially photovoltaic (PV) systems connected to inverter interfaces in distribution networks. However, renewable energy sources such as PV exhibit significant volatility, which puts enormous pressure on traditional voltage control methods, leading to frequent unexpected voltage fluctuations and voltage exceeding limits. Therefore, effective measures are urgently needed to address the voltage regulation problem in distribution networks.

[0003] Currently, voltage control methods in active distribution networks (ADNs) are mainly divided into three types: centralized control, distributed control, and local control. Centralized control transmits voltage and power data from the distribution network to a central controller for global optimization. While centralized control can achieve overall system optimization, it is highly dependent on communication infrastructure, and the entire system may be paralyzed if the central controller fails. Distributed control achieves overall coordination through local optimization via communication and information exchange between adjacent nodes. This method has a certain degree of robustness but still relies on parts of the communication network, and therefore may be affected by communication delays or failures. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a data-driven adaptive droop voltage control method.

[0005] The objective of this invention is achieved through the following technical solution: a data-driven adaptive droop voltage control method, which includes the following steps:

[0006] S1. Obtain time-series data of photovoltaic power output and load demand, and normalize the data.

[0007] S2. Clustering algorithms are used to extract multiple typical daily scenarios from the processed time-series data;

[0008] S3. For each typical operating day scenario, establish an optimal voltage control model with the objectives of minimizing voltage deviation and minimizing reactive power cost; solve the optimal voltage control model to obtain the optimal reactive power command for each photovoltaic inverter, and construct a voltage-reactive power sample dataset consisting of local voltage and the corresponding optimal reactive power command.

[0009] S4. For each photovoltaic inverter, a piecewise linear droop control curve is fitted using the Bayesian information criterion-piecewise linear regression algorithm based on the voltage-reactive power sample dataset. The number of inflection points, the position of the inflection points, and the slope of each segment of the piecewise linear droop control curve are determined by the Bayesian information criterion-piecewise linear regression algorithm, and satisfy the constraints of monotonically decreasing, continuity, and stability.

[0010] S5. Deploy the fitted droop control curve to the local controller of each photovoltaic inverter. Each photovoltaic inverter obtains the reactive power command to be output by querying or calculating the droop control curve based on the real-time voltage measurement value of its grid connection point, and executes the command to achieve decentralized voltage control without communication dependence.

[0011] Specifically, S1 includes,

[0012] The time series data is normalized using the following formula:

[0013] ;

[0014] In the formula, Per-unit data for photovoltaic or load applications; This refers to the raw power data of photovoltaic systems or loads. This refers to the maximum power value in the corresponding year's data;

[0015] The photovoltaic output and load power are mapped to the [0,1] interval by standardization.

[0016] Specifically, S2 includes calculating the average silhouette coefficient of all sample points under different cluster numbers, selecting the cluster number with the largest average silhouette coefficient as the optimal cluster number; using the K-means algorithm to cluster the time series data under the optimal cluster number, and taking the time series curve corresponding to each cluster center as the typical daily scenario of that class.

[0017] Specifically, the objective function of the optimal voltage control model in S3 is:

[0018] ;

[0019] In the formula, This is the reactive power vector for all photovoltaic inverter nodes configured in the system. and These are the relaxation variable vectors corresponding to the upper and lower limits of the node voltage constraints, respectively; , , All are diagonal weighted matrices, where the diagonal elements are non-negative weight coefficients. Used to measure the adjustment cost of the inverter's reactive power output. and These are used to penalize the degree of use of voltage upper and lower limit slack variables, respectively.

[0020] Specifically, the constraints of the optimal voltage control model include power flow constraints of distribution network branches, second-order cone relaxation constraints, photovoltaic inverter operation constraints, and node voltage safety constraints.

[0021] Specifically, S4 includes,

[0022] Based on the gradient change of the voltage-reactive power sample dataset, an initial set of inflection points is determined;

[0023] For each data interval divided by adjacent inflection points, the least squares method is used to fit a linear model, and a continuity constraint is applied to ensure that the predicted values ​​of adjacent segments are equal at the connection points.

[0024] The sum of squared residuals of the overall fit is calculated, and the Bayesian information criterion is introduced to evaluate and determine the optimal number of inflection points.

[0025] Solve for the slope of each linear segment of the piecewise linear droop control curve, and apply stability constraints that make the voltage-reactive power curve monotonically decreasing and satisfy Lipschitz continuity.

[0026] Specifically, the monotonically decreasing stability constraint requires that the slope of each linear segment of the piecewise linear droop control curve be negative.

[0027] Specifically, after the photovoltaic inverter performs voltage regulation based on the reactive power command, a steady-state convergence determination step is also included:

[0028] Calculate the voltage difference before and after adjustment. If the absolute value of the difference is less than the preset judgment threshold, the system is determined to be stable and the adjustment at the current moment ends. Otherwise, the adjusted node voltage is used as the new real-time voltage measurement value and re-inputted into the piecewise linear droop control curve for iterative adjustment until the convergence condition is met.

[0029] The present invention has the following advantages:

[0030] 1. The control method of this invention requires no communication and approximates the optimal performance of centralized control. Traditional centralized control relies on real-time communication and global measurement, which poses risks of single-point failure and communication delay. This invention embeds the centralized optimization results into the local droop curve, allowing each inverter to achieve a near-globally optimal reactive power response using only local voltage measurements. It achieves voltage regulation effects similar to centralized optimization under completely communication-free conditions, while simultaneously improving online calculation efficiency by hundreds of times.

