Power distribution network voltage control method based on data-driven power flow and sensitivity analysis

Abstract

The invention discloses a power distribution network voltage control method based on data-driven power flow and sensitivity analysis, and the method comprises the steps: training a back propagation neural network (BPNN) according to the historical power flow operation data of a power distribution network, constructing a data-driven nonlinear power flow regression model, and achieving the power flow calculation independent of the line parameters of the power distribution network; according to the influence of the active and reactive changes of the node on the voltage amplitude, a voltage-active and voltage-reactive sensitivity matrix is obtained by using a least square (LS) method, and the matrix is used as a technical support for voltage control; a power distribution network voltage control model is constructed based on the obtained sensitivity analysis value, and effective control over the voltage of the power distribution network is achieved; and finally, verifying the effectiveness of the method provided by the invention through an IEEE33 node experiment.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network operation and control, and particularly relates to a novel distribution network voltage control method integrating data-driven power flow modeling technology and sensitivity analysis. Background Art

[0002] In recent years, with the continuous promotion of the dual-carbon goal, the structure of China's power system is gradually transforming into a new power system. However, with the access of more and more clean energy sources such as wind and solar, due to the characteristics of the volatility and randomness of their output power, the phenomena of power flow reverse transmission and voltage over-limit frequently occur in the entire distribution network, posing a severe challenge to the safe and reliable operation of the distribution network.

[0003] Power flow calculation, as the basis of voltage control, can effectively perceive the real-time operation state of the distribution network and analyze the sensitivity coefficient matrix by calculating the power equations of each node, thereby providing technical support for voltage control. The literature "Distributed Voltage Control of Distribution Networks with High Penetration of Photovoltaic" realizes distributed voltage control based on the voltage-active power and voltage-reactive power sensitivity matrices and utilizes the voltage regulation function of photovoltaic inverters. The literature "Active Distribution Network Dynamic Cluster Voltage Control Considering Node Power Reserve and GIN Centrality" establishes an active distribution network voltage control model based on the voltage sensitivity matrix and solves the model through the dynamic particle swarm optimization (D-PSO). The literature "Multi-Time Scale Voltage Control Method for Distribution Networks with High Proportion of Distributed Photovoltaic Considering Reactive Power Regulation of Converters" first studies the action mechanism of converter reactive power regulation on the distribution network voltage based on the voltage-reactive power sensitivity matrix, and proposes a multi-time scale voltage control method for distribution networks considering the reactive power regulation ability of converters. The above-mentioned literatures all achieve voltage control based on voltage sensitivity, and the acquisition of the sensitivity matrix often depends on power flow calculation and line parameters. However, for the actual distribution network, due to lack of maintenance and the fact that environmental factors will greatly affect the specific line parameters, it is difficult to obtain the line parameters of the actual distribution network, making it difficult to apply the above methods in practice.

[0004] To address this issue, the literature "A Real-time Voltage Optimization Control Method for Distribution Networks Based on Deep Reinforcement Learning" proposes a voltage control method for distribution networks based on multi-agent deep reinforcement learning. Through the interaction between multiple agents and the environment, voltage control without relying on specific line parameters is achieved. Based on this, the literature "Distribution Network Voltage Control Based on Integrated Experience Safety Reinforcement Learning" further models the safety operation constraints of the distribution network, formulating the constrained voltage control problem as a Markov decision process to ensure that the control strategy can meet the operation constraints of the distribution network. Both of the above methods achieve voltage control of the distribution network through reinforcement learning. However, this method has a high simulation environment cost, is complex to construct, and is prone to unstable training processes. We expect to obtain a method that can calculate the voltage sensitivity matrix without relying on specific line parameters and thereby achieve voltage control of the distribution network.

[0005] With the emergence of intelligent measurement devices, it has become possible to fit the mapping relationship between node power and voltage information through data-driven methods. The literature "Data-driven power flow linearization: A regression approach" uses partial least squares (PLS) and Bayesian (BYS) linear regression methods to construct a regression model for active and reactive power at distribution network nodes to node voltage and phase, verifying that this method can achieve power flow calculation in the distribution network without relying on specific line parameters. However, this paper does not consider the impact of data collinearity on the power flow solution. To address this issue, the literature "A data-driven approach to linearize power flow equations considering measurement noise" proposes an LS linearized power flow regression method based on complete orthogonal decomposition. The literature "Data based linear power flow model: investigation of a least-squares based approximation" combines the physical model with the data-driven method to achieve physical-data joint-driven power flow linear regression. Although the linear regression method can achieve power flow calculation in the distribution network, it often fails to capture the non-linear characteristics of the power flow equation, resulting in relatively large calculation errors.

[0006] First, to address the problem that the linear regression method is difficult to capture the non - linear characteristics of power flow equations, the present invention constructs a non - linear power flow regression model by fitting the power flow equations with BPNN. As a commonly used neural network at present, BPNN can approximate the power flow equations, and its back - propagation algorithm can be used to update the weights to improve the fitting ability of the model. Further, by constructing an equation between the voltage change and the node injection power change rate, the sensitivity coefficient matrix is obtained through LS, which is used to guide the voltage control of the distribution network. Thus, the voltage sensitivity matrix can be obtained without relying on the distribution network line parameters. Finally, a sensitivity - based voltage control model is constructed, and the voltage control of the distribution network is realized through photovoltaic inverters and energy storage. Summary of the Invention

[0007] The present invention aims to solve the problem of voltage fluctuations in distribution networks caused by the access of large - scale renewable energy sources such as wind energy and photovoltaic energy, so as to ensure the safe and stable operation of the distribution network. Traditional voltage control methods based on voltage sensitivity usually rely on complete and accurate line parameter information. However, in actual distribution networks, it is often difficult to obtain full - scale and high - precision line parameters. In recent years, although voltage control methods based on reinforcement learning can, to a certain extent, reasonably regulate the system voltage, these methods generally have problems such as high simulation environment construction costs, complex implementation, and unstable training processes, which limit their wide application in engineering. Therefore, this paper proposes a new distribution network voltage control method that combines data - driven power flow modeling and sensitivity analysis.

[0008] To solve the above - mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] A distribution network voltage control method based on data - driven power flow and sensitivity analysis, comprising the following steps:

[0010] S1: Train BPNN according to historical power flow operation data to construct a data - driven non - linear power flow regression model to achieve power flow calculation without relying on distribution network line parameters;

[0011] S2: Establish the relationship between the node voltage magnitude change and the node injection power change, and based on the constructed data - driven non - linear power flow regression model, use the least - squares method LS to analyze the sensitivity of voltage - reactive power and voltage - active power;

[0012] S3: Based on the sensitivity analysis, build a distribution network voltage control model, and realize the voltage control of the distribution network by reasonably controlling the charge and discharge of energy storage and photovoltaic inverters through this model.

[0013] In step S1, it includes the following steps:

[0014] In Step 1.1, the power flow operation equations in polar coordinates are introduced, and power flow operation data are generated based on node loads and the output of wind and solar power.

[0015] In Step 1.2, a nonlinear power flow regression model of the distribution network based on BPNN is constructed, and historical power flow operation data are divided into a training set and a test set for training and performance testing.

[0016] In Step 1.1, the polar coordinate equation is as follows:

[0017]

[0018] In the formula, i is the node number of the distribution network, i = 1, 2,..., N; P i,DG , Q i,DG , P i,LD and Q i,LD are the distributed output and load magnitude of the node respectively; the magnitude of the distributed power output of the node is the sum of the wind and solar power output of the node; U i is the voltage magnitude of node i; θ ij is the voltage phase angle difference between node i and node j; g ij and b ij are the real part and imaginary part of the element in the i-th row and j-th column of the admittance matrix, that is, conductance and susceptance.

