Power distribution network photovoltaic acceptance capability evaluation method based on non-linear voltage sensitivity

Abstract

The invention discloses a power distribution network photovoltaic acceptance capability evaluation method based on nonlinear voltage sensitivity, and the method comprises the steps: obtaining the linear voltage sensitivity of a power distribution network through a deep neural network based on the historical operation data of a three-phase power distribution network; deriving nonlinear voltage sensitivity according to a three-phase power flow equation of the power distribution network, and representing the nonlinear voltage sensitivity by linear voltage sensitivity; secondly, proposing a dynamic correction strategy for the non-linear voltage sensitivity between in-phase and out-phase nodes; and finally, establishing a capacity configuration optimization model of the photovoltaic power supply in a multi-node multi-phase access mode, and realizing efficient solution of the optimization model by adopting a sparrow search algorithm to obtain the maximum access capacity of the photovoltaic power supply under the voltage safety constraint. The method still has high calculation precision when the boundary scene coverage rate of the historical operation data of the power distribution network is low, the accuracy of the photovoltaic acceptance capability of the power distribution network is improved, planning and operation of the power distribution network can be guided, and the safety and stability performance of the low-voltage power distribution network under large-scale distributed photovoltaic access is improved.

Description

Technical Field

[0001] This invention belongs to the field of distributed renewable energy grid integration capacity assessment technology, and particularly relates to a method for assessing the photovoltaic integration capacity of distribution networks based on nonlinear voltage sensitivity. Background Technology

[0002] With the large-scale integration of distributed renewable energy sources, the distribution network is gradually transforming from a simple power network that receives and distributes electricity to users into a power network that integrates generation, grid, and load, and flexibly couples with the upper-level grid. Due to the strong randomness of distributed renewable energy sources, the risk of voltage and power flow exceeding limits in the distribution network increases. Therefore, accurately assessing the distributed photovoltaic (PV) integration capacity of the distribution network is of great significance for ensuring its safe and reliable operation.

[0003] Power flow calculation is a prerequisite for analyzing the renewable energy integration capacity of distribution networks. Distribution network power flow analysis relies on a complete network topology and accurate line parameters. However, due to inaccurate or unmeasurable parameters in distribution networks, distributed generation capacity analysis based on mathematical models is difficult to apply to practical systems. Currently widely used smart meters provide measurement information such as node voltage, active power, and reactive power in the distribution network. This rich historical and real-time data provides a foundation for data modeling in distribution network power flow analysis. However, the insufficient coverage of boundary conditions by historical data limits the extrapolation capability of data-driven power flow analysis methods under extreme operating conditions.

[0004] Against this backdrop, how to accurately assess the photovoltaic acceptance capacity of the distribution network and improve the safe operation level of the distribution network in the absence of accurate topology and line impedance has become an urgent problem to be solved in this field. Summary of the Invention

[0005] Purpose of the Invention: This invention aims to address the problem of inaccurate photovoltaic (PV) acceptance capacity assessment in existing three-phase asymmetrical distribution networks due to factors such as unknown topology, unclear line parameters, and three-phase imbalance. This invention proposes a PV acceptance capacity assessment method that integrates data-driven and nonlinear sensitivity approaches. First, the linear voltage sensitivity of the distribution network is obtained based on a data-driven method. Then, the nonlinear voltage sensitivity is derived by combining the distribution network power flow model and expressed as linear sensitivity. By combining data-driven and nonlinear sensitivity approaches, the accuracy of PV acceptance capacity assessment under extreme conditions is effectively improved, ensuring the safe operation of the distribution network.

[0006] Technical solution: The present invention provides a method for assessing the photovoltaic (PV) integration capacity of a distribution network based on nonlinear voltage sensitivity, comprising the following steps:

[0007] Step 1: For a three-phase unbalanced distribution network, obtain historical data on the three-phase active power, reactive power, and voltage amplitude of all nodes;

[0008] Step 2: Construct a fully connected deep neural network FCDNN model, using the three-phase active power and reactive power of all nodes as inputs and the three-phase voltage amplitude as outputs. Divide the historical data into training and test sets, and train the FCDNN model based on the training set data to obtain the linear result of node voltage relative to node power.

[0009] Step 3: Perform Taylor expansion of the nodal power equations of the three-phase unbalanced distribution network, derive the nonlinear voltage sensitivity of the in-phase nodes, and express it using linear voltage sensitivity.

[0010] Step 4: Using the numerical normalization method of sequence impedance ratio, obtain the nonlinear voltage sensitivity of the out-of-phase node and express it as linear voltage sensitivity.

[0011] Step 5: Derive the rate of change of nonlinear voltage sensitivity under multi-node photovoltaic access, and realize the dynamic correction of nonlinear voltage sensitivity under multi-node distributed photovoltaic access;

[0012] Step 6: Construct the objective function for photovoltaic (PV) integration capacity, and solve it using the Sparrow Search Algorithm (SSA) to obtain the maximum grid-connected capacity of PV power sources with voltage safety constraints.

[0013] Furthermore, in step 1, the historical data includes historical data on the power and voltage amplitude of the three-phase nodes in the distribution network measured by smart meters, with a sampling interval of 15-20 minutes, expressed as follows: { [ P A Q A P B Q B P C Q C ] ， [ U A U B U C ] } ,in, , and These represent the active power loads at each node of phases A, B, and C of the distribution network. Taking phase A as an example... P A = [ P 1 t a P 2 t a ⋯ P nt a ] The subscript n represents the number of nodes, t represents the sampling time, and the superscript a represents phase a; , and These are the reactive loads at each node of phases A, B, and C of the distribution network, respectively. , and These represent the voltage amplitudes at each node of phases A, B, and C of the distribution network.

[0014] Furthermore, step 2 specifically involves: constructing a fully connected deep neural network FCDNN model, including three hidden layers, with the number of neurons in each layer not less than the input dimension, and the activation function being ReLU; model training uses an L2-regularized mean squared error loss function, as shown in equation (1):

[0015] (1)

[0016] In the formula, This represents the output of the i-th node in the FCDNN network. This represents the actual output of the i-th node; b and n represent the weights and biases of the FCDNN network, respectively; d express or The number of samples;

[0017] Using the active and reactive power of the three-phase nodes in the distribution network as inputs and the three-phase voltage amplitude as outputs, the system is trained separately for each phase. Taking phase A as an example, its node voltage-power deep neural network is trained. It can be represented as:

[0018] { U A = F DNN A ( [ P A P B P C Q A Q B Q C ] T ) U A = [ U 1 a U 2 a ⋯ U n a ] T (2)

[0019] Based on historical data of power and voltage amplitude at three-phase nodes in the distribution network measured by smart meters, the FCDNN network is trained to obtain the weights of the FCDNN network for each phase of the distribution network. and bias ;

[0020] Based on the FCDNN network, the linear sensitivity matrix of node voltage relative to node power in a three-phase asymmetrical distribution network is obtained by differentiating its output with respect to the input, as shown in equations (3) and (4):

[0021] (3)

[0022] { Y = U − μ U σ U X = { [ P , Q ] T − μ PQ } / σ PQ (4)

[0023] In the formula, m represents the number of layers in the FCDNN; and These represent the standard deviations of the node voltage magnitude and the node power, respectively. and The average values ​​of node voltage amplitude and node power, respectively; Let Y represent the derivative of the activation function at layer m; Y and X are the network's output and input, respectively. This represents partial differential operations.