[0031] 2. This invention extracts typical day data based on optimal clustering, achieving year-round generalization capability with minimal data volume. It employs K-means clustering guided by silhouette coefficients to automatically determine the optimal number of clusters, extracting the most representative typical day scenarios from real-world data throughout the year. Control curves trained on a small number of typical days achieve results highly similar to those trained on full data in continuous simulations throughout the year, significantly reducing the amount of training data and the burden of offline computation.

[0032] 3. The personalized droop curve of this invention has strong adaptability. Employing the BIC-PLR algorithm, it automatically determines the optimal number, location, and slope of each segment of the droop curve for each inverter, achieving precise matching with the node electrical characteristics. The fitting residual is strictly controlled within ±0.004 pu, significantly outperforming the fixed-inflection-point method. Even under scenarios with severe photovoltaic and load fluctuations, it can strictly control the entire grid voltage within a safe range. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the adaptive droop voltage control method of the present invention;

[0034] Figure 2 This is a graph showing the silhouette coefficient as a function of the number of clusters.

[0035] Figure 3 This is a diagram of a radial power distribution network with N nodes.

[0036] Figure 4 This is a schematic diagram of the local voltage control process for the VQ droop curve.

[0037] Figure 5 A schematic diagram of an IEEE 34-node test system;

[0038] Figure 6 A schematic diagram of the normalized curve for annual photovoltaic power output;

[0039] Figure 7 A schematic diagram of the normalized curve for annual load data;

[0040] Figure 8 This is a schematic diagram of the control curve fitted by the adaptive droop voltage control method of the present invention;

[0041] Figure 9 Fit a residual distribution histogram for all nodes in the network;

[0042] Figure 10 This is a diagram showing the comparison of the average absolute error of all nodes in the network.

[0043] Figure 11 This is a schematic diagram of the voltage curve under no voltage control.

[0044] Figure 12 This is a schematic diagram of the voltage curve under the voltage control method of the present invention;

[0045] Figure 13 This is a schematic diagram of the voltage curve under the centralized optimal voltage control method.

[0046] Figure 14 The voltage curve is shown under traditional standard voltage droop control.

[0047] Figure 15 This is a schematic diagram of the typical daily average total reactive power control cost;

[0048] Figure 16 A schematic diagram showing the absolute deviation between reactive power and the centralized optimal setpoint.

[0049] Figure 17 This is a schematic diagram comparing the daily average voltage deviation throughout the year under different training strategies. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0051] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0052] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0053] The present invention will be further described below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0054] like Figures 1 to 17 As shown, a data-driven adaptive droop voltage control method includes the following steps:

[0055] S1. Obtain time-series data of photovoltaic power output and load demand, and normalize the data.

[0056] In this embodiment, annual photovoltaic power generation and load time-series data collected in a certain region are used as the research basis. The data sampling interval is 5 minutes, and 288 data points are recorded every day throughout the year. Let the photovoltaic active power output and load power at time t be respectively... and The time series data is normalized using the following formula:

[0057] ;

[0058] In the formula, For per-unit data of photovoltaic or load, This refers to the raw power data of photovoltaic systems or loads. This refers to the maximum power value in the corresponding year's data;

[0059] By standardizing the photovoltaic output and load power to the [0,1] interval, the differences in dimensions and scales are eliminated while maintaining the original time series trend. Based on this, the photovoltaic and load time series data for day i can be uniformly represented as a single feature vector.

[0060] ;

[0061] This vector fully characterizes the time-series characteristics of photovoltaic output and load demand changes over time within a single day.

[0062] S2. Clustering algorithms are used to extract multiple typical daily scenarios from the processed time-series data;

[0063] In this embodiment, by cluster extraction, the analysis based on annual photovoltaic and load data is simplified to analysis using only photovoltaic and load data from a few typical days that are sufficient to represent the characteristics of the annual data. Specifically, S2 includes:

[0064] The average silhouette coefficient of all sample points under different cluster numbers is calculated as follows:

[0065] First, calculate the average distance between sample point i and other sample points within its cluster, denoted as . :

[0066] ;

[0067] In the formula, The cluster to which sample point i belongs; This represents the number of samples in the cluster. The distance between sample point i and sample point j;

[0068] Then, the average distance between sample point i and all sample points in its nearest neighbor cluster is calculated, denoted as . Its definition is:

[0069] ;

[0070] In the formula, C is the divisor. Other clusters besides the one mentioned above; the silhouette coefficient of sample point i is defined as:

[0071] ;

[0072] In the formula, The profile coefficient has a value range of [-1, 1]. When the value is close to 1, it indicates that sample point i has a high similarity to samples within its own cluster, while also exhibiting good distinguishability from other clusters; when... When the value is close to 0, it indicates that the sample is located near the boundary of different clusters; when... A negative value indicates that the sample may have been assigned to an inappropriate cluster.

[0073] The cluster number with the largest average silhouette coefficient is selected as the optimal cluster number. To evaluate the overall clustering effect under a given cluster number k, the average silhouette coefficient of all sample points is calculated as the evaluation index. By comparing and analyzing the average silhouette coefficients under different cluster numbers, the comprehensive performance of the clustering results in terms of intra-cluster compactness and inter-cluster separation can be quantitatively evaluated. Within a certain range, the silhouette coefficients for different numbers of clusters are calculated and compared, such as... Figure 2 As shown, it can be observed that the average silhouette coefficient reaches its maximum value when the number of clusters is 5, indicating that the clustering results at this point achieve an optimal balance between maintaining intra-cluster similarity and inter-cluster discriminability. Therefore, this embodiment selects a clustering number of... The optimal number of clusters for annual photovoltaic and load data is used as the basis for subsequent typical daily clustering and representative operation scenario construction.