[0019] In Step 1.2, the proposed BPNN consists of an input layer, a hidden layer, and an output layer; the input layer is used to receive the original input data, the hidden layer is used to obtain high-dimensional abstract features; the output layer is used to output the final calculation result; its training process is divided into two stages, namely forward and backward propagation; in the forward propagation stage, the input information is transmitted through the network, and the output of each layer is the input of the next layer; the backward propagation stage is used to update the weights of the network to reduce the error between the final output result of the model and the actual value;

[0020] The training process of BPNN includes the following steps:

[0021] Step (1) Data normalization processing:

[0022]

[0023] In the formula, z i represents the value before normalization; z i ′ represents the value after normalization, z max and z min represent the maximum and minimum values in the data sample;

[0024] Step (2) Network initialization:

[0025] Set the number of nodes in the network input layer, the number of nodes in the hidden layer, and the number of nodes in the output layer; the connection weights between the neurons in the input layer and the hidden layer, and between the hidden layer and the output layer; the number of nodes in the input layer is a, the number of nodes in the hidden layer is c, and the number of nodes in the output layer is b; the connection weight w between the output layer and the hidden layer sd , and the connection weight w between the hidden layer and the output layer du ; the threshold b of the hidden layer d , and the threshold v of the output layer u ;

[0026] Step (3) Calculate the output of the hidden layer:

[0027]

[0028] In the formula, h d is the output of the d-th neuron in the hidden layer; w sd is the connection weight between the s-th neuron in the input layer and the d-th neuron in the hidden layer; f is the activation function, generally the ReLU activation function, ReLU(Z) = max(Z, 0),

[0029] Step (4) Calculate the output of the output layer:

[0030]

[0031] In the formula, is the output of the u-th neuron in the output layer; w du is the connection weight between the d-th neuron in the hidden layer and the u-th neuron in the output layer; f is the activation function, the same as the activation function of the hidden layer;

[0032] Step (5) Update the weights according to the objective function:

[0033] Generally, the mean square error (MSE) is taken as the objective function, and its expression is as follows:

[0034]

[0035] In the formula, u is the u-th neuron in the output layer, and m represents the number of samples; represents the output value of the output layer, is the actual value;

[0036] For a given learning rate l_rate, the change in the weights from the output layer to the hidden layer can be calculated by the following formula:

[0037]

[0038] The change in the weights from the hidden layer to the input layer is:

[0039]

[0040] Then the update amount of the weight is as follows:

[0041]

[0042] Step (6) Threshold update:

[0043] The threshold update is similar to the weight update. The calculation formula for the threshold update of the output layer is as follows:

[0044]

[0045] Then the update amount of the weight is as follows:

[0046]

[0047] Based on the above, the present invention uses the node wind and light output and the load size as the input of the model; the node voltage amplitude and phase angle as the output, constructs a power flow regression model based on BPNN; and divides the historical power flow operation data into a training set and a test set, and trains and tests the performance of the BPNN model.

[0048] In step S2, the following steps are included:

[0049] In step 2.1, establish a relationship between the change in voltage amplitude and the change in node injection power;

[0050] In step 2.2, based on the constructed data-driven non-linear power flow regression model, use the least squares method to realize the sensitivity matrix analysis.

[0051] In step 2.1, establish a relationship between the change in voltage amplitude and the change in node injection power, and a relationship between the current node voltage amplitude, the initial voltage, and the changes in node active power and reactive power:

[0052] The change in node voltage amplitude and the change in power injected into each node satisfy the following relationship:

[0053]

[0054] where N is the number of distribution network nodes; ΔU N×1 is the change matrix of the voltage amplitude of each node; ΔP N×1 , ΔQ N×1 are the change matrices of the active power and reactive power injected into the nodes respectively; are the voltage-active and voltage-reactive sensitivity matrices respectively, and their magnitudes determine the influence of the changes in node active power and reactive power on the voltage amplitude;

[0055] Node voltage U IIn addition to being affected by its own initial voltage it is also related to the active power change ΔP J and reactive power change ΔQ J injected into each node. The relationship is as follows:

[0056]

[0057] In the formula, are the elements of the matrix in the I-th row and J-th column respectively.

[0058] In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method LS is used to realize the voltage-reactive power sensitivity analysis:

[0059] Step (1): Record the voltage and power of each node in the current state, control the active power change ΔP = 0, generate the reactive power change matrix ΔQ according to the changes in the wind and light output and load, and calculate the voltage change when the reactive power changes, that is, ΔU Q ;

[0060] Step (2): Use the least squares method LS to analyze the voltage-reactive power sensitivity matrix:

[0061] Construct the objective function, that is:

[0062]

[0063] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0064] Define the error vector:

[0065]

[0066] In the formula, e Q is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0067] Construct the normal equation:

[0068]

[0069] In the formula, F Q is the normal equation for the voltage-reactive power sensitivity matrix.

[0070] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0071]

[0072] Since ΔQ is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it by treating ΔQ as a constant matrix, and the voltage-reactive power sensitivity matrix is obtained as follows:

[0073]

[0074] In step 2.2, based on the constructed data-driven nonlinear power flow regression model, the least squares method LS is used to realize the analysis of voltage-active power sensitivity:

[0075] Step (1) Record the voltages and powers of each node in the current state, control the reactive power change amount ΔQ = 0, generate the active power change amount matrix ΔP according to the changes in the wind and light output and the load, and calculate the voltage change when the active power changes, that is, ΔU, through the trained BPNN power flow regression model P ;

[0076] Step (2), use the least squares method LS to analyze the voltage-active power sensitivity matrix:

[0077] To realize the sensitivity analysis using the least squares method LS, it is first necessary to construct an objective function, that is:

[0078]

[0079] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0080] Define the error vector:

[0081]

[0082] In the formula, e P is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0083] Construct the normal equation:

[0084]

[0085] In the formula, F P is the normal equation about the voltage-active power sensitivity matrix.

[0086] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0087]

[0088] Since ΔP is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it by treating ΔP as a constant matrix, and the voltage-active power sensitivity matrix is obtained as follows:

[0089]

[0090] In step S3, a distribution network voltage control model based on sensitivity analysis is constructed as follows:

[0091] With the aim of improving voltage quality and system operation economy, the objective function is:

[0092]

[0093] In the formula, T is the regulation time; C a is the cost coefficient of voltage over-limit; ΔU i,t is the voltage offset of node i at time t; C ESS is the operation cost coefficient of energy storage; are the charging power and discharging power of the Bth energy storage within time t respectively; C p , C q are the cost coefficients of calling photovoltaic inverters; are the active power and reactive power provided by the Ath photovoltaic inverter within time t, that is, the active and reactive output powers of photovoltaic power generation;

[0094] The constraint conditions are:

[0095] U min ≤U≤U max (27)

[0096]

[0097] In the formula, U min , U max are the upper and lower limits of voltage amplitude, generally set to 0.95 - 1.05 times of the rated voltage; is the square of the capacity of the Ath photovoltaic inverter, is the square of the active power and reactive power provided by the Ath photovoltaic inverter, that is, the square of the active and reactive output powers of photovoltaic power generation; P min , P max are the upper and lower limits of the charge and discharge power of energy storage; are the charging power and discharging power of the Bth energy storage within time t respectively; is the remaining energy of the Bth energy storage at time t, is the remaining energy of the Bth energy storage at time t - 1, are the minimum energy and maximum energy of energy storage respectively, is the rated capacity of the Bth energy storage, η B is the charge and discharge efficiency of the Bth energy storage;

[0098] Based on the above method with sensitivity analysis as the foundation, a distribution network voltage control model is established; the distribution network voltage control is achieved through the reasonable control of energy storage charging and discharging and photovoltaic inverters, and Gurobi is used for solution.

[0099] A method for analyzing the sensitivity of voltage-reactive power and voltage-active power includes the following steps:

[0100] In step 2.1, a relationship between the change in voltage magnitude and the change in nodal injection power is constructed;

[0101] In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method is used to achieve the sensitivity matrix analysis.

[0102] In step 2.1, a relationship between the change in voltage magnitude and the change in nodal injection power, as well as a relationship between the current nodal voltage magnitude, the initial voltage, and the changes in nodal active power and reactive power are constructed:

[0103] The change in nodal voltage magnitude and the change in power injected into each node satisfy the following relationship:

[0104]

[0105] In the formula, N is the number of distribution network nodes; ΔU N×1 is the change matrix of voltage magnitudes of each node; ΔP N×1 , ΔQ N×1 are the change matrices of active power and reactive power injected into the nodes respectively; are the voltage-active power and voltage-reactive power sensitivity matrices respectively, and their sizes determine the influence of nodal active and reactive changes on the voltage magnitude;

[0106] The nodal voltage U I in addition to being affected by its own initial voltage is also related to the change in active power ΔP J injected into each node, and the change in reactive power ΔQ J , and its relationship formula is:

[0107]

[0108] In the formula, are the elements of the matrix in the I-th row and J-th column respectively.