[0024] Furthermore, step 3 specifically involves: deriving the nonlinear voltage sensitivity of the in-phase node and expressing it using the linear voltage sensitivity shown in equation (3), specifically:

[0025] Taking node i of phase a as an example, the active power of this node can be expressed as follows according to the power flow equation:

[0026] (5)

[0027] In the formula, for The active power injected into phase node i; for The voltage amplitude at phase node i; for The voltage amplitude at phase node j; and They are respectively Phase node i and Conductivity and susceptance between phase nodes j; This is the phase angle difference between the two mentioned above; for The self-conductance of phase node i;

[0028] According to (5), use This can be expressed as follows, and its Taylor expansion near the running point yields:

[0029] (6)

[0030] in, express The steady-state value of active power at phase node i; The differential symbol; for The steady-state value; ; ~ The coefficients for each order are as follows:

[0031] (7)

[0032] in, ;

[0033] (8)

[0034] In the above formula, for The partial derivative of the voltage at phase node i with respect to its own active power is defined as the linear self-sensitivity; since the resistance of the line is much higher than the reactance in the low-voltage distribution network, equation (8) is approximately:

[0035] (9)

[0036] Other coefficients are derived from this:

[0037] (10)

[0038] (11)

[0039] Therefore, when there are only When the power fluctuation at phase node i is ignored, the higher-order terms above the fourth order in equation (6) can be obtained as follows: The change in voltage at phase node i is:

[0040] (12)

[0041] In order to obtain Phase node j ( voltage of ) The derivative can be expressed by the following equation:

[0042] (13)

[0043] in, express voltage pair at phase node j The nonlinear sensitivity of the power at phase node i;

[0044] Therefore, when When the active power of phase node i fluctuates, The voltage expression for phase node j is:

[0045] (14).

[0046] Furthermore, step 4 specifically involves the derivation of the nonlinear voltage sensitivity of the out-of-phase node, which includes:

[0047] The power equation for node i in phase A is expressed as:

[0048] (15)

[0049] In Equation (7), when calculating the linear sensitivity of the voltage, it is assumed that the power angle difference between adjacent nodes in phase is small, thus there exists , and If the relationship is used when calculating the voltage sensitivity of the out-of-phase node, then the voltage values ​​of phase b and phase c in equation (15) are "converted" to phase A, that is:

[0050] (16)

[0051] Comparing equations (15) and (16), we can obtain:

[0052] The line impedance ratio r between different phase nodes can be basically determined based on the line type; therefore, if power fluctuation occurs at phase a node i, taking phase b node as an example, the voltage of node j can be written in the following form by analogy with equation (14):

[0053] (17)

[0054] In the formula, The sensitivity of the voltage at node j on phase B to the power at node i on phase A is given by equation (15). and parameter In equation (17) For the actual self-sensitivity of node i on phase A, based on numerical equivalence... and parameter ;Will Completely equivalent to the values ​​in phase A, the self-sensitivity involved in the nonlinear solution in equation (17) is... It should also be based on numerical equivalence. and parameter Furthermore, from equation (9), we can see that... Then equation (17) should be modified as follows:

[0055] (18)

[0056] Similarly, the voltage at node j of phase C Represented as:

[0057] (19)

[0058] The correction of the linear self-sensitivity A phase applied to equations (18) and (19).

[0059] Furthermore, step 5 specifically involves the following process: When multiple photovoltaic power sources are connected to the system, the nonlinear voltage sensitivity correction process for in-phase nodes is as follows:

[0060] Given that a photovoltaic (PV) power source is connected to node i, a second PV power source is proposed to be connected to node j. The impact of the PV power source connection at node j on the linear sensitivity of the node voltage after a power change at node i in phase A is analyzed. This impact is defined as... Taking observation node k as an example, right Voltage sensitivity Impact Indicates the sensitivity correction parameters of each phase power to each phase voltage. There are nine in total; power changes have occurred at node i of phase A. At the same time, the sensitivity of power at different locations to distribution network voltage is analyzed and corrected.

[0061] When the power at node i of phase A changes At that time, the phase voltages of node i in phase A and other nodes j can be expressed as:

[0062] (20)

[0063] In the formula, This indicates the change in power at node i of phase a. Voltage at phase node j; voltage self-sensitivity slope at any node j in phase a. Suppose that at this time, node i of phase a has no power change, and only node j of phase a has a power change, and adjust the amount of its power change. To satisfy:

[0064] (twenty one)

[0065] Even if the voltage at node j of phase A changes only at the power at node i of phase A. Or only the power fluctuation at node j of phase A. If the voltage sensitivity remains equal, then the self-voltage sensitivity of node j in phase A is equal at this time; therefore, it can be deduced that:

[0066] (twenty two)

[0067] In the formula, The voltage change at node j of phase A and the power change at node i of phase A are as follows: The voltage ratio before and after; when the power fluctuation at node j of phase A is At that time, its self-sensitivity slope The rates of change are as follows:

[0068] (twenty three)

[0069] If let The above formula can then be expressed as:

[0070] (twenty four)

[0071] In the formula, For only the power fluctuation at node j of phase A, Or only the power fluctuation at node i of phase A is The rate of change of the self-sensitivity of the preceding and following nodes j satisfy the following conditions: By combining equations (22) and (23), the value can be solved.