[0074] The K-means algorithm is used to cluster the time series data at the optimal number of clusters, and the time series curve corresponding to each cluster center is used as the typical daily scenario of that cluster.

[0075] Let the annual photovoltaic and load time series dataset be:

[0076] ;

[0077] In the formula, Let be the feature vector corresponding to day i; d is the feature dimension;

[0078] The K-means algorithm iteratively updates the cluster centers and sample affiliations. Its objective function can be expressed as minimizing the sum of squared errors within each cluster, i.e.:

[0079] ;

[0080] In the formula, r represents the center vector of the j-th cluster; ij Let be the resistance of any line (i,j); The sample attribution indicator variable is defined as follows:

[0081] ;

[0082] During the clustering process, the algorithm first randomly initializes cluster centers, and then sequentially performs two steps: sample allocation and cluster center update, until the clustering results converge or the maximum number of iterations is reached. Ultimately, the cluster centers in each class can be regarded as the average feature of all samples in that class, representing the typical characteristics of the corresponding operating scenario.

[0083] Based on the above K-means clustering results, this embodiment uses the photovoltaic and load time series curves corresponding to the cluster centers of each cluster as the typical operating days of that cluster, thereby constructing a representative scenario of the annual operating status, as follows:

[0084] Input: Normalized time-series dataset of photovoltaic power and load for the whole year ;

[0085] Output: Maximum number of clusters Typical daily scene set , Let be the cluster center of the i-th class.

[0086] initialization: Maximum average profile coefficient From the number of candidate clusters arrive ;

[0087] Execute the K-means algorithm on the dataset Divide into k clusters;

[0088] Each sample in the dataset Calculate the average distance from sample i to other samples in the same cluster. ;

[0089] Calculate the average distance from sample i to all samples in the nearest neighbor cluster. ;

[0090] Calculate the silhouette coefficient of sample i;

[0091] Calculate the average silhouette coefficient of the entire sample under the current k:

[0092] ;

[0093] if Update the maximum profile coefficient: Record the current optimal cluster number: Save the current cluster centers as a typical day set: .

[0094] This embodiment uses silhouette coefficients to automatically determine the optimal number of clusters and employs K-means clustering to extract a small number of typical daily scenarios. This significantly reduces the computational complexity of offline optimization and curve training while ensuring the strong generalization ability of the control strategy throughout the year, forming the foundation for achieving efficient data-driven operations.

[0095] S3. For each typical operating day scenario, establish an optimal voltage control model with the objectives of minimizing voltage deviation and minimizing reactive power cost; solve the optimal voltage control model to obtain the optimal reactive power command for each photovoltaic inverter, and construct a voltage-reactive power sample dataset consisting of local voltage and the corresponding optimal reactive power command.

[0096] In this embodiment, an offline centralized optimization algorithm is used to calculate the optimal reactive power compensation for different typical solar inverters, in order to minimize the voltage deviation of the entire system. The specific method is as follows:

[0097] First, establish an active distribution network power flow model:

[0098] Suppose there exists an active distribution network with N nodes, and all its nodes are represented as a set. And represent all lines as ,in .in This refers to the set of nodes configured with photovoltaic inverters. For each node... Inverter reactive power output As the main control variable, active power output Determined by the photovoltaic output curve. The net power injected at a node is determined jointly by photovoltaic power generation and load, expressed as:

[0099] ;

[0100] ;

[0101] In the formula, , The active and reactive power outputs of the photovoltaic inverter at node i; , Let i be the active and reactive power demand of the load at node i; For nodes Injected active power; node Injected reactive power;

[0102] Node 0 represents the reference node, and the remaining nodes are load nodes or distributed power supply access nodes. For example... Figure 3 As shown, the power flow model of the distribution network is a tree topology containing N-1 lines. The voltage magnitude at any node i is represented by V. i Similarly, using , Let r represent the injected power at node i. The resistance and reactance of any line (i,j) are represented by r. ij x ij Similarly, P represents... ij Q ij This represents the power transmitted from node i to node j;

[0103] For each line The DistFlow equation adapted to a tree-like distribution network structure can be given as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] In the formula, This represents the active power transmitted from node i to node j. This refers to all nodes in the network that are connected to node j and are on the side of node j that are furthest from the balancing node; The square of the line current amplitude; This represents the active power transmitted from node j to node k. The reactive power transmitted from node i to node j; This represents the reactive power transmitted from node j to node k. Let be the voltage at node i.

[0108] Then, an optimal voltage control model is constructed, with the objective function being:

[0109] ;

[0110] In the formula, This is the reactive power vector for all photovoltaic inverter nodes configured in the system. and These are the relaxation variable vectors corresponding to the upper and lower limits of the node voltage constraints, respectively. They are used to relax the voltage constraints under extreme operating conditions or when reactive power regulation capability is limited, so as to ensure the feasibility of the optimization problem. , , All are diagonal weighted matrices, where the diagonal elements are non-negative weight coefficients. Used to measure the adjustment cost of inverter reactive power output, in order to avoid unnecessary reactive power support. and These are used to penalize the degree of use of voltage upper and lower limit slack variables, respectively. The weights corresponding to the slack variables are significantly greater than the reactive power output weights, so as to ensure that slack variables are only activated when voltage constraints cannot be met, thereby prioritizing the safety of distribution network voltage operation.