[0109] In step 2.2, when using the least squares method LS to achieve the voltage-reactive power sensitivity analysis, specifically:

[0110] Step (1): Record the voltages and powers of each node in the current state, control the change in active power ΔP = 0, generate the reactive power change matrix ΔQ according to the changes in wind and light output and load, and calculate the voltage change when the reactive power changes, i.e., ΔU, through the trained BPNN power flow regression model. Q ;

[0111] Step (2): Use the least squares method LS to analyze the voltage-reactive power sensitivity matrix:

[0112] Construct the objective function, i.e.:

[0113]

[0114] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0115] Define the error vector:

[0116]

[0117] In the formula, e Q is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0118] Construct the normal equation:

[0119]

[0120] In the formula, F Q is the normal equation about the voltage-reactive power sensitivity matrix.

[0121] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0122]

[0123] Since ΔQ is a matrix of small changes and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it, regard ΔQ as a constant matrix, and obtain the voltage-reactive power sensitivity matrix as:

[0124]

[0125] In step 2.2, use the least squares method LS to achieve voltage-active power sensitivity analysis, specifically:

[0126] Step (1): Record the voltages and powers of each node in the current state, control the change in reactive power ΔQ = 0, generate the active power change matrix ΔP according to the changes in wind and light output and load, and calculate the voltage change when the active power changes, i.e., ΔU, through the trained BPNN power flow regression model. P ;

[0127] Step (2), use the least squares method LS to analyze the voltage-active power sensitivity matrix:

[0128] To implement sensitivity analysis using the least squares method LS, it is first necessary to construct an objective function, that is:

[0129]

[0130] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0131] Define the error vector:

[0132]

[0133] In the formula, e P is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0134] Construct the normal equation:

[0135]

[0136] In the formula, F P is the normal equation for the voltage-active power sensitivity matrix.

[0137] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0138]

[0139] Since ΔP is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it and regard ΔP as a constant matrix to obtain the voltage-active power sensitivity matrix as:

[0140]

[0141] A distribution network voltage control model based on sensitivity analysis, with the goal of improving voltage quality and system operation economy, then the objective function is:

[0142]

[0143] In the formula, T is the regulation time; C a is the voltage violation cost coefficient; ΔU i,t is the voltage offset of node i at time t; C ESS is the energy storage operation cost coefficient; are the charging power and discharging power of the Bth energy storage within time t respectively; C p 、C q are the cost coefficients for calling the photovoltaic inverter; It is the active power and reactive power provided by the A-th photovoltaic inverter within time t, that is, the active and reactive output powers of photovoltaic power generation.

[0144] The constraint conditions of the model are as follows:

[0145] U min ≤U≤U max (27)

[0146]

[0147] In the formula, U min 、U max are the upper and lower limits of the voltage amplitude, generally set to 0.95 - 1.05 times the rated voltage; is the square of the capacity of the A-th photovoltaic inverter, is the square of the active power and reactive power provided by the A-th photovoltaic inverter, that is, the square of the active and reactive output powers of photovoltaic power generation; P min 、P max are the upper and lower limits of the charge and discharge power of the energy storage; are respectively the charging power and discharging power of the B-th energy storage within time t; is the remaining energy of the B-th energy storage at time t, is the remaining energy of the B-th energy storage at time t - 1, are respectively the minimum energy and maximum energy of the energy storage, is the rated capacity of the B-th energy storage, η B is the charge and discharge efficiency of the B-th energy storage.

[0148] Compared with the prior art, the present invention has the following technical effects:

[0149] 1) The method proposed by the present invention does not depend on the complete and accurate distribution network topology structure and line parameters, but constructs the power flow mapping relationship by collecting the active power, reactive power and voltage data of the nodes and using the data-driven method. Compared with the traditional voltage control method based on the explicit model of the power flow equation or the sensitivity theory, it greatly reduces the dependence on the network frame information, enhances the feasibility of the method in the deployment and popularization in the actual complex distribution network, and is especially suitable for the distribution system environment with imperfect secondary equipment and incomplete parameters.

[0150] 2) Compared with the voltage control method based on reinforcement learning, the present invention adopts the strategy of combining data-driven and sensitivity analysis, and the training process is simpler and more stable, with lower computational complexity, avoiding the defects of high training cost and unstable convergence cost of the reinforcement learning model. In practical applications, only simple processing of the input data is required to achieve the rapid calculation of the power flow, obtain the sensitivity matrix, and further perform voltage control.

[0151] 3) On the basis of data - driven, the present invention introduces voltage sensitivity analysis, making the control strategy not only have good data adaptability, but also retain the physical interpretability of the voltage - power relationship in traditional power flow theory. By establishing a direct linearized approximation relationship between power perturbation and voltage response, the degree of influence of each node on the system voltage can be clarified, assisting in formulating precise control measures.

[0152] 4) The constructed control model based on voltage sensitivity can accurately analyze the impact of power changes on voltage, achieve higher - precision and higher - efficiency voltage regulation, and ensure the safe and stable operation of the distribution network under the access of a high proportion of distributed power sources. Moreover, the present invention makes full use of the advantages of data resources in a data - driven manner, without relying on traditional modeling means, and is more in line with the development needs of the digitalization and intelligentization of modern distribution networks. Brief Description of the Drawings

[0153] The present invention will be further described below in conjunction with the drawings and embodiments:

[0154] Figure 1 is the flow chart of the present invention;

[0155] Figure 2 is the schematic diagram of the BPNN neural network structure;

[0156] Figure 3 is the schematic diagram of the IEEE 33 - node topological structure. Detailed Embodiment

[0157] A distribution network voltage control method based on data - driven power flow and sensitivity analysis includes the following steps:

[0158] S1: Train the BPNN according to historical power flow operation data to construct a data - driven non - linear power flow regression model to achieve power flow calculation independent of distribution network line parameters;

[0159] S2: Establish the relationship between the change in node voltage amplitude and the change in node injection power, and based on the constructed data - driven non - linear power flow regression model, use the least - squares method LS to achieve the analysis of voltage - reactive and voltage - active sensitivities;

[0160] S3: Based on sensitivity analysis, build a distribution network voltage control model, and realize distribution network voltage control through the reasonable control of energy storage charge - discharge and photovoltaic inverters by this model.

[0161] In step S1, it includes the following steps:

[0162] In step 1.1, introduce the power flow operation equation in polar coordinates to generate power flow operation data with node load and wind - solar output;

[0163] In Step 1.2, a non-linear power flow regression model of the distribution network based on BPNN is constructed, and the historical power flow operation data is divided into a training set and a test set for training and performance testing.

[0164] In Step 1.1, the polar coordinate equation is:

[0165]

[0166] where i is the distribution network node number, i = 1, 2,..., N; P i,DG , Q i,DG , P i,LD and Q i,LD are the distributed output and load size of the node respectively; the distributed power output size of the node is the sum of the wind and light outputs of the node; U i is the voltage amplitude of node i; θ ij is the voltage phase angle difference between node i and node j; g ij and b ij are the real and imaginary parts of the element in the i-th row and j-th column of the admittance matrix, that is, conductance and susceptance.