[0072] For other phases Voltage and power fluctuations at other nodes k The voltage ratio before and after is known. When only the power of node j in phase A changes hour, voltage at phase node k It can be obtained according to equation (20); under this condition, This indicates that the voltage at node j of phase A is , The voltage at phase node k is Sensitivity at time; and based on the voltage of node j in phase A. , Phase node k voltage is True sensitivity compared to, The final correction value is expressed as:

[0073] (25)

[0074] Therefore, when there is already a photovoltaic power source at node i of phase A in the distribution network, and the power is... At that time, the power fluctuation of node j in phase A affects itself and other nodes k (i⊆k) and other phases. The voltage function can be expressed as:

[0075] (26)

[0076] (27)

[0077] When multiple photovoltaic power sources are connected to the system, the linear voltage sensitivity correction process for out-of-phase nodes is as follows:

[0078] When the observation node k is located in phase a, the following proportional relationship is constructed according to the definition of equation (2):

[0079] (28)

[0080] In the formula This represents the existing power change at node i in phase A. Sensitivity of voltage at node k of phase A to power at node j of phase A The rate of change of this sensitivity has been solved in equation (24); similarly This represents the existing power change at node i in phase A. Sensitivity of voltage k at phase A node to power j at phase B node According to the power flow equation, the impedance and phase angle are not zero only when node j is adjacent to k. Ignoring the numerical changes caused by the phase angle difference, it can be seen that the proportion on the left side of equation (28) is not affected by the line and phase angle parameters. Simplifying the above equation, we can obtain:

[0081] (29)

[0082] Therefore, the rate of change of the voltage at each node k in phase A with respect to the power at the out-of-phase node is... With rate of change Related, specifically:

[0083] (30)

[0084] When the observation node k is located in phase B, since the second power fluctuation node is located in phase B, the rate of change of the voltage sensitivity of each node k in phase B to the power of its in-phase nodes is expressed as:

[0085] (31)

[0086] (32)

[0087] In the formula This means that only the B-phase node j generates power fluctuations. At that time, so that its own voltage satisfies ;

[0088] When the observation node k is located in phase C, construct a proportional equation as shown in equation (28):

[0089] (33)

[0090] In the formula This indicates that there is already power fluctuation at node i in phase A. Sensitivity of voltage at node k in phase C to power at node j in phase C Similarly This indicates that there is already power fluctuation at node i in phase A. Sensitivity of the voltage at node k of phase C to the power at node j of phase B Therefore, the rate of change of the sensitivity of the k-voltage at each node of phase C to the power at the out-of-phase node is... for:

[0091] (34)

[0092] In the formula, There is a power fluctuation at node i in phase A. Before and after, the rate of change of the sensitivity of the voltage at phase C node k to the self-phase node j.

[0093] Furthermore, step 6 specifically involves: constructing the objective function for photovoltaic (PV) integration capacity, solving it using the Sparrow Search Algorithm (SSA), and obtaining the maximum grid-connected capacity of PV power sources with voltage safety constraints. This includes the following steps:

[0094] The objective function is to maximize the photovoltaic (PV) installed capacity connected to each node, and the variables to be optimized are the PV installed capacity of each phase at each node. P PV = [ P 1 . pv a , P 1 . pv b , ⋯ , P n . pv b , P n . pv c ] The objective function is as follows:

[0095] (35)

[0096] In the formula As a discriminant factor, that is, if a certain sample If the three-phase voltage at node i does not satisfy the constraint condition of equation (38), then ; for Photovoltaic access capacity of phase node i;

[0097] Constraints include node voltage safety constraints, three-phase voltage imbalance constraints, and upper limit of photovoltaic installed capacity. Constraints, etc., are as follows:

[0098] Voltage safety constraints:

[0099] (36)

[0100] Three-phase voltage imbalance constraint:

[0101] (37)

[0102] Upper limit constraints on photovoltaic installation capacity for each phase and node:

[0103] (38)

[0104] The Sparrow Search Algorithm (SSA) is used for optimization. When running the SSA algorithm, the discoverer's position is updated in each iteration as follows:

[0105] (39)

[0106] In the formula, t is the current iteration number. The maximum number of iterations is set. A random number within the range [0,1]. These are normally distributed random numbers. A uniformly random number in [0,1] is used as the warning value. The set security value; This indicates that the environment is safe, and the individual moves to a location near the current location; If the environment is dangerous, the individual will randomly leave its current location; followers will compete with the discoverer, and their location updates are described as follows:

[0107] (40)

[0108] In the formula, The optimal position occupied by the discoverer. The worst position, Sort by fitness value, if If the fitness value of the i-th follower is poor and it has not obtained food, it will fly elsewhere to forage; otherwise, the follower will move to the vicinity of the optimal position to obtain food. The positions of the warning followers in the population are randomly generated, accounting for 10% to 20% of the total population, and their positions are described as follows:

[0109] (41)

[0110] In the formula, Z is the step size control parameter for random numbers distributed according to the standard normal distribution, where Z is a random number within the range [-1, 1]. This represents the current individual fitness value. and These are the optimal and worst fitness values, respectively. To prevent constants with a denominator of 0, when the warning device is in the optimal position, it will move to another position near itself; otherwise, it will move closer to the optimal position.

[0111] This invention also discloses a distribution network photovoltaic (PV) integration capacity assessment system based on nonlinear voltage sensitivity, comprising:

[0112] Data-driven linear voltage sensitivity prediction module: Based on the three-phase active power, reactive power and voltage amplitude of each node in the distribution network as historical datasets, a fully connected deep neural network model is constructed. The historical dataset is divided into test set and validation set according to the proportion. The voltage linear sensitivity is obtained based on the test set data.

[0113] Nonlinear sensitivity derivation module: Based on the system power flow equation, the nonlinear voltage sensitivity of in-phase self-nodes, in-phase opposite-nodes, and opposite-phase nodes is derived.

[0114] Sensitivity correction module: used to correct nonlinear voltage sensitivity under multiple photovoltaic power source access conditions, and obtain voltage sensitivity results under multiple photovoltaic power source access conditions;

[0115] Photovoltaic Adoption Capacity Optimization Module: Constructs a photovoltaic adoption capacity optimization model with voltage safety and three-phase imbalance constraints, and uses the sparrow search algorithm to obtain the maximum photovoltaic adoption capacity of the distribution network.

[0116] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0117] The present invention also discloses a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method of the present invention.

[0118] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0119] (1) Get rid of topology and parameter dependence: The data-driven modeling method based on deep neural networks in this invention can achieve high-precision estimation and sensitivity extraction of three-phase node voltage under the condition of unknown distribution network topology and line parameters, which significantly improves the applicability and actual deployment capability.

[0120] (2) Strong nonlinear accurate modeling capability: A voltage extrapolation method based on a high-order nonlinear sensitivity function is proposed, which can effectively characterize the voltage nonlinear response caused by power disturbance, and is far superior to the local fitting capability of the traditional linear model, thus improving the overall prediction accuracy.

[0121] (3) Supports three-phase imbalance and coupling characteristics: Through the normalization mapping of dissimilar nodes and the construction method of sensitivity function, the voltage coupling relationship between the three phases can be accurately reflected, which is suitable for complex operating scenarios such as multi-source disturbances and load asymmetry.

[0122] (4) Sensitivity correction mechanism enhances adaptability: By combining the equivalent constraints before and after node perturbation, the dynamic change rate of sensitivity is derived to realize the online correction capability of the model and improve the adaptability of the method to changes in operating state.

[0123] (5) High-efficiency acceptance capacity assessment: Voltage extrapolation is used to replace iterative power flow calculation, and the sparrow search algorithm is combined to perform optimal access configuration for multiple nodes, taking into account both speed and accuracy. It is suitable for large-scale distributed power source acceptance capacity assessment.