[0111] The constraints of the optimal voltage control model include:

[0112] Distribution network branch power flow constraints:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] In the formula, and The squares of the voltage magnitudes at nodes i and j; It is the square of the line current amplitude.

[0118] Second-order cone relaxation constraint:

[0119] ;

[0120] Photovoltaic inverter operating constraints:

[0121] ;

[0122] ;

[0123] In the formula, Contributing to photovoltaic power generation; The reactive power output of the photovoltaic inverter is used as the main control variable. This refers to the rated apparent power capacity of the inverter. and These represent the lower and upper limits of the inverter's reactive power output, respectively. .

[0124] Node voltage safety constraints:

[0125] ;

[0126] ;

[0127] ;

[0128] In the formula, and These are the lower and upper limits of the square of the node voltage magnitude, respectively; and These are the slack variables for the lower and upper voltage limits, respectively. A large penalty coefficient is applied to these two variables in the objective function to ensure that only minor voltage exceedances are allowed when necessary. The voltage at the slack node is set to a per-unit value of 1 p.u.

[0129] Finally, the centralized voltage optimization problem is solved, generating a dataset for training the data-driven model. Local voltage-optimal reactive power (VQ) sample pairs are generated by centralized optimal power flow calculations.

[0130] For any photovoltaic inverter node i in an active distribution network, extract its local node voltage amplitude at different times under all operating scenarios. And the optimal reactive power reference command allocated by the centralized optimization model. Based on this, an offline training sample set for the photovoltaic inverter is constructed:

[0131] ;

[0132] In the formula, N is the total number of valid training samples.

[0133] S4. For each photovoltaic inverter, a piecewise linear droop control curve is fitted using the Bayesian information criterion-piecewise linear regression algorithm based on the voltage-reactive power sample dataset. The number of inflection points, the position of the inflection points, and the slope of each segment of the piecewise linear droop control curve are determined by the Bayesian information criterion-piecewise linear regression algorithm, and satisfy the constraints of monotonically decreasing, continuity, and stability.

[0134] This embodiment is based on the optimal voltage-reactive power data obtained through centralized SOCP optimization. The BIC-PLR algorithm is used to train and generate personalized VQ droop control curves for each photovoltaic inverter in the system. This algorithm aims to automatically and accurately determine the number and location of inflection points, as well as the slope and intercept of each segment of the droop control curve for each inverter. The specific method is as follows:

[0135] First, based on the gradient changes in the voltage-reactive power sample dataset, an initial set of inflection points is determined. Considering that the transition of VQ sample points between the dead zone, linear regulation zone, and capacity saturation zone is usually accompanied by drastic changes in nonlinear gradients, this paper uses the gradient change method to capture the inflection point positions of the VQ droop control curve, and the initial set of inflection points is determined. The calculation formula is:

[0136] ;

[0137] In the formula, For local voltage datasets; This is the optimal reactive power compensation dataset corresponding to voltage. This gradient-based initialization method can effectively locate potential inflection regions of the drooping curve, thereby accelerating the convergence speed of subsequent optimization algorithms.

[0138] Subsequently, for adjacent inflection points (i.e. and For each data interval m divided into segments, a linear model is fitted using the least squares method. The linear regression equation within that segment is expressed as:

[0139] ;

[0140] In the formula, These are the predicted values ​​from piecewise linear regression; and and represent the slope and intercept of the regression line in the m-th segment, respectively; the objective of solving for the model parameters is to minimize the sum of squared residuals within this segment:

[0141] ;

[0142] To ensure the safe application of the spliced ​​multi-segment straight lines to the physical controller of a practical inverter, strict mathematical constraints are introduced to limit the optimization space. To prevent a step jump in reactive power output during inverter switching at inflection points, the predicted values ​​of adjacent segments at the connection points must be strictly equal to satisfy continuity constraints.

[0143] ;

[0144] This is the leftmost extreme point of the j-th inflection point; Let be the right limit point of the j-th inflection point.

[0145] To improve the control accuracy of weak voltage nodes and highly sensitive nodes, this invention further introduces a weighted piecewise linear regression mechanism based on the electrical sensitivity of the nodes.

[0146] Traditional piecewise linear regression methods assume that all node samples have equal importance during model training. However, in active distribution networks, different nodes exhibit significantly different voltage sensitivities to reactive power changes due to variations in line impedance, electrical distance, and topological location. Nodes located at feeder ends or in high-impedance areas are particularly prone to voltage fluctuations that can cause network-wide voltage exceedance issues. Therefore, this invention defines a node electrical sensitivity index as follows:

[0147] ;

[0148] In the formula, For nodes Voltage-reactive power sensitivity; For nodes The voltage; For nodes Reactive power injection. Normalized weighting coefficients are constructed based on node sensitivity:

[0149] ;

[0150] In the formula, Let be the weight coefficient of the i-th node, and introduce it into the piecewise linear regression objective function to construct the weighted sum of squared residuals:

[0151] ;

[0152] In the formula, This represents all sample points belonging to the j-th data segment. After calculating the total error of the piecewise linear regression model, to avoid overfitting or underfitting, BIC is introduced to evaluate and determine the optimal number of inflection points. Its calculation formula is:

[0153] ;

[0154] In the formula, n is the total number of VQ sample points in the original dataset; The total number of parameters to be calculated in the model represents the total number of parameters. Each linear regression segment includes two independent parameters: slope and intercept. By iteratively adjusting the number and position of inflection points and recalculating the BIC values ​​under different configurations, the model that minimizes the BIC value is selected as the optimal choice. Through this mechanism, voltage-sensitive nodes receive higher weights during curve training, thereby ensuring that the generated personalized VQ droop control curve prioritizes the voltage stability of critical nodes, improves the voltage regulation capability in weak node regions, and enhances the overall network voltage security and control robustness under complex operating scenarios.