[0167] In Step 1.2, the proposed BPNN consists of an input layer, a hidden layer, and an output layer; the input layer is used to receive the original input data, the hidden layer is used to obtain high-dimensional abstract features; the output layer is used to output the final calculation result; its training process is divided into two stages, namely forward and backward propagation; in the forward propagation stage, the input information is transmitted through the network, and the output of each layer is the input of the next layer; the backward propagation stage is used to update the weights of the network to reduce the error between the final output result of the model and the actual value;

[0168] The training process of BPNN includes the following steps:

[0169] Step (1) Data normalization processing:

[0170]

[0171] where z i represents the value before normalization; z i ' represents the value after normalization, z max and z min represent the maximum and minimum values in the data sample;

[0172] Step (2) Network initialization:

[0173] Set the number of nodes in the network input layer, the number of nodes in the hidden layer, and the number of nodes in the output layer; the connection weights between the neurons in the input layer and the hidden layer, and between the hidden layer and the output layer; the number of nodes in the input layer is a, the number of nodes in the hidden layer is c, and the number of nodes in the output layer is b; the connection weight w between the output layer and the hidden layer sd , and the connection weight w between the hidden layer and the output layer du ; the threshold b of the hidden layer d , and the threshold v of the output layer u ;

[0174] Step (3) Calculate the output of the hidden layer:

[0175]

[0176] In the formula, h d is the output of the d-th neuron in the hidden layer; w sd is the connection weight between the s-th neuron in the input layer and the d-th neuron in the hidden layer; f is the activation function, generally the ReLU activation function, ReLU(Z) = max(Z, 0),

[0177] Step (4) Calculate the output of the output layer:

[0178]

[0179] In the formula, is the output of the u-th neuron in the output layer; w du is the connection weight between the d-th neuron in the hidden layer and the u-th neuron in the output layer; f is the activation function, the same as the activation function of the hidden layer;

[0180] Step (5) Update the weights according to the objective function:

[0181] Generally, the mean square error (MSE) is taken as the objective function, and its expression is as follows:

[0182]

[0183] In the formula, u is the u-th neuron in the output layer, and m represents the number of samples; represents the output value of the output layer, is the actual value;

[0184] For a given learning rate l_rate, the change in the weights from the output layer to the hidden layer can be calculated by the following formula:

[0185]

[0186] The change in the weights from the hidden layer to the input layer is:

[0187]

[0188] Then the update amount of the weight is as follows:

[0189]

[0190] Step (6) Threshold update:

[0191] The threshold update is similar to the weight update. The calculation formula for the threshold update of the output layer is as follows:

[0192]

[0193] Then the update amount of the weight is as follows:

[0194]

[0195] Based on the above, the present invention uses the node wind and light output and the load size as the input of the model; the node voltage amplitude and phase angle as the output, constructs a power flow regression model based on BPNN; and divides the historical power flow operation data into a training set and a test set, and trains and performs performance tests on the BPNN model.

[0196] In step S2, the following steps are included:

[0197] In step 2.1, establish the relationship between the change in voltage amplitude and the change in node injection power;

[0198] In step 2.2, based on the constructed data-driven non-linear power flow regression model, use the least squares method to achieve the sensitivity matrix analysis.

[0199] In step 2.1, establish the relationship between the change in voltage amplitude and the change in node injection power, and the relationship between the current node voltage amplitude, the initial voltage, and the change in node active power and reactive power:

[0200] The change in node voltage amplitude and the change in power injected into each node satisfy the following relationship:

[0201]

[0202] In the formula, N is the number of distribution network nodes; ΔU N×1 is the change matrix of the voltage amplitude of each node; ΔP N×1 , ΔQ N×1 are the change matrices of the active power and reactive power injected into the nodes respectively; are the voltage-active and voltage-reactive sensitivity matrices respectively, and their magnitudes determine the influence of the change in node active and reactive power on the voltage amplitude;

[0203] Node voltage U IIn addition to being affected by its own initial voltage , it is also related to the active power change ΔP J and reactive power change ΔQ J injected into each node. The relationship is as follows:

[0204]

[0205] In the formula, are the elements of the matrix in the I-th row and J-th column respectively.

[0206] In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method LS is used to realize the voltage-reactive power sensitivity analysis:

[0207] Step (1) Record the voltage and power of each node in the current state, control the active power change ΔP = 0, generate the reactive power change matrix ΔQ according to the changes in the wind and light output and load, and calculate the voltage change ΔU when the reactive power changes through the trained BPNN power flow regression model Q ;

[0208] Step (2), use the least squares method LS to analyze the voltage-reactive power sensitivity matrix:

[0209] Construct the objective function, that is:

[0210]

[0211] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0212] Define the error vector:

[0213]

[0214] In the formula, e Q is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0215] Construct the normal equation:

[0216]

[0217] In the formula, F Q is the normal equation for the voltage-reactive power sensitivity matrix.

[0218] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0219]

[0220] Since ΔQ is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it by treating ΔQ as a constant matrix, and the voltage-reactive power sensitivity matrix is obtained as follows:

[0221]

[0222] In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method LS is used to realize the analysis of voltage-active power sensitivity:

[0223] Step (1) Record the voltages and powers of each node in the current state, control the reactive power change amount ΔQ = 0, generate the active power change amount matrix ΔP according to the changes in the wind and light output and the load, and calculate the voltage change when the active power changes through the trained BPNN power flow regression model, that is, ΔU P ;

[0224] Step (2), use the least squares method LS to analyze the voltage-active power sensitivity matrix:

[0225] To realize the sensitivity analysis using the least squares method LS, it is first necessary to construct an objective function, that is:

[0226]

[0227] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0228] Define the error vector:

[0229]

[0230] In the formula, e P is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0231] Construct the normal equation:

[0232]

[0233] In the formula, F P is the normal equation for the voltage-active power sensitivity matrix.

[0234] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0235]

[0236] Since ΔP is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it by treating ΔP as a constant matrix, and the voltage-active power sensitivity matrix is obtained as follows:

[0237]

[0238] In step S3, a distribution network voltage control model based on sensitivity analysis is constructed as follows:

[0239] The objective of the present invention is to improve voltage quality and system operation economy, so the objective function is:

[0240]

[0241] In the formula, T is the regulation time; C a is the voltage violation cost coefficient; ΔU i,t is the voltage offset of node i at time t; C ESS is the energy storage operation cost coefficient; are the charging power and discharging power of the Bth energy storage within time t respectively; C p , C q are the cost coefficients for calling photovoltaic inverters; is the active power and reactive power provided by the Ath photovoltaic inverter within time t, that is, the active and reactive output powers of photovoltaic power generation;

[0242] The constraint conditions are:

[0243] U min ≤U≤U max (27)

[0244]

[0245] In the formula, U min , U max are the upper and lower limits of the voltage amplitude, generally set to 0.95 - 1.05 times the rated voltage; is the square of the capacity of the Ath photovoltaic inverter, is the square of the active power and reactive power provided by the Ath photovoltaic inverter, that is, the square of the active and reactive output powers of photovoltaic power generation; P min , P max are the upper and lower limits of the energy storage charge and discharge power; are the charging power and discharging power of the Bth energy storage within time t respectively; is the remaining energy of the Bth energy storage at time t, is the remaining energy of the Bth energy storage at time t - 1, are the minimum energy and maximum energy of the energy storage respectively, is the rated capacity of the Bth energy storage, η B is the charge and discharge efficiency of the Bth energy storage;

[0246] Based on the above method with sensitivity analysis as the foundation, a voltage control model for the distribution network was established; the voltage control of the distribution network was achieved through the reasonable control of energy storage charging and discharging and photovoltaic inverters, and Gurobi was used for solution.

[0247] A method for analyzing the sensitivity of voltage-reactive power and voltage-active power includes the following steps:

[0248] In step 2.1, establish a relationship between the change in voltage magnitude and the change in node injection power;

[0249] In step 2.2, based on the established data-driven non-linear power flow regression model, use the least squares method to achieve the sensitivity matrix analysis.

[0250] In step 2.1, establish a relationship between the change in voltage magnitude and the change in node injection power, and a relationship between the current node voltage magnitude, the initial voltage, and the changes in node active power and reactive power:

[0251] The change in node voltage magnitude and the change in power injected into each node satisfy the following relationship:

[0252]

[0253] where N is the number of nodes in the distribution network; ΔU N×1 is the change matrix of each node voltage magnitude; ΔP N×1 , ΔQ N×1 are the change matrices of node injection active power and reactive power respectively; are the voltage-active power and voltage-reactive power sensitivity matrices respectively, and their magnitudes determine the influence of node active and reactive changes on the voltage magnitude;

[0254] The node voltage U I in addition to being affected by its own initial voltage , is also related to the active change amount ΔP J injected into each node, and the reactive change amount ΔQ J , and its relationship is:

[0255]

[0256] where are the elements of the matrix in the I-th row and J-th column respectively.