[0124] (6) It has engineering applicability and transferability: The model parameters are trained from historical data, and have good generalization ability and regional transferability, which are applicable to various scenarios such as urban power distribution networks and rural microgrids. Attached Figure Description

[0125] Figure 1 This is a flowchart of the method of the present invention;

[0126] Figure 2 The system topology for the 906 low-voltage distribution network case study;

[0127] Figure 3 The structure of a fully connected deep learning network;

[0128] Figure 4 The average error of the voltage at each phase and node is obtained based on the load data in the test set after training the DNN.

[0129] Figure 5 These are the voltage values ​​of each phase and node under a certain load after training.

[0130] Figure 6 This refers to the self-voltage sensitivity of each node obtained after training using the training parameters.

[0131] Figure 7 This section describes the voltage error when the voltage of each node in the example system is extrapolated to the voltage threshold under both linear and nonlinear conditions.

[0132] Figure 8 The extrapolation error of the voltage at each node of each phase when the photovoltaic power at each load node of phase A rises to the distribution network voltage threshold;

[0133] Figure 9 This shows the change in voltage at each phase node with varying photovoltaic power at node 14 of phase A, regardless of whether there is prior photovoltaic power supply.

[0134] Figure 10 The photovoltaic installed capacity of each node is obtained based on the power flow calculation program and the method of this invention. Detailed Implementation

[0135] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0136] Example:

[0137] Step 1, with Figure 2 Taking the 906-node three-phase unbalanced distribution system as an example, historical data on the three-phase active power, reactive power, and voltage amplitude of all nodes are obtained. The load data of this system comes from a low-voltage distribution network in Fuyang City, Anhui Province. The load data selected is the entire year of 2020, with a sampling interval of 15 minutes. The load data is substituted into the example for power flow calculation to obtain the voltage amplitude of each node. The historical data is represented as follows: { [ P A Q A P B Q B P C Q C ] ， [ U A U B U C ] } ,in, , and These represent the active power loads at each node of phases A, B, and C of the distribution network. Taking phase A as an example... P A = [ P 1 t a P 2 t a ⋯ P nt a ] The subscript n represents the number of nodes, t represents the sampling time, and the superscript a represents phase a; , and These are the reactive loads at each node of phases A, B, and C of the distribution network, respectively. , and These represent the voltage amplitudes at each node of phases A, B, and C of the distribution network.

[0138] Step 2, Build Figure 3 The model shown is a fully connected deep neural network (FCDNN). The deep neural network structure used is a four-layer fully connected network, with ReLU (Rectified Linear Unit) activation function in each layer. The relevant hyperparameter configurations of the neural network are shown in Table 1.

[0139] Table 1. Structure and main parameters of FCDNN

[0140]

[0141] The model training uses an L2-regularized mean squared error loss function, as shown in equation (1):

[0142] (1)

[0143] In the formula, This represents the output of the i-th node in the FCDNN network. This represents the actual output of the i-th node; b and n represent the weights and biases of the FCDNN network, respectively; d express or The number of samples.

[0144] The active and reactive power of the three-phase nodes in the distribution network are used as inputs, and the three-phase voltage amplitude is used as the output. Each phase is trained separately. Taking phase A as an example, its node power-voltage deep neural network... It can be represented as:

[0145] { U A = F DNN A ( [ P A P B P C Q A Q B Q C ] T ) U A = [ U 1 a U 2 a ⋯ U n a ] T (2)

[0146] Historical data was randomly divided into a test set and a validation set at an 8:2 ratio, and the weights of the FCDNN network for each phase of the distribution network were obtained accordingly. and bias Based on the FCDNN network, the linear sensitivity matrix of node voltage relative to node power in a three-phase asymmetrical distribution network is obtained by differentiating its output with respect to the input, as shown in equations (3) and (4):

[0147] (3)

[0148] { Y = U − μ U σ U X = { [ P , Q ] T − μ PQ } / σ PQ (4)

[0149] In the formula, m represents the number of layers in the FCDNN; and These represent the standard deviations of the node voltage magnitude and the node power, respectively. and The average values ​​of node voltage amplitude and node power, respectively; Y represents the derivative of the activation function at layer m; Y and X are the network's output and input, respectively. This represents partial differential operations.

[0150] After training, testing was performed using 20% ​​of the test set data, and the mean square error (MSE) of the three-phase voltages a, b, and c were obtained as follows: , and The average absolute error of voltage at all nodes of the three phases abc is as follows: Figure 4 As shown. To illustrate the voltage fitting effect of the trained model, Figure 5 The prediction results of each phase voltage at each node for a given training sample are shown.

[0151] Based on its trained weights and bias The linear voltage sensitivity matrix of the distribution network nodes can be obtained by differentiating the output of the neural network with respect to the input using the chain rule. Taking the sensitivity of each node in the distribution network to its own photovoltaic power as an example, the sensitivity calculated based on the DNN parameters is compared with the actual value, and the results are as follows. Figure 6 As shown in the figure. Furthermore, the statistical results of the average sensitivity error of the voltage at each phase and node to the photovoltaic power at each node are listed in Table 2.

[0152] Table 2 Average sensitivity error of each node in the three phases

[0153]

[0154] Table 2 shows that the voltage and sensitivity values ​​obtained based on FCDNN training have high accuracy, indicating that the voltage sensitivity predicted by the FCDNN network has high accuracy within the historical data range of the distribution network. However, when the distribution network operates in boundary scenarios, the voltage sensitivity may have deviations.

[0155] Step 3: Perform Taylor expansion of the nodal power equations of the three-phase unbalanced distribution network, derive the nonlinear voltage sensitivity of the in-phase nodes, and express it using linear voltage sensitivity.

[0156] Taking node i of phase a as an example, the active power of this node can be expressed as follows according to the power flow equation:

[0157] (5)

[0158] In the formula, for The active power injected into phase node i; for The voltage amplitude at phase node i; for The voltage amplitude at phase node j; and They are respectively Phase node i and Conductivity and susceptance between phase nodes j; This is the phase angle difference between the two mentioned above; for Self-conductance of phase node i.

[0159] According to (5), use This can be expressed as follows, and its Taylor expansion near the running point yields:

[0160] (6)

[0161] in, express The steady-state value of active power at phase node i; The differential symbol; for The steady-state value; ; ~ The coefficients for each order are as follows:

[0162] (7)

[0163] in,

[0164] (8)

[0165] In the above formula, for The partial derivative of the voltage at phase node i with respect to its own active power is defined as the linear self-sensitivity. Since the resistance of the line in a low-voltage distribution network is much higher than its reactance, equation (8) can be approximated as:

[0166] (9)

[0167] Other coefficients can also be derived from this:

[0168] (10)

[0169] (11)

[0170] Therefore, when there are only When the power fluctuation at phase node i is ignored, the higher-order terms above the fourth order in equation (6) can be obtained as follows: The change in voltage at phase node i is:

[0171] (12)

[0172] In order to obtain Phase node j ( voltage of ) The derivative can be expressed by the following equation:

[0173] (13)

[0174] in, express voltage pair at phase node j The nonlinear sensitivity of the power at phase node i.