[0155] To solve for the slope of each linear segment of the piecewise linear droop control curve, stability constraints are applied to ensure that the voltage-reactive power curve is monotonically decreasing and satisfies Lipschitz continuity. During iterative training, to ensure the closed-loop stability of the underlying non-incremental controller, the BIC-PLR algorithm mandates that the learned VQ curve satisfy monotonically decreasing and Lipschitz continuity characteristics. Therefore, a stability margin constraint is added when solving for the slope of each segment.

[0156] ;

[0157] ;

[0158] In the formula, The maximum absolute slope vector assigned to the VQ curve of each photovoltaic inverter, i.e. Defined as the maximum absolute value of the slope among all linear segments corresponding to node n; It is a symmetric positive definite matrix with all positive elements, and its specific value is uniquely determined by the feeder topology and line impedance parameters of the distribution network. This is the preset system stability margin constant; This is a column vector of all 1s that matches the dimension. This embodiment incorporates three constraints: continuity constraint; monotonically decreasing constraint; and stability margin constraint based on the Lipschitz condition to prevent local voltage oscillations; avoid reactive power surges during inverter switching at inflection points; and ensure the convergence of the distributed closed-loop control system.

[0159] The VQ control curve training algorithm based on BIC-PLR is as follows:

[0160] Input: Local voltage dataset Optimal reactive power compensation dataset The maximum absolute slope vector corresponding to each photovoltaic inverter The preset system stability margin constant ;

[0161] Output: Optimal set of breakpoints And the linear regression parameters for each segment:

[0162] ;

[0163] In the formula, This is the optimal set of breakpoints obtained after iterative optimization; This indicates the position of the j-th optimal breakpoint; This represents the optimal set of piecewise linear regression parameters. Let be the optimal slope of the m-th segment; Let M be the optimal intercept for m segments; M is the total number of segments.

[0164] Initialization: Set the maximum number of segments Convergence threshold , ,

[0165] Maximum absolute slope: ;

[0166] First, from For each candidate segment number up to k, the initial inflection point is first calculated using a gradient-based method; then, the iterative optimization process begins.

[0167] from Up to M, in each iteration, for each data interval under the current number of segments, the restricted least squares method is used to calculate the local linear regression parameters (slope and intercept) of that segment, and a continuity constraint is applied to ensure that the function values ​​of adjacent segments are strictly equal at the connection points; at the same time, a stability constraint is applied. That is, the slope of each segment must satisfy the monotonically decreasing condition and the Lipschitz continuity condition determined by the network topology and the preset margin.

[0168] After completing the parameter calculation for all segments, calculate the total sum of squared residuals of the current model across the entire dataset, and then calculate the Bayesian information criterion value based on these residuals and the number of model parameters. ;

[0169] If the current Bayesian information criterion value is less than the minimum criterion value already recorded. Then update the minimum criterion value. And save the current set of inflection points. and the corresponding piecewise regression parameters As the best candidate;

[0170] Repeat the above iterative process until the change in the Bayesian information criterion value between two consecutive iterations is less than the preset convergence threshold. until;

[0171] After all candidate segments have been traversed, the algorithm returns the optimal set of breakpoints that minimizes the Bayesian information criterion value, along with the corresponding linear regression parameters for each segment.

[0172] in, and This represents the slope boundary vector used in the training constraints. and They represent vectors respectively and The nth element corresponds to the nth node in the system.

[0173] This embodiment determines the optimal number of inflection points, inflection point locations, and the slope and intercept of each segment of the droop curve for each photovoltaic inverter, while satisfying the constraints of monotonically decreasing, continuous, and network stability. This algorithm enables precise matching of each control curve with the electrical characteristics of the nodes, achieving a significantly better fitting accuracy than the fixed inflection point method.

[0174] S5. Deploy the fitted droop control curve to the local controller of each photovoltaic inverter. Each photovoltaic inverter obtains the reactive power command to be output by querying or calculating the droop control curve based on the real-time voltage measurement value of its grid connection point, and executes the command to achieve decentralized voltage control without communication dependence.

[0175] In this embodiment, a piecewise linear local VQ control model is generated for each node photovoltaic inverter in the following form, and the linear regression equation within this piecewise segment is expressed as:

[0176] ;

[0177] During actual distribution network operation, each photovoltaic inverter deploys its own customized control model in the underlying local controller. The inverter only needs to collect the local voltage signal Z at the grid connection point in real time to directly substitute it into the aforementioned piecewise function to calculate the corresponding reactive power reference command. .