[0257] In step 2.2, when using the least squares method LS to achieve voltage-reactive power sensitivity analysis, specifically:

[0258] Step (1): Record the voltages and powers of each node in the current state, control the change in active power ΔP = 0, generate the reactive power change matrix ΔQ according to the changes in wind and light output and load, and calculate the voltage change when the reactive power changes, i.e., ΔU, through the trained BPNN power flow regression model. Q ;

[0259] Step (2): Use the least squares method LS to analyze the voltage-reactive power sensitivity matrix:

[0260] Construct the objective function, i.e.:

[0261]

[0262] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0263] Define the error vector:

[0264]

[0265] In the formula, e Q is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0266] Construct the normal equation:

[0267]

[0268] In the formula, F Q is the normal equation about the voltage-reactive power sensitivity matrix.

[0269] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0270]

[0271] Since ΔQ is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it, regard ΔQ as a constant matrix, and obtain the voltage-reactive power sensitivity matrix as:

[0272]

[0273] In step 2.2, use the least squares method LS to achieve voltage-active power sensitivity analysis, specifically:

[0274] Step (1): Record the voltages and powers of each node in the current state, control the change in reactive power ΔQ = 0, generate the active power change matrix ΔP according to the changes in wind and light output and load, and calculate the voltage change when the active power changes, i.e., ΔU, through the trained BPNN power flow regression model. P ;

[0275] Step (2), the least squares method LS is used to analyze the voltage-active power sensitivity matrix:

[0276] To implement sensitivity analysis using the least squares method LS, it is first necessary to construct an objective function, that is:

[0277]

[0278] In the formula, ||·|| is the norm of the matrix, and the Frobenius norm is generally used;

[0279] Define the error vector:

[0280]

[0281] In the formula, e P is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0282] Construct the normal equation:

[0283]

[0284] In the formula, F P is the normal equation for the voltage-active power sensitivity matrix.

[0285] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0286]

[0287] Since ΔP is a matrix of small change amounts and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it by treating ΔP as a constant matrix, and the voltage-active power sensitivity matrix is obtained as:

[0288]

[0289] A distribution network voltage control model based on sensitivity analysis, with the goal of improving voltage quality and system operation economy, the objective function is:

[0290]

[0291] In the formula, T is the regulation time; C a is the voltage violation cost coefficient; ΔU i,t is the voltage offset of node i at time t; C ESS is the energy storage operation cost coefficient; are the charging power and discharging power of the Bth energy storage within time t respectively; C p , C q are the cost coefficients for calling the photovoltaic inverter; $P_{A}(t)$ and $Q_{A}(t)$ are the active power and reactive power provided by the $A$-th photovoltaic inverter within time $t$, that is, the active and reactive output powers of photovoltaic power generation.

[0292] The constraint conditions are:

[0293] $U$ min $U_{min} \leq U \leq U_{max}$ max (27)

[0294]

[0295] In the formula, $U_{min}$ min and $U_{max}$ max are the upper and lower limits of the voltage amplitude, generally set to 0.95 - 1.05 times the rated voltage; $S_{A}^{2}$ is the square of the capacity of the $A$-th photovoltaic inverter, $P_{A}^{2}(t)+Q_{A}^{2}(t)$ is the square of the active power and reactive power provided by the $A$-th photovoltaic inverter, that is, the square of the active and reactive output powers of photovoltaic power generation; $P_{B}^{+}(t)$ min and $P_{B}^{-}(t)$ max are the upper and lower limits of the charge and discharge power of the energy storage; $P_{B}^{+}(t)$ and $P_{B}^{-}(t)$ are the charging power and discharging power of the $B$-th energy storage within time $t$ respectively; $E_{B}(t)$ is the remaining energy of the $B$-th energy storage at time $t$, $E_{B}(t - 1)$ is the remaining energy of the $B$-th energy storage at time $t - 1$, $E_{min}$ and $E_{max}$ are the minimum energy and maximum energy of the energy storage respectively, $C_{B}$ is the rated capacity of the $B$-th energy storage, $\eta_{B}$ B is the charge and discharge efficiency of the $B$-th energy storage.

[0296] Compared with the traditional sensitivity - based voltage control method that relies on complete power grid parameters, the present invention fits the power flow equation through BPNN. Only by collecting node power and voltage data can it realize the non - linear mapping from active and reactive power to voltage amplitude and phase angle, significantly reducing the dependence on the grid structure and line parameters and enhancing the applicability of the voltage control method in actual complex distribution networks. At the same time, compared with the problem that the reinforcement learning method requires a large number of simulation interactions and complex environment construction, this method directly analyzes the voltage sensitivity matrix through the least - squares method LS, avoiding the risks of unstable training and difficult convergence. The finally constructed control model based on voltage sensitivity can achieve precise regulation of node voltage, has theoretical physical interpretability and engineering feasibility, and provides effective technical support for improving the operation safety and intelligent level of renewable energy distribution networks.

[0297] Such as Figure 1As shown in the figure, a distribution network voltage control method based on data-driven power flow calculation and sensitivity analysis. First, the back propagation neural network (BPNN) is trained according to the historical power flow operation data of the distribution network to construct a data-driven non-linear power flow regression model, realizing power flow calculation without relying on the line parameters of the distribution network. Then, according to the influence of the active and reactive power changes of the nodes on the voltage amplitude, the least square (LS) method is used to obtain the voltage-active power and voltage-reactive power sensitivity matrices as the technical support for voltage control. Based on the obtained sensitivity analysis values, a distribution network voltage control model is constructed to effectively control the voltage of the distribution network. Finally, the effectiveness of the proposed method in this paper is verified by the IEEE 33-node experiment.

[0298] As Figure 2 shown, the BPNN power flow regression model proposed by the present invention consists of an input layer, a hidden layer, and an output layer. The inputs of the model are the active power, reactive power, and load of the nodes; the outputs of the model are the voltage amplitude and phase angle.

[0299] As Figure 3 shown, the example used in the present invention is an improved IEEE 33-node system. Photovoltaic power sources with a capacity of 1.2 MW are connected to nodes 16 and 32, and wind turbines with a capacity of 1.5 MW are connected to nodes 8, 21, and 25. The power factors of the wind and light are both 0.9. The loads of each node and the relevant wind and light data all come from the measured data of a certain area in the northwest of China.

[0300] The specific implementation process is as follows:

[0301] In step 1, the BPNN is trained according to the historical power flow operation data to construct a data-driven non-linear power flow regression model, specifically as follows:

[0302] In step 1.1, the power flow operation equation in polar coordinates is introduced, and the power flow operation data is generated with the node load and the wind and light output:

[0303] The power flow calculation of the power system is a method to simulate the distribution of parameters such as voltage, current, and power in the power network. It determines the stable operating point of the power network under a certain operating state by mathematically modeling and solving equations for each node of the power grid. Power flow calculation plays an important role in the operation of the power system. It can provide a scientific basis for power grid dispatching, safety analysis, optimal operation, fault handling, and planning and expansion, etc., to ensure the safe, economic, and efficient operation of the power system. The polar coordinate equation based on the physical model is:

[0304]

[0305] In the formula, i is the distribution network node number, i = 1, 2,..., N; P i,DG 、Qi,DG , P i,LD , and Q i,LD are the node distributed output and the load size respectively; the node distributed power output size is the sum of the node wind and light outputs; U i is the voltage amplitude of node i; θ ij is the voltage phase angle difference between node i and node j; g ij and b ij are the real and imaginary parts of the element in the i-th row and j-th column of the admittance matrix, that is, conductance and susceptance.

[0306] According to Equation (1) and the node wind and light outputs and load size, we can solve the node voltage amplitude and its phase angle, and thus use a data-driven method to learn the mapping relationship between the sizes of wind, light, and load and the node voltage and phase angle.

[0307] In Step 1.2, a nonlinear power flow regression model of the distribution network based on BPNN is constructed, and the historical power flow operation data is divided into a training set and a test set for training and performance testing:

[0308] BPNN is a multi-layer feedforward neural network trained by the error backpropagation algorithm. It is mainly used for problems such as function approximation, pattern recognition, and classification. Different from other neural network algorithms, BPNN can use the gradient descent method to adjust the weights and thresholds to minimize the mean square error between the actual output value and the expected value of the network.

[0309] The proposed BPNN consists of an input layer, a hidden layer, and an output layer; the input layer is used to receive the original input data, the hidden layer is used to obtain high-dimensional abstract features; the output layer is used to output the final calculation result. Its training process is generally divided into two stages, namely forward and backward propagation. In the forward propagation stage, the input information is transmitted through the network, and the output of each layer is the input of the next layer. The backward propagation stage is used to update the weights of the network to reduce the error between the final output result of the model and the actual value.