[0175] Therefore, when When the active power of phase node i fluctuates, The general expression for the voltage at phase node j (including node i) is:

[0176] (14)

[0177] Step 4: Using the numerical normalization method of sequence impedance ratio, obtain the nonlinear voltage sensitivity of the out-of-phase node and express it as linear voltage sensitivity.

[0178] The power equation for node i in phase A is expressed as:

[0179] (15)

[0180] Note that when calculating the linear sensitivity of the voltage in equation (7), it is assumed that the power angle difference between adjacent nodes in phase is small, thus there exists , and If we wish to use this relationship when calculating the voltage sensitivity of out-of-phase nodes, we need to "convert" the voltage values ​​of phase b and phase c in equation (15) to phase A, that is:

[0181] (16)

[0182] Comparing equations (15) and (16), we can obtain:

[0183] The line impedance ratio r between different phase nodes can be basically determined based on the line type. Therefore, if power fluctuation occurs at node i of phase a, taking node b as an example, the voltage of node j can be written in the following form by analogy with equation (14):

[0184] (17)

[0185] In the formula, The sensitivity of the voltage at node j on phase B to the power at node i on phase A is given by equation (15). and parameter In equation (17) For the actual self-sensitivity of node i on phase A, based on numerical equivalence... and parameter Therefore, if one wishes to... Completely equivalent to the values ​​in phase A, the self-sensitivity involved in the nonlinear solution in equation (17) is... It should also be based on numerical equivalence. and parameter , rather than the actual value. And from equation (9), we can see... Then equation (17) should be modified as follows:

[0186] (18)

[0187] Similarly, the voltage at node j of phase C Represented as:

[0188] (19)

[0189] It should be noted that Equation (16) numerically "reduces" each phase to phase A, so it does not change the derivative value between node voltage and power at the numerical level. Therefore, it can be applied to the correction of the linear self-sensitivity (phase A) in Equations (18) and (19).

[0190] Figure 7 Taking phase A node as an example, the nonlinear extrapolated voltage errors of each phase at other nodes are presented when the node voltage of power fluctuation reaches a threshold. The statistical results of the mean square error (MSE) and relative variation error of each phase voltage are shown in Table 3.

[0191] Table 3. Extrapolated voltage error at each phase node

[0192]

[0193] Step 5: Derive the rate of change of nonlinear voltage sensitivity under multi-node photovoltaic access, and realize the dynamic correction of nonlinear voltage sensitivity under multi-node distributed photovoltaic access;

[0194] Given that a photovoltaic (PV) power source is connected to node i, a second PV power source is proposed to be connected to node j. The impact of the PV power source connection at node j on the linear sensitivity of the node voltage after a power change at node i in phase A is analyzed. This impact is defined as... .

[0195] Taking observation node k as an example, right Voltage sensitivity The impact (using the rate of change) This indicates that the sensitivity correction parameters for the power of each phase to the voltage of each phase are as follows. There are nine in total. A power change has already occurred at node i of phase A. At the same time, the sensitivity of power at different locations to distribution network voltage is analyzed and corrected.

[0196] When the power at node i of phase A changes At that time, the phase voltages of node i in phase A and other nodes j can be expressed as:

[0197] (20)

[0198] In the formula, This indicates the change in power at node i of phase a. The voltage at phase node j. According to equation (8), the slope of the voltage self-sensitivity at any node j in phase a is... This value is mainly related to its own voltage. Therefore, assuming that there is no power change at phase a node i, and only phase a node j experiences a power change, and adjusting the amount of its power change... To satisfy:

[0199] (twenty one)

[0200] Even if the voltage at node j of phase A changes only at the power at node i of phase A. Or only the power fluctuation at node j of phase A. If the voltage sensitivity remains equal, then the self-voltage sensitivity of node j in phase A can also be considered equal. Therefore, it can be deduced that:

[0201] (twenty two)

[0202] In the formula, The voltage change at node j of phase A and the power change at node i of phase A are as follows: The voltage ratio before and after is a known quantity; while the power variable of phase A node j is artificially set to make equation (21) hold. The unknown quantity. When the power fluctuation at node j of phase A is... At that time, its self-sensitivity slope The rates of change are as follows:

[0203] (twenty three)

[0204] If let The above formula can then be expressed as

[0205] (twenty four)

[0206] In the formula, For only the power fluctuation at node j of phase A, Or only the power fluctuation at node i of phase A is The rate of change of the self-sensitivity of the preceding and following nodes j satisfy the following conditions: By combining equations (22) and (23), the value can be solved.

[0207] For other phases Voltage and power fluctuations at other nodes k The voltage ratio before and after is known. When only the power at node j of phase A changes hour, voltage at phase node k It can be obtained from equation (20). Under this condition, This indicates that the voltage at node j of phase A is , The voltage at phase node k is Sensitivity at time. Compared to the voltage at phase A node j. , Phase node k voltage is True sensitivity compared to, Further revisions are needed. Therefore, The final correction value is expressed as:

[0208] (25)

[0209] Therefore, when there is already a photovoltaic power source at node i of phase A in the distribution network, and the power is... At that time, the power fluctuation of node j in phase A affects itself and other nodes k (i⊆k) and other phases. The voltage function can be expressed as:

[0210] (26)

[0211] (27)

[0212] In step 5, when multiple photovoltaic power sources are connected to the system, the linear voltage sensitivity correction process for the out-of-phase node is as follows:

[0213] When the observation node k is located in phase a, the following proportional relationship is constructed according to the definition of equation (2):

[0214] (28)

[0215] In the formula This represents the existing power change at node i in phase A. Sensitivity of voltage at node k of phase A to power at node j of phase A The rate of change of this sensitivity has been solved in equation (24); similarly This represents the existing power change at node i in phase A. Sensitivity of voltage k at phase A node to power j at phase B node The sensitivity is to be solved. According to the power flow equation, the impedance and phase angle are not zero only when node j is adjacent to k. Ignoring the numerical changes caused by the phase angle difference, it can be seen that the proportion on the left side of equation (28) is almost unaffected by the line and phase angle parameters. Simplifying the above equation, we can obtain:

[0216] (29)

[0217] Therefore, the rate of change of the voltage at each node k in phase A with respect to the power at the out-of-phase node (node ​​j in phase B) With rate of change Related, specifically:

[0218] (30)

[0219] When the observation node k is located in phase B, since the second power fluctuation node is located in phase B, similar to equations (22~25), the rate of change of the voltage of each node k in phase B with respect to the power of its in-phase node (node ​​j in phase B) can be expressed as:

[0220] (31)

[0221] (32)

[0222] Similarly, in the formula This means that only the B-phase node j generates power fluctuations. At that time, so that its own voltage satisfies .