[0178] Unlike traditional droop control strategies that employ a uniform approach across the entire network with a fixed number of inflection points and a constant slope, this embodiment utilizes a personalized droop curve generated by the BIC-PLR algorithm. The number of inflection points, their distribution, and the control slope of each segment are all optimized based on a deep fitting of offline globally optimal data. To clearly illustrate the closed-loop feedback and interaction mechanism of this customized droop control curve in the actual voltage regulation process, this invention presents its control execution flow, as follows: Figure 4 As shown, the system first acquires and inputs the current real-time voltage signal at the grid connection point of the photovoltaic inverter. Then, this voltage state quantity is substituted into the customized piecewise linear droop control curve generated by the fitting process. Based on the precise matching of this customized curve to the local electrical characteristics, the required reactive power compensation command under the current operating condition is obtained through mapping calculation. The photovoltaic inverter injects or absorbs corresponding reactive power into the grid according to this instruction in order to perform local voltage regulation.

[0179] After the photovoltaic inverter performs voltage regulation, the change in reactive power will cause a physical response in the power grid. The system needs to calculate the power flow and compare the node voltage changes before and after regulation to determine steady-state convergence. If the absolute value of the voltage difference before and after regulation is less than the set judgment threshold (i.e., 10), the system will determine the convergence. -4If the voltage difference before and after adjustment is greater than or equal to 10, it indicates that the local grid voltage has stabilized within the allowable range after the inverter response, the iteration process at the current moment ends, and the final steady-state voltage after adjustment at the current moment is directly output; otherwise, if the voltage difference before and after adjustment is greater than or equal to 10, it indicates that the local grid voltage has stabilized within the allowable range, the iteration process at the current moment ends, and the final steady-state voltage after adjustment is directly output; -4 If pu indicates that the system has not reached a steady state, the system needs to read the node voltage updated by the grid response, use it as input again in the droop curve, and use the photovoltaic inverter to regulate the voltage again.

[0180] In existing technologies, the BIC-PLR algorithm is typically used only as a general data fitting method, with its main goal being to improve the fitting accuracy of piecewise linear models. However, in active distribution network voltage control scenarios, directly using traditional piecewise regression methods presents the following problems:

[0181] 1. The electrical positions of different nodes vary greatly, and a uniform fitting method is insufficient to reflect the differences in the impact of nodes on the overall network voltage stability;

[0182] 2. The fitted curve may have problems such as excessive slope and discontinuous segments, which can easily cause local oscillations in the inverter or system instability;

[0183] 3. Under different seasons and different combinations of photovoltaic output and load, the VQ relationship has obvious nonlinearity and scenario dependence, and the traditional fixed structure droop curve is difficult to take into account the year-round operating conditions;

[0184] 4. Traditional droop control parameters usually rely on manual experience to set, making it difficult to approximate the results of centralized optimization.

[0185] To address problem 1, this invention improves the control accuracy of weak-voltage and highly sensitive nodes by adding a weighted piecewise linear regression mechanism based on node electrical sensitivity. In this embodiment, the global optimization results of centralized optimal power flow are embedded into the local droop control curves of each photovoltaic inverter through offline training. This allows the inverter to output near-globally optimal reactive power using only local voltage measurements, completely eliminating the need for communication infrastructure. In actual operation, each inverter only needs to measure the grid connection point voltage in real time and quickly obtain reactive power commands through table lookup or linear calculation, without requiring online optimization or communication interaction. This approach offers advantages such as fast response, simple implementation, and high reliability. This framework effectively unifies the performance of distributed control and centralized optimization.

[0186] Implementation Cases

[0187] To verify the effectiveness and superiority of the proposed data-driven adaptive droop voltage control method, a comprehensive simulation analysis was conducted on an IEEE 34-node active distribution network test system. The simulation was based on a standard IEEE 34-node distribution feeder system with a nominal voltage level of 24.9 kV. To fully highlight the severity of voltage fluctuations under high-proportion renewable energy integration, the R / X ratio of the lines in the system was adjusted to... The substation's first-end node 0 serves as the balancing node, with a constant voltage of 1.0 pu. The remaining 33 nodes are all connected to photovoltaic inverters with a rated capacity of 9 kVA. Figure 5 The topology of the test system is shown, and the proposed data-driven adaptive droop voltage control method will be applied to all these photovoltaic nodes. Key parameters involved in the simulation are detailed in Table 1.

[0188] Table 1 Parameter Settings

[0189] parameter numerical values illustrate / p.u. 1.0 Balance node reference voltage 0.05 The proportion of random noise applied to the source load time series data / kVA 9 Rated apparent power capacity of photovoltaic inverters at each node / p.u. [0.95,1.05] Safety voltage boundary of load node / p.u. [-0.10,0.10] Reactive power output boundary of photovoltaic inverter / min 5 Sampling period 10 Maximum number of inflection points allowed <![CDATA[10 -3 ]]> Inflection threshold of the BIC-PLR optimization algorithm / p.u. <![CDATA[10 -4 ]]> Accuracy threshold for steady-state convergence determination in power flow iterative calculation

[0190] To obtain a high-quality sample dataset for learning and fitting local control strategies, one year's worth of real photovoltaic (PV) and load data for a specific region was used. After data normalization, 5% random white noise was added to simulate the spatial distribution differences in operating characteristics among different nodes. The per-unit processed annual PV and load data curves are shown below. Figure 6 and Figure 7 As shown in the figure. Subsequently, K-means clustering analysis was performed using the silhouette coefficient-based evaluation method to extract five representative typical daily scenarios. The photovoltaic output curves and load curves of the five extracted typical days are shown in the figure. Figure 8 and Figure 9 As shown. For these five typical operating scenarios, the MOSEK solver was used to solve the centralized optimal voltage control model, and the optimized optimal reactive power command and corresponding node voltage data were collected as a sample dataset.