[0310] The training process of BPNN includes the following steps:

[0311] Step (1) Data normalization processing:

[0312]

[0313] In the formula, z i represents the value before normalization; z i ′ represents the value after normalization, z max and z min represent the maximum and minimum values in the data sample.

[0314] Step (2) Network initialization:

[0315] Set the number of nodes in the network input layer, the number of nodes in the hidden layer, and the number of nodes in the output layer; the connection weights between the neurons in the input layer and the hidden layer, and between the hidden layer and the output layer. The number of nodes in the input layer is a, the number of nodes in the hidden layer is c, and the number of nodes in the output layer is b; the connection weight w between the output layer and the hidden layer sd , and the connection weight w between the hidden layer and the output layer du ; the threshold b of the hidden layer d , and the threshold v of the output layer u .

[0316] Step (3) Calculate the output of the hidden layer:

[0317]

[0318] In the formula, h d is the output of the d-th neuron in the hidden layer; w sd is the connection weight between the s-th neuron in the input layer and the d-th neuron in the hidden layer; f is the activation function, and generally the ReLU activation function is adopted, ReLU(Z) = max(Z, 0),

[0319] Step (4) Calculate the output of the output layer:

[0320]

[0321] In the formula, is the output of the u-th neuron in the output layer; w du is the connection weight between the d-th neuron in the hidden layer and the u-th neuron in the output layer; f is the activation function, the same as the activation function of the hidden layer.

[0322] Step (5) Update the weights according to the objective function:

[0323] Generally, the mean square error (MSE) is taken as the objective function, and its expression is as follows:

[0324]

[0325] In the formula, u is the u-th neuron in the output layer, and m represents the number of samples; represents the output value of the output layer, is the actual value.

[0326] For a given learning rate l_rate, the change in the weights from the output layer to the hidden layer can be calculated by the following formula:

[0327]

[0328] The change in the weights from the hidden layer to the input layer is:

[0329]

[0330] Then the update amount of the weight is:

[0331]

[0332] Step (6) Threshold update:

[0333] The threshold update is similar to the weight update. The calculation formula for the threshold update of the output layer is as follows:

[0334]

[0335] Then the update amount of the weight is:

[0336]

[0337] Based on the above, the present invention uses the node wind and light output and the load size as the input of the model; the node voltage amplitude and phase angle as the output, and constructs a power flow regression model based on BPNN. And the historical power flow operation data is divided into a training set and a test set to train and perform performance testing on the BPNN model.

[0338] In step 2, according to the relationship between the node voltage amplitude change and the node injection power change, and the BPNN power flow regression model, LS is used to realize the sensitivity analysis of voltage-reactive power and voltage-active power, specifically as follows:

[0339] In step 2.1, construct the relationship formula between the node voltage amplitude change and the node injection power change, and the relationship formula between the current node voltage amplitude and the initial voltage and the node active power and reactive power changes:

[0340] The node voltage amplitude change and the power change injected into each node satisfy the following relationship:

[0341]

[0342] In the formula, N is the number of distribution network nodes; ΔU N×1 is the change matrix of the voltage amplitude of each node; ΔP N×1 , ΔQ N×1 are the change matrices of the active power and reactive power injected into the nodes respectively; are the voltage-active power and voltage-reactive power sensitivity matrices respectively, and their sizes determine the influence of the node active and reactive changes on the voltage amplitude.

[0343] The node voltage U I In addition to being affected by its own initial voltage , it is also related to the active power change amount ΔP injected into each node J, reactive power change ΔQ J is related, and its relationship is:

[0344]

[0345] In the formula, are respectively the elements of the matrix in the I-th row and J-th column.

[0346] In step 2.2, when implementing voltage-reactive power sensitivity analysis based on the constructed data-driven nonlinear power flow regression model using the least squares method LS, specifically:

[0347] Step (1) Record the voltage and power of each node in the current state, control the active power change ΔP = 0, generate the reactive power change matrix ΔQ according to the changes in wind-solar power output and load, and calculate the voltage change ΔU when the reactive power changes through the trained BPNN power flow regression model Q ;

[0348] Step (2), use the least squares method LS to analyze the voltage-reactive power sensitivity matrix:

[0349] Construct the objective function, that is:

[0350]

[0351] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0352] Define the error vector:

[0353]

[0354] In the formula, e Q is an N-dimensional vector, and N is the number of distribution network nodes;

[0355] Construct the normal equation:

[0356]

[0357] In the formula, F Q is the normal equation about the voltage-reactive power sensitivity matrix.

[0358] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0359]

[0360] Since ΔQ is a small change matrix and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it, regard ΔQ as a constant matrix, and obtain the voltage-reactive power sensitivity matrix as:

[0361]

[0362] In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method LS is used to realize the voltage-active power sensitivity analysis, specifically as follows:

[0363] Step (1) Record the voltage and power of each node in the current state, control the reactive power change amount ΔQ = 0, generate the active power change amount matrix ΔP according to the changes in the wind-solar output and load, and calculate the voltage change ΔU when the active power changes through the trained BPNN power flow regression model P ;

[0364] Step (2), use the least squares method LS to analyze the voltage-active power sensitivity matrix:

[0365] To realize the sensitivity analysis by using the least squares method LS, it is first necessary to construct an objective function, that is:

[0366]

[0367] In the formula, ||·|| is the norm of the matrix, and generally the Frobenius norm is used;

[0368] Define the error vector:

[0369]

[0370] In the formula, e P is an N-dimensional vector, and N is the number of nodes in the distribution network;

[0371] Construct the normal equation:

[0372]

[0373] In the formula, F P is the normal equation for the voltage-active power sensitivity matrix.

[0374] Take the derivative of both sides of the equation with respect to and set the derivative equal to zero to obtain:

[0375]

[0376] Since ΔP is a small change amount matrix and its determinant is close to zero, it is difficult to directly solve the normal equation; we simplify it, regard ΔP as a constant matrix, and obtain the voltage-active power sensitivity matrix as:

[0377]

[0378] This method utilizes the relationship between the change in node voltage and the change in power, and solves it through the least squares method LS, thereby quickly obtaining the voltage sensitivity matrix. Compared with the traditional physical method of deriving the Jacobian matrix relying on the parameters of the distribution network, this method does not require a complete network topology and accurate line parameters, significantly improving its applicability in actual distribution networks with incomplete parameters. Compared with the method of obtaining sensitivity based on optimization iteration, the least squares method LS is simple in calculation, fast in convergence speed, has higher stability and practicability, and can provide efficient and interpretable sensitivity support for voltage control strategies.

[0379] In step 3, a distribution network voltage control model based on sensitivity analysis is constructed as follows:

[0380] The objective of the present invention is to improve voltage quality and system operation economy, so the objective function is:

[0381]

[0382] In the formula, T is the regulation time; C a is the voltage violation cost coefficient; ΔU i,t is the voltage offset of node i at time t; C ESS is the energy storage operation cost coefficient; are the charging power and discharging power of the Bth energy storage within time t respectively; C p , C q are the cost coefficients for calling the photovoltaic inverter; is the active power and reactive power provided by the Ath photovoltaic inverter within time t, that is, the active and reactive output powers of photovoltaic power generation.

[0383] The constraint conditions are:

[0384] U min ≤U≤U max (27)

[0385]

[0386] In the formula, U min , U max are the upper and lower limits of the voltage amplitude, generally set to 0.95 - 1.05 times the rated voltage; is the square of the capacity of the Ath photovoltaic inverter, is the square of the active power and reactive power provided by the Ath photovoltaic inverter, that is, the square of the active and reactive output powers of photovoltaic power generation; P min , P max are the upper and lower limits of the energy storage charge and discharge power; are the charging power and discharging power of the Bth energy storage within time t respectively; is the remaining energy of the B-th energy storage at time t, is the remaining energy of the B-th energy storage at time t-1, are the minimum energy and maximum energy of the energy storage respectively, is the rated capacity of the B-th energy storage, η B is the charge-discharge efficiency of the B-th energy storage.

[0387] Based on sensitivity analysis, a distribution network voltage control model is built. The distribution network voltage control is realized by reasonably controlling the charge and discharge of the energy storage and the photovoltaic inverter.