[0223] When the observation node k is located in phase C, it is similar to solving... Construct a proportion as shown in equation (28):

[0224] (33)

[0225] In the formula This indicates that there is already power fluctuation at node i in phase A. Sensitivity of voltage at node k in phase C to power at node j in phase C Similarly This indicates that there is already power fluctuation at node i in phase A. Sensitivity of the voltage at node k of phase C to the power at node j of phase B This sensitivity is to be solved. Therefore, the rate of change of the sensitivity of the voltage at node k of phase C to the power at the out-of-phase node (node ​​j of phase B) is... for:

[0226] (34)

[0227] In the formula, There is a power fluctuation at node i in phase A. Before and after, the rate of change of the sensitivity of the voltage at the C-phase node k to the self-phase node j can be solved by analogy based on equation (31).

[0228] Figure 2 In the example, it is assumed that photovoltaic (PV) power sources are configured at nodes 20-22, with a total rated power of 20kW. Furthermore, it is planned to connect a new PV power source to node 14 (phase A). To analyze the voltage changes at each phase node after the PV power source is connected to node 14, nodes 14A, 26B, and 43C are selected as representative nodes. The voltage sensitivity of node 14 after the PV power source is connected is compared. See [link to example]. Figure 8 As shown.

[0229] It is evident that without sensitivity correction, the voltage sensitivity error increases significantly with the increase in the number of distributed power sources connected. To verify the necessity of the sensitivity correction method under multi-point photovoltaic power connection, the average relative error statistics of the sensitivity of each phase voltage to each phase power before and after correction are shown in Table 4.

[0230] Table 4. Relative error (%) before and after correction of the sensitivity of each phase node

[0231]

[0232] In this invention, several photovoltaic access scenarios were constructed as shown in Table 5:

[0233] Table 5 Distributed Energy Access Scenarios

[0234]

[0235] Combining the above sensitivity correction method with the initial sensitivity results of FCDNN, the extrapolated voltage results for each scenario are as follows: Figure 9 As shown in the figure. Meanwhile, the statistical results of voltage errors before and after sensitivity correction are summarized in Table 6.

[0236] Table 6. Voltage error in various scenarios before and after sensitivity correction.

[0237]

[0238] Depend on Figure 9 As shown in Table 6, when multiple PV power sources are connected in the same phase, there is a significant mutual suppression effect on voltage. Similar suppression interactions are also observed between dissimilar and similar distributed power sources. Therefore, by rationally configuring the distributed energy access capacity of each phase and node, the penetration rate of distributed power sources can be effectively increased while ensuring the voltage safety of the distribution network.

[0239] Step 6: Construct the objective function for photovoltaic (PV) integration capacity and solve it using the Sparrow Search Algorithm (SSA) to obtain the maximum grid-connected capacity of PV power sources with voltage safety constraints.

[0240] The objective function is to maximize the photovoltaic (PV) installed capacity connected to each node, and the variables to be optimized are the PV installed capacity of each phase at each node. P PV = [ P 1 . pv a , P 1 . pv b , ⋯ , P n . pv b , P n . pv c ] The objective function is as follows:

[0241] (35)

[0242] In the formula As a discriminant factor, that is, if a certain sample If the three-phase voltage at node i does not satisfy the constraint condition of equation (38), then ; for Photovoltaic access capacity of phase node i.

[0243] Constraints include node voltage safety constraints, three-phase voltage imbalance constraints, and upper limit of photovoltaic installed capacity. Constraints, etc., are as follows:

[0244] Voltage safety constraints:

[0245] (36)

[0246] Three-phase voltage imbalance constraint:

[0247] (37)

[0248] Upper limit constraints on photovoltaic installation capacity for each phase and node:

[0249] (38)

[0250] The voltage at each node was calculated using the methods described in steps 1-5.

[0251] The Sparrow Search Algorithm (SSA) is used for optimization. When running the SSA algorithm, the discoverer with a better fitness value will prioritize obtaining food during the search process and will be responsible for finding food for the population and guiding the foraging direction for followers. Compared with other sparrows, the discoverer can obtain a larger foraging range. The discoverer's position is updated in each iteration as follows:

[0252] (39)

[0253] In the formula, t is the current iteration number. The maximum number of iterations is set. A random number within the range [0,1]. These are normally distributed random numbers. A uniformly random number in [0,1] is used as the warning value. The set security value. This indicates that the environment is safe, and the individual moves to a location near the current location; If the environment is dangerous, the individual will randomly leave its current location. Followers will compete with the discoverer, and their location updates are described below:

[0254] (40)

[0255] In the formula, The optimal position occupied by the discoverer. The worst position, Sort by fitness value, if If the i-th follower has a poor fitness value and has not obtained food, it is considered to have flown elsewhere to forage. Otherwise, the follower moves to the vicinity of the optimal location to obtain food. The positions of the warning followers in the population are randomly generated, accounting for 10% to 20% of the total population, and their positions are described as follows:

[0256] (41)

[0257] In the formula, Z is the step size control parameter for random numbers distributed according to the standard normal distribution, where Z is a random number within the range [-1, 1]. This represents the current individual fitness value. and These are the optimal and worst fitness values, respectively. To prevent constants with a denominator of 0, when the warning device is in its optimal position, it will move to another nearby position; otherwise, it will move closer to the optimal position. Assuming all nodes in the distribution network are photovoltaic nodes, the optimal installed capacity distribution obtained by using the two voltage sensitivity solution methods described above is compared as follows: Figure 10 As shown, the nonlinear voltage sensitivity method proposed in this invention has only a small deviation from the power flow calculation results in the assessment of acceptable capacity, with an average error of about 2%.

Claims

1. A method for evaluating the photovoltaic (PV) hosting capacity of a power distribution network based on nonlinear voltage sensitivity, characterized in that, Includes the following steps: Step 1: For a three-phase unbalanced distribution network, obtain historical data on the three-phase active power, reactive power, and voltage amplitude of all nodes; Step 2: Construct a fully connected deep neural network FCDNN model, using the three-phase active power and reactive power of all nodes as inputs and the three-phase voltage amplitude as outputs. Divide the historical data into training and test sets, and train the FCDNN model based on the training set data to obtain the linear result of node voltage relative to node power. Step 3: Perform Taylor expansion of the nodal power equations of the three-phase unbalanced distribution network, derive the nonlinear voltage sensitivity of the in-phase nodes, and express it using linear voltage sensitivity. Step 4: Using the numerical normalization method of sequence impedance ratio, obtain the nonlinear voltage sensitivity of the out-of-phase node and express it as linear voltage sensitivity. Step 5: Derive the rate of change of nonlinear voltage sensitivity under multi-node photovoltaic access, and realize the dynamic correction of nonlinear voltage sensitivity under multi-node distributed photovoltaic access; Step 6: Construct the objective function for photovoltaic (PV) integration capacity, and solve it using the Sparrow Search Algorithm (SSA) to obtain the maximum grid-connected capacity of PV power sources with voltage safety constraints.