[0191] After obtaining the centralized optimal voltage-reactive power data pairs, the BIC-PLR algorithm is used to train personalized piecewise linear VQ control curves for all 33 photovoltaic inverters in the system, excluding the reference node. In the algorithm parameter settings, the maximum allowable number of breakpoints is set to... The convergence threshold is set to Furthermore, during the piecewise linear regression process, continuity constraints are enforced at the breakpoints.

[0192] Figure 9The figure presents personalized control curves fitted from 33 nodes across the entire network. As shown in the figure, unlike traditional standard droop control with fixed parameters, these curves exhibit node specificity, with variations in the number and location of inflection points and the slope of each segment. A magnified view further reveals significant differences in the fine structure of the control curves at different nodes in areas of dense reactive response.

[0193] To evaluate the fitting accuracy of the proposed BIC-PLR algorithm, Figure 9 and Figure 10 A comprehensive statistical and comparative analysis was conducted on the fitting errors of 33 personalized droop control curves. The frequency distribution of the fitting residuals for all nodes is shown below. Figure 9 As shown, the residual is defined as the difference between the reactive power output value obtained from curve fitting and the optimal reactive power reference value obtained from centralized optimization. The figure shows that the vast majority of prediction residuals are strictly distributed within... Within the range of pu. This result demonstrates that the proposed algorithm has high accuracy in capturing the operational patterns of centralized optimization algorithms. Figure 10 The mean absolute error (MAE) of the proposed BIC-PLR algorithm across 33 nodes in the entire network was further compared with that of the traditional fixed inflection point fitting method. The comparison results show that the MAE of the BIC-PLR algorithm is consistently below 0.001 pu across all nodes, significantly lower than that of the traditional fixed-structure fitting method. This result fully validates the effectiveness of personalized VQ control curve fitting in improving local control accuracy.

[0194] To evaluate the voltage regulation effectiveness of the trained data-driven personalized droop control strategy, photovoltaic and load data from "Typical Day 3," one of the five typical days with the most severe source-load fluctuations, were selected as the test scenario. Four control scenarios were compared in the simulation. The data-driven VQ personalized droop control curve derived above was applied to the local photovoltaic inverter to provide reactive power support and regulate the node voltage.

[0195] Figure 11 This demonstrates the voltage distribution across 33 nodes without voltage control. Figure 12The results of voltage regulation after applying the proposed strategy are presented. In the two sub-figures, each curve represents the voltage evolution trajectory of a specific node over 24 hours. As can be seen from the figures, without voltage control, severe overvoltage occurred during the midday period due to high photovoltaic output, while undervoltage occurred in the evening due to increased load. It can be seen that after applying the proposed strategy, the system voltage was effectively suppressed and, in most cases, smoothly recovered to the normal operating range [0.95, 1.05] pu. This result fully demonstrates the effectiveness of the data-driven adaptive droop voltage control method of this invention.

[0196] To further verify the near-optimality of the proposed method, the proposed strategy is systematically compared with the centralized SOCP optimal control scheme and the traditional fixed parameter droop control in terms of voltage regulation effect, reactive power control cost, and reactive power command tracking accuracy. Figure 13 and Figure 14 The voltage variation curves under centralized optimization and standard droop control are shown respectively. As can be seen from the figures, compared with… Figure 11 Compared to the voltage-free control scenario, all three control methods significantly improved the system's voltage regulation capability. The centralized scheme provided the theoretically optimal voltage distribution, while the proposed method demonstrated a control effect highly similar to it, effectively maintaining the voltage within safe limits under most operating conditions. In contrast, traditional droop control, due to its fixed parameters and lack of personalized design, had relatively limited overall regulation effect. To further quantify the comparison, Table 2, using the centralized optimal setting as a benchmark, statistically analyzed the average voltage deviation of 33 nodes across the entire network over five consecutive typical days. The results show that the proposed method is superior to standard droop control in terms of deviation control, demonstrating a stronger ability to approximate the optimal solution.

[0197] Table 2 Comparison of average node voltage deviation under different control strategies

[0198] typical day Typical day 1 Typical day 2 Typical day 3 Typical day 4 Typical day 5 Standard droop control 0.14% 0.19% 0.24% 0.06% 0.19% Control method of the present invention 0.02% 0.05% 0.03% 0.01% 0.02%

[0199] Figure 15 The average total reactive power control cost was compared across five typical days. Although the reactive power consumption of the proposed strategy was slightly higher than that of the centralized optimal method during peak compensation periods, it still maintained a near-optimal economic operating level from an overall daily perspective. While fixed parameter droop control had the lowest reactive power cost, it came at the cost of sacrificing voltage regulation quality. Figure 16 This further demonstrates the absolute deviation between the reactive power output of the distributed control method and the optimal setpoint of the centralized method. The evolution over time. As shown in the figure, the reactive power tracking deviation of the proposed method is always strictly less than that of the fixed parameter droop control, indicating that it has better consistency with the centralized optimal reference command.

[0200] To evaluate the adaptability of the proposed data-driven droop control method under different operating conditions and to verify the effectiveness of the clustering strategy, a long-term continuous simulation test was carried out based on real photovoltaic-load time series data for 365 days throughout the year. Three different droop control curve training strategies were compared: (1) the strategy proposed in this invention, which is based on training based on 5 typical daily scenarios extracted by optimal clustering; (2) the annual data training strategy, which is based on training based on full data for 365 days throughout the year; and (3) the traditional standard droop control strategy, which is based on 2 fixed inflection points and a constant slope

[19] . Figure 17 The evolution of the system's daily average voltage deviation throughout the year under the three different strategies described above is shown, with the voltage deviation calculated based on the results of centralized optimal control.