[0388] The distribution network voltage control model constructed by the present invention based on data-driven sensitivity analysis aims to improve the voltage quality and enhance the system operation economy. The response relationship between voltage and power regulation is accurately described by the voltage sensitivity matrix, and then the precise control of the node voltage is realized. Relying on historical or real-time operation data, combining the BPNN and the least squares method LS sensitivity solution method, a control optimization framework with physical interpretability and practical implementability is constructed without relying on the complete power grid topology and line parameters. Compared with the traditional topology-based modeling method, this model has stronger robustness and adaptability; compared with the black-box control methods such as reinforcement learning, it performs better in terms of clear optimization objectives and controllable calculations. The objective function of the model comprehensively considers the minimization of voltage deviation and the minimization of operation cost, taking into account both voltage quality and system economy, and can realize a more practical and engineering-valued voltage control strategy.

[0389] The present invention aims to solve the problem of voltage fluctuations in the distribution network caused by the access of large-scale renewable energy such as wind energy and photovoltaic power, so as to ensure the safe and stable operation of the distribution network. Traditional voltage control methods based on voltage sensitivity usually rely on complete and accurate line parameter information. However, in actual distribution networks, it is often difficult to obtain full and high-precision line parameters. In recent years, although voltage control methods based on reinforcement learning can, to a certain extent, reasonably regulate the system voltage, these methods generally have problems such as high simulation environment construction costs, complex implementation, and unstable training processes, which limit their wide application in engineering. With the continuous popularization and deployment of intelligent measurement devices, data-driven methods have become an important means to achieve power flow calculation and voltage control. Therefore, this paper proposes a new type of distribution network voltage control method that combines data-driven power flow modeling and sensitivity analysis. This method uses BPNN to model the power flow equation and constructs a non-linear mapping relationship between node active and reactive power and voltage amplitude and phase angle. On this basis, by analyzing the relationship between voltage change and power change, LS is used to solve the voltage sensitivity matrix, and a voltage control model based on sensitivity is further established. This method not only effectively avoids the dependence on network parameters, but also has high modeling accuracy and good control performance, and can achieve efficient and reasonable regulation of the distribution network voltage.

[0390] Embodiment

[0391] The example used in the present invention is the improved IEEE 33-node system. Photovoltaic power sources with a capacity of 1.2 MW are connected to nodes 16 and 32, and wind turbines with a capacity of 1.5 MW are connected to nodes 8, 21, and 25. The wind and light power factors are both 0.9. The loads of each node and the relevant wind and light data are all from the measured data of a certain area in the northwest of China. Power flow operation data is generated through Matpower7.1, and the data samples are divided into a training set and a test set according to a ratio of 8:2. The time required for different methods is recorded during the training and testing processes.

[0392] To verify the accuracy of the BPNN power flow regression model, the present invention selects PLS, BYS, and support vector regression (SVR) as comparison models. The root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are used as evaluation indicators, and their expressions are as follows:

[0393]

[0394] In the formula, M is the number of samples; YV is the true value of the power flow output for the Vth test sample, is the estimated value of the power flow output for the Vth test sample. The smaller the evaluation index, the higher the accuracy of the model.

[0395] To verify the effectiveness of the voltage control method proposed in this paper, the present invention uses droop control, twin delayed deep deterministic policy gradient algorithm (TD3), and multi-agent twin delayed deep deterministic policy gradient (MATD3PG) as comparison methods, and records the average voltage deviation (the average voltage deviation is the average of the voltage deviations of each node at all times of a day), maximum voltage, minimum voltage, network loss, and average calculation time after voltage control by different methods. The results are shown in Table 7.

[0396] Table 1 Power flow regression accuracy of different methods

[0397]

[0398] Table 2 Comparison of time performance of different methods

[0399]

[0400] It can be seen from Table 1 that compared with PLS, BYS, and SVR, the RMSE of the voltage amplitude of the data-driven power flow regression method adopted by the present invention is reduced by 19.86%, 13.38%, and 8.53% respectively, the MAE is reduced by 24.59%, 34.41%, and 14.02% respectively, and the MAPE is reduced by 12.9%, 18.18%, and 6.89% respectively. This shows that the method of the present invention can better fit the power flow equation and achieve accurate calculation of the power flow. This is mainly because the backpropagation mechanism of BPNN enables it to update the parameters of the model according to the results of each training, so that the model can better learn the power flow regression task. It can be obtained from Table 2 that although the training time of BPNN is long, the online test time is significantly less than that of the traditional Newton-Raphson method. In practical applications, rapid and accurate calculation of the power flow can be achieved only after simple processing of the input data.

[0401] Table 3 Voltage-reactive power sensitivity matrix based on LS

[0402]

[0403] Table 4 Voltage-active power sensitivity matrix based on LS

[0404]

[0405]

[0406] Table 5 Voltage-Reactive Power Sensitivity Matrix Based on Physical Model

[0407]

[0408]

[0409] Table 6 Voltage-Active Power Sensitivity Matrix Based on Physical Model

[0410]

[0411]

[0412] By comparing the voltage sensitivity matrices obtained based on LS and physical models in Tables 3 - 6, it can be seen that the sensitivity matrix solved by the present invention has a small gap with the sensitivity matrix obtained based on the physical model. This indicates that the sensitivity matrix obtained by LS can be used to guide the subsequent voltage control of the distribution network. In addition, the reactive power sensitivity shows a positive value, indicating that the new energy output of the system is large, and there is a phenomenon of power supply exceeding demand, which shows that the voltage can be controlled by adjusting the reactive power.

[0413] Table 7 Performance Comparison of Different Voltage Control Methods

[0414]

[0415] From the perspective of the average voltage deviation, the control result of the method of the present invention is the best, only 0.0083 pu, lower than the droop control, TD3, and MATD3PG, indicating that it has stronger voltage regulation accuracy. In terms of the maximum voltage, the upper voltage limit after the control of this method is 1.0254 pu, significantly lower than the control results of MATD3PG and droop control, and can effectively suppress the problem of high voltage; in the dimension of the minimum voltage, this method can maintain the lower voltage limit of the system at 0.9854 pu, avoiding the low voltage situation in the TD3 method, further reflecting its comprehensive ability to suppress voltage fluctuations.

[0416] From the perspective of system network loss, the method of the present invention reduces the system energy loss to 47.53 MW·h, which is 4.3%, 14.47% and 11.75% lower than the other three methods respectively. It can be seen that the method of the present invention is superior to other methods in terms of economy. In addition, in terms of calculation efficiency, the average calculation time of the method of the present invention is 53.71 s, which is slightly higher than that of TD3 and MATD3PG, but significantly better than traditional droop control. Considering that this method does not depend on grid topology information and has good control performance, this calculation efficiency is acceptable in engineering practice and has the feasibility of deployment.

Claims

1. A method for controlling the voltage of a distribution network based on data-driven power flow and sensitivity analysis, characterized in that, It includes the following steps: S1: Train the BPNN according to the historical power flow operation data to construct a data-driven non-linear power flow regression model to achieve power flow calculation independent of the distribution network line parameters; S2: Establish the relationship between the change in node voltage amplitude and the change in node injection power, and based on the constructed data-driven non-linear power flow regression model, use the least squares method LS to achieve the analysis of the sensitivity of voltage-reactive power and voltage-active power; S3: Based on the sensitivity analysis, build a distribution network voltage control model, and realize the distribution network voltage control through the reasonable control of energy storage charging and discharging and photovoltaic inverters by this model.

2. The method according to claim 1, wherein In step S1, it includes the following steps: In step 1.1, introduce the power flow operation equation in polar coordinates to generate power flow operation data with node load and wind-solar output; In step 1.2, construct a non-linear power flow regression model of the distribution network based on BPNN, and divide the historical power flow operation data into a training set and a test set to train and perform performance testing on it.

3. The method according to claim 2, wherein In step 1.1, the polar coordinate equation is: where \(i\) is the node number of the distribution network, \(i = 1, 2,\cdots, N\); \(P\) i，DG , \(Q\) i，DG , \(P\) i，LD and \(Q\) i，LD are the distributed output and load magnitude of the node respectively; the magnitude of the distributed power output of the node is the sum of the wind and light outputs of the node; \(U\) i is the voltage magnitude of node \(i\); \(\theta\) ij is the voltage phase angle difference between node \(i\) and node \(j\); \(g\) ij and \(b\) ij are the real and imaginary parts of the \(i\)-th row and \(j\)-th column elements of the admittance matrix, that is, conductance and susceptance.