2. The method for assessing the photovoltaic integration capacity of a distribution network based on nonlinear voltage sensitivity according to claim 1, characterized in that, In step 1, the historical data includes historical data on the power and voltage amplitude of the three-phase nodes in the distribution network measured by smart meters, with a sampling interval of 15-20 minutes, as shown below: ,in, , and These represent the active power loads at each node of phases A, B, and C of the distribution network. Taking phase A as an example... The subscript n represents the number of nodes, t represents the sampling time, and the superscript a represents phase a; , and These are the reactive loads at each node of phases A, B, and C of the distribution network, respectively. , and These represent the voltage amplitudes at each node of phases A, B, and C of the distribution network.

3. The method for assessing the photovoltaic integration capacity of a distribution network based on nonlinear voltage sensitivity according to claim 2, characterized in that, Step 2 specifically involves constructing a fully connected deep neural network (FCDNN) model, comprising three hidden layers, with each layer having a number of neurons no less than the input dimension, and using ReLU as the activation function; the model training employs an L2-regularized mean squared error loss function, as shown in equation (1): (1) In the formula, This represents the output of the i-th node in the FCDNN network. This represents the actual output of the i-th node; b and n represent the weights and biases of the FCDNN network, respectively; d express or The number of samples; Using the active and reactive power of the three-phase nodes in the distribution network as inputs and the three-phase voltage amplitude as outputs, the system is trained separately for each phase. Taking phase A as an example, its node voltage-power deep neural network is trained. It can be represented as: (2) Based on historical data of power and voltage amplitude at three-phase nodes in the distribution network measured by smart meters, the FCDNN network is trained to obtain the weights of the FCDNN network for each phase of the distribution network. and bias ; Based on the FCDNN network, the linear sensitivity matrix of node voltage relative to node power in a three-phase asymmetrical distribution network is obtained by differentiating its output with respect to the input, as shown in equations (3) and (4): (3) (4) In the formula, m represents the number of layers in the FCDNN; and These represent the standard deviations of the node voltage magnitude and the node power, respectively. and The average values ​​of node voltage amplitude and node power, respectively; Y represents the derivative of the activation function at layer m; Y and X are the network's output and input, respectively. This represents partial differential operations.

4. The method for assessing the photovoltaic integration capacity of a distribution network based on nonlinear voltage sensitivity according to claim 3, characterized in that, Step 3 specifically involves: deriving the nonlinear voltage sensitivity of the in-phase node and expressing it using the linear voltage sensitivity shown in equation (3), specifically: Taking node i of phase a as an example, the active power of this node can be expressed as follows according to the power flow equation: (5) In the formula, for The active power injected into phase node i; for The voltage amplitude at phase node i; for The voltage amplitude at phase node j; and They are respectively Phase node i and Conductivity and susceptance between phase nodes j; This is the phase angle difference between the two mentioned above; for The self-conductance of phase node i; According to (5), use This can be expressed as follows, and its Taylor expansion near the running point yields: (6) in, express The steady-state value of active power at phase node i; The differential symbol; for The steady-state value; ; ~ The coefficients for each order are as follows: (7) in, ; (8) In the above formula, for The partial derivative of the voltage at phase node i with respect to its own active power is defined as the linear self-sensitivity; since the resistance of the line is much higher than the reactance in the low-voltage distribution network, equation (8) is approximately: (9) Other coefficients are derived from this: (10) (11) Therefore, when there are only When the power fluctuation at phase node i is ignored, the higher-order terms above the fourth order in equation (6) can be obtained as follows: The change in voltage at phase node i is: (12) In order to obtain Phase node j ( voltage of ) The derivative can be expressed by the following equation: (13) in, express voltage pair at phase node j The nonlinear sensitivity of the power at phase node i; Therefore, when When the active power of phase node i fluctuates, The voltage expression for phase node j is: (14)。 5. The method for assessing the photovoltaic integration capacity of a distribution network based on nonlinear voltage sensitivity according to claim 4, characterized in that, Step 4 specifically involves the derivation of the nonlinear voltage sensitivity of the out-of-phase node, including: The power equation for node i in phase A is expressed as: (15) In Equation (7), when calculating the linear sensitivity of the voltage, it is assumed that the power angle difference between adjacent nodes in phase is small, thus there exists , and If the relationship is used when calculating the voltage sensitivity of the out-of-phase node, then the voltage values ​​of phase b and phase c in equation (15) are "converted" to phase A, that is: (16) Comparing equations (15) and (16), we can obtain: ; The line impedance ratio r between different phase nodes can be basically determined based on the line type; therefore, if power fluctuation occurs at phase a node i, taking phase b node as an example, the voltage of node j can be written in the following form by analogy with equation (14): (17) In the formula, The sensitivity of the voltage at node j on phase B to the power at node i on phase A is given by equation (15). and parameter In equation (17) For the actual self-sensitivity of node i on phase A, based on numerical equivalence... and parameter ;Will Completely equivalent to the values ​​in phase A, the self-sensitivity involved in the nonlinear solution in equation (17) is... It should also be based on numerical equivalence. and parameter Furthermore, from equation (9), we can see that... Then equation (17) should be modified as follows: (18) Similarly, the voltage at node j of phase C Represented as: (19) The correction of the linear self-sensitivity A phase applied to equations (18) and (19).