[0201] Depend on Figure 17 It can be seen that the training strategy based on typical daily clustering has an overall voltage control performance that is highly similar to that of the training strategy based on year-round data, with only minor deviations occurring during periods of extremely drastic photovoltaic or load fluctuations. In contrast, the traditional standard droop control strategy consistently generates larger voltage deviations throughout the entire year's operating cycle, reflecting the insufficient adaptability of the fixed-parameter method in the face of complex and variable operating conditions.

[0202] The above verification results demonstrate that the clustering-based typical day extraction strategy proposed in this invention can maintain excellent voltage control performance while significantly reducing the amount of training data and computation. Only a small amount of typical training data is required to achieve control performance close to that of training with data from the entire year, achieving good adaptation to unknown and complex operating conditions throughout the year with lower computational cost. Furthermore, these results further verify the effectiveness and practical value of the proposed optimal clustering strategy.

[0203] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention, or modify it into equivalent embodiments, without departing from the scope of the present invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technology of the present invention without departing from the scope of the present invention are within the protection scope of the present invention.

Claims

1. A data-driven adaptive droop voltage control method, characterized in that: The method includes the following steps: S1. Obtain time-series data of photovoltaic power output and load demand, and normalize the data. S2. Clustering algorithms are used to extract multiple typical daily scenarios from the processed time-series data; S3. For each typical operating day scenario, establish an optimal voltage control model with the objectives of minimizing voltage deviation and minimizing reactive power cost; solve the optimal voltage control model to obtain the optimal reactive power command for each photovoltaic inverter, and construct a voltage-reactive power sample dataset consisting of local voltage and the corresponding optimal reactive power command. S4. For each photovoltaic inverter, a piecewise linear droop control curve is fitted using the Bayesian information criterion-piecewise linear regression algorithm based on the voltage-reactive power sample dataset. The number of inflection points, the position of the inflection points, and the slope of each segment of the piecewise linear droop control curve are determined by the Bayesian information criterion-piecewise linear regression algorithm, and satisfy the constraints of monotonically decreasing, continuity, and stability. S5. Deploy the fitted droop control curve to the local controller of each photovoltaic inverter. Each photovoltaic inverter obtains the reactive power command to be output by querying or calculating the droop control curve based on the real-time voltage measurement value of its grid connection point, and executes the command to achieve decentralized voltage control without communication dependence.

2. The data-driven adaptive droop voltage control method according to claim 1, characterized in that: S1 specifically includes, The time series data is normalized using the following formula: ； In the formula, Per-unit data for photovoltaic or load applications; This refers to the raw power data of the photovoltaic system or load. This refers to the maximum power value in the corresponding year's data; The photovoltaic output and load power are mapped to the [0,1] interval by standardization.

3. The data-driven adaptive droop voltage control method according to claim 1, characterized in that: S2 specifically includes: calculating the average profile coefficient of all sample points under different numbers of clusters, selecting the number of clusters with the largest average profile coefficient as the optimal number of clusters; using the K-means algorithm to cluster the time series data under the optimal number of clusters, and taking the time series curve corresponding to each cluster center as the typical daily scenario of that class.

4. The data-driven adaptive droop voltage control method according to claim 1, characterized in that: The objective function of the optimal voltage control model in S3 is: ； In the formula, This is the reactive power vector for all photovoltaic inverter nodes configured in the system. and These are the relaxation variable vectors corresponding to the upper and lower limits of the node voltage constraints, respectively; , , All are diagonal weighted matrices, where the diagonal elements are non-negative weight coefficients. Used to measure the adjustment cost of the inverter's reactive power output. and These are used to penalize the degree of use of voltage upper and lower limit slack variables, respectively.

5. The data-driven adaptive droop voltage control method according to claim 1, characterized in that: The constraints of the optimal voltage control model include power flow constraints of distribution network branches, second-order cone relaxation constraints, photovoltaic inverter operation constraints, and node voltage safety constraints.

6. The data-driven adaptive droop voltage control method according to claim 1, characterized in that: S4 specifically includes, Based on the gradient change of the voltage-reactive power sample dataset, an initial set of inflection points is determined; For each data interval divided by adjacent inflection points, the least squares method is used to fit a linear model, and a continuity constraint is applied to ensure that the predicted values ​​of adjacent segments are equal at the connection points. The sum of squared residuals of the overall fit is calculated, and the Bayesian information criterion is introduced to evaluate and determine the optimal number of inflection points. Solve for the slope of each linear segment of the piecewise linear droop control curve, and apply stability constraints that make the voltage-reactive power curve monotonically decreasing and satisfy Lipschitz continuity.

7. The data-driven adaptive droop voltage control method according to claim 6, characterized in that: The monotonically decreasing stability constraint mandates that the slope of each linear segment of the piecewise linear droop control curve be negative.

8. The data-driven adaptive droop voltage control method according to claim 6, characterized in that: After the photovoltaic inverter performs voltage regulation based on the reactive power command, a steady-state convergence determination step is also included: Calculate the voltage difference before and after adjustment. If the absolute value of the difference is less than a preset judgment threshold, the system is determined to be stable, and the adjustment at the current moment ends. Otherwise, the adjusted node voltage is used as the new real-time voltage measurement value and re-inputted into the piecewise linear droop control curve for iterative adjustment until the convergence condition is met.

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