4. The method according to claim 2, wherein, In step 1.2, the proposed BPNN consists of an input layer, a hidden layer, and an output layer; the input layer is used to receive the original input data, the hidden layer is used to obtain high-dimensional abstract features; the output layer is used to output the final calculation result; Its training process is divided into two stages, namely forward and backward propagation; In the forward propagation stage, the input information is transmitted through the network, and the output of each layer is the input of the next layer; The backward propagation stage is used to update the weights of the network to reduce the error between the final output result of the model and the actual value; The training process of BPNN includes the following steps: Step (1) Data normalization processing: where z i represents the value before normalization; z i ′ represents the value after normalization, z max and z min represent the maximum and minimum values in the data sample; Step (2) Network initialization: Set the number of nodes in the network input layer, the number of nodes in the hidden layer, and the number of nodes in the output layer; the connection weights between the neurons in the input layer and the hidden layer, and between the hidden layer and the output layer; the number of nodes in the input layer is a, the number of nodes in the hidden layer is c, and the number of nodes in the output layer is b; the connection weight w between the output layer and the hidden layer sd , and the connection weight w between the hidden layer and the output layer du ; the threshold b of the hidden layer d , and the threshold v of the output layer u ; Step (3) Calculate the output of the hidden layer: where h d is the output of the d-th neuron in the hidden layer; w sd is the connection weight between the s-th neuron in the input layer and the d-th neuron in the hidden layer; f is the activation function, using the ReLU activation function, ReLU(Z) = max(Z, 0), Step (4) Calculate the output of the output layer: Wherein, is the output of the u-th neuron in the output layer; w du is the connection weight between the d-th neuron in the hidden layer and the u-th neuron in the output layer; f is the activation function, the same as the activation function of the hidden layer; Step (5) Update the weights according to the objective function: Take the mean square error MSE as the objective function, and its expression is as follows: Wherein, u is the u-th neuron of the output layer, and m represents the number of samples; represents the output value of the output layer, is the actual value; For a given learning rate l_rate, the change in the weights from the output layer to the hidden layer is calculated by the following formula: The change in the weights from the hidden layer to the input layer is: Then the update amount of the weights is: Step (6) Threshold update: The threshold update is similar to the weight update. The calculation formula for the threshold update of the output layer is as follows: Then the update amount of the weights is: Based on the above steps, use the node wind-solar output and load size as the input of the model; use the node voltage amplitude and phase angle as the output to construct a power flow regression model based on BPNN; and divide the historical power flow operation data into a training set and a test set to train and perform performance testing on the BPNN model.

5. The method according to any one of claims 1 to 4, characterized in that In step S2, it includes the following steps: In step 2.1, construct the relationship formula between the change in voltage amplitude and the change in node injection power; In step 2.2, based on the constructed data-driven non-linear power flow regression model, use the least squares method to achieve the sensitivity matrix analysis.

6. The method according to claim 5, wherein In step 2.1, construct the relationship formula between the change in voltage amplitude and the change in node injection power and the relationship formula between the current node voltage amplitude and the initial voltage and the change in node active power and reactive power: The variation of the node voltage amplitude and the variation of the power injected into each node satisfy the following relationship: where N is the number of nodes in the distribution network; ΔU N×1 is the change matrix of the voltage magnitudes of each node; ΔP N×1 , ΔQ N×1 are the change matrices of the active power and reactive power injected into the nodes respectively; are the voltage - active power and voltage - reactive power sensitivity matrices respectively, and their magnitudes determine the influence of the active and reactive power changes at the nodes on the voltage magnitude; Node voltage U I In addition to being affected by its own initial voltage it is also related to the active power change ΔP J and reactive power change ΔQ J injected into each node. The relationship is as follows: In the formula, are respectively the matrix the element in the I-th row and J-th column.

7. The method according to claim 5 or 6, characterized in that, In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method LS is used to realize the analysis of voltage-reactive power sensitivity: Step (1): Record the voltage and power of each node in the current state, control the change in active power ΔP = 0, generate a reactive power change matrix ΔQ according to the changes in wind and light output and load, and calculate the voltage change when the reactive power changes, that is, ΔU, through the trained BPNN power flow regression model Q ; Step (2), use the least squares method LS to analyze the voltage-reactive power sensitivity matrix: Construct the objective function, that is: where ||·|| is the norm of the matrix, and the Frobenius norm is used; Define the error vector: where e Q is an N-dimensional vector, and N is the number of nodes in the distribution network; Construct the normal equation: where F Q is the normal equation for the voltage-reactive power sensitivity matrix; Differentiate both sides of the equation with respect to and set the derivative equal to zero, we get: Since ΔQ is a matrix of small changes and its determinant is close to zero, it is difficult to directly solve the normal equation; Simplify it, regard ΔQ as a constant matrix, and the voltage-reactive power sensitivity matrix is:

8. The method according to claim 5 or 6, characterized in that, In step 2.2, based on the constructed data-driven non-linear power flow regression model, the least squares method LS is used to realize the analysis of voltage-active power sensitivity: Step (1): Record the voltages and powers of each node in the current state, control the change in reactive power ΔQ = 0, generate the active power change matrix ΔP according to the changes in wind and light output and load, and calculate the voltage change when the active power changes, i.e., ΔU, through the trained BPNN power flow regression model P ; Step (2), use the least squares method LS to analyze the voltage-active power sensitivity matrix: To realize the sensitivity analysis by the least squares method LS, it is first necessary to construct the objective function, that is: where ||·|| is the norm of the matrix, and the Frobenius norm is used; Define the error vector: where, e P is an N-dimensional vector, and N is the number of nodes in the distribution network; Construct the normal equation: where F P is the normal equation for the voltage-active power sensitivity matrix; Differentiate both sides of the equation with respect to and set the derivative equal to zero, we get: Since ΔP is a matrix of small changes and its determinant is close to zero, it is difficult to directly solve the normal equation; Simplify it, regard ΔP as a constant matrix, and the voltage-active power sensitivity matrix is:

9. The method according to claim 1 or 2 or 3 or 4 or 6, characterized in that, In step S3, construct a distribution network voltage control model based on sensitivity analysis, specifically as follows: With the goal of improving voltage quality and system operation economy, the objective function is: Where T is the regulation time; C a is the cost coefficient of voltage over-limit; ΔU i，t is the voltage deviation of node i at time t; C ESS is the operation cost coefficient of energy storage; are the charging power and discharging power of the Bth energy storage within time t respectively; C p 、C q are the cost coefficients of calling photovoltaic inverters; are the active power and reactive power provided by the Ath photovoltaic inverter within time t, that is, the active and reactive output powers of photovoltaic power generation; The constraint conditions are: U min ≤U≤U max (27) where U min and U max are the upper and lower limits of the voltage amplitude, set to 0.95 to 1.05 times the rated voltage; is the square of the capacity of the A-th photovoltaic inverter, is the square of the active power and reactive power provided by the A-th photovoltaic inverter, that is, the square of the active and reactive output powers of photovoltaic power generation; P min and P max are the upper and lower limits of the energy storage charge and discharge power; are the charging power and discharging power of the B-th energy storage within the time t, respectively; is the remaining energy of the B-th energy storage at time t, is the remaining energy of the B-th energy storage at time t - 1, are the minimum energy and maximum energy of the energy storage, respectively, is the rated capacity of the B-th energy storage, and η B is the charge and discharge efficiency of the B-th energy storage; Based on the above method, a distribution network voltage control model is built based on sensitivity analysis; the distribution network voltage control is realized by reasonably controlling the charge and discharge of energy storage and the photovoltaic inverter, and Gurobi is used for solving.

10. A method for analyzing the sensitivity of voltage-reactive power and voltage-active power, characterized in that, It includes the following steps: In step 2.1, construct the relationship between the variation of the voltage amplitude and the variation of the power injected into the node; In step 2.2, based on the constructed data-driven non-linear power flow regression model, use the least squares method to analyze the sensitivity matrix.

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