6. The method for assessing the photovoltaic integration capacity of a distribution network based on nonlinear voltage sensitivity according to claim 1, characterized in that, Step 5 specifically involves the following process for correcting the nonlinear voltage sensitivity of in-phase nodes when multiple photovoltaic power sources are connected to the system: Given that a photovoltaic (PV) power source is connected to node i, a second PV power source is proposed to be connected to node j. The impact of the PV power source connection at node j on the linear sensitivity of the node voltage after a power change at node i in phase A is analyzed. This impact is defined as... ; Taking observation node k as an example, right Voltage sensitivity Impact Indicates the sensitivity correction parameters of each phase power to each phase voltage. There are nine in total; power changes have occurred at node i of phase A. At the same time, the sensitivity of power at different locations to distribution network voltage is analyzed and corrected. When the power at node i of phase A changes At that time, the phase voltages of node i in phase A and other nodes j can be expressed as: (20) In the formula, This indicates the change in power at node i of phase a. Voltage at phase node j; voltage self-sensitivity slope at any node j in phase a. Suppose that at this time, node i of phase a has no power change, and only node j of phase a has a power change, and adjust the amount of its power change. To satisfy: (21) Even if the voltage at node j of phase A changes only at the power at node i of phase A. Or only the power fluctuation at node j of phase A. If the voltage sensitivity remains equal, then the self-voltage sensitivity of node j in phase A is equal at this time; therefore, it can be deduced that: (22) In the formula, The voltage change at node j of phase A and the power change at node i of phase A are as follows: The voltage ratio before and after; when the power fluctuation at node j of phase A is At that time, its self-sensitivity slope The rates of change are as follows: (23) If let The above formula can then be expressed as: (24) In the formula, For only the power fluctuation at node j of phase A, Or only the power fluctuation at node i of phase A is The rate of change of the self-sensitivity of the preceding and following nodes j satisfy the following conditions: By combining equations (22) and (23), the value can be solved. For other phases Voltage and power fluctuations at other nodes k The voltage ratio before and after is known. ; When only the power at node j of phase A changes hour, voltage at phase node k It can be obtained according to equation (20); under this condition, This indicates that the voltage at node j of phase A is , The voltage at phase node k is Sensitivity at time; and based on the voltage of node j in phase A. , Phase node k voltage is True sensitivity compared to, The final correction value is expressed as: (25) Therefore, when there is already a photovoltaic power source at node i of phase A in the distribution network, and the power is... At that time, the power fluctuation of node j in phase A affects itself and other nodes k (i⊆k) and other phases. The voltage function can be expressed as: (26) (27) When multiple photovoltaic power sources are connected to the system, the linear voltage sensitivity correction process for out-of-phase nodes is as follows: When the observation node k is located in phase a, the following proportional relationship is constructed according to the definition of equation (2): (28) In the formula This represents the existing power change at node i in phase A. Sensitivity of voltage at node k of phase A to power at node j of phase A The rate of change of this sensitivity has been solved in equation (24); similarly This represents the existing power change at node i in phase A. Sensitivity of voltage k at phase A node to power j at phase B node According to the power flow equation, the impedance and phase angle are not zero only when node j is adjacent to k. Ignoring the numerical changes caused by the phase angle difference, it can be seen that the proportion on the left side of equation (28) is not affected by the line and phase angle parameters. Simplifying the above equation, we can obtain: (29) Therefore, the rate of change of the voltage at each node k in phase A with respect to the power at the out-of-phase node is... With rate of change Related, specifically: (30) When the observation node k is located in phase B, since the second power fluctuation node is located in phase B, the rate of change of the voltage sensitivity of each node k in phase B to the power of its in-phase nodes is expressed as: (31) (32) In the formula This means that only the B-phase node j generates power fluctuations. At that time, so that its own voltage satisfies ; When the observation node k is located in phase C, construct a proportional equation as shown in equation (28): (33) In the formula This indicates that there is already power fluctuation at node i in phase A. Sensitivity of voltage at node k in phase C to power at node j in phase C Similarly This indicates that there is already power fluctuation at node i in phase A. Sensitivity of the voltage at node k of phase C to the power at node j of phase B Therefore, the rate of change of the sensitivity of the k-voltage at each node of phase C to the power at the out-of-phase node is... for: (34) In the formula, There is a power fluctuation at node i in phase A. Before and after, the rate of change of the sensitivity of the voltage at phase C node k to the self-phase node j.

7. The method for assessing the photovoltaic integration capacity of a distribution network based on nonlinear voltage sensitivity according to claim 1, characterized in that, Step 6 specifically involves: constructing the objective function for photovoltaic (PV) integration capacity, solving it using the Sparrow Search Algorithm (SSA), and obtaining the maximum grid-connected capacity of PV power sources with voltage safety constraints. This includes the following steps: The objective function is to maximize the photovoltaic (PV) installed capacity connected to each node, and the variables to be optimized are the PV installed capacity of each phase at each node. The objective function is as follows: (35) In the formula As a discriminant factor, that is, if a certain sample If the three-phase voltage at node i does not satisfy the constraint condition of equation (38), then ; for Photovoltaic access capacity of phase node i; Constraints include node voltage safety constraints, three-phase voltage imbalance constraints, and upper limit of photovoltaic installed capacity. Constraints, etc., are as follows: Voltage safety constraints: (36) Three-phase voltage imbalance constraint: (37) Photovoltaic installation capacity limits for each phase and node: (38) The Sparrow Search Algorithm (SSA) is used for optimization. When running the SSA algorithm, the discoverer's position is updated in each iteration as follows: (39) In the formula, t is the current iteration number. The maximum number of iterations is set. A random number within the range [0,1]. These are normally distributed random numbers. A uniformly random number in [0,1] is used as the warning value. The set security value; This indicates that the environment is safe, and the individual moves to a location near the current location; If the environment is dangerous, the individual will randomly leave its current location; followers will compete with the discoverer, and their location updates are described as follows: (40) In the formula, The optimal position occupied by the discoverer. The worst position, Sort by fitness value, if If the fitness value of the i-th follower is considered poor and it has not obtained food, it will fly elsewhere to forage; otherwise, the follower will move to the vicinity of the optimal position to obtain food. The positions of the warning followers in the population are randomly generated, accounting for 10% to 20% of the total population, and their positions are described as follows: (41) In the formula, Z is the step size control parameter for random numbers distributed according to the standard normal distribution, where Z is a random number within the range [-1, 1]. This represents the current individual fitness value. and These are the optimal and worst fitness values, respectively. To prevent constants with a denominator of 0, when the warning device is in the optimal position, it will move to another position near itself; otherwise, it will move closer to the optimal position.

8. A distribution network photovoltaic integration capacity assessment system based on nonlinear voltage sensitivity, used to implement the method described in claims 1-7, characterized in that, include: Data-driven linear voltage sensitivity prediction module: Based on the three-phase active power, reactive power and voltage amplitude of each node in the distribution network as historical datasets, a fully connected deep neural network model is constructed. The historical dataset is divided into test set and validation set according to the proportion. The voltage linear sensitivity is obtained based on the test set data. Nonlinear sensitivity derivation module: Based on the system power flow equation, the nonlinear voltage sensitivity of in-phase self-nodes, in-phase opposite-nodes, and opposite-phase nodes is derived. Sensitivity correction module: used to correct nonlinear voltage sensitivity under multiple photovoltaic power source access conditions, and obtain voltage sensitivity results under multiple photovoltaic power source access conditions; Photovoltaic Adoption Capacity Optimization Module: Constructs a photovoltaic adoption capacity optimization model with voltage safety and three-phase imbalance constraints, and uses the sparrow search algorithm to obtain the maximum photovoltaic adoption capacity of the distribution network.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of claim 1.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of claim 1.

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